Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal

High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equation for the mass-flux velocity, $a_j$, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the $a_j$ transport equation is shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.

Figure 1

Schematic representation of the three RT mixing configurations considered. The direction of the initial gravity vector is indicated as $g_0$.

Figure 2

Mixing layer width as a function of time (in blue) overplotted with gravity as a function of time (in green) for configuration 1.

Figure 3

Contours of density (mg/${\mathrm{cm}}^3$) in the $y=\pi$ plane for LES of configuration 1 at three different time instants: (a) $t$ = 10 ms, (b) $t$ = 30 ms, and (c) $t$ = 70 ms.

Figure 4

Comparison between LES and RANS of mixing layer width $h_{99}$ vs time for configuration 1.

Figure 5

Comparison between LES and RANS of time history of two turbulence variables for configuration 1: (a) maximum TKE, $k$, and (b) maximum mass-flux velocity, $a_z$.

Figure 6

Comparison between LES and RANS of mixedness ${\mathrm{\Theta }}_{13}$ vs time for configuration 1.

Figure 7

Contours of density (mg/${\mathrm{cm}}^3$) in the $y=\pi$ plane for LES of configuration 2 at three different time instants: (a) $t$ = 10 ms, (b) $t$ = 30 ms, and (c) $t$ = 70 ms.

Figure 8

Comparison between LES and RANS of mixing layer width $h_{99}$ vs time for configuration 2.

Figure 9

Comparison between LES and RANS of mixedness vs time for configuration 2: (a) ${\mathrm{\Theta }}_{12}$ and (b) ${\mathrm{\Theta }}_{13}$.

Figure 10

Contours of density (mg/${\mathrm{cm}}^3$) in the $y=\pi$ plane for LES of configuration 3 at three different time instants: (a) $t$ = 20 ms, (b) $t$ = 40 ms, and (c) $t$ = 60 ms.

Figure 11

Comparison between LES and RANS of mixing layer width $h_{99}$ vs time for configuration 3.

Figure 12

Comparison between LES and RANS of spatial profiles at $t=t_{\text{thresh}}$ in configuration 3: (a) average mass fraction of light material, ${\tilde{Y}}_L$, and (b) the density-specific-volume covariance $b$.

Figure 13

Comparison between LES and RANS of time history of two turbulence variables in configuration 3 at the lower interface ($z=-\pi /4$): (a) TKE, $k$, and (b) mass-flux velocity, $a_z$. Reversal time $t_{\text{rev}}$ is indicated for reference with a dashed black line.

Figure 14

Exploration of RANS solution sensitivity to initialization of $k$ and $a_z$ in configuration 1: (a) Mixing layer width $h_{99}$ vs time for $k\text{−}L\text{−}a$ model using Eq. (26) with several choices for $k_0$ when $a_{z,t=0}$ is given by Eq. (35c) (solid lines) and when $a_{z,t=0}=0$ (dashed lines). (b) Mixing layer width $h_{99}$ vs time for $k\text{−}L\text{−}a$ model using Eq. (25) with several choices for $k_0$ when $a_{z,t=0}=0$.