an overview of turbulent flows.pdf

8/20/2019 An Overview of Turbulent Flows.pdf

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Introduction to Turbulent Flows

Dr. Murat Koksal


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I am an old man now, and when I die and go to heaven there

are two matters on which I hope for enlightenment. One isquantum electrodynamics and the other is turbulent motion

in fluids. And about the former, I am rather optimistic.

Sir Horace Lamb (1932)

Turbulence was probably invented by the Devil on the

seventh day of Creation when the Good Lord wasn’t looking.

Peter Bradshaw (1994)


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Outline

• General characteristics of turbulent flows

• Movies on turbulent flows

• Scales of turbulence – Energy Cascade• Turbulence closure problem

• Turbulence modeling


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What is turbulent fluid motion?

“Turbulent fluid motion is an irregular condition of

flow in which various quantities show a random

variation with time and space coordinates, so that

statistically distinct average values can be

discerned” (Hinze, 1975).


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Why do we study turbulent flows?

• Virtually all flows of practical interest are

turbulent:

– Flows past airplanes, rockets, ships, automobiles,

– Flows in chemical reactors, mixers, combustion

chambers and engines,

– Flows in oil and gas pipelines, – Boundary layer in earth’s atmosphere, currents in

oceans, motion of clouds.


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Historical Background

• In 1500, Leonardo da Vinci recognized that there weretwo states of fluid motion: regular/ordered vsirregular/disordered. He called the latter as “LaTurbolenza”.

• In 1839, Hagen rediscovered the two states of fluidmotion in his experiments carried out in a brass pipe.

• In 1883, Reynolds carried out his famous dye

experiments and defined the transition to turbulence.


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Hagen’s Experiments

Flow, V

Horizontal Pipe

P = ?

P

V

P~V

P~V1.75


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Reynolds’s Experiments and Transition to

Turbulence

The transition to turbulent flow depends on the

Reynolds number, Re.

Re = inertial force/viscous force

Inertial force ~ u2/l

Viscous force ~ u/l2

Re = ul/ = [Velocity Scale][Length Scale] / [Viscosity]

For a pipe flow:

v

DV

ityviskinematic

Diameter Velocity Average av

cos

Re


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Transitional Re

For pipe flows, transitional Reynolds number is ~ 2300.

This value depends on roughness of the pipe, pipe

entrance conditions and external perturbations such as

noise and vibration. The transition to turbulence can be

delayed up to Re = 50, 000.

We usually consider a pipe flow to be fully turbulent

when Re > 50, 000.

For a flow over a flat plate, the transition Reynoldsnumber is ~ 500,000.


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Why does transition occur?

• For small enough length scales and low enough velocities, when Re is not too large, viscous forcesoutweigh the inertial forces. Any perturbation is quicklydampened by the viscosity.

• However, as Re increases, viscous stresses areovercome by fluids inertia and the laminar motionbecomes UNSTABLE. Any perturbation grows quickly,the motion becomes 3-D marked by rapid velocity and

pressure fluctuations.


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What is turbulent fluid motion?

“Turbulent fluid motion is an irregular condition of

flow in which various quantities show a random

variation with time and space coordinates, so that

statistically distinct average values can be

discerned” (Hinze, 1975).


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General Characteristics of Turbulent Flows

• IRREGULARITY: Turbulent flows are described as irregularand random. This is attributed to eddying motion defined aslocal swirling motion where the vorticity can be quite severe.Turbulent eddies appear at a wide RANGE OF SIZES andgive rise to vigorous mixing.

FLOW

D

Eddies in a typical turbulent pipe flow


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• LARGE REYNOLDS NUMBER: Turbulent flows occur atlarge Reynolds numbers as the inertial forces outweigh theviscous forces.

• INSTABILITY AND NONLINEARITY: Turbulencedevelops as an instability of laminar flow.

• DIFFUSIVITY: In turbulent flows, mass, momentum and heattransfer take place at a much larger rate than laminar flows.Reynolds’s dye experiment is a good example of increasedmass transfer as the flow becomes turbulent. Due to enhancedmomentum transfer, turbulent flows experience larger resistancein pipes, on aircraft’s wings and ships’ hulls. On the other hand,

the delay of separation causes reduction in drag in the case ofbluff bodies.



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Question – Which velocity profile belongs

to turbulent flow? Why?

Flow


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Which one of the below is a turbulent flow?


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• CONTINUUM: Turbulence is a continuum phenomena. Even,the smallest eddies in a turbulent flow are far larger than

molecular length scale.

• TURBULENT FLOW VS TURBULENT FLUID: Turbulence is the property of flow not the property of the fluid.

Any fluid flow with a Re > Retr can become turbulent.

• DISSIPATION: Turbulent flows consist of a continuousspectrum of scales of eddies from largest to the smallest.Energy is taken from the mean flow by deforming it, istransferred to smaller eddies by means of vortex stretching until

viscous forces dissipate it. This is known as energy cascade. Without an energy supply, turbulence decays rapidly.



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Energy Spectrum of Turbulence/

Scales in Turbulent Flows

“Big whirls have little whirls that feed on

their velocity. Little whirls have lesser

whirls, and so on to viscosity” Richardson


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Pipe Flow

If D = 10 cm, U = 2 m/s, Re = 80,000

lt ~ 1.22 mm

f ~ 80 Hz

~ 0.25 m

f = 1/ ~ 22 600 Hz


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In summary….

• Turbulence is dominated by large energy bearingeddies. They produce the energy for turbulence by

shearing the mean flow and they are responsible for

enhanced mixing.

• Small eddies dissipate the energy transferred to them

due to viscous forces. However, the rate of energy

dissipation is controlled by the rate of energy they

receive from larger eddies.

an overview of turbulent flows.pdf

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