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A Methodology for Simulating Compressible Turbulent Flows

[+] Author and Article Information
Hermann F. Fasel

Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, Arizona, 85721faselh@email.arizona.edu

Dominic A. von Terzi

Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, Arizona, 85721dominic@email.arizona.edu

Richard D. Sandberg

Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, Arizona, 85721richard@email.arizona.edu

J. Appl. Mech 73(3), 405-412 (Sep 30, 2005) (8 pages) doi:10.1115/1.2150231 History: Received January 15, 2004; Revised September 30, 2005

A flow simulation Methodology (FSM) is presented for computing the time-dependent behavior of complex compressible turbulent flows. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The objective of FSM is to provide the proper amount of turbulence modeling for the unresolved scales while directly computing the largest scales. The strategy is implemented by using state-of-the-art turbulence models (as developed for Reynolds averaged Navier-Stokes (RANS)) and scaling of the model terms with a “contribution function.” The contribution function is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is determined during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that it approaches direct numerical simulations (DNS) in the fine-grid limit and such that it provides modeling of all scales in the coarse-grid limit and thus approaches a RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in large eddy simulation (LES). However, FSM is distinctly different from LES in that it allows for a consistent transition between RANS, LES, and DNS within the same simulation depending on the local flow behavior and “physical” resolution. As a consequence, FSM should require considerably fewer grid points for a given calculation than would be necessary for a LES. This conjecture is substantiated by employing FSM to calculate the flow over a backward-facing step and a plane wake behind a bluff body, both at low Mach number, and supersonic axisymmetric wakes. These examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating (physically) complex flows, and, on the other hand, demonstrate the potential of the FSM approach for simulations of turbulent compressible flows for complex geometries.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 3

Base pressure coefficient cp (a) and centerline streamwise velocity (b): DNS (—), axisymmetric RANS with EASM (—∙—) and STKE model (--), three-dimensional RANS with STKE model (⋯), FSM (STKE) with β=6×10−4 (+), β=10−3 (◻), and β=2×10−3 (엯) FSM (EASM) with β=10−3 (∎); ReD=30,000, M=2.46

Grahic Jump Location
Figure 4

Mean radial velocity field (a,b) and mean pressure field (c,d) for DNS (a,c) and FSM (STKE) with β=2×10−3 (b,d); ReD=30,000, M=2.46

Grahic Jump Location
Figure 5

Base pressure coefficient cp (a) and centerline streamwise velocity (b): DNS (—), axisymmetric RANS with STKE model (--), FSM (EASM) with β=10−3 (∎), β=2×10−3 (●), β=4×10−3 (◆); ReD=60,000, M=2.46

Grahic Jump Location
Figure 6

Vortex visualization for the supersonic wake using instantaneous iso-contours of Q=0.1 for DNS (a) and FSM with β=10−3 (b); black shaded plane represents the base of the body; ReD=60,000, M=2.46

Grahic Jump Location
Figure 1

Instantaneous z-vorticity contours in the z=0 plane of the backward-facing step flow for DNS (a), FSM (EASM), with β=8×10−3 on base line grid (b) and RANS (EASM) with XT=4 on coarse grid (c); f(Δ∕LK) of the FSM (d); ReH=3,000, M=0.25

Grahic Jump Location
Figure 2

Vortex visualization for the plane wake using instantaneous iso-contours of Q=1 for DNS (a) and FSM (b); black shaded plane represents the base of the body; 0⩽x⩽10, −3.9⩽y⩽3.9, −4⩽z⩽4, ReD=1,000, M=0.25

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