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Physics of turbulence

muna Al_khaswneh

Dr.Ahmad Al-salaymeh

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Introduction

Turbulence cannot exist by itself, however; it requires a continuous supply of energy& changes in velocity& direction .

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Objective

• The Definition of turbulence • Examples of turbulence • Boundary layer• Study Reynolds numbers• Study the differential continuity equation• Study Navier-Stocks equation• Kolmogorov theory• Laminar-turbulent transitionProblems of turbulence

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Definition & properties

It is a flow with disordered in time & space .

1-three-dimensionality.

2-Unsteadiness.

3-strong vorticity.

4-Unpredictability.

5-Broad spectrum.

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Reynolds number

1. inertia forces 2. viscous forces

1. ρ u2 , ρ: fluid density ,u : fluid speed

2. μ u , μ: viscous fluid , d : diameter fluid d

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Re = inertia forces viscous forces

= ρ d u μ

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So that Reynolds number depend on fluid properties as ; speed , pipe diameter ,viscosity & density .

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Random pipe

210 310 410 510 Re

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Boundary layer

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Laminar-turbulent transition

.

1. Linear stability theory .

2. Primary instability of free shear flow .

3. Later stage of transition in free shear flows .

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Continuity equation

The conservation of mass principle is applied to the control volume

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Continuity equation

For three dimension (our interest )

x

z

yΔy

Δx

Δz

u = uxî + uyў +uzќ

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Continuity equation

0. u or 0Dt

D

0).( uDt

D

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Navier-stokes equation

the momentum translate with tow ways & tow forces

ways1. Convection transition 2. Molecular transitionforces1.Gravity force2.Pressure force

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Forces

1.Gravity force

Pressure force

gzyx )(

zyPP xxx

)(

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Convection transition

0)(

)(

)(

xy

zx

zy

uuuu

uuuu

uuuu

zzxzx

yyxyx

xxxxx

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Molecular transition

Shear stress

dx

d

dy

d

dz

d

u

u

u

xxx

xyx

xzx

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Molecular transition

0)

)

)

)()(

)()(

)()(

(

(

(

xy

zx

zy

zzxzzxz

yyxyyxy

xxxxxxx

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gPDt

Du x ).(

For x direction

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Navier-stokes equation

ugPDt

Du 2

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Newtonian equation

).(3

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).(3

22

).(3

22

uz

u zzz

uy

u y

yy

ux

u xxx

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stocks equation

)(

)(

)(

zx

yzzy

xy

uu

uu

uu

xzxzzx

zy

yxyz

yxyxxy

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Kolmogorov theory

1. The physics of turbulence is the same in all turbulent system .

2. It is independent of large scale forcing & small scale dissipative

3. Fluctuation occur in an incompressible medium-density

4.Energy flows from large scales to small scales .

27pressure (drop)

flow(averagespeed)

laminar

turbulent

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Primary instability of free shear flow

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Primary instability of free shear flow

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Later stage of transition in free shear flows .

Some vorticity remains between the vortices , we will call it {secondary instability} .

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Problems

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The endThank you