Research Papers

Numerical Study of Transitional Rough Wall Boundary Layer

[+] Author and Article Information
Witold Elsner

e-mail: warzecha@imc.pcz.czest.pl

Piotr Warzecha

e-mail: welsner@imc.pcz.czest.plInstitute of Thermal Machinery,
Czestochowa University of Technology,
Czestochowa 42-201, Poland

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 19, 2012; final manuscript received December 21, 2012; published online September 23, 2013. Editor: David Wisler.

J. Turbomach 136(1), 011010 (Sep 23, 2013) (11 pages) Paper No: TURBO-12-1195; doi: 10.1115/1.4023467 History: Received September 19, 2012; Revised December 21, 2012

This paper presents the verification of the boundary layer modeling approach, which relies on a γ-Reθt model proposed by Menter et al. (2006, “A Correlation-Based Transition Model using Local Variables—Part I: Model Formation,” J. Turbomach., 128(3), pp. 413–422). This model was extended by laminar-turbulent transition correlations proposed by Piotrowski et al. (2008, “Transition Prediction on Turbine Blade Profile with Intermittency Transport Equation,” Proceedings of the ASME Turbo Expo, Paper No. GT2008-50796) as well as Stripf et al.'s (2009, “Extended Models for Transitional Rough Wall Boundary Layers with Heat Transfer—Part I: Model Formulation,” J. Turbomach., 131(3), 031016) correlations, which take into account the effects of surface roughness. To blend between the laminar and fully turbulent boundary layer over rough wall, the modified intermittency equation is used. To verify the model, a flat plate with zero and nonzero pressure gradient test cases as well as the high pressure turbine blade case were chosen. Furthermore, the model was applied for unsteady calculations of the turbine blade profile as well as the Lou and Hourmouziadis (2000, “Separation Bubbles Under Steady and Periodic-Unsteady Main Flow Conditions,” J. Turbomach., 122(4), pp. 634–643) flat plate test case, with an induced pressure profile typical for a suction side of highly-loaded turbine airfoil. The combined effect of roughness and wake passing were studied. The studies proved that the proposed modeling approach (ITMR hereinafter) appeared to be sufficiently precise and enabled for a qualitatively correct prediction of the boundary layer development for the tested simple flow configurations. The results of unsteady calculations indicated that the combined impact of wakes and the surface roughness could be beneficial for the efficiency of the blade rows, but mainly in the case of strong separation occurring on highly-loaded blade profiles. It was also demonstrated that the roughness hardly influences the location of wake induced transition, but has an impact on the flow in between the wakes.

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Fig. 1

Skin friction coefficient Cf for zero-pressure gradient test case: (a) Uα = 27 m/s, (b) Uα = 42 m/s

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Fig. 2

Skin friction coefficient distribution as a function of θ/r for zero pressure gradient

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Fig. 3

Evolution of velocity U (a) and skin friction coefficient Cf (b) for nonzero pressure gradient test case (Uα = 26 m/s)

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Fig. 4

Shear stress (numerical results) and Nusselt number (experimental results) distribution (a) and shape factor distribution (b) for various surface roughnesses for the HPTV blade

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Fig. 5

Test section (a) and pressure coefficient distribution (b)

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Fig. 6

Shear stress (a) and shape factor (b) for test cases (ITM corresponds to smooth wall)

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Fig. 7

Velocity profile (a) and s–t diagram of velocity in the free stream flow (b)

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Fig. 8

S–t diagram of shear stress (a) and shape factor (b) for smooth test case. S–t diagram of shear stress (c) and shape factor (d) for rough surface ITMR26 test case.

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Fig. 9

Pressure coefficient (a) and turbine blade N3-60 geometry (b)

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Fig. 10

kr/δ* parameter (a) and shape factor (b) for various steady test cases

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Fig. 11

Inlet profiles for unsteady simulations: velocity U (a) turbulent kinetic energy k and specific dissipation rate ω (b)

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Fig. 12

S–t diagram of skin friction coefficient (a) and shape factor (b) for smooth test case. S–t diagram of skin friction coefficient (c) and shape factor (d) for rough K40 test case.

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Fig. 13

Time traces of Cf at the location (a) Ss = 0.3, (b) Ss = 0.65, (c) Ss = 0.85, and (d) Ss = 0.95

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Fig. 14

Time traces of θ at the location (a) Ss = 0.3, (b) Ss = 0.65, (c) Ss = 0.85, and (d) Ss = 0.95




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