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Research Papers

Large-Eddy Simulation With Zonal Near Wall Treatment of Flow and Heat Transfer in a Ribbed Duct for the Internal Cooling of Turbine Blades

[+] Author and Article Information
Sunil Patil

e-mail: psunil@vt.edu

Danesh Tafti

e-mail: dtafti@vt.edu

Virginia Tech,
Blacksburg, Virginia 24061

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) Division of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received November 20, 2011; final manuscript received November 29, 2011; published online March 25, 2013. Editor: David Wisler.

J. Turbomach 135(3), 031006 (Mar 25, 2013) (11 pages) Paper No: TURBO-11-1245; doi: 10.1115/1.4006640 History: Received November 20, 2011; Revised November 29, 2011

Large eddy simulations of flow and heat transfer in a square ribbed duct with rib height to hydraulic diameter of 0.1 and 0.05 and rib pitch to rib height ratio of 10 and 20 are carried out with the near wall region being modeled with a zonal two layer model. A novel formulation is used for solving the turbulent boundary layer equation for the effective tangential velocity in a generalized co-ordinate system in the near wall zonal treatment. A methodology to model the heat transfer in the zonal near wall layer in the large eddy simulations (LES) framework is presented. This general approach is explained for both Dirichlet and Neumann wall boundary conditions. Reynolds numbers of 20,000 and 60,000 are investigated. Predictions with wall modeled LES are compared with the hydrodynamic and heat transfer experimental data of (Rau et al. 1998, “The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel,”ASME J. Turbomach., 120, pp. 368–375). and (Han et al. 1986, “Measurement of Heat Transfer and Pressure Drop in Rectangular Channels With Turbulence Promoters,” NASA Report No. 4015), and wall resolved LES data of Tafti (Tafti, 2004, “Evaluating the Role of Subgrid Stress Modeling in a Ribbed Duct for the Internal Cooling of Turbine Blades,” Int. J. Heat Fluid Flow 26, pp. 92–104). Friction factor, heat transfer coefficient, mean flow as well as turbulent statistics match available data closely with very good accuracy. Wall modeled LES at high Reynolds numbers as presented in this paper reduces the overall computational complexity by factors of 60–140 compared to resolved LES, without any significant loss in accuracy.

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Figures

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Fig. 1

Wall normal virtual grid for wall model, embedded in the LES grid (P is the off wall outer LES node and W is the normal projection of P on the wall)

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Fig. 2

(a) Computational domain, and mesh at (b) z = 0.5 section (c) x = 0.5 section; for ribbed duct calculations

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Fig. 3

Validation of heat transfer wall model in a turbulent channel flow (a) mean velocity profile (b) Variation of rms turbulent Reynolds stresses (c) mean temperature profile

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Fig. 6

Contours of Nusselt number on (a) smooth wall and ribbed wall, and (b) rib side 1 (c) rib side 2 (only half of the rib is shown) (Re = 20,000)

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Fig. 7

Comparison of Nusselt augmentation with experimental data of Rau et al. [1] at (a) ribbed wall at center plane, y=0, z=0.5 (b) smooth wall at e/2 upstream of rib, z=0, x=0.4 (Re = 20,000)

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Fig. 4

(a) Mean streamline distribution in the z-symmetry (z=0.5) plane (b) Contours of mean spanwise flow velocity near smooth wall (z=0.07) at Re = 20,000

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Fig. 5

Distribution of Reynolds normal stresses and shear stress at center plane (z=0.5), and variation of RMS turbulence quantities at center plane (z=0.5,x=1) (Re = 20,000)

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Fig. 8

Mean streamline distribution in the z-symmetry (z=0.5) plane (Re = 60,000)

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Fig. 9

Reynolds stresses and at center plane (z=0.5, (x'/e)=8.5) (Re = 60,000)

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Fig. 10

Comparison of Nusselt augmentation with experimental data of Han et al. [2] at center plane (z=0.5, y=0) (Re = 60,000)

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