Modeling of Rayleigh-Taylor mixing using single-fluid models

Turbulence mixing models of different degree of complexity are investigated for Rayleigh-Taylor mixing flows with reference to high-resolution implicit large eddy simulations. The models considered, in order of increasing complexity, comprise the (i) two-equation K-L, (ii) three-equation K-L-a, (iii) four-equation K-L-a-b, and (iv) Besnard-Harlow-Rauenzahn (BHR-2). The above models are implemented in the same numerical framework to minimize the computational uncertainty. The impact of the various approximations represented by the different models is investigated for canonical one-dimensional (1D) Rayleigh-Taylor mixing and for the more complex (2D on average) case of the tilted-rig experiment, aiming to understand the balance between accuracy and complexity. The results provide guidance on the relative merits of various turbulence models over a variety of conditions.

Figure 1

Self-similar growth of $W$ (cm) and $K_{\text{max}}({\mathrm{cm}}^2/{\mathrm{s}}^2)$.

Figure 2

Profiles of (a) $\tilde{f}$ and (b) $K$ vs. $X/W$ at $t=10\mathrm{s}$.

Figure 3

Profiles of (a) $a_x$ and (b) $b$ vs. $X/W$ at $t=10\mathrm{s}$.

Figure 4

Time evolution of $b_{\max }$ for self-similar RT mixing.

Figure 5

Time evolution of $W$ (cm) and $K_{\text{max}}({\mathrm{cm}}^2/{\mathrm{s}}^2$) for RT mixing using the BHR-2 model; effect of grid resolution.

Figure 6

Contour plots of $\overline{f}, \theta$, and $\tilde{k}$ at $\tau =1.741$ using [(a)–(c)] TURMOIL [65] and [(d)–(f)] CNS3D, respectively.

Figure 7

Bubble and spike plumes position vs. scaled time ($\tau$).

Figure 8

Integral mixing width ($W$) vs. scaled time ($\tau$).

Figure 9

Mass fraction (${\tilde{F}}_H$) contour plot at $\tau =1.741$; (a) K-L, (b) K-L-a, (c) K-L-a-b, (d) BHR-2, and (e) iLES.

Figure 10

$K/K_{\text{ref}}$ ($K_{\text{ref}}=2.114{\mathrm{cm}}^2/{\mathrm{ms}}^2$) at $\tau =1.741$; (a) K-L, (b) K-L-a, (c) K-L-a-b, (d) BHR-2, and (e) iLES.

Figure 11

$a_z/a_z^{\text{ref}}(a_z^{\text{ref}}=0.5\mathrm{m}/\mathrm{s}$) at $\tau =1.741$; (a) K-L-a, (b) K-L-a-b, (c) BHR-2, and (d) iLES.

Figure 12

$b/b_{\text{ref}}$ ($b_{\text{ref}}=0.16$) at $\tau =1.741$; (a) K-L-a, (b) K-L-a-b, (c) BHR-2, and (d) iLES.

Figure 13

$a_x$ contours at $\tau =1.741$; minimum (blue) $-0.05$ m/s, maximum (red) 0.15 m/s; (a) BHR-2, and (b) iLES.

Figure 14

Mass fraction (${\tilde{F}}_H$) at $\tau =1.741$; (a) BHR-2, (b) BHR-2 with $S_F$, (c) BHR-2 with MSTD, and (d) iLES.