Showing papers on "Oblique shock published in 1993"

Equatorial Disk Formation Around Rotating Stars Due to Ram Pressure Confinement by the Stellar Wind

Abstract: The axisymmetric 2D supersonic solution of a rotating, radiation-driven stellar wind presently obtained by a simple approximation predicts the formation of a dense equatorial disk, when the star's rotation rate lies above a threshold value that depends on the ratio of the wind's terminal speed to the escape speed of the star. The disk is formed because the trajectories of the wind leaving the stellar surface at high latitudes carry it down to the equatorial plane; there, the material passes through a standing oblique shock atop the disk; it is therefore the ram pressure of the polar wind that compresses and confines the disk.

Shock/boundary-layer interaction control with vortex generators and passive cavity

Abstract: This paper describes an experimental comparison of two passive approaches for controlling the shock interaction with a turbulent boundary layer: low-profile vortex generators and a passive cavity (porous wall with a shallow cavity underneath). This investigation is the first known direct comparison of the two methods wherein the advantages and disadvantages of both are revealed. The experiments were conducted with a normal shock wave in an axisymmetric wind tunnel. The shock strength (M = 1.56-1.65) was of sufficient magnitude to induce a large separation bubble, thus causing substantial boundary-layer losses. The low-profile vortex generators were found to significantly suppress the shock-induced separation and improve the boundary-layer characteristics downstream of the shock. However, the suppression of the separation bubble decreased the extent of the low total pressure loss region associated with the lambda foot shock system which results in a lower mass-averaged total pressure downstream of the shock. The passive cavity substantially reduced the total pressure loss through the shock system (and thus wave drag) by causing a more isentropic compression over a larger lateral extent. However, the boundary-layer losses downstream of the shock were significantly increased.

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 disks.

Upstream waves, shocklets, short large‐amplitude magnetic structures and the cyclic behavior of oblique quasi‐parallel collisionless shocks

Abstract: The re-formation process of more oblique quasi-parallel shocks is investigated using one-dimensional hybrid simulations. Several types of simulations have been performed. The simulation of a shock with a magnetic field-shock normal angle of 30° shows that a more oblique quasi-parallel shock exhibits reformation cycles with a larger length scale, that is of about 20 ion inertial lengths. This is considerably larger than the distance specularly reflected ions are able to propagate upstream before they are deflected so that their velocity in the shock normal direction is close to zero. These cycles are due to steepening and growth of upstream waves into pulsationlike structures when they are convected into the region of strongly increasing diffuse ion density immediately upstream of the shock. When the steepening wave packet crashes into the shock, the shock ramp dispersively radiates whistler waves into the region between the shock ramp and the approaching wave, while the steepening of the pulsation leads to phase standing whistler waves on the upstream side. Entropy production occurs either at the shock ramp or at the upstream edge of the pulsation when the steepening process has produced a large kink in the magnetic field and is due to nonadiabatic motion of the incident solar wind ions. In order to analyze the wave steepening, upstream waves have been isolated, and their subsequent interaction with a hot, tenuous ion beam representing the diffuse backstreaming ions has been studied. When an upstream wave is convected into or a region with increasing hot beam density, the wave steepens and becomes a pulsationlike wave packet. In order for the wave to grow to a pulsationlike structure the characteristic scale length of the density increase has to be of the same order as the wavelength of the original magnetosonic wave. Similar results are obtained when counterstreaming beam of hot ions is injected into a solar wind which does not initially contain a wave field. In this case the polarization of the pulsations depends on the hot beam temperature. The strong density increase of hot beam ions in these simulations is due to the steady injection of beam ions in a solar wind with an embedded field which is inclined relative to the solar wind direction. In the shock simulation the shock itself is the steady source of the hot backstreaming ions. These simulations suggest that upstream waves, shocklets, and short large-amplitude magnetic structures are all the same entity in different stages of their development and play a crucial role in re-forming oblique quasi-parallel shocks.

Magnetic structure of the low beta, quasi‐perpendicular shock

Abstract: The structure of the low-beta quasi-perpendicular shock is examined in view of ISEE 1 and 2 magnetic field measurements. An analysis of shock overshoots indicates that the strength of the overshoots of low-beta, quasi-perpendicular shocks increases as the ratio of the Mach number to the first critical Mach number increases. Wave analysis indicates that the power of the downstream waves also increases as a function of this ratio of criticality. The thickness of the shock is a factor of 1-2 times greater than a precursor wavelength, countering the conjecture that the shock is the last amplified cycle of the precursor wave.

Hybrid simulations of the effects of interstellar pickup hydrogen on the solar wind termination shock

Abstract: Hybrid (kinetic ions/fluid electrons) plasma simulations are used to study the effects of a population of energetic interstellar pickup hydrogen ions on the solar wind termination shock. The pickup hydrogen is treated as a second ion species in the simulations, and thus the effects of the pick-ups on the shock, as well as the effects of the shock on the pickups, are treated in a fully self-consistent manner. For quasi-perpendicular shocks with 10-20 percent pickup hydrogen the pickup ions manifest themselves in a small foot ahead of the shock ramp caused by pickup ion reflection. For oblique shocks with smaller angles between the field and the shock normal, a large fraction of the pickup ions are reflected and move back upstream where they excite large amplitude magnetosonic waves which steepen into shocklets. These backstreaming pickup ions may provide advance warning of a spacecraft encounter with the termination shock.

The impact of a shock wave on porous compressible foams

Abstract: A phenomenological study of the processes occurring when a shock wave interacts with porous polyester and polyether foams has been undertaken. Plane shock waves generated in a shock tube were reflected off a slab of foam mounted against the back wall of the tube. Tests were conducted with an initial shock wave Mach number of 1.4 and a 70 mm thick slab of foam. The reduction in reflected shock wave strength and substantial increase in the back wall pressure over that for rigid wall reflection, found by other workers, were confirmed. Piezoelectric pressure transducers were used to record the pressure before, alongside and behind the foam specimen. Schlieren photographs of the flow were made and showed some features not previously reported. In particular it is shown that there is a flow of gas across the face of the foam at some point of the process. Previous investigations of this interaction process have assumed that the face of the foam is a contact surface. Short duration photographs of the distortion of the foam were taken, enabling the wave propagation in the foam material itself to be studied. It is established that the front of this compaction wave in the foam material moves at considerably lower velocity (- 90 m/s) than the gas wave as detected by the pressure transducers (- 200 m/s). This result contrasts with the assumption made in previous work that the two-phase medium behaves essentially as a homogeneous substance. A simple physical model based on a zone of compacted material in the foam acting as a high-resistance flow barrier, is proposed to explain the observed phenomena.

Engineering approach to the prediction of shock patterns in bounded high-speed flows

Abstract: A two-dimensional symmetric wedge configuration representative of a single high-speed intake in steady flow was investigated. The analysis presented here is intended as an engineering approach for estimating certain features of the internal shock system. The primary interest here is the prediction of the size and location of the almost-normal shock wave that develops when the leading-edge shocks intersect at angles above a certain critical value that is less than the wedge detachment angle. The almost-normal shock wave is frequently referred to as the 'Mach stem', Parametric studies enabled the sensitivity of the Mach stem height to various flowfield parameters to be examined, thus indicating how accurately these parameters must be measured in a given experiment. Results of these predictions were compared with those of a steady-flow experiment performed at nominal freestream Mach numbers from 2.8 to 5. The predicted stem heights were consistently lower than the mean experimental values, attributable both to experimental uncertainties and to certain simplifying assumptions used in the analysis. Modification of these assumptions to better represent the test environment improved the analytical results.

Two‐dimensional simulations of supercritical quasi‐parallel shocks: Upstream waves, downstream waves, and shock re‐formation

Abstract: Two-dimensional hybrid (particle ions, massless fluid electrons) simulations of quasi-parallel collisionless shocks are carried out in order to investigate the upstream wave properties, the shock re-formation process, and the downstream turbulence. The two-dimensional simulations confirm the results of earlier one-dimensional simulations. When backstreaming diffuse ions are retained re-formation of a shock with an upstream magnetic field - shock normal angle of ΘBno = 30° occurs as a result of upstream low-frequency waves which steepen, become pulsationlike structures and take over as the re-formed shock. The upstream waves are initially aligned with the shock normal; later in the run the waves become more and more aligned with the upstream magnetic field. However, when approaching the shock, the wave vectors are refracted in the region of increasing diffuse ion density into the shock normal direction so that shock re-formation is again coherent along the shock surface. In addition, re-formation on a smaller scale and out of phase along the shock front is due to more or less specularly reflected ions. Re-formation of a ΘBno = 10° shock is due to locally at the shock ramp emerging waves. These are attributed to the so-called interface instability in the region of partial overlap between the incident cold solar wind and part of the hot downstream distribution. These waves emerge in phase along the shock surface and thus re-formation is in this more parallel case also coherent along the shock. At medium Alfven Mach number (MA ∼ 5) shocks, upstream waves which are aligned with the upstream magnetic field are convected into the shock and produce ripples on the shock surface. At higher Mach number (MA ∼ 9) the shock surface becomes less coherent and the local value of the shock normal - magnetic field angle varies greatly. The re-formation length scale is larger than in the lower Mach number case. The turbulence downstream reflects the two mechanisms of shock reformation: in the ΘBno = 30° case the upstream pulsations are mode converted when convected through the shock layer. In the ΘBno = 10° case the downstream turbulence results from the local instability at the shock front.

Motion of the heliospheric termination shock - A gas dynamic model

Abstract: A simple quantitative model is presented for the heliospheric termination shock's anticipated movement in response to upstream solar wind condition variations, under the assumption that the termination shock is initially a strong gasdynamic shock that is at rest relative to the sun, and that there is a discontinuous increase or decrease in the dynamical pressure upstream of the shock. The model suggests that the termination shock is constantly in motion, and that the mean position of the shock lies near the mean equilibrium position which corresponds to the balance between the mean solar wind dynamical pressure and the mean interstellar pressure.

Head-on Collision of Normal Shock Waves with Rigid Porous Materials

Abstract: The head-011 collision of a planar shock wave with a rigid porous material has been investigated experimentally. The study indicated that unlike the reflection from a flexible porous material, where the transmitted compression waves do not converge to a sharp shock wave, in the case of a rigid porous material the transmitted compression waves do converge to a sharp shock wave, which decays as it propagates along the porous material.

Three-dimensional shock-wave/boundary-layer interactions with bleed

Abstract: Computations were performed to investigate the physics of three-dimensi onal, shock-wave/boundary-layer interactions on a flat plate in which fluid in the boundary layer was bled through a circular hole into a plenum to control shock-wave induced flow separation. This study revealed two underlying mechanisms by which bleed holes can control shock-wave/boundary-layer interactions. It also showed how bleed-hole placement relative to where the incident shock wave impinges affects upstream, spanwise, and downstream influence lengths. This study is based on the ensemble-averaged, full compressible Navier-Stokes equations closed by the BaldwinLomax turbulence model. Solutions to these equations were obtained by an implicit, partially split, two-factored method with flux-vector splitting on a chimera overlapping grid.

The role of magnetic loops in particle acceleration at nearly perpendicular shocks

Abstract: The acceleration of superthermal ions is investigated when a planar shock that is on average nearly perpendicular propagates through a plasma in which the magnetic field is the superposition of a constant uniform component plus a random field of transverse hydromagnetic fluctuations. The importance of the broadband nature of the transverse magnetic fluctuations in mediating ion acceleration at nearly perpendicular shocks is pointed out. Specifically, the fluctuations are composed of short-wavelength components which scatter ions in pitch angle and long-wavelength components which are responsible for a spatial meandering of field lines about the mean field. At nearly perpendicular shocks the field line meandering produces a distribution of transient loops along the shock. As an application of this model, the acceleration of a superthermal monoenergetic population of seed protons at a perpendicular shock is investigated by integrating along the exact phase-space orbits.

Mach 10 bow-shock behavior of a forward-facing nose cavity

Abstract: A detailed description of the bow-shock behavior associated with a conical-walled cavity with a flat circular base at M(infinity) = 10 is presented. An experimental test was performed on this configuration, and measurements of shock-oscillation frequency and amplitude, as well as shock shape, were recorded by a number of techniques. A laser-interferometer system was used for the first time during this test to determine bow-shock oscillation frequency in a nonintrusive manner. The primary behavior was a stable, periodically oscillating bow shock. Attention is also given to a violent bow-shock instability.

Observations of an intermediate shock in interplanetary space

Abstract: An interplanetary intermediate shock is identified from the bulk velocity, number density, and temperature of the solar wind protons and the three components of the interplanetary magnetic field observed by Voyager 1 on May 1 (day 122), 1980, when the spacecraft was at a distance of about 9 AU from the Sun. It is shown by a best fit procedure that the measured plasma and magnetic field on both sides of the discontinuity satisfy the Rankine-Hugoniot relations for a magnetohydrodynamic (MHD) intermediate shock. This shock satisfies the following conditions. (1) The normal Alfven-Mach number (MA = Vn*/VA) is greater than unity in the preshock state and less than unity in the postshock state. (2) Both the fast-mode Mach number (Mf = Vn*/Vf) in the preshock state and the slow-mode Mach number (Msl = Vn*/Vsl) in the postshock state are less man unity, but the slow-mode Mach number is greater than unity in the preshock state. (3) The projected components of the magnetic fields in the shock front for the pre- and postshock states have opposite signs. (4) The magnitudes of the magnetic fields decrease from the preshock to the postshock states. In the above expression, VA is the Alfven speed based on the magnetic field component normal to the shock front, Vn* is the component of the bulk velocity normal to the shock front and measured in the shock frame of reference, and Vf and Vsl are the speeds of the fast- and slow-mode magnetosonic waves in the direction of the shock normal, respectively. The discontinuity event in our discussion cannot be a rotational discontinuity because the Walen's relation is not satisfied. The identified intermediate, shock has MA = 1.04, θBn = 37°, and β = 0.56, where θBn is the angle between the preshock magnetic field and the shock normal direction and β is the ratio of thermal to magnetic energy densities. Using these parameters, a numerical solution of the MHD equations for the shock is obtained. The simulated profiles of the bulk velocity, number density, temperature, and magnetic fields of the pre-and postshock states agree with those of the observed values. The same parameters are used to simulate an intermediate shock using a hybrid numerical code in which full ion dynamics is retained while electron inertial force is neglected. The results of this simulation are compared with high-resolution magnetic field data with a time resolution of 1.92-s averages. The shock thickness of about 70 c/ωpi predicted from the hybrid code agrees with the observations. The general behavior of the magnetic field in the shock transition region is also very similar for the simulated and observed results. The macro- and microstructures of the intermediate shock obtained from the MHD and hybrid models resemble the observed structures.

Prediction of fluctuating pressure in attached and separated turbulent boundary-layer flow

Abstract: A methodology is presented that predicts the fluctuating pressure and power spectra for attached zeropressure gradient and separated turbulent boundary-layer flow on smooth and rough surfaces. Attached flow conditions use a prediction technique that employs a transformation of boundary-layer properties from the compressible to the incompressible plane where a comparison can be made to an extensive data base. For a rough wall, it is shown that the rms pressure, which scales with wall shear, can be predicted by augmenting the smooth wall value by the rough/smooth skin-friction ratio. Relative to nonattached flow, represented by two-dimensional compression corner and three-dimensional fin-generated shock/boundary-layer interactions, the rms pressure is shown to scale with approach flow conditions and the oblique shock in viscid pressure rise. For this situation, a new in viscid angle has been defined as = a + /3 sin^U/M) where a is the shock generator angle and /3 is a parameter based on two-dimensional or three-dimensional interactions. Both rms pressure and power spectra have been correlated in terms of undisturbed approach flow boundary-layer parameters and modified inviscid shock strength relations to provide engineering solutions for the design resolution to complex flow problems.

Isolator-combustor interaction in a dual-mode scramjet engine

Abstract: A constant-area diffuser, or 'isolator', is required in both the ramjet and scramjet operating regimes of a dual-mode engine configuration in order to prevent unstarts due to pressure feedback from the combustor. Because the nature of the combustor-isolator interaction is different in the two operational modes, however, attention is presently given to the use of thermal vs kinetic energy coordinates for these interaction processes' visualization. The results of the analysis thus conducted indicate that the isolator requires severe flow separation at combustor entry, and that its entropy-generating characteristics are more severe than an equivalent oblique shock. A constant-area diffuser is only marginally able to contain the equivalent normal shock required for subsonic combustor entry.

The injection and acceleration of particles in oblique shocks - A unified Monte Carlo description

Abstract: Important problems are discussed concerning the effects of shock geometry on the injection of thermal particles and the process of standard Fermi particle acceleration in general. In pursuit of a self-consistent model that simultaneously describes shock structure and particle acceleration in shocks of arbitrary obliquity, a Monte Carlo simulation developed for parallel shocks is generalized to address oblique geometries. Attention is given to initial results concerning the ways in which injection and acceleration efficiency varies with obliquity and Mach number.

Shock Formation in Overexpanded Tip Leakage Flow

Abstract: Shock formation due to overexpansion of supersonic flow at the inlet to the tip clearance gap of a turbomachine has been studied. The flow was modeled of a water table using a sharp-edged rectangular channel. The flow exhibited an oblique hydraulic jump starting on the channel sidewall near the channel entrance. This flow was analyzed using hydraulic theory. The results suggest a model for the formation of the jump. The hydraulic analogy between free surface water flows and compressible gas flows is used to predict the location and strength of oblique shocks in analogous tip leakage flows. Features of the flow development are found to be similar to those of compressible flow in sharp-edged orifices

Vortex distortion during vortex-surface interaction in a Mach 3 stream

Abstract: An experimental study has been conducted in Mach 3 wind tunnel to investigate the behavior of supersonic vortices as they interact with a wedge surface placed in their passage. The experimental setup was arranged so that interactions resulted in a close encounter of the vortex core and the wedge leading edge. Spark shadow photographs of the flowfield along the pressure measurements on the wedge surface were used to study the interaction problem. In their most organized form, distortion of streamwise vortices upon interacting with the wedge was found to result in formation of symmetric detached shock fronts far upstream of the wedge leading edge followed by an apparent slip surface separating a subsonic region from a supersonic zone. Interaction experiments leading to substantial changes in the structure of vortices revealed that the supersonic vortex distortion has strong resemblances to the incompressible 'B-breakdown' reported in the literature. Experimental results also indicate that the interaction strongly depends on the vortex strength and vortex proximity to the wedge leading edge, and the generated flowfield was found to be highly unsteady. Interaction of concentrated streamwise vortices with the oblique shock formed over the wedge surface resulted in formation of a locally three-dimensional shock wave with a limited subsonic region downstream of the shock.

An Experiment on Free Turbulence/Shock Wave Interaction

Abstract: Grid generated turbulence impinging on a standing normal shock wave is probed by LDV. The results show that the weak turbulence coming from the grid suffers no net amplification when traversing the shock, and that it decays more rapidly downstream. LDV accuracy in the vicinity of the shock is discussed. The results are analysed in the framework of available linear theories.

Time-sequenced and spectrally filtered Rayleigh imaging of shock wave and boundary layer structure for inlet characterization

Abstract: Multiple pulsed Rayleigh imaging and filtered Rayleigh scattering are used to generate images of a complex boundary layer structure, shock wave/boundary layer interactions, and crossing shock waves. Time-sequenced Rayleigh images taken with a visible, double-pulsed laser system show the evolution of boundary layer structure of the internal flow in a generic cross-shock inlet. The images taken in the inlet give insight into 3D effects caused by the inlet geometry and may be used for modeling the complex flows.

Adaptive finite volume upwind approach on mixed quadrilateral-triangular meshes

Abstract: An adaptive cell-vertex finite volume upwind approach on unstructured mixed quadrilateral-triangular meshes, where the quadrilaterals are directionally stretched in the flow regions having one-dimensional features, has been developed to solve the unsteady Euler equations. In the present approach, the Runge-Kutta time integration, Roe's Riemann solver, MUSCL differencing with characteristic interpolation variables, a new treatment of the rotated extrapolation boundary condition, and a modified technique of the global/local regeneration for directionally stretched meshes are included. By using different combinations of interpolation variables, limiter functions, and numerical implementations of boundary conditions, a systematic study is made to understand the characteristics of the current approach. In this work, the isolated oblique shock problem, shock reflection at a wall, supersonic flow passing through a channel with a 4% circular arc bump, transonic flows around single- and two-element airfoils, as well as the shock propagation in a channel are investigated. It is concluded that the present solution procedure demonstrates good convergence performance and provides accurate and high-resolution results for the steady and unsteady inviscid flows.

Forbidden line formation in hydromagnetic disk winds. I: Oblique shocks

Abstract: The observed broad, blueshifted, low-excitation metallic forbidden emission lines, [O I] λ6300, [S II] λλ6730, 6716 and [N II] λ6548, associated with young stellar objects (YSOs), are probes of the low-density regions of energetic outflows on scales ranging from 10 to 70 AU from the central engine. We investigate the idea that such lines are generating in oblique hydromagnetic shock waves in recollimating disk winds from YSOs. We solve for the typical postshock physical conditions that arise in such shocks. We find that conditions appropriate for forbidden line emission are produced in oblique shocks with modest fast magnetosonic Mach numbers n 1 between 2 to 4. The highest velocity and density gas in the shocks is concentrated most toward the flow axis

A parametric study of bleed in shock boundary layer interactions

Abstract: A numerical investigation was conducted to study the effect of bleed configuration on oblique-shock wave/turbulent boundary-layer interactions. Bleed is applied through a normal slot across the shock impingement location. The numerical solution to the compressible Navier-Stokes equations is obtained for the turbulent flow throughout the interaction zone and inside the bleed slot for bleed mass flow rates up to 57 percent of the boundary layer mass flow upstream of the interaction. The results indicate that the bleed slot performance improves as the slot width decreases and the length to width ratio increases. This is reflected as an increase in the bleed discharge coefficient and total pressure, and a reduction in the boundary layer momentum and displacement thickness downstream.

Low and high frequency waves generated by gyrophase bunched ions at oblique shocks

Abstract: The interaction of the solar wind with gyrophase bunched ions reflected at an oblique (ΘBn = 45°) shock ( MA=8) is simulated using a 1D hybrid code. These ions are unstable to low frequency hydromagnetic waves as well as whistler waves. At some point in the hydromagnetic wave growth ion trapping occurs which restricts the local distribution in gyrophase to a higher degree than the input distribution. Given the growth rate of the MHD waves, gyrophase mixing is ineffective in isotropising the ions, except at the leading edge of the injected distribution.

Mach reflection of detonation waves

Abstract: The diffraction of a nominally planar gaseous detonation at a wedge was investigated to determine the critical wedge angle for transition from regular to Mach reflection. Experiments were conducted in a square 83-mm cross-section detonation tube using stoichiometric mixtures of hydrogen-oxygen at 0.2 bars. Experimental results for the triple-point trajectory angle produced during Mach reflection were obtained using the smoke foil technique and are compared with analytic calculations made using three-shock theory and the oblique detonation polars. Measurements of the cell size behind the overdriven Mach stem are also reported. Both analytic and experimental results are compared with work from previous investigations to address apparent discrepancies in the existing literature. Introduction The motivation for this study is to resolve discrepancies in previous investigations regarding Mach reflection of a detonation wave. Whereas the diffraction of a shock wave by a wedge in a nonreactive gas has been the topic of considerable investigation, the reactive (detonation) case has received only limited attention in studies by Ong, Gvozdeva and Predvoditeleva, Manzhalei and Subbotin, Gavrilenko et al., Gavrilenko and Prokhorov > and Edwards et al. In each of these investigations, the detonation is given similar treatment as a nonreactive shock and standard inviscid twoand three-shock theories applied to predict the triple-point trajectory and the critical angle for transition from regular to Mach reflection. Although detonations can be simplistically analyzed as shock waves followed by a thin chemical reaction zone, there are notable differences between the dynamics of nonreactive shocks and detonations. Copyright © 1991 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Graduate Student. Department of Aeronautical Engineering. * Associate Professor. Department of Mechanical Engineering.