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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Observational test of shock drift and Fermi acceleration on a seed particle population upstream of earth's bow shock

The efficiency of proposed shock acceleration mechanisms as they operate at the bow shock in the presence of a seed energetic particle population was examined using data from simultaneous observations of energetic solar-origin protons, carried out by the IMP 7 and 8 spacecraft in the vicinity of the quasi-parallel (dawn) and quasi-perpendicular (dusk) regions of the earth's bow shock, respectively. The results of observations (which include acceleration effects in the intensities of the energetic protons with energies as high as 4 MeV observed at the vicinity of the dusk bow shock, but no evidence for any particle acceleration at the energy equal to or above 50 keV at the dawn side of the bow shock) indicate that the acceleration of a seed particle population occurs only at the quasi-perpendicular bow shock through shock drift acceleration and that the major source of observed upstream ion populations is the leakage of magnetospheric ions of energies not less than 50 keV, rather than in situ acceleration.

Anagnostopoulos, G. C.↗
NASA NTRS1991

Shock loading predictions from application of indicial theory to shock-turbulence interactions

A sequence of steps that permits prediction of some of the characteristics of the pressure field beneath a fluctuating shock wave from knowledge of the oncoming turbulent boundary layer is presented. The theory first predicts the power spectrum and pdf of the position and velocity of the shock wave, which are then used to obtain the shock frequency distribution, and the pdf of the pressure field, as a function of position within the interaction region. To test the validity of the crucial assumption of linearity, the indicial response of a normal shock is calculated from numerical simulation. This indicial response, after being fit by a simple relaxation model, is used to predict the shock position and velocity spectra, along with the shock passage frequency distribution. The low frequency portion of the shock spectra, where most of the energy is concentrated, is satisfactorily predicted by this method.

Keefe, Laurence R.↗
NASA NTRS1992

Shock drift acceleration of energetic protons at a planetary bow shock

Results are presented of numerical orbit integrations of the interaction of suprathermal charged particles (protons) with a planetary bow shock, performed in order to investigate the effect of the changing geometry of the shock, due to its curvature, on the kinematics of the particle/shock interaction. Results obtained for both the 2D and 3D bow-shock geometries show that the introduction of shock curvature to the shock in the simulations leads to an increase of the reflection probability of incident suprathermal protons. It was also found that the curvature of the planetary bow shock allows protons to enter at a given value of theta(Bn) (where theta(Bn) is the angle between the local shock normal and the incident magnetic field) and to exit at a different theta(Bn) value. The result has consequences in the characteristics of the energetic charged particle environment in the planetary foreshock.

Giacalone, Joe↗
NASA NTRS1994

On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds

The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. Shocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the intercloud medium. This paper presents a comprehensive numerical study of the simplest case of the interaction between a shock wave and a spherical cloud, in which the shock far from the cloud is steady and planar, and in which radiative losses, thermal conduction, magnetic fields, and gravitational forces are all neglected. As a result, the problem is completely specified by two numbers: the Mach number of the shock, M, and the ratio of the density of the cloud to that of the intercloud medium, Chi. For strong shocks we show that the dependence on M scales out, so the primary independent parameter is Chi. Variations from this simple case are also considered: the potential effect of radiative losses is assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the cloud is studied by using a cylindrical cloud instead of a spherical one; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind. Local adaptive mesh refinement techniques with a second-order, two-fluid, two-dimensional Godunov hydrodynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that about 100 zones per cloud radius are needed for accurate results; previous calculations have generally used about a third of this number. The results of the calculations are analyzed in terms of global quantities which provide an overall description of te shocked cloud: the size and shape of the cloud, the mean density, the mean pressure, the mean velocity, the velocity dispersion, and the total circulation.

Klein, Richard I.↗
NASA NTRS1994

Shock normal determination for multiple-ion shocks

We have adapted the single-ion Vinas and Scudder (1986) solution to the Rankine-Hugoniot (R-H) problem to a multiple-on solution. Using this technique, we can calculate a shock normal direction, shock speed, best estimate of the upstream and downstream magnetic field and plasma asymptotic states, and theta(sub Bn), the angle between the shock normal and the upstream magnetic field. We test the multi-ion solution with a theoretical case but are restricted to a perpendicular shock in order to close the multi-ion Rankine-Hugoniot equations. For this test case both single-ion and multi-ion solutions are equally valid. We examine parameter regimes to look for differences between single-ion and multi-ion solutions of the R-H equations, and we find that the largest differences occur for quasi-parallel shocks, small values of solar wind speed, large values of heavy ion density, and very strong and very weak shocks. For both the inbound and outbound crossing of comet Halley we have a slow solar wind speed, small values of water group ions and fairly weak shocks. We examine both the quasi-perpendicular inbound crossing and the quasi-parallel outbound crossing at comet Halley.

Kessel, R. L.↗
NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗
NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Abstract Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗
NASA NTRS2021

Evaluating the De Hoffmann-Teller Cross-Shock 2 Potential at Real Collisionless Shocks

Shock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub-populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann-Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields in space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high-quality field and plasma measurements from NASA’s Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann-Teller frame transformation to include time variability, and conclude that in practice these face difficulties inherent in the 3D time-dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann-Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

Steven J Schwartz↗
NASA NTRSDate not supplied

The Zircon-Reidite Shock Transformation: A Tem Study of Reidite Produced at A Newly Established 21.2 GPa Shock Pressure Threshold

The high-pressure polymorph of zircon (Zr2SiO4) is reidite, a phase with the scheelite structure that was first discovered to form at ca. 12 GPa in static high-pressure experiments [1]. Reidite was subsequently found to occur in naturally shocked zircons from several terrestrial impact localities [2,3], as well as in shock recovery-reverberation experiments performed above 20 GPa [4]. The nature and distribution of reidite occurrences in terrestrial impact localities has pointed to its potential use as a shock pressure indicator, as well as to the importance of understanding its age-reset effects in zircon geochronology [3]. In this study we have used coordinated SEM/Electron Backscatter Diffraction (EBSD) and Field-Emission Scanning Transmission Electron Microscopy (FE-STEM) to study the micro- and nanostructure of reidite and its shocked zircon host produced at 21.2 GPa under experimental shock recovery/reverberation conditions [5]. Our results document the TEM microstructure of reidite formed at a 21.2 GPa experimental shock pressure that is significantly lower than that observed in previous studies [4]. At these conditions the sample developed a diverse set of microstructures that have not been previously documented on the TEM scale.

shock metamorphism↗
NASA NTRS1976

Gasdynamics and shock dynamics of weak shock waves

Experiments in weak-shock dynamics were conducted using a 17-in. diameter shock tube. Weak shocks were generated in air by a compressed nitrogen driver gas; the incident shock waves were brought to a focus by reflecting them from concave cylindrical reflectors at the endwall of the tube. It was found that the behavior of a shock discontinuity at a focus is determined by nonlinear gasdynamic processes. Consideration is also given to nonlinear resonance phenomena, i.e., phenomena associated with oscillatory motion in ducts, with amplitude so large that weak shocks occur. Attention is given to nonlinear resonance in open and closed tubes and to thermal and relaxation effects.

Sturtevant, B.↗
NASA NTRS1983

Multiple spacecraft observations of interplanetary shocks Four spacecraft determination of shock normals

ISEE 1, 2, 3, IMP 8, and Prognoz 7 observations of interplanetary shocks in 1978 and 1979 provide five instances where a single shock is observed by four spacecraft. These observations are used to determine best-fit normals for these five shocks. In addition to providing well-documented shocks for future investigations these data allow the evaluation of the accuracy of several shock normal determination techniques. When the angle between upstream and downstream magnetic field is greater than 20 deg, magnetic coplanarity can be an accurate single spacecraft method. However, no technique based solely on the magnetic measurements at one or multiple sites was universally accurate. Thus, the use of overdetermined shock normal solutions, utilizing plasma measurements, separation vectors, and time delays together with magnetic constraints, is recommended whenever possible.

Russell, C. T.↗
NASA NTRS1989

Effect of leading edge sweep on shock-shock interference at Mach 8

These Mach 8 experimental results are applicable to the details of a shock-shock interference that may occur on an engine inlet of a hypersonic vehicle from a swept forebody shock interacting with a swept cowl leading edge bow shock or from a swept splitter plate shock interacting with a swept fuel injection strut bow shock. Peak surface pressure and heat transfer rate on the cylinder were about 10 and 30 times the undisturbed flow stagnation point value, respectively, for the 0 deg sweep test. A comparison of the 15 deg and 30 deg swept results with the 0 deg swept results shows that peak pressure was reduced about 13 percent and 44 percent, respectively, and peak heat transfer rate was reduced about 7 percent and 27 percent, respectively.

Glass, Christopher E.↗
NASA NTRS1989

Influence of shock-shock interactions on the blunt body flow field at hypersonic flight speeds

The effect of shock impingement on the blunt leading edge of the inlet cowl of a scramjet engine is investigated numerically. The impinging shock is caused by the vehicle forebody. The interaction of this forebody shock with the cowl leading edge shock results in a very complex flowfield containing local regions of high pressure and intense heating. In the present investigation, this complex flowfield is calculated by solving the full Navier-Stokes equations using a finite-volume flux splitting technique due to Van Leer. Results are also obtained for the downstream effects into the inlet of the leading edge shock-shock interactions. Results of the present numerical investigation are compared with available experimental results.

Singh, D. J.↗
NASA NTRS1991

Multiple shock-shock interference on a cylindrical leading edge

The details of an experimental study of shock wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet are presented. This Mach 8 study has provided the first detailed pressure and heat transfer rate distributions on a cylinder resulting from a two-dimensional shockwave interference pattern created by two incident oblique shock waves intersecting the cylinder bow shock wave. The peak heat transfer rate was 38 times the undisturbed flow stagnation point level and occurred when the two oblique shock waves coalesced prior to intersecting the cylinder bow shock wave. Development of pressure deflection diagrams identified a new interference pattern consisting of concomitant supersonic jets separated from each other by a shear layer and submerged in the subsonic region between the bow shock wave and body.

Wieting, Allan R.↗
NASA NTRS1993

Viscous hypersonic shock-shock interaction on a blunt body at high altitude

The shock interaction produced when an incident oblique shock impinges on a blunt body, such as an engine inlet cowl lip of a hypersonic vehicle, is investigated for high altitude flight conditions. A perfect gas, Navier-Stokes numerical simulation of this problem at various altitudes representing continuum through transitional conditions is performed using the modified flux vector splitting method of Steger and Warming (1979). Two series of solutions are produced. First, a number-of-shock-positions are studied at a particular altitude and Mach number. Second, given a fixed shock position and Mach number, the interaction is investigated at several altitudes ranging from continuum to transitional flow conditions. It is shown that the interaction becomes fundamentally different as the density is lowered, and its effect on the overheating problem is progressively diminished. The maximum stagnation point heating at the highest altitude is reached only when the incident shock misses the cowl lip completely, and any interaction with the cowl bow shock that does occur takes place downstream and thus has little effect on the conditions at the stagnation point.

Comeaux, Keith A.↗
NASA NTRS1994

Numerical simulation of shock-induced combustion past blunt bodies using shock-fitting technique

Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier-Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one-dimensional wave-interaction model than before.

Ahuja, J. K.↗
NASA NTRS1994

Numerical Simulation of Shock-Induced Combustion Past Blunt Bodies Using Shock-Fitting Technique

Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one dimensional wave-interaction model than before.

Ahuja, J. K.↗