High-Pass Filtered Eddy-Viscosity Models for Large-Eddy Simulations of Compressible Wall-Bounded Flows

[+] Author and Article Information
Steffen Stolz

Institute of Fluid Dynamics,  ETH Zurich, CH-8092 Zürich, Switzerlandstolz@ifd.mavt.ethz.ch

J. Fluids Eng 127(4), 666-673 (Feb 18, 2005) (8 pages) doi:10.1115/1.1949652 History: Received August 13, 2004; Revised February 18, 2005

In this contribution we consider large-eddy simulation (LES) using the high-pass filtered (HPF) Smagorinsky model of a spatially developing supersonic turbulent boundary layer at a Mach number of 2.5 and momentum-thickness Reynolds numbers at inflow of 4500. The HPF eddy-viscosity models employ high-pass filtered quantities instead of the full velocity field for the computation of the subgrid-scale (SGS) model terms. This approach has been proposed independently by Vreman (Vreman, A. W., 2003, Phys. Fluids, 15, pp. L61–L64) and Stolz (Stolz, S., Schlatter, P., Meyer, D., and Kleiser, L., 2003, in Direct and Large Eddy Simulation V, Kluwer, Dordrecht, pp. 81–88). Different from classical eddy-viscosity models, such as the Smagorinsky model (Smagorinsky, J., 1963, Mon. Weath. Rev, 93, pp. 99–164) or the structure-function model (Métais, O. and Lesieur, M., 1992, J. Fluid Mech., 239, pp. 157–194) which are among the most often employed SGS models for LES, the HPF eddy-viscosity models do need neither van Driest wall damping functions for a correct prediction of the viscous sublayer of wall-bounded turbulent flows nor a dynamic determination of the coefficient. Furthermore, the HPF eddy-viscosity models are formulated locally and three-dimensionally in space. For compressible flows the model is supplemented by a HPF eddy-diffusivity ansatz for the SGS heat flux in the energy equation. Turbulent inflow conditions are generated by a rescaling and recycling technique in which the mean and fluctuating part of the turbulent boundary layer at some distance downstream of inflow is rescaled and reintroduced at the inflow position (Stolz, S. and Adams, N. A., 2003, Phys. Fluids, 15, pp. 2389–2412).

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Schematic of the rescaling and recycling technique

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Figure 2

Reynolds number Reδ2 based on the momentum thickness δ2 and the viscosity at the wall νw shown with thick lines for the LES with HPF Smagorinsky model over the downstream coordinate; thin lines indicate transient regions at the inflow due to the RRM procedure and due to the sponge-layer at outflow

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Figure 3

(a) Skin friction coefficient CF and (b) shape factor H12 over Reδ2; —HPF Smagorinsky model and —엯—ADM; × experiments of Coles (23,28), Mabey (23,25) and Shutts (23), ● DNS data of Guarini (29), ----regression of experimental data (Cf=0.01026Reδ2−0.21,H12=6.71Reδ2−0.062), ----regression ± standard deviation

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Figure 4

Mean-flow profiles, —⟨ũ1⟩,⋯⋯∙∙ ⟨ρu1¯⟩, ----⟨T̃⟩, and —∙—(⟨T̃⟩−Tw)∕(T∞−Tw); Lines: LES, Symbols: Experiments of Mabey (23); (a) HPF Smagorinsky model and (b) ADM

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Figure 5

Downstream-velocity profiles scaled in wall units, ----⟨ũ1⟩+ and —⟨ũ1⟩+,VD for the HPF Smagorinsky model, --엯--⟨ũ1⟩+ and —엯—⟨ũ1⟩+,VD for ADM (shifted by 10); also shown are the linear law, —and the logarithmic law with ln(x3+)∕0.4+5.1,----

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Figure 6

Mean-flow profiles in outer scaling ⟨ũ1⟩∞+,VD−⟨ũ1⟩+,VD: —HPF Smagorinsky model (scale on bottom), —엯—ADM (scale on top), and ----law of the wake −4.7ln(z∕L)−6.74

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Figure 7

Favre-averaged total temperature Ť0, —HPF Smagorinsky model

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Figure 8

Reynolds normal stresses normalized with ρwuτ2: solid lines ⟨ρ¯ũ1″ũ1″⟩, dashed lines ⟨ρ¯ũ2″ũ2″⟩, and long- dashed lines ⟨ρ¯ũ3″ũ3″⟩; —HPF Smagorinsky model and —엯—ADM; symbols are DNS data of Spalart (33), ×Reθ=1410 and +Reθ=670

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Figure 9

Reynolds shear stress ⟨ρ¯ũ1″ũ3″⟩∕uτ2, —HPF Smagorinsky model and —엯—ADM; Symbols are incompressible DNS data of Spalart (33), ×Reθ=1410 and +Reθ=670

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Figure 10

Turbulence Mach number Mt for HPF Smagorinsky model, —and fluctuating Mach number M′, ----

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Figure 11

Relative Favre fluctuations of the total temperature Ť0, ----, and of the temperature T̃, —for HPF Smagorinsky model

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Figure 12

Instantaneous ωz distribution for HPF Smagorinsky model in a x1‐x2 plane; x3+≈11

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Figure 13

Two-point correlations for HPF Smagorinsky model in (a) x2 direction and x1 direction at x3+≈11; ----ρ, —u,⋯⋯∙∙ v, —w, and —∙—T

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Figure 14

Instantaneous density distribution in a x1‐x3 plane, 0.4<ρ¯<1.1




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