In the present work, the behavior of a millimeter-scale cold-gas thruster operating with the noble gases neon, argon, krypton and xenon is investigated both experimentally and numerically. In the experimental setup, the cold-gas thruster operates under vacuum conditions and the pressure drop in the system is measured at several fixed mass flow rates ranging between 0.178 mg/s and 3.568 mg/s. The estimated Knudsen numbers for all the studied cases are above the continuum flow limit 0.01. At the higher mass flow rates the studied flows are in the slip-flow regime while at the lower mass flow rates, the transition regime is reached. The experimental pressure results are compared with numerical simulations based on the compressible Navier-Stokes equations with a no-slip boundary condition and with simulations based on the Direct Simulation Monte Carlo (DSMC) method. At high values of Kn, the pressure results of the Navier-Stokes based simulations show high deviations from both the DSMC and the experimental results. This is a consequence of the discrepancy between the no-slip boundary condition used for the Navier-Stokes simulations and gas rarefaction effects in the micronozzle becoming dominant at the lower mass flow rates.
Based on the comparison between the experimental results and the Navier-Stokes based simulations, a Knudsen-dependent correcting function with four gas-independent accommodation coefficients is developed. The accommodation coefficients allow the accurate estimation of the actual pressure drop along the nozzle based on usually computationally inexpensive Navier-Stokes simulations with no-slip boundary conditions. The flexibility of the proposed approach is advantageous for the study of experimental setups operating at a large range of mass flow rates, where several flow regimes might exist, provided that a rigorous numerical distinction between continuum, slip-flow and transition regime is not essential.