O. Gregoire et al., A two-time-scale turbulence model for compressible flows: Turbulence dominated by mean deformation interaction, PHYS FLUIDS, 11(12), 1999, pp. 3793-3807
The multiple-time-scale concept is applied to develop a turbulence model fo
r compressible flows. Transport equations for the turbulent kinetic energie
s and the energy transfer rates are linked to each domain of the turbulent
spectrum. The model coefficients are calibrated, with respect to simple flo
ws, by using a new method which takes advantage of the spectral character o
f the model. One innovation of this method is to use, as a component, the C
G model [V. M. Canuto and I. Goldman, Phys. Rev. Lett. 54, 430 (1985)] whic
h gives the large scale spectrum as a function of the instability-generatin
g turbulence. Then, the two-time-scale model, with its complete set of coef
ficients, has been successfully applied to the simulation of plane mixing l
ayers and homogeneous shear flows. A significant issue of this work is the
study of the behavior of the two-time-scale model when a shock wave interac
ts with a homogeneous turbulence. We first compare model results with exper
imental data for a 2.8 Mach number interaction [D. Alem, Ph.D. thesis, Univ
ersite de Poitiers, 1995]. The decrease of the integral length scale, predi
cted by the linear analysis, is reproduced with the two-time-scale model, w
hich, moreover, recovered the rate of reduction measured by Alem. The ampli
fication of the turbulence level through the shock wave is also consistent
with the measurements. Then, we confront our results with a direct numerica
l simulation of the shock-turbulence interaction at M=1.2 [S. Lee , J. Flui
d Mech. 251, 533 (1993)]. The spectrum of the turbulence injected in the in
flow region of the direct numerical simulation appeared to be far from the
freely decaying state. The two-time-scale model, which accounts for the spe
ctral nonequilibrium effects, is able to recover the spatial decrease of tu
rbulence in the inflow region whereas a single-time-scale model fails. More
over, the profiles for the turbulent kinetic energy and its dissipation rat
e over all the calculation domain are much better reproduced with the two-t
ime-scale model than with the primary k-epsilon model. (C) 1999 American In
stitute of Physics. [S1070-6631(99)02412-5].