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TECHNICAL PAPERS

Near-Wall Turbulent Pressure Diffusion Modeling and Influence in Three-Dimensional Secondary Flows

[+] Author and Article Information
E. Sauret

Institut d’Alembert, Université Pierre et Marie Curie, 75005 Paris, France

I. Vallet

Institut d’Alembert, Université Pierre et Marie Curie, 75005 Paris, Francevallet@ccr.jussieu.fr

J. Fluids Eng 129(5), 634-642 (Sep 14, 2006) (9 pages) doi:10.1115/1.2723811 History: Received July 19, 2006; Revised September 14, 2006

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Redistribution coefficient C2H(A)

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Figure 2

Turbulent pressure-diffusion coefficient CSP

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Figure 3

Comparison of a priori prediction, and of computed results (a posteriori prediction) using the present model with and without pressure diffusion and the GV‐C2H-modified RSM, with DNS data (1) of triple-velocity correlations for plane channel flow (Reτ=180, Cf=8.18×10−3, ReB=5600)

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Figure 4

Comparison of computational results using the present model and the GV‐C2H-modified RSM, with DNS data (1) of turbulent diffusion due to velocity fluctuations diju for plane channel flow (Reτ=180, Cf=8.18×10−3, ReB=5600)

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Figure 5

Comparison of computational results using the present model with DNS data (1) of pressure diffusion term dijp for plane channel flow (Reτ=180, Cf=8.18×10−3, ReB=5600)

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Figure 6

Comparison of grid-converged computations with measurements (45) of wall-pressure (a) and skin-friction (b) x-wise distributions, for Reda-Murphy (45) incident-shock-wave interaction (M∞=2.9, Reδ0=0.97×106, ΔϑSW=13deg) using the present model with and without turbulent pressure diffusion dijp, the GV and GV‐C2H-modified RSMs (iso-Machs computed with the present RSM)

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Figure 7

Comparison of computations with measurements (46) of isentropic-wall Mach number M̆is on the sidewall (z=0) at the y-symmetry plane (y=40mm) of the transonic square nozzle configuration of Ott (46) (only 1∕4 of the symmetric nozzle is shown) for two outflow-static-to-inflow-total pressure ratios πS−T=0.636,0.669 (Tui=2%; ℓTi=0.020m; 241×121×97 grid), using the present model with and without turbulent pressure diffusion dijp, the GV and the GV‐C2H-modified RSMs; iso-Machs computed with the present RSM at z=2mm

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Figure 8

Mach number isosurface at a value of M̆=0.1 for the transonic square nozzle configuration of Ott (46) (only 1∕4 of the symmetric nozzle is shown) for two outflow-static-to-inflow-total pressure ratios πS‐T=0.636,0.669, using the present model with and without turbulent pressure diffusion dijp.

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Figure 9

Partial view of the NTUA annular cascade (47), illustrating Mach levels near the hub (the xRθ frame is located at the x=+0.15m station), and comparison of measured (47) and computed spanwise (ς) distributions of pitchwise-averaged flow angle αM and axial velocity component VxM at the outlet (x=+0.15m), using the present model with and without pressure diffusion dijp, the GV and the GV‐C2H-modified RSMs, and the Launder-Sharma k‐ε closure (53) (ṁ=13.2kgs−1; Tui=4%; ℓTi=0.04m; griḏDE (49))

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