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Showing papers on "Oblique shock published in 2001"


Journal ArticleDOI
TL;DR: In this article, the acceleration of charged particles near ultra-relativistic shocks is considered and the acceleration spectrum is shown to be a power law, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law.
Abstract: We consider the acceleration of charged particles near ultra-relativistic shocks, with Lorentz factor Gamma_s >> 1. We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultra-relativistic shocks is a power law, N(E) \propto E^{-s}, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law. We confirm that the ultra-relativistic equivalent of Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle theta_c \approx 1/Gamma_s around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: Delta theta ~ 1/Gamma_s. This limits the energy change per shock crossing cycle to Delta E ~ E, except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor ~ Gamma_s^2 for those particles that are scattered back across the shock into the upstream region.

605 citations


Journal ArticleDOI
TL;DR: In this article, a review of the physical mechanisms of the periodic shock motion on airfoils at transonic flow conditions are associated with the phenomenon of buffeting, and various modes of shock wave motion for different flow conditions and airfoil configurations are described.

333 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of bifurcated shock structures on shock-flame interactions and deflagration-to-detonation transition (DDT) in shock-tube experiments are examined.

122 citations


Journal ArticleDOI
TL;DR: In this paper, a supersonic nonequilibrium plasma wind tunnel was used to study the effects of ionization on supersonically ionized gas flows in the presence of a high-pressure aerodynamically stabilized dc discharge in the tunnel plenum and a transverse rf discharge in a test section.
Abstract: Experimental studies of shock modification in weakly ionized supersonic gas flows are discussed. In these experiments, a supersonic nonequilibrium plasma wind tunnel, which produces a highly nonequilibrium plasma flow with the low gas kinetic temperature at M = 2, is used. Supersonic flow is maintained at complete steady state. The flow is ionized by a high-pressure aerodynamically stabilized dc discharge in the tunnel plenum and by a transverse rf discharge in the supersonic test section. The dc discharge is primarily used for the supersonic flow visualization, whereas the rf discharge provides high electron density in the supersonic test section. High-pressure flow visualization produced by the plasma makes all features of the supersonic flow, including shocks, boundary layers, expansion waves, and wakes, clearly visible. Attached oblique shock structure on the nose of a 35-deg wedge with and without rf ionization in a M = 2 flow is studied in various nitrogen-helium mixtures. It is found that the use of the rf discharge increases the shock angle by 14 deg, from 99 to 113 deg, which corresponds to a Mach number reduction from M = 2.0 to 1.8. Time-dependent measurements of the oblique shock angle show that the time for the shock weakening by the rf plasma, as well as the shock recovery time after the plasma is turned off, is of the order of seconds. Because the flow residence time in the test section is of the order of 10 μs, this result suggests a purely thermal mechanism of shock weakening due to heating of the boundary layers and the nozzle walls by the rf discharge. Gas flow temperature measurements in the test section using infrared emission spectroscopy, with carbon monoxide as a thermometric element, are consistent with the observed shock angle change. This shows that shock weakening by the plasma is a purely thermal effect. The results demonstrate the feasibility of both sustaining uniform ionization in cold supersonic nitrogen and airflows and the use of nonequilibrium plasmas for supersonic flow control. This opens a possibility for the use of transverse stable rf discharges for magnetohydrodynamic energy extraction and/or acceleration of supersonic airflows.

96 citations


Journal ArticleDOI
TL;DR: In this article, the authors applied the methodology developed in Part I [Comp. Fluids (2000), submitted for publication] to study underwater shock refracting at a gas-water interface.

78 citations


Book
01 Jan 2001
TL;DR: In this article, the second-order boundary-layer theory was used to explain the acceleration of a two-dimensional or axisymmetric flow over a flat plate. But it is not applicable to a one-dimensional flow.
Abstract: BASIC CONCEPTS Background Discussion The Conservation Equations Classical Thermodynamics Kinematics ADVANCED GAS DYNAMICS Euler Equations Shock Wave Dynamics The Hodograph Transformation and Limit Lines The Substitution Principle Calorically Imperfect Flows Sweep Interaction of an Expansion Wave with a Shock Wave Unsteady, One-Dimensional Flow VISCOUS/INVISCID DYNAMICS Coordinate Systems and Related Topics Force and Moment Analysis EXACT SOLUTIONS FOR A VISCOUS FLOW Rayleigh Flow Couette Flow Stagnation Point Flow LAMINAR BOUNDARY-LAYER THEORY FOR STEADY TWO-DIMENSIONAL OR AXISYMMETRIC FLOW Incompressible Flow over a Flat Plate Large Reynolds Number Flow Incompressible Boundary-Layer Theory Compressible Boundary-Layer Theory Supersonic Boundary-Layer Examples Second-Order Boundary-Layer Theory APPENDICES Summary of Equations from Vector and Tensor Analysis Jacobian Theory Oblique Shock Wave Angle Conditions on the Downstream Side of a Steady Shock Wave in a Two-Dimensional or Axisymmetric Flow of a Perfect Gas Method of Characteristic for a Single, First-Order PDE Tangential Derivatives on the Downstream Side of a Shock in the x1 and x2 Directions Conservation and Vector Equations in Orthogonal Curvilineas Coordinates xi Conservation Equations in Body-Oriented Coordinates Summary of Compressible, Similar Boundary-Layer Equations Second-Order Boundary-Layer Equations for Supersonic, Rotational Flow over a Flat Plate

78 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of flow three-dimensionalality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally, and characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configurations, have been found in the numerical simulations.
Abstract: New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown.

75 citations


Journal ArticleDOI
TL;DR: In this article, the authors performed a superposed epoch analysis of low frequency, magnetic power spectra some minutes up-stream and downstream of the bow shock, and found a dominance of the left-hand polarized component at frequencies just below the ion-cyclotron frequency.
Abstract: . We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of low frequency, magnetic power spectra some minutes up-stream and downstream of the bow shock. The events are devided into categories depending on the angle θBn between bow shock normal and interplanetary magnetic field, and on plasma-β. In the foreshock upstream of the quasi-parallel bow shock, the power of the magnetic fluctuations is roughly 1 order of magnitude larger (δB ~ 4 nT for frequencies 0.01–0.04 Hz) than upstream of the quasi-perpendicular shock. There is no significant difference in the magnetic power spectra upstream and downstream of the quasi-parallel bow shock; only at the shock itself, is the magnetic power enhanced by a factor of 4. This enhancement may be due to either an amplification of convecting upstream waves or to wave generation at the shock interface. On the contrary, downstream of the quasi-perpendicular shock, the magnetic wave activity is considerably higher than upstream. Down-stream of the quasi-perpendicular low-β bow shock, we find a dominance of the left-hand polarized component at frequencies just below the ion-cyclotron frequency, with amplitudes of about 3 nT. These waves are identified as ion-cyclotron waves, which grow in a low-β regime due to the proton temperature anisotropy. We find a strong correlation of this anisotropy with the intensity of the left-hand polarized component. Downstream of some nearly perpendicular (θBn ≈ 90°) high-β crossings, mirror waves are identified. However, there are also cases where the conditions for mirror modes are met downstream of the nearly perpendicular shock, but no mirror waves are observed. Key words. Interplanetary physics (plasma waves and turbulence) – Magnetospheric physics (magnetosheath; plasma waves and instabilities)

75 citations


Journal ArticleDOI
TL;DR: In this article, an exact solution in the limit of weak spot amplitudes is elaborated, using the linear interaction analysis theory and the procedure of decomposition proposed by Ribner (Technical Report No. 1164, NACA, 1953).
Abstract: The interaction of a cylindrical element of hot or cold gas (the “entropy spot”) with a shock wave is considered. An exact solution in the limit of weak spot amplitudes is elaborated, using the linear interaction analysis theory and the procedure of decomposition proposed by Ribner (Technical Report No. 1164, NACA, 1953). The method is applied to an entropy spot with a Gaussian profile. Results are presented for a wide range of shock Mach numbers, with a special interest at M1=2. The resulting vorticity field consists of a pair of primary counter-rotating vortices, as well as a pair of secondary vortices of opposite sign and weaker amplitude. An expression for the circulation in half a plane is derived and compared to existing results. The pressure field consists of a cylindrical acoustic wave which propagates away from the transmitted spot and an evanescent nonpropagative field confined behind the shock. For a hot spot, the cylindrical wave is a rarefaction wave on its forward front and a compression wav...

70 citations


Journal ArticleDOI
TL;DR: In this article, a near-wall Reynolds-stress closure that is independent of the distance from the wall and of the normal to the normal is developed and validated by comparison with experimental data in a two-dimensional compression corner oblique shockwave/boundary layer interaction at Mach 3.
Abstract: A near-wall Reynolds-stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated.Particularattention wasgiven intheapplicabilityofthemodeltocomplex three-dimensional e ows with shock waves and boundary-layer separation. In the separated e ow region, measurements andmodelcomputations indicatethatthe e atnessparameter Aoftheanisotropy tensor aij approaches unity. Therefore, controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure‐strain isotropization of production model coefe cienton A. Echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants.The modelisinitiallycomparedwithmeasurementsforcompressiblee at-plateboundary-layere ows.Itisthenvalidated by comparison with experimental data in a two-dimensional compression corner oblique shock-wave/boundarylayer interaction at Mach 3. Finally the model is applied to the computation of the three-dimensional interaction of a Mach 1.5‐1.8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall, and results are compared with measurements. One important advantage of the proposed model is its robustness in complex three-dimensional e ows. A detailed discussion of therange of validity of the model and possible improvements is presented.

64 citations


Journal ArticleDOI
TL;DR: In this article, an experimental study of the plasma effect on the structure of an attached conical shock front appearing at the front end of a cone-shaped model has been carried out in a Mach 2.5 stream.
Abstract: An experimental study of the plasma effect on the structure of an attached conical shock front appearing at the front end of a cone-shaped model has been carried out in a Mach 2.5 stream. The tip and the body of the model are designed as the cathode and anode, which are separated by a conical-shaped ceramic insulator providing a 5 mm gap for gaseous discharge. The electric field intensity near the cathode is enhanced by the sharpness of the tip. The experimental results show that the diffused discharge can produce plasma distributed symmetrically around the tip in the region in front of the shock wave. It is observed that such plasma can cause shock wave moving upstream with its shock front detached from the model. The shock front is also becoming more and more diffusive and having an increasing shock angle as seen in the shadow video graphs of the flow. A physical mechanism of the observed plasma effect on this type of shock wave is also presented.

Journal ArticleDOI
TL;DR: In this article, a van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations.
Abstract: Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.

Journal ArticleDOI
TL;DR: In this article, the exact critical conditions delineating the number and character of shock transitions were derived by reformulating the upstream boundary conditions in terms of two individual Mach numbers defined with respect to the cosmic-ray and gas sound speeds, respectively.
Abstract: The acceleration of relativistic particles due to repeated scattering across a shock wave remains the most attractive model for the production of energetic cosmic rays. This process has been analyzed extensively during the past two decades using the ``two-fluid'' model of diffusive shock acceleration. It is well known that 1, 2, or 3 distinct solutions for the flow structure can be found depending on the upstream parameters. The precise nature of the critical conditions delineating the number and character of shock transitions has remained unclear, mainly due to the inappropriate choice of parameters used in the determination of the upstream boundary conditions. We derive the exact critical conditions by reformulating the upstream boundary conditions in terms of two individual Mach numbers defined with respect to the cosmic-ray and gas sound speeds, respectively. The gas and cosmic-ray adiabatic indices are assumed to remain constant throughout the flow, although they may have arbitrary, independent values. Our results provide for the first time a complete, analytical classification of the parameter space of shock transitions in the two-fluid model. When multiple solutions are possible, we propose using the associated entropy distributions as a means for indentifying the most stable configuration.

Journal ArticleDOI
TL;DR: In this article, the interaction of ions with the ramp of a quasiparallel shock is investigated, where specular reflections are experienced either by the cross-shock electrostatic potential or by mirroring as the magnetic field is bent and compressed through the ramp.
Abstract: For a particle to be accelerated diffusively at a shock by the first-order Fermi acceleration mechanism, the particle must be sufficiently energetic that it can scatter across all the micro- and macrostructure of the shock, experiencing compression between the converging upstream and downstream states. This is the well-known “injection problem.” Here the interaction of ions with the ramp of a quasiparallel shock is investigated. Some ions incident on the shock experience specular reflection, caused either by the cross-shock electrostatic potential or by mirroring as the magnetic field is bent and compressed through the ramp. Scattering of reflected ions by self-generated and pre-existing turbulence in the region upstream of the shock then acts to trap backstreaming ions and return them to the ramp, where some experience further reflections. Such repeated reflections and scattering energize a subpopulation of ions up to energies sufficiently large that they can be diffusively shock accelerated. Two ion dis...

Journal ArticleDOI
TL;DR: In this paper, the effects of entropy gradients on shock formation from a compression wave were determined using a wave front expansion in Cartesian and in spherical polar coordinates, and the principal result is an analytical criterion for the time and place of shock formation, for a wave propagating into a field of smoothly varying entropy.
Abstract: The steepening of a normal compression wave into a shock in a homentropic flow field is understood well through the method of characteristics. In a non-homentropic flow field, however, shock formation from a compression wave is more complex. The effects of entropy (or sound speed) gradients on shock formation from a compression wave are determined using a wave front expansion in Cartesian and in spherical polar coordinates. The latter problem has application to the intense energy focusing of sonoluminescence, particularly when applied to a spherically collapsing gas. The principal result is an analytical criterion for the time and place of shock formation, for a wave propagating into a field of smoothly varying entropy.

Journal ArticleDOI
TL;DR: In this article, high power, pulsed microwaves are beamed forward of a model in a Mach 6 flow using an on-board, Ku-band horn, and a thin precursor plasma is generated just ahead of the bow shock in the low density free stream.
Abstract: High power, pulsed microwaves are beamed forward of a model in a Mach 6 flow using an on-board, Ku-band horn. A thin “precursor” plasma is generated just ahead of the bow shock in the low density free stream. Temporal and spatial analysis of the microwave E-field and plasma conductivity in the supersonic flow field indicate that the plasma reflects a large proportion of the microwave power in an individual pulse as soon as the plasma frequency exceeds the wave frequency. Possible methods for more efficient deposition of power in the free stream are discussed which could lead to increased interaction with the shock.

Journal ArticleDOI
TL;DR: In this article, large-scale flow in the dayside magnetosheath is calculated by using a three-dimensional anisotropic MHD model for the case when the angle between the interplanetary magnetic field and the solar wind velocity is 45°.
Abstract: Large-scale flow in the dayside magnetosheath is calculated by using a three-dimensional anisotropic MHD model for the case when the angle between the interplanetary magnetic field and the solar wind velocity is 45°. The behavior of plasma and magnetic field parameters downstream of the quasi-perpendicular and quasi-parallel bow shocks is compared in the results from a single calculation. The model includes a limit on the proton temperature anisotropy based upon thresholds for onset of the ion cyclotron and mirror instabilities. Results are presented for three different values of the isotropization rate. The model shows the existence of the plasma depletion layer, corresponding to an increase of the magnetic field intensity and a decrease of the plasma density near the magnetopause, for all angles of the bow shock normal relative to the interplanetary magnetic field. There is a thin layer downstream of the quasi-parallel shock where T‖p > T⊥p. The magnetosheath regions are shown where the threshold conditions for ion cyclotron and mirror instabilities are satisfied.

Journal ArticleDOI
TL;DR: In this paper, a numerical analysis was carried out to study the interaction of the reflected shock with incident boundary layer and contact surface in reflected shock tunnels and the driver gas contamination of the hot flow, in tailored conditions.
Abstract: A numerical analysis was carried out to study the interaction of the reflected shock with incident boundary layer and contact surface in reflected shock tunnels and the driver gas contamination of the hot flow, in tailored conditions. Navier-Stokes equations were solved with a multiblock finite volume method in a shock tube and a nozzle. Different suction devices, such as a corner slit, a corner slit prolongated by a sleeve, and a conical ring, were tested for their capability of delaying this contamination effect. The results show that the driver gas passes through a bifurcated shock foot as a jet and causes premature contamination of the driven gas. They also show why the suction induced by a corner slit is inefficient for delaying the contamination. Located just behind the bifurcated shock foot after the shock/interface interaction, the sleeve device captures driver gas upstream and leads to an improvement in the driver gas arrival time by a factor of 1.8. Finally, based on the present numerical investigation, a new conical ring device is proposed, with a horizontal and vertical suction, which further increases this factor to 2.5

Journal ArticleDOI
TL;DR: In this article, a collisionless curved shock is analyzed in a supercritical regime with the help of a two-dimensional electromagnetic full particle code, and it is shown that local back-streaming distributions have two components: (i) a high parallel energy component corresponding to backstreaming electrons characterized by a field-aligned bump-in-tail or beam signature, and (ii) a low energy parallel component characterized by the loss cone signature (mirrored electron).
Abstract: A collisionless curved shock is analyzed in a supercritical regime with the help of a two-dimensional electromagnetic full particle code. Curvature effects are included self-consistently and allow one to follow continuously the transition from a narrow and step-like strictly perpendicular shock to a wider and more turbulent oblique shock within the quasi-perpendicular range 65° < θBn < 90°. Present results reproduce the formation of the electron foreshock without any simplifying assumptions. In agreement with experimental data, local bump-on-tail parallel distribution functions are well recovered in the foreshock region and correspond to electrons backstreaming along the magnetic field lines. Present detailed analysis shows that local back-streaming distributions have two components: (i) a high parallel energy component corresponding to back-streaming electrons characterized by a field-aligned bump-in-tail or beam signature, and (ii) a low-energy parallel component characterized by a loss cone signature (mirrored electron). Two types of bump-in-tail patterns, broad and narrow, are identified at short and large distances from the curved shock, respectively, and are due to different contributions of these two components according to the local impact of the time-of-flight effects. Present results allow one to identify more clearly the nature of the bump-in-tail pattern evidenced experimentally (narrow type). These also confirm that mirroring electrons make the dominant contribution to the bump-in-tail pattern in the total distribution in agreement with previous studies. Results suggest that low and high parallel energy populations are intimately related and may contribute together to the upstream wave turbulence.

Patent
31 May 2001
TL;DR: In this paper, a fluid is modified by emitting energy to form an extended path in the fluid; heating fluid along the path to form a volume of heated fluid expanding outwardly from the path; and directing a path.
Abstract: A shock wave in a fluid is modified by emitting energy to form an extended path in the fluid; heating fluid along the path to form a volume of heated fluid expanding outwardly from the path; and directing a path. The volume of heated fluid passes through the shock wave and modifies the shock wave. This eliminates or reduces a pressure difference between fluid on opposite sides of the shock wave. Electromagnetic and/or electric discharge can be used to heat the fluid along the path. This application has uses in reducing the drag on a body passing through the fluid, noise reduction, and steering a body through the fluid. An apparatus is also disclosed.

Journal ArticleDOI
TL;DR: In this article, the interaction between shock waves and turbulent boundary layers in a Mach 2.5 wind tunnel has been visualized by a megahertz-rate imaging system, where the shock waves were produced by two-dimensional compression corners having angles of 14 and 24 deg, and the flows were, respectively, attached and separated.
Abstract: The interactions between shock waves and turbulent boundary layers in a Mach 2.5 wind tunnel have been visualized by a megahertz-rate imaging system. The shock waves were produced by two-dimensional compression corners having angles of 14 and 24 deg, and the flows were, respectively, attached and separated. At the compression corner, the sequential images clearly indicate the correlation between the shock motion and the incoming turbulent boundary layer. Some large eddies in the boundary layer cause the shock to move in the streamwise direction for distances as large as the boundary-layer thickness at a frequency as high as large-eddy frequency (U e /δ), but other eddies seem to have minor effect on the shock wave. The images also indicate how the shock waves influence the boundary-layer structures

Journal ArticleDOI
TL;DR: The underwater acoustic field in water entry of a 352 m/s blunt body has been investigated by pressure measurements as discussed by the authors, and the experimental results show that from the initial stage to the later stage of water entry, there are: (1) a high peak pressure caused by the compressible behavior in high speed solid/liquid impact; (2) a negative pressure region caused by expansion waves which are generated when the initial primary shock wave detaches from the solid body and the high pressure region is released; and (3) a significant motion of the fluid particles driven by the shock
Abstract: The underwater acoustic field in water entry of a 352 m/s blunt body has been investigated by pressure measurements. The experimental results show that from the initial stage to the later stage of water entry, there are: (1) a high peak pressure caused by the compressible behavior in high speed solid/liquid impact; (2) a negative pressure region caused by the expansion waves which are generated when the initial primary shock wave detaches from the solid body and the high pressure region is released; and (3) a significant motion of the fluid particles driven by the shock wave. It is found that at the entry velocity of this experiment, the shock wave behaves like an acoustic wave in water. The wave has a stronger energy distribution on the forward direction and a weaker energy distribution on the lateral direction.

Journal ArticleDOI
TL;DR: In this paper, the authors study the magnetic field and plasma param- eters downstream of a fast shock, as functions of upstream parameters and downstream pressure anisotropy, and compare their theory with plasma and magnetic field parameters measured by the WIND spacecraft.
Abstract: Taking into account the pressure anisotropy in the solar wind, we study the magnetic field and plasma param- eters downstream of a fast shock, as functions of upstream parameters and downstream pressure anisotropy. In our the- oretical approach, we model two cases: a) the perpendicular shock and b) the oblique shock. We use two threshold condi- tions of plasma instabilities as additional equations to bound the range of pressure anisotropy. The criterion of the mirror instability is used for pressure anisotropy p?/pk > 1. Anal- ogously, the criterion of the fire-hose instability is taken into account for pressure anisotropy p?/pk < 1. We found that the variations of the parallel pressure, the parallel tempera- ture, and the tangential component of the velocity are most sensitive to the pressure anisotropy downstream of the shock. Finally, we compare our theory with plasma and magnetic field parameters measured by the WIND spacecraft.

Journal ArticleDOI
TL;DR: In this paper, spectral and angular distributions of the accelerated electrons using the theory of shock drift acceleration at curved shocks are presented, which leads to the conclusion that the acceleration is strongly modified by some additional processes which could be pitch angle scattering of electrons in the shock layer, or spatial/temporal changes of the shock front.
Abstract: Spikes of energetic (1–100 keV) electrons have been observed at the nearly perpendicular Earth's bow shock and at traveling interplanetary shocks and have been explained as solar wind electrons accelerated by the shock drift mechanism. We present spectral and angular distributions of the accelerated electrons using the theory of shock drift acceleration at curved shocks. The influence of various shock parameters on these distributions is extensively discussed here. The theoretical fluxes of accelerated electrons are highly anisotropic, and their spectra cannot be fitted by a power law. The spectra strongly depends on the location near the shock, and they are harder for upstream electrons: the highest fluxes can be found in the regions of the shock with θBn ≈ 86°–88°. The fluxes of reflected electrons increase with decreasing shock curvature or shock thickness, while fluxes of transmitted electrons do not depend significantly on these parameters. The magnetic field profile shapes through the shock have no large effect on the acceleration. A higher upstream plasma velocity (Mach number) results in larger electron fluxes. These basic properties of electron distributions are then qualitatively compared with observational facts. These comparisons lead us to the conclusion that the shock drift acceleration is strongly modified by some additional processes, which could be pitch angle scattering of electrons in the shock layer, or spatial/temporal changes of the shock front.

Proceedings ArticleDOI
08 Jan 2001
TL;DR: The effect of streamwise slots on the interaction of a normal shock wave / turbulent boundary layer has been investigated experimentally at a Mach number of 1.3 by Smith et al. as discussed by the authors.
Abstract: The effect of streamwise slots on the interaction of a normal shock wave / turbulent boundary layer has been investigated experimentally at a Mach number of 1.3. The surface pressure distribution for the controlled interaction was found to be significantly smeared, featuring a distinct plateau. This was due to a change in shock structure from a typical unseparated normal shock wave boundary layer interaction to a large bifurcated Lambda type shock pattern. Boundary layer velocity measurements downstream of the slots revealed a strong spanwise variation of boundary layer properties whereas the modified shock structure was relatively twodimensional. Oil flow visualisation indicated that in the presence of slots the boundary layer surface flow was highly three dimensional and confirmed that the effect of slots was mainly due to suction and blowing similar to that for passive control with uniform surface ventilation. Three hole probe measurements confirmed that the boundary layer was three dimensional and that the slots introduced vortical motion into the flowfield. Results indicate that when applied to an aerofoil, the control device has the potential to reduce wave drag while incurring only small viscous penalties. The introduction of streamwise vorticity may also be beneficial to delay trailing edge separation and the device is thought to be capable of postponing buffet onset. © 2001 by A N Smith.

Proceedings ArticleDOI
08 Jul 2001
TL;DR: In this paper, boundary conditions for subsonic inflow, bleed, and outflow are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets.
Abstract: Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.

Journal ArticleDOI
TL;DR: In this paper, a thin wall-based model consisting of a cylindrically blunted plate and a wedge serving as an oblique shock generator was used for heat transfer measurements on the cylinder surface.

Journal ArticleDOI
TL;DR: In this paper, the relativistic acceleration of fast ions in an oblique shock wave was studied theoretically and numerically, and it was shown that the acceleration process could be repeated indefinitely.
Abstract: Motions of nonthermal, fast ions in an oblique shock wave are studied theoretically and numerically. After the encounter with a shock wave, some of the fast ions get to move with it. Their energies then increase once in each gyroperiod. Their momenta parallel to the magnetic field also increase. Thus, these particles eventually escape, going away ahead of the wave. However, it is theoretically predicted that under certain circumstances, owing to relativistic effects, particles cannot go faster in the direction of the shock propagation than the wave. Some particles therefore cannot escape from the wave. Accordingly, the acceleration could be repeated indefinitely. This idea is examined by means of a one-dimensional, relativistic, electromagnetic, particle simulation code with full ion and electron dynamics. The simulations demonstrate that the repeated acceleration of relativistic ions does occur. The acceleration processes were observed to continue until the end of simulation run. Also, it is shown that a...

Journal ArticleDOI
TL;DR: In this paper, the reflection of planar shock waves from straight wedges in dust-gas suspensions is investigated numerically, and the GRP shock capturing scheme and the MacCormac scheme are applied to solve the governing equations of the gaseous and solid phases, respectively.
Abstract: The reflection of planar shock waves from straight wedges in dust-gas suspensions is investigated numerically The GRP shock capturing scheme and the MacCormac scheme are applied to solve the governing equations of the gaseous and solid phases, respectively These two schemes have a second-order accuracy both in time and space It is shown that the presence of the dust significantly affects the shock-wave-reflection-induced flow field The incident shock wave attenuates and hence unlike the shock wave reflection phenomenon in a pure gas, the flow field in the present case is not pseudo steady

Journal ArticleDOI
TL;DR: In this paper, a mathematical model of the shape of a cylindrical shock implosion in the form of a generalized hyperbola was proposed, and the smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supported the analogy.
Abstract: Oblique shock reflection from an axis of symmetry is studied using Whitham's theory of geometrical shock dynamics, and the results are compared with previous numerical simulations of the phenomenon by Hornung (2000). The shock shapes (for strong and weak shocks), and the location of the shock-shock (for strong shocks), are in good agreement with the numerical results, though the detail of the shock reflection structure is, of course, not resolved by shock dynamics. A guess at a mathematical form of the shock shape based on an analogy with the Guderley singularity in cylindrical shock implosion, in the form of a generalized hyperbola, fits the shock shape very well. The smooth variation of the exponent in this equation with initial shock angle from the Guderley value at zero to 0.5 at 90° supports the analogy. Finally, steady-flow shock reflection from a symmetry axis is related to the self-similar flow.