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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Hugoniot equation of state of anorthite glass and lunar anorthosite

Twenty-one Hugoniot experiments were conducted on an amorphous material of anorthite composition, in the pressure range 8-120 GPa, using both routine and new methods. Two Hugoniot measurements at about 120 GPa were made on lunar gabbroic anorthosite (Apollo 15,418). Theoretical Hugoniots are constructed for both materials assuming they are disproportionate to their component oxides. These accurately predict the P-p behavior of the lunar anorthosite Hugoniot at 120 GPa and the anorthite glass Hugoniot above 50 GPa, but overestimate the shock temperatures of anorthite glass. The mixed oxide model fails to predict the release paths of either material. It is concluded that the mixed oxide model is a good description of the bulk properties of the high-pressure phases of anorthite, but does not represent the actual phases. A significant enrichment of calcic refractory material in the earth's lower mantle is not precluded by the bulk properties of the anorthite high-pressure phases.

Boslough, M. B.↗
NASA NTRS1986

A parametric study of slow shock Rankine-Hugoniot solutions and critical Mach numbers

The relationship between Rankine-Hugoniot solutions and critical Mach numbers is studied. The range of upstream parameters for which the resistivity or thermal conduction provide all the dissipation required by the slow shock Rankine-Hugoniot relations are evaluated. The calculation of the critical Mach number by analyzing the flux of shock catching ions is examined. It is observed that the properties of slow shocks depend on shock normal angle, and the ratio of the sound and Alfven speeds upstream. The Rankine-Hugoniot solutions are applicable to the analysis of spacecraft observations of slow shocks.

Edmiston, J. P.↗
NASA NTRS1986

The resolved layer of a collisionless, high beta, supercritical, quasi-perpendicular shock wave. I - Rankine-Hugoniot geometry, currents, and stationarity

Data collected by the ISEE dual-spacecraft mission (on November 7, 1977) on a slowly moving, supercritical, high-beta, quasi-perpendicular bow shock are presented, and the local geometry, spatial scales, and stationarity of this shock wave are assessed in a self-consistent Rankine-Hugoniot-constrained frame of reference. Included are spatial profiles of the ac and dc magnetic and electric fields, electron and proton fluid velocities, current densities, electron and proton number densities, temperatures, pressures, and partial densities of the reflected protons. The observed layer profile is shown to be nearly phase standing and one-dimensional in a Rankine-Hugoniot frame, empirically determined by the magnetofluid parameters outside the layer proper.

Scudder, J. D.↗
NASA NTRS1993

A generalized version of the Rankine-Hugoniot relations including ionization, dissociation and related phenomena

For purposes of computing shocks in stellars atmospheres and winds we have developed a generalized version of the Rankine-Hugoniot relations including ionization, dissociation, radiation and related phenomena such as excitation, rotation and vibration of molecules. The new equations are given in analytical form. They are valid as long as the internal energy E, the total pressure P, and the first adiabatic coefficient gamma(sub 1) can be evaluated. However, we have not treated shock structures. In the case of non-LTE we have to employ an approximation for gamma(sub 1) because in that case no definition exists. Our new version of the Rankine-Hugoniot relations can easily be used for many purposes including ab-initio modeling. In our derivation we introduce a parameter gamma(sub H), which is definded as the ratio of the enthalpy H (sometimes called heat function w) to the internal energy E (sometimes called U). Using this parameter we solve the equations for changing mu and (d(natural log P)/d(natural log rho))(sub ad) identically equal to gamma(sub 1) on both sides of the shock. Both gamma(sub H) and gamma(sub 1), and also mu are functions of pressure P and temperature T. We present: (1) the derivation, (2) examples of gamma(sub 1) (P,T) and gamma(sub H) (P,T) which include/exclude ionization and radiation, and (3) as an example the differences in post-shock parameters as function of the pre-shock temperature for the case with ionization and without radiation.

Nieuwenhuijzen, H.↗
NASA NTRS1972

Modification of the Rankine-Hugoniot relations for shocks in space.

The Rankine-Hugoniot (R-H) equations for hydromagnetic shocks are extended to take into consideration the energy flux and momentum flux due to waves and/or turbulence and/or heat flow in the vicinity of shocks. Eighteen shocks obseved in space were analyzed. It is found that, in order to satisfy the R-H relations with the values of measured parameters in space, waves and/or turbulence and/or heat flow are needed for the shocks with a Mach number of greater than 2, and no waves and/or turbulence are needed to satisfy the R-H equations for the shocks with a Mach number of less than 2. A discussion of the waves, turbulence, and heat flow is given. Fluctuations may considerably affect the time-averaged R-H relations.

Chao, J. K.↗
NASA NTRS1980

Estimation of uncertainty in isotherms deduced from Hugoniots resulting from shockwave generated defects

The problem of how defect concentrations produced in a shock experiment affect the isothermal equation of state is considered. From the few experimental results available that bear directly on this question, it appears the effect could be substantial, i.e., the pressure in material free of defects may be 10-25% lower at a given volume than the isothermal pressure deduced from Hugoniot data on the assumption that defects are negligible in the shocked material. This correction caused by the presence of defects is called the defect pressure.

Ruoff, A. L.↗
NASA NTRS1989

MHD intermediate shock discontinuities. I - Rankine-Hugoniot conditions

Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic.

Kennel, C. F.↗
NASA NTRS1980

Shock effects in olivine and implications for Hugoniot data

New observations of shock deformation in single-crystal olivine are presented for the range in peak pressures from about 16 to 75 GPa. A nonequilibrium model is suggested for the behavior of olivine under shock which explains the densification associated with a mixed-phase region and which is consistent with all available observations, yet which bears little similarity to the equilibrium behavior of olivine at high pressure.

Jeanloz, R.↗
NASA NTRS1985

Fast and optimal solution to the Rankine-Hugoniot problem

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.↗
NASA NTRS1986

Fast and optimal solution to the 'Rankine-Hugoniot problem'

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.↗
NASA NTRS1991

Effect of void-size distribution on the Hugoniot state at low shock pressures

In most theoretical and experimental investigations into the shock response of underdense solid media, the influence of the medium's mesostructure on the resulting pressure and degree of compaction has not been taken into account. In typical cases examined, shock pressures are well in excess of 1 GPa and this approach is clearly justified. However, at low pressures, calculations show that the distribution of void sizes can affect the final state achieved upon shocking the medium from a given initial porosity. This paper analyzes the response of porous aluminum to low pressure shocking and demonstrates a dependence of the final shocked state on the distribution of void sizes.

Griffiths, David J.↗
NASA NTRS1994

An improved solution to the 'Rankine-Hugoniot' problem

This paper presents an extension of the nonlinear least squares fitting technique of Vinas and Scudder (1986) (VS), which finds the physical and geometrical properties of nondissipational magnetohydrodynamic (MHD) shocks. The new method incorporates plasma temperature observations in the form of normal momentum flux and energy density flux conservation as well as plasma density, velocity, and magnetic field data. The new technique is capable of using known standard deviations in the individual measurement points to properly weight the fitting procedure. The new fitting code is validated through the analysis of synthetic shocks with known physical and geometrical properties. Finally, it is compared to the original VS method and the preaveraged velocity coplanarity technique.

Szabo, A.↗
NASA NTRS1973

Shock compression of a recrystallized anorthositic rock from Apollo 15

Hugoniot measurements on 15,418, a recrystallized and brecciated gabbroic anorthosite, yield a value of the Hugoniot elastic limit (HEL) varying from 45 to 70 kbar as the final shock pressure is varied from 70 to 280 kbar. Above the HEL and to 150 kbar, the pressure-density Hugoniot is closely described by a hydrostatic equation of state constructed from ultrasonic data for single-crystal plagioclase and pyroxene. Above 150 kbar, the Hugoniot states indicate that a series of one or more shock-induced phase changes are occurring in the plagioclase and pyroxene. From Hugoniot data for both the single-crystal minerals and the Frederick diabase, we infer that the shock-induced high-pressure phases in 15,418 probably consists of a 3.71 g/cu cm density, high-pressure structure for plagioclase and a 4.70 g/cu cm perovskite-type structure for pyroxene.

Ahrens, T. J.↗
NASA NTRS1976

The sodium chloride primary pressure gauge

The failure of a central force model for sodium chloride is discussed. It is noted that it does not closely satisfy the Cauchy conditions at low temperatures, and that it fails the central force requirement of the Love condition. The available shock data for sodium chloride and its analysis is examined, and two reasons why the Hugoniot transformation pressure is likely to be less than 231 kbar are discussed. The important (but unjustified) theoretical assumptions made in converting Hugoniot to isothermal data is discussed; it is noted that serious error can enter for very large pressures for a given material and that at such high pressures the isothermal data should thus be considered only semiquantitative even if the Hugoniot data itself is accurate. An alternate method of estimating the isothermal transformation pressure from the Hugoniot transformation pressure is used. This method is based on the temperature derivative of the transformation pressure. On this basis it is concluded that an upper bound for the isothermal transformation of NaCl (to a CsCl-type structure) at room temperature is 257 kbar; it is noted that the actual value may be considerably less than this.

Ruoff, A. L.↗
NASA NTRS1983

Shock-wave properties and high-pressure equations of state of geophysically important materials

Shock wave (Hugoniot), shock temperature, and release data are presented for several geophysically important, refractory materials. A sensitive multichannel optical pyrometer was developed to measure shock temperatures (2500 to 5600 K at pressures from 48 to 117 GPa) in anorthite (CaAl2Si2O8) glass. Shock temperatures of 3750 to 6000 K at pressures from 140 to 182 GPa were measured in calcium oxide (CaO). Temperature data were used to constrain the energetics of the B1-B2 phase transition at 70 GPa in CaO, and to construct a finite strain equation of state for CaO consistent with previous Hugoniot data. The CaO equation of state was used with equation of state parameters of other oxides to construct a theoretical mixed oxide Hugoniot of anorthite, which is in agreement with new Hugoniot data above about 50 GPa, determined using experimental techniques developed. The mixed oxide model, however, overestimates the shock temperatures, and does not accurately predict measured release paths.

Boslough, M. B.↗