1

TURBULENCE MODELLING

Prof. Paul Tucker

given by Tom Hynes

2

STRUCTURE

The formidable turbulence modelling

task

Overview RANS modelling

Overview LES

Discuss mixing LES & RANS models

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KEY ROLE OF TURBULENCE

Drag generation

Heat transfer

Particle dispersion

Scalar mixing

Sound generation

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TURBULENCE

da Vinci - describes the

“clouds as scattered and torn” Van Gogh Transition

l

y+

5

FORMIDABLE TASK

“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 is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic” Sir Horace Lamb

FRS (1849-1934) 2nd Wrangler Trinity College

“Turbulence is the last great unsolved problem in classical physics” Richard Feynman (Nobel Prize in Physics - quantum

electrodynamics )

Do not even know the Karman constant (l = y – 0.38 < < 0.45) or if it is a constant!!! – Spalart (2006) 2% decrease in gives 1%

decrease in predicted aircraft drag

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MODEL BASIS

Phenomenological – but we do not fully understand the phenomena!!!

Spalart & Allmaras (1994) – La Recherche Aerospatiale, No 1, 5-21

Abstract – A transport equation for turbulent viscosity is assembled based

on empiricism and arguments of dimensional analysis ……

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DICTIONARY DEFINITION

Empiricism

- Philosophy. the doctrine that all

knowledge is derived from sense

experience.

- Undue reliance upon experience, as in

medicine; quackery.

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WHAT IS RANS MODELLING

NS(u)=0

NS(U+u’)=0 – time average

RANS(U)=0

Identical to NS(U) but μ = μt + μ

u = U + u’

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SA MODEL BASIS

DtDt

C1St Diffusion Term[C2,]

Shearing for production

tt μS

Dt

μDρ 2Γ

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CALIBRATION

2D mixing layer

Wake

Calibration suggests 0.6<σ<1; 0.1375< C1<0.1275 & 0.6< C2<0.7

Pick:2/3, 0.1355, 0.622. Acknowledge plane

jet spreading rate 38% too high

( )2010= UΔ.max

( )2060= UΔ.max

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HEAT TRANSFER

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URANS

Linear

models

Non-linear

models

OK - has spectral

gap - unusual Liu and Tucker (2007)

IJNME

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URANS

T [K]

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The Resolved Solution in Different Approaches

By Strelets group

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WHAT IS LES?

LES = Resolve all large eddies RANS = Resolve time average of flow

x

y

Resolved/solved forModelled < 2

l

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DNS, LES & RANS IN A CHANNEL

From K. Hanjalic

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L. F. Richardson’s (1922) Rhyme & Kolmogorov (1941)

•Big whorls have little whorls,

which feed on their velocity,

and little whorls have lesser whorls,

and so on to viscosity (in the molecular

sense).

•Kolmogorov (1941),

smaller whorls or

eddies isotropic

Energy α k-5/3

Big whorls

Scale separation

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LES FILTERING

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KEY LES PROBLEM

Hinze (1975)

•Resolving streaks

•Trent 1000 fan at cruise 107

•LES Cost α Re2.5*

•Hybrid LES-RANS Cost α Re0.5

y+=90

*Piomelli, AIAA-2008-396 DES type problem –

By Forsythe, Wurtzler,

Squires, Cobalt

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CHAPMAN (1975) – THE DREAM

1014 flops N = 109 -> Road

Runner (2008) 1015 flops

Chow and Moin (2012)

confirmed Chapman’s estimates

GPUs provide cheap computing

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LES RESOLUTION REQUIREMENTS

Adapted from Leschziner (2009), Piomelli and Balaras (2002)

LES

Hybrid

Fan –

eng

ine s

ca

le

N ≠ f(Re)

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GRID REQUIREMENTS

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WING-FLAP [Re = 23 x 106, 3.3 million cells]

ZONAL ILES-RANS vorticity contours

Model CL

% Error

RANS +24

Zonal (I)LES-RANS -5

(I)LES -16

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PROBLEM AEROSPACE FLOWS

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CHEVRON ILES-RANS

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Flow Visualization

U

u’u’

u’v’

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6 x 106

12 x 106

50 x 106

Vorticity Contours

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SENSITIVITY TO REAL INFLOW/

GEOMETRY

Geometry and Near Nozzle

Blocking Structure

Vorticity Contours

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Pylon Geometry

Instantaneous Streamwise Velocity Time Averaged Streamwise Velocity

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JET PYLON-WING-FLAP INTERACTION AND

MORE

u

|grad(ρ)|

Mesh

Blocking

Topology

Rig tests difficult!!

Big noise impact

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COMPRESSOR/TURBINE LES

s

DONE USING ‘YOUR’ CODE

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NEW PHYSICS AND

PALLIATIVES . Vorticity magnitude

isosurfaces

RANS SA

RANS-SA-HJ

LES

Cpt,PA

s

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NEW PHYSICS - ENDWALLS

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FAN BLADE

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CUTBACK TRAILING EDGES

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RIBBED PASSAGE

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HIGH PRESSURE COMPRESSOR DRUM & LAB SEALS

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TURBINE BLADE

Interface

Re ≈ 0.6 million, N > 5 million

10% DS

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LPT LES/DNS

Iso-surface contours of Vorticity Magnitude

(From DNS)

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EXPLORE NEW PHYSICS

Turbine blade surface topography

damaged by Spallation

Blade vibration alters reattchment location by 8%

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DES of F-15 Post-Stall

By

Forsythe,

Wurtzler,

Squires,

Cobalt

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Work of L. Hedges, NASA Funded

URANS

DES

Vorticity

Magnitude

SRANS, Partly Converged

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Generic Heavy Truck in Cross-Wind

By Wurtzler, Forsythe, Cobalt

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RUNWAY IN CROSSWIND

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LES SIMULATIONS

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Combustion Noise

URANS + LES + High-

Fidelity Models

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Open rotor engines

•Today’s aircraft

fly from London to

Berlin, a distance

of 581 miles, on

six tonnes of fuel.

•Planes with

open-rotor

engines could fly

nearly 900 miles,

or from London to

Rome, on the

same amount.

48

BFM: WAKE MODELLING

49 Surface Mesh: Full View

BIFURCATED INTAKE

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Surface Mesh: Lips detail

BIFURCATED INTAKE

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Surface Mesh: Vanes and Branches

BIFURCATED INTAKE

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Surface Mesh: Vanes detail

BIFURCATED INTAKE

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Y0 PLANE

Total Pressure Contours

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Y0 PLANE

Vtheta Contours showing asymmetric flow in XZ and XY planes and due to wake

entrainment

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BIFURCATED INTAKE

Surface Mesh: Full View

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CONCLUSIONS

Vast number of RANS models, choice can have substantial impact - CFD use a specialist activity

CFD predict correct delta’s

To predict exact levels extreme insights into turbulence model and many other CFD aspects + calibration data

Many practical flows are highly three dimensional in which inviscid pressure driven structures occur and then turbulence stresses become less important

However, if the 3D structures are unsteady in nature, other challenges arise

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CONCLUSIONS

URANS can help

Zonal RANS-LES & LES with take over

but when?

Depends on HPC/GPU developments

Zonal RANS-LES & LES still need

physical insight by analyst

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SCALE SEPARATION