Incident Shock Mach Number Research Articles

218 画像処理による炭酸ガス中の弱い衝撃波の観測

In order to obtain small density variations in flow field, an image processing system for analyzing interferograms is developed. A Mach-Zehnder interferometer is used for visualization of flow field, and images are directly taken by a CCD-camera. The image is displayed immediately after each shot, and processed on a personal computer. Using this system, weak shock waves in carbon dioxide are observed for incident shock Mach number 1.02 to 1.06 and initial pressure 147 to 196 kPa. This paper presents the detail of density distribution of flow fields, which are generated by weak shock waves, passing over a hemicylinder and reflecting from wedges, in carbon dioxide.

Collision of a shock wave with obstacles in a combustible mixture

For flame propagation in tubes or channels filled with obstacles, it was observed that deflagration to detonation transition (DDT) occurred mostly in the vicinity of an obstacle. Furthermore, onset of detonation originated near the upstream side of the obstacle. This observation suggests that the interaction between the leading shock front of an accelerated flame with the obstacles along its path plays an important role in the transition process. To understand this interaction, initiation of detonation resulting from a collision of a shock wave with obstacles (repeated baffles and wedge-baffle combination) was studied in a 9 × 9 cm channel containing hydrogen-oxygen mixtures. Stroboscopic schlieren photographs showed that shock-focusing, from shock diffraction and reflection, can create local hot spots capable of causing a strong ignition develops into a detonation wave. For collision of a shock wave with a wedge-baffle combination in a stoichiometric H 2O 2 mixture at 7.9 kPa (60 torr) initial pressure, the critical incident shock Mach number was measured to be about 2.25. This critical value depends on the wedge angle as well as the size of the baffle obstacle. Even though the effects of turbulence in DDT have been well documented, present results suggest that for highly accelerated flames (with flame speed approaching that of a CJ deflagration), local heating by shock-focusing, resulting from a collision of the leading shock with obstacles, is sufficient to cause transition to detonation.

Deformation Problems of Gas Interfaces of Different Densities Generated by Shock Waves. Light/Heavy Interface.

This paper reports numerical and analytical studies of the interaction problem between a gas interface of different densities and shock waves. The interface is formed between air and SF6 (light/heavy interface, i. e., the incident shock wave propagates from air to SF6), and there is a sinusoidal perturbation on the initial interface. The interface deformation process and the growth rate of a sinusoidal perturbation on the interface are investigated after shock wave interaction. Numerical simulation is carried out using the second-order TVD finite difference scheme, and the Euler equations are solved. Theoretical impulsive growth rate obtained using the stable velocities on the interface after shock interaction is compared with results of the numerical simulation. In the case of incident shock Mach numbers Ms < 2 and amplitudes of perturbed interface η0k < 1, good agreement is obtained.

Numerical Analysis of Reflection of Weak Shock Waves by Symmetric V-Shaped Reflector.

Analytical solutions of the wave equation for pressure fields generated by reflection of plane waves from symmetric V-shaped reflectors consisting of two triangles are expressed as three combinations of a function which represents pressure field induced around a wedge or a corner. In order to compare the analytical results of the wave equation with numerical results of gasdynamics, simulations are conducted for reflection of a plane shock wave at the incident shock Mach number of 1.05 from several V-shaped reflectors employing an explicit TVD scheme. Comparisons of pressure fields between the computed and the analytical results show good agreement.

Simulations of Shock Reflection Phenomena in Noncondensable and Condensable Gases.

Simulations are performed for reflection of shock waves at an end wall in noncondensable and condensable gases in a shock tube by numerically solving the Navier-Stokes equations subject to the appropriate boundary conditions using the explicit TVD scheme. Numerical solutions obtained here are compared with those of the Boltzmann equation of BGK type. Good qualitative agreements are obtained between the two solutions for both noncondensable and condensable cases. Hence, the Navier-Stokes equations with the appropriate boundary conditions are shown to be adequate for simulations of gasdynamics phenomena on a scale of the mean free path. Some appreciable discrepancies, however, appear between the numerical solutions of the Navier-Stokes equations and those of the Boltzmann equation as the incident-shock Mach number increase.

Experimental and computational studies focusing processes of shock waves reflected from parabolic reflectors

This paper describes experimental and numerical studies of the focusing process of shock waves reflected from various shapes of a parabolic reflector. The effect of incident shock strength on the focusing process was also investigated. Experiments were carried out in a conventional shock tube and a test gas was air for incident shock Mach numbers ranging from 1.1 to 2.0. In the experiments, the process of shock focusing was visualized by schlieren method. Numerical simulations were conducted for incident shock Mach numbers up to 3.0 by solving the two-dimensional unsteady Euler equations. The numerical results were compared with experiment for various parabolic reflector shapes and for various incident shock Mach numbers. Based on the experimental and computational results, the pattern of shock focusing and shock focusing mechanism are discussed.

Shock wave interaction with area changes in ducts

Whitham's approximation for handling shock wave propagation in area changes (reductions) in a duct was checked in comparison with a numerical solution. Also the Whitham approximation for shock wave propagation from a constant cross-sectional duct to a duct of a smaller cross-sectional area was studied and compared with a numerical solution. It was found that for modest incident shock Mach numbers and modest area reductions the Whitham approximation provided a fair solution for the shock Mach number and for the post-shock pressure. For higher shock Mach numbers and/or area reductions, large discrepancies exit between the approximate and exact solutions. A wider range of applicability of the Whitham approximation is found for the monotonical area reduction case; it is quite narrow for the passage of a shock wave from a wider to a narrower duct case. In addition, the effect of the extent of the area change region on the time required for reaching a quasi-steady flow was studied. It was shown that the longer the area change segment is, the longer it takes to reach a quasi-steady flow.

One-Dimensional Interaction between Shock Wave and Low-Porosity Foam. 1st Report. Experiments.

Experimental studies on the interaction between a shock wave and a low-porosity foam are conducted by using a shock tube 125 mm in inner diameter and 10080 mm in length. The density of the experimental polyurethane foam is 284 kg/m3. Stress-strain relationships of the foam are investigated experimentally. The purpose is to investigate the effect of the impact of the gas dynamic shock wave on the unsteady deformation of the foam. One end of the foam is fixed to the end wall of the shock tube, and the shock tube flow is initiated by the quick acting valve. Experiments are conducted in the shock tube for incident shock Mach numbers of 1.7 and 1.9. Experimental time histories of the surface stress of the foam at the end of the shock tube show damping vibrations approaching the gas dynamic pressure of the reflected shock wave, and the peak stresses amount to several times the pressure of the reflected shock wave.

Experimental Analysis of Reflected Shock Behavior over a Wedge with Suface Roughness. Local Behavior.

Detailed experimental analysis has been made on shock reflection over a wedge with surface roughness in a shock tube. The incident shock Mach number M was 1. 43. The experimental parameters were the reflecting wedge angle and the size of gutters. The wave structure is similar amongst model wedges. Detailed measurement into the triple point trajectory shows that it is not a straight line but a slowly varying curve with a kink point where the slope of the tangent to the curve increases discontinuously and that the kink point coincides with the location where the secondary shock, formed by the accumulation of waves reflected from gutters, overtakes the triple point. Three effective values are introduced for experimental analysis of this essentially unsteady phenomenon. Before the kink point the effective angles of incidence and reflection differ greatly from those obtained from the three-shock theory. The angles agree fairly well with the theory beyond this point.

Deformation, Collapse and Interaction of Two Tandem Liquid Columns Exposed to a Shock Wave.

This paper describes deformation, collapse and interaction of two tandem liquid columns exposed to a shock wave and shock-induced high-speed airflow. Experiments are conducted in a shock tube for incident shock Mach number 1.47 in air. Shattering processes of two tandem water columns set in the airflow direction are observed using holographic interferometry. The shattering process is characterized by three stages ; however, the shattering mechanism is different in the last stage. Time variations of longitudinal and transverse diameters, and mass of the two shattering water columns are measured from the interferograms. Experimental results are compared with results for a single water column. It is revealed that a strong interference exists between the two tandem water columns.

Numerical Analysis of Shock Waves Reflected from an Axisymmetrical Parabolic Wall.

Computational studies of the reflection process of a planar shock wave on an axisymmetrical parabolic wall were performed. The effects of the incident shock strength and depth of the reflector on the reflection process and on the maximum pressure and temperature were discussed in comparison with two-dimensional cases. The results are as follows. 1) The shape of reflected shock waves varies from a crossed pattern to an uncrossed one with an increase in the incident shock strength. 2) The pressure amplitude has a very large value near a sound wave, but shows a rapid decrease and has a minimum value with the incident shock strength. Then it increases slightly and levels off for incident shock Mach numbers stronger than 4 in a monoatomic gas. 3) After the shock focusing is achieved, clear discontinuities in density and temperature are formed in the region behind the reflected shock wave.

Stability of Converging Cylindrical Shock Waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.

Stability of converging cylindrical shock waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.

An Experimental Study of Reflected Shock Wave Structure over a Wedge with Surface Roughness. 2nd Report. On the Local Structure.

Detailed experimental analysis was made on the shock reflection over a wedge with surface roughness in a shock tube. The roughness was made by gutters carved on the wedge. The incident shock Mach number was Ms=1.43. The experimental parameters were the wedge angle and size of gutters. The wave configuration in the neighborhood of the triple point on the wedge is found to be nearly similar between model wedges. Detailed insight into the triple point trajectory shows that it is not a straight line but a slowly varying curve with a kink point where the slope of the tangent to the curve increases discontinuously and that the kink point coincides with the location where the secondly developed shock wave from the gutters overtakes the triple point. The local trajectory angle was found to decrease monotonously from the leading edge to the kink point, where it increases discontinuously. It then begins to decrease again, but not as steeply as the first decreasing region. The effective incident and reflective angles differ much from the ones obtained from the three-shock theory in front of the kink point. The angles coincide fairly well after this point. It is concluded that the secondary shock wave developed from gutters plays an important role for the structue of the reflected waves in the region investigated.

Stability of converging cylindrical shock waves.

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.

A102 斜面上における反射衝撃波の画像解析

The experiment on oblique shock reflection has been carried out by means of a shock tube and a model wedge. The incident shock Mach number M was about 1.42 and the working gas was air. Waves were visualized and analyzed by schlieren photography. Attention was focused on the quantitative analysis of the unsteady behavior of the triple point. The evolution of waves were discussed from the viewpoint of its effect on the behavior of the triple point. The rarefaction wave generated at each corner of bumps pulled the triple point down, and consequently the value of the angle of reflection ?? increased abruptly.

An experimental study of reflected shock wave structure over a wedge with surface roughness.

The detailed wave structure of a reflected shock wave over a wedge with surface roughness is examined. The rough wedge has regular, two-dimensional geometric protuberances. The shape of protuberances was square in cross section and the spacing was the same as its height. The protuberances varied in size from 0.5 to 8 mm. The incident shock Mach number M was 1.4 and wedge angle varied from 20°to 45°. It is found that the geometric wave structure varies as time proceeds and a pseudostationary (self-similar) state is not attained in our experimental conditions. However the wave configurations are similar as long as the numbers of protuberances over which the incident wave traverses are the same. It is also found that there are four types of shock reflection corresponding to transition. They are MR→MR, MR→RR→MR, RR→MR, and RR→RR.

The interaction of a shock wave with the boundary layer in a reflected shock tunnel

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.

Computation of shock wave reflection by circular cylinders

The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The diffraction was followed through about 6 radii of travel of the incident shock past the cylinder. A broad range of incident shock Mach numbers are covered. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross, which included both experimental schlieren pictures and theoretical calculations using Whitham's ray/shock theory, and results of the present finite-difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects that are not accounted for by the Euler equations.