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Series solution to describe hydrodynamic phase flow field during hypervelocity impact of compressible penetrating particle into ideal fluid - Hugoniot equation of state
Solutions of the Hugoniot shock equations and Meyer expansion equations are plotted in such a manner as to permit the pressure distribution, the local Mach number, and the angles of shock waves on arbitrary sharp-nose airfoils at supersonic speeds to be obtained directly. (author)
Calculation of supersonic flow field with Rankine-Hugoniot equations to compute flow properties across shock
Shock wave structure in ionized hydrogen, using Eddington approximation to solve Rankine- Hugoniot jump equation
Zero pressure densities of rock Hugoniots in high pressure phases compared with phase transitions of rock forming minerals
Radiation effects on shock wave structure from stellar postshock emission spectra observations, discussing deviations from Rankine-Hugoniot relation
Rankine-Hugoniot relations applied to shock discontinuities measured by magnetic field and plasma instruments on Explorer 34
Shock discontinuities in solar wind measured by magnetic field and plasma instruments on Explorer 34, applying Rankine-Hugoniot relations
Hugoniot equation of state measurements from shock wave loading study of Coconino sandstone
Alfven waves effect on MHD fast shock from numerical solution of extended Rankine-Hugoniot equations
Shock normal calculation by applying least squares technique to combined geomagnetic field and plasma data from single satellite, assuming Rankine-Hugoniot conservation relations
Shock wave data for Bamle enstatite in 60-480 kb range, considering Hugoniot elastic limit and phase transition produced shock front
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
An equation of state is developed for metals in the high-pressure high-temperature region that can be extended in a thermodynamically consistent manner to the vapor phase. The constants are obtained from observed thermodynamic properties and are specified for Al, Fe, Cu, Ni, Pb, and W. This equation of state was checked against experimental data by computing the Hugoniot curves for normal and porous samples for cases where experimental data are available. Also, the velocity of sound and release isentropes were computed for various shock conditions.
Magnetic-field data obtained in the earth's bow-shock region with a high-resolution triaxial fluxgate magnetometer aboard the Ogo 5 satellite have been correlated with a theory of Tidman and Northrop (1968). These authors have shown that either of two hypotheses about the nature of low-frequency magnetic waves could be invoked to explain previous observations. We have observed exponentially decaying upstream waves that are consistent with only one of these hypotheses. This observation allows use of the theory to infer the local shock velocity and frequency of driving currents within the shock. This method of finding the shock velocity is less sensitive to errors in the plasma parameters than is the method based on the Rankine-Hugoniot relations.
Hugoniot measurements on iron-silicate garnet demonstrate that above a shock pressure of about 205 kbar transition to a high-pressure phase(s), having an apparent zero-pressure density and bulk modulus of 4.44 g/cu cm and 3.3 Mbar, occurs. Crystal chemical systematics and Debye-Scherrer X-ray patterns of a recovered phase(s), which may be the shock-induced high-pressure form, suggest possible formation of a phase with a density of 4.48/cu cm. Occurrence of such a polymorph of garnet in the mantle would give rise to an increase in density and seismic velocity below 600 km in the earth.
This paper deals with the influence of thermal anisotropy on least-squares estimates of interplanetary shock parameters and the associated normals by using the Rankine-Hugoniot equations. A practical theorem is given for quantitatively correcting for anisotropic effects by weighting the before and after magnetic fields by the same 'anisotropy parameter' h. The quantity h depends only on the thermal anisotropies before and after the shock and on the angles between the magnetic fields and the shock normal. It is shown that, for fast shocks and for a liberal range of realistic conditions, the quantity h lies in the range from 0.90 to 1.22. The theorem can also be applied to most slow shocks, but in those instances h usually should be lower and sometimes markedly lower than unity.
The detailed plasma (except for electrons) and magnetic field data from Pioneer 7 are presented for a proposed double-shock ensemble. The Ames Research Center plasma probe data are compared with that of the MIT probe. These data are compared with MHD theory to show that the discontinuities themselves satisfy the magnetic Hugoniot equations. The data are also compared with the theoretical predictions for the double-shock structure. The theory requires as input only the forward shock velocity, the original ambient solar wind conditions, and a reasonable assumption regarding the density and azimuthal magnetic field in the 'new' solar wind which is detected after passage of the reverse shock. A unique solution is then obtained for the theoretical piston and reverse shock positions as well as for the temporal plasma behavior for both infinite and finite electrical conductivities.