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Research Papers

Calculation of High-Lift Cascades in Low Pressure Turbine Conditions Using a Three-Equation Model

[+] Author and Article Information
Roberto Pacciani

Department of Energy Engineering “Sergio Stecco”, University of Florence, via di Santa Marta, 3, 50139 Firenze, Italyroberto.pacciani@.unifi.it

Michele Marconcini

Department of Energy Engineering “Sergio Stecco”, University of Florence, via di Santa Marta, 3, 50139 Firenze, Italy

Atabak Fadai-Ghotbi, Sylvain Lardeau, Michael A. Leschziner

 Imperial College London, Prince Consort Road, London SW7 2AZ, UK

J. Turbomach 133(3), 031016 (Nov 18, 2010) (9 pages) doi:10.1115/1.4001237 History: Received September 03, 2009; Revised September 18, 2009; Published November 18, 2010; Online November 18, 2010

A three-equation model has been applied to the prediction of separation-induced transition in high-lift low-Reynolds-number cascade flows. Classical turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually overpredict the separation length, the main reason for this being the slow rise of the turbulent kinetic energy in the early stage of the separation process. The proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase in the nonturbulent fluctuations in the pretransitional and transitional region to be taken into account. The model is derived from that of Lardeau (2004, “Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure,” Flow, Turbul. Combust., 73, pp. 49–76), which was originally formulated to predict bypass transition for attached flows, subject to a wide range of freestream turbulence intensity. A new production term is proposed, based on the mean shear and a laminar eddy-viscosity concept. After a validation of the model for a flat-plate boundary layer, subjected to an adverse pressure gradient, the T106 and T2 cascades, recently tested at the von Kármán Institute, are selected as test cases to assess the ability of the model to predict the flow around high-lift cascades in conditions representative of those in low-pressure turbines. Good agreement with experimental data, in terms of blade-load distributions, separation onset, reattachment locations, and losses, is found over a wide range of Reynolds-number values.

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Figures

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Figure 1

Flat-plate boundary layer in adverse pressure gradient imposed by the upper contoured wall: ○ DNS (25), — LKE model, – – – original AJL model. (a) Mesh, (b) velocity profiles, and (c) profiles of total kinetic energy ktot=k+kℓ.

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Figure 2

T106C—single-block C-type grid 593×97

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Figure 3

T106C cascade: isentropic Mach-number distribution. (a) Re2,is=1.6⋅105, (b) Re2,is=1.2⋅105, and (c) Re2,is=0.8⋅105.

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Figure 4

T106C cascade: (a) exit-flow angle and (b) kinetic energy loss (%) as a function of Re2,is

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Figure 5

T106C cascade. Distribution of wall-shear-stress, laminar, and turbulent kinetic energy along the suction side.

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Figure 6

T106C cascade Re2,is=1.2⋅105: (a) laminar kinetic energy contours, (b) turbulent kinetic energy contours, and (c) total kinetic energy contours superimposed onto streamlines in the separated region

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Figure 7

T106C cascade. Local Reynolds number at (a) maximum separation-bubble-thickness location and (b) reattachment. Comparison with the Hatman and Wang correlation (11).

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Figure 8

T106C cascade Re2,is=0.8⋅105: (a) wall-shear-stress, laminar, and turbulent kinetic energy distributions along the suction side and (b) total kinetic energy contours superimposed onto streamlines in the separated region

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Figure 9

T2 cascade: isentropic Mach-number distribution. (a) Re2,is=2.5⋅105, (b) Re2,is=1.6⋅105, and (c) Re2,is=105.

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Figure 10

T2 cascade: kinetic energy loss (%) as a function of Re2,is

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