Modelling Laminar-Turbulent Transition Processes

2011 ANSYS, Inc. May 14, 20121

Gilles Eggenspieler, Ph. D.Senior Product Manager

What is Laminar-Turbulent Transition in Wall Boundary Layers?

Laminar boundary layer Layered flow without any (or low level) of disturbances

Only at moderate Reynolds numbers

Low wall shear stress and low heat transfer

Prone to separation under weak pressure gradients

Turbulent boundary layer:

2011 ANSYS, Inc. May 14, 20122

Chaotic three-dimensional unsteady disturbances present

At moderate to high Reynolds numbers

High wall shear stress and heat transfer

Much less prone to separation under pressure gradients

Laminar-Turbulent Transition: Disturbances inside or outside the laminar boundary layer

trigger instability

Small disturbances grow and eventually become dominant

Laminar boundary layer switches to turbulent state (Flat plate

transitional Reynolds numbers ~104 106)

Effects of Transition Wall shear stress

Higher wall shear for turbulent flows (more resistance in

pipe flow, higher drag for airfoils, )

Heat transfer Heat transfer is strongly dependent on state of boundary

layer

Much higher heat transfer in turbulent boundary layer

Separation behaviour

Laminar separation

2011 ANSYS, Inc. May 14, 20123

Separation behaviour Separation point/line can change drastically between

laminar and turbulent flows.

Turbulent flow much more robust than laminar flow. Stays

attached even at larger pressure gradients

Efficiency

Axial turbo machines perform different in laminar and

turbulent stage

Wind turbines have different characteristics

Small scale devices change characteristics depending on

flow regime

Turbulent separation

Natural Transition

Low freestream turbulence

( Tu~0-0.5%)

Typical Examples:

Wind Turbine blades

Fans of jet engines

2011 ANSYS, Inc. May 14, 20124

Fans of jet engines

Helicopter blades

Any aerodynamic body

moving in still air

Picture from White: Viscous Fluid Flow, McGraw Hill, 1991

23 100%

kTu

U

=

Bypass TransitionExternal disturbance leading to instability

Bypass transition ( Tu~ 0.5-

10%)

High freestream turbulence

forces the laminar

boundary layer into

transition far upstream of Turbulent spot

2011 ANSYS, Inc. May 14, 20125

Picture from:

S. Heiken, R. Demuth, Laurien, E.: Visualization of Bypass-Transition Simulations using Particles (ZAMM)

transition far upstream of

the natural transition

location

Typical Examples:

Turbomachinery flows

All flows in high freestream

turbulence environment

(internal flows)

Turbulent spot

Separation Induced Transition

Strong Inflexional Instability Produces Turbulence in the Boundary Layer

Most important transition mechanism in engineering flows!

2011 ANSYS, Inc. May 14, 20126

Laminar boundary layer separates and attaches as turbulent boundary layer

Transition takes place after a laminar separation of the boundary layer.

Leads to a very rapid growth of disturbances and to transition.

Can occur in any device with a pressure gradients in the laminar region.

If flow is computed fully turbulent, the separation is missed entirely.

Examples: fans, wind turbines, helicopter blades, axial turbomachines.

Transition Model Requirements

Compatible with modern CFD code:

Unknown application

Complex geometries

Unknown grid topology

Unstructured meshes

Parallel codes domain decomposition

Fully Turbulent

2011 ANSYS, Inc. May 14, 20127

Requirements:

Different transition mechanisms

Natural transition

Bypass transition

Robust

No excessive grid resolution

Laminar Flow

Transitional

Challenges Transition Modelling Combination of linear and non-linear physical processes

Linear process can be captured by linear stability analysis

Coupling of Navier-Stokes code with laminar boundary layer code and

stability analysis code very complex

Empirical criterion (en) required

Only applicable to simple and known geometries (airfoils)

Cannot capture all physical effects (no bypass transition)

2011 ANSYS, Inc. May 14, 20128

Cannot capture all physical effects (no bypass transition)

Not suitable for general-purpose CFD codes

RANS Models

Have failed historically to predict correct transition location

Low Reynolds number models have been tested for decades but proved

unsuitable

Local Correlation based Transition Models (LCTM)

Developed by ANSYS to resolve gap in CFD feature matrix (-Re model)

Machinery: Non-local formulations

Algebraic Operations: Find stagnation point Move downstream from boundary

layer profile to boundary layer profile Compute Re for each profile Obtain Ret from correlation using Tu

and at boundary layer edge and

dyUu

Uu

=

0

1

U

=Re

UkTu 3/2=

2011 ANSYS, Inc. May 14, 20129

and at boundary layer edge and compare with Re

If Re > Ret activate turbulence model

New Formulation (LCTM): Avoid any algebraic formulation and

formulate conditions locally Use only transport equations (like in

turbulence model)

8/5400Re = Tut

t ReRe

Transition onset

Transition Onset CorrelationsTransition onset is affected

by: Free-stream turbulence

turbulence intensity (Tu=FSTI)

Pressure gradients ()Right: Correlation of Abu-

dyUu

Uu

=

0

1

U

=Re

2011 ANSYS, Inc. May 14, 201210

Right: Correlation of Abu-

Ghannam and Shaw Low Tu late transition

(natural transition High Tu early transition

(bypass transition) Effect of pressure gradient

),(Re = Tuft

Re t

ANSYS Model based on Intermittency

Intermittency:

Laminar flow:

Turbulent flow

turb

lam turb

t

t t =

+

0 =

2011 ANSYS, Inc. May 14, 201211

Turbulent flow

Transition

Goal is transport equation for using exp. correlations and local formulation

1 =

0 1<

Transport Equation for Ret

2500

Ut

=

( ) ( ) ( )

+

+=

+

j

ttt

jt

j

tjtxx

Px

Ut

eR~eR~eR~

( )( )ttttt FtcP = 0.1eR~Re

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The function Fonset

requires the critical Reynolds number from the

correlation

Tu and are computed at the boundary layer edge non-local Second transport equation required to transport information on Ret

into the boundary layer (by diffusion term)

This second transport equation will be eliminated din future versions

of the mode.

),(Re = Tuft

Modification to SST Turbulence Model

( )

+

+=

+

jtk

jkkj

j x

kx

DPkux

kt

~~)()(

2SP tk = kDk *=

2011 ANSYS, Inc. May 14, 201213

k kP P=% ( )min max( ,0.1),1.0k kD D=% The intermittency is introduced into the source terms of the ST

turbulence model

At the critical Reynolds number the SST model is activated

Main effect is through production term Pk

Summary Transition Model Formulation 2 Transport Equations

Intermittency () Equation Fraction of time of turbulent vs laminar flow Transition onset controlled by relation between vorticity Reynolds

number and Ret Transition Onset Reynolds number Equation (will be removed

from future versions) Used to pass information about freestream conditions into b.l.

e.g. impinging wakes

2011 ANSYS, Inc. May 14, 201214

e.g. impinging wakes New Empirical Correlation

Similar to Abu-Ghannam and Shaw, improvements for Natural transition

Modification for Separation Induced Transition Forces rapid transition once laminar sep. occurs Locally Intermittency can be larger than one

-Re Model

Flat Plate Results: dp/dx=0T3A: FSTI = 3.5 % (~ 39000 hexahedra)

2011 ANSYS, Inc. May 14, 201215

Mesh guidelines: y+ < 1 wall normal expansion ratio ~1.1 good resolution of streamwise direction

T3B

FSTI = 6.5 %

T3A

FSTI = 3.5 %

Flat Plate Results: dp/dx=0

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T3A-

FSTI = 0.9 % Schubauer and

Klebanoff

FSTI = 0.18 %

T3C5

FSTI = 2.5 %

Flat Plate Results: dp/dx (variation in Re number)

T3C2

FSTI = 2.5 %

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T3C3

FSTI = 2.5 %

T3C4

FSTI = 2.5 %

Comparison CFX-Fluent

T3C2 (transition near suction peak)

FSTI = 2.5 %

T3C4 (separation induced transition)

FSTI = 2.5 %

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Aerospatial A Airfoil

Transition on suction side due

to laminar separation

Transition model predicts that

effect

Important:

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Important: The wall shear stress in the region

past transition is higher than in the fully turbulent simulation

The turbulent boundary layer can therefore overcome the adverse pressure gradient better

Less separation near trailing edge

McDonnell Douglas 30P-30N 3-Element Flap

Tu ContourRe = 9 millionMach = 0.2C = 0.5588 mAoA = 8

Exp. hot film transition location measured

Main lower transition:

CFX = 0.587

Exp. = 0.526

2011 ANSYS, Inc. May 14, 201220

Slat transition:

CFX = -0.056

Exp.= -0.057

Error: 0.1 %

measured as f(x/c)

Main upper transition:

CFX = 0.068

Exp. = 0.057

Error: 1.1 %

Error: 6.1 %Flap transition:

CFX = 0.909

Exp. = 0.931

Error: 2.2 %

Separation Induced Transition forLP-Turbine

Pratt and Whitney Pak-B LP

turbine blade

Transition Model

Experiment ExperimentTransition Model

Transition Model

Laminar separation bubble size f(Re, Tu)

2011 ANSYS, Inc. May 14, 201221

Increasing Rex

turbine blade

Rex= 50 000, 75 000 and

100 000

FSTI = 0.08, 2.25, 6.0

percent

Plateau indicates laminar

separation bubble

Model predicts that effect

Computations performed

by Suzen and Huang, Univ.

of Kentucky

Transition Model

Experiment

Test Cases: 3D RGW Compressor Cascade

Hub Vortex

Laminar Separation

2011 ANSYS, Inc. May 14, 201222

RGW Compressor (RWTH Aachen)

FSTI = 1.25 %

Rex = 430 000

Tip Vortex

Separation Bubble

Transition

Loss coefficient, (Yp) = 0.097

Yp = (poinlet

- pooutlet

)/pdynoutlet

Test Cases: 3D RGW Compressor Cascade

Flow

2011 ANSYS, Inc. May 14, 201223

Experimental Oil Flow

Yp = 0.097

Transition Model

Yp = 0.11

Fully Turbulent

Yp = 0.19

3D laminar separation bubble on suction side of blade

Fully turbulent simulation predicts incorrect flow topology

Transition model gets topology right

Strong improvement in loss coefficient Yp

Transitional flow has lower Yp!

Yp = (poinlet

- pooutlet

)/pdynoutlet

Examples of Validation Studies:NASA Rotor 37 test case

Computations are performed on a series of hex scalable meshes with 0.4, 1.5, 4.5 and 11.5 million nodes for single passage

The mesh with 4.5 million nodes provides for virtually grid-independent solution

The -Re-SST model predicts the total pressure ratio of the compressor much better then the SST and k- models

k- model on the coarse mesh produces correct results due to error cancellation

2011 ANSYS, Inc. May 14, 201224 Mass Flow / Choke Mass Flow

T

o

t

a

l

P

r

e

s

s

u

r

e

R

a

t

i

o

0.9 0.92 0.94 0.96 0.98 11.

9

2

2

.

1

2

.

2

experimentSST Mesh1SST Mesh2SST Mesh3

Mass Flow / Choke Mass Flow

T

o

t

a

l

P

r

e

s

s

u

r

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R

a

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0.9 0.92 0.94 0.96 0.98 11.

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2

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1

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experimentk- Mesh1k- Mesh2k- Mesh3

Mass Flow / Choke Mass Flow

T

o

t

a

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P

r

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s

s

u

r

e

R

a

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i

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0.9 0.92 0.94 0.96 0.98 11.

9

2

2

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1

2

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2

experimentSST+TM Mesh2SST+TM Mesh3SST SST-TMk-epsilon

0.4106 nodes

1.5106 nodes

4.5106 nodes

11.5106 nodes

Total Pressure Ratio

Summary

The Local Correlation-based Transition Modelling (LCTM) concept closes a gap in the model offering of modern CFD codes

Formulation allows the combination of detailed experimental data (correlation) with transport equations for the intermittency.

Correlation based transition model has been developed Based strictly on local variables Applicable to unstructured-grid massively parallelized codes

2011 ANSYS, Inc. May 14, 201225

Applicable to unstructured-grid massively parallelized codes Onset prediction is completely automatically

User must specify correct values of inlet k, Validated for a wide range of 2-D and 3-D turbomachinery and

aeronautical test cases Computational effort is moderate. Model implemented in CFX and Fluent