Intro to Turbulence

7/24/2019 Intro to Turbulence

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For

more

information

on

the

topics

covered

in

this

Lecture

Please

see

Introduction

to

CFD

Finite

Volume

Method

by

Malalasekera and

Versteeg


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. ree tur u ent ows: m x ng ayers, ets an wa es.

2. Mixin la er forms at the interface of two re ions:

one with fast and the other with slow moving fluid.

3. Jet A region of highspeed flow completely

.

4. Wake formed behind an object in a flow slow

moving region is surrounded by fast moving fluid.


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1. Velocity changes across an initially thin layer are important

in all three flows.

.

in the flow direction from the point where the different

streams initially meet

.

and rapid widening of the region across which the velocity

changes take place.

.

scales. Large eddies with a size comparable to the width

across the flow are occurring alongside eddies of very

.


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Visualisationofajetflow:Source:VanDyke(1982)


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1. The flow inside the jet region is fully turbulent, but the flow

in the outer region far away from the jet is smooth and

.

2. The position of the edge of the turbulent zone is determined

by the (timedependent) passage of individual large eddies.

the surrounding region. During the resulting bursts ofturbulent activity in the outer region called intermittency

zone.

4. This process is termed entrainment and is the main cause of

the s readin of turbulent flows includin wall boundar

layers) in the flow direction.


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stationary surrounding fluid..

decrease in magnitude in the flow direction.

. s causes t e ecrease o t e mean spee o t e et at ts centre ne.4. Similarly the difference between the speed of the wake fluid and its fast

moving surroundings will decrease in the flow direction.

5. In mixing layers the width of the layer containing the velocity change

continues to increase in the flow direction but the overall velocity

difference between the two outer regions is unaltered.


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1. Experimental observations show that after a certain distance their

.

2. Only the local environment appears to control the turbulence in the flow.. e appropr a e eng sca e s e a w .

4. We find that if yis the distance in the crossstream direction

U and U re resent the maximum & minimum mean velocit at a distance x

downstream of the source.

, ,

g and h are independent of distance x in the flow direction.

uc ows are ca e se preserv ng.


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The turbulence structure also reaches a selfpreserving state, although

after a greater distance from the flow source than the mean velocity.

The velocity scale Urefis, as above, (UmaxUmin) for a mixing layer and

wakes and Umax for jets.

The precise form of functions f, g, h and f1, f2, and f 3 varies from flow

.


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MixingLayer


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W k


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Wake


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Flat late boundar la er and i e flow

1. Due to the presence of the solid boundary, the flowbehaviour and turbulence structure are considerably

different from free turbulent flows.

2. Dimensional analysis has greatly assisted in correlating the

experimental data.

3. In turbulent thin shear la er flows a Re nolds number based

on a length scale L in the flow direction (or pipe radius) ReL

is always very large (e.g. U = 1 m/s, L = 0.1 m and = 106

m2 s ives Re = 105 .

4. This implies that the inertia forces are overwhelmingly

larger than the viscous forces at these scales.


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=

dominate in the flow far away from the wall. As y is

decreased to zero, Reynolds number based on y will also

decrease to zero.

2. Just beforeyreaches zero there will be a range of values of y

for which Rey is of the order of 1.

3. In this re ion 0<


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.

and does not depend on free stream parameters.

2. The mean flow velocity only depends on the distance y

,

shear stress w.

Intro to Turbulence

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