Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena

Transcription

1 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena Ya. B. Zel'dovich and Yu. P. Raizer Academy of Sciences, Moscow Edited by Wallace D. Hayes and Ronald F. Probstein Princeton University Massachusetts Institute of Technology DOVER PUBLICATIONS, INC. Mineola, New York

2 Contents PREFACE TO THE DOVER EDITION EDITORS' FOREWORD PREFACE TO THE ENGLISH EDITION PREFACE TO THE FIRST RUSSIAN EDITION PREFACE TO THE SECOND RUSSIAN EDITION vi vii xi ХШ XVÜ I. Elements of gasdynamics and the classical theory of shock waves 1. Continuous flow of an inviscid nonconducting gas 1 1. The equations of gasdynamics 1 2. Lagrangian coordinates 4 3. Sound waves 7 4. Spherical sound waves Characteristics Plane isentropic flow. Riemann invariants Plane isentropic gas flow in a bounded region Simple waves Distortion of the wave form in a traveling wave of finite amplitude. Some properties of simple waves The rarefaction wave The centered rarefaction wave as an example of self-similar gas motion ' On the impossibility of the existence of a centered compression wave Shock waves Introduction to the gasdynamics of shock waves Hugoniot curves Shock waves in a perfect gas with constant specific heats Geometric interpretation of the laws governing compression shocks Impossibility of rarefaction shock waves in a fluid with normal thermodynamic properties Weak shock waves Shock waves in a fluid with anomalous thermodynamic properties XIX

3 XX CONTENTS 3. Viscosity and heat conduction in gasdynamics Equations of one-dimensional gas flow Remarks on the second viscosity coefficient Remarks on the absorption of sound The structure and thickness of a weak shock front Various problems Propagation of an arbitrary discontinuity Strong explosion in a homogeneous atmosphere Approximate treatment of a strong explosion Remarks on the point explosion with counterpressure Sudden isentropic expansion of a spherical gas cloud into vacuum Conditions for the self-similar sudden expansion of a gas cloud into vacuum 104 II. Thermal radiation and radiant heat exchange in a medium 1. Introduction and basic concepts Mechanisms of emission, absorption, and scattering of light in gases Equilibrium radiation and the concept of a perfect black body Induced emission 118 4a. Induced emission of radiation in the classical and quantum theories and the laser effect The radiative transfer equation Integral expressions for the radiation intensity Radiation from a plane layer The brightness temperature of the surface of a nonuniformly heated body Motion of a fluid taking into account radiant heat exchange The diffusion approximation The "forward-reverse" approximation Local equilibrium and the approximation of radiation heat conduction Relationship between the diffusion approximation and the radiation heat conduction approximation Radiative equilibrium in stellar photospheres Solution to the plane photosphere problem Radiation energy losses of a heated body Hydrodynamic equations accounting for radiation energy and pressure and radiant heat exchange The number of photons as an invariant of the classical electromagnetic field 172 III. Thermodynamic properties of gases at high temperatures 1. Gas of noninteracting particles Perfect gas with constant specific heats and invariant number of particles 176

4 CONTENTS XXI 2. Calculation of thermodynamic functions using partition functions Dissociation of diatomic molecules Chemical reactions Ionization and electronic excitation The electronic partition function and the role of the excitation energy of atoms Approximate methods of calculation in the region of multiple ionization Interpolation formulas and the effective adiabatic exponent The Hugoniot curve with dissociation and ionization The Hugoniot relations with equilibrium radiation Gases with Coulomb interactions Rarefied ionized gases Dense gases. Elements of Fermi Dirac statistics for an electron gas The Thomas Fermi model of an atom and highly compressed cold materials Calculation of thermodynamic functions of a hot dense gas by the Thomas Fermi method 229 IV. Shock tubes 1. The use of shock tubes for studying kinetics in chemical physics Principle of operation Elementary shock tube theory Electromagnetic shock tubes' Methods of measurement for various quantities 243 V. Absorption and emission of radiation in gases at high temperatures 1. Introduction. Types of electronic transitions 246 I. Continuous spectra Bremsstrahlung emission from an electron in the Coulomb field of an ion 248 2a. Bremsstrahlung emission from an electron scattered by a neutral atom Free-free transitions in a high-temperature ionized gas Cross section for the capture of an electron by an ion with the emission of a photon Cross section for the bound-free absorption of light by atoms and ions Continuous absorption coefficient in a gas of hydrogen-like atoms Continuous absorption of light in a monatomic gas in the singly ionized region Radiation mean free paths for multiply ionized gas atoms 277

5 ххн CONTENTS 8а. Absorption of light in a weakly ionized gas Atomic line spectra Classical theory of spectral lines Quantum theory of spectral lines. Oscillator strength The absorption spectrum of hydrogen-like atoms. Remarks on the effect of spectral lines on the Rosseland mean free path Oscillator strengths for the continuum. The sum rule Radiative emission in spectral lines Molecular band spectra Energy levels of diatomic molecules Structure of molecular spectra The Frank-Condon principle Probability of molecular transitions with the emission of light Light absorption coefficient in lines Molecular absorption at high temperatures More exact calculation of the molecular absorption coefficient at high temperatures Air Radiative properties of high-temperature air Breakdown and heating of a gas under the action of a concentrated laser beam Breakdown Absorption of a laser beam and heating of a gas after initial breakdown 343 VI. Rates of relaxation processes in gases 1. Molecular gases Establishment of thermodynamic equilibrium Excitation of molecular rotations Rate equations for the relaxation of molecular vibrational energy Probability of vibrational excitation and the relaxation time Rate equation for dissocation of diatomic molecules and the relaxation time Atom recombination rates and dissociation rates for diatomic molecules Chemical reactions and the activated complex method Oxidation of nitrogen Rate of formation of nitrogen dioxide at high temperatures Ionization and recombination. Electronic excitation and deexcitation Basic mechanisms Ionization of unexcited atoms by electron impact 386

6 CONTENTS ХХШ 12. Excitation of atoms from the ground state by electron impact. Deexcitation Ionization of excited atoms by electron impact Impact transitions between excited states of an atom Ionization and excitation by heavy particle collisions Photoionization and photorecombination Electron-ion recombination by three-body collisions (elementary theory) A more rigorous theory of recombination by three-body collisions Ionization and recombination in air Plasma Relaxation in a plasma 416 The Cited References, Author Index, and Subject Index listed on this page relate to chapters I -VI only. All three items for the entire work are listed at the end of the Contents. CITED REFERENCES 422 APPENDIX: SOME OFTEN USED CONSTANTS, RELATIONS BETWEEN UNITS, AND FORMULAS 441 AUTHOR INDEX 447 SUBJECT INDEX 452 VII. Shock wave structure in gases 1. Introduction The shock front Viscous shock front The role of viscosity and heat conduction in the formation of a shock front Diffusion in a binary gas mixture Diffusion in a shock wave propagating through a binary mixture The relaxation layer Shock waves in a gas with slow excitation of some degrees of freedom Excitation of molecular vibrations Dissociation of diatomic molecules Shock waves in air Ionization in a monatomic gas Ionization in air Shock waves in a plasma Polarization of a plasma and the creation of an electric field in a shock wave Radiant heat exchange in a shock front Qualitative picture Approximate formulation of the problem of the front structure The subcritical shock wave The supercritical shock wave Shock waves at high energy densities and radiation pressures 543

7 XXIV Contents VIII. Physical and chemical kinetics in hydrodynamic processes 1. Dynamics of a nonequilibrium gas The gasdynamic equations in the absence of thermodynamic equilibrium Entropy increase Anomalous dispersion and absorption of ultrasound The dispersion law and the absorption coefficient for ultrasound Chemical reactions Oxidation of nitrogen in strong explosions in air Disturbance of thermodynamic equilibrium in the sudden expansion of a gas into vacuum Sudden expansion of a gas cloud Freezing effect Disturbance of ionization equilibrium The kinetics of recombination and cooling of the gas following the disturbance of ionization equilibrium Vapor condensation in an isentropic expansion Saturated vapor and the origin of condensation centers The thermodynamics and kinetics of the condensation process Condensation in a cloud of evaporated fluid suddenly expanding into vacuum On the problem of the mechanism of formation of cosmic dust. Remarks on laboratory investigations of condensation 595 IX. Radiative phenomena in shock waves and in strong explosions in air 1. Luminosity of strong shock fronts in gases Qualitative dependence of the brightness temperature on the true temperature behind the front Photon absorption in cold air Maximum brightness temperature for air Limiting luminosity of very strong waves in air Optical phenomena observed in strong explosions and the cooling of the air by radiation General description of luminous phenomena Breakaway of the shock front from the boundary of the fireball Minimum luminosity effect of the fireball Radiation cooling of air Origin of the temperature drop the cooling wave 628

8 Contents XXV 10. Energy balance and propagation velocity of the cooling wave Contraction of the cooling wave toward the center The spark discharge in air Structure of cooling wave fronts Statement of the problem Radiation flux from the surface of the wave front Temperature distribution in the front of a strong wave Consideration of adiabatic cooling 648 X. Thermal waves 1. The thermal conductivity of a fluid Nonlinear (radiation) heat conduction Characteristic features of heat propagation by linear and nonlinear heat conduction The law of propagation of thermal waves from an instantaneous plane source Self-similar thermal waves from an instantaneous plane source Propagation of heat from an instantaneous point source Some self-similar plane problems Remarks on the penetration of heat into moving media Self-similar solutions as limiting solutions of nonself-similar problems Heat transfer by nonequilibrium radiation 681 XI. Shock waves in solids 1. Introduction Thermodynamic properties of solids at high pressures and temperatures Compression of a cold material Thermal motion of atoms Equation of state for a material whose atoms undergo small vibrations Thermal excitation of electrons A three-term equation of state The Hugoniot curve Hugoniot curve for a condensed substance Analytical representation of Hugoniot curves Weak shock waves Shock compression of porous materials Emergence of weak shock waves from the free surface of a solid Experimental methods of determining Hugoniot curves for solids Determination of cold compression curves from the results of shock compression experiments 730

9 XXVI Contents 3. Acoustic waves and splitting of waves Til 14. Static deformation of a solid Transition of a solid medium into the plastic state Propagation speed of acoustic waves Splitting of compression and unloading waves Measurement of the speed of sound in a material compressed by a shock wave Phase transitions and splitting of shock waves Rarefaction shock waves in a medium undergoing a phase transition Phenomena associated with the emergence of a very strong shock wave at the free surface of a body Limiting cases of the solid and gaseous states of an unloaded material Criterion for complete vaporization of a material on unloading Experimental determination of temperature and entropy behind a very strong shock by investigating the unloaded material in the gas phase Luminosity of metallic vapors in unloading Remarks on the basic possibility of measuring the entropy behind a shock wave from the luminosity during unloading Some other phenomena Electrical conductivity of nonmetals behind shock waves Measuring the index of refraction of a material compressed by a shock wave 781 XII. Some self-similar processes in gasdynamics 1. Introduction Transformation groups admissible by the gasdynamic equations Self-similar motions Conditions for self-similar motion Two types of self-similar solutions Implosion of a spherical shock wave and the collapse of bubbles in a liquid Statement of the problem of an imploding shock wave Basic equations Analysis of the equations Numerical results for the solutions Collapse of bubbles. The Rayleigh problem Collapse of bubbles. Effect of compressibility and viscosity The emergence of a shock wave at the surface of a star Propagation of a shock wave for a power-law decrease in density On explosions of Supernovae and the origin of cosmic rays 817

10 Contents xxvu 4. Motion of a gas under the action of an impulsive load Statement of the problem and general character of the motion Self-similar solutions and the energy and momentum conservation laws Solution of the equations Limitations on the similarity exponent imposed by conservation of momentum and energy Passage of the nonself-similar motion into the limiting regime and the " infinite " energy in the self-similar solution Concentrated impact on the surface of a gas (explosion at the surface) Results from simplified considerations of the self-similar motions for concentrated and line impacts Impact of a very high-speed meteorite on the surface of a planet Strong explosion in an infinite porous medium Propagation of shock waves in an inhomogeneous atmosphere with an exponential density distribution Strong point explosion Self-similar motion of a shock wave in the direction of increasing density Application of the self-similar solution to an explosion Self-similar motion of a shock wave in the direction of decreasing density Application to an explosion 859 CITED REFERENCES 864 APPENDIX: SOME OFTEN USED CONSTANTS, RELATIONS BETWEEN UNITS, AND FORMULAS 881 AUTHOR INDEX 887 SUBJECT INDEX 896