Showing papers on "Oblique shock published in 1994"

Detonation structures behind oblique shocks

Abstract: Detonation structures generated by wedge‐induced, oblique shocks in hydrogen–oxygen–nitrogen mixtures were investigated by time‐dependent numerical simulations. The simulations show a multidimensional detonation structure consisting of the following elements: (1) a nonreactive, oblique shock, (2) an induction zone, (3) a set of deflagration waves, and (4) a ‘‘reactive shock,’’ in which the shock front is closely coupled with the energy release. In a wide range of flow and mixture conditions, this structure is stable and very resilient to disturbances in the flow. The entire detonation structure is steady on the wedge when the flow behind the structure is completely supersonic. If a part of the flow behind the structure is subsonic, the entire structure may become detached from the wedge and move upstream continuously.

On the mechanism of unsteady shock oscillation in shock wave/turbulent boundary layer interactions

Abstract: An experimental investigation into the mechanism of shock wave oscillation in compression ramp-generated shock wave/turbulent boundary layer interactions is presented. Particular emphasis is focused upon documenting the respective roles played by both burst-sweep events in the turbulent boundary layer immediately upstream of the interaction and the downstream separated shear layer upon unsteady shock front motion. Unlike the majority of compression ramp experiments which involve bulk separation and large-scale shock motion, consideration is given here to comparatively “weak” interactions in which the streamwise spatial excursion of the shock front is always less than one boundary layer thickness. In this manner any shock motion due to upstream burst-sweep events should be more apparent in relation to that oscillation associated with the separated region. A discrete Hilbert transform-based conditional sampling technique is used to obtain wall pressure measurements conditioned to burst-sweep events. The conditional sampling technique forms the basis by which the instantaneous shock motion is conditioned to the occurrence of upstream bursting. The relationship between the separation bubble and shock motion is also explored in detail. The results of the experiments indicate that the separation bubble represents a first-order effect on shock oscillation. Although it is demonstrated theoretically that the burst-sweep cycle can also give rise to unsteady shock motion of much lower amplitude, the experiments clearly demonstrate that there is no discernible statistical relationship between burst events and spanwise coherent shock front motion.

Simulation of Thick Accretion Disks with Standing Shocks by Smoothed Particle Hydrodynamics

Abstract: We present results of numerical simulation of inviscid thick accretion disks and wind flows around black holes. We use Smoothed Particle Hydrodynamics (SPH) technique for this purpose. Formation of thick disks are found to be preceded by shock waves travelling away from the centrifugal barrier. For a large range of the parameter space, the travelling shock settles at a distance close to the location obtained by a one-and-a-half dimensional model of inviscid accretion disks. Occasionally, it is observed that accretion processes are aided by the formation of oblique shock waves, particularly in the initial transient phase. The post-shock region (where infall velocity suddenly becomes very small) resembles that of the usual model of thick accretion disk discussed in the literature, though they have considerable turbulence. The flow subsequently becomes supersonic before falling into the black hole. In a large number of cases which we simulate, we find the formation of strong winds which are hot and subsonic when originated from the disk surface very close to the black hole but become supersonic within a few tens of the Schwarzschild radius of the blackhole. In the case of accretion of high angular momentum flow, very little amount of matter is accreted directly onto the black hole. Most of the matter is, however, first squeezed to a small volume close to the black hole, and subsequently expands and is expelled as a strong wind. It is quite possible that this expulsion of matter and the formation of cosmic radio jets is aided by the shock heating in the inner parts of the accretion

Experimental investigation of a supersonic swept ramp injector using laser-induced iodine fluorescence

Abstract: Planar measurements of injectant mole fraction and temperature have been conducted in a nonreacting supersonic combustor configured with underexpanded injection in the base of a swept ramp. The temperature measurements were conducted with a Mach 2 test section inlet in streamwise planes perpendicular to the test section wall on which the ramp was mounted. Injection concentration measurements, conducted in cross flow planes with both Mach 2 and Mach 2.9 free stream conditions, dramatically illustrate the domination of the mixing process by streamwise vorticity generated by the ramp. These measurements, conducted using a nonintrusive optical technique (laser-induced iodine fluorescence), provide an accurate and extensive experimental data base for the validation of computation fluid dynamic codes for the calculation of highly three-dimensional supersonic combustor flow fields.

Potential theory for regular and mach reflection of a shock at a wedge

Abstract: If a plane shock hits a wedge, a self-similar pattern of reflected shocks travels outward as the shock moves forward in time. The nature of the pattern is explored for weak incident shocks (strength b) and small wedge angles 2θw through potential theory, a number of different scalings, some study of mixed equations and matching asymptotics for the different scalings. The self-similar equations are of mixed type. A linearization gives a linear mixed flow valid away from a sonic curve. Near the sonic curve a shock solution is constructed in another scaling except near the zone of interaction between the incident shock and the wall where a special scaling is used. The parameter β = c1θ2w(γ + 1)b ranges from 0 to ∞. Here γ is the polytropic constant and C1 is the sound speed behind the incident shock. For β > 2 regular reflection (weak or strong) can occur and the whole pattern is reconstructed to lowest order in shock strength. For β < 1/2 Mach reflection occurs and the flow behind the reflection is subsonic and can be constructed in principle (with an open elliptic problem) and matched. The case β = 0 can be solved. For 1/2 < β < 2 or even larger β the flow behind a Mach reflection may be transonic and further investigation must be made to determine what happens. The basic pattern of reflection is an almost semi-circular shock issuing, for regular reflection, from the reflection point on the wedge and for Mach reflection, matched with a local interaction flow. Assuming their nature, choosing the least entropy generation, the weak regular reflection will occur for β sufficiently large (von Neumann paradox). An accumulation point of vorticity occurs on the wedge above the leading point. © 1994 John Wiley & Sons, Inc.

Nonstationary flows and shock waves

Abstract: 1. Introduction 2. Shock waves on earth and in space 3. Transition fronts 4. One-dimensional flows in a simple shock tube 5. Shock tubes with area change 6. Boundary-layer effects 7. Two-dimensional studies of oblique shock-wave reflection and diffraction 8. Spherical and cylindrical shock-tube analogues and flow simulation 10. Dusty-gas shock tube 11. Real-gas effects on shock-tube flows 12. Implosion waves and applications 13. Shock-tube construction and instrumentation 14. Closing comments Index

A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity

Abstract: This work investigates the two-dimensional flow of a shock wave over a circular light-gas inhomogeneity in a channel with finite width. The pressure gradient from the shock wave interacts with the density gradient at the edge of the inhomogeneity to deposit vorticity around the perimeter, and the structure rolls up into a pair of counter-rotating vortices. The aim of this study is to develop an understanding of the scaling laws for the flow field produced by this interaction at times long after the passage of the shock across the inhomogeneity. Numerical simulations are performed for various initial conditions and the results are used to guide the development of relatively simple algebraic models that characterize the dynamics of the vortex pair, and that allow extrapolation of the numerical results to conditions more nearly of interest in practical situations. The models are not derived directly from the equations of motion but depend on these equations and on intuition guided by the numerical results. Agreement between simulations and models is generally good except for a vortex-spacing model which is less satisfactory. A practical application of this shock-induced vortical flow is rapid and efficient mixing of fuel and oxidizer in a SCRAMJET combustion chamber. One possible injector design uses the interaction of an oblique shock wave with a jet of light fuel to generate vorticity which stirs and mixes the two fluids and lifts the burning jet away from the combustor wall. Marble proposed an analogy between this three-dimensional steady flow and the two-dimensional unsteady problem of the present investigation. Comparison is made between closely corresponding three-dimensional steady and two-dimensional unsteady flows, and a mathematical description of Marble's analogy is proposed.

Ion injection and acceleration at quasi‐perpendicular shocks

Abstract: We present and discuss results of a new model for ion injections and acceleration at quasi-perpendicular collisionless shocks. We use the one-dimensional hybrid simulation (kinetic ions/fluid electrons) and impose an assumption on the ion motion so that diffusion across the magnetic field (normal to the shock front) is possible. These motions are otherwise suppressed by both one- and two-dimensional simulations. We find that, even in strictly perpendicular shocks, when scattering normal to the field is included, a fraction of the incident ions are accelerated to suprathermal energies. When reasonable scattering times are considered, only pickup ions are injected, whereas thermal solar wind ions are not. The acceleration of these ions is very rapid. We have found that a few of the initially low-energy pickup ions can reach many tens to a few hundred times the plasma ramming energy in less than 100 gyroperiods. Furthermore, highly field aligned energetic ions are found to exist upstream of the slightly oblique shock. The most direct applications of this study is toward the interpretation of observations of both solar wind and interstellar pickup ion distributions in the vicinity of interplanetary shocks which are most often quasi-perpendicular. This work also directly addresses a fundamental issue with regard to our current understanding of the anomalous component of cosmic rays.

Probability density function approach for compressible turbulent reacting flows

Abstract: The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.

Shock wave development in the collapse of a cloud of bubbles

Abstract: A numerical simulation of the collapse of a cloud of bubbles has been used to demonstrate the development of an inwardly propagating shock wave which grows rapidly in magnitude. The fully non-linear nonbarotropic homogeneous flow equations are coupled with single bubble dynamics and solved by a stable numerical scheme. The computational results demonstrate the structure of the shock wave as well as its strengthening effect due to the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields. This appears to confirm the speculation of Morch and his co-workers that such shock formation is an important part of cloud collapse.

Errors when shock waves interact due to numerical shock width

Abstract: A simple test problem proposed by Noh, a cold gas with uniform initial particle velocity directed towards a rigid wall, demonstrates a generic problem with numerical shock capturing algorithms at boundaries that Noh called “excess wall heating” The same type of numerical error is shown to occur when shock waves interact. The underlying cause is due to the numerical shock profile. The error can be understood from an analysis of the asymptotic solution of the partial differential equations when an artificial viscosity is added. The position of the front for a numerical shock wave can be defined by matching the total mass in the profile to that of a discontinuous shock. There is then a difference in the total energy of the numerical wave relative to a discontinuous shock. Moreover, the relative energy depends on the strength of the shock. The error when shock waves interact results from the difference in the relative energies between the incoming and outgoing shock waves. A conservative differencing scheme c...

Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection

Abstract: Some phenomena involving intersection of weak shock waves at small angles are considered: the focusing of curved fronts at aretes, the transition between regular and irregular reflection of oblique shock waves on rigid walls and the diffraction patterns arising behind obstacles. The intersection of three shock waves plays a central role in most of these phenomena, giving rise to the von Neumann paradox of oblique shock reflection and to the curious transition between linear and fully nonlinear focusing investigated experimentally by Sturtevant and Kulkarny [J. Fluid Mech. 73, 651 (1976)]. This ‘‘triple‐point paradox’’ is studied in the context of an asymptotic model, and a solution is proposed that involves an unusual kind of singularity.

Experimental, analytical, and computational methods applied to hypersonic compression ramp flows

Abstract: Experimental data on fully laminar and transitional shock-wave/boundary-layer interactions in two-dimensional compression corners are provided and used for the validation of two full Navier-Stokes solvers, as well as for checking the capabilities and limitations of simple analytical prediction methods. Viscous pressure interaction, free interaction, and inviscid oblique shock theory are found to predict well the pressure levels on the flat plate upstream of the interaction, within the separated region, and downstream of the interaction, respectively. The reference temperature theory is found to perform well in attached flow regimes both upstream and downstream of the interaction region and to provide the basis for a universal peak heating correlation law. Full Navier-Stokes computations are necessary, however, to predict the extent of the interaction region and the associated influence on the pressure distribution (control effectiveness) as well as the detailed heat transfer distribution. To achieve this, very fine gridding coupled with the use of strict convergence criteria (based on the evolution of the location of the separation point rather than on standard density residuals) is shown to be necessary. It is finally shown that, although sophisticated turbulence models need to be further developed before the detailed characteristics of fully turbulent shock-wave/boundary-layer interactions may be predicted, transitional interactions (where transition typically occurs in the neighborhood of reattachment) may be adequately handled by algebraic turbulence models "switched on" just downstream of reattachment.

Experimental and computational studies focusing processes of shock waves reflected from parabolic reflectors

Abstract: This paper describes experimental and numerical studies of the focusing process of shock waves reflected from various shapes of a parabolic reflector. The effect of incident shock strength on the focusing process was also investigated. Experiments were carried out in a conventional shock tube and a test gas was air for incident shock Mach numbers ranging from 1.1 to 2.0. In the experiments, the process of shock focusing was visualized by schlieren method. Numerical simulations were conducted for incident shock Mach numbers up to 3.0 by solving the two-dimensional unsteady Euler equations. The numerical results were compared with experiment for various parabolic reflector shapes and for various incident shock Mach numbers. Based on the experimental and computational results, the pattern of shock focusing and shock focusing mechanism are discussed.

Electron dynamics in two‐ and one‐dimensional oblique supercritical collisionless magnetosonic shocks

Abstract: Two- and one-dimensional fully electromagnetic, bounded, particle (for both electrons and ions) codes are used in order to study electron dynamics in collisionless magnetosonic shocks propagating in supercritical regime and quasi-perpendicular direction (90° > θ0 > 45°); θ0 is the angle between the shock normal and the upstream magnetic field. The purpose of the study consists in comparing electrons behavior in one-dimensional (“pseudo-oblique”) nonresistive shocks and in two-dimensional resistive oblique shocks. Resistive effects related to plasma microinstabilities can be self-consistently included in two-dimensional particle codes in contrast with one-dimensional particle codes. Present two-dimensional results reproduce local electron distribution functions (in particular, downstream “flat tops”) in a self-consistent way and in good agreement with observational results. On the other hand, one-dimensional results exhibit either local enlarged Maxwellian distributions with a partial tail, or a flat top distribution according to the particle density n. These results emphasize that (1) the differences observed between one- and two-dimensional codes may be explained in terms of a critical particle density nc used in the one-dimensional code; (2) the evidence of flat tops in both two- and one-dimensional results (provided that n > nc) proves that the macroscopic potential jump at the shock front is mainly responsible for their formation; (3) microscopic effects (herein related to the self-consistent cross-field/field-aligned currents instabilities) may represent a complementary mechanism for filling the flat top distribution; (4) some relaxation of the unstable electron flat top distribution (T∥/T⊥ ≫ 1) is observed when penetrating further into the downstream region, which means that the main filling mechanisms are localized in the ramp of the shock. Moreover, a detailed study of two-dimensional results shows that both resistive and nonresistive configurations can be easily distinguished for θ0 ≈ 90°, but not any more for large deviations of θ0 from 90° for which the self-consistent magnetic field rotates noticeably out of the coplanarity plane at the shock front.

Supersonic flow in the second-throat ejector-diffuser system

Abstract: A computational analysis of the two-dimensional supersonic inviscid flowfield in a second-throat ejector-diffuser (STED) system is presented. A second-order high-resolution scheme for solving the new Lagrangian Euler equations is employed to accurately resolve the complicated shock patterns and associated slip lines and their interactions. A parametric study covering a variety of Xst and Ost is implemented to investigate their effects on the flow structure in STED as well as its performance. Results suggest that the averaged Mach number along the entrance plane of the second throat is a suitable criterion for the justification of the performance of STED. With this criterion, an optimal design insuring the largest pressure recovery can be achieved.

A theoretical review of diffusive shock acceleration

Abstract: We discuss the fundamental ideas of particle acceleration in plasma shocks with emphasis on those features that are required to produce the 'universal' power-law spectrum. We compare shock acceleration with the more familiar second-order or stochastic acceleration and see that they are not too different in many respects. We discuss the features of shock acceleration that make it appealing and some of its problems as well.

On one-dimensional planar and nonplanar shock waves in a relaxing gas

Abstract: The paper examines the evolutionary behavior of shock waves of arbitrary strength propagating through a relaxing gas in a duct with spatially varying cross section. An infinite system of transport equations, governing the strength of a shock wave and the induced discontinuities behind it, are derived in order to study the kinematics of the shock front. The infinite system of transport equations, when subjected to a truncation approximation, provides an efficient system of only finite number of ordinary differential equations describing the shock propagation problem. The analysis, which accounts for the dynamical coupling between the shock fronts and the flow behind them, describes correctly the nonlinear steepening effects of the flow behind the shocks. Effects of relaxation on the evolutionary behavior of shocks are discussed. The first‐order truncation approximation accurately describes the decay behavior of weak shocks; the usual decay laws for weak shocks in a nonrelaxing gas are exactly recovered. The results concerning shocks of arbitrary strength are compared with the characteristic rule. In the limit of vanishing shock strength, the transport equation for the first‐order induced discontinuity leads to an exact description of an acceleration wave. In the strong shock limit, the second‐order truncation criterion leads to a propagation law for imploding shocks which is in agreement (within 5% error) with the Guderley’s exact similarity solution.

Grains in shocks in weakly ionized clouds – II. Magnetic field rotation in oblique shocks

Abstract: A four-fluid treatment of oblique C-type shocks in magnetized dark molecular clouds is presented. The four fluids are those consisting of neutrals, ions, electrons and negatively charged spherical grains of uniform size and composition. The charged particles couple to the neutrals by frictional interaction and their motion is described by the drift approximation. In an oblique shock, a current is set up which has a component parallel to the magnetic field component transverse to the shock velocity; this component of the current induces rotation of the magnetic field around the shock propagation direction. We give steady solutions for oblique C-type shocks for which the propagation speed is only slightly above the coupled Alfven speed of about 2.2 km s −1

Gasdynamic enhancement of nonpremixed combustion

Abstract: To promote efficient performance of very high speed air-breathing propulsion systems, the combustor Mach number must be of the order of six for a flight Mach number of 18. Because of this high gas speed through the combustor, mixing rates of hydrogen fuel with air must be very rapid in order to allow a combustor of reasonable length. It is proposed to enhance the rate of mixing and combustion of hydrogen and air, and thereby reduce combustor length, through the introduction of streamwise vorticity generated by the interaction of a weak oblique shock wave with the density gradient between air and a cylindrical jet of hydrogen. Because of the high Mach number flow in the combustor, the oblique shock traverses the jet at a small angle with respect to the free stream direction, and the principle of slender body theory allows one conceptually to replace the three-dimensional steady flow with a two-dimensional unsteady flow. As a consequence, two-dimensional time-dependent computational studies and an extensive experimental shock tube investigation were employed to assess mixing rates for the steady flow in the combustor. The results indicated that under realistic conditions, adequate mixing could be accomplished within 1 ms, a rate that was technologically interesting. Encouraged by these experiments, a “practical” injector, utilizing shock-enhanced mixing, was designed for a combustor having a free stream Mach number of 6.0. A detailed aerodynamic and mixing investigation was carried out in the Mach 6 High Reynolds Number Tunnel at the NASA-Langley Research Center. The results confirmed both the details and the overall effectiveness of the shock-enhanced mixing concept.

Airfoil pressure measurements during oblique shock-wave/vortex interaction in a Mach 3 stream

Abstract: An experimental investigation of the interaction between streamwise discrete vortices and oblique shocks formed over a two-dimensional wedge surface was conducted in a Mach 3 blowdown wind tunnel. An instrumented two-dimensional wedge was placed downstream of a semiispan wing so that the trailing tip vortex would arbitrarily interact with the shock wave formed over the wedge surface. The experiments were designed to simulate interaction of streamwise vortices from upstream bodies with shock waves formed over aft surfaces as might be encountered in supersonic flight of aircraft and missiles. The influence of vortex strength and vortex-airfoil vertical separation distance on the interaction was examined.

A unified theory of aerodynamic and condensation shock waves in vapor‐droplet flows with or without a carrier gas

Abstract: A unified theory for aerodynamic and condensation shock waves in vapor‐droplet flows in the presence of an inert carrier gas is presented. Same conservation equations apply across discontinuous models for both types of wave. Exact (as well as approximate), explicit analytical jump conditions across such discontinuities are derived subject to several boundary conditions. Collectively they may be called the generalized Rankine–Hugoniot equations for vapor‐droplet mixtures. All the equations derived are general and can be applied in the case of a pure vapor‐droplet flow by letting the mass fraction of the carrier gas go to zero. Much physical insight may be obtained from this integral analysis. It is shown that four types of aerodynamic shock waves (viz., equilibrium partly dispersed, equilibrium fully dispersed, partly dispersed with complete evaporation, and fully dispersed with complete evaporation) may occur. Conditions for each type of these waves to occur are specified and the appropriate jump conditio...

Monte Carlo simulations of particle acceleration at oblique shocks

Abstract: The Fermi shock acceleration mechanism may be responsible for the production of high-energy cosmic rays in a wide variety of environments. Modeling of this phenomenon has largely focused on plane-parallel shocks, and one of the most promising techniques for its study is the Monte Carlo simulation of particle transport in shocked fluid flows. One of the principal problems in shock acceleration theory is the mechanism and efficiency of injection of particles from the thermal gas into the accelerated population. The Monte Carlo technique is ideally suited to addressing the injection problem directly, and previous applications of it to the quasi-parallel Earth bow shock led to very successful modeling of proton and heavy ion spectra, as well as other observed quantities. Recently this technique has been extended to oblique shock geometries, in which the upstream magnetic field makes a significant angle Theta(sub B1) to the shock normal. Spectral resutls from test particle Monte Carlo simulations of cosmic-ray acceleration at oblique, nonrelativistic shocks are presented. The results show that low Mach number shocks have injection efficiencies that are relatively insensitive to (though not independent of) the shock obliquity, but that there is a dramatic drop in efficiency for shocks of Mach number 30 or more as the obliquity increases above 15 deg. Cosmic-ray distributions just upstream of the shock reveal prominent bumps at energies below the thermal peak; these disappear far upstream but might be observable features close to astrophysical shocks.

Experimental Study of Interactions of Shock Wave With Free-Stream Turbulence

Abstract: Phenomena related to turbulence interactions with shock waves have been studied in detail. The present investigation is focused on interactions of a normal shock wave with homogeneous/grid-generated turbulence. When a shock wave formed in a shock-tube is passed through a grid, the induced flow behind the shock has the features of a compressible flow with free-stream turbulence. The decaying turbulence is subjected to an interaction with the reflected shock traveling in the opposite direction. Data were sampled simultaneously from four channels of high frequency response pressure transducers and dual hot-wires probes. A cold-wire was used to provide instantaneous total temperature measurements while a single hot-wire provided instantaneous mass flux measurements. Amplification of velocity and temperature fluctuations and dissipative length scales has been found in all experiments. Velocity fluctuations of large eddies are amplified more than the fluctuations of small eddies. The dissipative length scale, however, of the large eddies is amplified less than the length scale of the small eddies

Physics of Coanda jet detachment at high-pressure ratio

Abstract: Experimental measurements of surface pressure for an underexpanded two-dimensional supersonic Coanda flow with static conditions exterior to the jet flow was obtained for a fixed slot height to a radius ratio of 0.04. The data demonstrate that an oblique shock forms near the jet exit plane which vectors the jet flow from the curved surface at a pressure ratio of 7.6. The jet detachment occurs at a pressure ratio which is a function of the ratio of slot height to cylinder radius. An increase in the pressure ratio to 11.5 before jet detachment has been demonstrated by the translation of the upper wall providing for a converging-diverging geometry. The physics of the Coanda expansion and the jet detachment are qualitatively described using an optical schlieren system. A compressible in viscid model was derived analytically to demonstrate the variation in Mach number and surface pressure as a function of the geometric parameters with increasing pressure ratio.

Numerical Study of Transient Flow Phenomena in Shock Tunnels

Abstract: Computational fluid dynamics (CFD) was used to study some transient flow features that can occur during the startup process of a shoch tunnel. The investigation concentrated on two areas: (1) the flow near the endwall of the driven tube during shock reflection and (2) the transient flow in the nozzle. The driven tube calculations were inviscid and focused on the study of a vortex system that was seen to form at the driven tube's axis of symmetry. The nozzle flow calculations examined viscous and inviscid effects during nozzle startup. The CFD solutions of the nozzle flows were compared with experimental data to demonstrate the effectiveness of the numerical analysis.

Shock wave stabilization apparatus and method

Abstract: An apparatus and method of stabilizing unstable shock waves on the surface of a body induce shock waves to form prematurely at a particular location on a surface of the body and fix that location such that shock waves will form consistently and persistently at that location on the surface of the body. Boundary layer flow separates from the surface of the body at that location and can be prevented from reattaching to the surface. Shock wave oscillations due to interactions with the separated boundary layer flow are prevented, thereby minimizing vibrations induced in the body. The apparatus has a flow accelerating surface and a discontinuity in the accelerating surface. The accelerating surface causes local fluid flow over the surface of the body to accelerate and prematurely and consistently form a shock wave at the point where the discontinuity is located. The discontinuity causes separation of the boundary layer flow from the body surface and fixes the location where the boundary layer flow separation occurs. The method prematurely forms a shock wave at a set location on the surface of the body and fixes both the formation of shock waves to the set location and the separation point where the boundary layer detaches from the surface of the body.

Oblique shocks and the combined Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov instabilities

Abstract: This Letter considers the evolution of perturbations at an interface between two fluids subjected to an oblique shock. The normal component of the shock generates the Richtmyer–Meshkov (RM) instability, and the parallel component generates the Kelvin–Helmholtz (KH) instability. If a constant normal acceleration is also present it induces the Rayleigh–Taylor (RT) instability or, depending on the sign of gA (g=acceleration, A=Atwood number), it acts to stabilize the KH and RM instabilities. Treating the shock as an instantaneous acceleration, analytic formulas are derived for the evolution of the perturbations. This Letter illustrates with an application to inertial‐confinement‐fusion capsules.