No abstract

In this paper, the expansion of xenon, argon, krypton, and neon gases through a Laval nozzle is studied experimentally and numerically. The pressurized gases are accelerated through the nozzle into a vacuum chamber in an attempt to simulate the operating conditions of a cold-gas thruster for attitude control of a micro-satellite. The gases are evaluated at several mass flow rates ranging between 0.178 mg/s and 3.568 mg/s. The Re numbers are low (8–256) and the estimated values of Kn number lie between 0.33 and 0.02 (transition and slip-flow regime). Direct Simulation Monte Carlo (DSMC) and continuum-based simulations with a no-slip boundary condition are performed. The DSMC and the experimental results show good agreement in the range Kn > 0.1, while the Navier-Stokes results describe the experimental data more accurately for Kn < 0.05. Comparison between the experimental and Navier-Stokes results shows high deviations at the lower mass flow rates and higher Kn numbers. A relation describing the deviation of the pressure drop through the nozzle as a function of Kn is obtained. For gases with small collision cross sections, the experimental pressure results deviate more strongly from the no-slip assumption. From the analysis of the developed function, it is possible to correct the pressure results for the studied gases, both in the slip-flow and transition regimes, with four gas-independent accommodation coefficients. The thrust delivered by the cold-gas thruster and the specific impulse is determined based on the numerical results. Furthermore, an increase of the thickness of the viscous boundary layer through the diffuser of the micronozzle is observed. This results in a shock-less decrease of the Mach number and the flow velocity, which penalizes thrust efficiency. The negative effect of the viscous boundary layer on thrust efficiency can be lowered through higher values of Re and a reduction of the diffuser length.

Molecular diameters are an important property of gases for numerous scientific and technical disciplines. Different measurement techniques for these diameters exist, each delivering a characteristic value. Their reliability in describing the flow of rarefied gases, however, has not yet been discussed, especially the case for the transitional range between continuum and ballistic flow. Here, we present a method to describe gas flows in straight channels with arbitrary cross sections for the whole Knudsen range by using a superposition model based on molecular diameters. This model allows us to determine a transition diameter from flow measurement data that paves the way for generalized calculations of gas behaviour under rarefied conditions linking continuum and free molecular regime.