Rarefied Nozzle Flow Computation Using the Viscosity-Based Direct Simulation Monte Carlo Method

Micro-nozzles are essential for enabling precise satellite attitude control and orbital maneuvers. Accurate prediction of performance parameters, including thrust and specific impulse, is critical, necessitating careful design of these nozzles. Given the high Knudsen numbers associated with micro-nozzle flows, rarefied gas dynamics often dominate, and conventional computational fluid dynamics (CFD) methods fail to capture accurate flow expansion behavior. The Direct Simulation Monte Carlo (DSMC) method, developed by Bird, is widely used for modeling rarefied flows; however, it has been primarily implemented on platforms like OpenFOAM and FORTRAN, with limited exploration in MATLAB. This study presents the development of a viscosity-based DSMC (μDSMC) simulation framework in MATLAB for analyzing rarefied gas expansion through micro-nozzles. Key boundary conditions, including upstream and downstream pressure conditions and thermal wall treatments with diffuse reflection, are incorporated into the code. The μDSMC results are validated against traditional DSMC outcomes, showing strong agreement. Grid convergence studies indicate that the radial grid size must be less than one-third of the mean free path, with a more relaxed requirement on axial grid size. Flow characteristics within micro-nozzles are evaluated across varying ambient pressures and gas species in terms of the back pressure ratio, effective exit flow ratio, and exit flow velocity. Studies indicated that a minimum back pressure ratio is required, beyond which the effective nozzle flow expansion is achieved. Parametric analysis further suggests that gases with lower molecular weights are preferable for achieving optimal expansion in micro-nozzles under low ambient pressures.