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In our study series, the first paper found that the negative pressure dissipation of density flux at the vertical transverse face of a shock leads to shock instability. Here, we present a general e...

A novel procedure for the Riemann solver flux calculation is proposed in this paper. With this simple normal velocity reconstruction procedure, all of the commonly used flux solvers (such as Goduno...

A rectangular hypersonic inlet is tested at the low-speed mode (Ma 5), the design mode (Ma 6), and the overspeed mode (Ma 7) to enrich the understanding of hypersonic-inlet unstart. A flow plug is placed at the duct exit to simulate the combustion-induced high pressure and initiate the inlet unstart. High-speed schlieren imaging and time-resolved pressure measurements are used simultaneously to record the unsteady-flow structures and surface pressures of the unstart process. The results indicate that the unstart processes are basically the same for the low-speed mode and the design mode. An unstart phenomenon dominated by the ramp-side flow separation, which exhibits violent fluctuations along the entire duct with a low frequency, is observed at these two operating modes. While operating at the overspeed mode, the strong shear layer, induced by the Mach reflection of the coalesced external oblique shock, divides the internal flow into two parts. The cowl side is filled by fully subsonic flow after the com...

Adaptive high-resolution simulations of gaseous detonation using a hot-jet initiation were conducted in supersonic combustible mixtures with spatially nonuniform species. The two-dimensional Euler equations were used as the governing equations in combination with a detailed hydrogen–oxygen reaction model. Three different groups of mixtures, which represent various degrees of chemical reactivity, were investigated. The results show that, when the mixtures generally have a high degree of chemical reactivity, detonation initiation can eventually be realized successfully by Mach reflection as well as the deflagration-to-detonation transition mechanism, independent of the spatial distribution of the mixtures in the channel. A recurring four-stage sequence of detonation initiation, detonation attenuation, initiation failure, and detonation reinitiation can be identified. When the mixtures generally have an intermediate degree of chemical reactivity, detonation combustion can be fully realized in the channel, wh...

This study explored inviscid supersonic corner flows induced by three-dimensional symmetrical intersecting compression wedges by introducing the spatial dimension reduction theoretical approach to transform the three-dimensional steady shock/shock interaction problem into a two-dimensional pseudosteady problem; this method allows not only wave configurations, which include regular reflection and Mach reflection, to be determined accurately, but also flowfield characteristics, which include density, temperature, pressure, and total pressure recovery coefficient near the regular reflection point (or in the vicinity of the Mach reflection triple point), as well as the location and the strength of the Mach stem. Theoretical results were compared to numerical simulation (performed by solving three-dimensional inviscid Euler equations with an non-oscillatory and non-free-parameters dissipative finite difference scheme) and analyzed thoroughly. The effects of inflow Mach number, sweep angle, and wedge angle on flowfield parameters and wave configurations were also considered. The influence of sweep angle is negligible, but the effects of Mach number and wedge angle are significant.

A viscous numerical simulation was performed to study the forebody shock reflection at the cowl under the condition of inflow Mach number higher than the design value for different forebody/cowl configurations. With the help of shock reflection theory and numerical simulation, it was found that the shock reflection changed from overall regular reflection wave configuration to overall Mach reflection wave configuration as the cowl angle decreased or the ramp angle increased. Mach reflection in this situation would be harmful; it could result in the shock propagating forward to cause a shock detachment at the cowl lip (the so-called local unstart of inlet in this paper). And the local unstart of inlet essentially resulted from the transition of forebody shock reflection from overall regular reflection to overall Mach reflection at the cowl. It was also found through comparison with inviscid analysis that the viscous effect had to be considered in the local unstart of inlet for practical applications. The ob...

Accepted: 2011-04-26, 資料番号: SA1002970000

This paper describes the numerical study of a shock focusing, that is, a planar shock wave impacting a concave surface. Cylindrical and parabolic reflectors are studied for different curvatures, depths and incident Mach numbers. Computations are carried out using a high-order low-dissipation bandwidth-optimized weighted essentially nonoscillatory method and both inviscid and viscous two-dimensional flow models are considered. The obtained results agree well with the experimental observations made by Skews et al. (Skews, B. W., Kleine, H., Barber, T., and Iannuccelli, M., "New Flow Features in a Cavity During Shock Wave Impact," 16th Australian Fluid Mechanics Conference, Univ. of Queensland, Brisbane, Australia, 2007) and Izumi et al. (Izumi, K., Aso, S., and Nishida, M., "Experimental and Computational Studies Focusing Processes of Shock Waves Reflected from Parabolic Reflectors," Shock Waves, Vol. 3, No. 3,1994, pp. 213-222) for the parabolic one. In the case of cylindrical reflectors, shocks interaction and fine structures as Kelvin-Helmholtz instabilities are recovered, and the computed angles of the transition from an inverse Mach reflection to a transitional regular reflection compare favorably with the analytical model of Ben-Dor (Ben-Dor, G., Shock Wave Reflection Phenomena, Springer-Verlag, New York, 1992) for relatively weak incident shock waves (M s ≤ 2). In the case of parabolic reflectors, the three types of focalization process are addressed and their own structure analyzed.

In this paper, spatial temperature profiles are examined in the nonequilibrium relaxation region behind a stationary shock wave in a hypervelocity air Mach 7.42 freestream. The normal shock wave is established through a Mach reflection from an opposing wedge arrangement in an expansion tube facility. Schlieren images confirm that the shock configuration is steady and the location is repeatable. Emission spectroscopy is used to identify dissociated species and to make vibrational temperature measurements using both the nitric oxide and the hydroxyl radical A-X band sequences. Temperature measurements are presented at selected locations behind the normal shock. LIFBASE is used as the simulation spectrum software for OH temperature-fitting; however, the need to access higher vibrational and rotational levels for NO leads to the use of an in-house developed algorithm. For NO, results demonstrate the contribution of higher vibrational and rotational levels to the spectra at the conditions of this study. Very good agreement is achieved between the experimentally measured NO vibrational temperatures and calculations performed using an existing state-resolved, three-dimensional forced-harmonic oscillator thermochemical model. The measured NO vibrational temperatures are significantly higher than the OH temperatures.

Measurements of the near-field pressure in an unheatedMach 0.85 round jet were performed simultaneously with far-field acoustic pressure measurements at Syracuse University’s Skytop Anechoic Chamber facility to directly quantify the strength and frequency content of the propagating portion of the jet’s near-field pressure. The largest contributions were determined to be at the lower wave numbers commonly associated with hydrodynamic pressure fluctuations. This indicates that large low-frequency hydrodynamic fluctuations are obscuring a significant source of acoustic fluctuations in the jet and dictates that care must be taken when using single point measurements of nearfield pressure spectral decay to differentiate between acoustic (propagating) and hydrodynamic (nonpropagating) fluctuations.

In this study, the problem of a planar blast wave in a duct with a sudden expansion is considered. An incident blast wave that contains two shock waves is arranged so that one pair of vortex rings induced by the first shock wave interacts with the second shock wave of the blast wave and with the reflected shock associated with the first shock wave. A high-resolution Euler/Navier-Stokes solver using a fifth-order weighted essentially nonoscillation scheme is employed to investigate the problem. After the Euler/Navier-Stokes solver is validated to be reasonably accurate, the flow fields induced by the shock/vortex interactions are investigated by computational shadowgraph and computational schlieren techniques. It is found that the trajectories formed by major ring-vortex centers may be different case by case, depending on the arrival time sequence of the second shock wave and the reflected shock wave. In particular, a third vortex ring may be developed, causing the trajectory's turn at some critical time in viscous-flow models. Because of viscous dissipation, consequently stronger vortex-ring strength predicted by the inviscid-flow model than that for the viscous-flow model can result in 14-32% lower pressures at the major ring-vortex centers in the inviscid flow compared with the turbulent flow during the time interval investigated for case A, and 20-32% for case B, and 21-38% for case C. Because of the boundary layer development along the duct wall after the sudden expansion, the reflection type of the first shock wave is changed from a regular reflection in the inviscid-flow case to a single Mach reflection that directly affects the arrival time of the reflected shock wave at the sharp corner. Moreover, the mechanism of the vortex ring formation based on the inviscid-flow model is analyzed. It is found that the term due to the dilation effect also plays a more important role in vorticity generation than the baroclinic term.

A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent. Nomenclature g = spacing between wedge and axis of symmetry M = Mach number P = pressure s = Mach stem height U = speed w = wedge length � = leading shock angle with respect to the freestream � = ratio of specific heats � = triple-point slip-line angle � = wedge angle with respect to the freestream � = Mach angle � = density � = triple-point reflected shock angle Subscripts

LL jets have noise generation due to turbulent mixing; suchmixingleadstotheproductionofReynoldsstresses,thesourceterm within the Lighthill acoustic analogy [1]. In addition to thissource,ajetthatpossessescoherent,large-scalestructuresthattravelwith velocities exceeding the local speed of sound will emit Machwave radiation, a highly efficient noise production mechanism. Theamplitudeofjetnoisescaleswiththejetareaandtheexitvelocitytoanangle-dependentpowern.Thereisdisagreement,however,inthevalueofn.Basedondimensionalanalysis,Lighthill[1]foundntobe8. In anextensive examination of jet noise scaling, Viswanathan [2]observed that n 9:8 for the measurement location (30 deg) andambient to total temperature ratio of unity examined in this work.Venkatesh et al. [3] presented an extensive set of subsonic jet noisemeasurements that show the region of maximum noise generationcoincides withthecollapseoftheuniform, irrotationaljetcore.Thistechnical note examines the impact of Mach number on themechanism of jet noise generation, the scaling of jet noise, and theregion of maximum noise generation. It does this throughexamination of the time and frequency domain properties of theshallow angle jet noise from Mach 0.9, and ideally expandedMach 1.3 and 2.0 jets.A recent set of experiments showed that a Mach 1.3 jet possesseslarge amplitude acoustic peaks within the time-domain data andthesepeakscouldbeusedtorelatethegenerationoffarfieldradiatedsound to the evolution of the mixing layer [4–7]. These acousticpeaks are examined in this technical note to characterize the noisegeneration mechanism and source region of the three jets. For allMachnumbersstudied,thelargeamplitudeacousticpeaksoriginatefrom an ellipsoid-shaped region that is centered past the end of thepotentialcoreandthenoisesourceregionnarrowsinthecross-streamwith increasing Mach numbers. Unlike at Mach 0.9 and 1.3, theMach2.0acousticpeakshavetemporalasymmetry,whichisrelatedtothechangeinnoisegenerationmechanismfromturbulencemixingto Mach wave emission.

The origin of the transition of the flow structure between free shock separation and restricted shock separation in a compressed truncated perfect nozzle is studied. A three-dimensional compressible Navier-Stokes solver is used to capture the nonaxisymmetric unsteady flow structure inside the nozzle. The transition is numerically reproduced under the experimental condition where the transition occurs. Until now, the transition has been numerically observed in a thrust optimized nozzle, a parabolic nozzle, and a highly compressed truncated perfect nozzle, where an internal shock generated from the nozzle throat is the characteristic. However, in the compressed truncated perfect nozzle studied here the internal shock is weak and cannot be detected by the well-known shock function. Therefore, a function is used to detect the compression and expansion and it is found that a low-expansion region exists inside the compressed truncated perfect nozzle. The transition is likely to occur when this region is broadened radially at a mixture ratio lower than the design value.

Numerical simulations of imploding shock waves for detonation initiation are reported. We solve the one-dimensional Navier-Stokes equations and two-dimensional Euler equations for chemically reactive flows by the space-time conservation element and solution element method. One-dimensional results in cylindrical coordinates show that a converging shock produced by breaking a diaphragm for an initial pressure ratio of 1:0.2 atm is able to successfully initiate a detonation in an argon-diluted hydrogen/oxygen mixture (0.2H 2 + 0.1O 2 + 0.7Ar) initially at 300 K. The result also shows a two-shock implosion system caused by the interaction between the reflected primary shock and the imploding contact discontinuity. Two-dimensional solutions focus on imploding polygonal shock fronts. In each polygonal section, the imploding shock is analogous to a planar shock wave entering a channel with converging walls leading to complex wave reflections. Similar to that in the one-dimensional results, pressure histories in the focal region show multiple implosions.

The gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme is extended to hypersonic flow simulations and thus shows that the compressible inviscid flow solutions of the simulations are efficiently and accurately obtained from the BGK scheme without the disastrous shock instability phenomenon that occurs in most hypersonic flow simulations involving strong shock waves. For this particular study, the effect of chemistry in hypersonic flows has not been taken into account. Hence, the assumption of calorically perfect gas is imposed in all simulations. The high-order resolution of the scheme is achieved by utilizing monotone upstream-centered schemes for conservation laws-type initial reconstruction. While, an implicit-type time-integration method known as the approximate factorization– alternating direction implicit is adopted for computing both steady and unsteady calculations. The gas-kinetic scheme is tested meticulously in four two-dimensional numerical examples, namely, the blunt-body problem, the double Mach reflection problem, the axisymmetric blunt-body problem, and the flow over a 15-deg ramp. The numerical results of the BGK scheme when compared with the other schemes and experimental data show that this numerical technique is robust, accurate, and stable for hypersonic flow.

The study of the transition from regular to Mach reflection of shock waves has received considerable attention over the past decade, particularly because of the differences found between numerical and experimental data sets. Whereas this has now been satisfactorily shown to be due to wind-tunnel noise, it raises the issue of the effects of unsteady, or dynamic, effects on transition. These are also of interest because they can arise both due to the reflecting surface changing incidence resulting from steady body motion over a surface of variable slope, or due to changes in angle of incidence of the body itself. In this study, a moving-body numerical scheme was used to study the transition between regular and Mach shock wave reflections on a plane surface in steady supersonic flows under different rates of body incidence change. A wedge in a steady supersonic flow was used to generate an oblique shock wave that was reflected off of an ideal boundary

An Nd:glass laser pulse (18 ns, 1.38 J) is focused in a tiny area of about 100-mum diam under ambient conditions to produce micro-shock waves. The laser is focused above a planar surface with a typical standoff distance of about 4 mm, The laser energy is focused inside a supersonic circular jet of carbon dioxide gas produced by a nozzle with internal diameter of 2.9 mm and external diameter of 8 mm, Nominal value of the Mach number of the jet is around 2 with the corresponding pressure ratio of 7.5 (stagnation pressure/static pressure at the exit of the nozzle), The interaction process of the micro-shock wave generated inside the supersonic jet with the plane wall is investigated using double-pulse holographic interferometry. A strong surface vortex field with subsequent generation of a side jet propagating outward along the plane wail is observed. The interaction of the micro-shock wave with the cellular structure of the supersonic jet does not seem to influence the near surface features of the flowfield. The development of the coherent structures near the nozzle exit due to the upstream propagation of pressure waves seems to be affected by the outward propagating micro-shock wave. Mach reflection is observed when the micro-shock wave interacts with the plane wall at a standoff distance of 4 mm, The Mach stem is slightly deflected, indicating strong boundary-layer and viscous effects near the wall. The interaction process is also simulated numerically using an axisymmetric transient laminar Navier-Stokes solver. Qualitative agreement between experimental and numerical results is good.

Shock-ree ection hysteresis and plume structure in a low-density, axisymmetric highly underexpanded air jet is examined using a Navier ‐Stokes e ow solver. This type of jet is found in a number of applications, e.g., rocket exhausts and fuel injectors. The plume structure is complex, involving the interaction of several e ow features, making this a demanding problem. Two types of shock ree ection appear to occur in the plume, regular and Mach, depending on the jet pressure ratio. The existence of a dual solution domain where either type may occur has been predicted, in agreement with experiment where the same phenomenon has been observed for a nitrogen jet. There is a hysteresis in the shock-ree ection type; the ree ection type observed in the dual-solution domain depends on the time history of the plume development. A quasi-steady approach is employed to calculate the entire hysteresis loop. An implicit, multiblock structured, e nite volume e ow solver is used. The results of the computational study are used to examine the structure of the plume and are compared with experimental data where possible. Some e ow features not initially recognized from experiment have been identie ed, notably curvature of the Mach disk, recirculation behind the Mach disk, and the regular ree ection having Mach-ree ection characteristics.

Different aspects of the transition between regular and Mach reflections of strong shock waves in steady flows are numerically studied. Two approaches-kinetic (the direct simulation Monte Carlo method) and continuum (Euler equations)-are used to investigate the hysteresis phenomenon in the flow about two symmetrical wedges in two- and three-dimensional statements. The dependence of the final shock wave configuration on initial conditions, the transition from regular to Mach reflection by means of flow perturbations, and three-dimensional effects are examined. The three-dimensionality of the flow is shown to increase the angles of transition from regular to Mach reflection and back and to decrease the Mach stem height

The Mach reflection wave configurations and the flowfields associated with two-dimensional supersonic free jets of overexpanded nozzles are analysed. Based on the two- and the three-shock theories along with the classical gasdynamics theory, an analytical model for calculating the height of Mach stem and the cell size of the jet are proposed

To better understand the shock wave reflection phenomenon in steady flows in general, and the transition between regular reflection and Mach reflection in particular, a two-dimensional flowfleld model and simulation over a wedge in supersonic flows was investigated. The numerical simulation enabled one to determine the height of the Mach stem in a Mach reflection wave configuration. The determination of the height was pointed out as one of the yet unsolved problems in steady shock wave reflections. The numerical results were compared both with steady flow experiments performed at nominal freestream flow Mach numbers ranging from 2.8 to 5 and with analytical results. Based on the presented numerical investigation, a new geometric parameter that controls the transition between regular reflection and Mach reflection wave configurations was extracted for the flow Mach number range 2.8-7.

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.

Introduction TWO shock-wave-reection conŽ gurations, regular re ection (RR) andMach re ection (MR), are possible in steady  ows.1 The RR and the MR consist of two and three shock waves, respectively.Two extreme angles of incidence are associatedwith the oblique re ection of a shock wave. They are the von Neumann A and the detachment AD angles (AD >AN ). For a given  ow Mach number, A is the smallest angle of incidence for which an MR is theoretically possible, and AD is the largest angle of incidence for which an RR is theoretically possible. Consequently, an MR is impossible for A AD . For incident angles in the range A ·A ·A both RR andMR are theoretically possible. Consequently, the RR$MR transition could take place at any angle of incidence A inside that range. The angle of incidence A is determined by the  ow Mach number M and wedge angle μw . Therefore, it is convenient to represent the detachment and von Neumann criteria in the (M; μw ) plane, as is shown in Fig. 1, where μ N w and μ D w , the wedge angles that correspond to the mentioned criteria, are shown for a perfect gas with a speciŽ c heats ratio of ° D 1:4. The curves μ N w .M/ and μ D w .M / divide the plane into three domains: a domain in which only RR is theoreticallypossible, a domain in which only MR is theoretically possible, and a domain, known as the dual-solutiondomain, in which both RR and MR are theoreticallypossible.Note that the curve correspondingto μ N w reaches a maximum value of μ N w;max D 20:92 deg at M D 4:46. At large values of M , the curves corresponding to both μ N w and μ D w approachasymptoticvaluesequal to 17.96and 32.02deg, respectively.

Fluctuating surface pressure measurements have been made near separation in a Mach 5, swept shock/turbulent boundary-layer interaction induced by a sharp fin at angles of attack of 16 and 18 deg. Pressure signals in the initial compression region indicate a «shuddering» compression system, in contrast to a translating separation shock reported in previous studies of sharp fin interactions at Mach 3. The results suggest that the frequency range of the shuddering may scale on the large-eddy frequency of the incoming boundary layer

Two simultaneous numerical investigations, using different codes, were conducted. The numerical method, in the first study, was the LCPFCT algorithm, which is a one-dimensional flux corrected transport algorithm, for solving generalized continuity equations, with fourth-order phase accuracy and minimum residual diffusion. A computer code based on a W-modified Godunov's scheme was developped and used in the second study. To complement these numerical studies, an experimental study was also conducted

The hysteresis phenomenon in the regular-Mach reflection transition in steady flow is reconsidered using modified and simplified DSMC methods

The stability of regular reflection and mach reflection in the dual solution was investigated experimentally. A pressure-measurement-based method was applied.

References Milton, B. E., "The Focusing of Shock Waves in Two-Dimensional and Axi-Symmetric Ducts," Proceedings of the International Workshop on Shock Wave Focusing, edited by K. Takayama, Inst. of Fluid Science, Tohoku Univ., Sendai, Japan, 1989, pp. 155-191. Milton, B. E., "Mach Reflection Using Ray-Shock Theory," AIAA Journal, Vol. 13, No. 11, 1975, pp. 1531-1533. Leer, B. V., "Flux-Vector Splitting for the Euler Equations," Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in Physics, Vol. 170, SpringerVerlag, 1982, pp. 507-512.

The structure of the contact discontinuity at the triple point of a pseudosteady Mach reflection was reconsidered, as it is known that in some cases the classical «three shock theory» fails to accurately predict the angles between the four discontinuities of the triple point. Based on experimental records, the slipstream was replaced by an angular mixing zone

Oblique shock-wave reflections in nitrogen for perfect and imperfect gases were investigated interferometrically in a 10x 18-cm shock tube. Comparisons are made with numerical experiments conducted by two different groups on regular and single-Mach reflections. Even though the analyses are for inviscid flows, the sidewall boundary-layer effects in the experiments are negligible, and the features of the calculated and actual inviscid flows are compared readily. It is found that the available numerical techniques will have to be modified or new approaches developed before acceptable agreement can be obtained between actual and numerical experiments. The very accurate interferometric data will provide a basis for comparison with future numerical methods, which also should include the two remaining cases of complexand double-Mach reflections as a test of their accuracy and applicability.

This paper presents an experimental study and a numerical simulation of the impingement of an oblique shock wave on a cylinder. The investigation was undertaken to attain two goals. The first goal was to experimentally investigate and document the complex three-dimensional shock wave and boundary-layer interaction occurring in practical problems, such as the shock-wave impingement from the Shuttle nose on an external fuel tank, and store interference on a supersonic tactical aircraft. The second goal was to carry out a comparison of experimental measurements and numerical computations of such complex flows. The experimental results revealed a complex flowfield with two separation zones, regions of cross flow, reflected shocks, and expansion fans. The numerical predictions agreed surprisingly well with the measured results, both on the surface and in the flowfield. However, some important flow details, such as the size and extent of the separation, and the reflected shock-wave system, were not predicted.

The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 x 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.

The Mach reflection associated with the passage of a shock wave over a wedge is treated in the limit of an ideal gas and a strong shock. In this limit, flow properties are functions only of wedge angle theta and the ratio of specific heats gamma. Numerical results are presented for gamma = 9/7, 7/5, and 5/3. Wedge angles are noted at which the transition from regular to double-Mach, to complex-Mach, and to simple-Mach reflection occurs. Characteristic velocities in the recirculation region associated with Mach reflection are estimated. Local surface pressure maxima, at the upstream and downstream edge of the recirculation region, are also estimated. The scale of the recirculation region increases with decrease in gamma, in accord with experimental observations. The wedge solution is used on a piecewise basis to estimate height-of-burst (HOB) flow fields. Normalized results are presented for HOB triple-point trajectory and surface pressure variation with range. The present results provide a convenient characterization of Mach reflection flow fields associated with both wedge and HOB flows. Validation of the HOB solution, however, is needed.

The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.

The unsteady, inviscid flowfield that results when a supersonic vehicle strikes a planar oblique shock wave, though difficult to simulate experimentally, is quite easy to model and compute numerically. The complicated flowfield, which contains multiple shock wave interactions, is determined using a second-order, shock-capturing, finite-difference approach which solves the time-dependent Euler equations under a self-similar transformation. A series of numerical results for a simple two-dimensional wedge is presented which describes the entire disturbed region, including the wave structure, and shows good agreement with the available two- and three-dimensional experimental data.

A numerical study was performed of the transition from regular to Mach reflection of oblique twodimensional shock waves in the region of Mach number and deflection angle where both types of reflection are theoretically possible. The calculations have been carried out at the molecular level using the direct-simulation Monte Carlo method. The study confirms that this approach can provide a practical alternative to finitedifference and finite-element methods for the computation of continuum flows, especially when a dedicated minicomputer is used instead of a large machine in a general computing center. However, there are difficulties in the resolution of flow features that have characteristic dimensions that are small in comparison with those of the overall flow field, and, in the present study, these precluded definitive conclusions about the type of reflection in the dual-solution region.

incident shock wave in shock tube kink in CMR reflected wave R first and second Mach stems in DMR self-similar Mach number (M) , = (u + v)/a Mach reflection (SMR, CMR, DMR, TDMR) incident shock wave (/) Mach number static pressure reflection point; point where RR =wave angle X,x' = first and second triple-point trajectory angles

A computational technique for two-dimensional unsteady Euler equations, based on a A-formulation and explicit shock fitting, is presented. Any number of shocks, of any shape and type, and their interactions can be treated by this technique, which does not require complicated logic and does not perform redundant calculations. The code is fast and the results are very accurate. Examples (transonic airfoils, shocks in ducts, intake flows, multiple Mach reflections) are presented and discussed.

Waves resulting from the expansion process are an important source of nonhomogeneit y in the supersonic flow downstream of nozzle arrays. Flows from radial nozzles are analyzed by a small-perturbation procedure that yields the first solutions for the near field in the two-dimensional case and for the entire field in three dimensions. Good agreement is found with method-of-characteristics calculations and with earlier interferometric measurements of integrated density disturbance. The complete solutions bring out the dependence of flow quality on nozzle dimension, Mach number, expansion angle, and ratio of specific heats. Application to laser cavity flow is discussed.