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

δ

δ

= ⋅

Bypass Transition

External 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 (γ-ReΘ model)

Machinery: Non-local formulations

Algebraic Operations:• Find stagnation point

• Move downstream from boundary layer profile to boundary layer profile

• Compute ReΘ for each profile

• Obtain ReΘt from correlation using Tuand λ at boundary layer edge and

dyU

u

U

u∫

−=δ

θ0

1 µθρ

θU=Re

U

kTu

3/2=

© 2011 ANSYS, Inc. May 14, 20129

and λΘ at boundary layer edge and compare with ReΘ

• If ReΘ > ReΘt activate turbulence model

New Formulation (LCTM):• Avoid any algebraic formulation and

formulate conditions locally

• Use only transport equations (like in turbulence model)

8/5400Re −= Tutθ

tθθ ReRe ≥

Transition onset

Transition Onset Correlations

Transition onset is affected

by:− Free-stream turbulence

turbulence intensity (Tu=FSTI)

− Pressure gradients (λθ)

Right: Correlation of Abu-

dyU

u

U

u∫

−=δ

θ0

1µθρ

θU=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 Θ= λθ Tuft

Re tθ

ANSYS Model based on Intermittency

• Intermittency:

• Laminar flow:

• Turbulent flow

turb

lam turb

t

t tγ =

+

0γ =

© 2011 ANSYS, Inc. May 14, 201211

• Turbulent flow

• Transition

• Goal is transport equation for γ using exp.

correlations and local formulation

1γ =

0 1γ< <

Transport Equation for Reθt

2

500

Ut

ρµ=

( ) ( ) ( )

∂∂+

∂∂+=

∂∂

+∂

∂

j

ttt

jt

j

tjt

xxP

x

U

tθ

θθθθ µµσ

ρρ eR~eR

~eR

~

( )( )ttttt Ft

cP θθθθθρ −−= 0.1eR

~Re

© 2011 ANSYS, Inc. May 14, 201212

• The function Fonset

requires the critical Reynolds number from the

correlation

• Tu and λΘ are computed at the boundary layer edge – non-local

• Second transport equation required to transport information on ReΘt

into the boundary layer (by diffusion term)

• This second transport equation will be eliminated din future versions

of the mode.

),(Re Θ= λθ Tuft

Modification to SST Turbulence Model

( )

∂∂+

∂∂+−=

∂∂+

∂∂

jtk

jkkj

j x

k

xDPku

xk

tµσµρρ ~~

)()(

2SP tk µ= ωρβ kDk*=

© 2011 ANSYS, Inc. May 14, 201213

k kP Pγ=% ( )min max( ,0.1),1.0k kD Dγ=%

• The intermittency γ 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 (γ) Equation� Fraction of time of turbulent vs laminar flow� Transition onset controlled by relation between vorticity Reynolds

number and Reθt− 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

γ-ReΘ Model

Flat Plate Results: dp/dx=0

T3A: 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

© 2011 ANSYS, Inc. May 14, 201216

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 %

© 2011 ANSYS, Inc. May 14, 201217

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 %

© 2011 ANSYS, Inc. May 14, 201218

Aerospatial A Airfoil

• Transition on suction side due

to laminar separation

• Transition model predicts that

effect

• Important:

© 2011 ANSYS, Inc. May 14, 201219

• 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 Experiment

Transition 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 γ-ReΘ-SST model predicts the total pressure ratio of the compressor much better then the SST and k-ε models

• k-ε model on the coarse mesh produces “correct” results due to error cancellation

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

To

talP

ress

ure

Rat

io

0.9 0.92 0.94 0.96 0.98 11.9

22.

12.

2

experimentSST Mesh1SST Mesh2SST Mesh3

Mass Flow / Choke Mass Flow

Tot

alP

ress

ure

Rat

io

0.9 0.92 0.94 0.96 0.98 11.9

22.

12.

2

experimentk-ε Mesh1k-ε Mesh2k-ε Mesh3

Mass Flow / Choke Mass Flow

To

talP

ress

ure

Rat

io

0.9 0.92 0.94 0.96 0.98 11.9

22.

12.

2

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

0.4·106 nodes

1.5·106 nodes

4.5·106 nodes

11.5·106 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, ω• 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