Showing papers on "Oblique shock published in 2007"

Magnetic field amplification by shocks in turbulent fluids

Abstract: We consider the effect of preexisting, large-scale, broadband turbulent density fluctuations on propagating hydromagnetic shock waves. We present results from several numerical simulations that solve the two-dimensional magnetohydrodynamic equations. In our simulations, a plasma containing large-scale, low-amplitude density and magnetic field turbulence is forced to flow into a rigid wall, forming a shock wave. We find that the density fluctuations not only distort the shape of the shock front and lead to a turbulent postshock fluid, but they also produce a number of important changes in the postshock magnetic field. The average downstream magnetic field is increased significantly, and large fluctuations in the magnetic vector occur, with the maximum field strength reaching levels such that magnetic stresses are important in the postshock region. The downstream field enhancement can be understood in terms of the stretching and forcing together of the magnetic field entrained within the turbulent fluid of the postshock flow. We suggest that these effects of the density fluctuations on the magnetic field are observed in astrophysical shock waves such as supernova blast waves and the heliospheric termination shock.

Bifurcations in shock-wave/laminar-boundary-layer interaction : global instability approach

Abstract: The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer. Various direct numerical simulations were carried out of a shock-wave/laminar-boundary-layer interaction (SWBLI). Three-dimensional unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.

Formation of hot flow anomalies and solitary shocks

Abstract: [1] Interaction of a tangential discontinuity (TD) with the bow shock is investigated by using electromagnetic, global hybrid simulations in which ions are treated kinetically via particle-in-cell methods and electrons form a massless fluid. On the basis of previous studies, it was expected that the interaction would result in the formation of a hot flow anomaly (HFA) propagating along the curved bow shock surface. The results are unexpected in two major ways. First, the hot flow anomaly is only formed during the interaction of the TD with the quasi-parallel side of the bow shock. The lack of a HFA on the perpendicular side is due to the inability of a large fraction of ions to escape into the solar wind, as is required for an HFA to form. Second, the interaction of the TD with the quasi-perpendicular portion of the bow shock results in a previously unknown, shock structure which we name the “solitary shock.” The solitary shock consists of a finite width (a few ion inertial length), fast magnetosonic shock-like structure followed by a relatively less compressed, more turbulent plasma with complex and spatially varying properties in the downstream region. We have determined that the formation of the solitary shock after the passage of the TD is due to the new direction of the interplanetary magnetic field. Further, this is not a transitory phenomena and when the interplanetary magnetic field cone angle is large (∼>50°) a significant portion of the bow shock surface is affected. Solitary shocks form in the regions where the motional electric field in the magnetosheath points away from the shock. We demonstrate that solitary shocks differ from regular quasi-perpendicular shocks due to differences in ion dissipation processes. We also present the results of a detailed survey of the effects of simulation parameters such as cell size, resistivity, system size, and 2.5-dimensional versus three-dimensional domains on the solitary shock solutions.

A Flexible 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. Prandtl-Meyer flow and oblique shock theory are utilized to provide flow properties over the surfaces of the vehicle. These flow properties are used to determine the steady forces and moments and are also included in the unsteady flow calculations. Thus, this work utilizes a combination of Prandtl-Meyer flow, oblique shock, and piston theory to calculate forces and moments. The unsteady effects include perturbations in the linear velocities and angular rates, due to rigid body motion. A flexible vehicle model is developed to take into account the aeroelastic behavior of the vehicle. The vehicle forebody and aftbody are modelled as cantilever beams fixed at the center-of-gravity. Piston theory is used to account for the changes in the forces and moments due to the flexing of the vehicle. 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.

Numerical investigation of supersonic nozzle flow separation

Abstract: Separation of supersonic flow in a planar convergent–divergent nozzle with moderate expansion ratio is investigated by solving the Reynolds-averaged Navier–Stokes equations with a two-equation k-!turbulence model. The focus of the study is on the structure of the fluid and wave phenomena associated with the flow separation. Computations are conducted for an exit-to-throat area ratio of 1.5 and for a range of nozzle pressure ratios. The results are compared with available experimental data in a nozzle of the same geometry. The flow separates by the action of a lambda shock, followed by a succession of expansion and compression waves. For 1:5 < NPR < 2:4, the computation reveals the possibility of asymmetric flow structure. The computationally obtained asymmetric flow structuresareconsistentwithpreviousexperimental flowvisualizationsstudies.Inaddition,other flowfeaturessuch asshocklocationandwallpressuredistributionsarealsoingoodagreementwiththeexperimentaldata.Thepresent study provides new information that confirms earlier conjectures on the flow–wave structure relevant to the instability of the separated flow in convergent–divergent nozzles of moderate expansion ratio.

Relativistic Collisionless Shocks in Unmagnetized Electron-Positron Plasmas

Abstract: We show that collisionless shock waves can be driven in unmagnetized electron-positron plasmas by performing a two-dimensional particle-in-cell simulation. At the shock transition region, strong magnetic fields are generated by a Weibel-like instability. The generated magnetic fields are strong enough to deflect the incoming particles from upstream of the shock at a large angle and provide an effective dissipation mechanism for the shock. The structure of the collisionless shock propagates at an almost constant speed. There is no linear wave corresponding to the shock wave, and therefore this can be regarded as a kind of "instability-driven" shock wave. The generated magnetic fields rapidly decay in the downstream region. It is also observed that a fraction of the thermalized particles in the downstream region return upstream through the shock transition region. These particles interact with the upstream incoming particles and cause the generation of charge-separated current filaments in the upstream of the shock, as well as the electrostatic beam instability. As a result, electric and magnetic fields are generated even upstream of the shock transition region. No efficient acceleration processes of particles were observed in our simulation.

Weak, strong and detached oblique shocks in gravity driven granular free-surface flows

Abstract: Hazardous natural flows such as snow-slab avalanches, debris flows, pyroclastic flows and lahars are part of a much wider class of dense gravity-driven granular free-surface flows that frequently occur in industrial processes as well as in foodstuffs in our kitchens! This paper investigates the formation of oblique granular shocks, when the oncoming flow is deflected by a wall or obstacle in such a way as to cause a rapid change in the flow height and velocity. The theory for non-accelerative slopes is qualitatively similar to that of gasdynamics. For a given deflection angle there are three possibilities: a weak shock may form close to the wall; a strong shock may extend across the chute; or the shock may detach from the tip. Weak shocks have been observed in both dense granular free-surface flows and granular gases. This paper shows how strong shocks can be triggered in chute experiments by careful control of the downstream boundary conditions. The resulting downstream flow height is much thicker than that of weak shocks and there is a marked decrease in the downstream velocity. Strong shocks therefore dissipate much more energy than weak shocks. An exact solution for the angle at which the flow detaches from the wedge is derived and this is shown to be in excellent agreement with experiment. It therefore provides a very useful criterion for determining whether the flow will detach. In experimental, industrial and geophysical flows the avalanche is usually accelerated, or decelerated, by the net effect of the gravitational acceleration and basal sliding friction as the slope inclination angle changes. The presence of these source terms necessarily leads to gradual changes in the flow height and velocity away from the shocks, and this in turn modifies the local Froude number of the flow. A shock-capturing non-oscillating central method is used to compute numerical solutions to the full problem. This shows that the experiments can be matched very closely when the source terms are included and explains the deviations away from the classical oblique-shock theory. We show that weak shocks bend towards the wedge on accelerative slopes and away from it on decelerative slopes. In both cases the presence of the source terms leads to a gradual increase in the downstream flow thickness along the wedge, which suggests that defensive dams should increase in height further down the slope, contrary to current design criteria but in accordance with field observations of snow-avalanche deposits from a defensive dam in Northwestern Iceland. Movies are available with the online version of the paper.

Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations

Abstract: New behavior of strictly perpendicular shocks in supercritical regime is analyzed with the help of both two-dimensional (2-D) hybrid and full particle electromagnetic simulations. Surprisingly, in both simulation cases, the shock front region appears to be dominated by emission of coherent large amplitude whistler waves for some plasma conditions and shock regimes. These whistler waves are oblique with respect to the shock normal as well as to the upstream magnetic field and are phase-standing in the shock rest frame. A parametric study shows that these whistler waves are emitted in 2-D perpendicular shocks and, simultaneously, the self-reformation of the shock front associated with reflected ions disappears; the 2-D shock front is almost quasi-stationary. In contrast, both corresponding one-dimensional (1-D) hybrid and full particle simulations performed in similar plasma and Mach regime conditions show that the self-reformation takes place for 1-D perpendicular shock. These results indicate that the emission of these 2-D whistler waves can inhibit the self-reformation in 2-D shocks. Possible generating mechanisms of these waves emissions and comparison with previous works are discussed.

Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections

Abstract: We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance.

Flow features resulting from shock wave impact on a cylindrical cavity

Abstract: The complex flow features that arise from the impact of a shock wave on a concave cavity are determined by means of high-speed video photography. Besides additional information on features that have previously been encountered in specific studies, such as those relating to shock wave reflection from a cylindrical wall and those associated with shock wave focusing, a number of new features become apparent when the interaction is studied over longer times using time-resolved imaging. The most notable of these new features occurs when two strong shear layers meet that have been generated earlier in the motion. Two jets can be formed, one facing forward and the other backward, with the first one folding back on itself. The shear layers themselves develop a Kelvin–Helmholtz instability which can be triggered by interaction with weak shear layers developed earlier in the motion. Movies are available with the online version of the paper.

Shock front instability associated with reflected ions at the perpendicular shock

Abstract: Two-dimensional hybrid simulations of perpendicular, supercritical collisionless shocks are carried out in a geometry with the magnetic field perpendicular to the simulation plane so that parallel propagating fluctuations, such as Alfven ion cyclotron waves, are suppressed. In terms of average profile and large downstream ion temperature anisotropy, the results resemble those from earlier one-dimensional hybrid simulations, and differ markedly from the results of two-dimensional simulations in which field-parallel propagating fluctuations are included. In addition, we find an instability at the shock front, in which a pattern of magnetic field and density enhancements propagates along the shock surface in the direction of gyration and at the average speed of the ions reflected at the shock. The instability mechanism depends on a spatio-temporal modulation of the fraction of reflected ions over the shock surface. The instability has a threshold that depends on the Mach number and the upstream ion plasma beta, being stabilized by an increased beta and decreased Mach number. In a realistic three-dimensional planar shock, this instability will be only one of several mechanisms contributing to shock front nonstationarity. However, at a three-dimensional curved shock, there is a region where the instability mechanism described may dominate.

Micro-ramp control for oblique shock wave / boundary layer interactions

Abstract: Supersonic engine intakes operating supercritically feature shock wave / boundary layer interactions (SBLIs), which are conventionally controlled using boundary layer bleed. The momentum loss of bleed flow causes high drag, compromising intake performance. Micro-ramp sub-boundary layer vortex generators (SBVGs) have been proposed as an alternative form of flow control for oblique SBLIs in order to reduce the bleed requirement. Experiments have been conducted at Mach 2.5 to characterise the flow details on such devices and investigate their ability to control the interaction between an oblique shock wave and the naturally grown turbulent boundary layer on the tunnel floor. Micro-ramps of four sizes with heights ranging from 25% to 75% of the uncontrolled boundary layer thickness were tested. The flow over all sizes of microramp was found to be similar, featuring streamwise counter-rotating vortices which entrain high momentum fluid, locally reducing the boundary layer displacement thickness. When installed ahead of the shock interaction it was found that the positioning of the micro-ramps is of limited importance. Micro-ramps did not eliminate flow separation. However, the previously two-dimensional separation was broken up into periodic three-dimensional separation zones. The interaction length was reduced and the pressure gradient across the interaction was increased.

Controlling the form of strong converging shocks by means of disturbances

Abstract: The influence of artificial disturbances on the behavior of strong converging cylindrical shocks is investigated experimentally and numerically. Ring-shaped shocks, generated in an annular cross sectional shock tube are transformed to converging cylindrical shocks in a thin cylindrical test section, mounted at the rear end of the shock tube. The converging cylindrical shocks are perturbed by small cylinders placed at different locations and in various patterns in the test section. Their influence on the shock convergence and reflection process is investigated. It is found that disturbances arranged in a symmetrical pattern will produce a symmetrical deformation of the converging shockfront. For example, a square formation produces a square-like shock and an octagon formation a shock with an octagonal front. This introduces an alternative way of tailoring the form of a converging shock, instead of using a specific form of a reflector boundary. The influence of disturbances arranged in non-symmetric patterns on the shape of the shockfront is also investigated.

Deflecting dams and the formation of oblique shocks in snow avalanches at Flateyri, Iceland

Abstract: Snow avalanches are a threat in many populated mountainous regions, and deflecting dams are often built to divert them away from people, and infrastructure, into less harmful areas. When an avalanche is deflected by a dam or wedge, it often generates rapid changes in the flow thickness and velocity, which can be modeled as an oblique shock wave. This paper reviews classical oblique shock theory, which was originally developed for shallow water flows, and uses it to make predictions of the maximum runup height on a deflecting dam, the downstream flow velocity, and the width of the channelized stream. The theory is used to investigate field observations of snow avalanches at Flateyri in Iceland, where a dam has deflected two avalanches away from the town and produced a channelized stream that flowed parallel to the dam. The results indicate that there is no one single set of upstream flow conditions that parameterizes the flow behavior, but the solution evolves as the avalanche propagates along the dam in response to the deceleration imposed by the slope. Fully time-dependent shock capturing numerical simulations of the Skollahvilft avalanche, which hit the dam on 21 February 1999, are used to show how the channelized stream widens as the avalanche slows down and thickens toward the end of the runout zone. The oblique shock relations nevertheless provide useful local order of magnitude estimates for the flow conditions immediately upstream of the shock.

Mach Stem Height and Growth Rate Predictions

Abstract: 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

Shock Reflection in Gas Dynamics

Abstract: This paper is about multi-dimensional shocks and their interactions. The latter take place either between two shocks or between a shock and a boundary. Our ultimate goal is the analysis of the reflection of a shock wave along a ramp, and then at a wedge. Various models may be considered, from the full Euler equations of a compressible fluid, to the Unsteady Transonic Small Disturbance (UTSD) equation. The reflection at a wedge displays a self-similar pattern that may be viewed as a two-dimensional Riemann problem. Most of mathematical problems remain open. Regular Reflection is the simplest situation and is well-understood along an infinite ramp. More complicated reflections occur when the strength of the incident shock increases and/or the angle between the material boundary and the shock front becomes large. This is the realm of Mach Reflection. Mach Reflection involves a so-called triple shock pattern, where typically the reflection of the incident shock detaches from the boundary, and a secondary shock, the Mach stem, ties the interaction point to the wall. The triple shock pattern is pure if it is made only of the incident, reflected and secondary shocks, but of no other wave. As predicted by J. von Neumann, pure triple shock structures are impossible. A common belief was that this impossibility is of thermodynamical nature. We prove here that the obstruction is of kinematical nature, thus is independent either of an equation of state or of an admissibility condition. This holds true for all situations: Euler models, irrotational flows and UTSD, the latter case having been known for a decade. Because the Regular Reflection problem along a wedge gathers several major technical difficulties (a free boundary, a domain singularity, a solution singularity, a mixed-type system of PDEs, a type degeneracy across the sonic line), its solvability is still far from our knowledge, except in the simplest context of potential flows with small incidence, a problem solved recently by G.-Q. Chen and M. Feldman. Good though partial results have been obtained by S. Canic et al. for the UTSD model and by Y. Zheng for the Euler system. As far as the Euler equations are concerned, we improve and derive with higher mathematical rigour our pointwise estimates of 1994. Our improvements concern most of the estimates: • We give a now rigorous proof of the minimum principle for the pressure, whenever the flow is piecewise smooth, • Our new bound of the size of the subsonic domain applies now to data of arbitrary strength and incidence, • This together with the observation that the entropy increases, yields much better pointwise estimates of field variables, • We prove that there must exist a vortical singularity, at least in the barotropic case: the vorticity of the flow may not be square integrable, • Last but not least, we give a rigorous justification that the flow is uniform between the ramp, the pseudo-sonic line and the reflected shock, the latter being straight.

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

Abstract: The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory (LST). To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number (based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow) and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations (PSE). At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wave numbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes.

Mach configuration in pseudo-stationary compressible flow

Abstract: When a shock front in unsteady compressible flow is moving along an inclined ramp, the incident shock will be reflected by the ramp, as it moves forward. In the process of reflection, various reflected wave pattern may occur depending on the slope of the ramp and the strength of the incident shock [14, 23]. This problem is one of the most important multidimensional prototype problems in gas dynamics. Generally, if the angle of inclination is larger than a critical value, then the reflected shock starting from the intersection of the incident shock with the ramp forms a smooth bubble, which expands when time goes on; such a reflection is called regular reflection. On the other hand, if the angle of inclination is small, then the intersection of the incident shock and the reflected shock will not touch the ramp, and an additional shock front called Mach stem appears, which connects the ramp with the intersection of the incident shock and the reflected shock. In this case three shock fronts meet at one point and form a triple shock configuration. An important fact is that the structure solely containing three shock fronts separating the neighborhood of the triple intersection into three zones with different continuous states does not exist [14, 27]. Many physical experiments indicate that there is a slip line issuing from the triple intersection. Such a local wave pattern is called Mach configuration or Mach structure. Correspondingly, the whole process of reflection is called Mach reflection. Because of the complexity of the whole picture of Mach reflection, it is natural and necessary to start work on getting a clear understanding of the local Mach configuration. Mach reflection also occurs in various other cases for compressible flow. For instance, in the study on oblique shock reflection in stationary compressible flow von Neumann indicated that (see [14, 25]) if the incident shock hit a wall with an angle larger than a critical value, then the reflection must be Mach reflection. Many physical experiments, approximate analysis and numerical computations verified the appearance of Mach configuration, and a tremendous amount of literature is devoted to study such problems (see [3, 4, 11, 19, 20, 24] and the references therein). However, for the rigorous proof on the stability of Mach configuration we can only mention a related result on stationary flow in [13].

Open-ended shock tube flows : Influence of pressure ratio and diaphragm position

Abstract: The influence of the pressure ratio and the diaphragm location on the flow from open-ended shock tubes is investigated. In contrast to previous studies, in which attention was focused on the discharge of the shock wave from the shock tube, we consider also the influence of the contact discontinuity and the expansion fan. It is found that if the pressure ratio is large enough to lead to supersonic flow behind the contact discontinuity, the flow at the open end relaxes from the conditions behind the contact discontinuity to sonic conditions once the tail of the expansion fan arrives at the open end. Theory indicates that the time scale over which the flow relaxes to sonic conditions is nearly independent of the initial Mach number. Also, the time scale is much longer than that required by the acceleration of subsonic conditions behind the contact discontinuity to sonic conditions. The relaxation process is shown to influence the evolution of the Mach-disk shock, the barrel shock, and the reflected shock wave in an underexpanded jet.

Whistler waves, core ion heating, and nonstationarity in oblique collisionless shocks

Abstract: One-dimensional full particle simulations of supercritical collisionless shocks with an ion and electron beta of 0.1 (particle to magnetic field pressure) over a wide Alfven Mach number range and range of shock normal-magnetic field angles between ΘBn=60° and ΘBn=80° are presented. The whistler critical Mach number Mw, below which a linear phase-standing whistler can exist, is proportional to the square root of the ion-to-electron mass ratio and to cosΘBn. In small mass ratio simulations of oblique shocks, Mw can be artificially small and close to the first critical Mach number Mc, above which the process of ion reflection is needed in order to achieve shock dissipation. We use in the simulations the physical ion-to-electron mass ratio so that Mc and Mw are well separated. This also allows excitation of the modified two-stream instability (MTSI) between incoming ions and electrons. We find that in oblique but close to perpendicular (ΘBn⩾80°) shocks, upstream whistler waves do occur, but reformation is due...

Numerical modeling of vortex/shock wave interaction and its transformation by localized energy deposition

Abstract: Three-dimensional unsteady Euler simulations are presented for the interaction of a streamwise vortex with an oblique shock of angle β = 23.3° at Mach 3 and 5. The flowfield features are analyzed for weak, moderate and strong interaction regimes. The details of the free recirculation zone at conditions of subsonic and supersonic flow on the vortex axis are considered. The vortex breakdown under conditions of a subsonic vortex core is characterized by a continuous growth and gradual degeneration of the region, unlike the supersonic core condition wherein a steady recirculation zone is achieved. The possibility of using a localized steady and pulsed periodic energy deposition on the vortex axis for stimulating the breakdown is demonstrated for various interaction regimes. It is shown that the formation of a subsonic wake downstream of an energy source lying on the vortex axis contributes to a more significant growth of the dimensions of the recirculation zone compared to the case when the vortex core remains supersonic. The possibility of achieving the effects similar to the steady case is demonstrated by the effect of a pulsed periodic energy source on the flow under consideration for corresponding equivalence parameters.

The experimental study of interaction between shock wave and turbulence

Abstract: The interaction between shock wave and turbulence has been studied in supersonic turbulent mix layer wind tunnel. The interaction between oblique shock wave and turbulent boundary layer and the influence of large vortex in mix layer on oblique shock wave have been observed by NPLS technique. From NPLS image, not only complex flow structure is observed but also time-dependent supersonic flow visualization is realized. The mechanism of interaction between shock wave and turbulence is discussed based on high quality NPLS image.

A Novel Oblique Detonation Structure and Its Stability

Abstract: Oblique detonation structures induced by the wedge in the supersonic combustible gas mixtures are simulated numerically. The results show that the stationary oblique detonation structures are influenced by the gas flow Mach number, and a novel critical oblique detonation structure, which is characterized by a more complicated wave system, appears in the low Mach number cases. By introducing the inflow disturbance, its nonstationary evolution process is illustrated and its stability is verified.

Current status of numerical flow prediction for separated nozzle flows

Abstract: European 'Flow Separation Control Device' group (FSCD) organized in collaboration with the French 'Aerodynamiques des tuyeres et Arriere-Corps' group (ATAC) a CFD workshop with test cases on different nozzle flow topics. One of these test cases (1A) was managed by the German Aerospace Center (DLR) and Astrium ST. The objective was to compute the flow inside a strongly over-expanded truncated ideal contour nozzle with respect to the prediction of location and shape of the flow separation, the oblique shock and the Mach disc. Experimental data were provided by DLR. An introduction to the test facility and the experimental setup is given. The numerical results are evaluated and compared to test data. A concluding synthesis illustrates the current status of nozzle flow computation.