IMPELLER POWER DRAW ACROSS THE FULL REYNOLDS ...

IMPELLER POWER DRAW

ACROSS THE FULL REYNOLDS NUMBER SPECTRUM

Thesis

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for

The Degree of

Master of Science in Chemical Engineering

By

Zheng Ma

Dayton, OH

August, 2014

ii

IMPELLER POWER DRAW


Name: Ma, Zheng

APPROVED BY:

______________________ ________________________

Kevin J. Myers, D.Sc., P.E. Eric E. Janz, P.E.

Advisory Committee Chairman Research Advisor

Research Advisor & Professor Chemineer Research &

Chemical & Materials Engineering Development Manager

NOV-Process & Flow

Technologies

________________________

Robert J. Wilkens, Ph.D., P.E.

Committee Member & Professor

Chemical & Materials Engineering

_______________________ ___________________________

John G. Weber, Ph.D. Eddy M. Rojas, Ph.D., M.A., P.E.

Associate Dean Dean, School of Engineering

School of Engineering

iii

ABSTRACT

IMPELLER POWER DRAW


Name: Ma, Zheng

University of Dayton

Research Advisors: Dr. Kevin J. Myers

Eric E. Janz

The objective of this work is to gain information that could be used to design full

scale mixing systems, and also could develop a design guide that can provide a reliable

prediction of the power draw of different types of impellers. To achieve this goal, the

power number behavior，including three operation regimes, the limits of the operation

regimes, and the effect of baffling on power number，was compared across the full

Reynolds number spectrum for Newtonian fluids in a laboratory-scale agitator. Six

industrially significant impellers were tested, including three radial flow impellers: D-6,

CD-6, and S-4, and also three axial flow impellers: P-4, SC-3, and HE-3.

Results in laminar regime indicate that baffling has no effect on power number in

this operation regime. There is an inversely proportional relationship between power

number and Reynolds number. The upper limit for this operation regime should be lower

than 10, the limit commonly noted in the literature. The product of power number and

iv

Reynolds number in this particular regime is approximately proportional to the number of

blades for these six impellers; however, other shape factors that were not included in this

study also contribute to it.

In turbulent operation, baffling has a significant effect on power number: the

power number for most impellers remains relatively constant in the baffled configuration

while that for unbaffled configuration decreases with increasing Reynolds number. The

impeller blade number is not the dominant factor that affects power number in this

regime. Two hydrofoil impellers, SC-3 and HE-3, exhibit much lower power numbers

when compared with the other impellers. Additionally, the impellers with higher power

numbers in baffled tank tend to have lower ratios between unbaffled power number and

average baffled power number when comparing at same Reynolds number.

No difference between two configurations, baffled and unbaffled, exists at low

Reynolds number end of transitional regime, and the difference starts at intermediate

Reynolds number and increases with an increase of Reynolds number. In the baffled

configuration, four out of six impellers exhibit a minimum power number. In the

unbaffled configuration, power numbers drop with increasing Reynolds number

throughout the entire transitional regime for all impellers. The ratio of unbaffled to

turbulent average power number for the six impellers retains a consistent order through

the entire Reynolds number range with two high efficiency impellers having the highest

ratio, then pitched blade impeller, and three radial flow impellers having the lowest ratios.

v

ACKNOWLEDGEMENTS

I would like to thank Dr. Kevin Myers for all the help he has given throughout the

past three years. Without his encouragement and guidance I would have never made it

this far. Dr. Myers gave me a great opportunity to pick up chemical engineering from

basics three years ago. He accepted me to work on this research so I can complete the

degree with a written thesis and get prepared for future study. I will be thankful to him

for his support and benefactions forever. I also want to thank Eric Janz who offered me

this opportunity to be part of the team and gave me the access to carry out this

experiment in the Chemineer laboratory. I want to express my thankfulness to Prof.

Robert Wilkens for being my committee member and providing constructive feedback on

my thesis. I would also like to thank Erin Duff, Robert Strong, and Michael Adams for

their support on both the laboratory measurements and my daily life.

I want to acknowledge everyone else who has offered support: my family for their

continuous love; my boyfriend, Zhengchao, as he has tried his best to take care of me and

been supportive all the way through; Jin, my best friend here in UD, for all the

suggestions and her willingness to share my joys and sorrows; Jie and his wife, Jing, who

encouraged me when I had a tough time. I would have failed my study here in UD

without those people.

vi

TABLE OF CONTENTS

ABSTRACT ................................................................................................................... iii

ACKNOWLEDGEMENTS ............................................................................................ v

LIST OF FIGURES ...................................................................................................... vii

LIST OF TABLES ......................................................................................................... ix

NOMENCLATURE ...................................................................................................... xi

.................................................................................... 1 CHAPTER 1 INTRODUCTION

1.1 Background ............................................................................................... 1

1.2 Power Number and Reynolds Number...................................................... 2

1.3 Rheology ................................................................................................... 4

1.4 System Geometry ...................................................................................... 5

1.5 Objective ................................................................................................... 6

.................................... 7 CHAPTER 2 EXPERIMENTAL SETUP AND PROCEDURE

2.1 Experimental Setup ................................................................................... 7

2.2 Viscosity Measurement ............................................................................. 9

2.3 Procedure ................................................................................................. 10

............................................................. 12 CHAPTER 3 RESULTS AND DISCUSSION

CHAPTER 4 CONCLUSIONS AND RECOMMENDATIONS ................................. 42

BIBLIOGRAPHY ......................................................................................................... 46

APPENDIX: RAW AND REDUCED EXPERIMENTAL DATA .............................. 47

vii

LIST OF FIGURES

Figure 1-1: Haake viscometer data for corn syrup at different temperatures (μ [=] Pa s) .. 5

Figure 2-1: Experimental apparatus .................................................................................... 8

Figure 2-2: Readout of torque and speed from agitator ...................................................... 9

Figure 2-3: Assembled agitator shaft and impeller ............................................................. 9

Figure 3-1: D-6 low Reynolds number data ..................................................................... 13

Figure 3-2: CD-6 low Reynolds number data ................................................................... 13

Figure 3-3: S-4 low Reynolds number data ...................................................................... 14

Figure 3-4: P-4 low Reynolds number data ...................................................................... 14

Figure 3-5: SC-3 low Reynolds number data ................................................................... 15

Figure 3-6: HE-3 low Reynolds number data ................................................................... 15

Figure 3-7: Comparison of baffled low Reynolds number data ....................................... 18

Figure 3-8: D-6 high Reynolds number data .................................................................... 19

Figure 3-9: CD-6 high Reynolds number data .................................................................. 19

Figure 3-10: S-4 high Reynolds number data ................................................................... 20

Figure 3-11: P-4 high Reynolds number data ................................................................... 20

Figure 3-12: SC-3 high Reynolds number data ................................................................ 21

Figure 3-13: HE-3 high Reynolds number data ................................................................ 21

Figure 3-14: Comparison of baffled high Reynolds number data .................................... 25

Figure 3-15: Comparison of unbaffled high Reynolds number data ................................ 26

viii

Figure 3-16: D-6 transitional Reynolds number data ....................................................... 27

Figure 3-17: CD-6 transitional Reynolds number data ..................................................... 27

Figure 3-18: S-4 transitional Reynolds number data ........................................................ 28

Figure 3-19: P-4 transitional Reynolds number data ........................................................ 28

Figure 3-20: SC-3 transitional Reynolds number data ..................................................... 29

Figure 3-21: HE-3 transitional Reynolds number data ..................................................... 29

Figure 3-22: Ratio of unbaffled to baffled power numbers in transitional and turbulent

operation ........................................................................................................................... 34

Figure 3-23: Ratio of unbaffled to turbulent average power numbers in transitional and

turbulent operation ............................................................................................................ 34

Figure 3-24: Ratio of baffled to turbulent average power numbers in transitional and

turbulent operation ............................................................................................................ 35

Figure 3-25: Comparison of all baffled power number data ............................................. 38

Figure 3-26: Comparison of all unbaffled power number data ......................................... 38

Figure 3-27: Baffled and unbaffled data of D-6 for all Reynolds numbers ...................... 39

Figure 3-28: Baffled and unbaffled data of CD-6 for all Reynolds numbers ................... 39

Figure 3-29: Baffled and unbaffled data of S-4 for all Reynolds numbers ...................... 40

Figure 3-30: Baffled and unbaffled data of P-4 for all Reynolds numbers ...................... 40

Figure 3-31: Baffled and unbaffled data of SC-3 for all Reynolds numbers .................... 41

Figure 3-32: Baffled and unbaffled data of HE-3 for all Reynolds numbers ................... 41

ix

LIST OF TABLES

Table 2-1: Impellers ............................................................................................................ 8

Table 3-1: Comparison of baffled and unbaffled Newtonian fluid KL values .................. 17

Table 3-2: Highest Reynolds number for laminar operation ............................................ 17

Table 3-3: Comparison of baffled Newtonian fluid turbulent power numbers ................ 23

Table 3-4: Unbaffled to baffled power number ratios in turbulent operation ................... 23

Table 3-5: Lowest Reynolds number for turbulent power number in baffled

configuration ..................................................................................................................... 24

Table 3-6: Power number comparison .............................................................................. 25

Table 3-7: Reynolds number range with baffled NP lower than average baffled

turbulent Np ....................................................................................................................... 31

Table 3-8: Unbaffled to baffled power number ratios in transitional operation ............... 33

Table 3-9:Unbaffled power number to turbulent average power number ratios in

transitional operation ........................................................................................................ 36

Table 3-10: Baffled power number to turbulent average power number ratios in

transitional operation ........................................................................................................ 37

Appendix 1: Raw and reduced data from impeller power draw experiments for baffled

D-6………………………………………………….............................…………………47

x

Appendix 2: Raw and reduced data from impeller power draw experiments for

unbaffled D-6 .................................................................................................................... 49


CD-6 .................................................................................................................................. 51


unbaffled CD-6 ................................................................................................................. 53


S-4 ..................................................................................................................................... 55


unbaffled S-4 ..................................................................................................................... 57


P-4 ..................................................................................................................................... 59


unbaffled P-4 ..................................................................................................................... 61


SC-3 .................................................................................................................................. 63


unbaffled SC-3 .................................................................................................................. 65


HE-3 .................................................................................................................................. 67


unbaffled HE-3 ................................................................................................................. 69

xi

NOMENCLATURE

A Impeller area which the fluid is pumped through (m2)

D Impeller diameter (m)

H Velocity head (Pa)

KL Constant that equals to the product of power number and Reynolds number in

laminar regime (-)

L Characteristic length (m)

M Torque (N∙m)

N Agitator rotational speed (rpm)

NP Power number (-)

NRe Reynolds number (-)

P Power draw (W)

Q Impeller pumping rate (m3/s)

T Tank diameter (m)

υ Fluid velocity (m/s)

W Impeller blade width (m)

Z Liquid level (m)

γ Shear rate (1/s)

μ Fluid viscosity (Pa∙s)

ρ Fluid density (kg/m3)

τ Shear stress (Pa)

1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

Agitation is the introduced motion of a material in a circulatory pattern inside a

container. This operation tends to reduce gradients in composition and properties.

During agitation, kinetic energy is transferred from a rotating impeller to the surrounding

fluid. Mechanical agitators are widely used in the chemical processing and related

industries as they speed interphase mass transfer and chemical reactions. Additionally,

the suspension of solids in liquids, the dispersion of liquids and gases, and the agitation

of dry solid powders are commonly encountered applications of agitation. Agitators are a

necessity in the processing industries due to their various applications.

Agitators must be designed from both mechanical and process viewpoints.

Mechanical design, such as the design of motor, gear reducer, seal, shaft, impellers and

tank, is essential for successful operation, and is usually determined by the component

manufacturer. However, process environment, such as fluid properties, desired process

results, and agitator’s power consumption, directly impact the mechanical design. Power

number, one of the most important parameters in mixing research and practice (Calabrese

et al., 2014), is used to predict the power requirement of a given agitation system and is

the main focus of this study.

2

In order to design full-scale mixing systems and develop a design guide that can

be used to reliably predict the different types of impellers’ power draw, this study

focused on the relationship between power number and Reynolds number for Newtonian

fluids in a laboratory-scale agitator across the spectrum of Reynolds number for six

industrially significant impellers.

1.2 POWER NUMBER AND REYNOLDS NUMBER

As mentioned, power number can be used to predict power consumption and is a

key consideration in both the mechanical and process design of an agitation system. The

power applied to the agitation system impeller produces velocity head, H, and pumping

capacity, Q, with the impeller power draw being the product of these two quantities

(Hemrajani et al., 2004):

( 1.1 )

The velocity head that provides the kinetic energy is dependent on the product of the

fluid density and the square of its velocity:

( 1.2 )

The fluid velocity near the impeller is directly proportional to the impeller tip (πND) and

thus:

( 1.3 )

The pumping capacity Q is the product of the fluid velocity and area through which the

fluid is pumped:

( )( ) ( 1.4 )

3

Then Equation 1.1 can be rewritten as:

( ) ( ) ( 1.5 )

The preceding result leads to the most commonly seen dimensionless form for the power

number, NP (Rushton et al., 1950):

( 1.6 )

The power number is a function of impeller type, Reynolds number, and

geometric parameters such as the impeller diameter to tank diameter ratio, D/T (Bates et

al., 1966). It can be seen from this equation that if the power number for a given system

is known, the power consumption, P, can be predicted from the fluid density, ρ, impeller

diameter, D, and rotational speed, N.

The Reynolds number is the ratio of inertial forces to viscous forces (McCabe et

al., 2005). It is defined as:

( 1.7 )

L represents a characteristic length, represents velocity, and μ represents the fluid

viscosity. For agitation, impeller diameter, D, is employed as characteristic length, and

the velocity is proportional to the impeller tip speed and can be replaced by the product of

impeller rotational speed and the impeller diameter:

( )

( 1.8 )

The Reynolds number can be used to classify the impeller operation regimes (McCabe et

al., 2005). In the laminar regime, the power number is inversely proportional to

Reynolds number (NP NRe-1

); in the turbulent regime, the power number is constant in

4

fully baffled tanks; and the transitional regime occurs at Reynolds numbers between the

laminar and turbulent regimes with the power number gradually changing from laminar

(inversely dependent on Reynolds number) to fully developed turbulent behavior

(Reynolds number independent). The laminar regime is generally taken to occur when

the Reynolds number is smaller than ten, and viscosity dominates in this regime. At high

Reynolds number of turbulent operation (i.e., NRe > 104), viscosity has little effect and the

process is mainly controlled by inertial forces. In transitional regime, both viscous and

inertial forces affect the process.

1.3 RHEOLOGY

Fluids can be classified as Newtonian and non-Newtonian depending upon the

relationship between shear stress and shear rate (Strong and Myers, 2013). For

Newtonian fluids, the shear stress, τ, is proportional to the local shear rate, γ, at every

point:

( 1.9 )

The constant of proportionality, μ, is known as Newtonian viscosity. It depends only on

the material and its temperature and pressure. Figure 1-1 presents the shear stress - shear

rate data taken using a Haake concentric cylinder viscometer for corn syrup at different

temperatures. It can be seen that the slope of shear stress-shear rate (the viscosity, μ) is

constant at each temperature, but it decreases with increasing temperature. Both water

and aqueous corn syrup solutions used in this study are Newtonian fluids.

5

Figure 1-1: Haake viscometer data for corn syrup at different temperatures (μ [=] Pa s)

1.4 SYSTEM GEOMETRY

Besides Reynolds number, system geometry, such as impeller geometry, impeller

clearance from the tank bottom, the ratio of impeller diameter to tank diameter, D/T, and

the baffles, etc., also has significant effect on power number. In this work, power draw

of different types of impellers has been studied since impeller geometry has been

considered as one major factor that influences power number.

According to the flow pattern produced by the impeller, impellers can be

classified as radial-flow, axial-flow, and mixed flow (Oldshue, 1983). Radial-flow

impellers, such as the D-6, CD-6, and S-4, generate discharge fluid flow perpendicular to

the impeller axis of rotation; when using axial-flow impellers, such as SC-3 and HE-3, in

turbulent operation, the fluid flows parallel to the impeller’s axis of rotation; for mixed

flow impeller, such as P-4, both radial and axial flow will be produced. Impellers can be

τ = 154 γ

τ = 118 γ

τ = 89.8 γ

τ = 67.5 γ

τ = 51.5 γ

τ = 39.7 γ

τ = 31.7 γ

τ = 25.3 γ 0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10 20 30 40 50

Shea

r S

tres

s (P

a)

Shear Rate (1/s)

T=20.5C

T=22.5C

T=24.5C

T=26.5C

T=28.5C

T=30.5C

T=32.5C

T=34.5C

6

further classified by the application. Propellers, pitched-blade turbines, and high-

efficiency impellers are normally used for low- to moderate-viscosity liquids, while

helical impellers and anchor agitators are employed for high viscosity liquids. For the six

impellers used in this study, SC-3 and HE-3 are high-efficiency impellers, and the other

four impellers, D-6, CD-6, P-4 and S-4, are turbines.

1.5 OBJECTIVE

The objective of this work is to gain information that could be used to design full

scale mixing systems, and also could develop a design guide that can provide a reliable

prediction of the power draw of different types of impellers. To achieve this goal,

extensive power number data was taken in Newtonian fluids on six industrially

significant impellers from Reynolds numbers less than 0.1 to greater than 100,000.

Power number behaviors of these impellers, including laminar operation, turbulent

operation, transitional operation, the Reynolds number limits of the operating regimes,

and the effect of baffling on power number were compared.

7

CHAPTER 2

EXPERIMENTAL SETUP AND PROCEDURE

2.1 EXPERIMENTAL SETUP

All experiments were performed in a flat-bottomed clear acrylic cylindrical tank

of 23.5 inches diameter. To broaden the understanding of the effects of impeller type on

power draw, ten different impellers that were supplied by Chemineer, Inc. (Dayton, OH)

were studied, although the data for only six impellers are reported in this thesis, with the

data of the other four impellers being proprietary. Table 2-1 shows the images of the

impellers and lists the impeller diameter to tank diameter ratios (D/T). The off-bottom

clearance for the impellers was set to 7.8 inches (C/T=1/3), while the liquid level to tank

diameter ratio was set equal to unity (Z/T=1).

A laboratory-scale mixer, shown Figure 2-1, was used in this study. A Baldor

(Fort Smith, AR) three phase electric motor (VM3558T) that was used as a power source

to provide shaft and impeller rotation was connected to a 4-speed gearshift transmission,

with gear ratios of 1:1, 1.33:1, 2:1 and 4:1. A zero velocity magnetic pickup was used as

transducer to measure the rotational speed, N. A 500 in∙lbf (56.5 N∙m) strain gauge was

used to measure shaft torque, M. Both the speed signal and torque signal were sent to a

Honeywell (Columbus, OH) conditioner indicator (Model 7541) with a digital readout.

This conditioner indicator is shown in Figure 2-2. Accurate determination of the power

8

draw, P, can be obtained by knowing the torque and speed of an agitator since .

Assembled agitator shaft with impeller is shown in Figure 2-3. The shaft has a 0.75 inch

diameter at the drive that reduced to a 0.50 inch diameter about midway along the shaft.

Impellers were mounted to the bottom end of the shaft with setscrews as shown in the

same figure.

Table 2-1: Impellers

Impeller D-6 CD-6 S-4 P-4 SC-3 HE-3

Diameter

(inch) 7.99 8.78 9.54 9.50 9.50 9.51

D/T

0.340 0.374 0.406 0.404 0.404 0.405

Figure 2-1: Experimental apparatus

9

Figure 2-2: Readout of torque and speed from agitator

Figure 2-3: Assembled agitator shaft and impeller

2.2 VISCOSITY MEASUREMENT

The viscosity data of Figure 1-1 was taken using a concentric cylinder Haake

viscometer designed to provide viscosity as a function of shear rate. This viscometer was

not used during power number testing because insertion of a sample in the viscometer

cup would change the sample temperature and thus its viscosity. Viscosity measurements

were performed by Brookfield DV-E Viscometer, Gardco® Standard Ford Viscosity Cups

10

and Cannon-Fenske Routine (Capillary) Viscometer from Cannon Instrument Company®

depending on the viscosity range. Brookfield DV-E Viscometer was employed when

viscosity was higher than 200 cp. This type of viscometer measures fluid dynamic

viscosity at given rotational speeds. After immersing a sensing element (spindle) in a

fluid, the viscous drag of the test fluid against the spindle is measured with a rotary

transducer that provides a torque signal. The range of measurement is affected by the

spindle’s rotational speed, size and shape, and the container in which the spindle is

rotating. For Newtonian fluids, viscosity appears in units of centipoise (cp) on the

viscometer’s display directly. Standard Ford Viscosity Cups were used to achieve better

accuracy when viscosity was between 50 and 200 cp. This viscometer is a simple gravity

device. By timing the flow of known volume of liquid passing through an orifice located

at the bottom of the Ford Cup, kinematic viscosity in mm2/s (cSt) can be determined by

referring to the corresponding conversion table. The dynamic viscosity can then be found

by multiplying the kinematic viscosity by the density of fluid in gram per milliliter (g/ml)

that is defined as its weight per unit volume. When viscosity was lower than 50 cp,

Cannon-Fenske Routine Viscometer was used. Similar to Standard Ford Viscosity Cups,

Cannon-Fenske Routine Viscometer measures kinematic viscosity instead of dynamic

viscosity using the time required for gravity flow of a fixed volume of fluid through a

capillary.

2.3 PROCEDURE

The experimental procedure began with agitating the Newtonian fluid to reach a

spatially uniform status. After that, the density of the Newtonian fluid was measured by

weighting a 100 ml volumetric flask sample that was taken from the tank. Temperature

11

and viscosity were recorded. In order to produce Reynolds number and power number

for the chosen impeller, readings of torque at various impeller rotational speeds were

required. Temperature and viscosity measurements were performed again after the power

number data collection process. The viscosity at each torque data point was estimated by

using the viscosities measured before and after data collection and linearly interpolating

based on torque. When at high viscosity (μ > 300 cp), the agitation process tended to

take a longer time than for agitation at lower viscosity. Temperature changed

significantly due to conversion of mechanical energy to thermal energy. That led to a

significant viscosity change as shown in Figure 1-1. At low viscosity (μ < 50 cp),

agitation in unbaffled tank led to the formation of a large surface vortex when the

Reynolds number is high (greater than about to 104). Data acquisition was stopped

before the vortex reached the impeller, and gaps in the data at higher Reynolds number

appeared due to the fact that data could be obtained at only a few speeds at each fluid

viscosity.

12

CHAPTER 3

RESULTS AND DISCUSSION

A key parameter in agitator design, power number strongly depends on both

Reynolds number and the impeller geometry. In advance of a study of impeller power

draw in non-Newtonian fluids, extensive data was taken in Newtonian fluids with both

baffled and unbaffled configurations. This section compares the power number behaviors

of these different impellers, including three operation regimes (laminar, transitional, and

turbulent), the Reynolds number limits of the operation regimes, and the effect of baffling

on power number.

Figures 3-1 through 3-6 present the measured power numbers as functions of

Reynolds number in the laminar regime (D-6 in Figure 3-1, CD-6 in Figure 3-2, S-4 in

Figure 3-3, P-4 in Figure 3-4, SC-3 in Figure 3-5, and HE-3 in Figure 3-6). As can been

clearly seen, the data for all six impellers in both baffled and unbaffled configurations

agree with each other, indicating that the baffling has no effect on power number at low

Reynolds number. Another point these impellers have in common is that the slopes of

the power number – Reynolds number relations on logarithmic coordinates are all equal

to -1, indicating that the power number in this regime is inversely proportional to

Reynolds number (NP NRe-1

, with data correlations included on each figure).

13

Figure 3-1: D-6 low Reynolds number data

Figure 3-2: CD-6 low Reynolds number data

NP = 60.7 NRe-1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)

Reynolds Number (NRe)

D-6 Baffled

D-6 Unbaffled

NP = 61.9 NRe-1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)


CD-6 Baffled

CD-6 Unbaffled

14

Figure 3-3: S-4 low Reynolds number data

Figure 3-4: P-4 low Reynolds number data

NP = 45.5 NRe-1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)


S-4 Baffled

S-4 Unbaffled

NP = 43.2 NRe-1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)


P-4 Baffled

P-4 Unbaffled

15

Figure 3-5: SC-3 low Reynolds number data

Figure 3-6: HE-3 low Reynolds number data

NP = 26.0 NRe-1

0.1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)


SC-3 Baffled

SC-3 Unbaffled

NP = 27.0 NRe-1

0.1

1

10

100

1,000

0.01 0.1 1 10 100

Po

wer

Num

ber

(N

P)


HE-3 Baffled

HE-3 Unbaffled

16

Due to the inversely proportional relationship, the product of power number and

Reynolds number in laminar regime is a constant as shown in Equation 3.1 below.

( 3.1 )

This constant KL also equals the impeller power number at a Reynolds number of one.

Table 3-1 presents the values of KL for different types of impeller. As can be seen, the

KL values of baffled and unbaffled configurations differ by no more than two percent for

all six impellers, reinforcing the conclusion that the baffles have no effect on impeller

power draw in laminar operation. Besides this, the small KL COV (coefficient of

variation, which equals the ratio of the standard deviation to the arithmetic average)

shows the low point to point variation in the data. Because of the lack of baffling effect,

it is reasonable to take a weighted average of the baffled and unbaffled KL values for

each impeller (weighted by the number of data points taken with each configuration.).

D-6 and P-4 values agree with literature KL values while the HE-3 is considerably lower.

Table 3-2 lists the laminar operation range for different impellers based on the

experimental results. The highest Reynolds number with less than ten percent difference

between the experimental power number value and that found from the data correlation

(Np= KL/NRe, with the baffled-unbaffled weighted average KL being used) is treated as

the highest laminar operation Reynolds number data point for each impeller. It is widely

accepted that laminar operation takes place when Reynolds number is less than 10. From

the results from this work, the upper limit for laminar operation should be lower than 10,

as four out of six impellers have their highest laminar operation Reynolds number smaller

than 10.

17

Table 3-1: Comparison of baffled and unbaffled Newtonian fluid KL values


Baffled

KL

Average 61.0 61.7 45.4 43.1 25.7 26.9

KL

COV**

2.6% 2.7% 2.5% 1.2% 3.3% 2.5%

Unbaffled

KL

Average 60.4 62.1 45.5 43.2 26.2 27.4

KL

COV**

2.7% 2.2% 2.1% 1.3% 3.1% 2.4%

Weighted KL

Average 60.7 61.9 45.5 43.2 26.0 27.2

Literature KL*

65 N/A N/A 44.5 N/A 43

* Literature KL values are from McCabe et al. [4]. ** COV = Coefficient of Variation = Standard Deviation/Arithmetic Average

Table 3-2: Highest Reynolds number for laminar operation


Highest NRe*

8.6 7.6 10.0 8.0 7.2 10.3

* The highest NRe with less than 10% difference between the experimental value and that found from the data correlation, Np= KL/NRe

According to Table 3-1, KL values seem to be affected only by the impeller’s

blade number, with the impellers that have the same number of blades having similar KL

values and impellers with more blades having higher KL values with the KL values being

roughly proportional to the number of blades. This phenomenon is illustrated graphically

in Figure 3-7, as CD-6 and D-6, S-4 and P-4, and SC-3 and HE-3 data almost coincide.

However, this conclusion is not applicable to all impellers. Other shape factors such as

the ratio between the width of impeller blades and the impeller diameter (W/D) (Smith,

1985) also contribute to the value of KL. One wide-blade impeller that was tested has a

KL value close to 100 with only three blades. This impeller’s data is not included here

due to confidentiality. Figure 3-7 presents only baffled data for these six impellers’

power number-Reynolds number laminar results since baffling doesn’t affect the data in

18

this regime. It should also be noticed that all data sets in this regime are parallel, which

reinforces what was said in the previous discussion that these impellers have same

exponent of -1 in their laminar regime power number-Reynolds number relations.

Figure 3-7: Comparison of baffled low Reynolds number data


Reynolds number in the turbulent regime (D-6 in Figure 3-8, CD-6 in Figure 3-9, S-4 in

Figure 3-10, P-4 in Figure 3-11, SC-3 in Figure 3-12, and HE-3 in Figure 3-13. Due to

their lower baffled turbulent power numbers, the SC-3 and HE-3 data plots use a different

y axis range than the other four impellers). The average baffled power number and

power-law correlations for the unbaffled power numbers are included as well. Baffling

has significant effect on power number in this regime for all six impellers: power number

stays relatively constant in the baffled tank while in the tank with no baffles installed, the

power number drops with increasing Reynolds number.

1

10

100

1,000

0.01 0.1 1 10

Po

wer

Num

ber

(N

p)


D-6

CD-6

S-4

P-4

SC-3

HE-3

19

Figure 3-8: D-6 high Reynolds number data

Figure 3-9: CD-6 high Reynolds number data

NP = 8.35 NRe-0.198

R² = 0.98

NP = 5.41

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6 Baffled

D-6 Unbaffled

NP = 5.55 NRe-0.184

R² = 0.99

NP = 2.79

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


CD-6 Baffled

CD-6 Unbaffled

20

Figure 3-10: S-4 high Reynolds number data

Figure 3-11: P-4 high Reynolds number data

NP = 4.14 NRe-0.162

R² = 0.97

NP = 3.10

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


S-4 Baffled

S-4 Unbaffled

NP = 2.42 NRe-0.144

R² = 0.98

NP = 1.15

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


P-4 Baffled

P-4 Unbaffled

21

Figure 3-12: SC-3 high Reynolds number data

Figure 3-13: HE-3 high Reynolds number data

NP = 1.13 NRe-0.144

R² = 0.98

NP = 0.503

0.1

1

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


SC-3 Baffled

SC-3 Unbaffled

NP = 0.695 NRe-0.120

R² = 0.94

NP = 0.309

0.1

1

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


HE-3 Baffled

HE-3 Unbaffled

22

Table 3-3 shows power number values for the six impellers in baffled tank when

the Reynolds number is larger than 104. In this range, SC-3 and HE-3 power numbers are

more than an order of magnitude lower than that of the D-6 (recall from Table 3-1 that

these power numbers vary by only a factor of two in the laminar regime). Their low

turbulent power numbers make the SC-3 and HE-3 impellers the popular choice when

mixing low or moderate viscosity liquids. CD-6 and S-4 have similar power numbers

which indicates the number of impeller blades is no longer the dominant factor that

affects power number in this regime. Comparison of the P-4 and S-4 power numbers

illustrates the impact that blade angle has on turbulent power number in baffled tanks. It

is normally considered that the turbulent power number in a baffled tank should remain

constant. According to the results in this work, the power numbers for D-6 and S-4 still

increase with increasing Reynolds number. The ranges in the power numbers of these

impellers is more than ten percent of the average values and they both have a relatively

large coefficient of variation when compared with the other impellers. When available,

the average values of the baffled impeller power numbers obtained during this work

agree with the literature values with less than 10% difference. For D-6, using 6.3 as its

turbulent power number as reported by Rushton et al. (1950) is considered to be high;

with 5.5 being more acceptable according to Bates et al. (1966).

In Table 3-4, power number ratio between unbaffled power number correlation

equation and baffled power number average has been used to examine the difference

between these two configurations. For all impellers, unbaffled power number continually

decreases with increasing Reynolds number. Besides this, the impellers with higher

power numbers in baffled tank tend to have lower power number ratios when comparing

23

at same Reynolds number. HE-3, the only impeller with power number ratio larger than

0.5 in the entire turbulent regime, has the lowest baffled power number.

Table 3-3: Comparison of baffled Newtonian fluid turbulent power numbers


Lowest NP 5.03 2.75 2.86 1.10 0.484 0.300

Highest

NP 5.70 2.84 3.28 1.18 0.521 0.321

NP

Average 5.41 2.79 3.10 1.15 0.503 0.309

Range

/Average 12.4% 3.2% 13.5% 7.0% 7.4% 6.8%

NP COV 4.3% 1.0% 4.8% 2.0% 2.4% 2.1%

Literature

NP*

4.8-5.5 [1]

6.3 [7]

2.9

[4] 3.1

[4]

1.1 [3]

1.27 [4]

N/A 0.28

[4]

* Literature NP values are from McCabe et al. [4], Rushton et al. [7], Bates et al. [1], and Deng [3]

Table 3-4: Unbaffled to baffled power number ratios in turbulent operation


Unbaffled NP 8.35 NRe

-0.198

5.55 NRe

-0.184

4.14 NRe

-0.162

2.42 NRe

-0.144

1.13 NRe

-0.144

0.696 NRe

-0.120

Average Baffled NP 5.41 2.79 3.10 1.15 0.503 0.309

NP Ratio

(Unbaffled NP /Baffled NP) 1.54 NRe

-0.198

1.99 NRe

-0.184

1.34 NRe

-0.162

2.10 NRe

-0.144

2.26 NRe

-0.144

2.25 NRe

-0.120

NRe NP Ratio

10,000 0.25 0.37 0.30 0.56 0.60 0.75

20,000 0.22 0.32 0.27 0.50 0.54 0.69

50,000 0.18 0.28 0.23 0.44 0.48 0.61

100,000 0.16 0.24 0.21 0.40 0.43 0.57

200,000 0.14 0.21 0.19 0.36 0.39 0.52

24

Table 3-5: Lowest Reynolds number for turbulent power number in baffled configuration


Average Np 5.41 2.79 3.10 1.15 0.503 0.309

Lowest NRe in the

±10% NP range 10,500 176 4160 2800 5790 1040

Corresponding Np 5.03 3.04 2.79 1.04 0.454 0.336

Table 3-5 shows the lowest Reynolds number for which power number remains

within 10% of the average turbulent power number in the baffled configuration. This

lowest Reynolds number for D-6 is higher than 10,000, the point that is generally

accepted as starting point for turbulent regime. For CD-6, the impeller with the lowest

power number coefficient of variation in Table 3-3, the lowest Reynolds number where

the power number is within 10% of its turbulent value is 176. This is considerably less

than 10,000, indicating that the baffled power number of the CD-6 is relatively constant

throughout much of the transitional regime. Except for CD-6 and HE-3, the power

numbers for the other four impellers are all lower than their average turbulent power

numbers, indicating that their power numbers exhibit a minimum in transitional operation.

Turbulent operation results for the six impellers are compared both quantitatively

(Table 3-6) and qualitatively (Figure 3-14 and 3-15 for baffled and unbaffled

configurations, respectively). In Table 3-6, the two configurations’ power numbers in

laminar and turbulent operation are normalized by the HE-3’s corresponding power

number to obtain the relative values. The relative unbaffled turbulent power number is

calculated by averaging the ratio of each impeller and the HE-3’s correlation power

numbers at five Reynolds numbers (10,000, 20,000, 50,000, 100,000, and 200,000). In

the laminar regime, D-6 has a power number that is twice that of the HE-3. In the

turbulent regime, the power numbers vary by a factor of 18 for these two impellers in

25

baffled operation. As has been discussed relative to Table 3-4, the turbulent power

number decreases significantly in the unbaffled configuration for D-6, but it is still four

times higher than that of the SC-3 and over five times higher than that of the HE-3.

Table 3-6: Power number comparison


Average Laminar KL 60.7 61.9 45.5 43.2 26.2 27.4

Relative Laminar KL 2.2 2.3 1.7 1.6 0.96 1

Average Baffled

Turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

Relative Baffled

Turbulent Np*

18 9.0 10 3.7 1.6 1

Relative Unbaffled

Turbulent Np*

5.2 4.0 3.8 2.7 1.3 1

* All relative power number values are normalized with respect to the HE-3

Figure 3-14: Comparison of baffled high Reynolds number data

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6

CD-6

S-4

P-4

SC-3

HE-3

26

Figure 3-15: Comparison of unbaffled high Reynolds number data


Reynolds number in the transitional regime (D-6 in Figure 3-16, CD-6 in Figure 3-17,

S-4 in Figure 3-18, P-4 in Figure 3-19, SC-3 in Figure 3-20, and HE-3 in Figure 3-21).

For reference, the baffled turbulent power number for each impeller is included in the

corresponding figure. Additionally, these figures include power law correlations for

unbaffled data at higher Reynolds numbers, with the Reynolds number range for each

curve noted below the corresponding power law equation. In the transitional regime,

baffling has no effect on the power number at low Reynolds number, as was observed in

the laminar regime. With increasing Reynolds number there is an increasing difference

between the unbaffled and baffled power numbers of all impellers, with the D-6 having

the biggest power number difference between the two configurations and the HE-3

having the least difference. Besides this, D-6, S-4, P-4, and SC-3 impellers, as was

0.1

1

10

1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6

CD-6

S-4

P-4

SC-3

HE-3

27

suggested when discussing baffled turbulent operation, exhibit a minimum power number

in baffled transitional operation. The CD-6, one of two impellers that have no minimum

power number in baffled transitional operation, has a power number higher than the

average turbulent power number by an average of 4% and a maximum of 8% for

Reynolds numbers between 490 and 2500.

Figure 3-16: D-6 transitional Reynolds number data

Figure 3-17: CD-6 transitional Reynolds number data

NP = 5.41

NP = 12.2 NRe-0.241

R² = 0.99

NRe = 210 - 10,200

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


D-6 Baffled

D-6 Unbaffled

NP = 2.79

NP = 10.3 NRe-0.253

R² = 1.00

NRe = 20 - 10,500

0.1

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


CD-6 Baffled

CD-6 Unbaffled

28

Figure 3-18: S-4 transitional Reynolds number data

Figure 3-19: P-4 transitional Reynolds number data

NP = 3.1

NP = 7.85 NRe-0.234

R² = 1.00

NRe = 200 - 10,500

0.1

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


S-4 Baffled

S-4 Unbaffled

NP = 1.15

NP = 3.77 NRe-0.193

R² = 0.99

NRe = 190 - 10,900

0.1

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


P-4 Baffled

P-4 Unbaffled

29

Figure 3-20: SC-3 transitional Reynolds number data

Figure 3-21: HE-3 transitional Reynolds number data

NP = 0.503

NP = 1.23 NRe-0.155

R² = 0.99

NRe = 960 - 8100

0.01

0.1

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


SC-3 Baffled

SC-3 Unbaffled

NP = 0.309 NP = 0.85 NRe-0.143

R² = 0.96

NRe = 970 - 9700

0.01

0.1

1

10

1 10 100 1,000 10,000 100,000

Po

wer

Num

ber

(N

P)


HE-3 Baffled

HE-3 Unbaffled

30

Table 3-7 presents the Reynolds number range for each impeller for which the

baffled power number is lower than the average baffled turbulent power number. This is

not applicable for CD-6 and HE-3 as their power numbers do not have a minimum in the

transitional regime. For the other four impellers, the lower Reynolds number value is the

lowest Reynolds number for which the measured power number is less than the turbulent

average value, while the upper Reynolds number is that for which the measured power

number is more than ten percent less than the turbulent average value (as in Table 3-5).

Also, the lower Reynolds number value can be either from baffled or unbaffled

configuration since baffling makes no difference in the results at low Reynolds number,

but the upper Reynolds number limit is from baffled configuration only. For D-6 and S-4,

two impellers that have relatively high coefficients of variation in their average baffled

turbulent power numbers according to Table 3-3, this Reynolds number range extends

through more than two orders of magnitude. For the P-4, which has the lowest

coefficient of variation in the average baffled turbulent power number among these four

impellers, the Reynolds number range is less than one order of magnitude.

Table 3-7 also presents the minimum transitional power number with its

corresponding Reynolds number for each impeller in the baffled configuration. Again,

this is not applicable for CD-6 and HE-3 as has been stated previously. For the other four

impellers, D-6 and S-4 have the minimum power number at relatively low Reynolds

number of approximately 200, while the P-4 and SC-3 have their minimum power

numbers at higher Reynolds number near 2000. The power number ratios between the

minimum power number and the average turbulent power number for S-4, P-4 and SC-3

31

are close to each other, ranging between eighty and ninety percent, while the ratio for the

D-6 is significantly lower than the rest with a value of 0.66.

Table 3-7: Reynolds number range with baffled NP lower than average baffled turbulent Np


Average baffled

turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

NRe range 18.7 - 10,500 N/A 35.7 - 4160 773 - 2800 504 – 5790 N/A

Minimum Np 3.56 N/A 2.47 1.02 0.422 N/A

Corresponding

NRe 200 N/A 200 2200 2000 N/A

NP Ratio

(Minimum NP /

Average

turbulent NP)

0.66 N/A 0.80 0.89 0.83 N/A

Figure 3-22 is plotted based on the result from Table 3-8 that presents the power

number ratios between baffled and unbaffled configurations in both transitional and

turbulent operation (Table 3-8 contains transitional data while the turbulent data was

previously presented in Table 3-4. Interpolation with approximately four adjacent data

points was used to generate the value at each particular Reynolds numbers in the table.).

The ratio for laminar operation is not included as baffling has no effect in this regime and

the ratio will be equal to one for all impellers. In the transitional regime, the ratios of

unbaffled to baffled power numbers for all impellers stay above 0.9 until the Reynolds

number reaches 200. When the Reynolds number is higher than 200, the ratios for three

radial flow impellers, D-6, CD-6 and S-4, drop significantly to lower than 0.75 and then

stay similar through the entire Reynolds number range. As Reynolds number hits 2000,

the ratio for P-4 is lower than 0.9 as well and leaves only the two hydrofoil impellers

above the 0.9 line. The unbaffled power number is about half of the baffled power

32

number at this Reynolds number for the three radial flow impellers. For Reynolds

number higher than 5,000, SC-3 and P-4 are similar with the SC-3 being a bit higher.

HE-3 is the only impeller that the unbaffled to baffled power number ratio remains above

0.5 in the entire Reynolds number range.

Figures 3-23 and 3-24 are generated from data in Tables 3-9 and 3-10,

respectively (again, data interpolation was used to generate these values at particular

Reynolds numbers). Figure 3-23 and Table 3-9 show the ratios between unbaffled power

numbers and turbulent average power numbers in transitional and turbulent operation (the

turbulent data in Figure 3-23 was previously presented in Table 3-4), while Figure 3-24

and Table 3-10 show the ratios between baffled power numbers and turbulent average

power numbers in the same Reynolds number range. In Figure 3-23, the ratios for the six

impellers retain the same order through the entire Reynolds number range with HE-3

having the highest unbaffled to turbulent average baffled power number ratio and the D-6

having the lowest ratio. When Reynolds number equals ten, the ratio for HE-3 is 8.96,

which is more than six times larger than the 1.35 ratio of the D-6. As expected, the ratios

of all impellers continually decrease with increasing Reynolds number. The baffled to

baffled turbulent average power number ratios in Figure 3-24 exhibit a similar trend as

that in Figure 3-23 for Reynolds numbers lower than 100. After that, the ratios start to

converge to one. It should be noticed that the ratios in Figure 3-24 for CD-6 and HE-3

stay above one in transitional operation, as there is no minimum power number point for

these two impellers in the baffled configuration. Laminar operation ratios are not

included for Figures 3-23 and 3-24 as this would compress the power number axis since

the ratios increase rapidly with decreasing Reynolds number. The ratios for laminar

33

operation at Reynolds number less than ten can be found by using the fact that the power

numbers are inversely proportional to Reynolds number in this regime.

Table 3-8: Unbaffled to baffled power number ratios in transitional operation


NRe

10

Unbaffled NP 7.29 7.32 5.02 4.65 2.97 2.77

Baffled NP 7.13 7.26 4.89 4.78 2.95 2.87

Ratio 1.02 1.01 1.03 0.97 1.00 0.97

20

Unbaffled NP 5.17 4.84 3.71 3.09 1.84 1.79

Baffled NP 5.32 4.95 3.70 3.22 1.85 1.80

Ratio 0.97 0.98 1.00 0.96 0.99 0.99

50

Unbaffled NP 4.03 3.84 2.82 2.01 1.12 1.05

Baffled NP 4.07 3.83 2.89 2.10 1.11 1.08

Ratio 0.99 1.00 0.97 0.96 1.00 0.97

100

Unbaffled NP 3.59 3.22 2.50 1.59 0.822 0.756

Baffled NP 3.73 3.32 2.64 1.63 0.832 0.738

Ratio 0.96 0.97 0.95 0.98 0.99 1.02

200

Unbaffled NP 3.29 2.70 2.27 1.36 0.624 0.541

Baffled NP 3.58 2.95 2.51 1.38 0.665 0.553

Ratio 0.92 0.92 0.90 0.99 0.93 0.98

500

Unbaffled NP 2.72 2.14 1.83 1.14 0.504 0.401

Baffled NP 3.86 2.90 2.69 1.21 0.507 0.409

Ratio 0.70 0.74 0.68 0.94 0.98 0.98

1,000

Unbaffled NP 2.30 1.80 1.56 0.99 0.420 0.318

Baffled NP 4.21 2.93 2.74 1.09 0.451 0.340

Ratio 0.55 0.61 0.57 0.91 0.93 0.94

2,000

Unbaffled NP 1.95 1.51 1.33 0.87 0.377 0.288

Baffled NP 4.67 2.98 2.72 1.05 0.412 0.317

Ratio 0.42 0.51 0.49 0.83 0.92 0.91

5,000

Unbaffled NP 1.56 1.20 1.07 0.73 0.327 0.253

Baffled NP 4.72 2.83 2.82 1.07 0.447 0.305

Ratio 0.33 0.42 0.38 0.68 0.73 0.83

10,000

Unbaffled NP 1.32 1.00 0.91 0.64 0.294 0.229

Baffled NP 4.97 2.80 2.83 1.12 0.494 0.310

Ratio 0.27 0.36 0.32 0.57 0.60 0.74

The highlighted values are the highest Reynolds number for which the ratio is greater than ninety percent.

34

Figure 3-22: Ratio of unbaffled to baffled power numbers in transitional and turbulent operation

Figure 3-23: Ratio of unbaffled to turbulent average power numbers in transitional and turbulent operation

Ratio = 0.9

Ratio = 0.5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

Rat

io (

Unb

affl

ed/B

affl

ed)


D-6

CD-6

S-4

P-4

SC-3

HE-3

0.1

1

10

1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Nu

mb

er R

atio

(U

nb

affl

ed/T

urb

ule

nt

Aver

age)


D-6

CD-6

S-4

P-4

SC-3

HE-3

35

Figure 3-24: Ratio of baffled to turbulent average power numbers in transitional and turbulent operation

0.1

1

10

1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

Rat

io (

Baf

fled

/Turb

ule

nt

Aver

age)


D-6

CD-6

S-4

P-4

SC-3

HE-3

36

Table 3-9: Unbaffled power number to turbulent average power number ratios in transitional operation


Average baffled turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

NRe

10

Np 7.29 7.32 5.02 4.65 2.97 2.77

Ratio 1.35 2.62 1.62 4.04 5.90 8.96

20

Np 5.17 4.84 3.71 3.09 1.84 1.79

Ratio 0.96 1.73 1.20 2.69 3.66 5.79

50

Np 4.03 3.84 2.82 2.01 1.12 1.05

Ratio 0.74 1.38 0.91 1.75 2.23 3.40

100

Np 3.59 3.22 2.50 1.59 0.822 0.756

Ratio 0.66 1.15 0.81 1.38 1.63 2.45

200

Np 3.29 2.70 2.27 1.36 0.624 0.541

Ratio 0.61 0.97 0.73 1.18 1.24 1.75

500

Np 2.72 2.14 1.83 1.14 0.504 0.401

Ratio 0.50 0.77 0.59 0.99 1.00 1.30

1,000

Np 2.30 1.80 1.56 0.99 0.420 0.318

Ratio 0.43 0.65 0.50 0.86 0.83 1.03

2,000

Np 1.95 1.51 1.33 0.87 0.377 0.288

Ratio 0.36 0.54 0.43 0.76 0.75 0.93

5,000

Np 1.56 1.20 1.07 0.73 0.327 0.253

Ratio 0.29 0.43 0.35 0.63 0.65 0.82

10,000

Np 1.32 1.00 0.91 0.64 0.294 0.229

Ratio 0.24 0.36 0.29 0.56 0.58 0.74

37

Table 3-10: Baffled power number to turbulent average power number ratios in transitional operation


Average baffled turbulent Np 5.41 2.79 3.10 1.15 0.503 0.309

NRe

10 Np 7.13 7.26 4.89 4.78 2.95 2.87

Ratio 1.32 2.60 1.58 4.16 5.86 9.29

20 Np 5.32 4.95 3.70 3.22 1.85 1.80

Ratio 0.98 1.77 1.19 2.80 3.68 5.83

50 Np 4.07 3.83 2.89 2.10 1.11 1.08

Ratio 0.75 1.37 0.93 1.83 2.21 3.50

100 Np 3.73 3.32 2.64 1.63 0.832 0.738

Ratio 0.69 1.19 0.85 1.42 1.65 2.39

200 Np 3.58 2.95 2.51 1.38 0.665 0.553

Ratio 0.66 1.06 0.81 1.20 1.32 1.80

500 Np 3.86 2.90 2.69 1.24 0.507 0.409

Ratio 0.70 1.04 0.87 1.08 1.01 1.32

1,000 Np 4.21 2.93 2.74 1.09 0.451 0.340

Ratio 0.78 1.05 0.88 0.95 0.90 1.10

2,000 Np 4.67 2.98 2.72 1.05 0.412 0.317

Ratio 0.86 1.07 0.88 0.91 0.82 1.03

5,000 Np 4.72 2.83 2.82 1.07 0.447 0.305

Ratio 0.87 1.01 0.91 0.93 0.89 0.99

10,000 Np 4.97 2.80 2.83 1.12 0.494 0.310

Ratio 0.92 1.00 0.91 0.97 0.98 1.00

20,000 Np 5.22 2.81 2.97 1.13 0.496 0.307

Ratio 0.96 1.01 0.96 0.98 0.99 0.99

50,000 Np 5.42 2.80 3.10 1.14 0.503 0.309

Ratio 1.00 1.00 1.00 1.00 1.00 1.00

100,000 Np 5.58 2.80 3.19 1.16 0.508 0.311

Ratio 1.03 1 1.03 1 1.01 1.01

200,000 Np 5.74 2.79 3.30 1.17 0.514 0.312

Ratio 1.06 1 1.06 1.01 1.02 1.01

38

To conclude the power number data presentation, Figure 3-25 combines the

baffled data for all six impellers through the entire Reynolds number range, and Figure

3-26 compares the impellers’ unbaffled data. Figures 3-27 through 3-32 present the

baffled and unbaffled data of each impeller for all Reynolds numbers.

Figure 3-25: Comparison of all baffled power number data

Figure 3-26: Comparison of all unbaffled power number data

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6

CD-6

S-4

P-4

SC-3

HE-3

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6

CD-6

S-4

P-4

SC-3

HE-3

39

Figure 3-27: Baffled and unbaffled data of D-6 for all Reynolds numbers

Figure 3-28: Baffled and unbaffled data of CD-6 for all Reynolds numbers

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


D-6 Baffled

D-6 Unbaffled

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


CD-6 Baffled

CD-6 Unbaffled

40

Figure 3-29: Baffled and unbaffled data of S-4 for all Reynolds numbers

Figure 3-30: Baffled and unbaffled data of P-4 for all Reynolds numbers

0.1

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


S-4 Baffled

S-4 Unbaffled

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


P-4 Baffled

P-4 Unbaffled

41

Figure 3-31: Baffled and unbaffled data of SC-3 for all Reynolds numbers

Figure 3-32: Baffled and unbaffled data of HE-3 for all Reynolds numbers

0.10

1

10

100

1,000

0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


SC-3 Baffled

SC-3 Unbaffled

0.10

1

10

100

1,000

0.01 0.10 1 10 100 1,000 10,000 100,000 1,000,000

Po

wer

Num

ber

(N

P)


HE-3 Baffled

HE-3 Unbaffled

42

CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS

This work aimed to acquire design information for Newtonian fluid mixing,

focusing on measuring the power numbers of six different impellers across the full

Reynolds number spectrum. Power number behaviors of these six impellers were

compared in three operation regimes – laminar, turbulent, and transitional.

In laminar operation, baffling has no effect on power number for all six impellers.

The slope of the power number – Reynolds number relations on logarithmic coordinates

are all equal to -1, indicating an inversely proportional relationship between power

number and Reynolds number. It is widely accepted that laminar operation takes place

when Reynolds number is less than 10; however, four of the six impellers in this work

have their highest laminar operation Reynolds number smaller than 10, suggesting that

the upper limit for laminar operation should be lower than 10. The constant KL, the

product of power number and Reynolds number in this particular regime, is

approximately proportional to the number of blades based on the results from these six

impellers. However, this is not applicable for all the impellers. Other shape factors such

as the ratio between the width of impeller blades and the impeller diameter also

contribute to the parameter KL.

In turbulent operation, baffling has a significant effect on power number for all

six impellers with the power number continually decreasing with increasing Reynolds

43

number for unbaffled configuration while the power number in a baffled configuration

remains relatively constant for most impellers; however, the power number for D-6 and

S-4 still increase with increasing Reynolds number, with their power numbers increasing

by more than ten percent as the Reynolds number increases from 10,000 to 200,000. In

turbulent operation, the number of impeller blades is not the dominant factor that affects

power number. In the baffled configuration, two hydrofoil impellers exhibit much lower

power numbers when compared with the other impellers: the baffled power number range

of the six impellers was only a factor of two in the laminar regime and increased to 18 in

the turbulent regime. In the unbaffled configuration, power number decreases with

increasing Reynolds numbers with power-law exponents between -0.20 and -0.12

depending on impeller (NP = K NRen, -0.20 < n < -0.12). Additionally, the impellers with

higher power numbers in baffled tank tend to have lower ratios between unbaffled power

number and average baffled power number when comparing at same Reynolds number.

At the low Reynolds number end of transitional regime, the power numbers show

no difference between baffled and unbaffled configurations for all impellers. The

differences between the two configurations start at intermediate Reynolds numbers and

increase with an increase of Reynolds number. In the baffled configuration, four of six

impellers exhibit a minimum power number, with the D-6 and S-4 having the minimum

at Reynolds number of approximately 200 and the P-4 and SC-3 having their minima at

Reynolds number near 2000. Three of these impellers have ratios between the minimum

power number and the average turbulent power number that are close to each other, in the

range between eighty and ninety percent, while D-6 has a considerably lower ratio of

0.66. The range of Reynolds numbers for which the baffled transitional power number is

44

less than the baffled turbulent value extends through more than two orders of magnitude

for D-6 and S-4, around one order of magnitude for SC-3, and less than one order of

magnitude for P-4. The CD-6, one of two impellers that have no minimum power

number in baffled transitional operation, has a power number higher than the average

turbulent power number by an average of 4% and a maximum of 8% for Reynolds

numbers in the range of 490 and 2500. For HE-3, there is little difference between the

baffled power number and the average turbulent power number in the high Reynolds

number end of transitional regime (NRe > 1,000). In the unbaffled configuration, power

numbers drop with increasing Reynolds number throughout the entire transitional regime

for all impellers. The range of the exponent of power law correlations in unbaffled data

is between -0.25 and -0.14 (NP = K NRen, -0.25 < n < -0.14). The HE-3 has an unbaffled

to baffled power number ratio above 0.5 over the entire Reynolds number range, while

the ratios for the other five impellers are lower than 0.4 for high Reynolds number. For

the power number ratios between unbaffled and turbulent average power numbers, the

same order occurred throughout both transitional and turbulent operation, with this order

being the reverse of the order of the baffled turbulent power number (D-6 < S-4 < CD-6 <

P-4 < SC-3 < HE-3).

Extensive power number data has been taken for six industrially significant

impellers; power number behavior and significant trends have been identified and

compared; however, the data has a degree of uncertainty due to inherent uncertainty and

temporal variance in the system and the method of mentally averaging the visually

displayed torque data. An automated data acquisition system that can determine the

uncertainty of each data point statistically would help to improve this. Additional

45

uncertainty could be caused by the way viscosity was measured since the viscosity for

each torque data point was not measured. Finding a way to physically measure the

viscosity for every torque data point would help to achieve better accuracy.

Other variables such as different tank geometry (dish bottom, non-standard

baffling, etc.), impeller off-bottom clearance and impeller to tank diameter ratio and

system scale could be investigated in the future to learn about the effects these system

parameters might have on power draw. Additionally, non-Newtonian fluids power draw

measurements on these six impellers could be performed with the data of this work

providing a basis for comparison.

46

BIBLIOGRAPHY

1. Bates, R. L., P. L. Fondy, and J. G. Fenic. (1966). “Impeller characteristics and

power”, Chapter 3 in Mixing: Theory and Practice. V. W. Uhl and J. B. Gray (Eds.).

New York, Academic Press Inc.

2. Calabrese, R. V., S. M. Kresta, and M. Liu. (2014). "Recognizing the 21 Most

Influential Contributions To Mixing Research." Chemical Engineering Progress.

January: 20-29.

3. Deng, J. (May 2014). Mechanical Mixing of High Concentration Biomass Slurry.

Thesis, Chemical and Materials Engineering. University of Dayton. Dayton, Ohio.

Master of Science in Chemical Engineering.

4. McCabe, W. L., J. C. Smith, and P. Harriott. (2005). “Agitation and Mixing of

Liquids”, Chapter 9 in Unit Operations of Chemical Engineering. New York,

McGraw-Hill.

5. Oldshue, J. Y. (1983). Fluid Mixing Technology. New York: McGraw-Hill.

6. Hemrajani, R. R., and G. B. Tatterson. (2004). “Mechanically Stirred Vessels”,

Chapter 6 in Handbook of Industrial Mixing - Science and Practice. Paul, E. L., V. A.

Atiemo-Obeng, and S. M. Kresta (Eds.). Hoboken, John Wiley & Sons, Inc.

7. Rushton, J. H., E. W. Costich, and H. J. Everett. (1950). "Power characteristics of

mixing impellers." Chemical Engineering Progress 46: 395-404, and 467-479.

8. Strong, R. J., and K. J. Myers (November, 2013). "Introductory Rheology".

9. Smith, J. M. (1985). “Dispersion of Gases in Liquids: The Hydrodynamics of Gas

Dispersion in Low Viscosity Liquids”, Chapter 5 in Mixing of Liquids by Mechanical

Agitation. J. J. Ulbrecht and G. K. Patterson (Eds.). New York, Gordon and Breach

Science Publishers.

47

APPENDIX: RAW AND REDUCED EXPERIMENTAL DATA

Appendix 1: Raw and reduced data from impeller power draw experiments for baffled D-6

Impeller: D-6 Configuration: Baffled Diameter: 7.99'' D/T: 0.34

N (rpm) M (in lbf) SG (-) μ (cp) NP (-) NRe (-)

8 11.75 1.48 122886 909 0.066

23 35.15 1.48 122861 329 0.19

32.5 49.45 1.48 122845 232 0.27

44 66.525 1.48 122827 170 0.37

56 84.55 1.48 122807 133 0.47

68 103.2 1.48 122787 110 0.57

81 122.375 1.48 122767 92.3 0.67

94 140.25 1.48 122747 78.6 0.78

116 171 1.48 122714 62.9 0.97

74 50 1.42 57659 47.7 1.25

97.5 65.4 1.42 57279 35.9 1.65

115 76.9 1.42 57789 30.4 1.94

144.5 96.9 1.42 57867 24.2 2.43

177 119.6 1.42 57968 19.9 2.98

207 139 1.42 58054 16.9 3.48

74.5 7.675 1.40 8294 7.33 8.63

107 13.15 1.40 8292 6.09 12.4

188 33.125 1.40 8281 4.97 21.8

244 52.325 1.40 8271 4.66 28.4

281 67.075 1.40 8263 4.50 32.7

315 81.85 1.40 8255 4.37 36.7

355 100.9 1.40 8245 4.24 41.4

391 119.8 1.40 8235 4.15 45.6

390 119.1 1.40 8236 4.15 45.5

416 133.75 1.40 8228 4.10 48.6

415 132.9 1.40 8228 4.09 48.5

463 162.4 1.40 8213 4.01 54.2

462 161.6 1.40 8213 4.01 54.1

461 160.9 1.40 8214 4.01 53.9

460 160.5 1.40 8214 4.02 53.8

315.5 73 1.37 4123 4.07 59.5

112 8.775 1.37 1503 3.79 70.1

132.5 12.25 1.37 1501 3.78 83.0

173 20.625 1.37 1497 3.73 109

217 31.8 1.37 1492 3.66 137

250 41.675 1.37 1487 3.61 158

282.5 52.75 1.37 1482 3.58 179

313 64.475 1.37 1476 3.56 199

342 76.875 1.37 1470 3.56 219

372 91.925 1.37 1463 3.60 239

395 104.25 1.37 1457 3.62 255

417 116.3 1.37 1452 3.62 270

442 132.75 1.37 1444 3.68 288

466.5 149 1.37 1436 3.71 306

199 26.7 1.32 386 3.79 468

224.5 35.2 1.32 384 3.93 529

48

Appendix 1: Raw and reduced data from impeller power draw experiments for baffled D-6 (continued)

Impeller: D-6 Configuration: Baffled Diameter: 7.99'' D/T: 0.34


224.5 35.2 1.32 383 3.89 596

252 44 1.32 381 4.01 671

282 56.7 1.32 379 4.13 722

302 67 1.32 378 4.11 755

315 72.5 1.32 377 4.16 798

127.5 11.5 1.29 135 4.07 835

157 18 1.29 135 4.20 1028

202 30.65 1.29 135 4.32 1322

229 40.5 1.29 135 4.44 1499

254 50.3 1.29 135 4.48 1663

288.5 65.5 1.29 135 4.53 1888

312.5 78 1.29 135 4.59 2046

127 12.05 1.25 50.6 4.43 2154

181 25.55 1.25 50.6 4.63 3070

217.5 37.5 1.25 50.6 4.71 3689

255 52 1.25 50.6 4.75 4325

289.5 67.6 1.25 50.6 4.79 4910

315 80.5 1.25 50.6 4.82 5342

149.5 17.6 1.22 19.8 4.81 6298

200 31.75 1.22 19.8 4.85 8426

250 51.5 1.22 19.8 5.03 10532

300 74.35 1.22 19.8 5.04 12639

114 10.4 1.13 5.08 5.24 17447

149.5 18 1.13 5.08 5.27 22879

200 33.1 1.13 5.08 5.42 30608

250 51.6 1.13 5.08 5.40 38260

300 74.2 1.13 5.08 5.40 45912

118 10.2 1.00 1.09 5.45 74167

159 19.05 1.00 1.09 5.61 99937

210 33.75 1.00 1.09 5.70 131993

262 52.45 1.00 1.09 5.69 164677

304 70.25 1.00 1.09 5.66 191075

49

Appendix 2: Raw and reduced data from impeller power draw experiments for unbaffled D-6

Impeller: D-6 Configuration: Unbaffled Diameter: 7.99'' D/T: 0.34


8 11.75 1.48 122886 909 0.066

10.5 7.3 1.42 58284 346 0.18

19.5 13.5 1.42 58246 185 0.33

32 21.925 1.42 58195 112 0.54

50 34.9 1.42 58115 72.9 0.84

73.5 51.75 1.42 58012 50.1 1.24

97 67.7 1.42 57915 37.6 1.63

122 83.9 1.42 57815 29.5 2.06

159.5 109 1.42 57662 22.4 2.70

185 126 1.42 57558 19.2 3.13

216 142 1.42 57460 15.9 3.66

54 8.45 1.40 13753 15.4 3.77

70 11 1.40 13744 11.9 4.90

104 18 1.40 13720 8.82 7.29

182 38.4 1.40 13650 6.14 12.8

232 56.275 1.40 13589 5.54 16.4

264 69.275 1.40 13544 5.27 18.7

303 87.2 1.40 13482 5.03 21.6

337 104.1 1.40 13424 4.86 24.1

378 126.4 1.40 13348 4.69 27.2

104 9.2 1.37 3495 4.61 28.0

128 13.025 1.37 3485 4.31 34.5

165.5 20.675 1.37 3464 4.09 44.9

224 36.05 1.37 3422 3.89 61.6

276 53.15 1.37 3376 3.78 76.9

111 8.225 1.37 1252 3.62 83.4

140.5 12.85 1.37 1250 3.53 106

170.5 18.8 1.37 1248 3.50 128

196 24.625 1.37 1246 3.47 148

221 30.85 1.37 1244 3.42 167

239.5 35.75 1.37 1242 3.38 181

258 40.9 1.37 1240 3.33 196

279.5 46.65 1.37 1238 3.23 212

307 55.075 1.37 1235 3.16 234

162.5 14.75 1.34 589 3.09 254

205 22.975 1.34 586 3.02 322

232.5 29.05 1.34 584 2.97 367

264.5 37.1 1.34 581 2.93 419

152 11.8 1.32 321 2.88 428

181 15.9 1.32 322 2.73 509

222 23.45 1.32 323 2.68 623

250.5 29.25 1.32 323 2.62 701

274 34.5 1.32 324 2.59 766

192 16 1.31 223 2.45 776

238 23.4 1.31 223 2.34 962

273.5 29.4 1.31 223 2.22 1106

202 15.65 1.29 153 2.21 1169

227 19 1.29 153 2.12 1314

255.5 23.85 1.29 153 2.10 1479

287 29.65 1.29 153 2.07 1661

188 11.95 1.28 93.8 1.96 1766

213 15 1.28 93.8 1.91 2001

235.5 18.05 1.28 93.8 1.88 2213

265 22.3 1.28 93.8 1.84 2490

50

Appendix 2: Raw and reduced data from impeller power draw experiments for unbaffled D-6 (continued)

Impeller: D-6 Configuration: Unbaffled Diameter: 7.99'' D/T: 0.34


284.5 25.4 1.28 93.8 1.81 2673

181.5 9.35 1.25 53.2 1.68 2928

210 12.2 1.25 53.2 1.64 3388

235 15.25 1.25 53.2 1.64 3791

261 18.45 1.25 53.2 1.61 4210

281 21.25 1.25 53.2 1.60 4533

199 9.05 1.22 19.8 1.40 8384

220 10.9 1.22 19.8 1.38 9268

242 13.05 1.22 19.8 1.36 10195

265 15.55 1.22 19.8 1.35 11164

283 17.55 1.22 19.8 1.34 11922

233 8.5 1.14 5.00 1.02 36472

244 9.2 1.14 5.00 1.01 38193

256 10.05 1.14 5.00 1.00 40072

265 7.65 1.00 1.09 0.81 166562

51

Appendix 3: Raw and reduced data from impeller power draw experiments for baffled CD-6

Impeller: CD-6 Configuration: Baffled Diameter: 8.78'' D/T: 0.374


7 11.625 1.48 108357 738 0.079

19.5 34.075 1.4 107735 279 0.22

13 10.425 1.42 51786 201 0.30

23.5 19.4 1.42 51483 115 0.54

41.5 33.95 1.42 50993 64.3 0.96

60.5 48.775 1.42 50493 43.5 1.41

94 74.475 1.42 49626 27.5 2.23

113.5 89.55 1.42 49118 22.7 2.72

141.5 110 1.42 48429 17.9 3.44

181 140 1.42 47417 13.9 4.49

57 11.05 1.40 11525 11.2 5.74

56 8 1.40 8518 8.44 7.63

69.5 10.85 1.40 8514 7.43 9.47

139 29.95 1.40 8487 5.13 19.0

77 8.1 1.37 3754 4.62 23.3

111 15.325 1.37 3753 4.20 33.6

147.5 25.225 1.37 3751 3.92 44.7

212 48 1.37 3746 3.61 64.3

256 67.65 1.37 3742 3.49 77.7

255 66.95 1.37 3742 3.48 77.4

291 85.45 1.37 3739 3.41 88.4

290 84.9 1.37 3739 3.41 88.1

327 105.15 1.37 3735 3.32 99.4

326 104.5 1.37 3735 3.32 99.1

349 118.3 1.37 3732 3.28 106

347 117 1.37 3732 3.28 106

369 130.45 1.37 3730 3.24 112

368 129.85 1.37 3730 3.24 112

389 143.25 1.37 3727 3.20 119

388 142.65 1.37 3727 3.20 118

417 162.3 1.37 3723 3.15 127

414 160.2 1.37 3724 3.16 126

428 169.85 1.37 3722 3.13 131

427 169.2 1.37 3722 3.14 130

426 168.2 1.37 3722 3.13 130

88 8.2 1.37 1499 3.11 149

119.5 14.375 1.37 1498 3.04 176

157 23.675 1.37 1497 2.97 203

196 35.35 1.37 1496 2.87 228

231 47.95 1.37 1495 2.84 245

267 62.575 1.37 1493 2.80 264

299 75.8 1.37 1491 2.78 280

321.5 86.9 1.37 1490 2.75 303

346 99.3 1.37 1489 2.75 302

367 110.85 1.37 1487 2.77 318

396 127.6 1.37 1486 2.78 332

395 127.15 1.37 1486 2.83 344

126 12.85 1.32 373 2.84 369

167 22.6 1.32 373 2.84 490

202.5 34.8 1.32 372 2.98 595

238.5 48.3 1.32 372 2.98 702

265 60.2 1.32 371 3.01 781

286.5 70.25 1.32 371 3.00 845

108 9.35 1.29 134 2.88 864

52

Appendix 3: Raw and reduced data from impeller power draw experiments for baffled CD-6 (continued)

Impeller: CD-6 Configuration: Baffled Diameter: 8.78'' D/T: 0.374


116.5 10.95 1.29 133.5 2.90 933

148 17.95 1.29 133.5 2.94 1185

189 29.9 1.29 133.5 3.01 1513

221 40.9 1.29 133.5 3.01 1769

252 53.3 1.29 133.5 3.02 2017

110.5 9.7 1.25 52.4 2.94 2185

127.5 12.85 1.25 52.4 2.93 2521

169.5 22.4 1.25 52.4 2.89 3352

208 33.5 1.25 52.4 2.87 4113

233.5 41.8 1.25 52.4 2.84 4618

274 57.6 1.25 52.4 2.84 5419

116.5 9.95 1.22 19.8 2.79 5926

150 16.5 1.22 19.8 2.79 7631

200.5 29.5 1.22 19.8 2.80 10200

250 45.75 1.22 19.8 2.79 12718

300 65.6 1.22 19.8 2.78 15261

121 9.95 1.14 5.05 2.77 22595

170 20.1 1.14 5.05 2.83 31744

221 33.9 1.14 5.05 2.83 41268

272 51.5 1.14 5.05 2.84 50791

135 10.8 1.09 1.00 2.75 102461

185 20.45 1.09 1.00 2.78 140410

236 33.4 1.09 1.00 2.79 179118

286.5 49 1.09 1.00 2.77 217446

53

Appendix 4: Raw and reduced data from impeller power draw experiments for unbaffled CD-6

Impeller: CD-6 Configuration: Unbaffled Diameter: 8.78'' D/T: 0.374


7 11.625 1.48 108357 738 0.079

19.5 34.075 1.48 107735 279 0.22

13.5 10.5 1.42 48250 188 0.33

23 18.1 1.42 48206 112 0.56

36.5 28.6 1.42 48145 70.0 0.89

48 37.65 1.42 48092 53.3 1.17

61 47.825 1.42 48033 41.9 1.49

75 58.7 1.42 47970 34.0 1.84

90 69.85 1.42 47906 28.1 2.21

112 86.85 1.42 47807 22.6 2.76

34.5 6.275 1.40 11523 17.4 3.47

57 11.05 1.40 11525 11.2 5.74

86 18 1.40 11529 8.05 8.66

143 36.15 1.40 11538 5.85 14.4

186 54.25 1.40 11546 5.19 18.7

73 7.825 1.37 3725 4.96 22.3

92 10.675 1.37 3719 4.26 28.1

130 19.475 1.37 3700 3.89 39.9

171.5 31.675 1.37 3674 3.64 53.0

214 46.75 1.37 3641 3.45 66.8

252 62.6 1.37 3607 3.33 79.3

283 76.7 1.37 3577 3.24 89.9

327 98.9 1.37 3529 3.13 105

358 115.9 1.37 3492 3.06 116

389 134.55 1.37 3452 3.01 128

154 20.35 1.37 1270 2.90 138

184.5 28.4 1.37 1269 2.82 165

209 35.3 1.37 1267 2.73 187

229 41.45 1.37 1266 2.67 205

251 48.475 1.37 1265 2.60 225

267 53.5 1.37 1264 2.54 240

155.5 17.425 1.34 590 2.49 293

179.5 22.75 1.34 590 2.44 339

194.5 26.1 1.34 590 2.38 367

214 30.75 1.34 590 2.32 403

234.5 36.25 1.34 591 2.27 442

253 41.35 1.34 591 2.23 476

174 17.85 1.32 314 2.08 604

216 26 1.32 312 1.96 754

235 30.575 1.32 311 1.95 823

251 34.75 1.32 310 1.94 882

136 9.15 1.29 134 1.78 1087

171.5 13.5 1.29 134 1.65 1371

205 18.6 1.29 134 1.59 1639

234.5 23.8 1.29 134 1.55 1874

248 26.15 1.29 134 1.53 1982

211 17.55 1.28 93.0 1.42 2413

238.5 21.8 1.28 93.0 1.38 2728

252 24.15 1.28 93.0 1.37 2882

173 10.1 1.25 53.0 1.25 3383

193 12.5 1.25 53.0 1.24 3774

214 15.05 1.25 53.0 1.22 4184

237 18 1.25 53.0 1.19 4634

263 22 1.25 53.0 1.18 5142

185 9.15 1.22 19.8 1.02 9411

54

Appendix 4: Raw and reduced data from impeller power draw experiments for unbaffled CD-6 (continued)

Impeller: CD-6 Configuration: Unbaffled Diameter: 8.78'' D/T: 0.374


207 11.25 1.22 19.8 1.00 10530

227 13.45 1.22 19.8 0.99 11548

249 16.05 1.22 19.8 0.99 12667

263 17.9 1.22 19.8 0.99 13379

230 9.75 1.14 5.00 0.75 43473

240 10.6 1.14 5.00 0.75 45363

260 8.75 1.00 1.09 0.60 197333

55

Appendix 5: Raw and reduced data from impeller power draw experiments for baffled S-4

Impeller: S-4 Configuration: Baffled Diameter: 9.54'' D/T: 0.406


7 13.2 1.48 122714 559 0.082

22.5 41.375 1.48 122485 170 0.27

12.5 9.75 1.42 53230 134 0.33

26.5 20.95 1.42 52832 64 0.70

40 31.5 1.42 52458 42.4 1.06

52.5 41.5 1.42 52103 32.4 1.40

74 57.75 1.42 51526 22.7 2.00

95.5 73.6 1.42 50963 17.4 2.60

97 73.35 1.42 49722 16.8 2.71

115.5 86.675 1.42 49224 14.0 3.26

135 100.75 1.42 48698 11.9 3.85

164 120.2 1.42 47971 9.62 4.75

196 142 1.42 47156 7.96 5.78

51.5 7.35 1.40 9823 6.05 7.18

71.5 11.35 1.40 9782 4.85 10.0

134 29.8 1.40 9590 3.62 19.1

182 50.25 1.40 9378 3.31 26.6

227 73.85 1.40 9133 3.13 34.1

262 94.8 1.40 8916 3.02 40.3

297 118.3 1.40 8673 2.93 46.9

296 117.8 1.40 8678 2.94 46.7

295 116.8 1.40 8688 2.93 46.5

293 115.2 1.40 8705 2.93 46.1

320 134.8 1.40 8501 2.87 51.6

318 133.2 1.40 8518 2.88 51.2

192 45.925 1.37 3973 2.78 64.8

239 69.05 1.37 3969 2.70 80.7

267 85.1 1.37 3966 2.66 90.3

300 106.05 1.37 3962 2.63 102

332 128.2 1.37 3958 2.60 112

331 127.8 1.37 3958 2.60 112

367 155 1.37 3954 2.57 124

366 154.3 1.37 3954 2.57 124

385 169.85 1.37 3951 2.56 131

384 168.85 1.37 3951 2.56 130

168.5 32.175 1.37 1549 2.53 146

191.5 41.025 1.37 1544 2.50 166

228 57.5 1.37 1536 2.47 199

249 69.6 1.37 1529 2.51 218

270.5 83.425 1.37 1522 2.54 238

280.5 90.3 1.37 1518 2.56 248

297 102.475 1.37 1512 2.59 263

312.5 114.05 1.37 1506 2.61 278

329.5 126.65 1.37 1499 2.60 295

119 16.1 1.33 496 2.61 313

148 25.9 1.33 496 2.71 389

176 36.8 1.33 496 2.72 463

94.5 10.15 1.31 230 2.65 528

115 15.25 1.31 230 2.69 643

143 23.8 1.31 229 2.71 802

178 37.6 1.31 228 2.77 1003

199 46.75 1.31 227 2.75 1125

225 59.8 1.31 226 2.75 1277

249 73.4 1.31 225 2.76 1420

266 84 1.31 224 2.77 1522

56

Appendix 5: Raw and reduced data from impeller power draw experiments for baffled S-4 (continued)

Impeller: S-4 Configuration: Baffled Diameter: 9.54'' D/T: 0.406


133 19.975 1.28 96.0 2.69 1740

174 35.2 1.28 96.0 2.77 2276

200 46.35 1.28 96.0 2.76 2616

233.5 63.4 1.28 96.0 2.77 3054

128 18.5 1.25 48.6 2.76 3220

165.5 31.25 1.25 48.6 2.79 4163

200 46.25 1.25 48.6 2.83 5031

235 64.5 1.25 48.6 2.86 5912

260 79 1.25 48.6 2.86 6541

123.5 16.9 1.22 19.8 2.79 7417

149.5 24.75 1.22 19.8 2.79 8979

190 41 1.22 19.8 2.86 11411

231 61.5 1.22 19.8 2.90 13874

97 10.2 1.13 5.13 2.92 20981

135 20.3 1.13 5.13 3.00 29201

167.5 32.2 1.13 5.13 3.10 36231

200 47 1.13 5.13 3.17 43261

238 67.3 1.13 5.13 3.21 51480

103 11 1.00 1.09 3.18 92294

150 23.5 1.00 1.09 3.20 134408

200 42.25 1.00 1.09 3.24 179211

252 68 1.00 1.09 3.28 225806

57

Appendix 6: Raw and reduced data from impeller power draw experiments for unbaffled S-4

Impeller: S-4 Configuration: Unbaffled Diameter: 9.54'' D/T: 0.406


7 13.2 1.48 122714 559 0.082

22.5 41.375 1.48 122485 170 0.27

12.5 9.75 1.42 53230 134 0.33

26.5 20.95 1.42 52832 64.2 0.70

40 31.5 1.42 52458 42.4 1.06

52.5 41.5 1.42 52103 32.4 1.40

74 57.75 1.42 51526 22.7 2.00

95.5 73.6 1.42 50963 17.4 2.60

121 92.6 1.42 50288 13.6 3.34

150 114 1.42 49528 10.9 4.21

182.5 136 1.42 48747 8.79 5.20

203.5 150 1.42 48250 7.80 5.86

53 8.55 1.40 10518 6.65 6.90

62 10.5 1.40 10527 5.97 8.07

108 22.8 1.40 10584 4.27 14.0

159 41.95 1.40 10674 3.62 20.4

199 61.25 1.40 10764 3.38 25.3

233.5 80.55 1.40 10854 3.23 29.5

262 97.85 1.40 10935 3.11 32.8

287 114.5 1.40 11012 3.04 35.7

286 113.6 1.40 11008 3.03 35.6

322 139.6 1.40 11129 2.94 39.6

321 138.675 1.40 11125 2.94 39.5

125.5 20.375 1.37 3806 2.89 44.2

170.5 35.5 1.37 3798 2.73 60.2

213 53.325 1.37 3788 2.62 75.4

241 66.725 1.37 3781 2.56 85.5

270 82.35 1.37 3772 2.52 96.0

304 102.6 1.37 3761 2.48 108

339 124.7 1.37 3748 2.42 121

367 145.35 1.37 3737 2.41 132

366 144.6 1.37 3737 2.41 131

394 166.8 1.37 3725 2.40 142

149.5 23.4 1.37 1293 2.34 155

168 29.425 1.37 1289 2.33 175

194.5 38.675 1.37 1284 2.28 203

214 45.025 1.37 1281 2.19 224

231 52.75 1.37 1276 2.21 243

252 61.175 1.37 1272 2.15 266

259 64.35 1.37 1270 2.14 273

136 16.4 1.34 532 2.02 336

165 22.95 1.34 533 1.92 407

190 29.475 1.34 533 1.86 468

205 33.775 1.34 534 1.83 504

223.5 39.25 1.34 535 1.79 549

149 16.5 1.32 313 1.73 613

178 22.7 1.32 312 1.67 734

210.5 30.8 1.32 311 1.62 872

234 37.35 1.32 310 1.59 972

116 8.68 1.29 134 1.53 1095

139 11.85 1.29 134 1.45 1312

164.5 16.05 1.29 134 1.41 1552

189 20.55 1.29 134 1.36 1783

208.5 24.6 1.29 134 1.34 1967

223 27.85 1.29 134 1.33 2104

58

Appendix 6: Raw and reduced data from impeller power draw experiments for unbaffled S-4 (continued)

Impeller: S-4 Configuration: Unbaffled Diameter: 9.54'' D/T: 0.406


177 16.55 1.28 97.5 1.26 2280

208 22.3 1.28 97.5 1.23 2679

231 27.3 1.28 97.5 1.22 2975

163 12.1 1.26 52.3 1.11 3843

187 15.8 1.26 52.3 1.10 4409

202 18 1.26 52.3 1.07 4763

225 21.9 1.26 52.3 1.05 5305

154 8.95 1.22 19.8 0.95 9249

174 11.2 1.22 19.8 0.93 10450

194 13.8 1.22 19.8 0.92 11651

217 17.1 1.22 19.8 0.91 13033

154 8.95 1.00 1.09 0.71 41060

174 11.2 1.00 1.09 0.71 43068

194 13.8 1.00 1.09 0.71 46416

207 8.475 1.00 1.09 0.61 185483

59

Appendix 7: Raw and reduced data from impeller power draw experiments for baffled P-4

Impeller: P-4 Configuration: Baffled Diameter: 9.50'' D/T: 0.404


6.5 11.05 1.48 121371 552 0.077

18 30.475 1.48 120843 198 0.21

26.5 44.9 1.48 120450 135 0.32

39 66.825 1.48 119854 92.7 0.47

47.5 80.9 1.48 119471 75.6 0.57

60 101.2 1.48 118919 59.3 0.72

79.5 130.25 1.48 118129 43.5 0.97

43.5 34.925 1.42 56532 40.6 1.06

54 43.3 1.42 56175 32.7 1.32

73 57.5 1.42 55571 23.7 1.81

100 78.4 1.42 54681 17.2 2.52

121 92.85 1.42 54066 13.9 3.08

151.5 115 1.42 53123 11.0 3.93

183 138.2 1.42 52136 9.07 4.84

56 10.1 1.40 12451 7.18 6.11

104 21.55 1.40 12310 4.44 11.5

150 35.45 1.40 12138 3.51 16.8

177 45 1.40 12020 3.20 20.0

207 56.825 1.40 11874 2.96 23.7

231 67 1.40 11749 2.80 26.7

259 79.375 1.40 11596 2.64 30.3

281.5 89.55 1.40 11470 2.52 33.3

311 104.1 1.40 11290 2.40 37.4

352 124.6 1.40 11037 2.24 43.3

387 144 1.40 10798 2.14 48.7

386 143 1.40 10810 2.14 48.5

187.5 29.9 1.37 4210 1.94 59.2

239.5 44.625 1.37 4193 1.77 76.0

297 63.975 1.37 4169 1.65 94.7

355 86.375 1.37 4142 1.56 114

400 106.175 1.37 4118 1.51 129

438 124.5 1.37 4096 1.48 142

468 139.9 1.37 4077 1.46 153

467 139.1 1.37 4078 1.45 152

492 152.6 1.37 4062 1.44 161

491 151.8 1.37 4063 1.44 161

516 165.9 1.37 4046 1.42 170

515 165.15 1.37 4047 1.42 169

527 171.5 1.37 4039 1.41 173

213 28.375 1.37 1594 1.43 178

250 37.575 1.37 1590 1.37 209

270.5 43.325 1.37 1587 1.35 227

306.5 55.225 1.37 1581 1.34 258

337.5 65.4 1.37 1576 1.31 285

374.5 79.4 1.37 1569 1.29 317

412.5 94.9 1.37 1561 1.27 351

149.5 11.85 1.34 506 1.23 385

190 18.85 1.34 505 1.22 490

251 31.975 1.34 503 1.18 650

297.5 43.45 1.34 501 1.14 773

326 50.5 1.34 500 1.11 849

169 13.25 1.31 234 1.10 922

222 22.15 1.31 233 1.07 1213

276.5 34.2 1.31 232 1.06 1514

318.5 45.25 1.31 232 1.06 1749

60

Appendix 7: Raw and reduced data from impeller power draw experiments for baffled P-4 (continued)

Impeller: P-4 Configuration: Baffled Diameter: 9.50'' D/T: 0.404


355.5 56.65 1.31 231 1.07 1956

166 11.6 1.28 96.0 1.02 2153

216 19.85 1.28 96.0 1.04 2802

270 31.3 1.28 96.0 1.04 3502

320 44.35 1.28 96.0 1.05 4151

354 54.65 1.28 96.0 1.06 4592

400 70.85 1.28 96.0 1.08 5188

244 25.55 1.25 48.9 1.07 6054

293.5 37.3 1.25 48.9 1.08 7282

340.5 50.85 1.25 48.9 1.10 8448

393.5 69.2 1.25 48.9 1.12 9763

419.5 79 1.25 48.9 1.12 10408

185 14.6 1.22 19.8 1.10 11018

238 24.55 1.22 19.8 1.11 14174

288 36.05 1.22 19.8 1.12 17152

344.5 52.4 1.22 19.8 1.13 20517

404 72.9 1.22 19.8 1.15 24061

160 10.8 1.14 4.96 1.16 35585

220 20.45 1.14 4.96 1.16 48929

281 33.5 1.14 4.96 1.17 62496

340 49 1.14 4.96 1.16 75617

401.5 68.1 1.14 4.96 1.16 89295

175 11.2 1.00 1.09 1.15 155497

224.5 18.55 1.00 1.09 1.15 199481

275 28 1.00 1.09 1.16 244353

330 40.5 1.00 1.09 1.16 293223

375 53 1.00 1.09 1.18 333208

61

Appendix 8: Raw and reduced data from impeller power draw experiments for unbaffled P-4

Impeller: P-4 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404


6.5 11.05 1.48 121371 552 0.077

18 30.475 1.48 120843 198 0.21

26.5 44.9 1.48 120450 135 0.32

39 66.825 1.48 119854 92.7 0.47

47.5 80.9 1.48 119471 75.6 0.57

60 101.2 1.48 118919 59.3 0.72

79.5 130.25 1.48 118129 43.5 0.97

38.5 22.1 1.42 40003 32.8 1.33

56 32.475 1.42 39988 22.8 1.93

74 43.3 1.42 39973 17.4 2.55

92 53.2 1.42 39958 13.8 3.17

103.5 59.55 1.42 39949 12.2 3.57

118 68.15 1.42 39936 10.8 4.07

130 74.225 1.42 39927 9.66 4.49

148.5 84.2 1.42 39913 8.40 5.13

168 95.5 1.42 39896 7.44 5.80

190 107.7 1.42 39879 6.56 6.57

218 124.7 1.42 39854 5.77 7.54

230 130 1.42 39846 5.40 7.96

87.5 14.3 1.40 10170 4.17 11.7

78.5 12.275 1.40 10171 4.44 10.5

141 27.8 1.40 10164 3.12 18.8

194 45 1.40 10157 2.67 26.0

242 63.55 1.40 10148 2.42 32.4

276 77.55 1.40 10142 2.27 37.0

318 96.3 1.40 10134 2.12 42.6

373 123.3 1.40 10122 1.98 50.1

372 122.675 1.40 10123 1.98 49.9

428 152.85 1.40 10109 1.86 57.5

427 152.2 1.40 10110 1.86 57.4

426 151.15 1.40 10110 1.86 57.3

172 24.875 1.37 3763 1.92 60.8

210 34.25 1.37 3755 1.77 74.4

255 47.125 1.37 3744 1.65 90.6

299 61.2 1.37 3733 1.56 107

334 74 1.37 3722 1.51 119

366 86.2 1.37 3712 1.47 131

136 11.825 1.37 1307 1.46 138

186 20.6 1.37 1305 1.36 189

211 26.05 1.37 1304 1.33 215

230 30.475 1.37 1303 1.31 235

252 36.575 1.37 1302 1.31 257

267.5 40.4 1.37 1301 1.29 273

148 12.075 1.36 683 1.27 285

187.5 18.65 1.36 692 1.22 357

223 25.65 1.36 702 1.19 419

247 30.25 1.36 708 1.14 460

176 14.6 1.32 425 1.11 531

201 18.5 1.32 424 1.08 607

230 24.1 1.32 424 1.08 695

238 25.8 1.32 424 1.08 719

181 14.5 1.32 314 1.05 737

212 19.475 1.32 314 1.03 862

226 21.8 1.32 314 1.01 918

177 13.2 1.31 223 1.00 1012

62

Appendix 8: Raw and reduced data from impeller power draw experiments for unbaffled P-4 (continued)

Impeller: P-4 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404


197 16.4 1.31 223 1.01 1126

216 18.8 1.31 96.8 0.82 2445

170 9.6 1.28 96.8 0.81 2574

180 11.1 1.28 96.8 0.81 2703

190 12.1 1.28 49.4 0.74 4109

200 13.3 1.28 49.4 0.74 4951

210 14.7 1.28 49.4 0.72 5694

166 8.2 1.26 49.4 0.70 6288

200 12 1.26 49.4 0.71 6758

230 15.3 1.26 19.8 0.64 10839

254 18.2 1.26 19.8 0.63 12090

273 21.5 1.26 19.8 0.62 13400

182 8.2 1.22 19.8 0.62 14353

203 10.15 1.22 5.00 0.51 44478

225 12.15 1.22 5.00 0.50 47798

241 14.05 1.22 5.00 0.50 51117

201 7.45 1.14 1.09 0.43 205256

63

Appendix 9: Raw and reduced data from impeller power draw experiments for baffled SC-3

Impeller: SC-3 Configuration: Baffled Diameter: 9.50'' D/T: 0.404


11.5 10.45 1.48 114300 163 0.15

27 26.7 1.48 113171 75.7 0.35

40 40.05 1.48 112244 51.7 0.52

57 56.75 1.48 111084 36.1 0.74

69 68.6 1.48 110260 29.8 0.91

84.5 82 1.48 109330 23.7 1.12

48 19.475 1.42 49035 18.6 1.35

69.5 28.2 1.42 48716 12.8 1.97

91 36.775 1.42 48403 9.76 2.59

108 43.325 1.42 48163 8.17 3.09

125.5 50.4 1.42 47905 7.04 3.61

159 64 1.42 47408 5.57 4.62

180.5 71 1.42 47152 4.79 5.28

207 82 1.42 46750 4.21 6.10

73 7.125 1.40 10140 2.98 9.78

98.5 10.425 1.40 10138 2.40 13.2

136 16 1.40 10135 1.93 18.2

189 25.45 1.40 10129 1.59 25.4

254 39.25 1.40 10120 1.36 34.1

303 50.85 1.40 10113 1.24 40.7

348 62.675 1.40 10105 1.15 46.8

390 74.3 1.40 10098 1.09 52.5

181.5 14.625 1.37 4023 1.01 60.0

52.5 24.725 1.37 3995 0.88 84.0

349 41.825 1.37 3947 0.78 118

426 58.075 1.37 3901 0.73 145

503 76.825 1.37 3849 0.69 174

552 89.675 1.37 3813 0.67 193

582.5 98.275 1.37 3789 0.66 204

596.5 101.975 1.37 3778 0.65 210

627 110.95 1.37 3753 0.64 222

626 110.6 1.37 3754 0.64 222

267.5 19.375 1.37 1438 0.62 247

319 26.6 1.37 1439 0.60 295

372 35.2 1.37 1441 0.58 343

418 41.175 1.37 1442 0.54 386

468 50.3 1.37 1443 0.52 431

520 60.4 1.37 1445 0.51 478

231 11.7 1.34 607 0.51 495

313.5 20.05 1.34 608 0.47 672

382 28.7 1.34 609 0.46 818

455 40 1.34 609 0.45 972

498.5 47.8 1.34 610 0.45 1064

459 39.5 1.32 313 0.45 1872

217 8.2 1.29 133 0.42 2044

238 9.95 1.29 133 0.43 2240

252 11.25 1.29 133 0.43 2371

290 15.1 1.29 133 0.43 2724

355 22.65 1.29 134 0.44 3324

400 28.95 1.29 134 0.44 3735

462 38.95 1.29 135 0.44 4295

501 46.7 1.29 135 0.45 4643

229 9.25 1.25 53.0 0.44 5242

253 11.4 1.25 53.0 0.45 5791

308 17.2 1.25 53.0 0.46 7050

64

Appendix 9: Raw and reduced data from impeller power draw experiments for baffled SC-3 (continued)

Impeller: SC-3 Configuration: Baffled Diameter: 9.50'' D/T: 0.404


369.5 25.4 1.25 53.0 0.47 8458

415.5 33.6 1.25 53.0 0.50 9511

466 42.25 1.25 53.0 0.50 10667

522 53.35 1.25 53.0 0.50 11949

236 10.5 1.22 19.8 0.48 14055

287 15.6 1.22 19.8 0.49 17093

338 21.7 1.22 19.8 0.49 20130

382 28 1.22 19.8 0.49 22751

446 38.65 1.22 19.8 0.50 26562

251 11.7 1.13 5.06 0.51 54540

301 16.9 1.13 5.06 0.51 65404

381.5 27 1.13 5.06 0.51 82896

451.5 38 1.13 5.06 0.51 98107

267 11.45 1.00 1.09 0.50 237244

321 16.85 1.00 1.09 0.51 285226

389.5 25.25 1.00 1.09 0.52 346092

506.5 42.7 1.00 1.09 0.52 450053

65

Appendix 10: Raw and reduced data from impeller power draw experiments for unbaffled SC-3

Impeller: SC-3 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404


11.5 10.45 1.48 114300 163 0.15

27 26.7 1.48 113171 75.7 0.35

40 40.05 1.48 112244 51.7 0.52

57 56.75 1.48 111084 36.1 0.74

69 68.6 1.48 110260 29.8 0.91

84.5 82 1.48 109330 23.7 1.12

53.5 25.25 1.42 55237 19.4 1.33

71 33.725 1.42 55033 14.7 1.78

90 42.875 1.42 54812 11.6 2.26

106.5 50.7 1.42 54623 9.83 2.69

135.5 64 1.42 54303 7.66 3.44

168 78.3 1.42 53958 6.10 4.29

202.5 93 1.42 53604 4.99 5.21

241.5 108.5 1.42 53230 4.09 6.25

70 8.35 1.40 13178 3.80 7.22

97.5 12.525 1.40 13115 2.94 10.1

156 22.525 1.40 12964 2.06 16.4

246 42.15 1.40 12667 1.55 26.4

317 60.975 1.40 12383 1.35 34.8

378 78.525 1.40 12117 1.23 42.4

436 96.85 1.40 11840 1.14 50.0

154 10.9 1.37 3698 1.05 55.4

204 17 1.37 3690 0.93 73.5

256 24.3 1.37 3681 0.85 92.5

320 34.725 1.37 3668 0.77 116

393 48.35 1.37 3652 0.71 143

457 61.7 1.37 3635 0.67 167

458 61.8 1.37 3635 0.67 168

515 74.6 1.37 3619 0.64 189

514 74.2 1.37 3620 0.64 189

188 9.55 1.37 1261 0.62 198

223.5 13.1 1.37 1259 0.60 236

270.5 18.55 1.37 1257 0.58 286

299.5 22.1 1.37 1255 0.56 317

326 25.7 1.37 1253 0.55 346

345.5 28.45 1.37 1252 0.54 367

263 16.05 1.35 781 0.54 443

299.5 19.5 1.35 781 0.50 504

330 23.05 1.35 782 0.49 555

226 10.4 1.33 527 0.48 555

266 14 1.33 520 0.46 661

292 16.55 1.33 516 0.45 733

310.5 18.45 1.33 512 0.45 784

326 20 1.33 510 0.44 828

263 12.55 1.32 392 0.43 860

294.5 15.5 1.32 394 0.42 959

321 18.4 1.32 395 0.42 1040

330 19.2 1.32 396 0.42 1068

288 14.4 1.32 316 0.41 1165

305.5 16 1.32 318 0.41 1228

329 18.65 1.32 321 0.41 1309

271 12.4 1.31 264 0.40 1310

294 14.55 1.31 264 0.40 1421

319 16.75 1.31 264 0.39 1542

246 9.3 1.29 134 0.37 2302

66

Appendix 10: Raw and reduced data from impeller power draw experiments for unbaffled SC-3 (continued)

Impeller: SC-3 Configuration: Unbaffled Diameter: 9.50'' D/T: 0.404


275 11.35 1.29 134 0.36 2573

292 12.6 1.29 134 0.36 2732

305 13.75 1.29 134 0.36 2854

256 9.25 1.28 96.0 0.34 3321

291 11.95 1.28 96.0 0.34 3775

301.5 12.5 1.28 96.0 0.33 3911

318 14.2 1.28 96.0 0.34 4125

331 15.15 1.28 96.0 0.34 4293

263 8.7 1.25 52.6 0.31 6066

286.5 10.25 1.25 52.6 0.31 6608

304 11.6 1.25 52.6 0.31 7012

321 12.9 1.25 52.6 0.31 7404

350 15.2 1.25 52.6 0.31 8073

280 8.55 1.22 19.8 0.28 16676

302 9.85 1.22 19.8 0.28 17986

324 11.2 1.22 19.8 0.27 19296

340 12.3 1.22 19.8 0.27 20249

301 7.35 1.14 5.00 0.22 66607

312.5 7.75 1.14 5.00 0.22 69152

313 6 1.00 1.09 0.19 278118

67

Appendix 11: Raw and reduced data from impeller power draw experiments for baffled HE-3

Impeller: HE-3 Configuration: Baffled Diameter: 9.51'' D/T: 0.405


7 6.65 1.48 114500 285 0.088

19.5 20.15 1.48 114056 111 0.25

33 34.05 1.48 113598 65.6 0.42

44 45.4 1.48 113225 49.2 0.56

57 58.02 1.48 112809 37.5 0.73

72 73.375 1.48 112304 29.7 0.92

90 90 1.48 111757 23.3 1.16

50 20.825 1.42 46615 18.2 1.48

70 28.275 1.42 46546 12.6 2.08

92 37.275 1.42 46462 9.63 2.73

111 45.45 1.42 46385 8.07 3.30

141.5 58.625 1.42 46262 6.40 4.22

175 72 1.42 46137 5.14 5.24

204 84 1.42 46025 4.41 6.12

75 7.6 1.40 11018 3.00 9.27

95 10.325 1.40 10992 2.54 11.8

171 22.65 1.40 10875 1.72 21.4

261 40.975 1.40 10701 1.33 33.2

287 47 1.40 10644 1.27 36.7

332 58.025 1.40 10539 1.17 42.9

376 69.55 1.40 10429 1.09 49.1

427 83.2 1.40 10300 1.01 56.5

489 100 1.40 10140 0.93 65.7

259 23.175 1.37 3947 0.78 87.5

362 39 1.37 3943 0.67 123

440 53 1.37 3934 0.62 149

510 67.125 1.37 3926 0.59 173

572 80.725 1.37 3918 0.56 195

624.5 92.25 1.37 3910 0.54 213

685 106.7 1.37 3904 0.52 234

751 123.7 1.37 3896 0.50 258

329 22.775 1.37 1464 0.48 299

387 30.45 1.37 1455 0.46 354

423.5 35.45 1.37 1449 0.45 389

464 40.325 1.37 1443 0.42 428

511.5 48.1 1.37 1434 0.42 475

559 55.45 1.37 1425 0.40 523

610.5 64.125 1.37 1414 0.39 575

640 69.65 1.37 1407 0.39 606

663 73.875 1.37 1402 0.38 630

259 10.7 1.34 533 0.37 634

349.5 18.275 1.34 529 0.35 862

419 25.5 1.34 525 0.34 1041

483.5 33.55 1.34 521 0.33 1212

529 39.75 1.34 517 0.33 1335

568 45.575 1.34 514 0.33 1442

610.5 52.45 1.34 510 0.33 1561

653.5 59.95 1.34 506 0.33 1685

406.5 21.55 1.31 231 0.31 2250

493.4 31.85 1.31 230 0.31 2733

566.5 42 1.31 230 0.31 3139

639 54.2 1.31 230 0.31 3544

682 62.1 1.31 230 0.32 3784

370 17.2 1.28 97 0.30 4760

462.5 27.25 1.28 97 0.31 5950

68

Appendix 11: Raw and reduced data from impeller power draw experiments for baffled HE-3 (continued)

Impeller: HE-3 Configuration: Baffled Diameter: 9.51'' D/T: 0.405


534.5 36.45 1.28 97 0.31 6876

602 46.5 1.28 97.0 0.31 7744

391 19 1.25 49.2 0.31 9668

463 26.8 1.25 49.2 0.31 11449

538 36.25 1.25 49.2 0.31 13303

614 47.3 1.25 49.2 0.31 15183

291.5 10 1.22 19.8 0.30 17397

387.5 17.9 1.22 19.8 0.30 23127

479 27.8 1.22 19.8 0.31 28588

546 36.05 1.22 19.8 0.31 32586

310 10.6 1.13 5.11 0.30 66920

380 15.9 1.13 5.11 0.30 82031

450.5 22.8 1.13 5.11 0.31 97250

518 29.4 1.13 5.11 0.30 111821

338 10.5 1.00 1.09 0.32 268362

414 15.5 1.00 1.09 0.32 328704

501 22.7 1.00 1.09 0.32 397780

577 30.4 1.00 1.09 0.32 458122

69

Appendix 12: Raw and reduced data from impeller power draw experiments for unbaffled HE-3

Impeller: HE-3 Configuration: Unbaffled Diameter: 9.51'' D/T: 0.405


7 6.65 1.48 114500 285 0.088

19.5 20.15 1.48 114056 111 0.25

33 34.05 1.48 113598 65.6 0.42

44 45.4 1.48 113225 49.2 0.56

57 58.02 1.48 112809 37.5 0.73

72 73.375 1.48 112304 29.7 0.92

90 90 1.48 111757 23.3 1.16

35.5 11.225 1.42 35511 19.5 1.38

50 16.1 1.42 35537 14.1 1.94

73 23.85 1.42 35579 9.79 2.83

93.5 29.95 1.42 35612 7.49 3.63

114.5 36.925 1.42 35649 6.16 4.44

136 44.75 1.42 35691 5.29 5.26

163 53.8 1.42 35740 4.43 6.30

186.5 61.725 1.42 35783 3.88 7.20

210.5 69.55 1.42 35825 3.43 8.12

234 76.875 1.42 35864 3.07 9.01

267 88 1.42 35924 2.70 10.3

103.5 12.15 1.40 11559 2.52 12.2

174 23.9 1.40 11434 1.75 20.7

248 39.025 1.40 11273 1.41 30.0

313 54.35 1.40 11110 1.23 38.4

117.5 7.325 1.37 4159 1.20 37.6

146 10.175 1.37 4152 1.08 46.9

198.5 16.125 1.37 4136 0.93 63.9

252 23.075 1.37 4118 0.82 81.5

307.5 30.925 1.37 4097 0.74 100

365 40.175 1.37 4073 0.68 119

422 50.15 1.37 4047 0.64 139

489 62.775 1.37 4014 0.60 162

539.5 72.95 1.37 3987 0.57 180

596 85.05 1.37 3955 0.54 201

194 8.775 1.37 1271 0.53 203

216.5 10.6 1.37 1269 0.51 227

265.5 15.05 1.37 1266 0.48 280

317 20.35 1.37 1261 0.46 335

362.5 25.35 1.37 1257 0.44 384

401.5 29.9 1.37 1253 0.42 427

245 10.875 1.36 728 0.42 444

293.5 14.775 1.36 732 0.39 529

345.5 19.725 1.36 737 0.38 618

247 9.8 1.33 507 0.37 632

270.5 11.55 1.33 506 0.37 693

335 16.45 1.33 506 0.34 859

354 18.2 1.33 505 0.34 909

376.5 20.2 1.33 505 0.33 967

319 14.1 1.32 395 0.33 1036

355 17.2 1.32 395 0.32 1154

375.5 19 1.32 395 0.32 1222

316.5 12.85 1.32 313 0.30 1294

340 14.6 1.32 313 0.30 1389

358 16.1 1.32 313 0.30 1462

325 13.125 1.31 264 0.29 1574

347.5 14.75 1.31 264 0.29 1683

359.5 15.8 1.31 264 0.29 1741

70

Appendix 12: Raw and reduced data from impeller power draw experiments for unbaffled HE-3 (continued)

Impeller: HE-3 Configuration: Unbaffled Diameter: 9.51'' D/T: 0.405


334 13.1 1.31 223 0.28 1913

350.5 14.45 1.31 223 0.28 2007

293 9.25 1.28 98.3 0.26 3721

315 10.5 1.28 98.3 0.26 4001

329 11.35 1.28 98.3 0.25 4179

343 12.5 1.28 98.3 0.26 4356

362 13.85 1.28 98.3 0.26 4598

381.5 15.25 1.28 98.3 0.25 4845

307 8.95 1.25 49.4 0.24 7550

325.5 10.1 1.25 49.4 0.24 8005

344 11.2 1.25 49.4 0.24 8460

371 13.2 1.25 49.4 0.24 9124

394 14.6 1.25 49.4 0.23 9690

313 8.1 1.22 19.8 0.21 18680

334.5 9.2 1.22 19.8 0.21 19964

359.5 10.7 1.22 19.8 0.21 21456

373 11.55 1.22 19.8 0.21 22261

332 6.9 1.14 5.00 0.17 73621

347 7.5 1.14 5.00 0.17 76948

344 5.6 1.00 1.09 0.17 273126

IMPELLER POWER DRAW ACROSS THE FULL REYNOLDS ...

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