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EXPERIMlENTAL INVESTIGATION OF THE WAW-TURBULENCE INTERACTION AT LOW REYNOLDS NUMBERS IN A HORIZONTAL

OPEN-C-L FLOW

Evangelos Stamatiou

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Graduate Department of Chemical Engineering and Applied Chemistry University of Toronto

@Copyright by Evangelos Stamatiou, i 998

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EXPERIMENTAL INVESTIGATION OF THl3 WAVETiTRBULENCE INTERACTION AT LOW LIQUID REYNOLDS NUMBERS IN A HORIZONTAL OPEN-CHANNEL FLOW

Evangelos Stamatiou

An abstract submitted in confomiity with the requirements for the degree of Master of Applied Science

Graduate Department of Chernical Engineering and Applied Chemistry University of Toronto

0 1998

The wave-turbulence interaction was experimentaly investigated in an open-charme1 with a

shear-£tee wavy surface using the photochrornic dye activation (PDA) technique. In the experiments

conducted, two-dimensional waves of different amplitudes, wavelengths and fiequencies were

superimposed on a turbulent open-channel flow via a mechanical wavemaker.

Within the range of Reynolds numbers ( g h =800-1600 based on liquid height) investigated,

the results showed that waves decremed wall turbulence levels with increases in the wave a m p h d e

and fkquency in cornparison with the undisturbed flow.

Flow visualization studies conducted indicated that the generd quaiitative appearance of

turbulence in wavy flows is similar to those in non-wavy flows.

Dr. Masahiro Kawaji for his superior supervision, guidance and financial support given

throughout this study.

Dr. G.J. Evans and Dr. O. T m s for their suggestions and recommendations given.

My coUeague, Mr. Peter M. -Y. Chung, who assisted me in performing the experimental part

of my thesis, and gave me many good advises in the programrning part of my thesis.

Mr. Paui Jowlabar, senior tutor in the Department of Chernical Engineering and Applied

Chemistry, who gave me rnany suggestions in the design of the wavemaker.

Dr. Akira Karjasaki, visiting professor fiom Japan, for his assistance and guidance in the

experimental part of my thesis.

Dr. Reza Karimi, who guided me in the use of Matlab programming and provided invaluable

information for understanding the physicai aspects of my thesis.

Dr. Kawaji's group who gave me a very pleasant and fiendly atmosphere throughout the

many hours that I worked in the laboratory.

0 My Fa* who provided me with emotional and financial support and was always there for

me.

TABLE OF CONTENTS

Page

Abstract

Acknowledgments

Table of Contents

List of Figures

List of Tables

List of Appendices

Nomenclature

CHAPTER 1 Introduction

1.1 Objectives and Scope of Thesis

1 -2 Outline of Thesis

CHAPTER 2 Literature Review

2.1 Statistical Investigation of Turbulent Open-Channel Hydrodynamics

2.2 Coherent Structures and FIow Visualization

2.3 Techniques for Turbulence Structure Investigation

2.3.1 Experimentai Techniques

2.3.1.1 Non sheared and non-wavy interfaces

2.3.1.2 Sheared and wavy flows

2.3.2 Statistical Approach

2.3.3 Numerical Methods

2 -4 Nomenclature and Fundamental Concepts

2.5 Sumrnary

CHAPTER 3 Experimental Apparatus and Measurement Techniques

3.1 FIow loop

3 -2 Experimental Setup

3.2.1 Eulerian Measurernents

3.2.2 Langrangian Measurements

3.3 Experimental Techniques and Measurements

3.3.1 The Photochrornic Dye Activation Technique

ii

iii

iv

vii

xii

xiii

xiv

1

3

5

6

6

9

13

12

13

15

17

18

20

21

22

22

25

25

28

29

29

3.3.2 Liquid Velocity Profile Measurements

3.3.3 Error Analysis in Experimental Measurements

CHAPTER 4 Quantitative Results and Discussion

4.1 Wavy, Turbulent Open-Channel Flow

4.2 Experimental Conditions

4.3 Wave Characteristics

4.4 Turbulence Statistics

4.5 Mean Properties

4.5.1 Mean Velocity Profiles

4.5.2 Dimensionless Velocity Profiles

4.5.3 Cornparison of Angular Interpolation and Average Height Techniques

4.5.4 Velocity History

4.5.5 Cross Spectral Density Fmctions

4.5.6 Error in Velocity Measurements

4.6 Turbulence Intensities

4.7 Reynolds Stress

4.8 Wall Turbulent Events

4.8.1 Bursting Frequency Evaluation from Power Spectral Density

4.8.2 Ejection Frequency Determination fiom Velocity Fluctuations

4.8.3 Visual Detection Method

4.8.3.1 Dependence of wall turbulent events on wave characteristics

4.8.3.2 Dependence of wall turbulent events on Reynolds number

4.8.3.3 Scaling laws

4.8.3 -4 Wall turbulent modification by interfacial waves

4.8.3.5 Frequency of turbulent events

4.9 Turbulence Suppression due to Waves: Lateral Movement of Traces

4.10 Summary

CHAPTER 5 Quantitative Results and Discussion

5.1 Suppression of Turbulence by Waves

5.2 Bursting Phenornena and Near-Wall Turbulent Structures

5 -3 Free Surface Turbulence Structures

5.3.1 Upwellings and Downdrafts

Pape

5.3.2 Attached Vortices and Spiral Eddies 129

5 -3 -3 Longitudinal Streamwise Vortices 129

5.4 Summary 135

CHAPTER 6 Conclusions and Recommendations 138

6.1 Conclusions 138

6.2 Recommendations 140

CHAPTER 7 References 142

LIST OF FIGURES

Fimre Number Title Page

Arch or horseshoe type vortices fonned at Merent

Reynolds numbers

Cartesian coordinate system

Experimentd and laser setup

Video setup and typical video images

Schematic representation of the trace image analysis to obtain

instantaneous velocity profiles

Velocity profile calculation using average heights

Velocity profile calculation using angie interpolation

method

Wave amplitude determination fiom trace endpoints

Wave velocity dependence on Reynolds number

Power spech 1 density for Wave 7

Distribution of streamwise velocity fluctuations for run 5 1

Distribution of streamwise velocity fluctuations for run 57



Skewness and flatness factors for runs 5 1 to 57

Skewness and flatness factors for nuis 71 to 77

Mean velocity profiles for different waves as a function of

dirnensionless distance fiom the bottom wall, y&.

Instantaneous and mean streamwise velocities for 77

Mean vertical velocity profiles for different waves as a

function of dimensionless distance from the bottom wall,

Y W / ~

Dimensionless s t r e d s e velocity profiles

Cornparison of the dimensionless law of the wall profiles

for angle interpolation and average height methods for runs 41,

vii

47,71 and 77.

VeIocity history for run 47

Velocity history for nin 53

VeIocity history for nui 57

Velocity history for nin 75

Cross correlation and cross covariance funcitons between

two streamwise velocities at yC=20 and 30 and for y'=20

and 90 for run 47.

Cross correlation and cross covariance functions between

the liquid height and streamwise velocity at yf=20 and 70

for run 47 71

Error bars for universal velocity profites for high and low

Reynolds numbers and for hi& and low wave amplitudes

and fkequencies 73

Normdized turbulent intensities as a fünction of dimension-

less distance, yC=ywu*dv, fiom the bottom wall for runs 11

to 17 75

Normalized turbulent intensities as a function of dirnension-

less distance, y'=y,u*,/v, kom the bottom wall for runs 41

and 43

Normdized turbulent intensities as a function of dirnension-

less distance, y+=y,vu*w/v, fiom the bottom wall for runs 51, 53

45, and 47

Normalized turbulent intensities as a function of dimension-

less distance, y+=ywu*w/v, fiom the bottom wall for nuis 71, 55

and 57 76

Normalized turbulent intensities as a fiinction of dirnension-

less distance, yf=ywu*w/v, fiom the bottom wall for runs 73, 75

and 77 77

Normalized Reynolds stresses plotted as a function of dimension-

less distance, c=yW/h, fiom the bottom wall for nins 1 1 to 17 80

Nomalized Reynolds stresses plotted as a fùnction of dimension-

viii

less distance, cyw/h, fimm the bottom wall for runs 41 and 43 80


less distance, cyW/h, fi-om the bottom wall for runs 5 1,53,45

and 47 81

Normalized Reynolds stresses plotted as a fùnction of dimension-

less distance, c=yW/h, fiom the bottom wall for nuis 71,55 and 57 81


less distance, c=yW/h, fiom the bottom wall for runs 73,75 and 77 82

Power spectral density for the instantaneous velocity data for

run 47 at different y+ positions

Power spectra density for the instantaneous velocity data for

nin 73 at different y+ positions

Typ' 4 trace deformations due to bursting action

Effect of wavelength on wall ejections

Effect of wave amplitude and fiequency on wall ejections for

selected runs

Ejection period dependence on Reynolds number for runs 11

to 77

Bursting penod dependence on Reynolds number for nuis 11

to 77

Instantaneous and mean velocity profiles for run 47



Langrangian streamwise velocity profiles for run 47

Langangian streamwise velocity profiles for run 57

Langrangian streamwise velocity profiles for run 75

Variation of wall turbulent event frequency with wall fiction

velocity for al1 nuis

Dimensionless fiequency of wall turbulent events

Schematic representation of the lateral displacement and

measurements taken using Mocha

Lateral fluctuation and instantaneous displacement of traces

measured fiom the centerline of the test section for non-wavy ( ~ 4 )

ix

and wavy flows (43 and 47)

Lateral fluctuation and instantaneous displacement of traces

measured fiom the centerline of the test section for non-wavy

(run7) and wavy flows (runs 73 and 77)

Quad images of trace motion in non-wavy (i-ii) and wavy (iii-vi)

open-channel flows

Sequential side view images of wall bursts for nin 77

Sequential side view images of a funne1 vortex for nin 77

Side view and end view of a vortex fûnnel

Formation of a vortex b e l near the bottom wall as seen fkom

the side for run 43

Formation of a vortex funne1 near the bottom wall as seen fiom

the side for nui 45

Formation of a vortex structure near the wdl as seen fiom

the borescope for run 43

Formation of a quasi-streamwise vortex for run 57 as seen f?om

the side

Formation of a quasi-streamwise vortex for run 57 as seen fiom

the borescope

Side view images of the sequential progression of a vortex ring

pair spinning in the spanwise direction for run 57

Sequence of images showing the formation of a spinning element

(circled) in the spanwise direction for CD = 3000

Sketch of a horseshoe and low speed streaks as visualized by

other researchers

Video sequences (Langrangian view) showing the upward motion

of the trace towards the interface resembling the splatting or

upwelling motion for nin 43

Video sequence showing the reflection of the fluid fiom the

interface towards the wall for Re D = 3 700

Upwelling motion of the fluid as visualized by the moving traces

£rom the side view

Eulerian top views showing the displacement of the traces for

m s 77 (a) and 47 (b)

Sketch of the formation of spiral eddies in tirne (a-d) as viewed

fiom the top with a moving camera

Sketch indicating the attached vortices with a vertical axis of

motion as shown from the side with a movuig camera

Sequence of images showmg the formation of spird eddies for

nui 41

Sequence of images showing the formation of spiral eddies for

run 41

End view image taken fiom the borescope, with a "kink" (circled

structure) indicating the interface position due to the reflection

of the trace by the fiee surface

End view image of a ring type structure near the interface formed

in the streamwise direction (circled structure)

DipoIe counter-rotating streamwise vortices occurring between

downdrafts and upwellings as predicted by Nagaosa and

Saito (1 997)

Formation of a longitudinal vortex ring sû-ucture close to the

interface region as seen from the borescope with a fixed

camera for nui 73

(a through d) Formation of a longitudinal vortex occurring near

the interface for nui 1 7

Sequence of images illustrating the formation of a vortex structure

(circled) with axis of rotation in the longitudinal direction for

Illn 43

Conceptual mode1 of the burst-interface interactions -

LIST OF TABLES

Coordinate system and geometrical terminology in

Cartesian coordinates 20

Physical properties of Van-Sol 715 at 24 OC 25

Summary of the sources of enor 38

Experimental conditions 40

Wave characteristics 44

Bursting and ejection periods for turbulent open-channe1

flows with mechanicdly generated waves 90

Frequency of wall turbulent events for wavy flows 106

xii

LIST OF APPENDICES

Appendix Title Pape

Calibration c w e for vohe te r

Fluid Properties

Thermal stratification

Program for velocity detennination

Cornparison of the log-law fiction velocity with

blasius formula

Program for universal velocity profiles calculation

Power spectral densities for waves 1,3 and 5

Skewness and Flatness Factors

Instantaneous velocity profiles

Dimensionless velocity profiles

Velocity histories

A-1

B-I

C-1

D-1

xiii

Nomenclature

f~

f ~ *

FFT

PSD

Mean wave amplitude fiom trace endpoints [ml

Maximum wave amplitude îrom trace endpoints [ml Integrai constant

Cross covariance fûnction between two input signals X and Y.

Molecular dinusivity [m2/s]

Hydraulic diameter [ml

Flatness factor

Dimensional ejection îrequency [s"]

Dimensionless ratio of ejection Eequencies of wavy over non-wavy flows

Fast Fourier Transform

Froude number

Frarne rate [Qs]

Sampling fiequency [Hz]

Wave fiequency [Hz]

Dimensional turbulent event fkequency (s-')

Dimensionless fkequency scaled with inner variables

Dimensionless fiequency scaled with mked variables

Dirnensionless fiequency scaled with outer variables

Gravitational constant [9.8 1 d s 2 ]

Power spectral density fiuiction

Liquid height [ml

Mean liquid height, [ml

Transport coefficient [mh]

Mean value of t h e series X(t)

Mean value of t h e series Y(t)

Number of observations

Number of divisions used for the angle interpolation technique

Number of elapsed fiames between successive traces

Power spectral density

xiv

Liquid volumetrÏc flow rate Diters per minute]

Liquid Reynolds nurnber based on hydraulic diameter determined at the center plane of

the Lquid flow

Liquid Reynolds number based on mean liquid height detemYned at the center plane of

the liquid flow

Liquid Reynolds nurnber based on hydraulic diarneter detemüned over the entire cross

sectional area of the liquid flow

Liquid Reynolds nurnber based on mean iiquid height detemiined over the entire cross

sectional area of the Iiquid flow

Cross correlation hc t ion between two input signals X and Y

Skewness factor

Surface renewal time [s]

Surface renewal time defined in Danckwerts' surface renewal mode1 [s]

Time [s]

Bursting period [s]

Mean bursting penod [s]

Normaiized bursting penod for wavy over non-wavy flows

Non-dimensional bursting period scaled with inner variables

Non-dimensional bursting period scaled with outer variables

Ejection period [s]

Mean ejection period [s]

Normalized ejection period of waves over non-waves

Nondimensional ejection period scaled with outer variables

Nondimensional ejection period scaled with inner variables

Mean sweep period [s]

Wave penod [s]

Non-dimensional wave period scaled with b e r variables

Period between successive wave crests [s]

Fluctuating streamwise velocity [m/s ]

WaiI fictionai velocity [mk]

lnstantaneous streamwise velocity [ds]

- U bulk

Y:, Yw

Y+

Dimensionless streamwise velocity, u / t ï k

Time-averaged stramwise velocity determined over the entire cross sectional area of

the liquid flow [ d s ]

Mean streamwise velocity determined at the center plane of the liquid flow [m/sl Maximum streawise velocity [ds ]

Stremwise turbulent intensities [m/s]

Reynolds stress

Wave velocity [ d s ]

~ t a n e o u s vertical velocit, using angle interpolation [d s ]

Mean vertical velocity using angle interpolation [ d s ]

Vertical turbulent intesities [m/s]

Width of channel Lm]

Mean location of the downstream measuring station used for the deterrnination of the

lateral displacement of the traces [ml

Vertical distance measured fiom the bottom w d [ml

Dirnensiodess vertical distance fiom the bottom w d , ub y , l v .

Fluctuahg lateral displacement of the traces f?om the centerline of trace formation [ml

ùisbntaneous lateral displacement of the traces fÏom the centerline of trace formation

[ml Mean lateral displacement of the traces form the centerhe 9f trace formation [ml

Lateral root mean square intensity [ml

Greek Letters

Time elapsed between two successive traces [s]

Horizontal displacement of traces [ml

Dimensionless distance between streaks

Increment in vertical direction [ml

i -exp(-yt/ 1 O)

xvi

Cole Wake Parameter

Maximum angle between two successive traces

Wavelength [ml

Kinernatic viscosity [m2/s]

lnterpolated angle [Oh]

Liquid density p9/rn3] T h e period or delay in measurements [s]

Wall shear stress [Pa]

Dimensionless distance fkom bottom wall &Jh)

Subscripts

B

E

h

inst

LM

RMS

S

W

wave

Bursting events

Ejection events

Liquid height

Instantaneous

Mean parameter

Root mean square

Sweep events

Wall

Wave

Superscripts

Fluctuating parameter

Normalized parameter

Dimensionless or inner variables

Mixed variables

Outer variables

xvii

Turbdent transport across fluid-fluid interfaces is of particdar interest since it has numerous

applications in industrial and environmental systerns. Furthmore, the wave-turbulence interaction

has been a subject of intense research over the fast several years due ta the importance of scalar

transfer across fluid-fluid interfaces in chemical, nuclear and petroleum plants as weU as in

environmental and geophysical sciences. k e include processes such as gas absorption, evaporation,

boiling, condensation, multipfiase transport, and a variety of environmental problerns such as the

aeration of rivers and lakes, and fluxes of scalars such as greenhouse gases, and sensible and latent

beat at the air-ocean interface. In most of these instances, the flow is turbulent and surface waves are

present with the Liquid side goveming the scalar transport across the gas-liquid interface. nius, wave-

turbulence interactions close to the interface are particdarly important in determining interface

transport rates.

The complexity of the geometry and mechanisms asociated with wavy open-channel flows

has resulted in the absence of models predicting these types of processes. Even the most sophisticated

models describing non-wavy flows rely on empirical constants, and do not simulate the physical detail

of turbulence structure near the interface, but rather focus only on the overall effect of turbulence on

the mean flow.

Most models, such as the d a c e renewal model and the eddy diffusivity models, relate the

transport coefficient (K) to parameters such as the molecular diffusivity (9) and the Surface renewal

time 0 which may be thought of as the mean time between turbulent bursts. Higbie's model (1935)

relates the transport rate with the surface renewal time and the molecular diffusivity:

1

Danckwerts' (1951) model allowed a randorn distribution of d a c e ages and gave:

where T is the mean t h e period between turbulent bursis as defined in Danckwerts' distribution

model. Thus, predicting the mean time interval between d a c e renewal patches, which are patches

believed to result due to the turbulent nature of the flow, is crucial in characterizing the bansport

Turbulent transport mechanisms in the wall and the turbulent core regions are now well

understood both quantitatively and qualitatively for turbulent flows in pipes and channels

[Cheremisinoff, 19861. However, the transport processes near gas-iiquid interfaces are less weli

understood and are stiil under intense investigation. This lack of understanding of the hydrodynamics

and transport mechanisms in the interface region, has given rise to many unanswered questions

peaainllig to the dominant mechanisms that govem interfacial transfer, as weli as the inaccuracy and

limited applicability of turbulence models to free surface flows. Hence, in order to properly

understand and predict the interfacial transport processes at wavy intefiaces, the turbulence

characteristics must be understood through both experimental and numerical investigations.

In view of the signiscance of the wave-turbulence interactions, a research program has k e n

underway to experimentally investigate the turbulence structure and transport mechanisms that exist in

liquid stmms bounded by a wavy gas-liquid interface and a solid w d , with the ultimate objective to

comprehend the interfacial scalar transport in industrial and environmental systems.

Previous work, which is much too extensive to review here, has elucidated the influence of the

wail and interface turbulence structures on the transport across non-wavy (shear-fke and sheared)

interfaces and wavy but sheared interfaces Ipashidi and Banejee (1988), Komori et al. (1989),

3

Banerjee (1992), Lorencez et al. (1997a)l. However, there has been a considerable lack of

understanding conceming the individual effécts of intedacial waves and shear on the modification of

turbulence transport near the interface region.

To facilitate the study of the wave-turbulence i n t e ~ o m , an experimental investigation has

been conducteci in which two-dimensional mechanicdy generated waves were imposed on a shear-

fke surface of a horizontal open-channel flow via a wavemaker. In particular, by separating waves

h m interfacial shear, the individuai effects of waves on turbulence could be distinguished fi-om those

due to interfacial shear. Issues such as the effect of mechanicaily generated waves on the general

qualitative aspects of turbulence near the £ke siirface, and the effects of wave amplitude, wave

fkquency and wavelength on turbulence structures were investigated

Qualitative investigations into many turbulent flows in the past have Ied to the identification of

dominant structures known as coherent or organized shzrctwes. A coherent or orguniked sîmcture

refers to an individual flow structure that appears to be regularly o c c ~ g in the flow. The presence

of these organized structures within the flow field cm be readily identified by flow visualization

techniques. The intennittency of these coherent structures has been shown in the past by many

researchem [e.g. Lorencenz et al. (1997a), Komon et al. (1993a)l to affect the interfacial transport

across gas-iiquid interfices, but one needs to properly comprehend the effect of waves on these

structures near the interfaces.

The main objectives of this research were to investigate the effect of two-dimensionai,

interfâcial waves on the turbulence characteristics in a horizontal open-channel flow without irnposing

any interfacial shear on the fiee d a c e , and to understand the wave-turbulence interactions by

4

comparing the flow characteristics between wavy and non-wavy flows under similar flow conditions.

In particdar, an emphasis was placed on undersbnding the turbulence characteristics near the

interface in the presence of shear-fixe, mechanically generated, two-dimensional interfacial waves.

Experiments were conducted at moderate Reynolds numbers (2500 to 4700 based on a hydraulic

diameter), with different wave amplitudes (0.63 to 1-98 mm) and wave fkquencies (0.8 to 1.2 Hz) that

were not covered in a previous work by Rashidi et al. (1 992).

To achieve these objectives, an open-channel flow loop was equipped with a two-dimensional

plmger-type mechanical wavemaker, which was designed and constructecl with a variable fkquency

and amplitude control. The photochromic dye activation technique was employed to obtain

sirnultaneous measurements of instantanmus velocity profiles at different liquid layer heights and

flow rates, in order to gain insights into the turbulence characteristics of unsheared wavy-stmtified

flow, and to M e r clarify the effect of intexfacial waves on turbulence. These measurements were

conducted in b t h the Eulerian and Lagrangian flanes of reference, using stationary and moving

vide0 cameras, respectively.

The resuits of this study are expected to provide immediate benefits to industrial applications

and the design of new induitrial equipment involving open-channel flows under similar flow

conditions peda et al. (19791. The range of Reynolds numbers studied in these applications varies

fiom 2.6 xl o3 to 1.3 x1 07, with the Liquid depth ranging fiom 0.057 to 347 cm peda et al. (1 9731.

Although the present range of Reynolds numbers and liquid depths investigated are at the

lower end of the ranges encountered in practical situations, there is an apparent lack of detailed

turbuience data for flows at low Reynolds nmbers. In addition, most direct numerical simulations at

present are applicable to low Reynolds number ranges for open-channel flows with a nondefomable

or snooth interface due to the computational cornplexity involved at higher Reynolds numbers. When

a deformable surface can be modeled succe~sfûlly, the present researcb work can be a useful reference

&ta source.

This research work is presented in this thesis as follows:

1. Chupter 2-Literature Review. In this chapter a brief literature review of the past experimental

and numerical work is given.

2. Chaper 3-Experimental Apparatus and Memurement Techniques. Here? the experimental

setup and measulement techniques are described.

3. Chpter 4-Quantitative Results and Discussion. This chapter presents the experimental results

and discusses in detail the experimental fïndings.

4. Chapter 5-Qdtitative Results and Discussion. In this chapter, the qualitative red t s attauied

fiom the video images and by flow visualization are presented and discussed.

5 . Chpter 6-Conclusions and Recommendations. This chapter gives a synopsis of the most

important conclusions drawn i?om the current experimental work and gives fuaher suggestions for

future research work.

6. Appendices-ihat include details of data, graphs and amputer programs used to carry out the

necessary numericd computations.

Past laboratory measurements of velocity and pressure fields in open-channel flows have

shown considerable alteration of turbulence owing to the presence of waves. In addition to this, the

resistance on the liquid side dominates the scalar d e r across a gas-iïquid interface, so there is a

need to clac the scalar t d e r mechanisms in relation to the turbulence structure on the iiquid side.

Thus, it is of great importance to know the turbulence characteristics in the presence of a mobile and

defomble boundary such as the d a c e waves in turbulent open-channel flows. Investigative

techniques in the area of open-channel flow with a defonnable boundary include two main categories.

The fi& group involves the study of hydrodynamics using a statistical approach, while the second is

mainiy focused on the visual characterization to investigate the scalar transfer mechanisms across the

interface. These techniques are briefly reviewed in the foIlowing sections.

Statistical techniques involve the meanirement of the velocity cornponents for the

characterization of the flow field dynamics. In general, to investigate the turbulence structure in open-

channel flows, the flow field has been divided into three sub-regions:

a) The wail or i ~ e r layer (yw/h<O. 15-0.2), where y, is the vertical distance fiom the bottom wall and

h is the liquid height. Here, the turbulence structure is controlled by the inner variables (ub ,v).

b) The fiee surface region (O.6<y&l.O) where the turbulence structure is controlled by the outer

variables (Ump(sl).

c) The intermediate region (0.15-0.3<y&0.6) where the turbulence structure is not strongly

innuenceci by either the inner or outer variables.

The statistical investigation of turbulent openchanne1 hydrodynamics focuses on the chamterkition

of turbulence quafltities such as mean velocity profiles, turbulence intensities, Reynolds stresses, eddy

difbivity and mixing length and their agreement with theoretidy predicted results.

In paaicdar, the velocity profile in the waU region has k e n investigated extensively in the

past and show to systematically deviate fiom the law of the d l . Nezu and Rodi (1986) re-

examined the log-law and determifled that it can only be stnctly applied to the near wall region.

Cebeci and Smith (1974) proposed a wake hct ion tbat describes the velocity profile near the

interface for a zero pressure gradient boundary layer. Studies conducted by many researchers [e.g.,

Tominaga and Nezu (1992), Cardoso et al. (1989)] showed that the Iaw of the wall can weii represent

the velocity profiles in open-channel flows with no shear at the inteiface for low Reynolds numbers

(R610,OOO based on hydraulic diameter). As the Reynolds number becomes larger, any deviations

fiom the log-Iaw cm be incorporated through the use of Coles' wake fiinction which involves a

Reynolds nurnber dependent parameter, Il.

Grass (1971) also studied the effects of channel bed roughness on the log-law profles. His

studies indicated that a lower value of the integral constant, A, corresponds to a rougher channel bed.

Furthemore, Rashidi et al. (1992), Rashidi and Banerjee (1990), Lorencez et al. (1997a) and Nasr-

Esfahany (1998) applied the log-law to open-channel flows with mechanically generated and wind

generated waves with very good agreement. Finally, in the studies c&ed out by Nezu et al. (1997) in

imsteady depth-varying flows, the Von-Karman constant (K) was determined to be constant whereas

the integral constant (A) varied according to the unsteadiness of the flow conditions. Especially

noticeable were their £hdings near the depth-varying fixe surface where the turbulence intensities

were shown to decrease.

8

The most interesting hding regarding turbulence intensities was repoxted by Komori et al.

(1982) who noticed a damping effect of the fke surface on the vertical velocity fluctuations in an

op-channel flow. Accordhg to their laser-Doppler anemometer (LDA) measiilements, they also

noticed a slight increase in the streamulse turbulence intensities close to the fi-ee d a c e , suggesting

that there might be a re-distribution of the turbulent kinetic energy close tc the firee surface. This was

later verifïed by Komori et al. (1987) who also found that the streamwise turbulence intensity slightly

increases with y& in the region close to the fke surface, white the vertical intensity is strongly

diminished in this region.

Regarding the eddy difkhi ty caiculated fiom mean velocity profiles in open-channel flows,

it was show by Ueda et al. (1977) and Hussain and Reynolds (1975) that the eddy diffusivity reaches

a maximum value at y d 4 . 4 5 while it approaches zen, near the fiee d a c e . Nezu and Rodi (1986)

also re-examinecl the distributions of eddy diaisivity and mixing length in open-channel flows

calculated fiom the mean velocity profiles, and detennined that they are dependent on the wake

fiinction, II. They also noticed a siguifiwit reduction in eddy viscosity near the d a c e . This has

important implications since the transfer of momentum, heat and mass in turbulent transport in hown

to be afEected by the motion of turbulent eddies whose intensity is described in terms of the eddy

diffusivity [Cheremisinoff, 19861.

Gayral et al. (1979) measured the Reynolds stresses in a wavy-stratified flow and determined

that the waves may play a s i w c a n t role in the momentum transport mechanism at the interface.

Previous work in this area includes investigations of Fabre et al. (1 983, 1987) who studied turbulence

structu~.: in cocurrent wavy flows. Their results showed an increase in the turbulence quantities near

the interface although they were unable to make turbulence measurements very close to the interface

and could not distinguish the velocity fluctuations due to wave motion fiom the turbulence

fluctuations.

9

Furthemore, investigations conducted by Howe et al. (1982), Papadimitrakis et al. (1988),

and Cheung and Street (1988) with wind generated and mechanically generated waves with variable

air fiow over a stationary liquid layer, showed that the velocïty profles in the water and au layers

were influenced by the presence of interfacial waves, wMe the temperature profiles were not Their

measurements also showed that the mean period between ejections at the interface depends on both

the wave and gas flow chsracteristics, and did not s d e with b e r or outer variables.

Kemp and Simmons (1982) conducted experiments in smooth and rough turbulent channel

flows with interfacial waves. Their velocity profiles measurements showed that the linear portion of

the velocity profiles in the near wall is the same for ail the cases for the smooth wall experiments,

indicaihg no change in the wall shear stress. Ln addition, their results showed that the maximum

streamwise turbulence intensity is increased substantially with waves and current coexistuig.

Vadim Borue et al. (1995) investigated the interaction of Surface waves rith turbulence in

M y developed open-channel turbulent flows using Direct Numerid Simulation (DNS). Their results

indicated that DNS simulations could predict the turbulence statistics quite accurately. However, their

computatiom were limited to "infinitesimally" small-amplitude surface waves and low Reynolds

number flows.

Most of the efforts in turbulence research in the last thirty years have ken directed to iden*,

characterize and predict the coherent components of turbulent motion through the use of flow

visualization experiments. Coherent structures are observed in various open-channel flows, such as

rivers and estuaries, and affect sediment transport significantly. It is apparent that these coherent

structures are responsible for the production and dissipation of turbulence and thus the study of the

turbulence structure is of fundamental importance to the understanding of open-channel

hydrodynamics. Coherent structures are observeci in mainly two regions. In the inner region, near the

10

Wall or charme1 bed, where binsfing phenomena occur quasi-paiodically that sustain mbdence, and

in the outer region (near the k e d a c e ) Acre boils and vortices exist

Coherent structures are dehed as persistent flow patterns with larger lifetime and/or spatial

extent than the turbulent integral d e s [Kaftori et ai. (1994)l. Coherent structures in the sheared

wavy interfkce region were shown to exist in numerous laboratory experimen~ [Nasr-Esfahany

(1 W8), Loreacez et al. (1 997a), Lam and Banerjee (1 99 111. Thus, coherent structures are an important

part of the turbulence characteristics in open-channe1 flows with wavy interfaces as well as smooth

interfaces.

The major objectives of studying coherent structures have k e n to predict the gross statistics of

turbulent flows, elucidate the dynamic phenomena responsible for the statistical properties that can

only be measured, and try to prpdict the: 3 through numencal modeling.

With these objectives in min& a major part of turbulence-structure research has focused on the

spatial and temporal characteristics related to the turbulence production, outnow motion, the

relatiomhip between outîlow motions and near wall turbulence interactions as well as the relationship

between fluctuating variables (pressure, wall shear stress) and coherent motions.

Near wall coherent structures clmsijîcation

In wall-bounded flows, many researchers Bobinson (1991), Kline et al. (1967), Rashidi et al.

(1 99 1), Kaftori et al. (1 99411 bave observed three types of coherent stmctures:

a) The high speed regions and low-speed streaks very close to the wali.

b) The streamwise and quasi-streamwise vortices.

c) The "active" periods consisting of sequences of ejections fiom the wall layer towards the outer

region and sweeps fiom the outer region towards the wall.

The quasi-streamwise vortices in the boundary layer appear to provoke all three types of coherent

structures and they are thought to be the upstream legs of horseshoe vortices Bobinson (1991),

Banejee (1 !JE)]. The wall region is thought to be populated by quasi-sûeamwise vortices whose axes

I I

are uicluied away fiom the wall with the angle of inclination increasing with distance from the wall

(see Figure 2.2-1). These quasi-streamwise vortices are closely associated with both ejections and

weeps.

Banerjee (1992), Komori et al. (1993a), and Kline and Reynolds (1967), among others,

determineci that horseshoe-shaped vortices may form an important element of turbulent boundaq

layers. By a vortex was meant a spinning fluid like a tornado, or whirlpool. Turbulence is made up of

several of these vortices that are bom, move around, interact and decay. Horseshoe type vortices are

rather short compareci to Iow-speed streaks that lie below them. Both horseshoe and hockey-stick

vortices appear to play an important role in generating turbulence (see Figure 2.2-1).

FLOW I\L

Figure 2.2-1: Arch or horseshoe type structures formed at different Reynolds numbers pobinson

(1 WO)].

A majority of turbulence production in the tusbulent boun- layer occurs in the buffer

region dirring intermittent and violent outward ejections of low-speed fluid during iiinishes of hi&-

speed fluid at a shallow angle toward the wall. This near-wall turbulence interaction is considered to

occur in an intermittent, quasi-cyclic sequence and it is generally referred to as "bwstingfl. nus,

b d g usually refers to the production of turbulence in the boundary layer via violent outward

12

eruptions of the near-wall fluid. From a stationary fiame of reference, it can be interpreted as the

passage of a relatively long-lived, single, quasi-streamwise vortex, which ejects fluid away h m the

wall by vortex motion. Bilrsting phenornena have k e n idenfineci by many researchm such as Kline

et al. (1967), Kim et al. (1 Wl), Corino and Brodkey (1969), Nychas et al. (1973), Grass (1971), Clack

and Markland (1971), among others. Before them, pioneer researchers lïke Einstein and Li (1956) and

Hanratty (1956) identifid that the viscous sublayer consists of coherent and o r g k d motions. Many

authors have used different definitions for the b d g motion as reviewed by Robinson (1991).

Robinson (1991), Kline and Robinson (1989a), Robinson (1 990) and Cantewell(1981) among

others, give excellent summaries of the characteristics of coherent structures that exist in turbulent

boundary layes.

Since the Iate l960's, a considerable amount of effort has ken devoted to the understanding of

complex turbulent ffows. This has resulted in the establishment of three approaches, which have ken,

or cm be potentiaiiy applied to other problems of engineering and geophysical interest. The £kt

approach relies on the experimental investigation of turbulence while the second relies on the use of

statistical averages for the flow variable of interest. The 1st approach uses numerical simulations to

investigate turbulence. The following sections present brief reviews of the above investigative

techniques.

23.1 Ehpetimenfsll Techniques

In view of the turbulence structure interaction with the fke surface, two broadly different

situations are distinguished. In the fïrst one, there is iittie or no shear imposed on the fkee surface so

the boundary condition is essentidy one of zen, shear stress. In the second, interfacial shear is

imposed (e.g. by the action of the wind), causing turbulence to be generated on the liquid side, much

in the same manner as at the solid wall.

13

2.3.1. ! Non sheared mrd non-wuvy int@mes

Kline et al. (1967) investigated and quantified the low-speedhigh speed phenornenon. They

found through a series of flow visualization experhnents using hydrogen bubbles that high speed and

low speed regions called streaks formed, which periodically lifted off, oscillated, became unstable and

evenhdly broke up chaotically. They named this senes of events as bursting.

Corino and Brodkey (1969) observed that ejections near the wail dominated in M y developed

high Reynolds n a b e r fiows and they estimatecl that these ejections account for 70% of the Reynolds

stresses measured. These resulîs were confïrrned by Kim et al. (1971) who showed that Wtually most

of the turbulent energy production in the range of O<y+<100 occm during the lifting and breakdown

of these streaks (where yt=y u; /v is the dimensionless distance fiom the bottom wall).

Willmarth and Lu (1972) studied the instantaneous Reynolds stresses near the w d and found

that very large values resulted during the bursting action. They also found that large contributions to

the Reynolds stresses occurred during the sweep phase in contradiction to the findings of Corho and

Brodkey (1969). Prior to their fïndings, most contributions to the Reynolds stresses were believed to

occur during the outfiow of low-speed fluid or ejections.

Rao et al. (1971) examined the bursting process in wall-bounded flows over a wide range of

Reynolds numbers based on the boundary layer thickness (600<R~<9000). Their results showed that

the mean bunting period scales with the oirter variables (u-, h) rather than with the inner variables

(ub ,v) even near the wall layer suggesting that bursts rnay be a general feature of ail turbulent flows.

Grass (1971) used hydrogen-bubble visuaiization technique to meanire structural features of

turbulent flow over smooth, transitiody, rough and M y rough walls. He found that ejections and

iurushes were present in turbulent flows irrespective of the d a c e roughness with the basic structure

of the organized motions appearing to be d e c t e d by the wall roughness.

14

Komon et al. (1982) investigated the turbulence structure in a shear fke open-channel flow

usùig laser-Doppler anernometry (LDA). Their r 4 t s showed that on average, fluctuations normal to

the intdace are dam@ whereas those that are pardel are enhanced. However, they experienc-d

f icul t ies near the interface region due to the disturbances generated by probes at the interface.

Rashidi and Banerjee (1988) investigated turbulence structures in horizontal Liquid films

bounded by a free surface and a walI using the hydrogen bubble traces generated in the liquid stream.

Their d t s indicated that the dominant flow structure is caused by periodic ejections of intensely

turbulent fluid (burst) with low streamwise momenhim fiom the wall region into the bulk fluid, which

it displaces and mixes slowly.

Kafton et al. (1994) investigated the turbulence structure of the turbulent boundary layer in a

horizontal open-channel flow by means of LDA and by flow visualization synchronized with LDA.

Their experiments indicated thiat the dominant structures in the wail region are large-scale sbeamwise

vortices, which originate at the bottom wail, grow, and expand into the outer flow region. These

strearnwise vortices have a shape of an expanding spiral, wound around a funne1 and are iaid

sideways in the flow direction. They detemiined that most of the observations of the wall turbulence

phenornena (e,g. quasi-streamwise vortices, ejections and çweeps) seem to be part of these h e l -

shaped vortices.

Hestroni and Mosyak (1996) studied the bursting process in turbulent boundary layers at low

Reynolds numbers in an open-channel using i n f i ad themography. They were also able to detect that

large-scale turbulent structures were ejected in the b d e r region towards the interface.

Furthemore, regions of upwehgs7 downdrafts and whirlpool-like attached vortices formed at

the edges of the upwellings that dominate the fixe surface turbulence characteristics in horizontal

open-charme1 flows were predicted numeridy by Pan and Banerjee (1995) and later verified

15

experimentally by Kumar et al. (1998). Their d t s indicated that the upwellings were related to

birrsts h m the bottom wall, while the eddies were seen to be generated at the edges of the upwellings.

Rashidi (1 997) also studied the interaction of bursting events (i.e. ejections and inflows) with

the fixe d a c e in turbulent channel flows using oxygen bubble visualization and image processing

techniques. His results also showed that the £low is dominated by the generation of wall ejections,

spanwinse vortices, and the interactions of these structures with the interface. He also provided M e r

evidence of the formation of horseshoe and hockeystick type vortices, and their relations to the

turbulent events.

2.3.1.2 Sheared mrd wuvyjlows

Komori et al. (1989) fkst investigated the surface renewd motions in the interfacial region

below a gas-iiquid interface in relation to bursting motions in the w d region. They suggested that the

surface renewd motions originate fiom the bursting motion and large scale energy containing eddies

control the mass transfer rate across a gas-liquid interface.

Rashidi and Banerjee (1990) and Rashidi et al. (1991) studied the turbulence structures near a

solid wail and a gas-liquid sheared interface in open-channel flows. The low speedhgh-speed sûeaks

which fomed near the sheared interface were shown to possess the same characteristics as the streaky

structures near the wall. The low-speed streaks that fomed near the sheared interfaces appeared to be

more pronounced than the wall streaks. These results were later verified numerically by Lam and

Banerjee (1992) using DNS.

Rashidi et al. (1992) studied the wave turbulence interactions in turbulent channel flows by

imposing two-dimensional waves of different wavelengths and amplitudes via a wavemaker. TheV

conditions were chosen such that their ejection hquencies were within the frequencies of intefiacial

waves. Their resuits showed the waves caused an increase in the number of wall ejections, giving nse

16

to an increase in the number of turbulence intensities and Reynolds stress, with the d t s correlating

better with wave amplitude. The ovemll effet of the d a c e waves they observed was to increase

turbulent levels. Their results, however, were in contradiction to Brereton et al. (1990) who noticed

negligible effects of the oscillation imposed on the outer region of a boundary Iayer in experiments

conducted at lower budejection fkquencies than the oscillations imposed by Rashidi et al. (1992).

Komori et al. (1993a) studied the turbulence structiae and mass transfer across a sheared,

wavy air-water intdace in a wind wave tank They showed that the mass tramfer across a sheared air-

water interface is more enhanced compared to an unsheared interface and atûibuted this phenomenon

to the turbulence structure existing near the air-water interface. They found that in weakly sheared

interfaces with s m d waves, the main mechanism of turbulence production is similar to the bursting

phenornena found by Rashidi and Banerjee (1990) but in the highly sheared region with bigger waves

the turbulence is generated by the waves.

Nasr-Esfahany and Kawaji (1996) studied the turbulence structure of a wavy two-phase

stratifieci fiow in a nearly horizontal rectangular duct Their experimental kdings showed that

turbulence generation at the interface is dominated by the shear imposcd at the fke surface and by the

waves produced at the interface, with large scale cellular motions extendhg deep into the Liquid.

These cellular motions were noticed to be stronger for waves with larger amplitudes and considered to

increase scaiar tramfer. However, their redts couid not distinguish whether this increase in scalar

tramfer was atîributed to the wave action or the irnposed shear since both were present during their

experiments.

Lorencez et al. (1997a) studied the interfacial momentun -fer in an open-channel flow

with both cocurrent and countercurrent stratifiecl ait-kerosene flows with a wavy interface using both

hot-film anemometry and the photochromic dye activation technique. They determined that in both

17

cocurrent and countercurrent wavy-stratifïed flows, the interfiacial shear and waves altered the

turbulence structure of the liquid phase sigifïcanty. They also detennined that the effect of

interfacial shear on the liquid layer was to retard the velocity profile near the interface and shift the

location of the maximum velocity to a point below the surface. They also found that large organized

motions are associated with waves in cocurrent and countercurrent flows (1997b) and were able to

predict the mass W e r coefficient for a wavy gas-liquid interface using an eddy ceii model. They

also determined that the vertical turbulence intensities incfease with wave amplitude.

Nasr-Esfahiuiy (1998) explored the turbulence struchue on the liquid side of a wavy-stratified

flow in a nearly horizontal openchamel flow using the Variable Interval T i e Average (VITA)

technique with hot film anemometry. His results showed that the shear-induced waves strongly

mod@ the turbulence structure near the interface on the liquid side increasing the fiequency of

occurrence of turbdence events in cocurrent flows. On the other hanci, turbulent events decreased for

countercurrent flow cases. He suggested that waves were responsible for the increasing trend in the

fkquency of the wall turbulent events in cocurrent flow cases. He also performed conditional

statiçtical averages of the turbulent events near the wavy interfaces, which indicated that positive

Reynolds stresses were produced in cocurrent flows, M e negative Reynolds stresses resulted for

countercurrent flows.

A number of conditional-sampling techniques have evolved to detemiine turbulent events

with certain predefined characteristics. Among the most popular ones are the variable-interval thne

average (VITA) method [Gupta et al. (1971), Blackwelder and Kaplan (197611, the u'v' quadrant

method Wallace et al. (1 972), Wiilmarth and Lu, (1972)l and the u-level method [Lu and Willmarth

18

(197311. Confusion has arisen eom cornparisons among the redts fiom different techniques. It has

also been difncdt to relate probedetected flow events with v i d y identified turbulence structures.

ûther statistical techniques commonly employed for the detennination of organized

turbulence motions include proper orthogonal decomposition PakeweU and Lumley (1969, Moi and

Moser (1 98911 and stochastic estimation of single point F o i n et al. (1 987)] and two-point tenson

[Adrian et al. (1979)l which are especially valuable for the characterization of streamwise vortical

structures near the w d .

233 Numehi Meth&

Two approaches to turbulent flow simulation have been utilized in the investigation of

turbulent structures: the large-eddy simulation (LES) and direct numerical simulation (DNS).

In the large-eddy simulation (LES) the mallest scales of the flow are rnodeled while the

remairing scales are computed directly with the three dimensional, timedependent Navier-Stokes

equations, which are avemged over the s m d scaies. This approach is based upon the observation that

the small scdes in turbulent n o m are nearly universal whereas the turbulent behaviour at larger scales

is a strong fiuiction of the flow geometry and gross flow parameters.

Direct numerical simulation (DNS) accmtely resolves the turbulent motion at all relevant

scales but at the expense of increased computational cost Quantitative turbulence structure

investigations require DNS because of the inadequate spatial resolution of near-wall features by the

LES rnethods. Application of DNS is extremely demanding of computational resources and thus is

limited to low Reynolds number flows with simple geometries such as charnel flows and boundary

layers. DNS is particulady important when simultaneous measurements of instantaneous velocity and

Scalar fields are required.

Lam and Banejee (1992) investigated numerically the flow between two surfaces at which

no-slip and k - s l i p conditions were imposed on both boundaries. They studied the effect of shear and

boundary conditions on the streaky st~~ctures under the influence of different shear rates that have

b e n applied to each boundary. These streaks are important because they have been observed to

periodicaily lifi off h m the wail, osciuate, become unstable, break down and Iead to the formation of

turbulent binsts. Bursts account for up to 70%-80% of the turbulence production or Reynolds stress as

predicted by Kim et al. (1 97 1) and W i i et al. (2 975).

Pan and Banerjee (1995) conducted the first DNS of fke d a c e flows with a flat gas-liquid

interface using a pseudospectral method. They clarified the formation of stredq structures and details

of turbulence statistics with and without interfaçial shear. Their numericd simulations showed that

three types of structures existed in non-wavy turbulent flows: the upwellings, dovmdrafts and attached

vortices. For sheared d a c e s under waves, the dominant structures observed were low-speed streaky

regions with bursts and sweeps occurring in the turbulent boundary layer. The effect of interfacial

waves on these structures is still unclear, although Komori et al. (1993a) observed a breakdown of

scaling with shear rate when three-dunensional waves are imposed.

Komon et al. (1993b) also perfomed DNS on a shear-fiee gas-liquid interface based on a

bomdary-fitting finite merence method. Their results indicated that organized b&g eddies are

lifted up fiom the near wall region and move to the k e surfkce as surface renewal eddies.

Nagaosa and Saito (1997) used DNS to investigate the relationship between turbdence

structures and Scala transfer mechanisms in both thermally unstratified and stratified fke-daces.

They suggested that the turbulent bursts generated at the wall boundaq reach the interfaces and their

energy is redistributecl to the surface-parallel directions by pressure Strain. This occurs because the

k e d a c e blocks the turbulence energy and therefore this turbulence energy generated fiom the

bottom wall has to re-distribute itself to the spanwise direction. They found the turbulence intensity in

20

the tramverse direction to incrûase near the fie d a c e while the turbulence in the streamwise

direction did not show an appreciable increase. Splattings were also predicted by DNS, wbich initiate

the formation of couter-rotating dipole vortices aligned in the streamwise direction with the splattings

occinring at the center of these vortices. The splattings initiate downward currents replacing the fke

surface fluid with fluid fiom the bulk by the rotational motion of these vortices. These DNS

predictions are yet to be verified experimentally.

Terminology and nomenclature used throughout this thesis are debed in this section to avoid

confusion. Names, symbols, and tenninology related to the Cartesian coordinate system are show in

Figure 2.61 and Table 2.4-1. Wall or "plus" units refer to n o d t i o n by the viscous length and

velocity scales, v / U; . Quantities that inciude the subscnpt "w" denote that the property is detemiined

at the wall region Fluctuating quazltities are denoted by a prime (e-g. u'), whereas the mean quantities

are indicated by a subscript "mean". Lnstantaneous parameters are shown in Italic or with a subscnpt

Streamwise or longitudinal direction is k the direction of flow and is referred to as the x-

orientation. "Transverse", "spanwise" or "lateral" is used interchangeably to designate vortices (or

anything else) with a prirnary orientation in the zdirection. Side view refers to the x-y plane view

fiame, top view refers to the x-z plane, and end view or incoming view refers to the y-z planar view.

Table 2.41. Coordinate system and geometricai terminology in Cartesian coordinates

I 1 Longituciinal

Tensor subscript 1

Top view (xz plane) Plan view Side view (yz plane) Vertical plane

Axis X

2

Axis name Streamwise

Y Axial Wall-normal

Figure 2.41. Cartesian cwrdinate system.

The importance of turbulent wavy flows in numerous industrial and environmental processes,

and the lack of information on the liquid layer hydrodynamics, especially turbulence structure and its

interaction with waves at low Reynolds number flows, provoked our curiosity for the investigation of

turbulent wavy fiows in an open-channeI. This thesis provides new experimental results covering the

low Reynolds numbers that can be easily tackled by direct numerical simulations. So far, due to the

complex geometry of the waves, most numericd simulations conducted have been limited to

"innniteshdly" small waves or non-wavy flows. Whenever fiiture numerical simulations of open-

channel flows with finite amplitude waves become available, the present experimental data can be

used for verification. Furthermore, there is a lack of understanding conceming the individual effects of

interfacial shear and waves on the modification of turbulence structures near the f?ee surface, since

most of the experiments to date involved studies of cocurrent or countercurrent wavy-stratified flows.

The present work focuses on the effect of waves without imposing any shear on the surface at low

Reynolds numbers.

The experirnents were conducted in a Plexiglas rectangdar channel equipped with facitities

enabling the investigation of a horizontal, open-channel flow with a shear-k , wavy gas-liquid

interface (fke dace ) .

The flow channe1 consisted of three main sections which were the inlet chamber, the main

test section, and the outlet chamber. A schematic diagram of the flow channel is shown in Figure 3.1-

1 -

The main test section was made up of three equal sections, 2.40 m long, 0.10 m wide and 0.05

m deep which were joined end-to-end by £langes with neoprene gaskets and açsembled to ensure that

the inside walls were flush. The test section was designed to ensure its cross section was constant

throughout its length, and to minimize deformation due to mechanical stress. The most important

consideration was the smoothness and flatness of the bottorn wall which was nachined with a

tolermce of 1 mm in 240 cm, and was glued and bolted down to the side wails korencez, 19941. In

addition, the liquid layer depth, h, ranged fiom 13 mm to 20 mm and the aspect ratio (width of

chaianevliquid height) fiom 7.5 to 5. This aspect ratio satided the criterion of w/h k i n g greater than

5, so that the velocity-dip phenornena caused by secondary currents did not occur in the centerline of

the channel as pointed out by Nem et al. (1997). The cross sectional mean velocity, hm, ranged fiom

O. 11 d s to 0.17 m/s, so the liquid Reynolds number based on the iiquid heigk Reh, ranged fkom 800

to 1600.

Ftow Dlrectlon

H.-cdContLcu - Photodiode ampllfied algnal to Nltrogen Laaer

aide vlew

Reclrculatlng Pump

k Meaauring atatlon 3,60-m from inlet chamber

4

Figure 3.1. Experimental and laser setup

nie experimental setup was also equipped with a plunger-type wavemaker (ZeromaxTM Model

JK2 plunger comected to a 114 HP motor) with an adjustable fkquency and amplitude controller that

was u t i h d to generate the mechanical waves. Great care was taken at the idet where wave

dissipative material was placed to minimize the effects of reflecting waves that could destroy the two-

dimensionality of the mechanically generated waves. Fiirthennore, the liquid temperatures at the idet

and outlet chambers were monitored using mercmy thennometers. Any temperature deviations of the

licpid that wae caused by the pirmp were d e d by changing the tap water flow rate through a

copper coi1 heat exchanger placed inside the inlet chamber. Efforts were made to maintain a constant

Liquid temperature throughout each experimental m. The maximum temperature deviation between

the inlet and outlet chambers never exceeded 2OC.

The working fluid was circulated by a 3/4 horsepower Marathon Electric centrifuga1 pump.

The recirculated liquid was continuously filtered by a strainer and a &dge mer to remove any

solids grtater than 20 p in diameter (Serfico Ltd., Model: HB-10-20-W). AU the piping was made of

3/4" diameter PVC pipes. The liquid flow rate was measured usïng Signet flow meter (Model: MK

584) with a signal conditioner (Model: MK 5 14). The flow meter was calibrated in advance to ensure

consistent readings. The calibration curve that relates the output voltage with the liquid flow rate is

given in Appendk A. The voltage output fiom the flow meter was measured using a digital

multimeter (Fluke, Model: 8050A) having an accmcy of f 0.03 V. The measurements were

performed d e r constant flow, temperature, and liquid height conditions were anained throughout the

test section.

The working fluid was deodorized kerosene (Van-Sol 715) with 0.008% concentration by

weight of photochromic dye (1,3,3 trimethyhdoline-6-nitro benzopiropyran or TNSB) to conduct

simultaneous measurements of Iiquid height fluctuations and velocity profiles as well as to visuaüze

the liquid flow structures. The propeaies of kerosene (Van-Sol 715) at nom temperature and

atmospheric pressure are given in Table 3.1. Properties of kerosene at dBerent operaîing

temperatures cm be found in Appendu B (Van Waters and Rogers Ltd.). The liquid properties and

their correspondhg temperatures for alI the runs conducted are a h &en in Appendix B.

Table 3.1-1 Physical Properties oi

--

3.2.1 Eulerian M m m m t s

Measurements were made at a station located 3.60 m away fiom the test section entrance (xfi

= 180 where h is the liquid height) to ensure M y developed flow. Previous investigators have used

xlh ratios of 80 to 122 [Kim et al. (1 987), Kaftori et al. (1 994)l. Hussain and Reynolds (1 975) used a

ratio of channel length to chme1 half width of 450 without a signincant change in their resultç

compared to lower aspect ratio experiments.

Van-sol715 at 24OC

The test section constructed fiom clear Plexiglas ailowed flow visualization and video

photography fiom the side, top and incoming views, enabled the viewing of the trace motions fiom al l

three directions simultaneously. The motion of the traces in the liquid phase was captured at 30

fbmes/second by two Hitachi (Model: VK-C370) high resolution (768 x 494 pixeis) colour CCD's

and a JVC (Model: GR-S77) camcorder (with a 470 horizontal h e s resolution) as show in Figure

3.2-1.

One Hitachi CCD was positioned h o h n t d y facing the side of the channel at a distance of

59 cm away fiom the central plane of the test section and was used to capture the streamwise motion

Surface Tension P W

Elecûical Conductivity (Nm) Rehctive Index

Figure 3.2-1. Video setup and typical video images.

of the traces generated by the laser in the vertical plane. The side view CCD was synchronized

externally using an extemai timer (Sony, Model: DC-77RR). The Sony timer dso ûiggered the light

h m a Stroboscope (Sugawara, Model: PS-240) such that the strobe light and the recorded images

fiom the side view camera would be synchronized (see Figures 3.1-1 and 3.2-1).

A second Hitachi CCD was mounted on a 14 cm long rigid borescope with a 6.0 mm outer

diameter (Model: 6.14) usuig a C-mount adapter with a 35 mm Minolta lens (Model: 535CE/1773),

and was placed 32.5 cm away fiom the center point of the pulsed laser source. The borescope had a

field of view fiom 4 mm to infinity.

The borescope-CCD arrangement was used to capture the spanwise motion of the traces

generated by the laser beam. It was observed that the borescope irnmersed in the flowing liquid

affecteci the flow approximately 2-3 cm upstrearn. To minimize this effect on the trace motion, the

borescope was placed at a sufncient downsûeam distance (32.5 cm) fiom the laser beam location

where the traces were formed. Thus, the presence of the borescope did not disturb the flow visualized

by the three CCD's. Flood lights (150 W) were placed dong the length of the test section to enable

viewing of the coherent structures using the borescope. It could be anticipated that the flood lights

places dong the test section could heat the liquid and cause t h e d stratification in the test section.

However, calculations perforrned indicated that the heating effect was negligible and could not have

caused natural convection in the flowing fluid. These calculations are provided in Appendix C.

Finally, a JVC VHS-C (Mdel: GR-S77) camcorder with a 75 W headlight mounted on top of

the test section was employed to capture the flow structures fiom above the iiquid surface. The images

fiom each CCD were directed to a Multivision quad unit (Model: MV 85) which combined the three

different camera views into one single smen that was recorded at 30 frames/s on a Super VHS video

tape using a Panasonic Super VHS VCR (Mode1 AG-7355). A fourth CCD (Sony, Model: DC-77RR)

was used with a time code generator (Fast Forward, Model: F'22) and the image was directed to the

input of the quad to enable the synchronization of the three different CCD images. The t h e code was

also required for the determination of velocity profiles fiom the side-view vide0 sequences.

The quad had a resolution of 5 12 x 480 pixels and a real-time display rate of 30 fielddsecond,

and was used to synchronize the images obtained fiom each CCD camera without the need of an

e x t d synchronization unit Because of the reduced molution of the quad images, each of the CCD

images was simultaneously r ecded using three different VCRs: a Panasonic Super VHS VCR

(Model: PV-S4580) for the side view, a Mitsubishi Super VHS VCR for the borescope view, and a

Hitachi VHS VCR for the top view as show in Figure 3.2-1.

Measurements were made along the last 1.5 meters of the second 2.40 m flanged test section,

with a starting point 3.60 m away fiom the inlet chamber to ensure M y developed flow. Again, the

three moving CCD cameras were used as the in Eulerian view for the side, top and incoming views,

respectively (two Hitachi high resolution colour CCDts (Model: VK-C370), and one JVC VHS-C

Model: GR-S77) camcorder). These cameras were mounted on a moving plaâorm attachecf to a

moving rail (see Figure 3.1-1). The rail table assembly consisted of a Lintech Twin Rail with a

camage linear bearings assembly driven through a belt mechanisrn with a 1/6 HP Boston Gear Motor

wasr-Esfahany (1998)l. The cameras mounted on the rail assernbly were moved with a coostant

speed in the direction of the liquid flow to record the motion of the traces in the Langrangian &me of

reference. The speed of the moving cameras was adjusted by controlling a DART (Nfodel: 250) speed

controller co~ec ted to a 1/6 HP Boston gear motor untd a coherent structure or trace codd be

followed along the length of the chamel.

The images fhn the three rnowig video cameras were combined dong with the time code

generator into a single image using a quad (Mdtivision, Model: MV85) in a similar arrangement as

described in the Eulerian view (section 33.1). Again, the image fxom the quad was recorded on a

Super VHS Panasonic VCR @dodel: AG-7355), while each of the other views was also recorded on

three separate VCR's as in the Eulerian view. The laser, lighting and video setup were exactly the

same as describeci earlier for the Eulerian view except for the moving cameras (see Figure 3.1-1 and

Figure 3.2-1).

33.1 The Photodmmic Dve Activation Techniaue

A non-intrusive photochromic dye tracer technique was employed to visualize the coherent

structures and obtain the velocity profles in a fùlly developed, wavy-stratifieci turbulent liquid flow. In

this technique, a dye material, TNSB, dissolved in a transparent liquid is irradiated with a beam of

diraviolet light popovich and Hummel (1967)l. The dye molecules abçorb the light energy

fiom the laser beam which dters their molecular structure resulting in temporary darkening of the

liquid containing the dye. When irradiated, the photochromic dye containhg solution undergoes a

reversible photochromic reaction; i.e. the colorless solution becomes colored to form a dark trace and

thus enabling the motion of this trace to be photographed. The light sources required to induce the

photochromic reaction are those emitting intensive UV radiation. In particdar, the TNSB dye absorbs

the UV light at a wavelength shorter than 360 nm. When activated, the dye in the organic solution

turns into a deep blue colour, enabling the flow visualization of

technique does not d o w slippage between the dye and the liquid

technique.

the turbulence structures. This

since it is a molecular tagging

The photochromic dye activation technique has been used extensively in the past to

investigate a variety of single-phase flow problem but only recent modifications in optics,

optunizaton in dye concentration, advances in high resolution video photography and computer-basai

image anaiysis have made this technique an atiractive tool for investigating turbulent structures near

the interface in both qualitative and quantitative terms mwaj i et al. (199311.

The photochromic dye, TNSB, u t i k d for the present investigation of the turbulence structure

and velocity profiles has the chernical name, I : 3 : 3 '-himet~Iindoline-6-nitrobeytzospiropyrm and is

. . . . only soluble in organic liquids. MinimiPng the dye concentration in the organic liquid maximizes the

penetmtion of the laser h, thus enabling the velocity profile deterrnination in the entire liquid

depth. On the other han& decreasing the dye concentration reduces the trace confrast resulting in poor

visibiiity of the traces that are diEcuIt to capture by video photography. It was determined that the

o p h u m TNSB concentration for the investigation of the turbulence structures in kerosene (Van-Sol

715) liquid was 80 ppm or 0.008% by weight. The concentration of TNSB in the working fluid was

determined by measlrring the light absorbance of the dye solution using a W spectrophotometer

(Turner, Model: 330) and a calibration curve. This concentration was detennined to be optimum for

captrrring the traces by video, however, the beam penetration was iirnited to about 15 mm for the

lasers usecl, and complete velocity profiles could not be obtained at high liquid flow rates. High Liquid

Reynolds numbers resulted in a liquid depth exceeding 15 mm, and thus complete velocity profiles

could not be obtained across the entire Liquid layer.

To overcome th& problem, two laser beams were utilized sirnultaneously: one beam

activahg the top half of the liquid, while the other beam activating the bottom half of the liquid. The

two lasers were externally synchronized, and aligned using a pin hole so that they entered on the

flowing liquid at exactly the same location. In particular, the continuous laser beam &om a He-Cd

laser (Kimmon, Model: M 3 102R-G) with a principal radiation at 325 nm and a maximum average

power of 200 mW, was chopped at a fkquency of 20 Hz using an optical chopper disk with 25 dots

(Stanford Research Systems, Model: SR 540). The chopped beam was reflected by a 99.99% UV

reflecting mirror and focused using a fused silica coated fwusing lem with a focal length of 25 cm.

The chopped laser b a r n f?om the He-Cd laser was directed at the centerline of the test section fkom

the bottom of the fIow channel at a measuring station Iocated 3.60 m away fiom the inlet chamber.

The second laser was a pulsed nitrogen laser operated at a pressure of 60 torr and emitting a

principal radiation at 337 nm with a maximum energy per pulse of 15 mJ (Laser Photonics, Model:

UV-24). This laser activateci the top haif of the liquid. The nitrogen laser was externally synchronized

to ensure that it had the same kquency as the He-Cd continuous laser. The extemal synchronization

of the pulsed nitmgen laser was perfomed by sending another laser beam generated fiom a He-Ne

laser through the same laser chopper slot as the He-Cd laser and directing this chopped laser b a r n to a

photodiode. The signal fiom the photodiode was amplified using a DC voltage power supply

operating at 10 VDC (NE, Model: RVC 36-1 5-UD7) and this ampiifïed signal triggered the nitrogen

laser. The nitrogen laser was set to extemal synchronization position for this purpose. The extemally

triggered beam from the pulsecf nitrogen laser was aligned and directed to the top of the test section

using a lem array with a focal length of 15 cm, at a measuring station located 3.60 m downstream of

the inlet chamber.

The two synchronized laser bearns (from nitrogen and He-Cd lasers) were aligned ushg

mirors and pin holes and the a l i m e n t and synchronization were c o b e d by video photography to

ensure that the laser bearns enter at exactly the same axial position and tune. A schematic diagram of

the laser setup is also show in Figure 3.1-1. The focal points of the two synchronized laser beams

were adjusted accordingiy using the mirrors to ensure that single, thin line traces were fonned in the

liquid flow. The nitmgen laser barn was passed through a pin hole filter sheet to allow only the

highest intensity part of the beam to be focused by the lem and penetrate the top half of the Liquid

layer.

The traces formed by the dye activation technique were captured uing n o d speed video

photography at 30 fiames per second as describe previously. The captured images were analyzed

fiame by fiame to characterize the waves, turbulent structure and flow characteristics.

335 Ld'wnrid VeIocih. Pro& Measmement9

The instantaneous velocity profiles and liquid height variations in the previously described test

section with two-dimensional mechanicdy generated waves imposed on the Liquid flow were

measured using the photochromic dye activation technique. The video images obtained in the Eulerian

fiame of reference were used to quant@ the experimental d t s , while the images obtained in the

Lagranpian fiame of reference were used to track the evolution of coherent structures in qualitative

t e m . Video images recorded by the side view camera were reviewed h e by h e and the trace

containing images were captured using a video h e grabber board (TARGAC) installed on a

Pentium based personal computer. The quality of the captured images were first enhanced by

adjusting the image histograrn feahire in Mocha 1.2 image analysis software, and then trace

coordinates were digitized manually. Digitized data contained the trace positions at different time

intervals as determined fkom the m e rate of the video cameras. The coordinate data were then fed to

a computer program written in Matlab 4.2C (see Appendix D), and a polynomid of different order

(between 2nd and 79 was fitted to the data (see Figure 33-1).

The velocity profiles in the flowing liquid was determinecl using two dif3erent methods. In the

srst method, the velocity profile in the wavy liquid Iayer was caicuiated by s W g the trace endpoints

at the gas-Liquid interface to the average liquid height in hvo successive b e s . This was performed

through extrapolation of the polynornial f i ~ e d to the dye trace in the lower Ievel liquid height (hi) and

Pentium Based Computer with Targa' Frame Grabber board.

Successive images captured using Mocha v. 1.2. The square points indicate the digitiied coordinates in pixels. These coordinates were fed to Matlab 4.2~.

Feed coordinate data to I

Digitized data - Polynomial fit

Polynomial fitted data using Matlab 4.2~. The polynornial fitted data were interpolated and they were used for the calculation of instantaneous velocity, shear stress,instantaneous liquid height and other turbulent quanties.

Figure 3.34. Schernatic representation of trace image analysis to obtain instantaneous velocity profiles.

interpolation of the polynomial fitted to the trace in the higher Ievel liquid height ( ' ) as indicated in

Figure 3.3-2 (1998)]. In this marner, streamwise velocity profïk~ codd be obtained by

simply dividing the trace displacement at the same height by the elapsed t h e interval. Although this

method leads to some deviations between the actual and calculated velocities close to the gas-liquid

interface, it does not influence the determination of the veiocity below the minimum liquid level and

near the Wall.

The second method for cornputhg the velocity profïie took into consideration the presence of

d a c e waves and the change in liquid height between two successive fiames containing the same dye

trace as show in Figure 3.3-3. uitially, the digitized trace coordinates obtained fiom Mocha were

fitted by polynomials of 2"* to 7' order. Then, the maximum angle, 0, fiom the horizontal of a line

connecting the endpoint of one polynomial to the endpoint of the other polynornial was detemiined as

shown in Figure 33-3.

To compute the trace displacement at aii the other heights, the first trace of height hl obtained

at time, ti, was divided into n equal segments of vertical length, Ay, as shown in Figure 3 3 3 . This

fked the nodes (xli,yIi ) in the first polynornial. Then, for each node in the f h t polynomial (xii,yli ),

the angle Bi was determined fiom the maximum angle, 0, and the total number of nodes, assumuig

the angle for each node varies linearly between zero at the bottom wall (at x4) and O at the endpoint

of the trace. A 6 g h t Line with a dope given by the interpolated angle, Bi, was then drawn through

the node (xli,yli). The intersection between the straight lïne and the second polynomial trace of height

hz obtained at time, t2, detemiined the new coordinates (x2i,y2i) of the second polynomial. The straight

line connecting the nodes (xliyli) and (~2i~2i) W ~ S assumed to give the path of the dye particle based

on the angle interpolation method.

Digitized data

- Polynomial fit h,+-

2

\. t v

Direction w - Figure 3.3-2. VeIocity profile calculation using average heights (Karimi, 1998).

Digitized data

' Polynomial fit

Flow t

Direction

Figure 3.33. Velocity profile calculation using angle interpolation method.

The horizontal and vertical distances traveled over the elapsed t h e ( A m i ) gave the

streamwise and vertical velocities, at each average elevation k1Cyii+yzi)n], respectively:

where m f i is the number of h m e s elapsed between the first and second traces, and fi is the h e

rate of the video images (30 fkames/sec). This is a modification of the method proposed by Park

(1997) and Park et al. (1998) for estimating the velocity field in a 90' elbow.

Most common sources of error introduced into measurements of liquid heights, streamwise

and vertical velocities, wave fiequencies and wave velocities arising fiom the use of the photochomic

dye activation and video imaging techniques are next considered.

Errors incurred in Liquid height measurements resulted fiom the video camera and VCR

performance. The maximum uncertainty in locating the interface and wall boundary was

approximately 7 pixels which contnbuted to maximum errors of 2% and 3% in the averaged liquid

height data for the highest and lowest Reynolds numbers, respectively.

Enoe in the velocity data resulted fiom trace thickness resolution, and the penetration of the

laser beams. The CCD provided hi& enough resolution (470 horizontal iines) redting in high degree

of accuracy in the liquid height and velocity measurementî. The Super VHS videotapes codd store up

to 525 horizontal resolution but the fiame grabber resolution was Limited to about 470 horizontal lines.

This provided high enough resolution in digitking the traces.

Camera s d g errors could d t due to the fast moving Iiquid causing signiscant velocity

gradients over a small liquid depth. However? traces were formed at 20 Hz, which traveled at

dcient ly slow speeds to be captured by vide0 cameras at 30 framedsec, resulting in an insignifiant

scanning error of the camera.

The trace thickness, which was generally dependent on the liquid Reynolds number and

degree of turbulence, was estimatecl to be 30 pixels wide at maximum. This was detemiined at the

middle point of the liquid depth for the highest liquid Reynolds number and highest wave a m p h d e

run (run 77). The trace thickness codd cause an error in the digitkation process and in velocity

calculations. To overcome this problem, the histogram of each trace image captured was narrowed

using Mocha, and the centerline of the trace fiom the point of contact with the waii to the gas-liquid

interface was followed. The maximum error incurred in estimating the centerline of the fomed traces

resulted in an approximately 1.5% error in the streamwise velocity data. This error was determined in

the middle plane of the liquid layer for the highest liquid flow rate Kun.

Additional errors involved in the velocity profiies could be attributed to fainmess of the traces

in the middle plane obtained at hi& Reynolds numbers and large Liquid depths. This error was

minimized by narrowing the histogram in Mocha and following the most defined path of the fomed

traces. It was estirnated that the most faint part of the traces resulted in a maximum gap between the

bottom and top traces of at most 40 pixels. The error red ts in the estimates of the path of the two

traces at the middle of the liquid depth. The maximum error in estimating the coordinates of the faint

part of the traces depends on estimahg the centerhe of the trace, which can be at rnost 4 to 5 pixels.

This resuited in another 1.5 % error in estimahg the streamwise velocities in the middle plane.

ûther errors in the velocity data could have been caused by misalignment and out-of-

synchronization of the two laser beams. Altbough attempts were made to align and synchronize the

two laser beams, emrs could result fiom outside disturbances, electrical wiring, and h m video

photography used for the laser beam adjustment. The laser beams were estimated to be rnisaligned in

the vertical plane by six (6) pixels at the most resuiting in an emr in the velocity data of about 2%.

Emrs associated with unsynchronized laser beams will result in a horizontal misalignment between

the top and bottom traces due to the time delay of at most six (6) pixels. This results in another 2%

error in the velocity calculation.

Enors were ais0 uivolved in determining the wave velocities at high wave fiquencies. There

was a considerable degree of uncertainty in high wave fkquencies since crests traveled out of the

view field within half a fiame. This htroduced a maximum estimated error in the wave celer@ of

20%. Table 3.3-1 lists all the sources of m r and their maximum estimated uncertainties.

Table 33-1 S- of the sources of error

Parameter Maximum Estimated Uncertainty

Liquid Height Measurements

-Due to vide0 photography 2% to 3%

Streamwise Velocity profiles

-Normal speed photography Negligible

-Resolution of images Negligible

-Trace thickness 1.5%

-Non penetrating laser beams 1 .S%

-MisaIignment of laser beams 2%

-Unsynchronized laser beams 2%

Total error in streamsie velocity data Total: 3.5%

Wavelength and wave speed

-No& speed photography 20% @ high wave speeds

The experimental data obtained and analyzed in this study are for M y developed, turbulent

open-channel flows with shear-fke, rnechanically generated waves imposed at the gas-liquid

interface. AU measurements were taken at the central plane of the channel at a rneasuring station

locaîed 3.60 m downstream k m the idet chamber.

-- - - - . - . - . - - - -

Table 4.2-1 summarizes the experirnental conditions for the various runs ~~ed out. A tobf

o f s k t y four runs were conducted covering various wave hquencies, amplitudes and liquid Reynolds

nmbers fkom which sixteen were chosen to be analyzed.

The experimental nuis d y z e d consisted of four different liquid Reynolds and Froude

numbers defineci based on the mean Liquid stream thickness, h, and the the-averaged liquid velocity

over the cross sectional ara, bulk -

U bulk Fr =- Jg.h

Table 4.2-1 Experimental conditions

QL is the rneasu~ed liquid ff ow rate obtained over the entire Iiquid cross sectional area in liters per minute (LPM), h is the mean liquid height, a the mean wave amplitude, a- the maximum mean wave amplitude, 7c the mean wavelength, and f ,, the wave fkquency. (O) Non-wavy fi ow runs obtaïned h m Chimg (1 998). (**)uM is the the-averaged streamwise velocity obtained at the center plane of the liquid flow f h n the sîreamwise instantaneous velocity profiles.

U~ .DH is the Reynolds number obtallied at the center plane of the liquid fiow. ReD =- Y

Run

2'3

11

13

15

17

4(3

41

43

45

&

Irsw

9.9

8-6

8.5

8.6

8.6

12.7

14.1

14.1

14.0

47

$9

51

53

55

57

7")

71

73

75

77

Notes:

14.1

14.1

15.4

15.4

15.4

153

16.6

18.1

18.1

18.1

18.0

- The liquid Reynolds number baseà on the hydraulic diameter (GD = UbuUc - DH , Where

v

4W. is the hydraulic diameter and W is the width of the test section), is also shown in

D'=W+2h

Table 4.2-1 and it is mughly thnx times the liquid Reynolds number given by equation 4.2-1. The

Reynolds numbers given in Table 4.2-1 are greater than 500, which sic.nifv that the flow is in the low

turbulent range wunson et al. (1 99011.

The wall friction velocity, UR,, shown in Table 4.2-1 was detemiined by fitting the mean

streamwise velocity profile data to the log-law profile expressed by equation 42-3:

U where u+ = yuw , y+ =- and u: = J r w - with t, being the wall shear stress, p the density of u w v P

the fluid at the opemting temperature and v the kinematic viscosity of the fluid. The wall fiction

velocities evaluated using equation 4.2-3 are given in Appendix E, and were in good agreement

(within 10%) with the BIasius formula [Rashidi et al. (1 99011.

The w d fiction velocities, obtained by fitting the experimentai data to the log-law, were used

to no& the turbulence quantities near the wali. The cornputer prograrn &en in Matlab 42C

that was used to determine the wall fiction velocity, u; , is given in the Appenàix F. The wave

amplitude, a, indicated in Table 4.2-1 represents the average liquid height deviations of the trace

endpoints fkom the mean liquid height kean) as shown in Figure 43-1. The liquid height deviations

(a~) were determinai h m the highest trace endpoints used to calculate the instantanmus velocity data

i j Digitized data

j - Polynomial fit

1 i N-number of instantaneous velocity profiles i a,=highest trace endpoint wave amplitude

Figure 4.2-1. Wave amplitude determination fiom trace endpoints.

as s h o w in Figure 4.2-1. The mean liquid height, represents the average height calculated

fiom the average trace endpoints as shown in Figure 42-1. In addition, the liquid height t h e bistory

was searched for the 10 largest liquid height values and these were averaged to obtain the extremum

values corresponding to the maximum wave amplitude, an, given in Table 4.2-1.

For each of the four liquid Reynolds and Froude number experiments cmied out, four

different wave fkquencies and amplitudes were analyzed, and a total of sixteen runs were analyzed.

The nrst digit of the nui number (1,4,5,7) indicated in Table 4.2-1 signifies the liquid Reynolds

number while the second digit (1,3,5,7) denotes the wave amplitude and fiequency for that particular

liquid Reynolds number.

It was possible to conduct experiments with two-dimensional surface waves with different

wave characteristics while keeping the Reynolds nurnber relatively constant for four different sets of

nms. As indicated previous1y9 runs 1,4,5 and 7 were conducted at different liquid Reynolds numbers

but invohed quite similar wave characteristics. Table 43-1 summarizes the mean wavelength, wave

fiequency and wave velocity for ali the nnis. As indicated in Table 4.3-1, the wavelength, wave

43

frequency and wave velocity are independent of the Reynolds number with some small deviations.

This is also indicated in Figure 4.3-1 where there seems to be no dependence of the wave velocity on

the liquid Reynolds number. The error bars shown in Figure 4.3-1 si& the deviations of 20 wave

velocity meanuements fiom their mean value.

80 1 1 1 1 1

Wave 1: h=31 cm, f,,=0.78 Hz, Ume=24 cm/s = Wave3: h=47 cm, fwe=0.87 Hz, U,,=41 cmls

Wave5: k 4 4 cm, fwe=l -03 Hz, U,,,=46 cmfs

Wave7: k=46 cm, fWe=1. 1 7 Hz, U-=53 cm/s

4 Wave 5 L

- ~ a v e 1 5 - d

Figure 4.3-1. Wave velocity dependence on Reynolds nurnber.

The wave velocity and fiequency were determined using the images captured fiom the side

view video camera. n i e wave velocity, Ui-, was deternùned fiom the horizontal displacement

(mûasured in pixels) of the wave crest over the elapsed fime that was indicated by the time code

generator in the recorded tape. The wave fiequency, f,,, on the other han& was detemiined by the

time elapsed or period between two successive wave crests, Tm,. This wave fiequency was

comparable with the wave fiequency obtained by the direct calibration of the wavemakerys paddle, as

44

shown in Tabie 43-1. This ùidicates that the downstream waves mainttained the same fkquency as

they propagated from the wave paddle to the measurement location.

Table 43-1. Wave characteristics

The wavelength, A, indicated in Table 43-1 was computed fiom the wave velocity and the

conesponding wave period as shown in equation 43-1.

For the purpose of comparing the experimental results, the wave characteristics iilustrated in

Table 43-1 are w d throughout this thesis. Thus, waves 1 and 3 have difEerent wavelength but

similar wave fiequency, while waves 5 and 7 have sirniiar wavelength but different wave fkequency.

U-e

[cm4 , 24.0

40.8

46.1

From the video sequences, ail waves were determined to be two-dimensional and sinusoidal

"th a hi& amplitude, deviating slightly from the two-dimensional profile. The two-dimensionality of

the d a c e waves could be verified accurately since the trace endpoint and the gas-liquid intefice

coincided. Higher wave amplitudes and Reynolds numbers than those indicated in Tables 4-24 and

43-1 codd not be tested in this experimental facility due to the s i e c a n t increase in the aspect ratio

(width of channeUmean liquid height) of the liquid layer at higher Reynolds numbers, and the

generation of three dimensional waves at higher wave fiequemies. An increase in the aspect ratio

would result in the generation of secondary flows generated by the side walls of the channel.

, Wave 7 I 45.7 I 1.2 I 1.17 I 53.3 ,

f [Hz] Video 0.78

0.87

1.03

Wave sequence

Wave 1

Wave 3

Wave 5

h [ c d

30.9

46.7

44.3

fW1 Paddle 0.80

0.85

1 .O

45

The SinusoidaI behaviour of the waves could also be deterniined by perfonning a power

spectmi analysis or Fourier decomposition of the Liquid height data The power spectral density (PSD)

hct ion describes the fkquency composition of the interfacial waves in ternis of energy. This

fünction is dehed as follows:

where j = f i , and R(s) is the ~~to-comeIation function commonly used in turbulence research for

the appropriate analysis of chaotic sigds. It is defined as:

where r is the time period of measurements, h is the mean Liquid height between two successive

frames, and T king the sampling time internal.

Using the above definition, the PSD functiom for different waves were evaluated using

Matlab's built-in FFT fiuiction. In particular, the code given in Appendix F initially interpolates the

digitized liquid height data at equal time intervals using Matlab's cubic spline function. Then, the

interpolated data were pas& through Matlab's FFT function and the PSD values were cornputed.

Figure 43-2 shows the PSD for the high amplitude waves (runs 17, 47, 57 and 77). The PSD for

other amplitude waves are given in Appendix G. Some of the calculated spectra displayed single

dominant peaks corresponding to the wave fkquency, which indicated that the waves were highly

sinusoiclal (nms 41,71 and 15). Most of the spectra, however, displayed two or more dominant peaks

indicating that the signal was in general periodic with discrete hquencies. Therefore, the power

spectra indicated that the waves were periodic but not necessarily of a single fkquency.

0.01 0.1

Frequency [Hz]

0.01 O. 1 1

Frequency [Hz]

0.1 1

Frequency [Hz]

0.01 o. 1 1

Frequency [Hz]

Figure 4.3-2. Power spectral density for wave 7. (') fs= sarnpiiig frequency

The display of multiple dominant peaks in the PSD is probably attributed to the low sarnpling

fiequency (24 Hz) of the digitized data More detailed characterization of the waves was not possible

due to the limitations of video recording rate. Thus, the waves could only be characterized as

sinusoiclal from the video pichires taken.

The velocity data obtained using the photochormic dye activation technique were analyzed

statistidy to obtain the central moment (mean value), the second moment (root mean square, RMS),

as well as the thud (skewness, S) and fointh (flatness, F) moments of the streamwise velocities. If

turbulent components were completely random, they would only be described by a normal density

hc t ion or a Gaussian distribution deterrnined by the secondsrder moment, i.e. the turbulence

intensity- However, this is not the case, and higher order moments are needed to describe turbulence.

This section focuses on these higher order moments and on the d y s i s of the velocity fluctuations.

The f k t and second moments are presented in sections 4.5 and 4.6, respectively, in greater detail.

Typical amplitude distributions of the streamwise velocity fluctuations (u' = u ,,, - u M ) and

the streamwise velocity distributions (u-) at various locations in the liquid stream for nins 51, 57,7 1

and 75 are shown in Figures 4.4-la through 4.4-ld, respectively. From these figures it is evident that

as the wave amplitude and fiquency increase, the distribution of the velocity fluctuations becomes

more normally distributed (gaussian) for values up to about 0.90. The normal distribution of

the velocity fluctuations could be attnbuted to the presence of periodic waves h m the wavemaker

which induces periodic fluctuations in the bulk flow. From these figures, it is also clear that the

amplitude of the velocity fluctuations is much greater near the wall, while towards the interface it is

sigdicantly reduced. This reduction in the fluctuations is probably aîûibuted to limited numbers of

wave crests that were analyzed. Furthemore, Figures 4.4-la to 4.4-Id indicate that the streamwise

velocity fluctuations are skewed towards the Iower-than-mean values at ail locations in the liquid

stream. To investigate this m e r , the skewness and fiatness factors of the streamwise velociv

fluctuations were detennifled.

Streamwise Velocity Distri bution u [rn/s]

Figure 4.4-la. Distribution of streamwise velocity fluctuations for run 5 1. %=4100, Fr0.34, hm-= 17.9 mm, a=0.63 mm, fWaYC=0.78 Hr, u*=0 .O 10 m/s. N= number of rneasurements for the velocity intervals shown.

Strearnwise Velocity Distribution u [mk]

Figure 4.4-1b. Distribution of streamwise velocity fluctuations for run 57.Rë=4100, Fr=0.34, hm-=18.1 mm, a=l.80 mm, f,=l.lg Hz, u* ,=O.O 1 1 m/s. N=number of measurements for the velocity intervals shown.

Strearnwise Velocity Distribution LI [mk]

Figure 4.4-lr Distribution of streamwise velocity fluctuations for nui 7 1. K % = N O O , F d . 3 7, km= 19.0 mm, a4.59 mm, f 2 . 7 8 Hi, U*~=O.O~ 1 d s . N=number of measurements for the velocity intervals shown.

Streamwise Velocity Distribution u [ds]

Figure 4.4-Id. Distniution of streamwise velocity fluctuations for rwi 75.ED=4700, F A . 3 6 , &,=19.0 mm, a=1.59 mm, f,=l -10 Hz, ~'~0.0 1 1 m/s. N=nurnber of measurements for the velocity intervals shown.

The skewness and flatness factors defined as S(u) = uw3

and F(u) = Ut4

-K 2 w- w2 (uf2

computed as a fùnction of channel depth, and are shown in Figures 4.4-2a,b for nuis 51 to 77. The

skewneçs and flatness façtors for other nuiç are included in Appendix H. In particular, the third-order

moment, the 'skewness facor', describes the asymmetry in the probability density hct ion, and it is an

important factor in describing bursting events. The fouah-order moment, on the other han& i.e., the

'flatness factor', describes the Uztennittency of turbulence.

Figures 4.4-2a and 4.4-2b show that (for most of the nuis) the s-&eamwise skewness has, on

average, slightly negative values. This result implies that a dominant structure consisting of an

Fi ure 4.4-2a. Skewness and flatness factors for runs 51 to 57. Solid and dotted lines indicate the mean 7 va ues for the particular run.

Figure 4.4-2b. Skewness and Flatness factors for runs 71 to 77. Solid and dotted Iines indicate the mean values for the wn.

ejection of low momentum fluid fiom the wall toward the interface followed by the deceleration of the

sûeamwise velocities is present and felt d the way to the interface. Many other researchers masr-

Esfahany (19981, Rashidi and Banerjee (198811 have reporteci negative skewness factors throughout

the flow depth for non-wavy unsheared interfaces. Nonetheles, the present data uIdicate that the

skewness is positive close to the w d for all of the runs. Previous researchers observed the same trend

near the waii region in sheared-wavy flows &am and Banerjee (1 992)]. The positive skewness factor

at the wall is probably attributed to the interaction of the interfise and the burst fhid emanating fiom

the bottom wall mainly observed in low-Reynolds number flows where the bursî can be felt ail the

way to the interface [Lam and Banerjee (199211. The flatuess data seem to be in rough agreement with

the flatness factors for open-channel flows with sheared interfaces computed by Lam and Banejee

(1992). However, at the wall the flatness factor is close to -3 rather than -4.5 as found by Lam and

Banerjee (1992) for sheared interfaces. The flatness factor for a gaussian distributed velocity profile

requires the mean flatness to be equal to 3 tluough the whole liquid depth. The value of the mean

flatness factors through the flow depth for some of the runs (runs 53,73, and 77) was approximately

equal to 3, indicating the gaussian nature of the streamwise velocity distribution. However, some runs

deviated &om the gaussian distribution displaying higher than 3 mean fiatness factors.

In order to obtain the velocity field quantitatively, the laser beam was chopped using an

optical chopper, and the resulting trace images were captured in a series of consecutive firames that

were analyzed to obtain about 100 instantaneous velocity profiles in each nin as it was explained in

Chapter 3, section 332. The mean properties obtained are described in the folIowing sections.

45.1 Mean Vekdv Profiles

Averaged strearnwise velocity profiles for aIl the nuis are plotted in Figure 4.5-1. These plots

are rearranged according to similar Reynolds numbers (determined at the center plane of the liquid

fiow), but different wave amplitudes and frequencies. The time-averaged streamwise velocity profile

was computed fiorn the mean of about 100 instantaneous velocity profiles obtained liom successive

fÎames as explained in Chapter 3, section 33.2. Appendix 1 contains the instantaneous velocity data

for all the d y z e d as a fiuiction of dimensional liquid height measured fiom the bottom wall, h.

The figures given in Appendix 1 include the mean and the instantaneous velocity pronles for about

100 instantanmus velocity profiles. The deviations of the instantmeou velocity profiles fiom the

mean velocity profile can be easily observed in each figure. Figure 4.5-2 gives a sample graph of

these instantaneous velocity profile plots for run 77.

Runl 1 : Run43: Run15: Runl7:

Figure 4.5-1. Mean velocity profiles for different waves as a function of dimensionless distance from the bottom wall, y Jh.

Figure 4.5-1 (continued): Mean velocity profiles for different nins as a function of dimensionless distance from the bottorn wall, y Jh.

Figure 4.5-2. Instantaneous and mean streamwise velocities for run 77.

0 Mean Sbeamwise Ve!ocity s e - . - - lnstantaneous Velocities Streamwise Velocities Ui [mls]

57

As indicated io Figure 4.5-1 and the plots aven in Appendk 1, the mean velocity prome

fiattens in the bulk region as wave fkquency and amplitude are increased for a given run series.

Comparing the results obtained for different wave a m p h d e s and fkquencies but similar wavelengths

(waves 5 and 7), it is observed that tbis effect is not due to the increase in the wall shear stress as

observed by Van Hoften and Karaki (1 976), Iwagaki and Asano (1 980) and Asano et al. (1 986) since

the wall shear stress for waves 5 and 7 did not change appreciably (see Table 4.2-1). On the other

han& the present results are in agreement with the hdings of Kemp and Simons (1982, 1983), who

conducted experiments in smooth and rough turbulent flows with interfacial waves. ïheir results

indicated that the linear proportion of the velocity profles nea. the wall is the same for al l cases for

smooth wall experiments, indicating that there is no change in wail shear s t ~ s s .

Furthemore, the present results show a mther flat mean streamwise velocity profile in the

bulk iiquid with a thin layer close to the interface moving faster. The flat mean velocity profile was

also observecl by Lorencez et al. (1997a) for cocurrent wavy fiows and it is probably atûibuted to the

presence of large waves which enhance vertical mixing as a result of inaeased wave amplitude

Forencez (1994)l. In examining the results depicted in Figure 4.5-1 more closely, it is apparent that

the main effects of introducing a wave and increasing the wave amplitude and fiequency are to reduce

the mean velocity in the interface layers and increase it in the turbulent boundary layer near the w d .

This is more evident for the higher liquid Reynolds number runs, when the nins with lower and higher

wave amplitudes and fkquencies are compared for the same liquid Reynolds nurnber. This effect is

ako consistent with the &ts of Kemp and Simons (1982). In their task to compare cocurrent wavy

flows with the linear addition of the separately measured unidirectional current and wave velocities

they detennined that the simple law of superposition did not hold. Their results suggested that the

measured velocities are larger near the boundary and srnailer in the outer region than for the added

component flows, with the latter trend becoming more pronounced in the highest wave cases. They

58

suggested that this effect resuits in diminishing the boundary layer thickness by the addition of waves

as their dcdations indicated.

The averaged vertical velocity profiies are also plotted in Figure 4.5-3 for al1 m. The

vertical velocities were computed using the angle interpolation technique as described in Chapter 3,

section 332. ui these pronles, the vertical velocities are very s m d compared to the mean strearnwise

velocities. For aü wave amplitudes and fkquencies examined, the vertical velocity profiles fall within

a band off 1.5 mm/s within experimental error. For three of the highest liquid Reynolds number nuis

(71,73 and 75) the mean vertical velocities were close to zero throughout the liquid flow depth. The

same effect was also observed by Cheung et ai. (1988) where their velocity profiles in mechanically

generated waves in open-channel flows were bounded within &S.

1 .O 1 " * " I O " " I " " - . O

0.9 - a . 0 . . +

0 . ! a i

Figure 4.53. Mean vertical velocity profiles for different waves as a function of dimensionless distance from the bottom wall, y Jh.

Figure 4.53 (continued). Mean vertical velocity profiles for different waves as a funciton of dirnensionless distance from the bottom wall, y&

The profile of the mean streamwise velocity non-dimensionalized by the wall fiiction velocity

is given in Figure 4.5-4. Additional graphs containing instantaneous velocity profiles are included in

Appendix J. Also shown in this figure is the theoretical mean-velocity profile (solid line) for non-

wavy shear-fiee open-channel flows wezu and Nagakawa (1993)l. The velocity profile data are

compared with equation 4.2-3 with the Von I(arman constant (~=0.41) and integral constant

(A=5.29) set to the values suggested by Nem and Nakagawa (1993).

The dirnensionless mean velocity profiles were obtained by fitting the wail fiction velocity

data to the law of the wail equation, in two regimes:

a) In the w d region for wy+<5, where V=y+.

b) In the turbulent core region for yC>30, where equation 4.2-3 applies.

After the wail fiction velocity was obtained by fitting the mean velocity profiles to the

universal velocity profile, the mean streamwise velocities were n o r m m by the wall fiction

velocity, and the resuits are plotted in Figure 4.5-4. The wake fùnction is only signifiant for

Reynolds numbers much greater than 10,000 (based on the liquid height) as suggested by Nezu and

Rodi (1986) and was not taken into consideration. The cornputer program which was used to obtain

the universal velocity profiles is given in Appendix F. As it is clear fiom the figure, the mean

velocity prome dadata measured using the photochrornic dye activation technique show good agreement

with the law of the wd in the turbulent core region (15<y+<70) excluding the interface region. For a l l

of the m, the data were above the theoretical curve for y' less than 10. The velocity profiles also f d

to correlate for values above 70, i.e., close to the interface region where there seems to be a steep

increase in the velocity profile. This deviation fiom the log-law is more pronounced for higher

Reynolds numbers with high amplitude waves. The same effect was also observed by Rashidi et al.

. . . .

. . . . . . . . . . . . . . . . - - -

. . . . . . . . . . . .

. . . . . . . . . . . .

. . .

. . . . . . . . . . . . - .. . . . ................ - ............ -

. . . . . .

..... . . . . . .. . . . . . . . - . . . . . . -.

. . . . .

. . i . . .- - . . . - . . . .

. . . . . . . . . . . . . .

1 10 100

Y+ -c Runll: 6,=2600, FF 0.30, unw=0.009 mlç, hm,=13.4 mm

Runl3: 6,=2500. Fr= 0.29, uW=0.009 mis, h-=13.4 mm -+- RunlS: &,=2600, FF 0.31, ~ ~ ~ = 0 . 0 1 0 d s , h-=13.1 mm -- Runl7: ~,=2600. F r 0.31, uaW=0.01 1 mis, h k l 3 . l mm - - Run41 : Eo=3800, Fr= 0.33, unw=O.OIO mk. h,,=l7.2 mm -- Run43: s0=3800, Fr= 0.34, ~'~=0.010 d s , h,,=j 7.0 mm --.- Run45: G,=3700. Fr= 0.33, uaw=O.O1 1 mis, h-=.1;7.2 mm - Run47: 6&,=3800. Fr= 0.34. u>=0.011 mis. h 4 1 7 . 0 mm -.-.m.-. RunS1: E,=4100, Fr= 0.34, unw=O.OIO mis, h,,=17.9 mm -+- Run53: Re,=4100, Fr= 0.35, unW=0.011 mis, h,,=17.7 mm -- Run55: Reo=4100, Fr= 0.34, unw=O.O1l m/s, h,,=17.8 mm - - Run57: z,=4100, Fr= 0.34, unW=O.Ol1 mis, h,,=18.1 mm -c- Run71: =,=4700, Fr= 0.37, ~*~=0.0106 mls, h,,,=l9.O mm - Run73: G0=4700, F r 0.36. uaw=O.Ol 1 d s . h 4 1 9 . 4 mm - Run75: &=4700, Fr= 0.37, unW=0.011 mis, h,,=19.0 mm ---+- Run77: &,,=4700. Fr= 0.36. unw=0.012 mis, h d 1 9 . 3 mm - Theoretical

Figure 4.54. Dirnensionless streamwise velocity profiles, u+=uluL versus y+=yu;/v

62

(1992) who noticed a systematic deviation h m the law of the wall in a turbdent open-chamel flow

with mechanidy generated waves.

4.53 Comr#uison of h d a r Intenw,lation and Ave- Heigbt Technimes

Figure 4.5-5 compares the mean streamwise velocity profiles obtained using the angle

interpolation and the average height techniques (see Chapter 3, section 33.2). As seen £tom this

figure, both methods yield very similar results in close agreement with the law of the wall.

45.4 velocitv Histon,

The velocity history data at different y positions for nins 47, 53, 57 and 75 are shown in

Figures 4.5-6a to 4.5-6d dong with the variations in the iiquid height with time (see Appendur K for

the velocity histories of other runs). These data illustrate the simultaneous time profiles of about 100

local strearnwise velocities and liquid height variations at merent distances fiom the bottom wall

under Merent flow conditions. From these velocity history data, the following remarks can be made:

i) Peaks and troughs in the instantaneous strearnwise velocity data appear to occur at the same

t h e instances at different y+ positions suggesting that a burst may travel &om the w d ali the

way to the interface (see, for instance, run 47 at t=6 sec in Figure 4.5-6a).

ii) The streamwise velocity fluctuations exhibited signifiant resemblance to the liquid height

variations induced by the mechanid wavemaker. This hplies that the liquid height

variations due to the waves have a strong effect on the fluctuations in the streamwise velocity

(see, for instance, nin 47 at t=6 sec, in Figure 45da). The streamwise velocity does not

follow exactly the trends of liquid height variations, but its magnitude increases with increase

in the liquid height and distance nom the bottom wall.

. . . . . . . . . . . . . . . . . . . . . . . . . .

Vle& titaf..,aw.6. f.*ë . . . . . . . . . . . . . ' . . . . - . . - . - . - . . . . - ..-...................................

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . - . . . _ .......................................................................................... .-- -- - ru671 ~ s i n ~ angle interpola& . . . _ . . . . . . . . . . _ . . . . . . . . . . . . . . . . _ . . . . . . . _ _ .......... __ ........................................__._ ........................ _. -- mn71 usjng..a~eras.hei9ht3..iii.~. . . . . . . . . . . . .:.. . . . . . . ..-. . . . . . . . . . . . r.. - -. .I. . . . . . . . . . . - ....................................... . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 - ... . ~ . . : . . . ~ .~7? .us i~g . .an@le ihterpqlaüqn:. ;. . . . . . . . . . . . .

3

. . . . . . .

1 10 1 O0

Y+ Figure 4.53. Cornparison of the dimensioneless law of the wall profiles for angle interpolation and average height methods for a n s 41,47,71 and 77.

0.08 -

-- 0.04 1 Moving Average

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 time [SI

... - - + y+-=80.0 or y=U-8 mm -- Moving Average

0.08

time fs]

0.04 7

l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...................... ..: . . . : .- .Y+?. 70.0 ~r.Y=12-I

. -- Mwing Average

tirne [s]

0 . 0 4 i . - - ; . . . : - . . : 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

time Es]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.5-6a. Velocity history for run 47. =,=3800, Fr=0.34, u*,,,,=O.011 m/ç.

........ . . . . . . . . . . . . . . . .................. .._............ ..... _ ........- . . . . . ....... -. .... _ _ -. yf=~,~.orF14.1. m... :. -.. . - .... ...... . . . . . . . . . i

........ . . . . . - . . . . . . . . ... Mo,&g-Average.. . . . .: - -.. . . . . .-

O 5 I O 15 20 25 30 35 40 45 50 time [SI

O 5 10 15 20 25 30 35 40 45 50 time [s]

. . . . . . . . . . . . . . . . . . ........ ............................... ..-. . . .

i .............-.............................. ............... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................. M6"mg - ........... Avewk... - ...... .- -- -

time [s]

time [s]

20 25

time [s]

Figure 4.5-6b. Velocity history for run 53, FeD=4100, Fr=0.35, u=0.011 mls.

-- 0.04

Moving Average 1 O 5 10 15 20 25 30 35

time [SI 0.24 , 1

O 5 10 15 20 25 30 35 time [s]

0.24 -

0.08 ......... . . . . . . . . . . . . . . . . . . . . : ..................... . . . . . . . . . . . . . . . . . . - y =30.0 or y=4.0 mm 0.04 1..- - . .MOYing Avefage.. . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -

15

time [s]

15

time [sj

Figure 4 . 5 6 ~ . Velocity history for run 57, FeD=4100, Fr-0.34, U*~=O.O~ 1 mls.

-- Moving Average 0.04

O 5 10 15 20 25 30 35 tirne [SI

0.24

0.20 - 4

=O-16 - Y s0.12 -

-7 Moving Average . 0.04

O 5 10 20 25 30 35 ' time [SI

-- 0.04 1 Moving Average

O 5 10 15 20 25 30 35 time [s]

0.04 ! O 5 10 15 20 25 30 3 5

tirne [s]

. . . . . . . . . . . . . . . . . . . . . . . .

O 5 10 15 20 25 30 35 time [s]

Figure 4.5-6d. Velocity history for run 75. =,=4700, Fr=0.37, u*,,,=O.Ol 1 mls.

68

fi) The presence of interfacial waves appears to induce significant modifications in the magnitude

of the streamwise velocity even very close to the wall region (y' ;2.20), for most parts of the

liquid layer, regardless of the wave amplitude.

To examine biis effect more closely, the cross correlation and cross variance firnctions of two

streamwise velacity sigoals at different positions were computed and compad. In addition, the

cross variation of one streamwise velocity at a fked position with the fluctuating liquid height was

alsoexamined.

455CrossS~DensitvF'lmctions

The cross-comlation function of two sets of random data descnbes the general dependence of

the values of one set of data on the other. In particdar, the relationship between the tirne histones of

velocity data at two positions (e.g. at y+=20 and y+=30) or between the velocity history at a fixed

position with the Liquid height history was investigated.

The cross correlation, Rm of two input signals is defined as [Zabaras (1 985)]:

where X and Y represent the input signais to be compared (e-g. sbreamwise velocity and liquid height).

The cross-covariance of the random data senes, X(t) and Y(t), is similarly defined as:

where mx and m, represent the mean values of the tirne senes X(t) and Y(t), respectively.

69

The cross correlation h c t i o n is used to determine the time delay of a signal detected at two

measurement points. If the distance between the measurement points is divided by the time delay

detected, then the celerity of propagation should correspond to the velocity of bursts.

Figure 4.5-7 shows the cross correlation and cross covariance between two pairs of

streamwise velocities. The cross correlations and cross covariance fimctions compared one pair of

strearnwise velocities at y+=20 and yC=30, and another pair at yC=20 and 90 for run 47, respectively.

Furthemore, Figure 4-58 shows the statistical functions for the correlation between the streamwise

velocity at two Merent positions, yf=20 and 70, with the corresponding liquid height t h e history

data. These figures, however, do not display any time delays and seem to express a strong relation

without any t h e delay between the input signals examined. The absence of a time delay may be due

to the fact that the bursts d d not have been identined to travel to the interface region due to the

smail viewing window that was used to capture the velocity data. Thus, the results indicated that the

cross covariance was not a suitable tool in interpreting the experimental r e d t s due to experirnental

setup limitations.

Nonetheless, the cross covariance graphs expressing the relationship between s-treamwise

velocities and the liquid height, revealed a çtronger dependence of the two fùnctions exarnined near

the liquid interface region (compare the cross covariance at yf=20 and yC=70 in Figure 4.5-8 at

t i m d ) . This higher peak in the cross covariance spectra at yf=70, expresses a greater degree of

dependence of the two examined hctions. This greater dependence between the two input signais at

a higher position could indicate tbat waves caused an increase in the velocity in the upper layers of the

liquid due to the velocity fluctuations induced by the wavemaker. The same effëct was shown in the

relationship berneen different streamwise velocities at different positions, where there seems to be a

slightly higher degree of correlation between the two pairs of streamwise velocities exarnined near the

wail region (compare cross covariance between one pair of streamwise velocities at yf=20 and 90 with

Cross Covariance Cross Correlation

Time delay [sec]

-1 O O 10

Time delay [sec]

Figure 4.54. Cross correlation and cross covariance functions between the liquid height and the streamwise velocity at y+=20 and 70 for nin 47.

another pair of streamwise velocities at yC=20 and 30 in Figure 4.5-7). The smder degree of

dependence between the velocity data near the wall and interface regions could indicate that the bursts

may not have trave1ed all the way to the interface region (this is expressed by a decrease in the peak of

the cross covariance at t imd) .

45.6 Emr m Velocitv Measuriemenîs

Figures 4.5-9a to 4.5-9d hdicate the error bars associated with the possible variations in the

velocity data due to enors in digitin'ng the traces for the high and low Reynolds nunbers, and hi&

and low wave amphdes and fiequencies, respectively. The uncertainty in the strearnwise velocity

data is introduced by various sources, namely:

(i) Measurement of Ax on the image processing tablet which depends on:

a) Coordinate clicking error.

b) Resolution of image.

c) Trace thichess and resolution.

d) Faint traces at high liquid Reynolds numbers.

e) Jiggling of the image during the m e capturing process.

The maximum error associated with the measurement of Ax was estimated to be seven pixels.

The effect of this error is shown by horizontal error bars in Figures 4.5-9a to 4.5-9d.

(ii) Measurement of At on the image processing tablet which cm be at most plus or minus half a

b e . T'us, the vertical error bars were obtained by running the Matlab universal profile

program given in Appendix F with i half a field, as this was determined as the uncertainty

associated with the error in the elapsed time when processing the results.

R, =Xûûor L =SIO (a) : 1 R;, =26ûûor R;. =810 k o r BUS Runl7 @) Error BM RUllll i h, = 13.4mm.a iO.63mm h, =13.lmm.a= 1.07mm

, . : , . I I : , . . 1

i 2s . , : . , ! , , , , . . ,

b 1 , ( i , 1 Ni , , . . '

' . 20- + - - - - - - - - , - - - - - - - - , - - - - - - - - - - - , / '

. 1

> l a = - - - - -

1 10 100 : 1 10 1 W v* I Y*

Figure 4.5-9. Error bars for universal velocity profiles for high and low Reynolds numbers, and for high and low wave ampiitudes and fiequencies.

--

To investigate fûrther the wave-turbulence interactions, the values of turbulence intensities

were also evaluated. The streamwise and vertical (angle interpolated) velocities were averaged to

obtain the mean values, and then the variances were computed and the square root was taken.

Turbulent components, u'and v', were evaluated as the deviation of the instantaneous velocities fiom

the the-averaged velocity obtained fiom about 100 instantaneous velocity data ( ut = u,,, - u M and

v u = v ,, - v ). Figures 4.6-la to 4.6-le show plots of the normalized streamwise and vertical M

turbulence intensities +MS - - h") * * and 7= *

V I U m d (v tL) ) as a function of dime11~ionIess

* ) h m the bottom w d . These graphs are arranged according to similar vertical distance ( = -

v

Reynolds numbers (determined at the center plane of the liquid flow), but different wave amplitudes

and ikquencies.

In these figures, Nem and Rodi's (1986) exponential correlations given by equations 4.6-1

and 4.6-2 for non-wavy open-channel flows are also plotted for cornparison.

RMS = 1.27 .exp Uw

ln comparing the results obtained here with other researchers' findings for non-wavy turbulent

fiows, it is observed that the streamwise intensities tend to increase in the interface region, whereas

they appear to decrease in the w d region as the wave amplitude and kquency increase. Most

researchers have reported peak U ~ U ; values of approximately 3 close to the wall for umheared

interfaces in openchamel flow masr-Esfahany and Kawaji (1996)], as well as in channel flow

et al. (198711. The present data are consistent with the previous hdings, but suggest that the peak

value of um&.& is reduced as the waves are irnposed on the liquid surface. Furthemore, for most of

the runs the sireamWise turbulent intensities measured lie above Nezu and Rodi's correlation in al1

cases, due to the effect of mechanicaüy generated waves. Figures 4.6-la through 4.6-le indicate that

Y+ Runll: ReD=2700, F~0.30, h,,=13.4 mm. aq.63 mm, A=32 cm, f,,-=0.78 Hz. u>=0.009 mls

T Runl3: Re,=2700, Fr=0.29, h-=13.4 mm, a=0.72 mm, A=53 cm, f-=0.86 Hz, ~*~=0.009 mis II R~n l5 : Re,=3000, Fr=O.31, h,,,=l3.l mm, a=0.90rnrn, A=44cm. f-=1 .O3 Hz, u*,=O.Ol O m/s O Runl7: ReD=320, F~0.31, h,,=l3.l mm. a=1.07rnm, 1 4 5 cm, fm=1,19 Hz, t~*~=O.Oll mls

- ~ ~ ~ * ~ 2 . 3 o e ~ ~ ( - ~ ~ ) * r + o . 3 0 y + ( ~ -0; r = i -=P(-Y+H 0)

- - - - - v&u*el .27*ap(-yJh)

Figure 4.6-la. Nomalized turbulent intensities as a function of dimensionless distance y+=y,uSv from the bottom wall for runs 11 to 17. Blank and solid symbols correspond to the same run.

Y + Run41: Re,=3600, F~0.33, h-=17.2 mm, a4.62 mm, A=31 cm, f-=O.77 Hz, u*,=0.010 mîs

r Run43: Re,=3800, F~0.34, hm=17.0 mm, a=1.02 mm, -3 cm, f-=0.87 Hz, u*,=0.010 mls

- U , / U ~ . ~ O ~ X ~ ( - ~ ~ ~ ) * ~ + O . ~ O ~ ' ( I -r); r= l -m-~+ l l o )

. . . .- v,/u*,p1.27*exp(-y&)

Figure 4.6-1 b. Nomalized turbulent intensities as a function of dimensionless distance yf=y,u;/v from the bottom wall for runs 41 and 43. Solid and blank symbols correspond to the same run.

Run51: ReD=3900, Fr-0.34, h = 1 7 . 9 mm, a4.63 mm, A=31 an, f-+.78 W. ~*~=0.010 m/s

* Run53: Re,=40W, Fr=0.35, h-=17.7 mm, a=0.60 mm. k=51 an, f-d.88 W. u*~=O.O~ 1 mis

i Run45: ReD=4000, Fr=0.33. h-47.2 mm, a=1.17 mm. A=47 an, f-=0.98 Hz. U*,~=O.O~~ mls

O Run47: ReD=4000, Fr=0.34, h,,=l7.O mm, a=l.16 mm, A49 cm, f = 1 . 0 9 Hz, u\=O.Oll mis

Figure 4.6-1c: Nomalized turbulent intensities as a function of dimensionless distance y'=yWuo JV

from the bottorn wall for runs 51, 53,45 and 47. Solid and blank symbols correspond to the same fun.

Y+ - Run71: ReD=4300, Fr=0.37, h,,,=19.0 mm. a=0.59 mm, A=30 an, f-=0.78 Hz, u',=0.011 mis

r Run55: ReD=4300, Fr=0.34, h,,=17.8 mm, a=1.41 mm, A=44 cm, f-=1.03 Hz. ~*~=0.011 m/s Run57:ReD=45W,Fr=O.34,h,,=18.1 mm,a=1.80mm,ic=45cm,f~=1.19Kz,u'w=0.011m/s

- u~~*~=2 .30exp( -y~h) '~+0 .30y+ ( i -~ ) ; r = ~ exp(-y+11 O)

- . . - . v /~*~=1.27*exp(-yJh) RMS

Figure 4.646: Nomalized turbulent intensities as a function of dimensionless distance y '=ywu*~~ from the bottorn wall for runs 71, 55 and 57. Solid and blank syrnbols correspond to the same run.

Run73: Reo=47W, Fr=0.36, h-=19.4 mm. a=t -13 mm, A=39 cm, f-=0.89 Hz. ~*~=0 .011 m/s r Run75: Re0=4700, Frc0.37. h-=19.0 mm, a=1.59 mm, h=42 cm, f-=1.1 O Hz. U*~=O.O~ 1 mis m Run77: Re,=5100, Fr=0.36, h,,=19.3 mm, a=1.98 mm, A45 an, f-=1.20 Hz, uœW=O.Ol2 mis - u~u*,,,=2.30exp(-yJh)*r+Ci.30y+(l -ï); T=l exp(-y+ll O)

- - - - - v&u*,=l: .27*ap(-y>)

Figure 4.6-le. Nonalized turbulent intensities as a function of dirnensionless distance y+=y,u>v h m the bottom wall for nins 73 to 77. Solid and btank symbols correspond to the same run.

the streamwise RMS values calculated are much higher than those predicted by Nem and Rodi's

correlation with some lower M S values existing in nuis 11 to 17, where the turbulent intensities

were much lower than those predicted by equation 4.6-1.

In examining closer Figure 4.6-la neur the wall region, this figure shows lower peak

uR&u; values close to the w d than those determined for non-wavy flows @eak RMS values are

much less than 3 in these figures), with higher amplitude and fkquency waves contnbuting to lower

peak RMS values. On the other hand, Figures 4.6-lb through 4.6-le show a much closer agreement

in the peak RMS values close to the waU region for low amplitude and fkquency waves with those

predicted by Nem and Rodi, with again higher amplitude and frequency waves having lower peak

RMS values compared to non-wavy open-channel flows (with the exception of run 53). It is apparent

fiom these plots that the turbulence intensity profiles for wavy flows have the same general trend as

the runs with non-wavy interfaces Dasr-Esfahany (199811 Le., the intensities for most of the runs

reach a peak value close to the wall Of=5-10). This implies tbat d a c e waves modify turbulence near

78

the waZl region. Thus, near the wall region, it is observed that turbulence intensities dimuiish with

incr~ases in wave amplitude and fkquency for nuis haWig simila.. flow conditions (with the exception

of run 53).

In exatninîng the effects of the superimposed d a c e waves in the outer region, it is apparent

that the streamwise turbulent intensities increase with increases in wave amphde and kquency.

This is probably attributed to the presence of mechanically generated waves that travel at a higher

speed with increase in wave amplitude and fiquency, thus contributing to greater streamwise

turbulent intensity values.

Firrthermore, by superimposing waves it is evident fkom these plots that the magnitude of the

streamwise turbulence intensities is inneased considerably compared to non-wavy surfaces away

fiom the wall for y+ values up to 90 (or y& = 0.90). Even the magnitude of the vertical turbulence

intensity increases with increasing wave amplitude and fiequency and does not vanish towards the

interface as in the non-wavy flow.

Thus, the introduction of mechanically generated waves causes an attenuation of the turbulent

intensities in the wall region (observed for most of the runs except run 53) and an enhancernent in the

buik and interfhce regions (aIl nins except run 17) with inames in wave amplitude and fiequency.

These resuits indicate that the turbulent energy generated by the waves is trançferred fiom the

interface to the bulk flow. Nonetheless, the waii region still remains the highest point of turbulence

production as indicated by the dominant peaks in the urcha/ u vç. y+ plots. Although the walI region

is stiu dominated by wall turbulence genention mechanism, the fke d a c e region begins to

signincantly contribute to the turbuience production in wavy flows, causing an enhancement in the

turbulence intensities in the buik and interface regions.

79

The same effects were obsefved by Nasr-Esfahany and Kawaji (1996) who noted that the

sûeamwise turbulence intensities near wall region are controiled by wall turbulence generation

phenornena (bursts), while the interfice was controiled by the imposed interfacial shear and the

resultirrg surface waves. They also noted that a cellular type fluid motion was stronger under the

waves with greateï amplitude than smaller amplitude suggestuig that these organized motions may be

responsible for the enhanceci scalar transfer across wavy and sheared gas-liquid interfaces.

The corresponding vertical turbulence intemities are seen to increase with an increase in wave

amplitude and fkequency (for ail the nins), however, the vertical velocities were hearly Uiterpoiated

and th= is possibly some error involved since the magnitude of the vertical velocities is very smaii

(smaller than 1 -5 mmis).

The suppression of the turbulence intensities with increasing wave amplitude and f?equency

can perhaps be better understood fiom the corresponding Reynolds stress profiles. These profiles

should indicate that as the wave amplitude and fkquency increase, the Reynolds stress values should

decrease near the wall and throughout the flow depth to indicate turbulence suppression. The

normalized Reynolds stresses shown in Figures 4.7-la to 4.7-le were computed fiom the averaged

momenhun equation given by equation 4.7-1 mezu and Rodi (1 986), Nem and Nakagawa (1 993)]:

where v is the kùlemtic viscosity, y, is the vertical distance measured fkom the bottom wall, and u*,

is the wall Fiction velocity. In highly turbulent flows, the second term of the nght hand side (RHS) of

equation 4.7-1 would be negligible and a Iinear distribution of dirnensionless Reynolds shear stress is

Runil: ReD=2700. u*,,,=0.009 mls, h,,=13.4 mm. a=0.63 mm. h=32 cm. f,=0.87 Hz - Runl3: ReD=2700, u*,=0.009 mls, h,,=13.4 mm, a=0.72 mm, h=53 cm. f,,=0.86 Hz

Runl5: ReD=3000, ~*~=0.010 mls, h,=13.1 mm. a=0.90 mm, A=44 cm, f d l . 0 3 Hz

Runl7: ReD=3200. ~*~=0.011 mls. h,,=13.1 mm, a=1.07 mm. h=45 cm. f,=1.19 Hz - - -u'v'lud,p(l - Y S )

Figure 4.7-1 a. Nomalized Reynolds stresses obtained from equation 4.7-1 plotted as a function of dimensionless distance, c=yJh, from the bottom wall for runs 11 to 17.

Run41: ReD=3600, u*,=0.010 m/s, h ,,,, =17.2 mm. a=0.62 mm. h=31 cm, f,,=0.77 Hz . Run43: Re,=3800, LJ*~=O.OI 0 mlç, h,,,=I 7.0 mm, a=1 .O2 mm, h=43 cm, f,=0.87 Hz - - -u'v'l~*~~=(l-yJh)

Figure 4.7-1 b. Normalized Reynolds stresses obtained from equation 4.7-1 plotted as a function of dirnensionless distance, g=yJh, from the bottom wall for runs 41 and 43.

- -

Run51: ReD=3900, u*,=0.010 m/s, h,=17.9 mm, a=0.63 mm, h=31 cm. f-=0.78 Hz . Run53: ReD=4000, U * ~ = O ~ O ~ I m/s. h-=17.7 mm, a=0.94 mm, h=51 cm. f,=0.88 Hz . Run45: ReD=4000, U*~=O.OI 1 rnls, hmm=17.2 mm. a=1.17 mm, h=47 cm, f,=0.98 Hz

Run47: ReD=4000, 1~*~=0.011 rnk, h,,=17.0 mm, a=1.16 mm, h=49 cm, f,=l.Og Hz - -U~V'/U~,=(I -y Jh)

Figure 4.7-1c. Normalized Reynolds stresses obtained from equation 4.7-1 plotted as a function of dimensionaless distance, g=yJh, from the bottom wall for runs 51, 53,45 and 47.

- - -

Run71: ReD=4300, u\=O.Oi 1 m/s, h,,=19.0 mm, a=0.59 mm. A=30 cm. fwve=0.78 Hz

Run55: Ree4300, ~*~=0.011 m/s, hmm=17.8 mm, a=1.41 mm, A=44 cm. fme=l .O3 Hz . Run57: ReD=4500, u*,=0.011 m/s, h,,=l8.l mm, a=1.80 mm, A=45 cm, fwe=l -19 Hz - - -UV/ uqW=(1 -),fi)

Figure 4.7-Id. Nomalized Reynolds stresses obtained from equation 4.7-2 plotted as a function of dimensionaless distance, g=yJh, from the bottom waB for runs 71, 55 and 57.

1 Run73: ReD=4700. u\=O.Oll mfs. h,=19.4 mm, a=l.l3 mm, A=39 cm. f,=0.89 Hz

1 . Run75: Re,-4700. u\=O.Oll m/s, h,,=19.0 mm. a=1.59 mm. A 4 2 cm. f,=1.10 Hz

1 Runn: Re,=5100. u>=0.012 m/s. h,,=19.3 mm. a=1.98 mm. A 4 5 cm. f,=1.20 Hz

Figure 4.71e. Normalized Reynolds stresses obtained from equation 4.7-1 plotted as a function of dimensionaless distance, g=y,,,,/h, from the bottom wall for mns 73 to 77.

expected. Since all of the experiments perfomed deal with moderate liquid Reynolds nurnbers, the

second term of RHS of equation 4.7-1 cannot be neglected, and a distribution lying below the linear

distribution is anticipated. This method of detennining the Reynolds stress was preferred to the actual

- determination of - u' v' -values fiom the product of the streamwise velocity fluctuations and the angle

- interpolated vertical velocity fluctuations, since considerabie scattering of the measured - u' v' -values

occurs near the bed and fke d a c e Pezu and Rodi (198611.

Since Reynolds stresses are produced during the ejection of Iow momentum nuid fiom

the wall towards the interface, a decrease or increase in the Reynolds stress with increasing wave

amplitude and fkquency will represent an enhancement or suppression of the turbulent events. In

examinhg more closeiy the normalized Reynolds stress obtained fiom the momentum equation, no

clear conclusions can be drawn as to whether the normalized Reynolds stress kcreases or decreases

with wave amplitude and fkquency. These graphs are arranged according to similar Reynolds

numbers (determinecl at the center plane of the liquid flow), but difEerent wave amplitudes and

83

fkquencies. Figures 4.7-la and 4.7-ld for instancey show a decrease in the Reynolds stress with

increasing wave amplitude and kquency near the wall region, while Figure 4.7-le shows a clear

enhancement of the Reynolds stress (comparing the lowest and highest wave amplitudes and

fiequencies) near the wall region. On the other hand, Figures 4.7-lc and 4.7-lb do not show any

particular trend with increasing wave ampïihde and fiequency for runs conducted under the similar

flow conditions. Enhancement of the Reynolds stress occurs for aimost of the runs near the interface

region caused by the mechanicaily generated waves. Thus, it appears that no clear conclusions can be

dtaw h m the nomdized Reynolds stresses, as to whether the surface waves due to their interaction

with the waU structures give rise to enhancement or suppression of the Reynolds stresses. One has to

look more closely at the wall ejections and b d g phenomena that occur undemeath the d a c e s

waves by examining the vida sequences for each of the m. The following section de& with this

issue.

- - - - - - - - - -

To facilitate the determination of the wall turbulent events, three different detection techniques

were used. In the fïrst technique, the velocity profile data at different heights were examined to detect

any decelerations in the velocity data. Since a w d ejection is nomiaily accompanied by a signincant

decrease in the streamwise velocity, the number of decelerations in the velocity data should

correspond to the fkquency of wall ejections. In the second method, the velocity data were examined

to obtain the fiequency of occurrence of the most dominant peak in the power spectra calculation. The

instantaneous velocity data (or fluctuations) were fed through a Fast Fourier Transform (FFT) filter,

and the most dominant peak of occurrence that should correspond to the binsting fkquency was

determined. Finally, in the visual detection methoci, the wall ejections were counted visually h m the

video sequences fiame by frame for each m. Each detection method is explaiaed in greater detail and

the results are presented in the following sections.

A velocity spectrum characteristic of the experirnental data was cornputed as the average of

the spectra e a g at diffe~nt y+ locations. The spectrum was computed as the Fourier transform of

the autocorrelation hction, dehed in a similar marner as in equations 43-2 and 4.3-3, except now

that the variable is the instanttaneous streamwise velocity, u, instead of the liquid height. Again,

Matlab's built-in FFT function was used to consîmct the power spectra for the velocity data at

différent y+ positions. The power spectrai density (PSD) hction of the time series, u(t), describes the

general fkquency composition of u(t) and is dehed for stationary data u(t) as in equation 43-2.

Figures 4.&la and 4.8-lb show some of the typical power spectra of the velocity data

obtained at seveml diffant positions for runs 47 and 73, respectively. The PSD data displayed

some dominant peaks, however, the results were rather scattered among different runs, and so no clear

conclusions could be obtained for the birrsting period. This lack of consistent trend in the results could

be attributed to the low sampling fkquency that was used in processing the digitized data It is

intereshg to note that run 47 exhibited the same dominant fkquency as the wave hquency, which

may indicate that the waves and bursting phenornena are coupled for that particular run, however, no

other clear evidence exists among difEerent nins to validate this observation.

4.û.2 Eiection Fmauency Detefinmation h m VeloQtv fichations

The ejection (TE) and bursting fi) periods can be evaluated quantitatively f?om the velocity

fluctuations, once an appropriate cnterion for detecting ejections and sweeps is established. 'The VITA

and threshold Quadrant techniques are amongst the most fiequenly used techniques for the

To obtain the ejection fkquencies using the streamwise velocity fluctuations, ail the

decelerations observed at a fked y+ position of 20 in the instantanmus velocity data were counted. It

is g e n d y accepted that the coherent structures fom in the region 5<yC<30 fkom the wdI [Hestroni

Peak @ Ir12 Hz Co

. . . . . 0.4 - -- - - - -. - - - - - - - . - .

0.0 -. -- - A o. 1 1

Frequency [Hz]

Frequency [Hz]

Peak @ 1.12 Hz 1,

Frequency [Hz]

Frequency [Hz]

y+=1 O ... -, . . . . . - - + - - Peak @1.12 Hz-

-,

Frequency [Hz]

Figure 4.8-la. Power spectral density for the instantaneous velocity data for run 47 at different y+ positions. %=3800, f,=l.Og Hz, sampling frequency=3.80 Hz.

0.50 - y+=80 Peak @ 0.58 Hz

0.25 - -- - - -

e

0.00

Frequency [Hz]

0.50 - Peak @ 0.34 Hz - y'=70

0.25 -. - -

0.00 o. 1 1

Frequency [Hz]

Frequency [Hz]

Frequency [Hz]

Frequency [Hz]

Figure 4.8-1 b. Power Spectra Density for the instantaneous velocity data for run 73 at different y+ positions.~,=4700, f,=0.89 Hz, sarnpling frequency=2.12 Hz.

87

and Mosyak (19961. In this region, the y+ position of 20-30 was chosen since it was used by many

researchers for their evaluation of ejection fkquencies mh id i et al. (1992) and Nasr-Estephany

(1 998), among others].

The criterion that was used to determine the ejection fkquency is that evev deceleration in the

streamwise velocity data at y+=20 was counted as an ejection. In particular, the cornputer program

given in Appendir F, counts an ejection event as a deceleration observed in the velocity data since an

ejection is usually a lift-off of low momenturn fluid that is accompanied with a decrease in the

streamwise velocity lpashidi and Banerjee (1988)l. The ejection fkquency, YB, is the total number of

decelerations observed in the velocity data over the sampling time interval. It was deteffnined that the

- average ejection period (Tg ) scaled with inner variables (u', , v ) was approximately equal to 78

(results not shown here). This ejection period was determinecl fiom the average ejection period of all

16 nuis conducted. According to Kim and Spalart (1987) this ejection period when scded with the

inner variables should be independent of the Reynolds nurnber. Nonetheless, the ejection period is

much higher than those given in the literature for non-waq- shear-fiee flows [Rashidi et al. (1 997),

Hestroni and Mosyak (1996)l and wavy shear-fie flows Ipashidi et al. (1992)], where the ejection

- period (Tg ) was determinecl to be approximately equal to 38 for both cases.

The discrepancy between the past and present results is probably attributed to the low

samphg fi-equency iised in this work (2-4 Hz). Typicdy speaking, the sampling fiequency should be

at lest two orders of magnitude -ter than the bursting fkquency (2.5 Hz) in order to capture the

biirsting events and to avoid background noise that may exkt in the velocity field signal.

The visual detection method was determined to be the most suitable technique for determining

the bursting period since none of the statistical detection methods could yield reliable d t s . In this

rnethod, the birrsting fkquency was determineci by counting the kquency of occurrences of coherent

motions in the video images, which is a simple but subjective ta&.

The sequence of bursting motions is a quasi-cyclic process that displays on average a nearly

periodic motion in space and t h e , but it is not p e r f d y periodic in either Face nor tune. In the visual

detection rnethod, the ejection and bursting fkquencies were determined by coimting the fkquency of

occurrence of coherent motions in the video sequences. In particular, an ejection was characterized as

a series of two or more similor defonned traces that are associated with the lif-up of vortical

stmctures. The fiequency of ejections,fE, was determined by counting the total number of ejections

over the sampling time interval.

A burst consists of several closely grouped ejections that occur intermittently in space and

t h e . Burst events fiom the video sequences were characterized as series of two or more ejections

m o n et al. (1994)l as it was determined fiom a series of dzfferentiy deformed traces. This is seen in

the vertical plane (side view) as a deceleration of the instantaneous velocity profiles near the waü

followed by the sudden ejection of the deformed traces fiom the wall that u d y resembles a

spanwise vortex. Thus, a burst includes several closely grouped ejections that are associated with the

lift-off and roll-up of the deformed traces. The burst f?equency,&, was readily determined by counting

the total number of bursts over the sampling time intemal.

The traces were deformed as previously observed by Rashidi and Banejee (1988) and

Lorencez et al. (1997a) as a consequence of the velocity fluctuations generated by the turbulent bursts

created near the lower wall region as shown in Figure 4.82. For each run, a video sequence of at least

30 seconds was analyzed and the bursts and ejection events were both counted twice independently.

Figure 4.û-2. Typical trace deformations due to bursting action.

Table 4.81 summarïzes the effect of d a c e waves on the wall ejection and bursting periods.

Table 4.8-1 also lists the non-dimensional bursting and ejection periods, T i and Tg, respectively.

These non-dimensionalized periods were obtained using the inner (u; ,v) and outer variables (U-JI)

as given by equations 4.8-1 and 4.8-2, respectively:

The non-dimensional wave period normalized by the inner variables (ub ,v) is also shown in

Table 4.8-1.

where T, is the wave period.

90

The non-dimensional wave @od, Tg, was in the range of ejection period in the undisturbed

flow, as this condition was d e t d e d to be necessary by Rashidi et al. (1992) in order to investigate

the dependence of turbulence on mechanically generated waves. This condition was met for most of

the mm as indicated in Table 4.&1. However, this study also involved wave periods that were higher

and lower than the ejection periods.

Table 4.8-1 Bursting and ejection periods for turbulent open-channel flows with mechanicdy generated waves.

+ T~,outer

59

59 ~-

95

280

38

34

50

74

24

43

43

44

G = - T;, ",W

1 .O

0.8 -

3 .6

7.1

1.2

1 .O

1.3

1.8

0.9

1 .O

1.2

1.5

. T; TB = -

2.0

2.0

3.5

11

1.5

1.4

2.0

3 .O

1 .O

1.8

2.0

2.1

+ T E , ~ ~ & r

14

11

46-

82

10

8 1

T&nner

63

51

230

450

57

49

11

13

15

17

41

43

130

180

270

280

T&nner

270

260

470

150

210

200

71

73

75

77

300

440

150

270

290

300

0.9

1.3

2.0

2.1

- Re,,

8 10

800

8 IO

8 10

1300

1300

19

25

38

36

45

47

51

53

T W

60

54

55

55

69

67

0.8

1.0

1.1

1.6

5

6

6

9

63

82

39

44

1600

1600

1600

1600

55

57

1300

1300

I l

14

7

7

63

55

77 33

8

9

1400

1400

1400

1400

72

68

77

66

58

42

51

65

62

64

44

66

91

To examine the effects of waves on turbulence, the nondimensional wall ejection and

bursting periods, T; and T; , were also evaluated as reported in Table 4.8-1. These nondimensional

ejection and bursting periods were nonnalized with the non-dimensional ejection and birrsting periods,

respectively, for non-wavy shear-fke turbulent flows as illustrated in equation 4.8-4.

T;= + *' and T'; = +

TB' (4.8-4)

&,no waver TB,^ w a w

The ejection and bursting periods for non-wavy shear-fke openchamel flows are reported

elsewhere [Chung (199811. These are the ejection and bursting penods that correspond to similar flow

conditions without d e superimposed surface waves.

The results of the dimensionless ejection and burstïng penod ratios, T; and ~;shown in

Table 4.8-1, clearly reveal that the number of wall events is substantidy altered by the presence of

mechanically generated waves. This modification of the wall turbulent events c m be M e r

investigated after a closer examination of its dependence on the wave characteristics and on liquid

Reynolds number.

4.U.l Dependence of wall turbulent men& on wme chat acte^

To study the dependence of wall events on the wave characteristics, plots of the w d events

versus the dimensionless wavelength and wave amplitude were made (Figures 4.8-3 and 4.8-4).

Figure 4.8-3 illustrates the relationship between the non-dimemional w d ejection period

(T; ) and the dimensionless wavelength, Wh. The ejection periods are scattered and do not show any

paaicular trend with increasing wavelength. Thus, the dimensionless ejection and bursting period

ratios shown in Table 4.8-1 reveal that there is no direct relationship between wall events and

wavelen&

Dimensioneless Wavelength, h/h

8

7 -

6 -

5 -

T,' = T; T;flownr 4 -

3 -

2 -

1 -

O

Figure 4.83. Effect of wavelength on wall ejections.

Increasing wave frequency

10 15 20 25 30 35 40 45

1 1 1 1 t 1

Dimensionless Amplitude, alh

. Run i senes: =,,=2500-2600 Run 4 series: ~D=3700-3800 . Run 5 series: &=4100 . Run 7 senes: ED=4700

_

Figure 4.84. Effect of wave amplitude and frequency on wall ejections for selected runs.

O -

- - -

-

- 0 . .

O a . . " a

w - m - . I I I 1 1 1

93

Figure 4.W shows a similar plot of the ejection periods for several çelected nms of sirnilar

fiow conditions (excludes nms 11 to 43) plotted as a h c t i o n of dimensionless wave amplitude, ah.

The ermr bars indicated in this figure represent the deviations in counting the fkquency of wall

ejections fiom their respective mean values for more than two independent visual counts pediormed.

Here, it appears that as the wave amplitude (and hence as the wave hqency) is increased,

the period of wall ejection increases (or the burst fkquency decreases). There seems to be a 50 to

100% increase in the wall ejection periods for the highest amplitude waves compared to non-wavy

flow under nearly similar fiow conditions. This clearly indicates that for most of the conditions listed

in Table 4.2-1, the d a c e waves caused suppression of the w d turbulence. This is in contradictio9

with the results obtained by Rashidi et al. (1992) who observed an increase in turbulence levels with

increasing wave amplitude, although their Reynolds numbers were weii above the range investigated

in this work. Furthemore, the effect of the modification of wall ejection periods with increasing wave

amplitude and fkquency is more pronounced in this M y . This effecf however, could not be

attributed solely to an increase in wave amplitude or fiequency since both parameters were varied

simultaneously due to the nature of the experiments conducted.

4.8.3.2 Dqendence of wrrU nrrbuCenf evem un R q m B number

Figrires 4.û-5 and 4.84 show plots of wall ejection (Tg) and bursting (TL) periods as a

hct ion of liquid Reynolds nurnber, respectively. The error bars indicated in these figures express the

uncertainties in counting the ejections and bursfing periods. These error bounds were estimatecl to be

f 15% fiom their mean time periods.

These graphs Uusfrate that the average ejection penods scaled with the inner variables, are

nearly independent of the iiquid Reynolds number, and have an average value of 55, with the

exception of the lowest Reynolds number, hi& wave amplitude nins (ru 15 and 17). The same

p Runs 71 to 77

Figure 4.8-5. Ejection pen'od dependence on Reynolds numbers for runs 11 to 77.

1 -"un:llto17 1 Runs 41 to 47 Runs 51 to 57 Runs 71 to 77

Figure 4.84. Bursting perîod dependence on Reynolds number for runs II to 77.

95

g e n e h t i o n applies to the burst pend, where again there seems to be no clear dependence on the

liquid Reynolds number. On average, the dunensionless burst period is determineci to be 252 as scaled

with the inna variables. The low Reynolds number flows seem to be completely 1-d for the

high amplitude and high fkquency cases (nms 11 and 17) as a consequence of the increased wave

amplitude and fkquency resuiting in a dramatic decrease in the bursting periods. Thu, it can be

stated that the average number of burst and ejection events for a given velocity field is independent of

the Reynolds number when scaled with the inner variables. The same effect was reported by Kim and

Spaiart (1987) in agreement with many other researchers' findings plackwelder and Haritonidis

(1 983), and Luchik and Tiederman (1 987), among others].

4.83.3 s ' h g lmcs

Scaling Iaws are useful tools in comparing the wall ejection and bursting fiequencies obtained

ftom different literature sources. These scaling Iaws are described by equations 4.&1 and 4.8-2.

Nonetheles, there is stiil a lack of consensus among past research studies on whether the fiequency of

occurrence of the wall events is best scaled by the inner (u ,v) or outer variables (Urmx,h).

Kim et ai. (1971), Rao et al. (1971), and Lu and W i a r t h (1973) suggested that the bursting

fkequency is ' k t described by the outer variables as expressed in equation 43-5 p e z u and

Nagakawa (1 993)] :

where Tg is the mean burstiflg period, T E is the mean ejection period, and Ts is the mean sweep

period. Equation 4.8-5 implies that a sequence of bursting motions is composed of one ejection and

one sweep on the average in space and tirne, and thus one can generally refer to any of the three

parameters, Te , T E and Ts as the bursting period wezu and Nakagawa (1 993)l. This indicates that

96

even though the bursting process is an inner-wall phenornenon, it is dnven by the outer part of the

boundary layer. The numerical values given in equation 4-85 are those for non-wavy flows.

In contrast with the outer scaling laws, Blackwelder and Haritonidis (1983), Willmarth and

Sharma (1 984), Rashidi (1997) and Hestroni and Mosyak (1996) ammg others have deterrnined that

the bursting and ejection periods in non-wavy and wavy flows with and without interfacial shear are

best described by the inner variables. Blackwelder and Haritonidis (1983) also demonstrated that one

could be rnisled to outer-variable scaling when the length of the probe used to detect the bursting

process exceeded 2Ov l u i , a criterion which was violated by many researchers in high Reynolds

number flows. Thus, in tenns of these variables, the nondimensional ejection and binsting periods for

non-wavy shear-fiee and wavy sheared flows are given by equations 4.M and 4.8-7, respectively

lpashidi (1 997), Hestroni and Mosyak (1 W6), Nezu and Nagakawa (1 993), among others].

a 2 a 2 - - u w

Uw -38andT; =TE-"87 TL =TE-- (wavy-sheared) (4.8-7) v v

Unlike the other researchers' hdings, Abedsson and Johansson (1984) reported that the

bursting hquency in turbulent channel flows are perhaps better scaled by a mixture (geometric mean)

of the outer and inner variables thus emphasizing the interaction between inner and outer variables.

The ejection and bursting muencies reported in Table 4.8-1 are seen to be best scaled by the

inner variables as opposed to outer and mixed variables. The results support the scaüng laws depicted

by equations 4-84 and 4.8-7, even though these equations were generalized for wavy-sheared anci

non-wavy shear-free flows. Rashidi et al. (1992) reported a non-dimensional ejection penod, Ti, of

38 for a shear-k, turbulent open-channel flow with mechanidy generated waves for a iiquid

97

Reynolds number of 5,000 based on the liquid height This value of 38 is much lower than those

obtained in this work and given in Table 411-1. This indiates that over the present range of Reynolds

numbers and wavelength, wave ampiitudes and fiequencies investigated, longer periods resulted

between ejection and burstïng events as compared to non-wavy and wavy-sheared turbulent flows.

The longer ejection period immediately translates to a suppression of turbulent events due to the

presence of mechanically generated waves.

As a consequence of the modification of the ejection periods due to the mechanically

generated waves, it is expected that the heat and mass M e r at the IÎee surface will also be affected.

At present, tbere are no data given under controlled conditions with mechanidy generaied waves

that predict the heat and m a s transfer rates at the fke d a c e by considering the measured

modifications in wall ejection processes. Nonetheless, in this section it was revealed that the transport

processes may well be affected by the presence of waves, not directly, but due to the mod$cation of

the tiabulence generation in the waZZ region. This modification in the wall region is M e r examined

in the following subsection.

4.8.3.4 Wd turbulence nmd@dbn by imkfnrjnl waver

The suppression of wall bursts by the surface waves can perhaps be best explained by closely

examining the instantaneous velocity profiles under a wavy d a c e over a small elapsed tirne. These

results are shown in Figures 4.8-7a through 4.û-7c for runs 47,57 and 75, respectively. These figures

contain the iiquid height fluctuations as well as the Ilistantaneous velocity variations with respect to

t h e . The instantaneous velocity profiles express the average velocity profile between two successive

traces.

In Figures 4.8-7a to 4.û-7c, the local liquid Reynolds number, the instantaneous average

streamwise velocities, and vertical velocities at the gas-liquid interface are also indicated. The sale

shown in these figures indicates the magnitude of the velocity vectors. From these plots, it is apparent

Figure 4.8-7a. lnstantaneous and mean velocity profiles for run 47. Re,= 4000 or Re,,=1400, Fr=0.34, u*,=0.011 m/s, uM=0.14 m/s, f,=1 .O9 HZ, h=49 cm, a=1.16 mm, h,,=I 7.0 mm, Uwe=53 cmls.

"'vertical angle interpolated velocities at gas-liquid interface.

time [s]

Figure 4.8-7b. lnstantaneous and mean velocity profiles for run 57. ReD=4500 or Re,,=1600, Fr=0.34, u',=0.011 m/s, u,=O.14 mls, f,=1.20 Hz, h=45 cm, a=1.80 mm, hmn=18.1 mm, U,=53 crnls.

(*)Vertical angle interpolated velocities at gas-liquid interface.

101

that the local Reynolds number undemeath the: wave tmghs is reduced signincantly fi0111 the mean

Reynolds number @th Reynolds numbers show in these plots were determined at the center plane

of the liquid flow). This indiCates that the flow is decelerated under the wave troughs and thus the flow

becornes less turbulent. This deceleration or laminarization effect is probably aîiributed to the low

speed regions that characterize wave troughs, resulting in Iower observable bursting fkequencies and

thus an o v d suppression of the turbulence levels. The same effect was observed in falling thin films

by Dukler (1977), Brauner and Maron (1983) and Brauner (1989) who noticed a decreae in the local

Reynolds nmbers. They observed that turbulence dominates in wave peaks and portion of the wave

back region, while the substrate remain laminar. This kmharhtioa effect of the wali and bulk

regions under wave troughs was also observed by Nasr-Esfahany (1998) where the production of

Reynolds shear stresses was noted to be suppressed for extremely high interfacial shear situations for

cocurrent flows.

The suppression of turbulence due to waves could dso be attributed to the enhanced mkhg

caused by the waves resulting in a quick dissipation of the wall turbulent bursts. The same effect was

observed by Lorencez et al. (1997a) in wavy-stratified two-phase flows. As Figures 4&7a to 4.û-7c

iilustrate, the mean velocity profles under the waves flattened throughout the entire liquid depth. E s

probably results in quick dissipation of the wall turbulent bursts when these bursts reach the upper

layers of the liquid.

As noted in Figures 4.8-7a to 4.û-7c, a relatively flat velocity profile existed in a signifïcant

portion of large amplitude waves undemeath the wave crests, which could indicate that a high level of

turbulence and mixing effects are associated with wave crests. Thus, turbulence effects dominate

under the wave crests and portion of the wave back region, while the wave troughs are lamina..

. . Figures 4.%7a to 4.û-7c clearly reveal that the flow is laminanzed under the wave troughs as

expressed by the presence of laminar parabolic velocity profiles.

102

Turbulence suppression is observeci due to the S t a b W o n e E i t that occm in the wave

troughs with increasing wave amplitude and fhquency. As kquency hcrease~, the number of wave

troughs inmases, resulting in greater suppression of the turbulence levels over time due to the

presence of mechanically generated waves.

The velocity profiles changing with time are m e r investigated in the Lmgrangian frame of

reference when one moves with the mean liquid velocity as shown in Figures 4.8-8a to 4 .88~ . These

figures illustrate that the flow underneath the crests has a net positive velocity whereas the velocity

undemeath the troughs is negative. In this coordinate system, the wall moves in the opposite direction

to which the wave is propagating, that is f?om the Zefi to the right of these figures (see the flow near

the bottom of the wali), with the wave crests always exhibiting large positive velocities. The large

velocity undemeath the wave crests is attributed to the presence of high amplitude and fiequency

waves which basically consist of a lump of £luid that aiways travels at a higher velocity than the mean

iiquid velocity. Since the waves were shown to be statistidy steady and did not grow with time,

continuity requires that the velocity tmdemeath the troughs to be negative to balance the strong

positive velocity present at the wave crests.

The overall picture f?om the Lagrangian &une of reference i s that the slow moving lump of

fluid under the wave troughs is continuously picked-up by the fast moving wave, resuiting in the

formation of a mixhg eddy near the fiontai region of the wave. The wave seems to shed liquid fiom

its back (after the crat), f o d g a new decelerathg layer near the wall, to be picked up by the riext

successive wave crest. The overail result is that wave troughs are always associated with slow moving

fluid resulting in a lamimwhition or stabilization effect of the liquid layer. This stabilization effect

results in a net decrease in the wall turbulence levels as indicated by the decrease in the wall ejection

periods. Thus it is speculated that the lower celerities associated with the wave troughs give rise to

lower velocities near the wall, which, in tum, result in greater stabilization of the shear layer.

**LPM= Liters per minute time [s]

Figure 4.8-8a. Langrangian strearnwise velocity profiles for fun 47. k,,=3800, Fr=0.34, u*w=O.O1l rnls, ~ ~ 0 . 1 4 rnls, f,,,a,,,,=1.09 Hz, h=49 cm, a=1.16 mm, h,,,,,=17.0 mm, Uwa,,,=53 c d s . Arrows indicate net direction of flow.

(') Vertical angle interpolated velocities at gas-liquid interface.

17.5 18.0 18.5 19.0 19.5 20.0 20.5 21 ,O 21.5 22.0 22.5

**LPM=liters per minute. tirne [s]

Figure 4.8-8b. Langrangian streamwise velocity profiles for run 57. ~ , = 4 1 0 0 , Fi-0.34, U*~=O.OI 1 nils, u,,,,=0.14 mis, fm=l -19 Hz, A=45 cm, a=1.80 mm, h,,=18.1 mm, UmVe=53 cmls. Arrows indicate net direction of flow.

(') Vertical angle interpolated velocities at gas-liquid interface.

29.0 29.5 30.0 30.5 31 .O 32.0

**LPM=liters per minute. time [s]

Figure 4.8-8c. Langrangian streamwise velocity profiles for run 75. Re,=4700, Fr=0.37, u\=O.Oll m/s, u,=0.16 mis, f,=1.10 Hz, h=42 cm, a-1.59 mm, h,,=19.0 mm, UmVe=46 cds . Arrows indicate net direction of flow.

'*) Vertical angle interpolated velocities at gas-liquid interface.

106

4.&3.S Fkque?tq of turbucpnf

Dimensional fkquencies of imbulent events, fd (s-'), dimensionles muencies scaled by the

+ f w v f w ~ h , outer variables, fgL = - inner variables, f, = - , and mixed variables, w U M

-of, , are a l l tabulateci in Table 4.8-2 for a l l of the m.

The variation of walI turbulent event hquency with the wall fiction velocity, u; , is shown

in Figure 4.89. This figure shows both the dimensional (a) and non-dimensional @) ejection

Table 4.82 Frequency of wall turbulent events for wavy flows

]Run

1 1

13

15

17

41

43

45

47

5 1

53

55

57

7 1

73

75

77

f,"

0.088

0.1 IO

0.025

0.0 14

0.121

0.147

0.1 16

0.086

O. 187

0.172

O. 155

0.121

0236

020 1

fin+

0.0 16

0.020

0.004

0.002

0.017

0.020

0.016

0.0 12

0.026

0.023

0.019

0.0 15

0.030

0.024

0.023

0.0 15

fiarn

0.037

0.047

0.01 1

0.006

0.046

0.055

0.043

0.032

0.069

0.063

0.500

0.043

0.084

0.069

O. 186

0.132

0.065

0.045

O runs41 to 77 runs 11 to 17

10

O runs 41 to 77 (b) runs 1 1 to 17

Figure 4.8-9. Variation of wall turbulent event frequencies with wall friction velocity for al1 runs.

1 O8

fkquencies. The dimensionles ejection fiquencies were nomialized by the non-wavy flow ejection

fiquencies obtained by Chung (1998) under the same flow conditions without the superimposed

waves. It is evident fkom this figure that the frequency of occurrence of the wall turbuient events is

independent of the w d fiidon velocity, except for the Iow liquid Reynolds number nms (run 11 to

17) where it appears that they are inversely proportionai.

The dimensionless fiequencies of the events scaied by the inner, outer and rnixed variables are

also ploüed in Figare 4.û-10. This figure illustrates that the fkquency of wall turbulent events is best

scaled with the inner variables, while the d t s seem to be rather scattered for the outer variables.

However, it appears fom this figure that none of these scaling parameters can collapse the data as a

hct ion of the Reynolds number, Le., the Reynolds number dependence is not completely removed.

A lnner Variables

A Outer Variables i Mixed Variables

A

A A

800 1000 1200 1400 - Reh

Figure 4.8-10. Dimensionless frequency of wall turbulent events.

To M e r ver@ the suppression of turbulence indicated by the attenuation of the bursting

fiquency as wave amplitude and m e n c y increase, another quantitative approach was used. In this

method, the lateral displacement of the traces generated was measured fiom the centerline of the test

section at a fixed downstream position. Accordhg to Kumar et ai. (1998), a burst is accompanied by

an upwelhg. Ifthe number of bu~sts decreases, the nurnber of upwellings should also decrease, which

will resdt in attenuation of the trace movement in the spanwise direction.

The spanwise displacement of the generated traces was mea~u~ed at a fked downstream

position as shown in Figure 4.9-1. The centerline was defïned as the line passing through the laser

ban injection point at which the traces were fïrst generated. The spanwise displacement fkom the

centeriine was rneasured at the center of the leading edge of the generated trace at a fixed downstrearn

position as iUusûated in Figure 4.9-1. This was necessary to ensure that the lateral displacement of the

tmce on the liquid surfàce was measured instead of in the bulk. The drawback of this method is that

any traces that were elongated in the spanwise direction could result in a signincant error in the

spanwise measurements. However, most traces analyzed were srnail in Length (1 mm or less) and did

not elongate significantly in the spanwise direction, thus did not involve a significant error in the

spanwise displacement measurement (see Figure 4.9-1). Nonetheless, the RMS lateral displacement

of the traces was not that significant and this resulted in a maximum estimatecl error of 20% for the

runs that showed the smallest lateral RUS displacement values.

From the top view itnages captured for runs 4 and 7 (no waves) and runs 43,47, 73 and 77

(with waves), about 100 lateral displacement data were measured for each r u . Figures 4.9-2 and 4.9-

3 show plots of the spanwise fluctuations of typical traces as a h c t i o n of time for runs 4 and 7,

Figure 4.9-1: Schematic representation of the lateral displacement and measurements taken using Mocha. The lateral displacement of the traces was measured at a downstream station at the center of the trace at its leading edge as the figure indicates. Cases (a) and (b) denote the best and worst case orientations for the traces. In case (b) there is a significant error in determining the lateral dispIacement. Most of the cases, however, were s h o w to k the same as case (a).

respectively. These fluctuations were obtained by subtracting the mean spanwise displacement fiom

the displacement data,

Zf=Zinrt -Zmm (4.9-1)

where & is the mean distance of about 100 spanwise displacement measurements computed using

MatIabfs mean bdt-in function, The

-J" Z - (2 ) . Attempts were made

station h m the center point of the laser

Iaterd root mean square value was also computed as:

among dzfferent mm to keep the downstream measuring

beam formation as constant as possible, however there were

1 l l

some mal1 deviatiom in the measurements. The maxilnum deviation of the downstream location

h m the centerline of the laser beam among diffkrent nuis was approximately + 0.5 cm.

In these figures, both the instantanmus and the fluctuating spanwise diplacements of the traces

is plotted as a hct ion of time. It is apparent that the mean displacement of the traces fiom their

centerline can be either negative or positive. However, it appears that the mean lateral displacernent

increases with increasing Reynolds number. For instance for Reynolds number increasing fiom 3946

(nm 4) to 4949 (run 7), the absolute value of the mean lateral displacemenf Lm, increases fiom 1.79

mm to 2.37 mm, as indicated in Figures 4.9-2 and 4.9-3, respectively.

A cornparison of the d t s for non-wavy and wavy flows shows clear attenuation of the

spanwise displacement of the traces when waves are imposed. This is indicated by the decrease in the

RMS of the lateral displacement. The RMS value without waves was about twice as large as those

with waves. There seemed to be no clear evidence of decrease in the RMS values associateci with

increasing wave amplitude, akhough the data suggested that there may actually be a slight increase in

the RMS values with increasing wave amplitude and hquency. Nonetheless, it is evident fiom these

redts that the wavy d a c e suppresses the lateral displacement of the traces, which could be a direct

result of a reduced bursting fiequency since a larger lateral displacement of the trace will correspond

to higher fkquency of upwellings. Traces are thought to be displaced by the upwellings originating

fiom the bottom wall due to bmst action. Since Kumar et al. (1998) suggested that a burst develops to

an upwehg, and the lateral displacernent of the traces is diminished wïth waves compared to non-

wavy flow, this immediately translates to fewer upweIIings and thus lower observable bursting

muencies. Nonetheless, the laterai displacement of the traces also depends on the intensity of the

binsrs. The presence of interfacial waves indicated that the intensity of the bwsts decreased resulting

in reducing the lateral displacement of the traces in cornpaison with the undisturbed flow. Thus, this

further verifïes that under the experirnental conditions indicated in Table 4.2-1, interfacial waves

time Es]

Run43: Zws=2.41 mm, L = 7 . 9 cm, Ga= -0.35 mm %=3800, u>=O.OlO mls

time [s]

n A 2' [mm] i 1 0 4 .---*---- zinSf [mm] Y

Run47: &=2.43 mm, &,=7.9 cm, &,,= -0.99 mm Ke,=3800, u*,,,=û.O11 m/s

4 6 time [s]

Figure 4.92. Lateral fluctuation and instantaneous displacement of traces measured from the centerline of the test section for non-wavy (run 4) and wavy flows (runs 43 and 47).

time (s]

4 6 time [sj

time [s]

20

Figure 4.93. Lateral fluctuating and instantaneous displacements of traces measured from the centeriine of the test section for non-wavy (nin 7) and wavy fiows (nins 73 and 77).

n

E 15 - E

- z' [mm] Run77: &,,=2.90 mm, Xm=8.4 cm, Lm= 2.66 mm

-.--9---- z re,=4700. uIrW=O.012 m/s h& [mm1

.- -10 -

m ,P -15 -

-20 I I 1 I

114

actuaUy suppressed the bursting fkquencies and thus turbulence in the present range of Reynolds

In this chapter, the wave-turbulencr interactions were investigated statiçiidy through the

evaluation of various turbulent quantities. When the results were compared with non-wavy flows, the

ejection fkquencies were seen to be sipniIicantly rnodifled by the presence of mechanidy generated

interfacial wava. The suppression effect noted appeared to be b e r correlated with increased wave

fkquency and amplitude but could not be atûibuted to either parameter due to the nature of the

experiments conducted in this investigation. The ejection and bursting frequencies appeared to be

independent of the Reynolds number when scaled with the inner variables with mean time p e n d of

55 and 252, respectively. However, no systematic trend in ejection and bursting fkequencies was noted

with regard to the wavelength. In exarnining the lateral displacement of the traces it was determined

that the RMS values decrease when waves are imposed on the fke surface, suggesting attenuation of

the upwelling intensities and muencies due to the reduction of the bursting intensities and

frequencies in the wall region caused by the presence of mechanicdy generated waves.

This modincation of turbulence due to the presence of mechanically generated waves, will

certainly modify transport processes, both at the wall and in the interface region. Flow visualization

facilitated fiirther examination of the dominant turbulence structures that are present in the interface

and w d reg-ions. Although others may consider this technique as subjective, it certainly provided a

good insight into the generd turbuience characteristics, which codd otherwise be difficult or even

impossible to obtain through the use of statistical analysis alone. In the next chapter, these structures

present at both boundaries are closely exarnined through a careful investigation of the video images

taken in the Eulerian and Langrangian -es of reference.

Coherent structures of turbulence are identïfied by 'organized' or 'ordered' motions of

fluid parcels that have a life cycle and cannot be solely described by conventional probabilistic

tools. Instead one must resort to detection tools to characterize these structures such as flow

visualization and probe measurements. Most coherent structures such as bursting phenomena

were identified not by probe measurements, but by flow visualization [Kline et al. (1967), Nezu

and Nagakawa (1 993)l.

In the present work as well, flow visualization enabled the investigation of the dominant

turbulent structures near the bottom wall and their interactions with wavy interfaces. Visual

pictures could provide valuable information with which one can constnict an outline of a

physical mode1 that descnbes the phenomena in a qualitative manner. This was performed by

sening up three CCD video cameras (at 30 frames per second and a shutter speed of 1/1000s)

recording the trace motion simultaneously in either the Eulerian or Langrangian frame of

reference as explained in the Chapter 3. The cameras were set up to provide the side, incoming

and top views. From the video images analyzed, the general qualitative aspects of wall

turbulence structures were detemiined to be similar between wavy and non-wavy flows, i.e.

sweeps and ejection cycles occur in both cases.

The main objective of flow visualization was to quant@ the fiequency of occurrence of

the coherent structures at both the bottom wall and the interface, and to provide further

information on the qualitative aspects of turbulence and coherent structures at both boundaries.

Il6

The former objective was met as descnbed in the previous chapter. The present chapter deals

with the general qualitative aspects of turbulence in wavy flows as cornpared to non-wavy flows.

- -

From a carefbi inspection of the simuitaneous video sequences fiom the side, top and end

view video cameras in the Ederian fiame of reference, the trace motion was observed to be

suppressed due to the presence of waves.

Figure 5.1-1 shows the video sequences fiom all there views in a quad window format in the

Eulerian h m e of reference. The top left window of each pichire represents the side view (labeled as

A), while the topright and bottom-nght windows represent the top view (labeled as B) and end view

(labeled as C), respectively. The bottom-lefi window was used to display the time code to follow the

trace motion fiom each of the three views. The flow in the quadrant A is fiom right to left as show in

the first pictue, while in quadrant B the flow is fiorn top to bottom of the picture as indicated by the

arrow. The flow direction in quadrant C is coming out of the page. The viewing windows for

quadrants A and B were 25 mm (vertical) by 30 mm (horizontal) and 100 mm by 100 mm,

respectively. The quadrant C is a perspective end view taken with a borescope located at 32.5 cm

downstream of the point of trace formation. The fiames (i) and (ii) in Figure 5.1-1 are fiom non-wavy

flow (run 4), while the rest are fiom a wavy flow under similar flow conditions (run 47).

From these images, it is evident that the traces in wavy flow retain theil identity and shape for

a more prolonged time and distance as comparai to non-wavy flow. This is best ilIustrated in the end

view (C quadrant) images as shown in Figure 5.1-1. As these end view images elucidate, the traces in

wavy flows tend to move in a stmighter path and retain their shape even at a position very close to the

borescope1s viewing window, a characteristic that is not observed in the trace images for non-wavy

flow. There the traces readily defomed and appeared to move in a more random marner (compare

11s

fiames (i) and (ii) h m nm 4 with fiames (i.ii)-(vi) h m nui 47). These characteristics were observed

more clearly with the highest amplitude and fkquency waves showing the les t trace deformation and

lateral riisp1acement of the traces. The top view Mages also suggested a decrûase in the lateral

movement of the traces, even though this was not quite evident h m the captured vida images due to

the small transverse displacement of the traces. Analyses of some of the top view images (see

Chapter 4, section 4.9) again indicaîed that there is a suppression of the lateral rnovement of the

traces due to the presence of waves.

Figure 5.2-1 shows the video images taken fiom the side view camera wîth the photochromic

dye traces in a wavy flow. These images indicate patches of fluids are k ing ejected towards the

interface due to the bursting phenornena occuning near the bottom wall. These effects appeared to be

more enhanced for higher Reynolds numbers, and they were generdy recognized by the formation of

quasi-streamwise vorîices near the wall, and the sudden lift up and eruptions of one or severai sections

of the vortices towards the interface. These events were seen in the video images as the folding and

deformation of the traces in the vertical plane and the sudden Lift up and roihg of several sections of

the folded loop of traces towards the intefiace as show in th is figure. The patches of fluid are

indicative of periods of intense turbulence activities cornpared to the surroundhg regions, and are

thought to be the highest region of turbulence production or Reynolds stresses [Grass (1971),

WiIlmarth and Lu (1 972), Nakagawa and Nem (1 977), Rashidi and Banerjee (1 99 l), Rashidi (1 99711.

Most of the bursts generated were observed fiom the video images to occur on the uphill side

of the wave crest, i.e. in fiont of the wave crest as shown in Figure 5.2-1. This suggests that the

presence of high amplitude waves alters the near-wail turbulence structure by generating bursting

activities at the bottom wdi following the passage of a wave crest This is probably due to the large

120

amplitude and fiesuency waves that bas idy consist of a lump of liquid near the interface Iayers

travelling at a much higher velocity than the mean liquid velocity due to the presence of mechanically

generated waves at the interface region (compare wave velocities in Table 4.3-1 with mean liquid

veiocities in Table 4.2-1). The slow moving fluid is continuously ovemin (picked-up) by the fast

travelling lump of liquid near the interfixe layers resulting in the formaton of a rolling eddy at the

fiontal region of the wave as seen in the video images.

This was also discussed in Chapter 4, where the velocity undemeath a wave crest was shown

to increase compared to the mean velocity, leading to the generation of an instabiïrty region and thus

the generation of burst events. From the video images and the quantitative results, the wave crests

have been shown to accelerate the fluid. For continuity to be preserved, the accelerated fluid should

move into a low-speed region causing an in-sweep or in-rush of the fluid This in-sweep or in-rush of

fluid interacts with the near d region causing the generarion of burseing events.

Flow visualization experiments perfomed also enabled the investigation of the dominant

structures present in the near wall region. Large scale quasi-stre;unwise vortices were observed that

originate near the bottom w d and expand with a tilted angle in a spiral or furinel shape into the outer

region. These images are clearly shown fiom the side view camera for the wavy flow under

investigation (see Figures 52-2 and 533b,c). These are similar to the funnel-shaped structures

shown by Kaftori et al. (1994) in a shear-he non-wavy open-channel flow (see Figure 533 a

through c). These hel-shaped vortices appear to dominate the wall turbulence phenornena observed

in the past, such as the quasi-streamwise vortices (which are believed to be the legs of a horseshoe

vortex) and ejections and sweeps. These quasi-streamwise structures present near the wall may also

represent the legs and the heads of horseshoe or hockey stick vortices as shown in the video images in

Figures 5.2-4a,b to 5.26. From the Eulerian side and end view video images, it is evident that quasi-

streamwise vortkes are forrned which are speculated to represent the legs of horseshoe or hockey stick

END VIEW

Figure 5.2-3a. Side view and end view of a vortex funne1 Wafto~-i et al., 19941.

Figure 5.2-3h and c. Formation of a vortex fünngnear the bottom wall as seen fiom the side for nins 43 (~%=3800,h.-,,=17.0 mm, a=1 .O2 mm), and 45 (R%=3700, h,=17.2 mm, a=1.17 mm).

Figure 52-4a and b. Formation of a vortex structure near the wall as seen from the borescope for run 43 (R%=3800, h-=17.0 mm, a=1.02 mm). Sequence of images are 1/10 seconds apart.

122

structures, since they were observeci by many researchers lpashidi (1 997), Black (1 96811 to occur at

about 20' angles Eom the bottom wall (see Figure 5.2-3b and F i 5.2-5). These Iraihg legs of the

loop in the wall region move outward fiom the waii region (ejection), and serve to pump fluid away

fiom the waii region towards the interface.

The bo~escope view (end view) also reveals the existence of this quasi-streamwise vortex

appearing near the wail in the quasi-streamwise direction which may form the traïling legs of the

horseshoe vortex (Figures 53-4a,b and 5.26). These figures show the video image of a near-wall

quasi-streamwise vortex (circled structure in Figure 5-24 and dotted h e in Figure 5.26) taken h m

the borescope view with a fked camera. The borescope view showed that these quasi-streamwise

vodces occur either to the left or to the right of the centerhe where the trace was generated. Quasi-

streamwise vortices appeared to extend towards the interface region with a tilted angle.

The presence of the head of the horseshoe vortex could also be seen in the side view images

taken in the Eulerian &me of reference for a wavy shear-fkee nirface (Figure 5.2-7 and 5-24)). niese

images reveal the presence of a series of ring type stmchires created near the intelface. These ring type

structures are believed to be caused by the presence of a spiruiing type fluid or vortex element having

its axis of rotation in the spanwise direction as clearly shown in Figure 52-8. These vortices are

believed to constitute the vortices of the head of a horseshoe, which have been observed by past

researchers to occur at about 45' angles as illustrated in Figure 5 2 3 [Rashidi (1997), Robinson

(1 99 l), Nezu and Nagakawa (1 993)].

Although the present experiments were performed at low Liquid Reynolds numbers, other

researchers have show that such bursts persist for distances of up to thousand wall units. These

bursts are ais0 responsible for the upwehgs and surface boils seen in nvers panejee (1992)], and in

the absence of interfacial shear, they are thought to interact with the d a c e in a peculiar manner

F i g u r e 5 . 2 - 5 . ( L e f t f i g u r e ) Formation of a quasi-streamwise vortex for run 57, fi,=4100, h,=18.1 mm, a=1.80 mm) as seen Rom the side view. The flow direction is in the positive x-diretion. Dotted fine indicates the motion of the trace.

F i g u r e 5 . 2 - 6 . ( R i g h t f i g u r e ) Formafion of a quasi-sfreannvise vortex for run 57 (&,=4100, h ,,,, =la. 1 mm, a=1.80 mm) as seen from the borescope. The flow direction is in the positive x-diretion. Dotted line indicates the motion of the trace.

Figure 5.2-7: (a through c). Side vierv images ofthe sequentialprogression ofa vorfex ring pair spinning in the spamise direction for run 57 (~,,=4101), h,=18.1 mm, a=I.BO mm). They could represent the head of a horseshoe sincc they appear to be formed at about 45" angle from the horizontal. Arrows indicate direction of rotation of vortices Le. spanwise axis of rotation.

Figure 5.2-8. Sequence of images showing the formation of a spinning element (circled) In the spamvise direction for &,=~ooo. Images (from Iefi to right) are separated by approximately 1/10 seconds. This vortex is believe to constitute the head of a horseshoe.

Figure 5.2-9. Sketch of a horseshoe and low speed streaks as visualized by other researchers. [Banerjee ( 1 992), Rashidi (1997)l.

125

bringing h h fluid to the interface resulting in the formation of " d a c e renewal" patches that are of

great importance for scalar tramfer across wavy inferfaces Fornori et al. (198911. This mechanistic

view at the fiee d a c e appears to be divided into two modes: the splats or upwellings, and the

attached-whirlpool like vortices or spiral eddies as discussed ne-

-

Persistent structures at the fiee slirface can be classfied as upwellings and downdrafts, and

attacheci vortices or spiral eddies. Recently Nagaosa and Saito (1997) numerically predicted the

presence of dipole strearnwise vortices with longitudinal axes of rotation at the free Surface which

contribute to the k e d a c e renewal and control the Scala. transfer at the gas-liquid interface. These

turbdent structures are investigated in great detail in the following sections.

53.1 UrneIfinas and Downdrafts

The first mode of the development of the burst involves the evolution of the burst k m the

bottom wall into a "splat" or "upwelling" [Banerjee (1992), Pan and Banerjee (1 999, Banerjee (1996),

Nagaosa and Saito (1997), Kumar et al. (1998)l. In this mechanism, the burst rises, reaches the

interface region and thus forming an upwelling. Once the raised fluid reaches the interface, its motion

is damped by the free surface re-distnbuting its energy into streamwise and spanwise directions in the

form of velocity fluctuations. This redistribution of kinetic energy does not always r e d t in a

spinning structure, but sometimes the resulting structure resernbles an impinging drop or jet on a

Surface named as a "splat".

The splatthg and anti-splatting motion of the fluid patches cm be easily visualized from the

side view with a moving camera The splatting pattern is a fluid patch originating at the bottom wall

that rises to the interface (see Figure 5.3-la). Once it reaches the interface, the "splat" or upwelling is

damped due to the blockage of the upward motion at the fke d a c e , re-distributing the energy into

Figure 5.3-la. Video seqeunces (Langrangian view) showing the upward motion of the trace towards the interface resembling the splatting or upweIling motion for nxn 43 (=,=3800, h,,-,=17.O mm, a=1.02 mm).

the tangentid directions. This in hun causes the burst fluid reaching the interface to slow dom and

evenWy tum back toward the wall, giving nse to a characteristic rolling structure as it was observed

by Rashidi and Banerjee for non-wavy flows (1988). For continuity to be presewed, an upwelhg

motion will require a downward flow of the fluid fiorn the interface to the buik flow, also known as a

downdraft or "anti-splat" as clearly seen in Figure 5.3-lb. A sketch of this splatting and anti-spaltting

motion is aIso shown in Figure 5.3-2.

The upwelling motion was dso thought to be related to the lateral displacement of the traces

h m the central plane of the laser injection point as viewed from the top vidm camera in the Eulerian

fiame of reference. It was observed f3om the video images that the traces did not aiways travel in a

straight path even very close to the initial location of the laser beam formation. It can be hypothesized

that if a burst reaches the interface as an upwelling patch fluid, then the b g h t path of the trace will

be altered resulting in a lateral displacement of the tmce fiom its centerline path Figure 5.3-3 shows

some top view images that reveal this speculated upwelling motion of the traces.

wavy shear-+e surface

Flow Direction

pattern

...........................

Figure 5.3-2 Upwelling motion of the fluid as visuafized by the moving traces frorn the side view.

Channel Mlldth=tOCm

Figure 5.3-3. Eulenan top views showing the displacement of the traces for mns 77(a) and 47(b). The sketch on the left shows the direction of flow, and the coordinate system. The viewing windows for the top view is 1 O cm O() by 10 cm (H).

The second mode of interaction between the bursts and the interface, involves the attachent

of a vortex structure at the fke d a c e , which gives rise to a spinning-tomado type fluid that stretches

in the flow direction. These attached vortices are persistent flow patterns which were shown to forrn at

the edges of the upwellings in a non-wavy f i e surface, with the main mechanism of their destruction

being through their interaction with a new upwelling pan and Banerjee (1995), Banerjee (1996),

Kumar et al. (1998)l.

From the video images taken fiom the top (and side views) with a movuig camera for a fixed

liquid Reynolds number, the existence of spiral eddies becarne evident. The spiral eddies are indicated

by the motion of three or more traces which change orientation with respect to each other as sketched

in Figures 53-4 and 5.3-5. In this hypothesized model, the trailing trace surpasses the Ieading trace(s),

while the leading trace at the end of this process becomes the trailing trace. This relative movement of

the traces occurs in a circular motion about the vertical mis, suggesting the existence of a spiral eddy

or attached vortex present at the interface. This circdar motion is speculated to represent the spiral

eddies previously shown by Kumar et al. (1998), Pan and Banerjee (19951, Banerjee (1996) and

Nagaosa and Saito (1997).

The formation of spiral eddies was also show fitom the side view images where spinning

elements are seen with a vertical axis of rotation (see Figures 5.3-6 and 53-7).

Images fiom the borescope (end view) revealed the presence of longitudinal vortex structures

near the interface with an axis of rotation in the streamwise direction. The existence of these structures

is shown in Figures 53-8a,b and 533. Although most traces usually exhibit a "kink'' shape (see

Figure 5.3-8a) expressing the sharp velocity gradient at the interface, the structures seen in Figures

Flow Flow

Figure 5.34. Sketch of the formation of spiral eddies in time (ad) as viewed from the top with a moving camem. Arrows indicate the relative motion of the traces.

wavy shear-fiee surface

Figure 5.35. Sketch indicating the attached vortices with a vertical axis of motion as shown from the side with a moving camera.

Figure 5.3-8a. End view image taken f rom the borescope, Figure 5.3-8b. End view image ofa ring iype structure near the interface w i t h a "kinkU(circ led structrtre) indicat ing the interface fbrmed In the streamwise direction (circled structure). The direction position due to the refection olfhe trace byfme surface. Direction of flow of flow is in the positive-direction (out of paper). The flow conditions is in the positive x-direction (out of page). The flow conditions are are for nin 77 with ReD=4700, h-=19.3, a=1,98 mm, Fr-0.39. for run 77 with Re,=4700, h ,,,, =19.3, a=1.98 mm, F ~ 0 . 3 9 .

Upward Mption

Figure 5.3-8c. Dipole counter-rotatinç streamwise vortices occurring between downdrafts and upwellings, as predicted by Nagaosa and Saito (1997).

Figure 53-9. (Left figure). Formation of a longitudinal vortex ring s t m ~ close to the inter/ace region as seen f iom the borescope wirh a fued amera for nul 73 (-Rë=4700, h-=19.4 mm, a1.13 mm).interface is identified by the reflection of the trace at the top of the image as indicated by the do- line. The direction of flow is in the positive x-direction (out of paper).

Figure 5.3-10 (a thmugh d). Formation of a longitudi~l vortex ocauring near the intedace for nur 17 (&=2600, h,=13.1 mm, a=1.07 mm). The sequence of images are separateci by 111 0 seconds. The direction o f f l ow i s i n t h e p o s i t i v e x - d i r e c t i o n ( o u t o f p a p e r ) .

134

5 M b and 5.3-9 are characterized by a vortex Nig oriented in the streamwise direction near the

interface region.

The formation of these vortex sanichires near the interface is also revealed in Figure 5.3- 10

(circled structure). This figure shows successive h m e s of the evolution of a strearnwise vortex

structure near the shear-fke wavy interfixe resembling the quasi-streamwise vortices f o d near the

bottom wall, suggesting the existence of rotating fluid present near the intdace with an axis of

rotation in the streamwise duection The formation of a lonpituduial vortex is speculated to be also

seen in the side view images in Figure 53-11. This figure shows succasive fiames of the evo1ution

of a spinning element onented in the longitudinal direction near a shear-fÏee wavy interface.

Figure 53-11 (a through d ) . Sequence of images illustraling the formation ofa vortex stmcture (cirele4 with mcis of rotation in the longiludinaf direcrionfor run 43 (%=3800, h,-=lï.O mm, a=1 .O2 mm). Images are separated by 1/10 seconds.

135

These observecl structures are simîlar to the ones predicted by Nagaosa and Saito (1997) and

observed h m the top of the Liquid surfke by Nash-Estephany (1998) in a non-wavy open-channel

flow as show in Figure 53-6c. The images taken with PDA techaique were not capable of capturing

the existence of a pair of cornter-rotating vortices due to the formation of single laser traces.

The existence of a single streamwise vortex as opposed to a pair as predicted by Nagaosa and

Saito (1997) could also be attnbuted to the interaction of two vortices d t i n g in the formation of one

larga longitudinal vortex as was obsemed in these experimental findings.

- - - - - --

The photochromic dye activation and image processing techniques were useful in v i d g

and characterizing the coherent structures present at both the soiid bottom wall and fiee iiquid surface.

Through a series of experiments conducted with varying liquid Reynolds numbers and wave

amplitudes, wave fiequencies, and wavelengths, it become clear that turbulent open-channel flows

with mechanically generated waves also displayed coherent structures.

The PDA technique revealed the presence of funne1 type, quasi-streamwise vox-tices near the

bottom wali which could weil represent the legs of horseshoe vortices. The presence of upwellings,

attached vortices or spiral eddies near the interface region was also apparent. These structures have

been shown to exist in non-wavy sheared and shear-fke flows pane rjee (1 W), Banerjee (1 9%),

Kaftori et al. (199411. The video sequenees and the PDA technique showed also the presence of

longitudhd vortices near the interface as predicted by Nagaosa and Saito (1997) and observed

experimentaily by Nasr-Esfahany (1 998).

The present experimental resuits and the observations fiom previous investigations can

perhaps be used to best illustrate the coherent structures in a sketch as shown in Figure 5.4-1. This

figure shows the overd mechanistic view at both boundaries in turbulent open-channel flow with

136

mechanically generated waves. It appears that low-speed streaks form near the sheared wall boundaty

as a resdt of the large shear rate at the wall IpashiOi and Banerjee (1988)l. These structures d o s e

ongin of formation is si i l l unknown, are liftecl up by the high momentun fluid passing above them in

the core flow, lesuItiog in the formation of quasi-streamwise vortices [Smith (1984), A d a r and

Smith (1987)l. These vortices were s h o w by the PDA technique to be elongated in the fl ow direction

resembling a hockey stick (single vortex) shape near the wall wead and Bandyopadhyay (1 98 l)] with

thek legs inclinecl at about 20' angle and their heads at approximately 45' from the bottom wall

[Rashidi (1997), Black (196811. These vortices tend to grow over a certain distance fiom the w d and

start to oscillate and interact with the higher rnomentum fluid above hem, ejecting the fluid away

fiom the wall. The ejected fluid nom the bottom w d reaches the interface as an "upwelling" or

"splatting" fluid patches that transport low momentum fluid fiom the wall towards the interface. The

upwelhg or the uplifted fluid fds back towards the wall as a "downdraft current" [Kumar et al.

(1998), Banerjee (1996), Pan and Banejee (1995)]. At the edges of these upwellings, spiral eddies are

formed which are persistent flow structures having their axis of rotation in the vertical axis [Kumar et

al. (1998)l.

This series of turbulence interactions, from their burst formation and travel towards the

interface, appears to characterize turbulent open-channel fiows with rnechanically generated waves, in

the same mamer as observed in non-wavy flows. The only ciifference is that the fkquency of

occurrence of these events is reduced by the presence of mechanically generated sudace waves as it

was previously discussed in Cbapter 4. It is interesting to note that the same turbulent events govem

open-channe1 flows with and without waves, however, the presence of surface waves is considered to

affect the transport processes at the interface, not directly, but by the modification of the near wall

turbulence generation.

Figure 5.4-1. Conceptual mode1 of the burst-interface interactions [modification from Rashidi, 19971

Wave-turbulence interactions in turbulent open-channel flows have been studied. A series of

experiments were conducted over a wide range of wave frequencies, amplitudes and wavelengths to

study the effect of mechanicdly generated waves on turbulence. Major conclusions and

recommendations for improvements are given in following sections.

A turbulent, horizontal open-channel flow with mechanically generated waves present at the

fiee surface was investigated experimentally over a wide range of moderate Reynolds numbers, wave

amplitudes and wave fiequencies. This was accomplished through the use of photochromic dye

activation and image processing techniques that enabled quantitative as well as qualitative evaluations

of the prescribed flow. Turbulence characteristics such as turbulence intensities and higher order

statistics were obtained through the measurernents of simultaneous velocity fields and local liquid

height variations. The visual investigation gave invaluable information on qualitative aspects of

turbulence that helped in the identification and description of coherent structures.

The main fïndings of the present work are s m a r i z e d below:

(a) The PDA technique yielded velocity profile data in good agreement with the law of the wall in

wavy open-channel flows in the turbulent core region (15<y+q0). In the interface region, the

results failed to match the law of the wall, while they were under-predicted by the correlation in

the wall region (0<~+40) (section 45.2).

139

(b) The presence of waves resulted in a relatively flat velocity profile in a signifiant portion of the

Liquid depth indicating that the waves have a m g effect on the flowing liquid (section 4.5.1).

(c) Investigation of the streamwise turbulence intensities revealed that imposed waves result in a

decrease in the streamise turbulent intensities in the wall region (as compared to non-wavy and

low amplitude wave flows). An ovemll suppression of the streamwise turbulence intensities at the

wall region (not interface) was observed with increasing wave amplitude and fiequency.

Nonetheless, the presence of waves was observed to cause in general an increase in the velocity

fluctuations near the interface region for y,/h values of up to 0.90 (section 4.6).

(d) Detailed investigations of the \val1 turbulent events through visual detection methods revealed that

the fiequency of bursts was reduced significantiy by the presence of waves (section 4.8.3). This

decrease in ejection and bursting fkquencies seemed to be better correlated with increasing wave

amplitude and wave 6equency (section 4.83.1). The ejection and bursting £iequencies detected

seemed to be best scaled by the inner variables (u , ,v), and were independent of the liquid

Reynolds nurnber (sections 4.8.33 and 4.8.3.2).

(e) The range of wave periods studied was determined to be lower, higher and within the order of

ejection periods (when scaled with the inner variables). However, the introduction of waves was

seen to afFect the fiequency of wall ejections especidy for increasing wave amplitude and wave

fiequency. This effect couid not be attributed to either of those parametes individually due to the

nature of the experirnents conducted.

(f) A M e r investigation on wavy and non-wavy flows revealed that the presence of waves reduces

the lateral motion of the liquid as indicated by the reduced lateral displacement of the traces

generated on the surface. This attenuation of the RMS values of the lateral displacernent was

speculated to be related to a decrease in the Eequency of upwehgs caused by the reduction in the

bursting frequencies due to the wave action (section 4.9).

140

(g) The overall decrease in turbulence Ievels for wavy flows was amibuted to the significant decrease

in the local Reynolds nurnber under the wave trou&. The effect was greater for large amplitude

and high fiequency waves. This had a stabiliPog eEect on the flow resulting in fewer observable

burçting and ejection events (section 4.8.3.4).

(h) Flow visualization based on images taken fiom the borescope and top views in wavy flow

conditions revealed that traces travel in a straight path, retaùling their shape as opposed to non-

wavy flows where the traces readily deformed. This m e r supports the suppression of turbulence

by the waves (section 53).

(i) Flow visualkation enabled the investigation of coherent structures present at both the waU and

interface boundaries leading to a reconstruction of a mechanistic mode1 as proposed by previous

researchers (sections 5.2, 5.3 and 5.4). From the video images taken, it was detemllned that the

general qualitative aspects of the wail and interfacial turbulence structures in wavy flows are

sirnilar to those depicted for non-wavy flows under sunilar conditions.

- - -

The photochromic dye activation technique yielded good statistics and provided sufficient

information for studying the flow structures in wavy open-channel turbulent flows. Nonetheless,

refinements in the experirnental procedure are fürther possible to produce more conclusive results.

This section gives usehl recomrnendations for future investigations that shodd provide a better

understanding of the hydrodynamics of wavy, turbulent open-channel flows.

(a) The present visualkation technique does not d o w two-dimensional velocity profile

measurements. lmplementation of the Particle Image Velocirnetry (Pm in combination with the

photochromic dye activation technique could result in the determination of two-dimensional

velocity profiles without the need for estimating the vertical velocities using interpolation

techniques.

141

(b) The use of a multiple grid trace technique may allow velocity measurements at all parts of the

waves simultaneously enabling the determination of shear stresses undemeath the wave troughs

and crests. This could M e r cl- the suppression phenomenon observed in this study.

(c) To distinguish whether the suppression phenomenon can be attributed to the wave kquency or

amplitude, experiments can be conducted with waves of similar amplitude but different

fiequencies, and vice versa. This will require the irnplementation and construction of a more

sophisticated wavemaker.

(d) To predict the mass transfer and heat tramfer effects under controiled conditions by establishg a

mode1 that describes the scalar transfer across unsheared wavy interfaces by considering the

modifications caused in the ejection processes.

(e) The implementation of a numerical simulation under similar flow conditions should provide a

useful insight into the turbulence suppression phenomenon observed in this study.

(f) The development of a new image processing technique, that will acquire thousands of images

such as in Matlab's 5.0 image analysis tool kit, wili help yield better statistical data.

(g) To develop a method to quantify the results extracted fiom the borescope view. This wiil possibly

require making identifiable marks inside the test section without disturbing the flow.

(h) To impose interfacial shear and mechanical waves simultaneously to understand their effects on

the turbulence structure and scalar transport.

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Appeadix A

Calibration Curve for Voltmeter

Calibration Curve

0.50 0.55 0.60

Voltage M

Appendix A- 1

Appendix B

Viscosity of the test fluid vs. Temperature

proposed fit Temperature, T PC]

Density of the test fluid vs. Temperature

18 20

O proposed fit

22 24 26 28

Temperature, T PC]

Appendix B- l

Appendix B Fluid Properties

1 !volts M ' QL [LPM] Th, OC Tom O C v [m21s] Wavemaker index (

Appendix B-2

Appendix C Thermal Stratification

This appendix provides some calculations to show that the background l i g h ~ g used to help in photographhg the moving fluid was not intense enough to cause thermal stratification. It was assumed that the lighting source heated the side walls of the test section at 70°C. A greater temperature will have caused the acrylic to melt. Flood lights (150W) were provided along the sides of the frst 3.6-m of the test section.

Step 1- Determine the temperature increase in the buk fluid caused fiom the lighting the side wall of the test section.

x=0.02 rn The heat flux is given by:

where x is the thickness of the acrylic test section, kA is the thermal conductivity of acrylic (0.25 W/mK), and hl is the heat transfer coefficient for kerosene due to forced convection.

The heat transfer coefficient for the flowïng fluid is cdcutated using the Dittus and Boelter empirical correlation for heating fluids in fully developed turbulent flows in smooth tubes:

- where h-118 (at measured experimental temperature 22OC), ReD =4700 (highest fluid flow). Thus the heat transfer coefficient is determined as follows:

Thus, the overall heat flux can be determined fiom equation (1) as follows:

The wall temperature can be now readily be evaluated as follows:

Appendix C-1

Appendix C Thermal Stratification

Step 2. Determined the effect of thermal stratification on fiee convection.

To determine if thermal stratification cm cause naturai convection, the Grassof number evaiuated at the mean film properties is determined:

pz- 1 = 3.14 x ~ o - ~ K - ~ Tf

v 2 6 kg 2 (1.77-10- -) m2s

For fiee convection to be important, the ratio of Grassof number to Reynolds number squared must be

Thus, fiee convection is not important, since this ratio is less than 10. Thus, thermal stratification, could not have caused natural convection, and forced convection due to the flowing fluid is the driving force of momentum.

References: Holman, J.P., "Heat Transfer", 7& edition in SI units, (McGraw-Hill, 1990).

Appendix D Program for velocity determination

%%%%%%%%%0/00/0%0/00/00/00/00/00/00/00/00/0%%0/00/00/00/0%0/00/00/00/00/0%0/00/0Y00/00/0%%0/0%%0/0%0/0%0/0%%%%Y00/00/0

%function angle8.m %This program has been written to curve fit the digitked data of dye traces created in a open channel flow and to %calculate the velocity profile along the hydrodynamic data using the angle interpolation and average heights Y~techniques as described in Chapter 3 -3. %Evangelos Stamatiou, M.A.Sc. Student %Depariment of Chernical Engineering and Applied Chemistryl University of Toronto copyright March 1998 %%%%%%%%%0/o0/00/00/00/00/00/00/00/00/o%%%%0/o%Yo%%YoYo0/o0/o0/o%0/oYo%0/oYoYoYo0/o%%0/o0/o%%Yo%~oYo%Y*0/oYo

% DECLARATION OF PHYSICAL PARAMETERS USED IN THIS PROGRAM % SE Scale factor for conversion of pixels to mm [16 pixels/mm] % fk Frarne rate used to record the images [30 frames/s] % a-: Aspect ratio for fi-ame grabber card. image maybe streched %in the horizontal direction YO when captured by the üame grabber. % del: DesÏred increment for the polynornial fitted data [O. 11 % dely: Desired increment for the velocity profiles [O. 11 % den: Liquid density at specified temperature % dynvis: Dynamic viscosity at specified temperature % rei: Local Reynolds nurnber % qi: Local flow rate [LPM] % mi: WaIl shear stress based on veIocity profiles Fa] % maxi: maximum strearnwise velocity [ d s ] [i=1,2,3] % maxi: maximum vertical velocity using angle interpolation [ d s ] [i=I,2,3] % umeani: mean strearnwise velocity [m/s] [i= 1,2,3] % i=l quantity detemined using the average height calculation % i=2 quantity determined using linear velocity profile calculation % i=3 quantity determined using angle interpolation method calculation.

c Iear; clc; CIE

% DECLARATION OF PHYSICAL PARAMEMTERS USED IN PROGRAM sf-16.3; ar=0.85; fr=3 O; del=O. 1 ; dely=O. 1 ; delya=O. I ; m . 1 ; delyi=0.00 1 ; den=754.92; dynvis=O.G0 140;

% READ INDEX DATA FILE LISTING THE INPUT FILES [datidx] % The datidx file is a list of pair of files that contain the digitized data % To calculate the velocity data, a pair of digitized input trace data is needed % OUT1.IDX Lists the output files containing velocity data using mean heights % 0Un.IDX Lists the output files containing velocity data calculated using linear vertical velocity method % OUT3.IDX Lists the output files containing velocity data using angle interpolation

fid 1 =fopen('dat.idx','rt'); fid2=fopen('out 1 .idx','wtl); fid3=fopen('out2.idx','wt'); fid4=fopen('out3 .idxl,'wt'); [d,count]=fscanf(fid 1 ,'%s1,[12,inf]);

Appendix D-1


sl='Enter number of Iocal vel ( )'; s 1 =str2mat(s 1); counter=count/2; count-1iumîstr(counter); if counter<lO

s 1 (length(s 1)-2)=count(l); elseif counter<=99

s 1 (length(s 1)-3)=count(l); s 1 (length(s 1)-2)=count(2);

elseif counter>=100 s l(Iength(s 1)-3)=count(l); s 1 (length(s 1)-2)=count(2); s 1 (length(s 1)- l)=count(3);

end numiv=input(s 1); j=o; d e l c o ~ n ~ ;

% AUTOMATICALLY load the digitized data files specified by the index file [datidx] for i=l :numiv,

if i=3O+-detcount, delcount=deIcount+30; end clear pxe f ; ctear pxe2; jj=iji-1; file=d(: Jj)';

% Open the digitized data for the first trace data specified by datidx if file -O

eval(['load ',file,'-ascii']) fiIe=strrep(file,'.dat',"); eval(['datal =',file,';']); jj=jj+l; fiIe=d(:&';

% Open the second trace digitized data specified by datidx if file -=O

eval(f load ',file,'-ascii']) file=strrep(file,'.dat',"); evat(~dataS=',fite,';'J);

% Conversion of trace data to real displacernent coordinates [pixels to mm] datal=(l/sf)*datal ; data2=( 1 /sf)*data2; y 1 =data 1 (: 2); xl=ar*datal(:, 1); y2=data2(:,2); x2=ar*data2(:, 1);

% Automatically determine the best poIynomia1 fit until error between polynomial % fitted data and real data is minimized or until the poiynornial order is greater than 8th order

% Polynomial fit digitized data for the first and second traces for ij=l :length(y2)- 1,

p l=polyf~t(yl,xl,ij);

Appendix D-2


p2=polyfit(y2,x2,ij); xS~olyval@2,y2); err2=sum ((x2 f-x2). A2);

if err2-2 break;

end if ij>7

break; end end

pj (i)=ij; y I i(ibiny 1 ; y2 i(i)-m iny2; x i i=polyval@ 1,y i i(Ï)); xZi=poIyval@2,y2i(i)); enz=lelO; ez=x2i-x 1 i)^2; while ezcerrz,

emz; y 1 i(i)=y 1 i(i)-delyi; y2i(i)==2i(i)-delyi; x 1 i=poIyval@ 1 ,y 1 i(i)); x2i=polyval(p2,y2i(i)); ez~(x2i-xl QA2;

end % Determine new wall position by the extrapolating the intersected polynomial fitted traces

wall(i)=miny 1-y 1 ici); wali(i)=miny2-y2i(i);

end end

end

Use the mean value as the wall position l e . the mean distance between extrapolated % and original wall position wailm=mean(wall); wallm=rnean(wall); Save wall.out waIh -ascii; jpo;

%Polynomial fitted data again using the new wall position as the new initial coordinate for kk=l :numiv,

kk kks=nurn2str(kk); jj=jj+ 1 ; file=d(:Jj)'; if file

evd(~1oad ',file,'-ascii']) fiIename=file; file=strrep(file,'.dat',"); eval(l<data 1 =',file,';']); n 1 =abs(file); jj-Ji+l; file=d(:g)'; if file -3

eval(['load ',file,'-ascii'])

Appendix D-3

Program for velocity determination

file=strrep(fi1e,'.dat1,"); evaI(~data2=',file,';']); nZ=abs(file);

% Code to determine the time elapsed from the input file narne if n l(length(n 1)-2)-a2(length(n2)-2)

n2(length(n2)-2- I (Iength(n 1)-2); nS(length(n2)-3)== 1 (Iength(n 1 )-3); xQ(length(n2)-41-7 1 (Iength(n 1 )-4); n2(length(n2)- lw(Iengh(n2)- l)+3 ; end n=n2-n 1 ; numfi=n(Iength(n)- 1 )* 1 O+n(length(n)); vno£k(kk)=numfr; data1 =(l/sf)*datal ; dataZ=(I /sf)*data2; y 1 =data l(:,2); x 1 =ar*data 1 (:, 1); P 1 =~olyfitO. 1 ,x 1 ,pjOdc));

% The x,y coordinate point are shifted to new mean wail position waIlm y1 im=min(y 1)-wallm; x 1 im=polyval@ 1 ,y1 im); xl=[xl im;x1]; yl=Lyl irn;yl]; y2=data2(:,2); x2=ar*data2(:, 1); y2 im=min@2)-wallm; x2im=x 1 im; x2=[x2irn;x2]; y2=Ey2im;y2]; xl=xl-xlim; yl=yl-ylim; x232-X2h; ~ 2 7 2 - y 2 i m ;

clear miny 1 clear mhy2 c lear maxy 1 clear maxy2

minyl=min(yl); miny2=min(y2); maxy l =max(y 1); maxy2=max(y2);

%Determine average height and liquid deviation avg=mean([maxy 1 maxy2 3); dev=((maxy I -maxy2)/avg) * 1 00; minx l=min(xl); minx2=min(x2); rnaxxl=max(xl); maxx2=max(x2);

% polynomial fit digitized data until error between digitized data and fitted data is % minimized or until the order is greater than 8th.

for ij=l Aength(y2)- 1, pI=polyfit(yI,xl,ij); pZ=poiyfit(y2,~2,ij); fif=po~yv~(p2,y2);

Appendix D-4


e ~2=sum((x2f-x2).~2); if err2-2

break; end if ij>7

break; end

end

clear y1 f clear y2f clear x l f clear x2f

% Interpolate data from using equal increments deiy between maximum and minimum heights % Evaluate the corresponding x coordinates for each of the two traces

O h Plot the curve fitted data for trace 1 and 2. pIot(x 1 ,y 1 ,'mol,x 1 f,y 1 f,'c-',x2,y2,'mo',x2f,y2f,'c-');grid; mum2str(d(:~)o; titIe(t); axis([min([rninx 1 minx21) max([maxx i maxx2l) O max([maxy 1 rnaxy2])]); xIabeI('x [mm]'); yIabel('y [mm]'); h=legend('mo','raw','c-';fit',- 1 ); figure(2); clf;

clear y 1 a clear y2a clear x 1 a clear x2a

y l a=rniny I :delya:maxy 1 ; y2a=rniny2:delya:maxy2; x l a=poIyvaI(p 1 ,y la); ~2a=polyvaI(p2,y2a);

clear len 1 clear Ien2

len 1 =Iength(y 1 a); lenS=length(ySa);

clear theta clear x2ii clear y 1 ii clear y2ii clear xl ii

O h Determination of the maximum angle to be used for angle interpolation

Appendix D-5


dY=Y22(len~thW)>y 1 (lengthOl1)); dx=x2(length(x2))-x 1 (length(x 1)); theta=atan(dy/dx)* 1 80/pi; y 1 ü=miny 1 :delya:maxy 1 ; x 1 ii=polyval@ 1 ,y 1 ii);

% Determination of the velocity profiles using angle interpolation clear deltheta clear fi clear bi clear dope clear dyii clear error clear f clear zeta clear x2ii clear y2ii clear dxii

% Angle interpolation code summary: if len Wen2

O h Divided the angle to n equal increments based on th deltheta=theta/len 1 ; fi=O; clear x2ii ctear y2ii clear error clear xnewii clear f error-0; for i%l:Ienl,

clear error clear xnewii if F -1

x 1 ii(l)=û; XI 0-1 ii(f); xl ii(l)=û;

e trace

y2ii(f)==l ii(Q; x2ii(£)=poIyval(p2,y2ii(f));

else % Evaluate the points on the first trace % Determine interscept and point on first trace

dyii=-tan(fi*pi/l80)*x f ii(f); bi=y 1 ii(f)+dyii; sIope=(yl ii(f)-bi)/xI ii(f);

XI-lii(f); y2ii(f)==lii(f); x2ii(f)==oiyval(p2,y2ii(f));

end error=(x2ii(f)-x 10)"2;

whiIe error>O.Ol & f-=l if error>lO

dxii= 1 ; elseif erro6=10

dxii=O. 1 ; elseif error<=l & error>=O. 1

Appendix D-6


dxii4.0 1 ; elseif error<O. 1

dxii=O.OO 1; end

% Determine the point in the second trace by incrementing dx until the two point intersect. xnewii=x 1 O-dxii; y2ii(f)=slope*xnewii+bi; x2ii(f)--poIyval@2,y2ii(f)); erroid~ii(f)-xnewii)^2; x 1 =ewii;

end ~ e t a ( ~ 1 ; fi=fi+deltheta; theta*;

end

elseif len2Xen 1 deltheta=theta/ien 1 ; fi*; clear y2ii ciear x2ii clear error clear xnewii clear f error=O;

for +l:lenl, clear xnewii clear error if f - - I

X I ii(l)=O; x 1 0 3 1 $0; y2ii(f)=y 1 ii(f); x7ii(f)==olyval(p2,y2ii(f));

eIse dyii=tan(fi*pi/l8O)*xl ii(f); bi=y 1 ii(f)-dyii; slope=(yl ii(f)-bi)/x 1 ii(f); x 1 0 3 i ii(f); y2ii(f)==l ii(f); ~2ii(f)~olyval(p2,y2ii(f));

end error=(x2ii(f)-x 10)^2;

while error>O.Ol & f i l if errors 10

dxii=l; elseif enor<= IO & error>=O. 1

dxii=û. 1; elseif erroS0.l

dxii=O.O I ; end

Appendix D-7

Appendix D for velocity determination

x 1-ewii; end

zeta(f)--f~; fi=f?+delthe ta; theta*;

end

end y2ii(Iength(y2ii)+- l)=y2(length(y2)); y Z ii(length6 1 ii)+ I )=y 1 (length(y1)); x2ii(length(x2ii)+ l)=x2(length(xZ)); x 1 ii(length(x 1 ii)+ 1)- 1 (length(x 1));

% % Calculate velocities using angle interpolation %

clear yang clear xvang clear uang clear vang

yvang=y2ii-y 1 ii; xvan@ii-x 1 ii; uang=xvangl(numfi* 1000Ifi); vang=yvang&mrnfi* 100OIfr); yang=(ySii+-y 1 ii)/2; xang=(x2ii+x 1 ii)/2;

,"

% Velocity calculation based on linear vertical velocity profile Y0

clear yy2 clear xx2

for e l :length(y 1 f), YY2(ff)=Y 1 f(ff)+dy i; xx2(n)=po~yval(p21~~2(rn); dyi-dy i+ddy ;

end Y0 % Velocity calculation using linear velocity profile Y0

yvelo-=-y 1 f; xvelo==-x 1 f; u=yvelo; u=xvelo/(numfk* l000/fi); v=yvelo/(numfi* 1000lf3; yavg=yy2; xavg=xx2;

Appendix D-8


yvelo-y2f -y 1 f; xvelMf-xl f ; u=xvelo/(numfk* lOOO/f?); v=yvelo/(numfP I000/fk); y a v m 1 f ; xav-f ;

end

'Y0 % Velocity calculation using average height '!A0

nn=abs(round(avg/dely)); pdi-2-p 1 ; clear r, clear vel; clear y; foi l-1 :M+I,

y(r)=(r- 1 )*dely ; vel(r)=@olyval@diff,y(r))/(numfP 1000/fr));

end

clear yvel2 clear xvel clear yvel clear yvelang clear xvelang

if dy-=O yveI2=[yavgr -ut]; xveI=[yavg' v'] ;

elseif dy--O yveD=[yavg -u]; xvel=[yavg v] ;

end

% Determination of maximum and minimum velocities for % subscript 1: Average heights % subscript 2: Linear vertical velocity profiles % subscript 3: AngIe interpolation

umin 1 -rnax(vel); urnax 1 =min(vel);

Appendix D-9


%Plot the instantaneous veiocity data for anlge interpolation and mean height methods if d y - 4 & l en l4en .2 & mean(vang-0

subplot(I,S, I ), pIot(u,yavg);grid; title('u-cornp'); axis([min(u) max(u) 0 maxQavg)]); xlabel('u [m/sI1); yIabeI('y [mm]');

subplot( I ,5,2), plot(v,yavg):grid; titIe('v-cornp'); axis([min(v) max(v) 0 maxbavg)]); xlabelcv lin [mk]');

subplot( l,5,3), plot(uang,yang);grid; title(zmax); axis([min(uang) max(uang) 0 max(yang)l); xIabe1Cu ang [ds]'); ylabelcy [mm]');

subplot(I,5,4), plot(vang,yang):grid; title('V ang'); axis([min(vang) max(vang) 0 rnax(yang)]); xIabel('v ang [m/s]');

subplot(l,5,5), plot(vel,y,'o');grid; title(t); axis([umax 1 umin 1 O max(y)]); xlabe1Cu [m/s]'); ylabel('y [mm]');

eIseif dy=0 1 mean(vang)=û subplot(l,2,1), pIot(u,yavg);grid; title(zmax); axis([min(u) max(u) O max(yavg)]); xIabel('u [m/sJ1); y labelCy [mm]'); subplot(l,2,2), plot(vel,y,'o');grid;

title(t); axis([umax 1 umin f O maxb)]); xlabelru [ds]'); ylabelry [mm]'); end

O h Calculation of local flowrate, reynolds number, average and maximum flowrates, and wall O h shear stress for velocity profiles % subscript I=Mean heights O h subscript 2=Linear vertical velocity % subscript 3=Angle interpolation

Appendix D- 10


mean=-deIy*sum(v)/max(y avg); vmean3=-deIy*sum(vang)/max(ymg);

umaxl=-umaxl; umin l=-unin 1 ; umax2-umax2; umin2-umin2; umax3=-umax3; umin3=-umin3;

% Store results to a single matrix for each method % resuitl=all parameters for average heights % result2=all parameters for linear velocity % resuIt3=all parameters for angle interpolation

result l=[[nurnfi,O;avg,O;dev,O;q i,û;re 1 ,O;umean 1 ,O;umâu 1 ,O;tw 1 ,O];yvel]; r e s u l t 2 = [ [ n u m f i , 0 ; a v g , O ; d e v , O ; q 2 , O ; r e l 2 , ] ; resu1t3=[[numfr,0;avg2,0;dev~O;q3,0;rel3,O;ue3,O;e3,O;ad,O;vm3,O;3,O;len(xvelg),O];xveiang; yvelang];

h2='havg [mm]';

h3='hdev [mm]';

h 1 O='umean 1 [mis]'; Appendix D- 1 1


h 1 1 ='mean 2 [m/s]'; hl2='umean 3 [ds]'; h 1 3='vmeanî [ds]'; h 14='vmean3 [ds]'; h 1 5='umax 1 [mk]'; h l6='umax2 [ds]'; h 1 7='umax3 [m/s]'; h 1 8='~nax2 [ds]'; h 19='max3 [m/s]' ; h2O='Tw 1 [Pa]'; h2 1 ='Tw2 [Pa 1'; h22='Tw3 [Pa]';

h=str2mat(hl ,h2,h3,h4,h7,hIO,h i5,h20); hh=strZmat(hl,h2,h3,h5,h8,hl I,h13,hld,h18,h21); bhh=str2ma@l,h2,b3,h6,h9~lS,h14,hl7,h19,h22); tabI=[num~avg;dev;ql;re1;umean 1;urnax 1;tw 11; tab2=[numfr;avg;dev;q2;reL2;umeanl;!;vmean;umaxS;vmax;tw2] ; tab3=[numfkavg2;dev2;q3;re13;umean3;vmean3;umax3 ;vmax3;tw3]; format short;

% Store results to output files % *.out-Yelocity data based on meaa heights % *.ou2=velocity data based on linear velocity % *.ou3=velocity data based on angle interpolation

fife=strrep(filename,'.dat','.out'); @rintf(fi&,'%sW,file); if file --O

eval(['save ',file,' result 1 -asci?]); for ii= 1 :Iength(tab 1),

htab l(ii,:)=sprintfi'%s %IO.Sf ,h(ii,:),tab l(ii)); end htab 1 sprhtf('%i %6.3e8,ij,yvel(l ,2))

end

file=strrep(fiIename,'.dat1,'.ou2'); fprintf(fid3,'0/o~W,file); if file -==

eval(['save ',file,' result2 -asci?]); for ii= 1 :length(tab2),

htab2(ii,:)=sprintf('%s %IO.Sf ,hh(ii7:),tab2(ii)); end htab2 sprintf('%i %6.3e1,ij,yvelS(1 2))

end

file=strrep(fitename,'.dat','.o3'); @rintf(fid4,'%sW,file); if file -;=O

evaI(rsave ',file,' resultj -asci?]); for ii= 1 :length(tab3),

htab3(ii,:)=sprintf('%s % 1 OSf,hhh(ii,:),tab3(ii)); end htab3

Appendix D- 12

Appendix D

sprintf('%i %.3e1,ij,yve1ang(l 2)) end

end end

end fcIose('alll);

Program for velocity determination

Appendix D- 13

Appendix E Blasius Correlation

u*, [ds] ubl,,l,.* [mis] % Deviation 0.0091

- 0.0078 14.4 0.0091 0.0077 15.4 0.01 00 0.0080 20.7 0.0108' - 0.0080 26.3 0.0099 i 0.0094 ' 5.9 0.01 O4 i - 0.0094 i 9.1 0.01 06 i 0.0093 i 12.9 0.01 O6 -- 0.0094, 10.9 0.0102 - 0.0097 ' 4.6 0.0106

- - 0.0098 1 7.3 0.01 12 - - 0.0097 13.4 0.01 13. - - -- 0.0096 1 15.1 0.01061 0.01 05 i 0.4 0.01 12i 0.01 03 j 7.9

, ~verage % Deviatio 11.5

Appendix E- 1

Appendix F Program for universai velocity profiles calculation

%function uniang8 %0/0%%0/00/00/0%0/00/00/00/00/0%~00/0~00/00/00/00/0%0/0%0/00/00/00/0%0/00/0%0/00/0%%0/00/00/00/0%0/0%0/00/00/00/00/00/00/00/00/00/0Y0~0%

%This program has been written to calculate the mean streamwise and vertical velocity fiom the angle interpolation %technique as well as to determine the wall fiction velocity and universal velocity profile. %Evangelos Stamatiou, M.A.Sc. Student %Department of Chernical Engineering and AppIied Chemistry, University of Toronto copyright March 1998 %0/0%%%%%%%%%0/0%%%%%0/00/00/0%%0/0%%%%0/0%0/0%%%0/0%%%%0/0%%%%%0/0~0%%0/0%~0~0%%Y0%

% DECLARATION OF PHYSICAL PARAMETERS USED IN THIS PROGRAM % delp: Desired increment for the polynomial fitted data % dely: Desired increment for the velocity profiles [O. I] % den: Liquid density at specified temperature % dynvis: Dynamic viscosity at specified temperature % rei: Local Reynolds number % nurnfr: number of h e s % 42: Local fïow rate &Pw % tw2: Wall shear stress based on velocity profiles Pa] % umax2: maximum streamwise velocity [mk] % max: maximum vertical velocity u s h g angle interpolation [m/s] % umean2: mean streamwise velocity [m/s] % vmean: mean vertical velocib using angle interpolation [m/s] % avg average liquid height [mm] % ycmax: interpolated liquid height fkorn about 100 liquid heights. % Umeanz: Average velocity profile obtained fkom about 100 instantaneous velocity profiles

clear; ti=clock; clc; %Declare input parameters de lyp= 1 ; den=754.92; dynvis=0.00 140; kinvis=dynvis/den;

% Read the output angle interpolated velocity data files created in angle8.m program £id 1 =fopen('out3 .idx','rt'); fid2=fopen('avg3 .out','w'); [o,count]=fscanf(fid 1 ,'%s1,[12,infJ); s='Enter number of local vel ( ) '; s=str2mat(s); counr;numSstr(çount); s(length(s)-3)=count(l); s(length(s)-2)=count(2); numiv=input(s); @rintf(fid2,'%sW,'filename numfr avgrn devm qm re2m umean2m vrneanm umax2m vmaxm twh ' ) ; f i w e ( l 1; clf;

%Read input files according to specified format. %First 12 rows of each input file contain the average quantities such as Iiquid height, number of frame etc. %Velocity profiles are contained in each file after the 12" row for ii= 1 :numiv,

file=o(:,ii)'; if file -=O

eval(['load ',file,'-ascii']) fiIe=strrep(file,'.ou3',");

Appendix F-1

Appendix F Program for universal vetocity profiles calculation

eval(['o3=',file,';']); xlength(ii)=ou3(11,1); ylength(ii)=xlength(ii)+l2; I(ii)=length(ou3Qlength(ii):length(ou3), 1)');

end end

for ji=l :numiv, file=o(:Ji)';

if file -O evaI(r1oad ', file,'-ascii']) file=strrep(file,'.o3',"); eval(~o3=',file,';'l); if l(ji)=dimmax,

loi); y IengthCji); j i; pax(: , 1)=0~3(ylength(ji):length(ou3), 1);

end end

end

%Calculate average quantities form average \. alues of instantaneous velocity data for i= 1 :numiv,

file=o(:,i)'; if file -O

eval(['load ',file,'-ascii']) file=strrep(file,'.ou3',"); eval(['o3=',file,';']); n(i,:)=abs(file); numfr(i)=ou3 ( 1,1); avg(i)=ou3(2,1); dev(i)=ou3(3,1); q2(i)=ou3(4, I ); re12(i)=ou3 (5, I ); umean2(i)=ou3 (6,I); mean(i)=ou3(7,1); umax2(i)=ou3(8,1); vmax(i)=ou3(9,1); tw2(i)=ou3(1 O, 1); y(:,i)=o3&lengtb(i):length(o3), 1); u(:,i)=ou3(ylength(i):length(ou3),2); v(:,i)=ou3(12:xlength(i),2); yz(1 :length(y(:,i)),i)=y(:,i); uz(1 :tength(u(:,i)),i)=u(:,i); vz(1 :Iength(v(:,i)),i)==:,i); I(i)=Iength@(:,i));

Appendix F-2

Appendix F Program for universal velocity profiles calculation

%Output the instantaneous quantities in avg3.out data file fprintf(fid2,'%s %6.X %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6.3f %6 .3fW,... o(:,i)',n-~fi(i),avg(i),dev(i),q2(i),re12(i),umean2(i),vmean(i),wn~(i),max(i),tw2(i)); ustar(i)=sqrt(tw2(i)/den); clear y; ciear u; clear v;

end end n=[n( 1 ,:);n] ; ncol=size(n,2); for j= 1 :numiv,

if n(j+ 1 pcol-2)-=n(j,ncol-2) ndifiQ, l)=n(j+l ,mol- 1)-n(j,ncol- 1)+3; ndiff0',.2)-li~+I ,ncol)-n(j,ncol);

else n d i m , l-(j+l ,mol-1)-n(j,ncol- 1); ndiff(j,2)=nQ+l ,ncoI)-n(j,ncoI);

end fniurn(i)=ndiff(i, 1 )* 1 O+ndiff(j,2);

end hum-*um+numfr./2; hum-llrium-hum(I ); times=cumsum(frnum/3 O); timern=îirnes/60;

%Interpolate instantaneous velocities and height to similar equal increments and determine the %average mean streamwise and vertical velocity profiles ycmin-in(rnin(yz)); y cmax=rnax(max(yz)); incr-ycmax/length(ymax); ycmax=ycmio:incr:ycmax;

for iii=l :numiv, file=o(:,iii)'; if file -=O

eval(['load ',file,'-ascii']) file=strrep(file,'.ou3',"); eval(['ou3=',file,';']); y(:,iii)=ou3&length(iii):Iength(ou3), 1); u(:,iii)=ou3(ylength(iii):Iength(ou3),2); ymin=min(min(y)); m-y=max(maxOl)); yc=ymin:incr:maxxy; lenyc=Iengthbc); Il(iii)=lenyc; clear y clear u

end end

for p= 1 :numiv,

Appendix F-3

Appendix F Program for universal veiocity profiles calculation

file=o(:,p)'; if fiIe 4 0

evai(r1oad ',file,'-ascii']) file=strrep(file,'.ou3 ',"); evd(rou3=',fiie,';']); y(:yp)=03~length@):length(03), 1); u(:,p)=ou3~iength@):length(ou3),2); ymin=min(min(y)); m=y=max(max&)); yc=ymin: incr:rnaxxy; ycz(1 :length(yc),p)==c'; ui=spline(y(:, p),u(:,p), yc); G(1: l ength(~i ) ,p~i ' ; clear y dear u clear ui clear yc clear p i n clear rnaxxy

end end

OhInterpolated mean streamwise velocity for Üj=l :maxcommon

[ro,si,v]=find(uizQü,:)); a=mean(v); Umeariz(üj)=a;

end

you+[ycrnaxf uiz Urneand; Save velangout yout -ascii;

%plot the mean velocity profile data plot(Urneanz,ycrnax,'go');grid on; title('loca1 and mean velocity'); xlabeltu [m/sl1); y labelfy [mm]'); h=legend('y','instantaneous','go','average',- 1 ); %axes@); figure(2); clf;

Appendix F-4


tw2m=mean(tw2); %Output the average quantities on avg3.out data file fprintf(fid2,'%s %Il .3f %6.3f %6.X %6.3f %6.3f %6.3f %6.3f %6.X %6.3f %6.3fW7 ... 1average1,num~,avgrn,devm,qm,re2m,umean2m,vmeanm,umax2m,vmaxm,tw2m);

% Universal Vetocity calculation load wall-out -ascii; ycom=ycmaxl; %Exclude the extrapolated data from the universal velocity profile calculation idex=fimd(ycom<wall); ycom=ycom(length(idex)+ 1 : length(ycom)); Umeari~=Umeanz(length(idex)-tI :length(Umeanz)); u-((length(idex)+ 1 :length(uiz)),:);

%Dechration of the theoretical curve to fit the resuIts yp= 1 :delyp:5; uP==; yuvd=ypl; Uuvd=Up1 ; yp=30:delyp:200; Up=5.287+1/0.4 12* log(yp); yuvd=U.Uvd;yp1]; Uuvd=[Uuvd;Upl] ; figure(5); clf;

%Iterate until the results collapse to the theoretical curve npass=1; nie70; nr=70; res=0.6; red=0.95; %Initially guess of the friction velocity determined from the average shear stress. Ustaq~sqrt(tw2dden); regs=O.OS; regd=regs; test= 1 e 10; testp=test; for ijk= 1 :npass,

ij k for kk=l :nit,

for ij= 1 :nr, m=rand; ran=rn-0.5; if ij=l

ran=O; end

% Incrernent U* Ustarn=Ustarp+ran*regd; if Ustarn>O

ypIusn=0.00 1 *ycom*Ustam/kinvis; Uplusn=Umeanz/Ustarn; Ugrad=gradient(Uplusn,yplusn); for j k= 1 :length(yplusn),

Appendix F-5


%fit the data in the wall region if yplusn(jk)<5

e(ik)=(UpIusn(jk)-ypl~sn(jk))~2; O h f i t the data in the turbulent core region

elseif yplusn(jk)>29.99999999999999 e(jk)=(vpIusn(jk)-5.287-log(yplusn(jk))/O4 12)"2;

else end

end

end clear e;

end end regd=regd*red; if testctestp

testp-test; Ustarp=Ustarf',

end end regs=regs*res; regd-regs;

end

Ublasius=O. 167*umean2m*(re2m"(-O. 1 25)); Ustar-out=vstarf Ublasius umean2m re2mJV; Save ustar-out Ustarout -ascii;

% Output parameters norrnalized by the fitted friction velocity twf=UstarfA2 * den; ypIusfW.00 1 *ycom*UstarfXinvis; Uplusf=Umeanz/Ustarf.,

uplusi=uiz/i]starf; yplusi=(0.00 1 *ycom*Ustarf)/kinvis; univi=Cyp tusi uplusi];

if Ienunivm>lentheo theo=[theo;zeros(Iength(univm)-length(theo),2)];

elseif lentheo>lenunivm univm=[univm;zeros(length(theo)-length(~~ivm),2)];

end uvelm=[theo univm univi]; Save univel.out uvelrn -ascii;

%plot the fitted and theoretical results on the screen semilogx(yplusf,Uplusf,'ro');grid on; axis([l max(yp1usf) 0 max(Uplusf)]);

Appendix F-6

Appendix F

hold on; semiIogx(yuvd,Uuvd,'y-');grid on; title('universa1 velocity'); xiabel('1ogy-i.'); ylabel('u+'); h=legend('y-','law of the waII','ro','experiment',- 1); axes@); tf+etime(clock,ti)/60; fclose('a1l'); sprintf('e1apsed time: %6.2f %s',tf,'min')

Program for universal velocity profiles calculation

Appendix F-7

Appendix G Power spectra for wave 1

. . . . . . . ... ....... ;.* i...:..:...... . . . . ...-. .......... - .' . .

: : i : i Peak Power @ ai89 .Hz . . . . . . . . . . . . . . . . . . . . . . . . . .............. ....... : ..... ;...:..i..:-.:.- : ............ i. \;. : .. . . . - . . . -1 . . . . . . . . . .

0.01 o. 1 1

Frequency [Hz]

Peak Power @ 0.64 Hz II

0.01 0.1 1

Frequency [Hz]

1 - Péak P&ër @ 0.83 Hz - - -

Frequency [Hz] Frequency [Hz]

Appendix G-1


0.01 0.1 1 0.0 1 o. 1 Frequency [Hz] Frequency [Hz]

Frequency [Hz]

Appendix G-2

Frequency [Hz]


0.01 o. 1 1

Frequency [Hz]

0.01 0.1 1

Frequency [Hz]

Peak Power @ 1 -08 Hz . . . . . . . . . . . .

Frequency [Hz]

0.01 o. 1 Frequency [Hz]

Appendix G-3

Appendix H Skewness and flatness factors

Skewness and Flatness factors for runs 1 1 to 17 plotted as a fiinction of dimensioneless distance fiom the bottom wall, yJh. Dotted and solid lines represent the mean values for the skewness and flatness, respectively.

Appendix H- 1

Appendix H Skewness and flatness factors

Skewness and Flatness factors for runs 41 to 47 plotted as a fiinetion of dimensioneless distance from the bottom w d , y+. Dotted and solid lines represent the mean values for the skewness and flatness, respectively.

Appendix H-2

Appendix I Instantaneous streamwise velocity profiles

15 14 -.1 Runl l-Wavei

TeD=2600 or Kë=ôlO hm=13.4 mm u,=0.11 rnk u',=0.009 m/s Wave Amplitude=0.63 mm Waveleng th=32 cm Wave Frequency=0.78 Hz

Streamwise Velocities Ui [ml -

0 Mean Streamwise Velocity Profile - - - - - - l nstantaneous Velocity profiles

Streamwise VeIocities ui [m/ç]

a Mean Streamwise Velocity Profile ----.-- lnstantaneous Velocity profiles

Appendix I- 1

Appendix 1 Instantaneous strearnwise velocity profiles

Streamwise Velocities uj

Mean Streamwise Velocity Profile -.--.-- lnstantaneous Velocity profiles

Streamwise Velocities ui [ d s ] 1 1

1 Mean Sbeamwise Velocity Profile 1 ---.-- Instantaneous Velocity profiIes

Appendix 1-2

Stearnwise Velocities Ui [WS]

O Mean Streamwise Velocity Profile Instantaneous Velocity profiles

Stearnwise Velocities u,- [Ws]

Mean Streamwise Velocity -.-sa- lnstantaneous Velocity profiles

Appendix 1-3

Append

20

18

16

- 14 E E - 12 r E - 10 *- al x P, 8 3 LT ï 6

4

2

O

Streamwise Velocities u, [mkj

1 Mean Sbearnwise Velocity --.-..- lnstantaneous Velocities

Streamwise Velocities o, [mls]

lnstantaneous Velocities

Appendix 1-4

Appendix I instantaneous streamwise veIocity profiles

I I I r 8 1 I I I 1 1 I L

Run51 -Wave?

KD=41 00 orGh=1400 h-=17.9 mm uy=0.14 mls u w=o.o10 m/ç

Wave AmpIitude=0.63 mn Wavelength=31 cm Wave Frequency=0.78 Hz

Streamwise Velocity u, [rnls]

Mean Streamwise Velocity .--.-. lnstantaneous Velocities

a . . . , . -

Run53-Wave3

Re,=4lOO or Eh=1400 h-=17.7 mm u,=0.14 rnls u w=o.O1l m/s Wave Amplitude=0.94 mm Wavelength=51 cm Wave Frequency=0.88 Hz

Streamwise Velocities ui [ d s ]

Mean Streamwise Velocity . -. - - - lnstantaneous Velocities

Appendix 1-5

Appendix 1 Instantaneous streamwise velocity profiles

0.00 0.05 O. 10 0.1 5 0.20 0.25

Streamwise Velocities u, [mls]

Mean Streamwise Velocity - - - - - - lnstantaneous Velocities

Streamwise Velocities U i [mis]

1 0 Mean Streamwise Velocity .-.a.. lnstantaneous Velocities

Appendix 1-6

Appendix 1 Instantaneous streamwise veIocity profiles

Streamwise Velocities u, [mls] Mean Streamwise Velocity Instantaneous Velocities

- Reo=4700 orreh=l 600 h,,,=19.4 mm u,=O. 155 mls

u w=O.O1 12 mis Wave Amplitude=l.l3 mm Wavelength=39 cm Wave Frequency=0.89 Hz

Streamwise Velocities ui [mis]

Mean Streamwise Velocity .--..- lnstantaneous Velocities

Appendix 1-7

Appendix 1 Instantaneous strearnwise velocity profiles

Run75- Wave5 - Re,=4700 or Ke,=l6OO hm=19.0 mm u,=0.16 rn/s U~~=O.OI 4 mis Wave Amplitude=I -59 mm Wavelength=42 cm Wave Frequency=l . 1 O Hz

0.00 0.05 0.10 0.1 5 0.20

Strearnwise Velocities ui [m/s]

1 Mean Streamwire Velocity ----.. lnstantaneous Velocity profiles

Appendix 1-8

Appendix J Dimensionless velocity profiles

Runl l-Wavel

q = 2 6 0 0 or K%=8 1 O b,=13.4 mm u,=U. 1 1 m/s u*,=0.009 m/s Wave Amplitude--0.63 mm Wave Frequency=0.78 Hz

.-- O !

1 10 100

Average Universal Velocity Profile Instantaneous Univeral Velocity ProfiIes Theoretical Results

i u,=O.I 1 m/s u*,=û.O09 rn/s Wave Amplitude=0.72 mm

15 . Wave Frequency0.86 Hz

Average Universal Velocity Profile -.-..-.. Instantaneous Univeral Velocity Profiles - Theoretical Results

Appendix J- 1

Appendix J Dirnensionless velocity profiles

4 Average Universal Velocity Profile .-.*--.- Instantaneous Univeral Velocity Profiles - Theoretical Results

1 4 Average Universal Velocity Profile I

-

........ 1 Instantaoeous Univeral Velocity Profiles - Theoretical Results

Run 17-Wave'l

%=2600 orTë=8 10

Appendix J-2

* . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... .. 1 k,=13.l mm

..- .--. ' . . - u,=O. 14 m/s

- - Wave Amplitude=l -07 mm .... - Wave Frequency= 1.1 9 Hz

......................... ......,.. ....... ...-. .. . . . . . . . . ,.. , .. ,.

__f.__I.---*-- . .

Appendix J Dimensiontess velocity profiles

Run41-Wavel

KE3800 orRZë=1300 km= 17.2 mm ~ ~ 4 . 1 3 mis u*,=O.OlO rn/s Wave AmpIitude=0.62 mm Wave FrequencH.77 Hz

1 10 LOO

1 4 Average Universal Veloeiiy Profile 1 -.-..-.- Instantaneous Univeral Velocity Profiles - Theoretical ResuIts

1 IO 100

Y+

Average Universal Velocity Profile ........ Instantaneous Univeral Velocity Profiles

Theoretical Results

Appendix 5-3

Appendix J Dhensionless velocity profiles

- - ReD=3700 or IGë= 1300 * _ _ .-.- _ - - - -. . . . . .. . - . . -. - - . .... .. ...... ....... .---. .. ...- ... .--.. . . .. - ... - - - - h,,=I7.2 mm a-_.

--. - ~ ~ 4 . 1 4 m/s -. . . -.. . - : .. u*,=O.O 1 1 m/s : Wave Amplitude= 1.17 mm - Wave Frequency=0.98 Hz .

A Average Universal Velocity Profile -.-..m.- Instantaneous Univeral Velocity ProfiIes - Theoretical Results

Average Universal Velocity Profile --....-- Instantaneous Univeral Velocity Profiles

Theoretical Results

Appendix 5-4

Appendix J Dimensionless velocity profiIes

A Average Universal Velocity Profile Instantaneous Univeral Velocity Profiles - Theoretical Results

1 1 O 100

Y+

Average Universal Velocity Profile ........ Instantaneous Univeral Velocity Profiles - Theoretical Results

Appendix J-5

Appendix J

Run55-Wave5

&=4 100 or K%=l4OO L = 1 7 . 8 mm ~ ~ 4 . 1 5 m / s * u @.O11 m/s Wave Amplitude= 1 -4 1 mm Wave Frequency= 1 -03 Hz


I

- -

A Average Universal Velocily Profile ..--.-.- Instantaneous Univeral Velocity Profiles - Theoretical Results

A Average Universal Velocity Profile ..-----. Instantaneous Univeral Velocity Profiles - Theoretical Results

Appendix 5-6

Appendix J

25 - - Run71-Wavel

&=4700 or Kë=l6OO 20 -- Luia=l9-0 mm -

- u,=O.ISm/s - u*,=O.O11 m/s - + 15 -.- Wave Amplitude=0.59 mm 3 - Wave Frequency=0.78 Hz

-


1

A Average Universal Velocity Profile Instantaneous UniveraI Velocity Profiles - Theoretical Results

Average Universal Velocity Profile Instantaneous Univeral Velocity Profiles

Appendix J-7

Appendix J Dirnensionless velocity profiles

A Average Universal Velocity Profile . . . . . . . . Instantaneous Univeral Velocity Profiles - Theoretical Results

J u,=O. 1 7 m/s ua,=O.O 12 m/s

15 . Wave Amditude=I -98 mm

Average Universal Velocity Profile . . - . . . . . Instantaneous Univeral Velocity Profiles - Theoretical Results

Appendix J-8

Appendix K Velocity histories

0.06 -- ' Moving Average 0.04

O 5 10 15 20 25 30 35 40 45 time [SI

O 5 10 15 20 25 30 35 40 45 tirne [s]

0.20 0.1 8 1 --O- y*=3OD or y 5 . 9 mm

0.04 1 I O 5 1 O 15 20 25 30 35 40 45

tirne [s]

0.16 1 -- Movïng Average . 1

time fsl

time [s]

Velocity History Runll : Re,=2600, Fr=O.31, u",=0.009 m/s

Appendix K-1


. + yC=60.0 ar y=11.7 mm

- -- Moving Average I

0.04+ - . q

O 5 10 15 20 25 30 35 t h e [s]

0.20 - 0.18 - - .

0.10 - 0.08 - 0.06 - y+= 50.0 y=9.7 mm -- 0.04 . Moving ~ v e n g e

O 5 1 O 15 20 25 30 35 tirne [s]

.. .

- - .

+ y*=30.0 a r y=5.8 mm -- Moving Average

15 time [s]

0.20 0.1 8 0.16 0.14 0.12 0.1 O 0.08 0.05 0.04

O 5 10 15 20 25 30 35 time [s]

12 O 5 10 15 20 25 30 35

time [s]

Velocity Hiotory Run13:~eD=2500, F~0 .29 , u',=0.009 mls.

Appendix K-2


time [s]

1 t 1

--O- yc=60,0 or j-10.6 mm - - -- Movîng Average

O 5 10 15 20 25 30 time [s]

1

+ y'=30.0 or jl=5.3 mm

t -- Moving Average I 15

time [SI

15

time [s]

time [s]

Velocity History Runl 5: Re,=2600. Fr=O.3Il u*,=0.010 mls

Appendix K-3


- - - . - . - + y*=60.0 or y=lO3 mm -- Moving Average

time [s] 7 1

+ - . y'=-50.0 or y=8.6 mm -- Mpving Average

I I

O 5 1 O 15 20 25 30 time [s]

--

-- - - -- - - - - - - . - -- -. --- - O 5 1 O 15 20 25 30

time [d

, . O 5 10 15

time [s]

Velocity History Runl7: Ü%=2600, F r 3 . 3 1, ut,=O.O 1 1 m/s.

Appendix K-4


.-- Moving Average 1

time [s]

1 - R - - . - . - - - - I

time [s] 1

- + y?=30.Oary=5.6mm -- Moving Average l

20 25 30

lime [s]

- -e- -y'=20.0 oc ~ 3 . 7 mm - - - . . Moving Average

20 25 30 time [s]

- -W. hm? 7.2 mm. a=0:62.mrn, f,=0.77 Hz

time [s]

Velocity History Run41: Ee,=3800. Fr=0.33, u>=O.OlO mls

Appendix K-5

Appendix K Veiocity histones

026 , 1

024 + 1 022 -

0.12 - . . 0.10 - - -

0.08 . . . 0.06 - -- Moving Average 0.04 -

O 5 10 15 20 25 30 35 40 45 tirne [s]

0.26 - 0.24 -

0.08 - y+= 701) or ; = l u mm 0.06 - -- Moving Average

time [s]

time [s]

Lime [s]

. - . - - - . . - . .- . . . . -

O 5 1 O 15 20 25

tirne [s]

Velocity History Run43: Fe,=3800. Fr=0.34, ~ *~=0 .010 rnls

Appendix K-6


I

O 5 1 O 15 20 25 30 35 40 45 time [SI

-+ y+= 70.0 aty=12.0 mm - - Moving Average

O 5 10 15 20 25 30 35 40 45 time [sj

W . " . .

O 5 1 O 15 20 25 30 35 40 45 time [s]

tirne [s] 19

... -- h,,=1 7.2 mm, a=?.17 mm, f-=O.û8 Hz -/

time [s]

Velocity Histow Run45: &=3700. Fr=0.33. uW=O.Oll m/s

Appendix K-7

Appendix K Vefocity histories

time [s] 0.28 , l

0.24 - -C-y+yï~ .~ or y127 mm - -- Mwing Average

time [s]

time [s]

- --

20 25 time [s]

20 - - - - -- h-=17.9 mm, a=0.63 mm, f-4-78 Hz - 19 ;

time [s]

Velocity History ~un51: E,=4 1 00, Fr=0.34. ~ * ~ = 0 . 0 10 m/s

Appendix K-8

Appendix K VeIocity histories

. + y+=8~.l) or y l 3 . 2 mm

0.06 . - 0.04 - -- Moving Average 0.02 7

O 5 10 15 20 25 30 35 40 time [s]

0.24 -

- + 70.0 or y=11.5 mm 0.06 - 0.04 - -- Moving Average 0.02 1 , . .

O 5 10 15 20 25 30 35 40 tirne [s]

0.24 1

0.22 . -. - - . - . .

O 5 10 15 20 25 30 35 40 time [s]

time [s]

time [sj

Velocity Ais tory ~un55:=,,=4 1 00, Fr4.34 , ut,=O.O 11 m/s

Appendix K-9


1

. . . . . - yc=80.0 or ~ 1 4 . 0 mm . . . . . . . -- Moving Average

1 >

O 5 10 15 20 25 30 35 40 45 time [s]

1 1

4 . . 1

O 5 1 O 15 20 25 30 35 40 45 time [s]

20 25

time [s]

y'=20-0 or y=35 mm Moving Average .

time [SI

time [s]

Velocity History Run71: iiëD=4700. Fr=0.37, U * ~ = O . O ~ 1 m k

Appendix K- 10

Appendix K Vefocity histories

0.08 - + yt=80.~ or y-13.2 rnrn -- Moving Average

0.04 O 1 O 20 30 40 50

time [s] 0.24 , i

- . . . . .

-- Moving Average 1

0.04 O 5 10 15 20 25 30 35 40 45 50

time [s] 024 7-

I -- Moving Average 0.04

O 5 10 15 20 25 30 35 40 45 50

tirne [s]

y'=20.0 or y=3.3 mni Moving Average

time [s]

time [SI Velocity History ~un73~~e,=4700, Fr=0.36. ~ * ~ = 0 . 0 1 1 mls

Appendix K- 1 1


0.08 . + yc=30 or y4.7 mm 0.06 - , , Moving Average 0.04 4

O 5 10 15 20 25 30 35 tirne Es]

O 5 10 15 20 25 30 35 tirne [s]

0.10 - 0.08 - 0.06 -

Moving Average

-O- y+= 70.0 or y=10.9 mm - - . -- -

-- Moving Average

O 5 1 O 15 20 25 30 35 time [s]

0.04 -. O 5 1 O j5 time [SI 20 25 30 35

time [s]

Velocity History ~ u n 7 7 : ~ , = 4 7 0 0 , Fr4.36, uC,=0.0 12 m/s

Appendix K- 12

INFORMATlON TO USERS - TSpace

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