Experimental and numerical modeling of rarefied gas flows through orifices and short tubes

Flow through circular orifices with thickness-to-diameter ratios varying from 0.015 to 1.2 is studied experimentally and numerically with kinetic and continuum approaches. Helium and nitrogen gases are used in the range of Reynolds numbers from 0.02 to over 700. Good agreement between experimental and numerical results is observed for mass flow and thrust corrected for the experimental facility background pressure. For thick-to-thin orifice ratios of mass flow and thrust vs pressure, a minimum is established. The thick orifice propulsion efficiency is much higher than that of a thin orifice. The effects of edge roundness and surface specularity on a thick orifice specific impulse were found to be relatively small. INTRODUCTION Rarefied gas flows through circular orifices and short and long tubes have been studied extensively in the past. Free molecular and transitional flow in tubes and ducts was first studied experimentally and theoretically by Knudsen [1] who examined the dependence of the conductance at different pressure and geometrical parameters. He observed a conductance minimum at Kn≈1 for long ducts and tubes. A qualitative explanation for conductance minimum was suggested in [2]. The minimum was attributed to a small population of molecules that enter the tube or reflect on the tube surface with a very small radial velocity. These molecules give a disproportionately large contribution to the mass flow at high Knudsen numbers. As the Knudsen number decreases, molecular collisions disrupt the path of such molecules, therefore decreasing the mass flow. Further increase in the molecular collision frequency results in an overall drift velocity that in turn increases the mass flow through the tube. The conductance and the transmission probabilities in long tubes and channels in the transitional flow has been extensively studied in the 1960s and 1970s, both experimentally [3] and analytically [4]. There were also quite a few studies aimed at flows through short tubes and apertures [5, 6]. Examples of such studies are [7] where the effect of round edges on mass flow was analyzed, and [8] where empirical fits were suggested for conductance of sharp-edged orifices and rectangular ducts. This type of flow was also investigated in detail in the past decade, most noticeably with respect to emerging micro and nanotechnologies (such as lubrication problems that deal with transitional flows in long channels and tubes) and porous media (represented by a single or multiple capillaries). Although many researchers have made significant contribution to the field, we mention here only [9, 10, 11]. Although an extensive knowledge has been accumulated on transitional flows in orifices and short tubes, there have been few investigations of orifice/tube that concentrate on momentum flux (or thrust) and specific impulse [12, 13]. The main goal of this work is to study experimentally and numerically the above parameters of thin-walled orifice and short circular tube geometries, and perform a comparatative analysis for different tube length and edge bluntness in a wide range of Reynolds numbers from free molecular to near-continuum regime. The study also extends the low end of the Reynolds number range that previous studies have investigated by extending operating conditions down to the free molecule flow regime. The experiments and computations were conducted at room temperature, used nitrogen and helium as test gases and varied the stagnation pressure from several millitorr to about 40 torr. The computations are performed using two different approaches: a kinetic approach (the direct simulation Monte Carlo method, DSMC) and a continuum approach (solution of the Navier-Stokes equations, NS hereafter).