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Showing papers on "Supersonic speed published in 2001"


Journal ArticleDOI
TL;DR: In this paper, the authors investigate the effect of the aft ramp angle on the character of the shear layer that spans the cavity in a nonreacting supersonic ship.
Abstract: Experimentalandcomputationalinvestigationsofthee owe eldassociatedwithseveralcavity-basede ameholders in a nonreacting supersonic e ow are described. All cavity e ows were of the open type, that is, length-to-depth ratio L/D<10. Two values of L/D were studied with several offset ratios (OR) and aft ramp angles µ. Results indicate that the aft ramp angle plays an important role in determining the character of the shear layer that spans the cavity. For a rectangular cavity with OR=1 and µ=90 deg, a compression wave forms as the e ow separates from the cavity’ s upstream corner. A strong recompression occurs at the aft wall, and the e ow is visibly unsteady. The pressure on the cavity fore wall decreases steadily and the recompression process occurs more gradually with decreasing aftrampangle.Higherdrag coefe cientsandshorterresidencetimesarefoundin cavitieswithshallower ramp angles.

398 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the propagation of a shock wave into an interstellar medium by two-dimensional numerical hydrodynamic calculation with cooling, heating, and thermal conduction.
Abstract: The propagation of a shock wave into an interstellar medium is investigated by two-dimensional numerical hydrodynamic calculation with cooling, heating, and thermal conduction. We present results of the high-resolution, two-dimensional calculations to follow the fragmentation that results from thermal instability in a shock-compressed layer. We find that the geometrically thin cooling layer behind the shock front fragments into small cloudlets. The cloudlets have supersonic velocity dispersion in the warm neutral medium, in which the fragments are embedded as cold condensations. The fragments tend to coalesce and become larger clouds.

382 citations


01 Nov 2001
TL;DR: In this paper, a direct-connect supersonic combustor was used to simulate flight conditions between Mach 4 and 6 at a dynamic pressure of 47.9 kPa and achieved sustained combustion at equivalence ratios between 0.25 and 0.75 using only a spark plug and no other external ignition aids.
Abstract: : Recent results from combustion experiments in a direct-connect supersonic combustor are presented. Successful ignition and sustained combustion of gaseous ethylene have been achieved using an injector/flameholder concept with low-angle, flush-wall fuel injection upstream of a wall cavity. Two interchangeable facility nozzles (Mach 1.8 and 2.2) were used to obtain combustor inlet flow properties that simulate flight conditions between Mach 4 and 6 at a dynamic pressure of 47.9 kPa. Mainstream combustion was achieved at equivalence ratios between 0.25 and 0.75 using only a spark plug and no other external ignition aids. Delta-force levels between 667 and 1779 N were measured, with corresponding combustor pressure ratios between 3.1 and 4.0. Video records of the flame zone show an intensely active combustion zone with rapid flame spreading. One-dimensional performance analysis of the test data indicates a combustion efficiency around 80% with an average combustor skin friction coefficient of 0.0028.

198 citations


Journal ArticleDOI
TL;DR: In this article, a code-friendly version of the Durbin model is proposed to enhance numerical stability, which alleviates the stiffness problem associated with the original model caused by the boundary conditions at walls.

191 citations


Journal ArticleDOI
TL;DR: In this article, a molecular beam source near the tip of a hollow high-speed rotor provides a means to shift the velocity distribution of the beam downward or upward over a wide range.
Abstract: Mounting a molecular beam source near the tip of a hollow high-speed rotor provides a means to shift the velocity distribution of the beam downward or upward over a wide range. We describe the construction of such a device and experiments and model calculations characterizing its operation, for both supersonic and effusive beams of rare gases, O2, CH3F, and SF6. For example, the flow velocity of a rotating supersonic beam of O2 was accelerated to above 1000 m/s (corresponding to a kinetic energy of 2200 K and deBroglie wavelength of 0.1 A) and decelerated (when seeded in Xe) to below 70 m/s (corresponding to a kinetic energy below 10 K and deBroglie wavelength of nearly 2 A). With improvements in prospect, the rotating beam source offers a versatile and relatively simple way to enhance techniques for manipulating molecular trajectories.

129 citations


Journal ArticleDOI
TL;DR: The flow is found to be supersonic with a speed of granular pressure disturbances (sound speed) equal to about 10% of the flow speed, and shocks are observed nearly identical to those in a su personic gas.
Abstract: We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge. We find the flow to be supersonic with a speed of granular pressure disturbances (sound speed) equal to about 10% of the flow speed, and we observe shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.

129 citations


Journal ArticleDOI
TL;DR: In this paper, a high-order method is used to perform large-eddy simulations of a supersonic compression-ramp flowfield, which employs an implicit approximately factored finite difference algorithm, which is used in conjunction with a 10th-order nondispersive filter.
Abstract: A high-order method is used to perform large-eddy simulations of a supersonic compression-ramp flowfield. The procedure employs an implicit approximately factored finite difference algorithm, which is used in conjunction with a 10th-order nondispersive filter. Spatial derivatives are approximated by a sixth-order compact scheme, and Newton-like subiterations are applied to achieve second-order temporal accuracy. In the region of strong shock waves, the compact differencing of convective fluxes is replaced locally by an upwind-biased scheme. Both the Smagorinsky and dynamic subgrid-scale stress models are incorporated in the simulations. Details of the method are summarized, and a number of computations are carried out. Comparisons are made between the respective solutions as well as with available experimental data and with previous numerical results

129 citations


Journal ArticleDOI
TL;DR: In this article, the effects of compressibility in low Reynolds number turbulent supersonic channel flow via a direct numerical simulation are studied in detail for the wall layer and the core region based on scatter plots.
Abstract: The effects of compressibility are studied in low Reynolds number turbulent supersonic channel flow via a direct numerical simulation. A pressure-velocity-entropy formulation of the compressible Navier-Stokes equations which is cast in a characteristic, non-conservative form and allows one to specify exact wall boundary conditions, consistent with the field equations, is integrated using a fifth-order compact upwind scheme for the Euler part, a fourth-order Pade scheme for the viscous terms and a third-order low-storage Runge-Kutta time integration method. Coleman et al fully developed supersonic channel flow at M?=?1.5 and Re?=?3000 is used to test the method. The nature of fluctuating variables is investigated in detail for the wall layer and the core region based on scatter plots. Fluctuations conditioned on sweeps and ejections in the wall layer are especially instructive, showing that positive temperature, entropy and total temperature fluctuations are mainly due to sweep events in this specific situ...

127 citations


Journal ArticleDOI
TL;DR: In this paper, wind-tunnel testing of a fixed-geometry hypersonic inlet with rectangular-to-elliptical shape transition has been conducted at Mach 6.2.
Abstract: Wind-tunnel testing of a hypersonic inlet with rectangular-to-elliptical shape transition has been conducted at Mach 6.2. These tests were performed to validate the use of a recently developed design methodology for fixed-geometry hypersonic inlets suitable for airframe integrated scramjets. Results indicated that flow features within the inlet were similar to design and that the inlet typically captured 96% of the available airflow. Typical mass-flow-weighted total pressure recoveries of 55% were obtained for compression ratios of 14.8 throughout the test program. Assessment of the inlet starting characteristics indicated that the inlet self-started at Mach 6.2 despite the fact that it had an internal contraction ratio well above the Kantrowitz limit (Kantrowitz, A,, and Donaldson, C., "Preliminary Investigation of Supersonic Diffusers," NACA WR L-713, 1945). These results demonstrate that high-performance, fixed-geometry inlets can be designed to combine a nearly rectangular capture with a smooth transition to an elliptical throat.

114 citations


Journal ArticleDOI
TL;DR: In this article, high-speed images of supercavitating underwater projectiles traveling up to and exceeding the speed of sound in water were captured using a variety of methods, including standard video, 16mm high speed, laser illuminated motion pictures, high speed gated intensified video, and stroboscope illuminated 35-mm still photography.
Abstract: High-speed images of supercavitating underwater projectiles traveling up to and exceeding the speed of sound in water were captured using a variety of methods. These images reveal information on projectile flight behavior, stability mechanisms, cavity shape, and in-barrel launch characteristics. This information was used to understand the physics of supercavitating bodies, verify computer models, aid failure analysis, and produce projectile launch package design modifications. In the supersonic tests, projectile shock waves were revealed. Imaging consisted of standard video, 16-mm high-speed, laser illuminated motion pictures, high-speed gated intensified video, and stroboscope illuminated 35-mm still photography. Both front-lit and shadowgraph configurations were used.

110 citations


Journal ArticleDOI
TL;DR: In this article, a focusing nozzle was developed and tested with a pulsed microplasma cluster source to obtain dense and collimated supersonic cluster beams with a divergence of 10 mrad and average densities of 3×1010 atoms/cm3 (2×1012) at 300 mm distance from the source nozzle.
Abstract: Intense and collimated supersonic cluster beams have been produced by exploiting inertial focusing effects. To this goal we have developed and tested a novel focusing nozzle (focuser). Using this device with a pulsed microplasma cluster source we have obtained cluster beams with a divergence of 10 mrad and average densities of 3×1010 atoms/cm3 (2×1012 atoms/cm3 pulsed) corresponding to deposition rates of 2 nm/s at 300 mm distance from the source nozzle. With a focusing nozzle cluster thermal relaxation and mass distribution in a supersonic expansion can be controlled. We have measured the cluster transverse velocities, with extremely high precision, by characterizing the cluster beam deposition on a substrate by an atomic force microscope. Besides the relevance for the understanding of relaxation processes in expanding jets, the inertial focusing of clusters has several important consequences for the synthesis of nanostructured films with controlled structure and for all the experimental techniques requi...

Journal ArticleDOI
TL;DR: In this paper, a supersonic nonequilibrium plasma wind tunnel was used to study the effects of ionization on supersonically ionized gas flows in the presence of a high-pressure aerodynamically stabilized dc discharge in the tunnel plenum and a transverse rf discharge in a test section.
Abstract: Experimental studies of shock modification in weakly ionized supersonic gas flows are discussed. In these experiments, a supersonic nonequilibrium plasma wind tunnel, which produces a highly nonequilibrium plasma flow with the low gas kinetic temperature at M = 2, is used. Supersonic flow is maintained at complete steady state. The flow is ionized by a high-pressure aerodynamically stabilized dc discharge in the tunnel plenum and by a transverse rf discharge in the supersonic test section. The dc discharge is primarily used for the supersonic flow visualization, whereas the rf discharge provides high electron density in the supersonic test section. High-pressure flow visualization produced by the plasma makes all features of the supersonic flow, including shocks, boundary layers, expansion waves, and wakes, clearly visible. Attached oblique shock structure on the nose of a 35-deg wedge with and without rf ionization in a M = 2 flow is studied in various nitrogen-helium mixtures. It is found that the use of the rf discharge increases the shock angle by 14 deg, from 99 to 113 deg, which corresponds to a Mach number reduction from M = 2.0 to 1.8. Time-dependent measurements of the oblique shock angle show that the time for the shock weakening by the rf plasma, as well as the shock recovery time after the plasma is turned off, is of the order of seconds. Because the flow residence time in the test section is of the order of 10 μs, this result suggests a purely thermal mechanism of shock weakening due to heating of the boundary layers and the nozzle walls by the rf discharge. Gas flow temperature measurements in the test section using infrared emission spectroscopy, with carbon monoxide as a thermometric element, are consistent with the observed shock angle change. This shows that shock weakening by the plasma is a purely thermal effect. The results demonstrate the feasibility of both sustaining uniform ionization in cold supersonic nitrogen and airflows and the use of nonequilibrium plasmas for supersonic flow control. This opens a possibility for the use of transverse stable rf discharges for magnetohydrodynamic energy extraction and/or acceleration of supersonic airflows.

Journal ArticleDOI
TL;DR: In this paper, a new collocated finite-volume-based solution procedure for predicting viscous compressible and incompressible flows is presented, which is equally applicable in the subsonic, transonic, and supersonic regimes.

Journal ArticleDOI
TL;DR: In this article, the aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using the Donnell nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account.
Abstract: The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated. Nonlinearities caused by large-amplitude shell motion are considered by using the Donnell nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear piston theory is applied to describe the fluid-structure interaction by using two different formulations, taking into account or neglecting the curvature correction term. The system is discretized by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for traveling-wave flutter of the shell and shell axisymmetric contraction. Results show that the system loses stability by standing-wave flutter through supercritical bifurcation; however, traveling-wave flutter appears with a very small increment of the freestream static pressure that is used as the bifurcation parameter. A very good agreement between theoretical and existing experimental data has been found for flutter amplitudes. The influence of internal static pressure has also been studied.

Journal ArticleDOI
TL;DR: In this paper, a detailed study of a steady axisymmetric supersonic jet of CO2, including experiment, theory, and numerical calculation, is presented, based on high-sensitivity Raman spectroscopy mapping.
Abstract: A comprehensive study of a steady axisymmetric supersonic jet of CO2, including experiment, theory, and numerical calculation, is presented The experimental part, based on high-sensitivity Raman spectroscopy mapping, provides absolute density and rotational temperature maps covering the significant regions of the jet: the zone of silence, barrel shock, Mach disk, and subsonic region beyond the Mach disk The interpretation is based on the quasi-gasdynamic (QGD) system of equations, and its generalization (QGDR) considering the translational–rotational breakdown of thermal equilibrium QGD and QGDR systems of equations are solved numerically in terms of a finite-difference algorithm with the steady state attained as the limit of a time-evolving process Numerical results show a good global agreement with experiment, and provide information on those quantities not measured in the experiment, like velocity field, Mach numbers, and pressures According to the calculation the subsonic part of the jet, downstream of the Mach disk, encloses a low-velocity recirculation vortex ring

Journal ArticleDOI
TL;DR: In this article, the non-linear propagation of a high-amplitude sawtooth waveform spiralling around a duct is calculated by two numerical simulation models and their validation is discussed critically.

Journal ArticleDOI
TL;DR: In this paper, the authors describe a continuous-e flow, direct-connect, high-enthalpy, supersonic combustion research facility with a variable-geometry heat-sink combustor and a variety of conventional and advanced instrumentation including a steam calorimeter and a thrust stand.
Abstract: Anew continuous-e ow,direct-connect,high-enthalpy, supersonic combustion researchfacility isdescribed. This test facility provides combustor inlet e ow conditions corresponding to e ight Mach numbers between 3.5 and 7, at dynamic pressures up to 95.8 kPa. Most of the major components of the new facility are water cooled (including the vitiated heater, the instrumentation and transition sections, and the facility nozzle and isolators ); the current exception is the variable-geometry heat-sink combustor. A variety of conventional and advanced instrumentation, including a steam calorimeter and a thrust stand, exists for accurate documentation of combustor inlet and exit conditions and performance parameters. In a recent calibration effort, pitot pressure surveys, total temperature surveys, and wall static pressure distributions were obtained for a wide range of inlet conditions using Mach 1.8 and 2.2 facility nozzles. In addition, three-dimensional numerical simulations of each test case were completed. Results from thecomputations compare favorably with experimental results for all cases and yield estimates of the integral boundary-layer properties at the isolator exit.

01 Oct 2001
TL;DR: Soures et al. as discussed by the authors investigated the propagation of a structured shock front within a radiation-driven target assembly, the formation of a supersonic jet of material, and the subsequent interaction of this jet with an ambient medium in which a second, ablatively driven shock wave is propagating.
Abstract: Supersonic fluid flow and the interaction of strong shock waves to produce jets of material are ubiquitous features of inertial confinement fusion (ICF), astrophysics, and other fields of high energy-density science. The availability of large laser systems provides an opportunity to investigate such hydrodynamic systems in the laboratory, and to test their modeling by radiation hydrocodes. We describe experiments to investigate the propagation of a structured shock front within a radiation-driven target assembly, the formation of a supersonic jet of material, and the subsequent interaction of this jet with an ambient medium in which a second, ablatively driven shock wave is propagating. The density distribution within the jet, the Kelvin–Helmholz roll-up at the tip of the jet, and the jet’s interaction with the counterpropagating shock are investigated by x-ray backlighting. The experiments were designed and modeled using radiation hydrocodes developed by Los Alamos National Laboratory, AWE, and Lawrence Livermore National Laboratory. The same hydrocodes are being used to model a large number of other ICF and high energy-density physics experiments. Excellent agreement between the different simulations and the experimental data is obtained, but only when the full geometry of the experiment, including both laser-heated hohlraum targets (driving the jet and counter-propagating shock), is included. The experiments were carried out at the University of Rochester’s Omega laser [J. M. Soures et al., Phys. Plasmas 3, 2108 (1996)].

Journal ArticleDOI
TL;DR: In this paper, a NACA 0012 airfoil is simulated using both particle and continuum approaches, in three different conditions: supersonic, transonic, and low subsonic.
Abstract: Raree ed gas e ows around a NACA 0012 airfoil are simulated using both particle and continuum approaches Three different conditions are considered: supersonic, transonic, and low subsonic In all three cases, the continuum approach solves the Navier ‐Stokes equations with a slip boundary condition on the airfoil surface For the supersonic and transonic cases, the particle method employed is the direct simulation Monte Carlo method Because of problems with this method at the low subsonic condition, caused by excessive statistical e uctuations, a new particle method called the information preservation technique is applied The computed density and velocity e owe elds are compared with experimental data and found to be in generally good agreement Some interesting features in the surface pressure distributions along the airfoil are found for these low-Reynolds-number e ows

Journal ArticleDOI
TL;DR: It is shown that the speed of amoving sound source is supersonic and that the Mach cone generated by the moving sound source forms the helical-shaped wave front of the screech tone for the helicals oscillation mode of the jet.
Abstract: The generation mechanism of the screech tone in the helical oscillation mode is mainly investigated using a series of instantaneous schlieren photographs. From the photographs, five evanescent sound sources are observed as prominent points along the jet axis. The sound source for the dominant helical oscillation mode is found to be the second prominent point which moves along a circular orbit in a plane perpendicular to the jet axis and just downstream of the rear edge of the third shock cell. It is shown that the speed of a moving sound source is supersonic and that the Mach cone generated by the moving sound source forms the helical-shaped wave front of the screech tone for the helical oscillation mode of the jet. This idea of the moving sound source is well supported by a measured directionality of the screech tone. Sound sources of the other oscillation modes appearing in the other pressure ratio ranges are also described.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional direct simulation Monte Carlo program for pressure boundaries using unstructured cells and its applications to typical micro-scale gas flows are described, including micro-manifold, micro-nozzle and slider air bearing.

Journal ArticleDOI
TL;DR: In this paper, a side-by-side experimental and computational effort was conducted to investigate the shock-wave bifurcation associated with a counterflow jet from a hemispherical cylinder.
Abstract: In recent plasma injection experiments, counterflow jet interaction has been identified as one of the mechanisms that significantly reduces the drag. There is a sudden change of the dynamic state from an oscillatory to nearly steady motion of this jet-shock interaction which depends on the relative magnitude of injection and the stagnation pressure. The shock-wave bifurcation associated with a counterflow jet from a hemispherical cylinder is investigated by a side-by-side experimental and computational effort. Shock-wave bifurcation has been discovered by the present experiments over the entire range of tested conditions in the Mach 6 wind tunnel. This oscillatory motion is sustained by the upstream propagation of selectively amplified frequencies from the free-shear layer to the Mach disk through the embedded subsonic domain. The breakdown of this feedback loop occurs when a higher injecting jet pressure creates a supersonic zone separating the interconnecting embedded subsonic domains

Journal ArticleDOI
TL;DR: The Peierls model, modified to account for drag and gradient effects, furnishes a kinetic relation between the applied shear stress and speed of uniformly moving dislocations, which predicts intersonic and supersonic speeds at high enough stress, but also regimes of unstable motion.
Abstract: The controversial issue of whether dislocations can travel faster than shear or longitudinal waves is investigated. The Peierls model, modified to account for drag and gradient effects, furnishes a kinetic relation between the applied shear stress and speed of uniformly moving dislocations. This relation predicts intersonic and supersonic speeds at high enough stress, but also regimes of unstable motion, in agreement with recent atomistic simulations.

Journal ArticleDOI
Hafner K, Zimmerman R1, Rohwer Er1, Dorfner R1, Kettrup A1 
TL;DR: A first field application of a mobile supersonic jet-REMPI mass spectrometer equipped with the novel inlet technique is reported; namely, the concentration of monochlorobenzene, which is an indicator for the formation and emission of toxic polychlorinated dibenzo-p-dioxins/furans, PCDD/F was measured on-line in the flue gas of a waste incineration plant.
Abstract: A new supersonic jet inlet system for resonance-enhanced multiphoton ionization time-of-flight mass spectrometry (REMPI-TOFMS), based on a fused-silica capillary with an integral nozzle has been developed. The new jet inlet system generates a supersonic molecular beam that originates in the center of the ion source of the time-of-flight mass spectrometer. Because of the design of the inlet system, high spatial overlap of sample and laser beam (i.e., increased detection sensitivity) and excellent jet beam qualities are achieved with good adiabatic cooling properties of analyte molecules (i.e., considerably enhanced optical selectivity of the REMPI process). Furthermore, the inlet is very robust and chemically inert and contains no moving parts. As a result of these properties, the new inlet is perfectly suited for field applications of jet-REMPI. A first field application of a mobile supersonic jet-REMPI mass spectrometer equipped with the novel inlet technique is reported; namely, the concentration of monochlorobenzene, which is an indicator for the formation and emission of toxic polychlorinated dibenzo-p-dioxins/furans, PCDD/F) was measured on-line in the flue gas of a waste incineration plant.



01 Jan 2001
TL;DR: In this paper, the de Laval nozzle is used as a simple cold-gas thruster to accelerate the fluid from a plenum to supersonic speeds in excess of Mach 4.
Abstract: We discuss approaches to the design and fabrication of supersonic micropropulsion systems. The core of the system is a de Laval nozzle which accelerates the fluid from a plenum, through a 30 micron throat. The flow is expanded downstream to supersonic speeds in excess of Mach 4. Using the nozzle as a simple cold-gas thruster, good Isp efficiencies are demonstrated, although side-wall boundary layer contamination and the limitations of MEMS fabrication technologies are apparent. The system performance is greatly improved by heating the flow in the plenum (i.e. a resistojet). This is achieved using integrated microheaters, designed to optimally heat the fluid with a minimum of pressure loss in the plenum. The heaters are fabricated in a novel manner, using silicon both as the structural material and the electrical heater element. The performance of the resistojet system is tested and compares favorably with the cold-gas efficiencies at similar Reynolds numbers.

Journal ArticleDOI
TL;DR: In this article, a van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations.
Abstract: Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.

Journal ArticleDOI
TL;DR: In this paper, a more realistic case of an axisymmetric nozzle impinging on a plate with a linear cut is considered, where the cut is assumed to be a circular hole directly underneath and concentric with the gas jet nozzle.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the acceleration due to expansion just cancels out the deceleration due to ion and electron neutral collisions at the sonic point, which is the point at which the singularity is resolved not by charge separation, as is the case for a sheath, but rather by a zero in numerator at the same spatial position as the zero in the denominator.
Abstract: As the area of a plasma increases, the plasma can accelerate smoothly from subsonic to supersonic velocity. The singularity which ordinarily occurs at the sonic velocity is resolved not by charge separation, as is the case for a sheath, but rather by a zero in the numerator at the same spatial position as the zero in the denominator, the sonic point. That is, at the sonic point, the acceleration due to expansion just cancels out the deceleration due to ion and electron neutral collisions. It turns out that, in this configuration, the plasma can accelerate to about three times the ion sound speed. The electron temperature is determined by the geometry, gas species, and, mostly, by the gas pressure. Applications to the production of a stream of neutrals for etching, and to space plasma propulsion are discussed.