Showing papers on "Supersonic speed published in 1999"

The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds

Abstract: Molecular clouds have broad line widths, which suggests turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. Classically, it was thought that supersonic hydrodynamical turbulence would dissipate its energy quickly but that the introduction of strong magnetic fields could maintain these motions. A previous paper has shown, however, that isothermal, compressible MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper, direct numerical computations of uniform, randomly driven turbulence with the ZEUS astrophysical MHD code are used to derive the value of the energy-dissipation coefficient, which is found to be with ηv = 0.21/π, where vrms is the root-mean-square (rms) velocity in the region, Ekin is the total kinetic energy in the region, m is the mass of the region, and is the driving wavenumber. The ratio τ of the formal decay time Ekin/kin of turbulence to the free-fall time of the gas can then be shown to be where Mrms is the rms Mach number, and κ is the ratio of the driving wavelength to the Jeans wavelength. It is likely that κ < 1 is required for turbulence to support gas against gravitational collapse, so the decay time will probably always be far less than the free-fall time in molecular clouds, again showing that turbulence there must be constantly and strongly driven. Finally, the typical decay time constant of the turbulence can be shown to be where is the driving wavelength.

Dynamical Friction in a Gaseous Medium

Abstract: Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber Mp traveling at velocity V through a uniform gaseous medium of density ρ0 and sound speed cs. This drag force acts in the direction - and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (≡V/cs>1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion ( 1, but is less efficient when <1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal ρ∝r−2 halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.

Spreading characteristics of compressible jets from nozzles of various geometries

Abstract: The spreading characteristics of jets from several asymmetric nozzles, and a set of rectangular orifices are compared, covering a jet Mach number range of 0.3-2.0. The effect of 'tabs' for a rectangular and a round nozzle is also included in the comparison. Compared to a round jet, the jets from the asymmetric nozzles spread only slightly more at subsonic conditions whereas at supersonic conditions, when 'screech' occurs, they spread much more. The dynamics of the azimuthal vortical structures of the jet, organized and intensified under the screeching condition, are thought to be responsible for the observed effect at supersonic conditions. Curiously, the jet from a 'lobed' nozzle spreads much less at supersonic condition compared to all other cases; this is due to the absence of screech with this nozzle. Screech stages inducing flapping, rather than varicose or helical, flow oscillation cause a more pronounced jet spreading. At subsonic conditions, only a slight increase in jet spreading with the asymmetric nozzles contrasts previous observations by others. The present results show that the spreading of most asymmetric jets is not much different from that of a round jet. This inference is further supported by data from the rectangular orifices. In fact, jets from the orifices with small aspect ratio (AR) exhibit virtually no increase in the spreading. A noticeable increase commences only when AR is larger than about 10. Thus, 'shear layer perimeter stretching', achieved with a larger AR for a given cross-sectional area of the orifice, by itself, proves to be a relatively inefficient mechanism for increasing jet spreading. In contrast, the presence of streamwise vortices or 'natural excitation' can cause a significant increase - effects that might explain the observations in the previous investigations. Thus far, the biggest increase in jet spreading is observed with the tabs. This is true in the subsonic regime, as well as in the supersonic regime, in spite of the fact that screech is eliminated by the tabs. The characteristic spreading of the tabbed jets is explained by the induced motion of the tab-generated streamwise vortex pairs. The tabs, however, incur thrust loss; the flow blockage and loss in thrust coefficient, vis-a-vis the spreading increase, are evaluated for various configurations.

Flow field and noise characteristics of a supersonic impinging jet

Abstract: This paper describes the results of a study examining the flow and acoustic characteristics of an axisymmetric supersonic jet issuing from a Mach 1.5 converging-diverging (C-D) nozzle and impinging on a ground plane. A large diameter circular plate was attached at the nozzle exit to measure the forces generated on the plate due to jet impingement. The experimental results described in this paper include lift loss, Particle Image Velocimetry (PIV) and acoustic measurements. Suckdown forces as high as 60% of the primary jet thrust were measured when the ground plane was very close to the jet exit. The PIV measurements were used to explain the increase in suckdown forces due to high entrainment velocities. The self-sustained oscillatory frequencies of the impinging jet were well-predicted using a feedback loop that utilizes the measured convection velocities of the large scale coherent vortical structures in the jet shear layer. Near field acoustic measurements indicate that the presence of the ground plane increases the OASPL by approximately 8 dB relative to a corresponding free jet. For moderately under expanded jets, the influence of the shock cells on the important flow features was found to be negligible except for close proximity of the ground plane.

Dislocations Faster than the Speed of Sound

Abstract: It is thought that dislocations cannot surpass the sound barrier at the shear wave velocity because the energy spent in radiation has a singularity there. Atomistic simulations show that dislocations can move faster than the speed of sound if they are created as supersonic dislocations at a strong stress concentration and are subjected to high shear stresses. This behavior is important for the understanding of low-temperature deformation processes such as mechanical twinning and may be relevant for the dynamics of tectonic faults. The motion of the dislocations at a speed of 2 times the shear wave velocity can be understood from a linear elastic analysis, but many of the peculiarities of the supersonic dislocations are dominated by nonlinear effects that require a realistic atomistic description.

Flight Data for Boundary-Layer Transition at Hypersonic and Supersonic Speeds

Abstract: Published e ight data for boundary-layer transition at hypersonic speeds are surveyed. The survey is limited to measurements reported in the open literature and carried out at hypersonic and high-supersonic speeds, on vehicles for which ablation is believed to be negligible or small. The emphasis is on work that may be suitable for validation of advanced transition-estimation methods that are based on simulation of the physical mechanisms, such as e N , the parabolized stability equations, and direct numerical simulations. Brief discussions are presented for each report. Known comparisons to the advanced simulation methods are also presented. Nomenclature Me = Mach number at the boundary-layer edge Res = Reynolds number at transition onset, based on arc length from the leading edge and local conditions at the boundary-layer edge ReT = Reynolds number at transition onset, based on arc length and conditions at the boundary-layer edge ReT/ft = unit Reynolds number per foot, at the boundary-layer edge at transition onset Reµ = Reynolds number at transition, usually onset, based on momentum thickness and conditions at the boundary-layer edge Te = temperature at the boundary-layer edge Tr = recovery temperature at the wall Tw = wall temperature xT = arc length to transition onset, from the nose µc = cone half-angle, deg

An experimental investigation of screech noise generation

Abstract: The screech noise generation process from supersonic underexpanded jets, issuing from a sonic nozzle at pressure ratios of 2.4 and 3.3 (fully expanded Mach number, Mj = 1.19 and 1.42), was investigated experimentally. The extremely detailed data provide a fresh, new look at the screech generation mechanism. Spark schlieren visualization at different phases of the screech cycle clearly shows the convection of the organized turbulent structures over a train of shock waves. The potential pressure field (hydrodynamic fluctuations) associated with the organized structures is fairly intense and extends outside the shear layer. The time evolution of the near-field pressure fluctuations was obtained from phase-averaged microphone measurements. Phase-matched combined views of schlieren photographs and pressure fluctuations show the sound generation process. The individual compression and rarefaction parts of the sound waves are found to be generated from similar hydrodynamic fluctuations. A partial interference between the upstream-propagating sound waves and the downstream-propagating hydrodynamic waves is found to be present along the jet boundary. The partial interference manifests itself as a standing wave in the root-mean-square pressure fluctuation data. The standing wavelength is found to be close to, but somewhat different from, the shock spacing. An outcome of the interference is a curious 'pause and go' motion of the sound waves along the jet periphery. Interestingly, a length scale identical to the standing wavelength is found to be present inside the jet shear layer. The coherent fluctuations and the convective velocity of the organized vortices are found to be modulated periodically, and the periodicity is found to match with the standing wavelength distance rather than the shock spacing. The reason for the appearance of this additional length scale, different from the shock spacing, could not be explained. Nevertheless, it is demonstrated that an exact screech frequency formula can be derived from the simple standing wave relationship. The exact relationship shows that the correct spacing between the sources, for a point source model similar to that of Powell (1953), should be a standing wavelength (not the shock spacing).

Mach cones in a coulomb lattice and a dusty plasma

Abstract: Mach cones, or V-shaped disturbances created by supersonic objects, have been detected in a two-dimensional Coulomb crystal. Electrically charged microspheres levitated in a glow-discharge plasma formed a dusty plasma, with particles arranged in a hexagonal lattice in a horizontal plane. Beneath this lattice plane, a sphere moved faster than the lattice sound speed. Mach cones were double, first compressive then rarefactive, due to the strongly coupled crystalline state. Molecular dynamics simulations using a Yukawa potential also show multiple Mach cones.

The Density PDFs of Supersonic Random Flows

Abstract: The question of the shape of the density PDF for supersonic turbulence is addressed, using both analytical and numerical methods For isothermal supersonic turbulence, the PDF is Log-Normal, with a width that scales approximately linearly with the Mach number For a polytropic equation of state, with an effective gamma smaller than one, the PDF becomes skewed and becomes reminiscent of (but not identical to) a power-law on the high density side Introduction The Probability Density Function of mass density is an important statistical property of the ISM that relates, for example, to gravitational collapse and star formation Log-Normal PDFs have been discussed occasionally in both the cosmological and interstellar contexts (Hubble 1934, Peebles 1980, Ostriker 1984, Zinnecker 1984, Coles & Jones 1991) Vazquez-Semadeni (1994) noticed that the density PDFs in his 2-D numerical simulations of turbulence were consistent with a Log-Normal, and discussed possible reasons for the lognormality Padoan et al (1997) showed that the standard deviation of the Log-Normal PDFs in their isothermal 3-D simulations was approximately equal to half the rms Mach number Scalo et al (1998) raised the questions of how a polytropic equation of state, and more generally a realistic ISM cooling function, might influence the PDF In this contribution we investigate the question of the shape of the PDF for isothermal and polytropic equations of state, using analytical methods and by looking at results from 3-D simulations of supersonic turbulence

Measurement of shock structure and shock–vortex interaction in underexpanded jets using Rayleigh scattering

Abstract: The density field of underexpanded supersonic free jets issuing from a choked circular nozzle was measured using a Rayleigh scattering-based technique. This reliable and nonintrusive technique is particularly suitable for high-speed flows and is fundamentally superior to the intrusive probes and particle-based techniques such as laser Doppler velocimetry. A continuous wave laser and photon counting electronics were employed for time and phase-averaged density measurements. The use of dust-free air for the entrained flow allowed measurements in the shear layer region. The free jets were produced in the plenum to ambient pressure ratio range of 1.88–5.75, which corresponded to a fully expanded Mach number range of 0.99⩽Mj⩽1.8. A comparative study of schlieren photographs and time-averaged density data provided insight into the shock-cell structures. The radial profiles obtained at various axial stations covering a downstream distance of 10 jet diameters show the development of the jet shear layer and the decay of the shock–cells. The supersonic free jets produced screech sound. A phase-averaged photon counting technique, using the screech tone as the trigger source, was used to measure the unsteady density variation. The phase-averaged density data show the evolution of the large-scale turbulent vortices that are found to be modulated periodically along the flow direction. A comparison with previously obtained data showing near-field pressure fluctuation and convective speed of the organized vortices reveals many interesting dynamics. All quantities show regular spatial modulation. The locations of local maxima in density fluctuations are found to coincide with the high convective speed and the antinode points in the near-field pressure fluctuation. Interestingly, the periodicity of modulation is found to be somewhat different from the shock spacing. Instead it shows that the standing wave system, known to exist in the near-field pressure fluctuation, extends into the jet shear layer. The standing wave is formed between the downstream moving Kelvin–Helmholtz instability waves and the upstream propagating part of sound waves. A detailed field measurement of the unsteady density fluctuation was conducted for the Mj=1.19 and 1.42 jets for which the near-field pressure fluctuation data were obtained previously. The phase-matched, combined plots of the density fluctuation present inside the jet flow, and the pressure fluctuation present just outside the jet boundary provide a charming insight into the shock–vortex interaction leading to the sound wave generation.

Motion of tracer particles in supersonic flows

Abstract: Factors that may act on particle motion in high-speed flow are investigated. The classical expressions of drag coefficient C D for a sphere are reviewed. Then, a drag expression is proposed, extending Cunningham’s method to higher velocities and Knudsen numbers. This law, valid from continuum to free molecule conditions, for Re≲200 and M≲1 (where Re and M are, respectively, the Reynolds and Mach numbers based on relative velocity), is used to compare calculated and experimental values of the drag coefficient, as well as the particle velocities across an oblique shock wave. Calculated results are found to be in agreement with experiments.

Planar visualizations of large-scale turbulent structures in axisymmetric supersonic separated flows

Abstract: The spatial evolution of large-scale turbulent structures in the shear layer of an axisymmetric, supersonic separated flow has been investigated. The experimental diagnostic used was planar visualization of condensed ethanol droplets that were suspended in the supersonic free stream. Spatial correlation analyses of large ensembles of images show that the mean side-view structure is highly strained and elliptical in shape and is inclined toward the local free stream direction. It is also shown that the effect of lateral streamline convergence for this axisymmetric case causes a reduction in side-view structure size and eccentricity at the reattachment point as compared to the planar case. End-view structures are wedge shaped, wider on the free-stream side than on the recirculation region or developing wake side. It is concluded that the wedge shape is caused by the axisymmetric confinement of the shear layer as it approaches the wake centerline. The average number of structures present in the end-view plan...

Fundamental studies of cavity-based flameholder concepts for supersonic combustors

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.

Measurements of Supersonic Helium/Air Mixture Jets

Abstract: An enhanced method of using helium/air mixture jets to simulate the aeroacoustic properties of hot jets is presented By using helium to reduce the jet density and increase the jet acoustic speed, unheated nominal Mach 15 jets are tested which have jet-to-ambient density and acoustic speed ratios which approximately match those from a hot jet with a jet-to-ambient static temperature ratio of 12 The jets are operated at a reduced Reynolds numbers (approximately 27,000) which allows the use of diagnostic measurement tools such as hot-wire anemometry and active control via glow discharge excitation Mean and fluctuating flowfield and acoustic measurements from a near perfectly expanded Mach 15 elliptic and round jet are presented Direct comparisons of the cold and simulated heated jets are made Compared to the pure air jets, the helium/air mixture jets showed increased instability wave phase speeds near or exceeding the ambient acoustic speed, increased noise levels, and increased coupling between the flowfield fluctuations and the radiated acoustic field These features are consistent with the theory of Mach wave radiation, the dominant noise source in high speed jets The data presented show that the helium/air simulation is able to capture the dominant noise characteristics of actual heated jets The use of this group of diagnostic measurement techniques is an added benefit of the simulation which is not available in conventional heated jet experiments

Noise Measurements in Supersonic Jets Treated with the Mach Wave Elimination Method

Abstract: We report noise measurements for perfectly expanded coaxial jets composed of a supersonic primary stream at velocity of 920 m/s and a coflow stream at conditions designed to prevent formation of Mach waves. Both the primary and secondary streams consisted of helium-air mixtures to simulate approximately the conditions of hot flows, The resulting sound field was compared to that emitted by a single jet at the conditions of the primary stream. Overall sound pressure levels (OASPL) and noise spectra were obtained at many radial and azimuthal positions around the jet exit. Equal-thrust comparisons were made by using geometric scaling. At equal thrust, Mach wave elimination reduced the near-field OASPL by 11 dB and the far-field OASPL by 5 dB. The mid-to-high-frequency region of the spectrum, which is most pertinent to aircraft noise, was reduced by 20 dB in the near field and by 9 dB in the far field. It is shown that Mach waves account for at least 85 % of the sound field most relevant to aircraft noise.

A numerical investigation of sound generation in supersonic jet screech

Abstract: : The noise of supersonic jet flows is due in part to the interaction between jet instability waves and the jet shock-cell structure. If no countermeasures are taken, the emitted shock-cell noise will re-excite certain instability wave modes at the nozzle lip and cause resonant feedback to occur. This feedback resonance, known as supersonic jet screech, causes the jet to flap violently at discrete frequencies and generate very strong, narrow banded tones. Jet screech has been shown to be a source of acoustic fatigue in the tail and nozzle structures of supersonic aircraft. It is important that methods for predicting the screech amplitude be developed. Screech sound generation is one such element. We isolate the interaction of an unsteady shear layer with a single oblique shock. To obtain an overall understanding of the phenomenon with fewest simplifications, we study this problem through the numerical solution of the Navier Stokes equations. We then consider idealizations which allow us to obtain a similar but wider range of results with specially linearized Euler equations. The findings of these r0sults motivate the use of geometric acoustics to describe the screech generation process. The Navier-Stokes and Euler simulations have revealed important details about the interaction process, how the acoustic field results, and why screech is so loud. The mechanism for sound production is found to be fundamentally different and more efficient when the instability waves are the large vortices typical of screech, than when they are small disturbances. Geometrical acoustics can be used to explain the leakage effect at high instability wave amplitude. We conclude that the mechanism for high amplitude screech generation is an unsteady modification to the velocity field by the instability waves that permits the incident shock to refract through the shear layer.

Nonlinear Flutter of Composite Panels Under Yawed Supersonic Flow Using Finite Elements

Abstract: A finite element formulation is presented for the effects of arbitrary flow direction on the large-amplitude supersonic flutter of composite panels. The von Karman large-deflection plate theory is used to account for large-amplitude limit-cyde oscillations, quasisteady first-order piston theory aerodynamics is employed for aerodynamic loading, and first-order shear deformation theory is used for laminated composite panels. An efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations. A modal participation is defined and the minimum number of linear modes for accurate and converged limit-cycle response can be ensured. Examples are given for isotropic and composite panels at yawed supersonic flow.

Deceleration by dynamical friction in a gaseous medium

Abstract: The drag force experienced by a gravitational body moving in a straight-line trajectory through a homogeneous isothermal gaseous medium of given sound speed is investigated numerically. For perturbers with constant velocity, linear theory describes successfully the temporal evolution and magnitude of the force. The result obtained recently by E. Ostriker—that for Mach numbers = 1-2 the force is stronger in a gaseous medium than in a collisionless medium, as described by the standard Chandrasekhar formula—is confirmed. The corresponding minimum impact radius rmin for a body described with a Plummer model with core radius Rsoft is rmin/Rsoft ≈ 2.25. When < 1, the drag force is strongly suppressed, which is consistent with Ostriker's results but in disagreement with the Chandrasekhar formula. However, when the perturber is decelerated by its own wake to < 1, the effective drag force remains initially somewhat larger than the value in the case of constant velocity because it takes some time to get rid of the wake that was generated during its supersonic history.

Surface Pressure Measurements in Supersonic Transverse Injection Flowfields

Abstract: Pressure-sensitive paint (PSP) was used to examine the surface pressures in flowfields generated by transverse injection of air through circular and elliptical nozzles into a supersonic freestream. Four jet-to-freestream momentum flux ratios (J) were investigated for each jet. Two different pressure paints (pyrene-based and PtOEP-based) were examined. Results of the paint comparison show that the PtOEP-based paint is significantly more temperature-sensitive than the pyrene-based paint. This results from its longer phosphorescence lifetime as compared to pyrene's short fluorescence lifetime. A comparison of the PSP results with conventional pressure measurements indicates good agreement between the two with no special fitting of the paint data. Results further show that jet operating conditions and injector geometry significantly affect the surface pressure field around a transverse jet. Increases in J dramatically alter the wall pressure field upstream and downstream of the injector. Injector geometry strongly affects the upstream extent of the separation region and the bow shock, and the character of the wake region downstream of the jet. Also, the effective back pressures computed from the PSP data for the elliptical injector cases are significantly higher than for the circular injector cases presenting a possible explanation for recently observed differences in transverse penetration.

Global existence of steady supersonic potential flow past a curved wedge with a piecewise smooth boundary

Abstract: In this paper we use a modified Glimm scheme to construct a global weak solution to the steady supersonic potential flow past a two-dimensional wedge with a piecewise smooth boundary, small vertex angle, and small total variation of the tangent angle along each side.

Supersonic coherent gas jet for providing gas into a liquid

Abstract: A system for establishing and maintaining a supersonic coherent gas jet, effective with either an oxidizing or an inert gas, employing a converging/diverging nozzle for establishment of a non-disruptive initial supersonic velocity, and a slower moving defined triple layered flame envelope coaxial with the jet for effective maintenance of the supersonic velocity The invention is particularly useful for providing gas into a pool of liquid

The formation of large-scale structures in supersonic magnetohydrodynamic flows

Abstract: In this paper we investigate the existence of an inverse cascade of magnetic helicity for statistically steady compressible magnetohydrodynamic flows with rms Mach numbers that go up to unity. This has been done by performing a set of three-dimensional numerical simulations that were carried out using the RIEMANN code for astrophysical fluid and magnetofluid dynamics [D. S. Balsara, Astrophys. J. Suppl. 116, 133 (1988)]. The random forcing is made up of ABC flows corresponding to helical wave patterns at an intermediate scale. Both time histories of integral quantities and Fourier spectra are shown, illustrating the inverse cascade process. The observed build-up of large-scale magnetic helical structures for a wide range of Mach numbers indicates that, in the context of the generation of the magnetic field of the Galaxy where supersonic flows are common, a dynamo mechanism based on the nonlinear dynamics of magnetic helicity may be at work.

Analysis of the dynamic characteristics of gas flow inside a laser cut kerf under high cut-assist gas pressure

Abstract: The behaviour of the cut-assist gas jet inside a simulating laser cut kerf for a supersonic and a conical nozzle tip were studied by a shadowgraphic technique under conditions of inlet stagnation pressure from 3 to 7 bar. The effects of the stand-off distance, kerf width, material thickness and the inlet stagnation pressure upon the dynamic characteristics and momentum thrust of the gas flow inside the cut kerf were investigated. It was found that under a gas pressure of 7 bar, the gas jet from a conical nozzle tip expands radially and the jet momentum deteriorates rapidly inside the kerf. The behaviour of the jet is strongly influenced by the stand-off distance and thickness of the workpiece. On the other hand, the gas jet from a supersonic nozzle inside the cut kerf has tidy boundary and uniform distribution of pressure and thrust. The sensitivity to the stand-off distance and the workpiece thickness of the supersonic nozzle are much less as compared with the conical nozzle. With the supersonic nozzle, a dross free clean cut on 5 mm stainless steel can be achieved at an inert cut-assist gas pressure as low as 5 bar instead of the normal operating range of 10 bar or above for the conical nozzle.

Aerodynamic beam generator for large particles

Abstract: A new type of aerodynamic particle beam generator is disclosed. This generator produces a tightly focused beam of large material particles at velocities ranging from a few feet per second to supersonic speeds, depending on the exact configuration and operating conditions. Such generators are of particular interest for use in additive fabrication techniques.