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At least 307 records · Page 17

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NASA NTRS1979

Release adiabat measurements on minerals: The effect of viscosity

The current inversion of pressure-particle velocity data for release from a high pressure shock state to a pressure-density path is analyzed. It is assumed that the release process is isentropic. It was shown that for geological materials below stresses of 150 GPa, the effective viscosity must be 1000 kg/m/s in order that the viscous (irreversible) work carried out on the material in the shock state remains small compared to the mechanical work recovered upon adiabatic rarefaction. The available data pertaining to the offset of the Rayleigh line from the Hugoniot for minerals, the magnitude of the shear stress in the high pressure shock state for minerals, and the direct measurements of the viscosities of several engineering materials shocked to pressures below 150 GPa yield effective viscosities of 1000 kg/m/s or less. An inferance that this indicates that the conditions for isentropic release of minerals from shock states are achieved, and a conclusion that the application of the Riemann integral to obtain pressure-density states along the release adiabats of minerals in shock experiments is valid are made.

Jeanloz, R.↗

NASA NTRS1979

Isentropic decompression of fluids from crustal and mantle pressures

Criteria are derived according to which the flow of single-phase magmatic fluids and the rarefaction expansion of low-viscosity liquids and gases may be considered approximately isentropic. Graphs of entropy vs. density with contours of constant pressure and mass fraction are used to examine the possible thermodynamic histories of H2O and CO2 decompressing isentropically from crustal and upper mantle pressures; these graphs offer a simple visual representation of a number of thermodynamic variables involved in isentropic processes. It is shown how the graphs can be used to examine the behavior of volatiles that (1) ascend in volcanic systems originating at different depths within the earth, and (2) decompress from a shock Hugoniot state. Entropy-density graphs are presented separately for H2O and CO2.

Kieffer, S. W.↗

NASA NTRS1979

Post-shock temperatures in minerals

An experimental technique for the measurement of post-shock temperatures in minerals is presented, and silicate post-shock temperature measurements are compared with theoretical calculations. The technique involves the use of infrared detectors to determine the brightness temperatures at 4.5 to 5.75 microns and 7 to 14 microns of samples shocked to between 5 and 30 GPa. Results obtained for aluminum 2024 and stainless steel 304, as well as for Bamble bronzite and synthetic crystal forsterite are found at low pressures to be considerably in excess of the temperatures predicted assuming a hydrodynamic rheology and isentropic release parallel to the Hugoniot. The results are shown to be in better agreement, however, with values calculated assuming elastoplastic behavior, and the post-shock temperatures of crystalline quartz are found to be in good agreement with those calculated by Mashimo et al. (1979) from release adiabat data.

Raikes, S. A.↗

NASA NTRS1979

Numerical solutions of the trans-relativistic shock relations

Using a slight modification of the Taub adiabat procedure, the paper solves the relativistic Rankine-Hugoniot (RH) relations for transrelativistic shocks in a nondegenerate Fermi gas. A parametric survey of numerical solutions of the RH relations is presented, making it possible to infer by interpolation from graphical displays the solutions to a variety of shocks. In addition, the transrelativistic nature of the solutions is explicit because when the upstream pressure is low, the shocks first approach those given by nonrelativistic strong shock theory and then approach the relativistic strong shock limit as the Mach number increases.

Fujimura, F. S.↗

NASA NTRS1980

Isotopic yields of Mg, Al from the carbon and neon zones in the explosion of a massive star

A model is developed for the nucleosynthetic yields from the supernova explosion of a massive star of the sort which has been proposed as the initiating event in the formation of the solar system by Cameron and Truran (1977). Calculations start with the Hugoniot curves, estimating the preshock conditions from a 25 solar masses model at the start of core collapse. It is shown that the products of static carbon burning dominate abundance patterns in the ejecta. Both explosive carbon burning and explosive neon burning contribute significantly to Al-26. The production of Al-26 in this model is consistent with the trigger hypothesis.

Morgan, J. A.↗

NASA NTRS1980

Unsteady transonic small disturbance theory with strong shock waves

A theory to correct the transonic small disturbance (TSD) equation to treat strong shock waves in unsteady flow is developed. The technique involves the addition of higher order terms, which are formally of negligible magnitude, to the low frequency TSD equation. These terms are then chosen such that any shock waves in the flow have strengths approximately equal to the appropriate Rankine-Hugoniot shock strength. Two correcting approaches are investigated. The first is to derive a correction for the mean steady flow and then simply use this corrected form for oscillatory flows. The second is to derive a correction for both steady and oscillatory parts of the flow. This second development is the most satisfactory and comparisons of the present results with Euler equation results are generally favorable, particularly regarding shock location, although there are some discrepancies in the pressure distribution in the leading edge region.

Kerlick, G. D.↗

NASA NTRS1981

Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows

A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.

Barnett, M.↗

NASA NTRS1981

Comments on high Mach number magnetosonic shocks

It is shown that the ion thermalization process required by the Hugoniot conditions for high Mach number magnetosonic shocks is controlled by loss cone type distributions, i.e., (partial differentiation of the ion distribution function/partial differentiation of the ion distribution energy component) zero, formed by a combination of ion reflection and gyration downstream. The thermalization length corresponds to few ion gyroradii, while the final distribution deviates substantially from Maxwellian. The results are applied to the Earth bow shock.

Papadopoulos, K.↗

NASA NTRS1982

Unsteady Transonic Small Disturbance theory with strong shock waves

Transonic Small Disturbance (TSD) theory is modified to yield steady and unsteady solutions in the case of strong shock waves (where the local Mach number ahead of the shock exceeds 1.3). The modification consists of an additional adjustable nonlinear term which allows the exact Rankine-Hugoniot shock jump relation to be satisfied at all times. The modified TSD theory is applied to steady and unsteady oscillatory transonic flows, and yields results which are in good agreement with solutions of the unsteady Euler equations, and which compare favorably with solutions of the full potential equation when shock waves are weak.

Kerlick, G. D.↗

NASA NTRS1982

Pressure distributions and shock shapes for a bent-nose biconic at incidence

Initial results of a NASA study of the lift-drag characteristics of a 12.84/7 deg biconic model intended for airbraking during atmospheric entry of probes to Mars, Venus, Saturn, and Titan are reported. Pressure distributions and shock shapes were measured in the Langley 20 in. Mach 6 tunnel with the spherically blunted bent-nose model set at angles from 0-25 deg. Pressure distributions and shock shapes where computed using the STEIN flowfield code, which features a MacCormack scheme to integrate the three-dimensional Euler equations, the Rankine-Hugoniot jump conditions to model shock waves as discontinuities, and requires a supersonic condition at every step. A comparison was made between measured and predicted values. The leeward shock angle was found to be predictable to within 3% for all angles of attack, while parabolized Navier-Stokes equations are regarded as offering more accurate results than the STEIN code for surface pressure distributions.

Miller, C. G., III↗

NASA NTRS1983

Semidirect computations for transonic flow

A semidirect method, driven by a Poisson solver, was developed for inviscid transonic flow computations. It is an extension of a recently introduced algorithm for solving subsonic rotational flows. Shocks are captured by implementing a form of artificial compressibility. Nonisentropic cases are computed using a shock tracking procedure coupled with the Rankine-Hugoniot relationships. Results are presented for both subsonic and transonic flows. For the test geometry, an unstaggered cascade of 20 percent thick circular arc airfoils at zero angle of attack, shocks are crisply resolved in supercritical situations and the algorithm converges rapidly. In addition, the convergence rate appears to be nearly independent of the entropy and vorticity production at the shock.

Swisshelm, J. M.↗

NASA NTRS1983

Shock temperatures of SiO2 and their geophysical implications

High pressure shock state temperatures of SiO2 were measured in specimens of single crystal alpha-quartz and fused quartz. Projectile impact and pyrometry techniques were employed to impart pressures in the 60-140 GPa range. Shock-induced phase transformations were observed near 70 and 50 GPa along the alpha- and fused-quartz Hugoniots. It is suggested that the transformation consists of melting of the shock-synthesized stishovite, with melting delayed by the superheating of the crystalline phase. Details of the stishovite-liquid phase boundaries have been determined, including stishovite melting at 4500 K under 70 GPa, with the melting accompanied by a relative volume change of about 2.7% and a latent heat of fusion of about 2.4 MJ/kg. At 100 GPa, an approximate limit of 3500 K for the melting of SiO2 is indicated for solid mantle mineral assemblages, such as the earth's mantle

Lyzenga, G. A.↗

NASA NTRS1983

Heterogeneous shock-induced thermal radiation in minerals

A 500-channel optical imaging intensifying and spectral digital recording system is used for recording the shock-induced radiation emitted from 406 to 821 nm from transparent minerals during the time interval that a shock wave propagates through the sample. The initial results obtained for single crystals of gypsum, calcite and halite in the 30 to 40 GPa (300 to 400 kbar) pressure range reveal grey-body emission spectra corresponding to temperatures in the 3000 to 4000 K range and emissivities ranging from 0.003 to 0.02. With gypsum and calcite, distinctive line spectra are superimposed on the thermal radiation. The observed color temperatures are greater than the Hugoniot temperature by a factor of 2 to 10; this is calculable on the basis of continuum thermodynamics and equation of state models for the shock states achieved in the three minerals. These observed high temperatures are thought to be real. It is concluded that a large number of closed spaced high temperature shear-band regions are being detected immediately behind the shock front.

Kondo, K.-I.↗

NASA NTRS1983

Shock conditions and shock wave structures in a steady flow in a dissipative fluid

More precisely, calling xi the reciprocal of the Reynolds number based on the shock wave curvature radius, the xi terms of the first order are systematically taken into account. The most important result is a system of formulas giving a correction of order xi for the various RANKINE-HUGONIOT conditions. The suggested formulas may for instance have to be used instead of the conventional ones to evaluate the loss of the total pressure across the detached shock wave which is found at the nose of a very small probe in supersonic flow.

Germain, P.↗

NASA NTRS1984

Shock wave properties of anorthosite and gabbro

Hugoniot data on San Gabriel anorthosite and San Marcos gabbro to 11 GPA are presented. Release paths in the stress-density plane and sound velocities are reported as determined from particl velocity data. Electrical interference effects precluded the determination of accurate release paths for the gabbro. Because of the loss of shear strength in the shocked state, the plastic behavior exhibited by anorthosite indicates that calculations of energy partitioning due to impact onto planetary surfaces based on elastic-plastic models may underestimate the amount of internal energy deposited in the impacted surface material.

Boslough, M. B.↗

NASA NTRS1983

Multiple spacecraft observations of interplanetary shocks ISEE three-dimensional plasma measurements

ISEE 1 and ISEE 3 three-dimensional solar wind plasma measurements are used together with magnetic field measurements across five previously studied interplanetary shocks to test the accuracy of the mixed-mode shock-normal determination technique and to test whether the shock properties are best approximated with a ratio of specific heats of 5/3 or 2. In the shocks examined, the assumption that the velocity jump was along the normal provided an estimate of the shock normal within 15 deg of the best fit normal 50 percent of the time and within 50 deg, 90 percent of the time. The mixed-mode normals lay within 12 deg of the best fit normal 50 percent of the time and within 36 deg, 90 percent of the time. Part of this deviation may be due to differences in the orientation of the local normal from that of the average normal. Finally, the jump in plasma and field across the shock is better predicted from the Rankine-Hugoniot equations using a ratio of specific heats of 5/3 rather than 2.

Russell, C. T.↗

NASA NTRS1984

Comparison of viscous-shock-layer heating analysis with Shuttle flight data in slip flow regime

Comparison of STS-2 Shuttle flight heating data along the windward centerline has been made with two-dimensional nonequilibrium viscous shock-layer solutions obtained with shock and wall-slip conditions at an altitude range of 90 to 110 km. The shock slip condition used is the modified Rankine-Hugoniot relations of Cheng as used by Davis, and the wall-slip conditions are based on the first order consideration derived from kinetic theory as given by Scott and Hendricks. The results indicate that the calculated heating distributions with slip boundary conditions agree better with the flight data than those without slip conditions. The agreement improves when the accommodation coefficient or freestream density is decreased to one-half, suggesting the possibility of less than full accommodation for the tile surface and (or) an overestimate of freestream density using the Jacchia-Roberts model. Heating reduction due to the slip effect becomes very pronounced as the flow becomes more rarefied, and the effect is more significant for the stagnation region than the aft region of the vehicle.

Shinn, J. L.↗

NASA NTRS1983

Temperatures of shock-induced shear instabilities and their relationship to fusion curves

New emission spectra for MgO and CaAl2Si2O8 (glass) are observed from 430 to 820 nm. Taken with previous data, it is suggested that transparent solids display three regimes of light emission upon shock compression to successively higher pressures: (1) characteristic radiation such as observed in MgO and previously in other minerals, (2) heterogeneous hot spot (greybody) radiation observed in CaAl2Si2O8 and previously in all transparent solids undergoing shock-induced phase transformations, and (3) blackbody emission observed in the high pressure phase regime in NaCl, SiO2, CaO, CaAl2Si2O8, and Mg2SiO4. The onset of the second regime may delineate the onset of shock-induced polymorphism whereas the onset of the third regime delineates the Hugoniot pressure required to achieve local thermal equilibrium in the shocked solid. It is also proposed that the hot spot temperatures and corresponding shock pressures determined in the second regime delineate points on the fusion curves of the high pressure phase.

Schmitt, D. R.↗