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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)Air Force Research Laboratory (AFMC) AFRL/PRS SPONSOR/MONITOR'S Pollux Drive NUMBER(S)Edwards AFB CA 93524-7048 AFRL-PR-ED-JA-2005-293 DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution unlimited. AFRL-ERS-PAS-2005-200. SUPPLEMENTARY NOTES©2006 American Institute of Physics, published in Physics of Fluids 18, 093601 (2006) 14. ABSTRACT Gas flows through orifices and short tubes have been extensively studied from the 1960s through the 1980s for both fundamental and practical reasons. These flows are a basic and often important element of various modern gas driven instruments. Recent advances in micro-and nanoscale technologies have paved the way for a g generation of miniaturized devices in various application areas, from clinical analyses to biochemical detection to aerospace propulsion. The latter is the main area of interest of this study, where rarefied gas flow into a vacuum through short tubes with thickness-to-diameter ratios varying from 0.015 to 1.2 is investigated both experimentally and numerically with kinetic and continuum approaches. Helium and nitrogen gases are used in the range of Reynolds numbers from 0.02 to 770 (based on the tube diameter), corresponding to Knudsen numbers from 40 down to about 0.001. Propulsion properties of relatively thin and thick tubes are examined. Good agreement between experimental and numerical results is observed for mass flow rate and momentum flux, the latter being corrected for the experimental facility background pressure. For thick-to-thin tube ratios of mass flow and momentum flux versus pressure, aminimum is observed at a Knudsen number of about 0.5. A short tube propulsion efficiency is shown to be much higher than that of a thin orifice. The effect of surface specularity on a thicker tube specific impulse was found to be relatively small. Measurements and computations of mass flow and momentum flux through short tubes in rarefied gases Gas flows through orifices and short tubes have been extensively studied from the 196...

Different aspects of the transition between regular and Mach re ections of strong shock waves in steady ows are numerically studied. Two approaches-kinetic (the direct simulation Monte Carlo method) and continuum (Euler equations)-are used to investigate the hysteresis phenomenon in the ow about two symmetrical wedges in two-and three-dimensional statements. The dependence of the nal shock wave con guration on initial conditions, the transition from regular to Mach re ection by means of ow perturbations, and three-dimensional effects are examined. The three-dimensionality of the ow is shown to increase the angles of transition from regular to Mach re ection and back and to decrease the Mach stem height. IntroductionT HE hypothesis that a hysteresis phenomenon may exist in the transition between regular re ections (RR) and Mach re ections (MR) of strong shock waves in steady ows was rst put forward by Hornung et al. 1 They assumed that, when the angle of incidence ® changes smoothly, the transition from RR to MR and the reverse transition occur at different ® values. An attempt to assess this hypothesis was performed experimentally by Hornung and Robinson 2 and gave a negative result: No hysteresis was observed. They concluded that a possible reason might be the disturbances present in wind-tunnel ow. 2 Recently, though, the hysteresis was obtained experimentally by Chpoun et al. 3; 4 and numerically by Ivanov et al. 5 using the direct simulation Monte Carlo (DSMC) method. In later papers by Ivanov et al. 6 -9 the hysteresis phenomenon was examined carefully using two numerical approaches: kinetic and continuum. These numerical studies proved the existence of the hysteresis in accordance with the prediction of Hornung et al. 1 As for the experimental results of Chpoun et al., 3 ;4 some details of this work, such as the angle of transition from RR to MR, ® tr , do not correspond to what comes from the hypothesis of Hornung et al. 1 (® tr was 37.2 deg instead of ® D D 39:3 deg for M D 4:96). This was probably caused by three-dimensionaleffects, which were fairly signi cant in these experiments, where a wedge model with a small spanwise size was used. The contradiction motivated conducting new experiments 10 where different aspect ratios, i.e., ratios of spanwise to streamwisesize, from 0.66 up to 3.75, were used. The existence of hysteresis was con rmed there, but the total agreement of experimental and numerical data was not obtained.The dif culties of experimental studies of the hysteresis phenomenon are caused by acoustic and other perturbations inherent in any aerodynamic wind tunnel and also the problem of obtaining results with no in uence of three-dimensionality.These dif culties may be easily avoided if a numerical simulation is performed. The numerical approach gives an opportunity of not only assessing the impact of different perturbations and three-dimensionality but also elaborating a strategy for future experimental work. This paper is aimed at continuing the numerical study of various aspects of the pr...

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