Thermorelaxing multicomponent flows investigated with a Baer-Nunziato-type model

In inertial confinement fusion (ICF) implosions, mixing the ablator into the fuel and the hot spot is one of the most adverse factors that lead to ignition degradation. Recent experiments in the Marble campaign at the Omega laser facility and the National Ignition Facility demonstrate the significance of the temperature separation in heterogeneous mixing flows [Haines et al., Nat. Commun. 11, 544 (2020)]. In the present work we provide an approach to deal with thermally disequilibrium multicomponent flows with the ultimate aim to investigate the temperature separation impact on mixing and fusion burn. The present work is twofold: (a) We derive a model governing the multicomponent flows in thermal disequilibrium with transport terms and (b) we use the derived model to study the Rayleigh-Taylor (RT) instability in thermally relaxing multicomponent systems. The model is reduced from the full disequilibrium multiphase Baer-Nunziato model in the limit of small Knudsen number $\text{Kn}\ll 1$. Velocity disequilibrium is closed with the diffusion laws and only one mass-weighted velocity is retained formally. Thus, the complex wave structure of the original Baer-Nunziato model is simplified to a large extent and the obtained model is much more computationally affordable. Moreover, the capability to deal with finite-temperature relaxation is kept. Efficient numerical methods for solving the proposed model are also presented. Equipped with the proposed model and numerical methods, we further investigate the impact of thermal relaxation on the RT instability development at the ICF deceleration stage. On the basis of numerical simulations, we have found that for the RT instability at an interface between the high-density low-temperature component and the low-density high-temperature component, the thermal relaxation significantly suppresses the development of the instability.

Figure 1

The typical mass fraction distribution on the Eulerian grid in the case of heterogeneous mixing.

Figure 2

The hierarchy of the reduced models of the Baer-Nunziato model.

Figure 3

The numerical results for the pure temperature relaxation problem. Top: component temperatures; middle: volume fractions; bottom: the pressure disequilibrium, measured as $\mathrm{\Delta }p=|p_1-p_2|$.

Figure 4

The relative error of pressure and temperature for the pure advection problem.

Figure 5

The convergence rate for the mass diffusion problem. Upper: the pure diffusion problem; lower: the advection-diffusion problem.

Figure 6

The numerical results in the pure diffusion problem for density, velocity, pressure, temperature, mass fraction, and volume fraction with the refinement of grid.

Figure 7

The numerical results in the pure-diffusion and advection-diffusion problems for density, velocity, pressure, temperature, mass fraction, and volume fraction.

Figure 8

The numerical results for the mass diffusion problem with viscous effect. “Vis. stress with $u_k/u_{\mathrm{av}}$”: numerical results obtained with the viscous stress being calculated with the component velocity and the mass-weighted velocity.

Figure 9

The numerical results for the mass diffusion problem with or without the barodiffusion effect.

Figure 10

The variable (component temperatures, the volume fraction, and the mass fraction) distributions after the shock travels through the mixing zone. Nondimensional temperatures displayed are $T_k/\left(1500\text{MK}\right)$. (a) The initial profile, (b) the numerical results at $t=6\times {10}^{-3}\mathrm{ns}$ with physical relaxation rate ${\eta }_{\mathrm{Phys}}$, (c) the numerical results with $100{\eta }_{\mathrm{Phys}}$, and (d) the numerical results with $\eta \to \infty$.

Figure 11

The initial condition for the RT instability problem. Top: mixture density and pressure; bottom: component temperature. The mixture density $\rho =\sum {\alpha }_k{\rho }_k$.

Figure 12

The distribution of the mixture density $\rho$ (left) and mass fraction $y_1$ (right) on series of refining grids (From top to bottom: $320\times 80$, $640\times 160$, $1280\times 320$, $2560\times 640$). Ten uniform contours from 0.01 to 0.99 for $y_1$ are displayed on the right.

Figure 13

The distribution of the mixture density $\rho$ (left) and mass fraction $y_1$ (right) with different relaxation rates $\eta$ at the time moment $t=0.2\mathrm{ns}$. From top to bottom: $\eta =0,1\times {10}^6,\infty ,$ and $\eta$ determined by physical model (last row). Ten uniform contours from 0.01 to 0.99 for $y_1$ are display on the right.

Figure 14

The evolution of the mixing length with time. Top and middle subfigures are the results corresponding to different relaxation rates $\eta$. The bottom subfigure shows the grid independence of the numerical results.