Turbulens – Teori och modellering · Turbulens –Teori och modellering. Introduction ... •High Reynolds number •Continuum. ... Osborne Reynolds (1883) Q UL Reynolds number:

Turbulens – Teori ochmodellering

Introduction

Two questions:

• Why did you chose this course?

• What are your expectations?

Turbulence – Theory and modelling

•Understanding the phenomena that affects the

transition from laminar to turbulent flow

•Knowledge about the theory for describing turbulent

flow

•Knowledge about turbulence models applicability

and limitations

•Ability to analyse a flow situation and chose a

propper modelling approach accordingly

Goals


•Be able to describe the physical mechanisms of the transition from

laminar to turbulent flow for a simple flow case

•Be able to explain Kolmogorov’s theory, including the basic

assumptions and the validity of the theory

•Be able to, from a phenomenological perspective, assess if a flow is

turbulent

•Be able to explain some of the important and basic terms of the subject

•Be able to describe the character of the turbulence in different flow

situations with respect to the properties and development of the

turbulence, and explain how the differences between these flow

situations are reflected in the modelling

Goals


•Be able to analyse a flow case and suggest a method for numerical

simulation with respect to governing equations, possible simplifications

and choice of turbulence model, and also to compare with alternative

methods.

•Be able to scrutinise and from given criteria estimate the credibility of

results from turbulent flow simulations

•Be able to actively participate in discussion of problems relevant for

the subject

•Be able to present, both orally and in writing, a technical report

containing analyses and choice of turbulence model

Goals (continued)


•To pass (grade 3) the following is required:

• Approved home works, lab-report and group study (GS)

• Participation in the computer exercises

•Oral exam for higher grade (grades 4 and 5)

•Participation in the laboratory exercise, computer exercises and the

guest lecture is mandatory.

•The home works are handed in individially. However, you are alowed,

even encouraged, to work in groups discussing the problems.

•The groups study is to be presented both in writing as well as orally.

One report per group.

Examination and requirements

Turbulence

Two questions

1. How would you describe turbulence? Think about key-words to characterise it.

2. Think about situations where turbulent flow is better than laminar and vice versa.

Turbulence

• Random

• 3D

• Diffusive

• Dissipative

• Property of the flow

• High Reynolds number

• Continuum

Turbulence

Big whirls have little whirls

Which feed on their velocity

Little whirls have lesser whirls

And so on to viscosity – in the

molecular sense

L F Richardson

Turbulence

I am an old man now, and when I die

and go to Heaven there are two matters

on which I hope enlightenment. One is

quantum electro-dynamics and the

other is turbulence of fluids. About the

former, I am really rather optimistic.

Sir Horace Lamb

outflow

Heating/Cooling

Impingement wall

nozzleMean Sherwood number Sherwood number fluctuation

0i

i

x

u

i

j

ij

j

i

jij

jiiF

xx

u

xx

p

x

uu

t

u

1

Models for

turbulence,

combustion etc.

Geometry

Mathematical

description Results

For example velocity, pressure,

temperature

Numerical

methods

Question

• Why do we need to model turbulence?

Turbulence modelling

Example:

Pipe flow, turbulent Reynolds number, Re = 10000

Relation between largest and smallest scales ~ Re3/4

No. of nodes ~ Re9/4 2109 ca. 30 gigabyte RAM

Conclusion: Model needed


Isotropic turbulence in a box


Direct simulation of isotropic turbulence

Required time at a computing rate of 82 Gflop

Re N N3 M N3M CPU time Memory

94 104 1.1E06 1.2E03 1.3E09 14s 18 Mb

375 214 1.0E07 3.3E03 3.2E10 6.6 min 150 Mb

1500 498 1.2E08 9.2E03 1.1E12 3.8 h 2 Gb

6000 1260 2.0E09 2.6E04 5.2E13 7.3 days 30 Gb

24000 3360 3.8E10 7.4E04 2.8E15 1.1 years 565 Gb

96000 9218 7.8E11 2.1E05 1.6E17 61 years 11 Tb

N3= number of grid points

M= number of time steps

N3M= total work required

Turbulence

Instantaneous velocity field of a round jet

Turbulence

Mean velocity

Turbulent

kinetic energy

Turbulence data have meaning only in a statistical sense


RANS models

A.Abdon och B. Sundén, Värmeöverföring, LTH

Turbulence

From http://www.featflow.de

Backward facing step

Discussion:

Are these flows laminar or

turbulent? Motivate.

Turbulence

Brief history:• 15th century, da Vinci, observations of turbulence

• 18th century, Euler, equations for inviscid flow

• Early 19th century, Navier and Stokes, the N-S equations

• 1883, Reynolds, flow instability in pipe flow

• 1904, Prandtl, boundary layer theory

• 1941, Kolmogorov, theory on turbulent scales

• 1963, Smagorinsky, first sub-grid scale model for LES

• 1970, Launder et al., two-equation model for turbulence

Turbulence

Leonardo da Vinci

Turbulence

Laminar

Turbulent

Osborne Reynolds (1883)

ULReReynolds number:

Turbulens – Teori och modellering · Turbulens –Teori och modellering. Introduction ... •High Reynolds number •Continuum. ... Osborne Reynolds (1883) Q UL Reynolds number:

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