The compressible mixing layer: an LES study

Theoretical and Computational Fluid Dynamics, Dec 2010

This article employs LES to simulate temporal mixing layers with Mach numbers ranging from M c  = 0.3 to M c  = 1.2. A form of approximate deconvolution together with a dynamic Smagorinsky subgrid model are employed as subgrid models. A large computational domain is used along with relatively good resolution. The LES results regarding growth rate, turbulence levels, turbulence anisotropy, and pressure–strain correlation show excellent agreement with those available from previous experimental and DNS results of the same flow configuration, underlining the effectiveness and accuracy of properly conducted LES. Coherent structures during the transitional stage change from spanwise aligned rollers to streamwise-aligned thinner vortices at high Mach number. In the quasi-self-similar turbulent stage, the resolved-scale vorticity is more isotropic at higher M c , and its vertical correlation length scale is smaller. The ratio of the vertical integral length scale of streamwise velocity fluctuation to a characteristic isotropic estimate is found to decrease with increasing M c . Thus, compressibility leads to increased spatial decorrelation of turbulence which is one reason for the reduction in pressure–strain correlation with increasing M c . The balance of the resolved-scale fluctuating vorticity is examined, and it is observed that the linear production by mean shear becomes less important compared to nonlinear vortex stretching at high M c . A spectral decomposition of the pressure fluctuations into low- and intermediate-to-high-wave numbers is performed. The low-wave number part of the pressure field is found not to correlate with the strain field, although it does have a significant contribution to the r.m.s of the fluctuating pressure. As a consequence, the pressure–strain correlation can be analyzed using a simplified Green’s function for the Poisson equation as is demonstrated here using the LES data.

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The compressible mixing layer: an LES study

H. Foysi S. Sarkar This article employs LES to simulate temporal mixing layers with Mach numbers ranging from Mc = 0.3 to Mc = 1.2. A form of approximate deconvolution together with a dynamic Smagorinsky subgrid model are employed as subgrid models. A large computational domain is used along with relatively good resolution. The LES results regarding growth rate, turbulence levels, turbulence anisotropy, and pressure-strain correlation show excellent agreement with those available from previous experimental and DNS results of the same flow configuration, underlining the effectiveness and accuracy of properly conducted LES. Coherent structures during the transitional stage change from spanwise aligned rollers to streamwise-aligned thinner vortices at high Mach number. In the quasi-self-similar turbulent stage, the resolved-scale vorticity is more isotropic at higher Mc, and its vertical correlation length scale is smaller. The ratio of the vertical integral length scale of streamwise velocity fluctuation to a characteristic isotropic estimate is found to decrease with increasing Mc. Thus, compressibility leads to increased spatial decorrelation of turbulence which is one reason for the reduction in pressure-strain correlation with increasing Mc. The balance of the resolved-scale fluctuating vorticity is examined, and it is observed that the linear production by mean shear becomes less important compared to nonlinear vortex stretching at high Mc. A spectral decomposition of the pressure fluctuations into low- and intermediate-to-high-wave numbers is performed. The low-wave number part of the pressure field is found not to correlate with the strain field, although it does have a significant contribution to the r.m.s of the fluctuating pressure. As a consequence, the pressure-strain correlation can be analyzed using a simplified Green's function for the Poisson equation as is demonstrated here using the LES data. Efficient technology for supersonic aviation, particularly scramjet engines, motivates the interest in compressible turbulent flows. Since compressible flows occur during mixing processes, the transition to turbulence, compression and combustion, simplified flow configurations need to be studied to isolate and distinguish between different compressibility effects, therefore enabling us to get a better understanding. One such simplified flow is the mixing layer between two streams, an important part of any engine. At high speeds, fluid compressibility has been found to strongly affect the behavior of the mixing layer. In order to characterize - such compressibility effects, the convective Mach number Mc has been introduced by Bogdanoff [3], defined as Mc = (U1 U2)/(c1 + c2), with U1, c1 and U2, c2 denoting the velocity and speed of sound in the high speed stream and low speed stream, respectively. Numerous investigations, experimentally [5,79,17,29,32,37] as well as numerically [13,14,23,28,34,39, 40,50,52] have tried to understand the influence of compressibility in mixing layers. One of the most important observations is the reduced turbulent shear layer growth rate with increasing convective Mach number [5,9,17,32,29], leading to a stabilization of the flow in the supersonic regime as shown by Sarkar [40]. This reduced thickness of the shear layer has been linked to the decreased turbulent production using an analytical expression by Vreman et al. [50]. In compressible uniform shear flow, the reduced turbulent kinetic energy growth rate has also been shown to be a consequence of reduced turbulent production [40]. This reduction in the turbulent production was shown by DNS studies to be associated with a decrease in the pressure fluctuations, reducing the pressurestrain terms in the turbulent stress balances, in the case of a shear layer by Vreman et al. [50]) and in the case of uniform shear by Sarkar [41]. Later, a study of the annular mixing layer by Freund et al. [13] and a mixing layer by Pantano et al. [28] also found a reduction in pressure fluctuations and pressurestrain terms among other results. The fluctuating pressure equation has been the subject of analysis to understand the observed compressibility effects. Pantano et al. [28] performed a Greens function analysis without shear for the center of the mixing layer and found that the finite speed of sound in compressible flow causes a time delay for a signal passing a turbulent eddy, causing thereby a decorrelation between adjacent points in this eddy. Recently, Thacker et al. [49] investigated the influence of compressibility on the rapid pressurestrain rate by deriving an exact Greens function for the convected wave equation for pressure fluctuations in homogeneous shear flow. They extended the work done by Papamoschou [30], who used ray theory to investigate the consequence of the wave operator on pressure fluctuations, instead of the usual Poisson equation in incompressible flow, and of Papamoschou et al. [31] who found reduced pr (...truncated)


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H. Foysi, S. Sarkar. The compressible mixing layer: an LES study, Theoretical and Computational Fluid Dynamics, 2010, pp. 565-588, Volume 24, Issue 6, DOI: 10.1007/s00162-009-0176-8