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TECHNICAL PAPERS

Reynolds-Stress Modeling of Three-Dimensional Secondary Flows With Emphasis on Turbulent Diffusion Closure

[+] Author and Article Information
I. Vallet

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

J. Appl. Mech 74(6), 1142-1156 (Jan 18, 2007) (15 pages) doi:10.1115/1.2722780 History: Received July 17, 2006; Revised January 18, 2007

The purpose of this paper is to assess the importance of the explicit dependence of turbulent diffusion on the gradients of mean-velocity modeling in second moment closures on three-dimensional (3D) detached and secondary flows prediction. Following recent theoretical work of Younis, Gatski, and Speziale, 2000, [Proc. Royal Society Lon. A, 456, pp. 909–920], we propose a triple-velocity correlation model, including the effects of the spatial gradients of mean velocity. A model for both the slow and rapid parts of the pressure-diffusion term was also developed and added to a wall-normal-free Reynolds-stress model. The present model is validated against 3D detached and secondary flows. Further developments, especially on the echo terms (which should appear in the formulation of pressure-velocity correlation), are discussed.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 2

A priori comparison of three triple velocity correlation closures ui′uj′ul′¯+=ui′uj′ul′¯∕uτ3 with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=395; y+=yuτ∕ν¯)

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Figure 3

A priori comparison of three triple velocity correlation closures ui′uj′ul′¯+=ui′uj′ul′¯∕uτ3 with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=590; y+=yuτ∕ν¯)

Grahic Jump Location
Figure 6

A priori comparison of turbulent-diffusion closures dijT=diju+dijp (dijT+=dijT∕(uτ4∕ν¯); y+=yuτ∕ν¯) with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=180, 395, 590)

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Figure 7

Comparison of measured (39) streamwise evolution of centerline velocity (y=z=a) with computations using four different RSMs for developing flow in a square duct (ReB=250,000, Tui=1%, lTi=50mm, δyi=δzi=0.1mm, Δyw+=Δzw+<0.5; 18×106 points grid discretizing 1∕4 of the square duct)

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Figure 8

Comparison of measurements (39) at the symmetry-plane (z=a, along y) and grid-converged computations using the four wall-normal-free RSMs at various axial locations x∕Dh, for developing turbulent flow in a square duct (ReB=250,000, Tui=1%, lTi=50mm, δyi=δzi=0.1mm, Δyw+=Δzw+<0.5; 18×106 points grids discretizing 1∕4 of the square duct)

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Figure 9

Comparison of measurements (39) at the corner-bisector (along yd) and grid-converged computations using the four wall-normal-free RSMs at various axial locations x∕Dh, for developing turbulent flow in a square duct (ReB=250,000, Tui=1%, lTi=50mm, δyi=δzi=0.1mm, Δyw+=Δzw+<0.5; 18×106 point grids discretizing 1∕4 of the square duct)

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Figure 10

Iso Mach-number in the S-duct of Wellborn (40), computed with the GV-RSM (ReCL=2.6×106,3.8×106 point grids)

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Figure 11

Comparison of computed and measured pressure coefficient Cp along the circumferential ϕEXP direction at four planes normal to the duct centerline, using four Reynolds-stress models (ReCL=2.6×106,3.8×106 point grids)

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Figure 12

Comparison of computed and measured pressure coefficient Cp along the centerline sCL∕d1 directions at three circumferential angles ϕEXP using four Reynolds-stress models (ReCL=2.6×106,3.8×106 point grid), with a zoom in the experimental separated flow region between sCL∕d1=2.02 and sCL∕d1=4.13

Grahic Jump Location
Figure 1

A priori comparison of three triple-velocity correlation closures ui′uj′ul′¯+=ui′uj′ul′¯∕uτ3 with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=180; y+=yuτ∕ν¯)

Grahic Jump Location
Figure 4

A priori comparison of pressure-velocity correlation closures p′ui′¯=p′ui′¯(1)+p′ui′¯(2) (Eqs. 30,31) with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=180, 395, 590); note that p′u′¯+ is one-order of magnitude larger than p′v′¯+ (p′ui′¯+=p′ui′¯∕(ρ¯uτ3); y+=yuτ∕ν¯)

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Figure 5

A priori comparison of pressure-diffusion closures d ijp+=∂(−p′ui′¯+δjy−p′uj′¯+δiy)∕∂y+ (d ijp+=d ijp∕(uτ4∕ν¯); y+=yuτ∕ν¯) with the DNS data of Moser (10) for fully developed plane channel flow (Reτ=180, 395, 590); note that d xyp+ is one-order of magnitude larger than d yyp+

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