Showing papers on "Oblique shock published in 2006"

Space and time organization in a shock-induced separated boundary layer

Abstract: The interaction of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.3 is experimentally investigated for a wide range of shock intensities. Characteristic time and length scales of the unsteady reflected shock and inside the downstream interaction region are obtained and compared with already existing results obtained in compression ramp experiments as well as in subsonic detached flows. Dimensionless characteristic frequencies are highlighted to characterize low-frequency shock unsteadiness as well as the different large scales which develop inside the initial part of the interaction. The possibility of describing the spatial development of the large scales inside the interaction zone using a mixing-layer scheme including compressibility effects is tested for a wide range of Mach numbers, shock intensities and geometrical configurations. Moreover, strong evidence of a statistical link between low-frequency shock movements and the downstream interaction is given. Finally, the downstream evolution of the structures shed into the boundary layer is characterized and shows features specific of our configuration.

Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M=2.25

Abstract: The interaction of a spatially developing adiabatic boundary layer flow at M∞=2.25 and Reθ=3725 with an impinging oblique shock wave (β=33.2°) is analyzed by means of direct numerical simulation of the compressible Navier-Stokes equations. Under the selected flow conditions the incoming boundary layer undergoes mild separation due to the adverse pressure gradient. Coherent structures are shed near the average separation point and the flow field exhibits large-scale low-frequency unsteadiness. The formation of the mixing layer is primarily responsible for the amplification of turbulence, which relaxes to an equilibrium state past the interaction. Complete equilibrium is attained in the inner part of the boundary layer, while in the outer region the relaxation process is incomplete. Far from the interaction zone, turbulence exhibits a universal behavior and it shows similarities with the incompressible case. The interaction of the coherent structures with the incident shock produces acoustic waves that prop...

Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation

Abstract: The intent of this study on micro-array flow control is to demonstrate the viability and economy of Response Surface Methodology (RSM) to determine optimal designs of micro-array actuation for controlling the shock wave turbulent boundary layer interactions within supersonic inlets and compare these concepts to conventional bleed performance. The term micro-array refers to micro-actuator arrays which have heights of 25 to 40 percent of the undisturbed supersonic boundary layer thickness. This study covers optimal control of shock wave turbulent boundary layer interactions using standard micro-vane, tapered micro-vane, and standard micro-ramp arrays at a free stream Mach number of 2.0. The effectiveness of the three micro-array devices was tested using a shock pressure rise induced by the 10 shock generator, which was sufficiently strong as to separate the turbulent supersonic boundary layer. The overall design purpose of the micro-arrays was to alter the properties of the supersonic boundary layer by introducing a cascade of counter-rotating micro-vortices in the near wall region. In this manner, the impact of the shock wave boundary layer (SWBL) interaction on the main flow field was minimized without boundary bleed.

Particle acceleration at perpendicular shock waves: Model and observations

Abstract: Received 7 November 2005; revised 17 February 2006; accepted 27 February 2006; published 23 June 2006. [1] On the basis of a recently developed nonlinear guiding center theory for the perpendicular spatial diffusion coefficient k? used to describe the transport of energetic particles, we construct a model for diffusive particle acceleration at highly perpendicular shocks, i.e., shocks whose upstream magnetic field is almost orthogonal to the shock normal. We use k? to investigate energetic particle anisotropy and injection energy at shocks of all obliquities, finding that at 1 AU, for example, parallel and perpendicular shocks can inject protons with equal facility. It is only at highly perpendicular shocks that very high injection energies are necessary. Similar results hold for the termination shock. Furthermore, the inclusion of self-consistent wave excitation at quasiparallel shocks in evaluating the particle acceleration timescale ensures that it is significantly smaller than that for highly perpendicular shocks at low to intermediate energies and comparable at high energies. Thus higher proton energies are achieved at quasiparallel rather than highly perpendicular interplanetary shocks within 1 AU. However, both injection energy and the acceleration timescale at highly perpendicular shocks are sensitive to assumptions about the ratio of the two-dimensional (2-D) correlation length scale to the slab correlation length scale l2D/lk. Model proton spectra and intensity profiles accelerated by a highly perpendicular interplanetary shock are compared to an identical but parallel interplanetary shock, revealing important distinctions. Finally, we present observations of highly perpendicular interplanetary shocks that show that the absence of upstream wave activity does not inhibit particle acceleration at a perpendicular shock. The accelerated particle distributions closely resemble those expected of diffusive shock acceleration, and observed at oblique shocks, an example of which is shown.

Skin Friction and Heat Flux Measurements in Shock Boundary Layer Interaction Flows

Abstract: Modern nonintrusive techniques are used to make skin-friction and heat transfer measurements in two shockwave/turbulent boundary-layer interactions (SWTBLIs). The two-dimensional SWTBLI is generated by impingement of an incident oblique shock wave on a flat-plate boundary layer. The three-dimensional SWTBLI results from the interaction of the swept shock generated by a fin with a flat-plate boundary layer. The measurements are made using the global interferometry skin-friction technique for the skin friction and the quantitative infrared thermography technique for the heat transfer rate. The results show that, for the two- and three-dimensional interactions, there is a clear difference in the behavior of skin friction and heat transfer as the strength of the shock is changed. This observation suggests that the analogy between momentum and heat transfer, which is the basis of many simplified physical models, is not valid in SWTBLIs. These new data supplement the previous measurements that include boundary-layer properties, surface pressure distributions, and patterns of the limiting streamlines. Taken together, these data complete a data set that is suited for computational fluid dynamics validation.

Application of PIV in a Mach 7 double-ramp flow

Abstract: The flow over a two-dimensional double compression ramp configuration is investigated by means of schlieren visualization, quantitative infrared thermography and particle image velocimetry (PIV) in a short-duration facility producing a free-stream flow at Mach 7. The study focuses upon the accuracy assessment of PIV in the hypersonic flow regime including flow facility effects such as repeatability of test conditions. The solid tracer particles are characterized by means of electron microscopy as well as by measuring the dynamic response across a planar oblique shock wave with PIV. The experiments display a strong variation in the light scattering intensity of the seeded flow over the flow field, due to the large flow compressibility. The mean velocity spatial distribution allows to clearly identify the shock pattern and the main features of the flow downstream of the shocks. However, the spatial resolution is insufficient to determine the wall flow properties. Furthermore the velocity data obtained with the PIV technique allow the determination of the spatial distribution of the Mach number under the hypothesis of adiabatic flow. The double ramp configuration with a variable second compression angle exhibits shock–shock interactions of Edney type VI or V for the lowest and highest ramp angle, respectively. A single heat transfer peak is detected with infrared thermography on the second ramp in case of a type VI interaction while for the type V shock interaction a double heat transfer peak is found. Shock wave angles measured with PIV are in good agreement with theory and the overall flow topology is consistent with schlieren visualization. Also in this respect the results are in agreement with compressible flow theory.

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

Abstract: We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach’s experiment for the compressible Euler system, i. e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.

Measurement of reflected-shock bifurcation over a wide range of gas composition and pressure

Abstract: To determine the extent and magnitude of reflected-shock bifurcation in shock-tube chemistry studies at elevated pressures, experiments were performed using a simple laser schlieren technique and a fast- response pressure transducer. The laser schlieren diagnostic provided a quantitative measurement of the normal-shock passage, an event normally obscured in pressure signals by the bifurcated region. A range of gas mixtures covering molecular weights from 14.7 to 44.0 and specific heat ratios from 1.29 to 1.51 was explored. The results were combined with a standard gas dynamic model to determine the time of arrival of the normal shock wave, the size and strength of the bifurcated region, and the characteristic passage times of dominant features. All results could be expressed in empirical correlations as functions of the gas properties and shock speed. The measured size of the bifurcation zone increased with increasing shock velocity and decreasing specific heat ratio, but displayed no pressure dependence for the conditions of this study (P 5 = 11 − 265 atm., T 5 = 780 − 1740 K).

Simulations of Electron Acceleration at Collisionless Shocks: The Effects of Surface Fluctuations

Abstract: Energetic electrons are a common feature of interplanetary shocks and planetary bow shocks, and they are invoked as a key component of models of nonthermal radio emission, such as solar radio bursts. A simulation study is carried out of electron acceleration for high Mach number, quasi-perpendicular shocks, typical of the shocks in the solar wind. Two-dimensional self-consistent hybrid shock simulations provide the electric and magnetic fields in which test particle electrons are followed. A range of different shock types, shock normal angles, and injection energies are studied. When the Mach number is low, or the simulation configuration suppresses fluctuations along the magnetic field direction, the results agree with theory assuming magnetic moment conserving reflection (or fast Fermi acceleration), with electron energy gains of a factor only 2-3. For high Mach numbers, with a realistic simulation configuration, the shock front has a dynamic rippled character. The corresponding electron energization is radically different: energy spectra display (1) considerably higher maximum energies than fast Fermi acceleration; (2) a plateau or shallow sloped region at intermediate energies 2-5 times the injection energy; (3) power-law falloff with increasing energy, for both upstream and downstream particles, with a slope decreasing as the shock normal angle approaches perpendicular; (4) sustained flux levels over a broader region of shock normal angle than for adiabatic reflection. All these features are in good qualitative agreement with observations, and show that dynamic structure in the shock surface at ion scales produces effective scattering and can be responsible for making high Mach number shocks effective sites for electron acceleration.

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

Abstract: A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

Free boundary problems for nonlinear wave systems : Mach stems for interacting shocks

Abstract: We study a family of two-dimensional Riemann problems for compressible flow modeled by the nonlinear wave system. The initial constant states are separated by two jump discontinuities, $x = \pm \ka...

Numerical MHD modeling of propagation of interplanetary shock through the magnetosheath

Abstract: [1] Propagation of an interplanetary (IP) shock through the bow shock and magnetosheath is studied using numerical results of a three-dimensional MHD model of the magnetosheath. According to already published theoretical studies, a fast forward shock passing through the bow shock would generate a train of new discontinuities including a slow expansion wave, a contact discontinuity, and a slow reversed shock. We have found that these particular discontinuities propagate with similar velocities and thus they cannot be distinguished in our calculations, and we observe one discontinuity that combines properties of all of them. We suggest that the same would be true for an analysis of experimental data. We have simulated three different ways of the magnetopause response to the IP shock. A comparison of these runs reveals that the magnetopause reaction defines the mode of reflected waves. Assuming a fast earthward motion of the magnetopause, about 240 km s−1 or more, we obtain that a fast rarefaction wave would propagate from the magnetopause toward the bow shock, while a slower magnetopause motion would result in a fast reversed shock. On the other hand, the speed of the IP shock propagation does not depend on the magnetopause response, and all three model runs confirm a deceleration of the modeled IP shock front in the magnetosheath in course of its motion from the subsolar region to the magnetosheath flanks.

Cosmic Ray Acceleration at Ultrarelativistic Shock Waves: Effects of a ``Realistic'' Magnetic Field Structure

Abstract: First-order Fermi acceleration processes at ultrarelativistic (γ ~ 5-30) shock waves are studied with Monte Carlo simulations. The accelerated particle spectra are derived by integrating the exact particle trajectories in a turbulent magnetic field near the shock. The magnetic field model upstream of the shock assumes finite-amplitude perturbations within a wide wavevector range and with a predefined wave power spectrum, imposed on the mean field component inclined at some angle to the shock normal. The downstream field structure is obtained as the compressed upstream field. We show that the main acceleration process at superluminal shocks is the particle compression at the shock. Formation of energetic spectral tails is possible in a limited energy range only for highly perturbed magnetic fields. Cutoffs in the spectra occur at low energies within the resonance energy range considered. These spectral features result from the anisotropic character of particle transport in the magnetic field downstream of the shock, where field compression produces effectively two-dimensional perturbations. We also present results for parallel shocks. Because of the turbulent field compression at the shock, the acceleration process becomes inefficient for larger turbulence amplitudes, and features observed in oblique shocks are recovered in this case. For small-amplitude perturbations, particle spectra are formed in the wide energy range, and modifications of the acceleration process due to the existence of long-wave perturbations are observed, as reported previously for mildly relativistic shocks. The critical turbulence amplitude required for efficient acceleration at parallel shocks decreases with increasing shock Lorentz factor γ. In both subluminal and superluminal shocks, an increase of γ leads to steeper spectra with lower cutoff energies. The spectra obtained for the "realistic" background conditions assumed in our simulations do not converge to the "universal" spectral index claimed in the literature. Thus, the role of the first-order Fermi acceleration in astrophysical sources hosting relativistic shocks requires serious reanalysis.

A Hypersonic Vehicle Model Developed With Piston Theory

Abstract: For high Mach number flows, M ≥ 4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional inviscid flow, a perpendicular column of fluid stays intact as it passes over a solid surface. Thus, the pressure at the surface can be calculated assuming the surface were a piston moving into a column of fluid. In this work, first-order piston theory is used to calculate the forces, moments, and stability derivatives for longitudinal motion of a hypersonic vehicle. Piston theory predicts a relationship between the local pressure on a surface and the normal component of fluid velocity produced by the surface’s motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow, oblique shock, or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. The unsteady effects, considered in this work, include perturbations in the linear velocities and angular rates, due to rigid body motion. This provides a more accurate model that agrees more closely with models derived using computational fluid dynamics or those derived by solving Euler equations. Additionally, piston theory yields an analytical model for the longitudinal motion of the vehicle, thus allowing design trade studies to be performed while still providing insight into the physics of the problem.

Stability of a Mach configuration

Abstract: When the incident angle constructed by the incident shock and the surface of the wall is greater than a critical value, the regular shock reflection could not occur, and the Mach shock reflection will occur instead [1, 2, 3, 4, 5, 6, 7] In this chapter we are going to study the occurrence of Mach reflection and its structure Mach configuration is a structure of nonlinear waves, including three shocks starting from a point and a contact discontinuity Besides, we will also give a classification on this structure according to the characteristic feature of the flow field, and particularly study the stability of Mach configuration The main references are [2, 8]

Attenuation of shock waves propagating in polyurethane foams

Abstract: Shock wave attenuation in polyurethane foams is investigated experimentally and numerically. This study is a part of research project regarding shock propagation in polyurethane foams with high-porosities $$\phi_{g}$$ = 0.951 ~ 0.977 and low densities of ρc = 27.6 ~55.8 kg/m3. Sixty Millimeter long cylindrical foams with various cell numbers and foam insertion condition were installed in a horizontal shock tube of 50 mm i.d. and 5.4 mm in length. Results of pressure measurements in air/foam combination are compared with CFD simulation solving the one-dimensional Euler equations. In the case of a foam B fixed on shock tube wall, pressures at the shock tube end wall increases relatively slowly comparing to non-fixed foam, free to move and a foam A fixed on shock tube wall. This implies that elastic inertia hardly contributes to pressure build up. Pressures behind a foam C fixed on shock tube wall decrease indicating that shock wave is degenerated into compression wave. Dimensionless impulse and attenuation factor decrease as the initial cell number increases. The momentum loss varies depending on cell structure and cell number.

Shock wave attenuation by grids and orifice plates

Abstract: The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.

Planar shock cylindrical focusing by a perfect-gas lens

Abstract: We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.

Ripples observed on the surface of the Earth's quasi‐perpendicular bow shock

Abstract: [1] Multipoint measurements from Cluster of a particularly slow encounter with the Earth's bow shock are presented. The shock is classified as high Mach number, quasi-perpendicular, and high plasma beta. Coherent oscillations of the plasma density and the magnetic field amplitude are seen in the foot and ramp of the shock with period approximately 15 s; the traversal of the shock layer lasts 2 min. The oscillation amplitude decreases upstream from a maximum value at the location of the shock overshoot so that it is confined within the shock layer. Phase differences in the oscillations as seen on the four Cluster spacecraft indicate that the oscillations are propagating, and cannot be explained by a one-dimensional shock profile fluctuating in position. Four-point timing shows that the oscillations correspond to ripples traveling across the surface of the shock, with wavelength 1000–2000 km and propagation direction roughly parallel to the magnetic field. The presence of these oscillations could have major implications for the analysis of crossings observed at higher relative shock-spacecraft speeds or where the interspacecraft spacing is larger and the shock velocity is changing.

Wind-Tunnel Setup for Investigations of Normal Shock Wave/Boundary Layer Interaction Control

Abstract: The use of wind-tunnel setup for study of normal shock wave/boundary layer interaction control, was investigated. The rectangular working section that was 114 mm wide, and 178 mm high at the straight downstream of the nozzle was used. The incoming airflow was partitioned by a plate of 6 mm thickness to overcome the problem of shock wave instability. The height of the upper and lower passage was maintained at 91 and 122 mm respectively. The incoming boundary layer thickness was 5.7 mm and the Reynolds number based on boundary-layer displacement thickness was approximately 25,000. It was observed that shock can be located above 3-D bump and large ?-shock structure whose front shock leg starts at the onset of control cab be analyzed. Result shows that wind-tunnel setup can be used to test various types of shock control at positions where conventional setups are unable to hold shock system due to shock instability.

Navier-Stokes computations in micro shock tubes

Abstract: Micro shock tube flows were simulated using unsteady 2D Navier–Stokes equations combined with boundary slip velocities and temperature jumps conditions. These simulations were performed using the parallel version of a multi-block finite-volume home code. Different initial low pressures and shock tube diameters allow to have the scaling ratio ReD/4L vary. The numerical results show a strong attenuation of the shock wave strength with a decrease of the hot flow values along the tube. When the scaling ratio decreases the shock waves can transform into compression waves. Comparison to the existing 1D models also shows the limit of these models.

Low‐frequency wave characteristics in the upstream and downstream regime of the terrestrial bow shock

Abstract: [1] Collisionless shocks in space are accompanied by the low-frequency waves of the magnetic field both upstream and downstream of the shock. However, characteristics of these waves in the plasma rest frame are poorly understood, since spatial scale such as wavelength is hardly determined using single or at best two spacecraft observations. Taking advantage of multipoint measurements of the Cluster spacecraft, we present a statistical study to reveal the rest frame properties of the waves in the terrestrial bow shock environment such as frequencies, wave numbers, phase velocities, propagation directions, polarization and transport ratios for the quasi-parallel and the quasi-perpendicular shock regimes and in the upstream region, the outer, the middle, and the inner magnetosheath. We find that the quasi-parallel shock upstream waves (or the foreshock waves) exhibit properties of the fast mode wave excited by the ion beam instability. Upstream of the quasi-perpendicular shock the waves also exhibit similar properties to the foreshock waves, but the wave mode identification needs further investigations. In the magnetosheath the waves exhibit properties which are persistent from the outer to the inner magnetosheath. They can be interpreted as the mirror mode coupled to the plasma inhomogeneity or as the slow mode. We also find an organization in the wave propagation pattern that the upstream waves propagate toward upstream, while the magnetosheath waves propagate toward the flank region and toward the magnetopause. It is concluded that wave properties are different between the upstream and the downstream regions, but they are similar between the quasi-parallel and the quasi-perpendicular shock regimes, suggesting that the upstream waves are not transmitted to the downstream region across the shock and that the downstream waves do not depend on the shock angle (between the upstream magnetic field and the shock normal direction).

Effect of interplanetary shock strengths and orientations on storm sudden commencement rise times

Abstract: We make a statistical survey of interplanetary (IP) shocks and storm sudden commencements (SSCs) observed between 1995 and 2004. We find that 75% of SSCs are associated with shocks, consistent with previous work. We use this survey to investigate the effect of the interplanetary shock strength and orientation on the SSC rise time. We find that the higher the speed of an IP shock, the less time it takes to sweep by the magnetosphere, and thus the shorter the rise time of the corresponding SSC. The orientation of an IP shock also effects the SSC rise time. Generally speaking, a highly oblique shock causes asymmetric compression of the magnetosphere with respect to the noon-midnight meridian, takes more time to sweep by magnetosphere, and thus results in a longer rise time of the SSC.

Aerodynamics of recirculating flow control devices for normal shock/boundary-layer interactions

Abstract: Passive methods of controlling shock/boundary-layer interactions (SBLIs) consist of a porous surface covering a cavity or a plenum located in the region of the SBLI. The present study focuses on the flowfield downstream of a Mach 1.42 SBLI controlled with various passive devices such as a conventional porous plate, a microporous plate, streamwise slots, a conventional mesoflap array, and a hybrid flap array. Qualitative analysis of the flowfield for the various control devices investigated was achieved with spark shadowgraph visualizations and surface oil-flow visualizations. Quantitative analysis was accomplished by measuring surface static pressure distributions and boundary layer velocity profiles. The flowfields downstream of the slot-controlled and hybrid flap array-controlled SBLIs were found to be highly three-dimensional, whereas the flowfields were predominantly two-dimensional for the remainder of the control devices. It was found that only the conventional mesoflap array had an improved total pressure recovery compared to the baseline solid wall.

Focusing of Strong Shocks in an Annular Shock Tube

Abstract: Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation—a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M s = 2.3 − 3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks.

Stability of transonic shocks for the full Euler system in supersonic flow past a wedge

Abstract: We study the stability of transonic shocks in steady supersonic flow past a wedge. It is known that in generic case such a problem admits two possible locations of the shock front, connecting the flow ahead of it and behind it. They can be distinguished as supersonic–supersonic shock and supersonic–subsonic shock (or transonic shock). Both these possible shocks satisfy the Rankine–Hugoniot conditions and the entropy condition. We prove that the transonic shock is conditionally stable under perturbation of the upstream flow or perturbation of wedge boundary. Copyright © 2005 John Wiley & Sons, Ltd.

Numerical Simulation of a Real Shcramjet Flowfield

Abstract: A shock-induced combustion ramjet (shcramjet) geometry is considered wherein the fuel, gaseous hydrogen, is injected in a two-oblique shock external compression inlet via cantilevered ramp injectors and a wall slot. The combustible mixture formed at the exit of the inlet is then ignited through the shock generated by the cowl of the engine. The numerical simulation of the three-dimensional flowfield of a shcramjet flying at M = 11 and at an altitude of 35 km was performed using the WARP code, in which multispecies Favre-averaged Navier-Stokes equations are closed by the k-w turbulence model and the Wilcox dilational dissipation correction, to account for compressibility effects at high turbulence Mach numbers. The hydrogen/air chemical reactions are modeled by Jachimowsky's nine species, 20 reaction model. It has been found that the combustor length resulting from the shock-induced process is of the order of 25-30% of the inlet length. The relatively low value of the fuel specific impulse obtained, 573 s, is mainly due to incomplete mixing achieved in the adopted inlet model. To the authors' knowledge, the paper contains the first ever proof, in the open scientific literature, of the feasibility of this hypersonic propulsion concept in realistic flow situations, by numerical simulation.

Experimental investigation of the electromagnetic effect on a shock layer around a blunt body in a weakly ionized flow

Abstract: A reentry vehicle is exposed to a partially ionized flow during the reentry flight. For such a flight, a strong magnet mounted on the vehicle, which generates the magnetic field around the vehicle, is suggested to affect a surrounding ionized flow and make it possible to control the flow. Such an electromagnetic effect on the flow is investigated experimentally by using a small arc-jet wind tunnel. In the experiment, the translational temperature distribution in the shock layer around a magnetized blunt body in a supersonic, weakly ionized, argon flow is determined by applying an absorption spectroscopic technique. For the absorption spectrum affected by the magnetic field, the temperature determination method was newly developed. The temperature distribution thus determined for the shock layer shows that the applied magnetic field significantly affects the shock layer or, specifically, the shock standoff distance and enhances it.

On the systematics of particle velocity histories in the shock-to-detonation transition regime

Abstract: Analysis of recent high quality, in-material gauge results from two cyclotetramethylene tetranitramine based explosives and one triamino trinitrobenzene based explosive has shown a number of significant correlations. These include the strong monotonic relationship between the local shock strength and the time to peak particle velocity along each particle path, and the simple scaling of velocity histories along the particle path that exists at a common local shock strength from shots with different initial conditions. Even shocks that have radically different evolutions, such as double shocks or those arising from thin pulses, show the same correlations once the catch-up of the second shock or rarefaction has occurred. From the correlations the strongest relationship is demonstrated to occur between the reaction and the local shock strength. Hence reaction, at least to first order, is a function of shock strength and time along the particle path, and is independent of local flow variables behind the shock such as pressure and temperature. Arguments are presented to suggest that shock entropy is the most likely measure of the shock strength which controls the reaction.