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-Re Transition Model

• Most empirical models unsuited to unstructured CFD– Use non-local quantities (e.g., streamwise distance, , etc.)

• -Re allows empirical correlations to be used as local quantities• Works with the SST k- turbulence model• Solves two additional transport equations

– Intermittency– Ret

• Developed by Menter and Langtry (of ANSYS)• Allows empirical correlations to be used as local quantities

– but critical correlations hitherto unpublished• CD-adapco have reverse-engineered these correlations with

assistance from university researchers in Thailand!• Validated for natural, bypass and laminar-separation transition

-Re Transition Model Equations

1/21 1 2 2 2( ) (1 ) ( 1)j t

onseta e a elength turbj j j

uF c S F c c F c P

x x x

2Re Re( ) (Re Re )(1 )500

j t ttt t t t t

j j j

u Uc Fx x x

4

exp / 4TturbF R

42 1 1min(max( ; ); 2)onset onset onsetF F F

1Re

2.193Reonsetc

F

3

3 max 1 / 2.5 ; 0TonsetF R

2

5Reexp10wakeF

2 3max( ; 0)onset onset onsetF F F 242

2

1min max exp ;1 ;1

1e

t wakee

cyF Fc

RTk

2

Re y

2

375 Re t

y U

Intermittency:

Local transition momentum thickness Reynolds number:unpublished

Model Calibration Using Ercoftac Data

t=Re c

0.01

0.1

1

10

100

1000

10000

0 250 500 750 1000 1250

Ret

Fle

ng

th

0

250

500

750

1000

1250

Rec

Flength=min(0.1exp(-0.022Ret+12)+0.57, 300)

Rec=min(0.625Ret+62), Ret)

Tu>1% Tu<1%

Calibrated Correlations

Ercoftac Flat Plate Test Results

Practical Application: F1 Rear Wing

Turbulent separation

Laminar separationTransiti

on

Photo courtesy of Renault F1