Showing papers on "Oblique shock published in 1981"
62 citations
TL;DR: Ben-Dor, Takayama, and Kawauchi as mentioned in this paper used a 5 × 7 cm ordinary pressure-driven shock tube to investigate the transition from regular reflection to Mach reflection.
Abstract: Shock reflections over a convex and a concave wedge were investigated by using a 5 × 7 cm ordinary pressure-driven shock tube. Dry air was used for both the driving and driven gases. The large difference between the transition from regular (RR) to Mach reflection (MR) and that from MR to RR was observed, confirming the results obtained by Ben-Dor, Takayama & Kawauchi (1980). These results contradict all of the previous theoretical transition criteria. A new theory on the transition between RR and MR was developed by applying Whitham's ‘ray shock’ theory. This new theory agrees quite well with the experimental results.
48 citations
12 Jan 1981
37 citations
TL;DR: In this article, the authors used the cold plasma approximation over all appropriate frequencies and directions with respect to the IMF to describe the phase and group velocities of the whistler wave in the bow shock.
Abstract: The presence of whistler mode waves in, and upstream from, the bow shock has been well established by observation. Theoretical descriptions of the mode under solar wind conditions have been relatively meagre, however, and it may not be generally appreciated how readily whistler waves generated in the shock could occupy most of the region ahead of the shock most of the time. Graphic descriptions of phase and group velocities and group velocity directions for typical solar wind parameters are presented by using the cold plasma approximation over all appropriate frequencies and directions with respect to the IMF. The relations of whistler phase and group velocities to observations of a quasi-perpendicular shock crossing by ISEE are illustrated.
34 citations
TL;DR: In this article, the initiation of detonation by planar shocks has been studied in a vertical shock tube in which a removable diaphragm allows a shock, generated in a buffer section, to be transmitted, without any reflection at the interface, into the gas mixture under test.
32 citations
TL;DR: In this paper, the theory and experiments for reflection of a laser beam from a 5.8 kbar shock in water for both parallel and perpendicular (to the plane of incidence) optical polarizations are presented.
Abstract: Theory and experiments are presented for reflection of a laser beam from a 5.8 kbar shock in water for both parallel and perpendicular (to the plane of incidence) optical polarizations. The theory is in closed form and valid in the nonlinear (large optical path length) region. Agreement between theory and experiment is obtained with a shock front thickness less than or equal to 4×10−6 cm.
31 citations
29 citations
22 citations
01 Jan 1981
TL;DR: In this paper, the authors used a simple method that was developed earlier to cluster points near the shocks and serve to introduce a new method of generating a shock aligned mesh, which can reduce the discretization error of the governing differential equations used to compute the solution.
Abstract: The use of shock capturing finite-difference techniques in computing flow fields containing shocks results in a smeared or oscillatory solution in the vicinity of the shocks. This smearing or oscillatory behavior is due to the discretized form of the governing differential equations used to compute the solution. The discretization error can be reduced by a proper clustering of mesh points in the region of the shock and by using shock aligned grids. This paper uses a simple method that was developed earlier to cluster points near the shocks and serves to introduce a new method of generating a shock aligned mesh. Applications to the one-dimensional inviscid Burgers' equation, supersonic flow over a wedge with the associated straight oblique shock, one- and two-dimensional inviscid flows through an expanding duct and the problem of a straight oblique shock in a uniform supersonic freestream are presented. Significant reduction in the oscillatory behavior of the solution is demonstrated.
21 citations
01 Jan 1981
TL;DR: In this paper, a comparison between the absolute flux values about 200 earth radii from the earth's bow shock and the flux values several Earth radii in front of the bow shock at two different energies was made.
Abstract: Four upstream energetic proton events (30 keV-75 keV), which were simultaneously observed by the ISEE-1 and ISEE-3 satellites, are investigated. A comparison was made between the absolute flux values about 200 earth radii from the bow shock and the flux values several earth radii in front of the bow shock at two different energies. Close to the bow shock the particle distribution is more or less isotropic and indicates relatively strong scattering of these particles in the upstream wave field. At ISEE-3 between 100 and 200 earth radii upstream from the earth's bow shock, the particles move essentially scatter-free from the general bow shock direction. The proton differential intensity at ISEE-3 is a factor of about 4-15 less than at ISEE-1 at 30 keV. The spectra at ISEE-1 are steeper than the spectra at ISEE-3. Flux ratios and spectra are discussed in terms of a first order Fermi acceleration model with a diffusion coefficient increasing approximately linearly with energy and a free escape boundary at some distance upstream.
20 citations
TL;DR: In this paper, the effect of the quantity of explosives on the stability and strength of cylindrically converging shock waves is investigated, and it has been shown that, for practical purposes, the approximation of shock trajectories by Guderley's formulas would be sufficiently acceptable in an unexpectedly wide region near the implosion center, and that the axial symmetry of the shock front is improved by increasing the amount of explosives.
Abstract: Cylindrically converging shock waves are produced by utilizing the detonation of cylindrical explosive shells. The production and the propagation of shock waves are observed by framing and streak camera photographs, and the trajectory of shock propagations is determined by using an electrical ionization probing system. The effect of the quantity of explosives on the stability, or the axial symmetry, of shock fronts and on the strength of shocks produced is investigated. It has been shown that, for practical purposes, the approximation of shock trajectories by Guderley’s formulas would be sufficiently acceptable in an unexpectedly wide region near the implosion center, and that the axial symmetry of the shock front is improved by increasing the quantity of explosives, and thus, strong shocks are produced by merely increasing the quantity of explosives. The reflected diverging shock seems to be very stable. Piezoelectric elements have also been used to detect reflected diverging waves.
TL;DR: In this article, a finite-difference method suitable for design calculations of finned bodies is described, which is achieved using a thin fin approximation that neglects fin thickness but retains a correct description of the fin surface slope.
Abstract: A finite-differe nce method suitable for design calculations of finned bodies is described. Efficient numerical calculations are achieved using a thin fin approximation that neglects fin thickness but retains a correct description of the fin surface slope. The resulting algorithm is suitable for treating relatively thin, straight fins with sharp edges. Methods for treating the fin leading and trailing edges are described that are dependent on the Mach number of the flow normal to the edge. The computed surface pressures are compared to experimental measurements taken on cruciform configurations with supersonic leading and trailing edges and to a swept wing body with detached leading-edge shocks. A semiempirical procedure is developed to treat the leading edges in the latter case. Measured and calculated pressures are in reasonable agreement in both the tested configurations.
TL;DR: In this article, the authors investigated the stability of converging cylindrical shock waves in an annular shock tube and found that initially symmetric shocks are found to retain their symmetry during implosion except at small radius where a breakdown in shock front curvature eventually occurs.
Abstract: S of converging cylindrical shock waves is investigated experimentally in an annular shock tube. Initially symmetric shocks are found to retain their symmetry during implosion except at small radius where a breakdown in shock front curvature eventually occurs. Artificially generated shock front perturbations are observed to promote this type of instability. In all cases, instability is manifest by the appearance of vortex pairs during the expansive shock motion which follows the implosion.
01 Jul 1981
TL;DR: In this paper, the interaction between the boundary layer on the shock tube side wall and the shock reflected from the end wall was investigated experimentally in the free piston shock tube T3, and the experiments were conduted at sufficiently high shock speed to produce vibrational excitation and dissociation in the case of nitrogen and carbon dioxide.
Abstract: : Several aspects of the interaction between the boundary layer on the shock tube side wall and the shock reflected from the end wall were investigated experimentally in the free piston shock tube T3. The experiments were conduted at sufficiently high shock speed to produce vibrational excitation and dissociation in the case of nitrogen and carbon dioxide, while the experiments in argon were restricted to the ideal gas range.
TL;DR: In this paper, a Chebyshev expansion approach is employed to solve the one dimensional compressible flow equations for flows with large gradients, and a technique for controlling oscillations is presented.
TL;DR: In this article, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow is investigated and the equations of motion and the initial and boundary conditions are linearized for small perturbations.
Abstract: The flow arising from an initial pressure discontinuity across a perturbed interface of two ideal gases is studied using analytical and numerical methods. In particular, the stability of the shock wave, the interface, and the rarefaction wave in the resulting flow are investigated. The equations of motion and the initial and boundary conditions are linearized for small perturbations, and a Fourier analysis is made in the lateral direction. The equations are then solved by the method of characteristics. The results show that the interface is unstable and its perturbations asymptotically acquire a constant rate of growth. The shock wave is stable and has rapidly damped oscillations, which appear to be unaffected by the instability of the interface.
TL;DR: In this paper, a model based on an one-dimensional approach to the flow of a liquid-gas mixture was proposed for transient two-phase flow through elastic tubes, where the bubbles and the liquid particles move with the same velocity.
Abstract: The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations
01 Jul 1981
TL;DR: The liquefaction shock wave, a compression shock which converts vapour into liquid, was experimentally produced as the reflected shock at the closed end of a shock tube in test fluids with many molecular degrees of freedom as discussed by the authors.
Abstract: : The liquefaction shock wave, a compression shock which converts vapour into liquid, has been experimentally produced as the reflected shock at the closed end of a shock tube in test fluids with many molecular degrees of freedom Measurements of pressure, temperature, index of refraction and shock velocity confirm the existence of the shock and its general conformity to classical Rankine-Hugoniot conditions Normal and stereoscopic photography confirms the existence of a clear liquid phase and reveals small two-phase torus-form vortex rings, which are formed in or near the shockfront and move in the same direction as, but less rapidly than the shock wave, ie, the rings move away from the closed end of the shock tube If the fluid behind the shock is a mixture of droplets and vapour (partial liquefaction) evidence of shock splitting at the phase boundary is found
TL;DR: In this article, the cavity characteristics of symmetrical wedge are clarified through the Mach number range and the results from normal and oblique shock waves of supersonic liquid flow are pointed out.
Abstract: Some notable features of normal and oblique shock waves of supersonic liquid flow are clarified and also the close relations of cavity streamline to the flow turning by expansion wave are pointed out. And then after defining the Mach number range for transonic and supersonic liquid flow by using the critical Mach number, the governing equations of parabolic and hyperbolic types for velocity potential are analytically solved by local linearization technique. Compressibility effects on the cavity characteristics of symmetrical wedge are clarified through the Mach number range . Comparisons are also made with the results from oblique shock relations.
30 Apr 1981
TL;DR: In this article, the transition boundaries for a triatomic gas between various types of shock-wave reflection configurations (regular reflection, single Mach reflection, complex Mach reflection and double Mach reflection) were studied experimentally using CO2 as the test gas.
Abstract: : Transition boundaries for a triatomic gas between various types of shock-wave reflection configurations--regular reflection (RR), single Mach reflection (SMR), complex Mach reflection (CMR), and double Mach reflection (DMR)--exhibited by a plane shock impinging on a compressive corner in a shock tube were studied experimentally using CO2 as the test gas. The shock Mach numbers ranged from 1.8 to 10.2, and the initial pressure from 3.5 to 80 torr at room temperature. The regions corresponding to the four types of reflection were obtained in terms of the shock Mach number, Ms, and the wedge angle, theta sub w. The resultant transition map in the Ms - theta sub w plane will be of value to future researchers in the field as an aid in designing their experiments. Excellent agreement was obtained between the transition boundary from CMR to DMR according to the criterion proposed by Ben-Dor & Glass that the flow downstream of the reflected shock should be sonic relative to the kink of the reflected shock for the transition to occur and the results of the present experiments. This fact will further confirm the validity of their criterion. The density contours of the flow fields were obtained by means of infinite-fringe interferograms, some of which, particularly those of CMR and DMR, were hitherto unavailable in the literature. They may prove valuable for comparison with the results of numerical simulation of the phenomena, which is currently the subject of intense research at various institutions.
01 Jul 1981
TL;DR: In this article, the effect of surface roughness on the shock transition over flat wedges in quasi-stationary flows is examined experimentally on the Institute of High Speed Mechanics 40 mm x 80 mm shock tube equipped with a double exposure holographic interferometer.
Abstract: : The effect of surface roughness on the shock transition over flat wedges in quasi-stationary flows is examined experimentally. For flat wedges saw-toothed roughnesses a mesh No. 40 sand paper and a mesh No. 320 sand paper were used. Experiments were conducted on the Institute of High Speed Mechanics 40 mm x 80 mm shock tube equipped with a double exposure holographic interferometer. The incident shock Mach number range was 1.04 to 4.0 for nitrogen or dry air. In the case of curved wedges, the shock transition angles were determined by means of streak camera technique with curved slits.
TL;DR: In this article, the authors examined the transport equations for the amplitude of 3D shock waves in nonlinear elastic fluids and showed that, with the exception of the term which contains the mean curvature of the shock surface, they are almost identical to the transport equation for 1-dimensional nonlinear solids if they replace the stress, strain and velocity in the latter by the pressure, specific volume and normal velocity, respectively.
TL;DR: In this article, a cylindrical reactive blast wave was generated in a rectangular shock tube by the incidence of a detonation wave on a two-dimensional converging-diverging nozzle, with a narrow throat, placed in the tube.
Abstract: Cylindrical reactive blast waves were generated in a rectangular shock tube by the incidence of a detonation wave on a two-dimensional converging-diverging nozzle, with a narrow throat, placed in the tube. The observed trajectories of the shock front and reaction zone in the diverging section show that the blast wave behaves in a similar manner to that of the lead shock in a detonation cell. One particular similarity is the abrupt rate of decay that occurs in both types of waves following the decoupling of the exothermic reaction zone from the frontal shock. From the post-shock density field, obtained by a Mach-Zehnder interferometer, and the velocity profile, it is shown how the locus of the reaction zone may be calculated. A comparison is made of the predicted and observed reaction zone trajectories for oxyacetylene at an initial pressure of 15 Torr; these agree well for an assumed value of the activation energy of 71 kJ mol-1 for this system. It is suggested that the nozzle technique could be used for induction-delay measurements in detonation waves.
TL;DR: In this article, the uniform density region that develops behind a rarefaction shock in planar geometry is modified by geometric divergence into a region of self-similar flow with nonvanishing gradients.
Abstract: The uniform density region that develops behind a rarefaction shock in planar geometry (and attaches downstream to the outer expansion flow) is shown to be modified by geometric divergence into a region of self‐similar flow with nonvanishing gradients. A single set of equations is derived that describes both shock and similarity flow. The longest gradient scale length in the transition region is shown to vary linearly with the radius at the shock.
31 Mar 1981
TL;DR: In this article, the main contribution is the development of the experimental technique of using exploding wires to generate N-waves in the UTIAS Travelling-Wave Sonic-Boom Simulator and from supersonic aircraft.
Abstract: : The present work has as its main contribution the development of the experimental technique of using exploding wires to generate N-waves. Consideration is also given to N-waves generated by sparks, in the UTIAS Travelling-Wave Sonic-Boom Simulator and from supersonic aircraft. (Author)
TL;DR: In this paper, a general theory of ionizing shock waves in a magnetic field has been constructed, which takes into account precursor ionization of a neutral gas ahead of the shock wave front, caused by photo-ionization, as well as by the impact ionization with electrons accelerated by a transverse electric field induced by the shock front in the incident flow of neutral gas.
Abstract: The general theory of ionizing shock waves in a magnetic field has been constructed. The theory takes into account precursor ionization of a neutral gas ahead of the shock wave front, caused by photo-ionization, as well as by the impact ionization with electrons accelerated by a transverse electric field induced by the shock front in the incident flow of a neutral gas. The concept of shock wave ionization stability, being basic in the theory of ionizing shock waves in a magnetic field, is introduced. An additional equation for the electric field in the shock wave is obtained. This equation, together with the investigation of the singular point in the downstream flow behind the shock wave front, provides all the information required for solving the problem. For example, this provides two additional boundary conditions for the shock waves of type 2, determining the value and direction of the electric field in the incident flow. One additional boundary condition determines a relation between the value and direction of the electric field for supersonic shock waves of type 3. There are no additional boundary conditions for supersonic shock waves of type 4. The electric field ahead of the shock front has two degrees of freedom. As well as for shocks of other types, its value is less than that of the transverse electric field at which an ionization wave could be emitted by the shock wave front (the ionization stability condition). The additional relationship for supersonic waves of type 4 determines the onset of an isomagnetic (viscous) jump in the structure of the shock wave front. The boundary conditions and ionizing shock wave structures, considered earlier by the authors of the present paper in the ' limit of electrostatic breakdown', as well as the structural determination of the electric field, considered earlier by Leonard, are limiting cases in the theory developed here. The ionizing shock wave structures are shown to transform from the GD regime at a low shock velocity to the MHD regime at an enhanced intensity of the shock wave. The abruptness of such a transition (e.g. the transition width on the Mach number scale) is determined by precursor photo-ionization.