Dr. Xia Wang

Assistant Professor

Department of Mechanical Engineering

Tel: 248-370-2224 Fax: 248-370-4416

Email: wang@oakland.edu

Contact Information:

Turbulent Boundary Layer

with separation

by Dr. Xia Wang

TBL-with separation

(x)

U0

U(x,y)

Separation

Reverse Flow

(x)

U0

U(x,y)

Separation

Reverse Flow

Favorable pressure gradient

(FPG)

Adverse Pressure Gradient

(APG)

xo

Zero pressure gradient(ZPG)

TBL separation is everywhere

Turbine Blade

DiffuserFlow around a carTaken from (Hucho and Sovran 1993)

Research Interests

• Can we characterize the turbulent boundary layers with eventual separation?

• How to predict the separation position?

• How can this instruct the car body design?

TBL Separation is an event!

IDITD D

Coherent structure

Detached flow

ID: Incipient Detachment 1%

ITD: Intermittent Transitory Detachment 20%

TD: Transitory Detachment 50%

D: Detachment Cf=0.0

Research Approach-Similarity Analysis

• The scales for the turbulent boundary layer flow are dictated by the equation and its boundary conditions alone.

• In the limit as Re, the equations of motion become independent of Re. Thus any scale or function expressing the solutions must also be independent of Pe. (Asymptotic Invariance Principle: AIP, George & Castillo 1997)

Research Approach-Similarity Analysis

• Apply similarity analysis to RANS

[ ]dPU U 1

U V uvdxx y yr

¥¶ ¶ - ¶+ @ + -

¶ ¶ ¶

U V0

x y¶ ¶

+ =¶ ¶

( ) ( ) ( )U x,y U U x,y 0 0 uv x, y 0 0 ¥® ¥ = ® = ® =

,*),,(

yfU

UUop

,*),,(/2

yoprdxdU

uv constdx

dP

dxdU

/2

/1~U

Pressure parameters

Log10 (, *, ) m

Lo

g1

0(

U

)m

/s

-3 -2 -1 01.1

1.15

1.2

1.25

1.3

1.35

1.4

linear fit =0.21

linear fit =0.23

linear fit *=0.22

Alving & Fernholz 1996Separation & Reattachment Flow

Separation

Reattachment Zone

Log10 (, * , ) m

Lo

g1

0(

U

)m

/s

-2 -1 01.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

linear fit =0.21

linear fit =0.26

linear fit *=0.17

Schubauer & Klebanoff 1948Strong APG with Separation

Separation

Separation Criterion

• Integral Momentum Equation

• Replacing the PG parameter from the similarity analysis

• At separation: Cf0

22

2fC dPd

Hdx U dx

1 22fC d

Hdx

sep

12H

Hsep=2.76 0.23

Results-1

*/

H

0 0.1 0.2 0.3 0.4 0.5 0.61.0

2.0

3.0

4.0

Marusic & Perry strong APG U=10 m/sMarusic & Perry strong APG U=30 m/sSKare & Krogstad stong APG near separationSchraub & Kline 1965 mild APGSchraub & Kline 1965 strong APGClauser Mild APGClausre Moderate APGBradshaw Mild APGBradshaw & Ferris APGPerry APG

Separation Zone

Equilibrium Flow without Separation

*/

H

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.81.0

2.0

3.0

4.0

5.0

6.0

Ludwieg & TillmanSimpson et al. 1977Simpson et al. 1981Schubauer & Klebanoff 1948Alving & Fernholz 1996Newman 1950H=1/(A-B*/)

Reattachement zone

Equibrium flowwithout separation

ITD and Separated

ITD or separated position is circled.

TBL without separation TBL with separation

Results-2

Consistent with Industrial Practices

• Hall (2003) : To avoid separation on compressor blades, Hsep<2.5

• Elsberry et al (2000): To keep an equilibrium on the verge of separation, Hsep<2.6

Consistent with Measure Results

• Sandborn & Kline (1961), Kline et al (1983), Sajben & Liao (1995) Hsep=2.7 for the

intermittent detachment.

• Fernholz & Alving (1990) : Hsep=2.850.1

• Alving & Fernholz (1996) : Hsep=2.78