Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: 248-370-2224Fax:...
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![Page 1: Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: 248-370-2224Fax: 248-370-4416 Email: wang@oakland.eduwang@oakland.edu Contact.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d7f5503460f94a62e10/html5/thumbnails/1.jpg)
Dr. Xia Wang
Assistant Professor
Department of Mechanical Engineering
Tel: 248-370-2224 Fax: 248-370-4416
Email: [email protected]
Contact Information:
![Page 2: Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: 248-370-2224Fax: 248-370-4416 Email: wang@oakland.eduwang@oakland.edu Contact.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d7f5503460f94a62e10/html5/thumbnails/2.jpg)
Turbulent Boundary Layer
with separation
by Dr. Xia Wang
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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)
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TBL separation is everywhere
Turbine Blade
DiffuserFlow around a carTaken from (Hucho and Sovran 1993)
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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?
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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
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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)
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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
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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
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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
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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
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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