A Vortex Damping Outflow Forcing for Multiphase Flows with Sharp Interfacial Jumps

Abstract

Outflow boundaries play an important role in multiphase fluid dynamics simulations that involve transition between liquid and vapor phases. These flows are dominated by low Weber numbers and a sharp jump in pressure, velocity, and temperature. Inadequate treatment of these jumps at the outlet generates undesirable fluid disturbances that propagate upstream and lead to instabilities within the computational domain. To mitigate these disturbances, we introduce a forcing term that can be applied to incompressible Navier-Stokes equations to enforce stability in the numerical solution. The forcing term acts as a damping mechanism to control vortices that are generated by droplet/bubbles in multiphase flows, and is designed to be a general formulation that can be coupled with a fixed pressure outflow boundary condition to simulate a variety of multiphase flow problems. We demonstrate its applicability to simulate pool and flow boiling problems, where bubble-induced vortices during evaporation and condensation present a challenge at the outflow. Validation and verification cases are chosen to quantify accuracy and stability of the proposed method in comparison to established benchmarks and reference solutions, along with detailed performance analysis for three-dimensional simulations on leadership supercomputing platforms. Computational experiments are performed using Flash-X, which is a composable open-source software instrument designed for multiscale fluid dynamics simulations on heterogeneous architectures.

Figures (19)

• Figure 1: Schematic of multiphase heat transfer problems: (a) Flow boiling (b) Pool boiling, showing vortices generated by gas bubbles along with boundary conditions for velocity ($u_i$), pressure ($P$), and temperature ($T$). The level-set function ($\phi$) implicitly tracks the liquid-gas interface ($\Gamma$). The inset (c) provides details of the contact line, the pressure jump, and the evaporative mass flux.
• Figure 2: Staggered computational grid highlighting faces ($\times$) and cell-centers ($\bullet$), $I_C$ denotes the cell-centers and $I_F$ if face-center. The liquid-gas interface, $\Gamma$, separates the two phases.
• Figure 3: (a) Schematic of a multi-level block structured AMR grid around the liquid-gas interface, $\phi=0$, (b) Distribution of scaled pressure, $\frac{P-P_{low}}{P_{high}-P_{low}}$, highlighting the jump in value between phases, and (c) Weak scaling of pressure Poisson solver on Summit summit
• Figure 4: Effect of artificial condensation on saturated nucleate boiling. Physical condensation does no exist since both the bubble and bulk liquid are at the saturation temperature, however, outflow forcing in DHRUV2019Sato2013 introduces artificial condensation which is non-physical ($t_1<t_2<t_3)$.
• Figure 5: (a) Staggered computational grid near the outflow with faces ($\times$) and cell-centers ($\bullet$), $I$ denotes the internal cells, $G$ denotes the guard cells, and $B$ is the domain boundary. (b) Shape of outflow profiles, $h_2$, for different buffer region lengths, $l_b$.