Showing papers on "Oblique shock published in 1999"

Blunt-Body Wave Drag Reduction Using Focused Energy Deposition

Abstract: A parametric computational study of energy deposition upstream of generic two-dimensional and axisymmetric blunt bodies at Mach numbers of 6.5 and 10 is performed utilizing a full Navier-Stokes computational fluid dynamics code. The energy deposition modifies the upstream shock structure and results in large wave drag reduction and very high power effectiveness. Specifically, drag is reduced to values as low as 30% of baseline drag (no energy deposited into flow) and power effectiveness ratios (ratio of thrust power saved to power deposited into the flow) of up to 33 are obtained. The fluid dynamic and thermodynamic bases of the observed drag reduction are examined

Flow Separation and Side-Loads in Rocket Nozzles

Abstract: Flow separation in nozzles of rocket engines is undesired because it can lead to dangerous lateral forces, which might damage the nozzle The origin of side-loads is not fully clear, although different possible origins were identified in the past Meanwhile, it seems to be clear that in thrust-optimized or parabolic nozzles, a major side-load is due to the transition of separation pattern from free shock separation to restricted shock separation and vice versa After a literature review, the reasons for the transition between the separation patterns are discussed, and the cap shock pattern, which is identified to be the cause of this transition, is closely analyzed It turns out that this pattern can be interpreted as an inverse Mach reflection of the internal shock at the centerline The separation and side-load behavior of thrust-optimized and parabolic nozzles is described in detail In order to be able to predict the pressure ratio pc/pa at which the transition of separation patterns occurs, a model is developed which uses TDK-data as an input With the oblique shock relations and a momentum balance, both the ratio of chamber to ambient pressure and the value of the lateral force can be predicted with fair accuracy

Holographic Interferometric Visualization of the Richtmyer-Meshkov Instability Induced by Cylindrical Shock Waves

Abstract: Results of quantitative holographic interferometric flow visualization of cylindrical interface instability induced by converging cylindrical shock waves are reported. Experiments were conducted in an annular vertical co-axial diaphragmless shock tube, in which cylindrical soap bubbles filled with He, Ne, Air, Ar, Kr, Xe and SF_6 were co-axially placed in its test section. Pressure histories at different radii during the shock wave implosion and reflection from the center were measured. Diagnostic method base on double exposure holographic interferometry was applied for the measurement of turbulent mixing zone at the interface. The observed cylindrical interfaces were found to have a higher growth rate of turbulent mixing zone than that of the plane shock / plane interface.

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.

Numerical Investigation of Supersonic Injection Using a Reynolds-Stress Turbulence Model

Abstract: Thefull,three-dimensionalFavre-averaged Navier -Stokesequations,coupledwiththesecond-orderZhang etal. (Zhang, H., So, R., Gatski, T., and Speziale, C., " A Near-Wall Second-Order Closure for Compressible Turbulent Flows,"Near-WallTurbulentFlows ,editedbyR. So,C.Speziale, andB.Launder,Elsevier,NewYork,1993,pp.209 - 218) Reynolds-stress turbulence and K-≤ models, were used to numerically simulate a 25-deg, Mach 1.8 injection into a Mach3.0 crosse ow.Detailed comparisonswith experimental data wereperformed.Analysis of theReynolds- stress turbulence model simulation results revealed physically consistent and accurate predictions for mean e ow and turbulent quantities, whereas the simulations with the K-≤ model resulted in nonphysical and inconsistent turbulence predictions. Analysis of the three-dimensional e owe eld simulation with the Reynolds-stress turbulence model shows that the shock structure downstream of the oblique barrel shock wasa mirrored image of theleeward side of the oblique barrel shock. Furthermore, the downstream location where vortical motion was initiated in the jet plume was caused by the recompression shock-induced vortices. These vortices were generated through the combined effects of the ine ow air upwash behind the plume and the mirrored oblique barrel shock.

Electron acceleration to ultrarelativistic energies in a collisionless oblique shock wave

Abstract: Electron motion in an oblique shock wave is studied by means of a one-dimensional, relativistic, electromagnetic, particle simulation code with full ion and electron dynamics. It is found that an oblique shock can produce electrons with ultrarelativistic energies; Lorentz factors with γ≳100 have been observed in our simulations. The physical mechanisms for the reflection and acceleration are discussed, and the maximum energy is estimated. If the electron reflection occurs near the end of a large-amplitude pulse, those particles will then be trapped in the pulse and gain a great deal of energy. The theory predicts that the electron energies can become especially high at certain propagation angles. This is verified by the simulations.

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.

Transport and Acceleration of Energetic Charged Particles near an Oblique Shock

Abstract: We have developed a numerical simulation code that treats the transport and acceleration of charged particles crossing an idealized oblique, nonrelativistic shock within the framework of pitch angle transport using a finite-difference method. We consider two applications: (1) to study the steady state acceleration of energetic particles at an oblique shock and (2) to explain observed precursors of Forbush decreases of Galactic cosmic rays before the arrival of an interplanetary shock induced by solar activity. For the former, we find that there is a jump in the particle intensity at the shock, which is stronger for more oblique shocks. Detailed pitch angle distributions are also presented. The simple model of a Forbush decrease explains the key features of observed precursors, an enhanced diurnal anisotropy extending several mean free paths upstream of the shock and a depletion of particles in a narrow loss cone within ~0.1 mean free path from the shock. Such precursors have practical applications for space weather prediction.

The structural response of cylindrical shells to internal shock loading

Abstract: The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with a numerical and experimental study on the structural response of a thin aluminum cylindrical shell to shock loading. Transient finite element calculations were carried out for a range of shock speeds. The results were compared to experimental results obtained with the GALCIT 6-in. shock tube facility. Both the experimental and the numerical results show an increase in amplitude near the critical velocity, as predicted by simple steady-state models for shells of infinite length. However, the finite length of the shell results in some transient phenomena. These phenomena are related to the reflection of structural waves and the development of the deflection profile when the shock wave enters the shell.

Optimization of Two-Dimensional Scramjet Inlets

Abstract: The classical optimization of two-dimension al supersonic inlets for maximum total pressure recovery is extended to two-dimensional scramjet inlets. The result that optimal supersonic inlets have shock waves of equal strength is often applied to scramjets. However the typical flow turning constraint required for scramjets, along with the lack of a terminating normal shock, lead to a more involved optimization problem. Despite this, optimization by the method of Lagrange multipliers indicates that scramjet inlets with maximum total pressure recovery have external shocks with almost equal strength. The optimal total pressure recovery and turning angles for some typical scramjet inlet configurations with up to five shocks are presented.

Shock wave deformation in shock-vortex interactions

Abstract: An initially planar shock wave can undergo significant distortion to its shape along with changes in its strength during the period of its interaction with a compressible vortex. This phenomenon is studied by numerically simulating the shock wave-vortex interaction with a high resolution shock-capturing scheme. Incident shock waves of various Mach numbers are made to interact with a compressible vortex and the dependence of the shock wave distortion on the strength of the incident shock wave is studied in detail. It is known that the type of complex shock structure formed in the later stages of a compressible vortex-shock wave interaction is dependent on the Mach number of the incident shock wave. A simple physical model based on the principle of shock wave reflection is proposed to explain this complex shock structure formation and its dependence on the relative strengths of the interacting vortex and shock wave.

Spurious Numerical Oscillations in Simulation of Supersonic Flows Using Shock-Capturing Schemes

Abstract: The numerical simulation of transitional and turbulent e ows in supersonic boundary layers often involves a physical process of a shock ‐disturbance wave interaction in complex multidimensional e owe elds. For such simulations, it is required that there be a high order of accuracy in capturing the shock waves without spurious numerical disturbances. Evaluation of the numerical oscillations generated behind a stationary bow shock by using high-order shock-capturing schemes in computing multidimensional steady supersonic e ow over a circular cylinderiscarriedout.Thenumerical methodsthatarestudied aretheTotalVariation Diminishing schemeand the Essentially Non-Oscillatory scheme. Although the general aerodynamic properties are appropriately captured by the shock-capturing schemes, it is shown that there are numerical oscillations in the gradients of the aerodynamic propertiesin the steady e owe eld behind the bow shock, such asfor vorticity. Thesespurious numerical oscillations in the e owe eld solution may hinder any attempt at tracking the propagation of physical disturbances behind the shock if unsteady simulations are carried out. They can be signie cant enough to pollute a e owe eld containing small physical disturbances. It is shown that the effects of grid ree nement do not reduce the oscillations but rather decreasetheir wavelength. It is also shown that, by roughly aligning the shock with the grid, the amplitude of these spurious oscillations can be reduced but not eliminated.

Shock structuring due to fabrication joints in targets

Abstract: The use of copper-doped beryllium ablators on National Ignition Facility [J. A. Paisner et al., Laser Focus World 30, 75 (1994)] targets, in place of plastic, can require the bonding together of hemispheres with a joint of differing composition. Indirect drive experiments have been conducted on the Nova laser [J. L. Emmet, W. F. Krupke, and J. B. Trenholme, Sov. J. Quantum Electron. 13, 1 (1983)], and the resulting shock structuring compared with code simulations. It is concluded that one of the available codes, the RAGE code [R. M. Baltrusaitis et al., Phys. Fluids 8, 2471 (1996)] provides useful insight into the effect of joints. This code is then employed to obtain a physical picture of the shock front nonuniformity in terms of a secondary rarefaction and an oblique shock interacting with the main shock that propagates in the absence of the joint. A simple analysis reinforces this picture.

Shock Oscillations in Diffuser Modeled by a Selective Noise Amplification

Abstract: Shock waves in supersonic flow oscillate under certain conditions. These oscillations usually have negative effects, especially for flow past transonic airfoils and in supersonic diffusers. It is therefore of practical importance to understand the origin and the consequences of these oscillations. We model and predict some physical characteristics of self-sustained shock oscillations in transonic diffuser flows. We first give the results of a quasi-one-dimensional stability analysis. The mean flow is calculated with a code solving the averaged Navier-Stokes equations. The present stability approach however is limited to the core region where the viscous effects can be neglected

Entrainment of fine particles from surfaces by impinging shock waves

Abstract: When a shock wave impinges on a surface, it reflects and propagates across the surface at supersonic velocity. The gas is impulsively accelerated by the passing shock wave. The resulting high-speed flow imparts sufficiently strong forces to particles on the surface to overcome strong adhesive forces and entrain the surface-bound particles into the gas. This paper describes an experimental study of the removal of fine particles from a surface by impinging shock waves. The surfaces examined in this study were glass slides on which uniformly sized (8.3 μm diameter), spherical polystyrene particles had been deposited. Shock waves were generated in a small, open-ended shock tube at various heights above and impingement angles to the surface. Particle detachment from the carefully prepared substrates was determined from images of the surfaces recorded before and after shock impingement. A single shock wave effectively cleaned a large surface area. The centerline length of the cleared region was used to characterize the efficacy of shock cleaning. A model based upon the far field solution for a point source surface shock provides a good fit to the clearance length data and yields an estimate to the threshold shock strength for particle removal.

Particle acceleration at oblique shocks and discontinuities of the density profile

Abstract: In the theory of diffusive acceleration at oblique shock fronts the question of the existence of a discontinuity of energetic particle density is contentious. The resolution of this problem is interesting from a theoretical point of view, and potentially for the interpretation of observations of parti- cle densities at heliospheric shocks and of high-resolution radio observations of the rims of supernova remnants. It can be shown analytically that an isotropic particle distribution at a shock front implies continuity of the particle density - whether or not the shock is oblique. However, if the obliquity of the shock induces an anisotropy, a jump is permitted. Both semi-analytic compu- tations and Monte-Carlo simulations are used to show that, for interesting parameter ranges, a jump is indeed produced, with accelerated particles concentrated in a precursor ahead of the shock front.

Characteristic analysis of a complex two-dimensional magnetohydrodynamic bow shock flow with steady compound shocks

Abstract: A simple, compact, and systematic derivation is given of the characteristic properties of the magnetohydrodynamic (MHD) equations with two independent variables (time-dependent MHD in the xt plane and steady MHD in the xy plane), based on the symmetrizable Galilean invariant form of the equations and using a matrix approach. A numerically obtained stationary planar field-aligned MHD bow shock flow with interacting shocks is then analyzed in terms of hyperbolic and elliptic regions, steady xy characteristics, limiting lines, and allowed shock transitions. With the help of this analysis, a wave structure present in the bow shock flow can be interpreted as a double steady compound shock. This interpretation is based on the complete analogy demonstrated in our analysis, between the xy characteristic structure of this novel steady compound shock and the xt characteristic structure of the well-known time-dependent MHD compound shock.

Field-aligned magnetohydrodynamic bow shock flows in the switch-on regime - Parameter study of the flow around a cylinder and results for the axi-symmetrical flow over a sphere

Abstract: A parameter study is undertaken for steady sym- metrical planar field-aligned MHD bow shock flows around a perfectly conducting cylinder. For sets of values of the inflow plasma and AlfvMach number (MA) which allow for switch-on shocks, a numerical solution is obtained which ex- hibits a complex bow shock shape and topology with multiple shock fronts and a dimpled leading front. For parameter val- ues outside the switch-on domain, a classical single-front bow shock flow is obtained. These results show that the and MA parameter regime for which the complex bow shock topology occurs, corresponds closely to the parameter regime for which switch-on shocks are possible. The axi-symmetrical field-aligned bow shock flow over a perfectly conducting sphere is then calculated for one set of values for and MA in the switch-on domain, resulting in a complex bow shock topology similar to the topology of the flow around a cylinder. These complex shock shapes and topologies may be en- countered in low- space plasmas. Fast coronal mass ejections moving away from the sun in the low- inner corona may induce preceding shock fronts with upstream parameters in the switch-on domain. Planetary and cometary bow shocks may have upstream parameters in the switch-on domain when the impinging solar wind occasionally becomes low-. The simulation results may be important for phenomena in the Earth's magnetosheath.

Origin, Injection, and Acceleration of CIR Particles: Theory Report of Working Group 7

Abstract: On the basis of the observational picture established in the report of Mason, von Steiger et al. (1999) the status of theoretical models on origin, injection, and acceleration of particles associated with Corotating Interaction Regions (CIRs) is reviewed. This includes diffusive or first-order Fermi acceleration at oblique shocks, adiabatic deceleration in the solar wind, stochastic acceleration in Alfven waves and oblique propagating magnetosonic waves, and shock surfing as possible injection mechanism to discriminate pickup ions from solar wind ions.

Self-consistent Alfv ´ en-wave transmission and test-particle acceleration at parallel shocks

Abstract: The transmission of Alfv´ en waves at parallel shocks is treated self-consistently, i.e., taking the pressure and energy flux exerted by the waves into account when determining the shock's gas compression ratio. The resulting test-particle ac- celeration and transport parameters at the shock are shown to be functions of five parameters: the Alfv ´ enic Mach number of the shock, the upstream plasma beta, and the cross helicity, magnetic amplitude, and power-spectral index of the upstream waves. In a large region of parameter space, the scattering-center compression ratio is significantly larger than the gas compres- sion ratio. For some conditions, it may get very large values that result in an extremely hard test-particle-energy spectrum of the cosmic-rays accelerated at the shock. This result is qualitatively the same as that obtained by the same authors under the "test- wave" approach, i.e., assuming that the waves have no impact on the shock's dynamics. However, the present analysis gives limits to the application of the previous results, and widens the scope of the previous analysis by removing a mathematical sin- gularity in shocks with squared Mach number approaching the test-wave-theory gas compression ratio.

Molecular dynamics simulation of a piston-driven shock wave in a hard sphere gas

Abstract: Molecular dynamics simulation is used to study the piston driven shock wave at Mach 15, 3, and 10 A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity The piston moves and a shock wave is generated All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method Property profiles are similar to those generated by direct simulation Monte-Carlo method The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task

DSMC Simulation of Shock/Shock Interactions: Emphasis on Type IV Interactions

Abstract: This paper presents the results of a numerical study of shock/shock interactions that include both the Edney type IV and type III interactions, with emphasis on the type IV interactions. Computations are made using the direct simulation Monte Carlo (DSMC) method of Bird for Mach 10 air flow, as produced in the ONERA R5Ch low-density wind tunnel. The simulations include the flow about a shock generator which creates a relatively weak oblique shock that impinges on a much stronger cylinder bow shock. The sensitivity and characteristics of the interactions are examined by varying the horizontal distance separating the shock generator leading edge and cylinder. Results of the simulation for one separation distance are compared with wind tunnel measurements. Comparisons are made for surface heating and pressure and for flow-field values of density and rotational temperatures, as obtained with the Dual-line Coherent Anti-Stokes Scattering (DL-CARS) technique. The comparisons between experiment and calculation yield a consistent description of the shock interaction features and a consistent description of the surface heating and pressure distributions, with the exception of the peak values-the computed values being greater than the measured values.

Unsteady-State Simulation of Model Ram Accelerator in Expansion Tube

Abstract: Steady- and unsteady-state numerical simulations have been carried out to investigate the ram accelerator flowfield that had been studied experimentally using an expansion tube facility at Stanford University. Navier-Stokes equations for chemically reactive flows were used for the modeling with a detailed hydrogen-air combustion mechanism. The governing equations were analyzed using a fully implicit and time-accurate total variation diminishing scheme. As a result, steady-state simulation reveals that the near-wall combustion regions are induced by aerodynamic heating in the separated flow region. This result agrees well with experiments in the case of the 2H 2 + O 2 + 17N 2 mixture but fails to reproduce the centerline combustion in the case of the 2H 2 + O 2 + 12N 2 mixture. To investigate the reason for this disagreement in the flow establishment process, unsteady-state simulations have been carried out, and the results show the detailed process of flow stabilization. The centerline combustion is revealed to be an intermediate process during flow stabilization. It is induced behind a Mach stem formed by the intersection of strong oblique shock waves at an early stage of the flow stabilization process

Oxyhydrogen combustion and detonation driven shock tube

Abstract: The performance of combustion driver ignited by multi-spark plugs distributed along axial direction has been analysed and tested. An improved ignition method with three circumferential equidistributed ignitors at main diaphragm has been presented, by which the produced incident shock waves have higher repeatability, and better steadiness in the pressure, temperature and velocity fields of flow behind the incident shock, and thus meets the requirements of aerodynamic experiment. The attachment of a damping section at the end of the driver can eliminate the high reflection pressure produced by detonation wave, and the backward detonation driver can be employed to generate high enthalpy and high density test flow. The incident shock wave produced by this method is well repeated and with weak attenuation. The reflection wave caused by the contracted section at the main diaphragm will weaken the unfavorable effect of rarefaction wave behind the detonation wave, which indicates that the forward detonation driver can be applied in the practice. For incident shock wave of identical strength, the initial pressure of the forward detonation driver is about 1 order of magnitude lower than that of backward detonation.

Two‐stream instability of electrons in the shock front

Abstract: During their collisionless motion in the shock front electrons are efficiently accelerated by the de Hoffman-Teller cross shock potential. Inside the shock ramp two electron beams are formed: those which are accelerated from upstream to downstream and those which come from the downstream region to match the upstream distribution. This electron distribution is two-stream unstable. We estimate the typical temporal and spatial scales on which the instability develops. We argue that this instability could result in fast relaxation of the electron beams and formation of the observed flattopped distributions.