Contact Information Dr Xia Wang Assistant Professor Department

Contact Information: Dr. Xia Wang Assistant Professor Department of Mechanical Engineering Tel: 248 -370 -2224 Fax: 248 -370 -4416 Email: wang@oakland. edu

Turbulent Boundary Layer with separation by Dr. Xia Wang

TBL-with separation Zero pressure gradient (ZPG) Favorable pressure gradient (FPG) Adverse Pressure Gradient (APG) U 0 d(x) xo Reverse Flow U(x, y) Separation

TBL separation is everywhere Turbine Blade Diffuser Flow around a car Taken 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! Coherent structure ID ITD D 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

Pressure parameters

Separation Criterion • Integral Momentum Equation • Replacing the PG parameter from the similarity analysis • At separation: Cf 0 Hsep=2. 76 0. 23

Results-1 TBL without separation TBL with separation

Results-2 Consistent with Measure Results 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 Sandborn & Kline (1961), Kline et al (1983), Sajben & Liao (1995) Hsep=2. 7 for the intermittent detachment. • Fernholz & Alving (1990) : Hsep=2. 85 0. 1 • Alving & Fernholz (1996) : Hsep=2. 78