Modelling of plume-plume interactions in space like environment via the hybrid DSMC-Fokker-Planck approach

Kurzfassung

Larger spacecraft typically use chemical propulsion systems for attitude and orbit control, or to maneuver during docking or landing. The thrusters operate by accelerating gas through a convergent-divergent nozzle, thus converting the gases internal energy to kinetic energy. In a vacuum environment, exhaust gases may interact with other vehicles or with the spacecraft itself, leading to undesired forces, heat fluxes, and potentially to a contamination of critical surfaces [1, 2]. Analysing plume expansion and interaction is therefore critical for spacecraft design. Numerically studying thruster plumes in a high-vacuum environment is notoriously difficult, as the flow passes though a wide range of flow regimes, from high-density and low speed in the nozzle reservoir, to low-density, highspeed, non-equilibrium flow downstream of the nozzle exit. The Direct Simulation Monte Carlo (DSMC) method [3] has been proven to be well suited to model rarefied and non-equilibrium flows. However, the method would be impractical in high-density regions of the plume, because of the computational cost incurred by computing inter-particle collisions. This problem has previously been tackled using hybrid continuum-particle methods. In this approach, the high-density region of the flow is treated with a NavierStokes solver, with the border of the continuum simulation domain providing the inflow conditions for the DSMC domain [4-6]. Whenever an expanding thruster plume interacts with adjacent surfaces, or the plume of a neighboring thruster, new areas of higher gas density form. These plume interaction zones produce flow patterns, that can have an appreciable impact on the surface pressure and heat flux [7]. To compute these areas of interaction with a hybrid approach, a spatially flexible, two-way coupling between code domains is required. We propose to use a coupled particle-particle method, in which the low-density domains of the flow are simulated using DSMC, and the high density areas are modeled by an approximated Boltzmann equation. One such approximation to the Boltzmann equation is the Fokker-Planck (FP) equation, which can be solved using a particle approach particularly compatible with DSMC [8, 9]: particle transport, and the treatment of the boundary conditions, is identical to DSMC. Merely updating the post-collision properties of the simulator particles is handled differently, thus a hybrid method can be be implemented with relatively minor modification to an existing DSMC code. This approach was shown to be an efficient way to model two-way coupled flows [10] and has been applied to simulations of single plumes, as well as to their interaction with a surface [11]. In this paper, we present results of a two-way coupled, hybrid DSMC-FP simulation of plume-plume interaction in a dual thurster configuration to demonstrate the feasibility of the approach for large scale applications.