Propagation and Reflection of Shock Waves

The following sections are included:

• PREFACE

• LIST OF SYMBOLS

• CONTENTS

The following sections are included:

• General remarks

• Interaction of shock waves
  • Head-on interaction of shock waves
  • Oblique interaction of shock waves

• Shock tube as an apparatus for obtaining shock waves in the laboratory

The following sections are included:

• Basic notions

• Compatibility conditions

• Ray method for calculation of unsteady shock waves

• Path of a particle behind a shock wave

• Distribution of flow parameters behind an unsteady curvilinear shock wave

The following sections are included:

• Linear interaction of shock waves with disturbances

• Propagation of a plane shock wave through a region of non-uniform density (nonlinear case)

• Nonlinear one-dimensional interaction of a weak disturbance with a shock wave

• Instability of shock waves

The following sections are included:

• Reflection of a plane wave from a body of arbitrary shape

• Transition from regular to Mach reflection

• Development of flow over a blunt body behind an incident shock wave
  • The interaction of a plane shock wave with a body
  • The interaction of a shock wave with a shock layer on a blunt body

The following sections are included:

• Reflection of a shock wave from a body with rectangular cavity

• Oscillations of the shock wave reflected from a body with cavity

• Shock focusing

• Resonant excitation of vortices behind the reflected shock wave

Propagation of a shock wave through a random medium is accompanied by nonlinear interaction of the wave with disturbances. The shock wave influences disturbances which in their turn can distort it or change its strength. The passage of a shock wave can enhance turbulent mixing (Alessandri et al. 1995)…

The motion of shock waves through particle-laden flows is of great importance for a number of practical problems, e.g. dust explosions and propulsion systems. The process is accompanied by some interesting phenomena. Shock waves decay while propagating in a gas-particle mixture. Relaxation effects arise due to differences in the rate of change for velocity and temperature between the phases…

A shock wave arises, when a breakdown occurs in a gas. Gas breakdown at optical frequencies can take place in the focused beam of a laser. The intensity of a laser beam necessary for it depends on many factors, namely, on the wavelength of laser light, gas pressure, duration of the laser pulse and so on. The formation of laser plasma occurs due to optical breakdown. It arises if the intensity of the laser beam reaches a threshold value. This value is proportional to Iω²/(τp₀), where I is the potential of ionization, ω is a frequency of laser radiation, τ is the duration of the laser pulse, p₀ is the initial gas pressure (Ready 1971). The threshold value is equal to ~ 10¹¹ W/cm² in the case of air (ruby laser; atmospheric pressure) and 10⁹ W/cm² in the case of carbon dioxide. For the first time the phenomenon of optical breakdown was studied in 1963 (Maker et al. 1964). It is interesting to note that similar processes were observed near a solid target (a low-threshold breakdown). The intensity of the beam may be reduced to 10⁷ W/cm² in the case of CO₂ laser. The phenomenon of a low-threshold breakdown was observed in 1973 (Barchukov et al. 1973). Shock waves that are produced by a focused laser beam were studied by Ramsden et al. (Ramsden and Davies 1964; Ramsden and Savic 1964). A surprising result was obtained, namely, after breakdown the spark developed asymmetrically. The luminous front moved towards the focusing lens at an initial velocity of 10⁷ cm/s. In order to explain this effect, a mechanism of a radiation-supported shock wave was proposed. After breakdown, a shock wave propagates into the undisturbed gas. Further absorption of the energy of radiation takes place in the plasma behind the shock front moving towards the lens, in the manner of a detonation wave. Light absorption in plasma is due to inverse Bremsstrahlung. A free electron absorbs a photon. The electron passes to a state of higher energy of continuous spectrum. The process must take place in the field of either an ion or an atom, or a molecule due to the law of momentum conservation…

A low-temperature plasma may be created by means of a glow discharge, in processes of combustion, by means of radiation. An interesting case is that of nonequilibrium plasma (electron temperature is not equal to that of ions or atoms). We assume the plasma to be neutral. Nevertheless, there arises an electric current in the presence of electric field. The processes that may pass in plasma are as follows: ionization, excitation of atoms and molecules, recombination, dissociation, radiation. We consider an ideal plasma (the Debye length is much greater than the mean distance between atoms and molecules)…

The following sections are included:

• APPENDIX A

• REFERENCES

• SUBJECT INDEX