Dr. Xia Wang
Assistant Professor
Department of Mechanical Engineering
Tel: 248-370-2224 Fax: 248-370-4416
Email: [email protected]
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
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