05-Dinamika Fluida Lanjut -Turbulent Flow

8/13/2019 05-Dinamika Fluida Lanjut -Turbulent Flow

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Lab. Mekanika F lui da Teknik Mesin-F TUI Dr.I r. Harinaldi, M .Eng

Universitas Indonesiaakultas Teknik Jurusan Teknik Mesin



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Introduction Turbulent flow is actually more likely to occur than laminar

flow in practical situations However, turbulent flow is a very complex process

Numerous persons have devoted considerable effort in

attempting to understand the variety of baffling aspects of

turbulence

Although a considerable amount of knowledge about the topichas been developed, the field of turbulent flow still remains

the least understood area of fluid mechanics

In this chapter we will learn only some of the very basic ideas

concerning turbulence


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Transition rom Laminar to Turbulent Consider a long pipe that is initially filled with a fluid at rest

A typical trace of the axial component of velocity measured ata given location in the flow, u = u(t), is shown in the figure


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Transition rom Laminar to TurbulentThe Nature of Turbulence Irregularity (random nature) is the distinguishing feature of

turbulent flow

The character of many of the important properties (pressure

drop, heat transfer, etc.) depends strongly on the existence

and nature of the turbulent fluctuations or randomness

Calculation of the heat transfer, pressure drop, and manyother parameters would not be possible without inclusion of

the seemingly small, but very important, effects associated

with the randomness of the flow

Mixing and heat and mass transfer processes are much

enhanced in turbulent flow compared to laminar flow


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Transition rom Laminar to TurbulentTurbulent Flow Regime and Inviscid Flow

In inviscid flow, the Reynolds number is infinite (because theviscosity is regarded as zero), and the flow most surely would

be turbulent

Reasonable results were obtained by using the inviscid

Bemoulli equation as the governing equation

The reason that inviscid analyses gave reasonable results isthat viscous effects were not very important and what is used

in the calculations was actually the time-averaged velocity


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Turbulent Shear Stress

Chaotic, random behavior of the various fluid parameters.Such variations occur in the three components of variable that

has a field description: Velocity

Pressure

vorticity

Temperature

Shear stress

Turbulent flows can be described in terms of their mean

values (denoted with an overbar) on which are superimposed

the fluctuations (denoted with a prime)

For velocity field:

( , , , ) velocity component in direction( , , , ) velocity component in direction( , , , ) velocity component in direction

u u x y z t xv v x y z t yw w x y z t z

Field Representation


7/17Lab. Mekanika F lui da Teknik Mesin-F TUI Dr.I r. Harinaldi, M .Eng


Mean (time average) valueof velocity (x -component)1 ( , , , )o

o

t T

tu u x y z t dt

T

Fluctuating part of

velocity (x -component)u u u

1 1 1 1 0o o oo o o

t T t T t T

t t tu u u dt udt u dt Tu Tu

T T T T

(Fluctuating part)

(Time average of Fluctuating part)

Mean and Fluctuation




Turbulent Intensity

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2 21

o

o

t T

tTI u u dt

T

Turbulent Parameter Turbulent intensity Reynolds shear Stress

Higher order turbulence

Time scale

One dimensional flow

Two dimensional flow

Turbulent intensity is often presented

as relative value to the reference

velocity, i.e mean velocity, free-

stream velocity, etc

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2 2

2

u vTI

Three dimensional flow

1/ 2

2 2 2

3

u v wTI



Turbulent Shear StressTurbulent Shear Stress It is tempting to extend the concept of viscous shear stress

for laminar flow : = (du/dy), by replacing u with averagevelocity

However numerous experimental and theoretical studies have

shown that such approach leads to completely incorrectresults, that is,

Different mechanism of shear stress production



Turbulent Shear StressTurbulent Shear Stress

lam turb

du

u vdy

Total Shear Stress:

Laminar shear stress

Turbuent shear stress (Reynolds shear stress)

The shear stress in turbulent flow is not merely proportional

to the gradient of the time-averaged velocity

It also contains a contribution due to the random fluctuationsof the x and y components of velocity

The density is involved because of the momentum transfer of

the fluid within the random eddies



Turbulent Shear StressEddy Viscosity An alternate form for the shear stress for turbulent flow is

given in terms of the eddy viscosity

du

dy

Although the concept of an eddy viscosity is intriguing, in

practice it is not an easy parameter to use

Unlike the absolute viscosity which is a known value for a

given fluid, the eddy viscosity is a function of both the fluid

and the flow conditions

That is, the eddy viscosity of water cannot be looked up in

handbooks-its value changes from one turbulent flow

condition to another and from one point in a turbulent flow to

another



Turbulent Shear StressMixing Length Theory The inability to accurately determine the Reynolds stress,u'v', is equivalent to not knowing the eddy viscosity Several semiempirical theories have been proposed to

determine approximate values of

L. Prandtl (1875 1953) proposed that the turbulent process

could be viewed as the random transport of bundles of fluidparticles over a certain distance, lm , the mix ing length, from a

region of one velocity to another region of a different velocity

By the use of some assumptions and physical reasoning, it

was concluded that the eddy viscosity was given by

2

m

dul

dy

Hence: 22

m

dul

dy


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Turbulent Velocity Profile Considerable information concerning turbulent velocity

profiles has been obtained through: the use of dimensional analysis

experimentation

semiempirical theoretical efforts

Within the viscous sublayer the viscous shear stress is

dominant compared with the turbulent stress, and the random,eddying nature of the flow is essentially absent

In the outer turbulent layer the Reynolds stress is dominant,

and there is considerable mixing and randomness to the flow.

The character of the flow within these two regions is entirely

different within the viscous sublayer the fluid viscosity is an important

parameter; the density is unimportant

In the outer layer the opposite is true


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Turbulent Shear StressStructure of Turbulent Flow in Pipe Although the relative magnitude of lamcompared to turbis a

complex function dependent on the specific flow involved,

typical measurements indicate the structure shown below


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Turbulent Velocity Profile The turbulent velocity profile in a smooth pipe

Subviscous layer (law of the wall)

*

*

u yu

u

* wall

y R r

u

Overlap region

*2,5ln 5,0

*

u yu

u

Central region

2,5ln*

cV u Ru y

1/

1

n

c

u r

V R

Power law

velocity


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Turbulent Velocity Profile Power Law Velocity Profile

Exponen nfor power law velocity

profile

Typical laminar flow and

turbulent flow velocity profile

05-Dinamika Fluida Lanjut -Turbulent Flow

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