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NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗

NASA NTRS1996

Computational considerations for the simulation of shock-induced sound

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order-accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order-accurate essentially nonoscillatory (ENO) method is used to investigate the solutions of inviscid, compressible flows with shocks in a quasi-one-dimensional nozzle flow. The design order of accuracy is achieved in the smooth regions of a steady-state test case. However, in an unsteady test case, only first-order results are obtained downstream of a sound-shock interaction. The difficulty in obtaining a globally high-order-accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem. Some of the difficult issues and ramifications for aeroacoustics simulations of flows with shocks that are raised by these results are discussed.

Casper, Jay↗

NASA NTRS1996

Screech Tones from Rectangular Jets with Spanwise Oblique Shock-Cell Structures

Understanding screech is especially important for the design of advanced aircraft because screech can cause sonic fatigue failure of aircraft structures. Although the connection between shock-cell spacing and screech frequency is well understood, the relation between non-uniformities in the shock-cell structures and the resulting amplitude, mode, and steadiness of screech have remained unexplored. This paper addresses the above issues by intentionally producing spanwise (larger nozzle dimension) variations in the shock-cell structures and studying the resulting spanwise screech mode. The spanwise oblique shock-cell structures were produced using imperfectly expanded convergent-divergent rectangular nozzles (aspect ratio = 5) with nonuniform exit geometries. Three geometries were studied: (a) a nozzle with a spanwise uniform edge, (b) a nozzle with a spanwise oblique (single bevelled) edge, and (c) a nozzle that had two spanwise oblique (double bevelled) cuts to form an arrowhead-shaped nozzle. For all nozzles considered, the screech mode was antisymmetric in the transverse (smaller nozzle dimension) direction allowing focus on changes in the spanwise direction. Three types of spanwise modes were observed: symmetric (1), antisymmetric (2), and oblique (3). The following significant results emerged: (1) for all cases the screech mode corresponds with the spanwise shock-cell structure, (2) when multiple screech modes are present, the technique presented here makes it possible to distinguish between coexisting and mutually exclusive modes, (3) the strength of shocks 3 and 4 influences the screech source amplitude and determines whether screech is unsteady. The results presented here offer hope for a better understanding of screech and for tailoring shock-containing jets to minimize fatigue failure of aircraft components.

Raman, Ganesh↗

NASA NTRS1997

F-16XL Wing Pressure Distributions and Shock Fence Results from Mach 1.4 to Mach 2.0

Chordwise pressure distributions were obtained in-flight on the upper and lower surfaces of the F-16XL ship 2 aircraft wing between Mach 1.4 and Mach 2.0. This experiment was conducted to determine the location of shock waves which could compromise or invalidate a follow-on test of a large chord laminar flow control suction panel. On the upper surface, the canopy closure shock crossed an area which would be covered by a proposed laminar flow suction panel. At the laminar flow experiment design Mach number of 1.9, 91 percent of the suction panel area would be forward of the shock. At Mach 1.4, that value reduces to 65 percent. On the lower surface, a shock from the inlet diverter would impinge on the proposed suction panel leading edge. A chordwise plate mounted vertically to deflect shock waves, called a shock fence, was installed between the inlet diverter and the leading edge. This plate was effective in reducing the pressure gradients caused by the inlet shock system.

Landers, Stephen F.↗

NASA NTRS1998

Flow and Turbulence Modeling and Computation of Shock Buffet Onset for Conventional and Supercritical Airfoils

Flow and turbulence models applied to the problem of shock buffet onset are studied. The accuracy of the interactive boundary layer and the thin-layer Navier-Stokes equations solved with recent upwind techniques using similar transport field equation turbulence models is assessed for standard steady test cases, including conditions having significant shock separation. The two methods are found to compare well in the shock buffet onset region of a supercritical airfoil that involves strong trailing-edge separation. A computational analysis using the interactive-boundary layer has revealed a Reynolds scaling effect in the shock buffet onset of the supercritical airfoil, which compares well with experiment. The methods are next applied to a conventional airfoil. Steady shock-separated computations of the conventional airfoil with the two methods compare well with experiment. Although the interactive boundary layer computations in the shock buffet region compare well with experiment for the conventional airfoil, the thin-layer Navier-Stokes computations do not. These findings are discussed in connection with possible mechanisms important in the onset of shock buffet and the constraints imposed by current numerical modeling techniques.

Bartels, Robert E.↗

NASA NTRS1995

A Transmission Electron Microscope Study of Experimentally Shocked Pregraphitic Carbon

A transmission electron microscope study of experimental shock metamorphism in natural pre-graphitic carbon simulates the response of the most common natural carbons to increased shock pressure. The d-spacings of this carbon are insensitive to the shock pressure and have no apparent diagnostic value, but progressive comminution occurs in response to increased shock pressure up to 59.6 GPa. The function, P = 869.1 x (size(sub minimum )(exp -0.83), describes the relationship between the minimum root-mean-square subgrain size (nm) and shock pressure (GPa). While a subgrain texture of natural pregraphitic carbons carries little information when pre-shock textures are unknown, this texture may go unnoticed as a shock metamorphic feature.

Rietmeijer, Frans J. M.↗

NASA NTRS1999

Unusual Bow Shock and Magnetopause Locations During May 11-12, 1999

On May 11 and 12, 1999, when the solar wind proton density dropped to only about 3% of its nominal value, WIND and IMP 8 (and possibly Lunar Prospector) encountered the Earth's bow shock at unusually large distances. These observations, at 57-63 Re, correspond to the most distant crossings of the bow shock ever recorded. This paper will present observations from Interball-1 and Geotail, showing the bow shock near its nominal position, and from IMP 8 and WIND (and perhaps Lunar Prospector) crossing the bow shock at increasing radial distances. The bow shock is extremely weak by the time of its observation by WIND. However, a clear jump in both the magnetic field strength and solar wind bulk velocity is quite apparent, although with no significant changes in solar wind proton density. The nature of this dissipating shock will be discussed. Also, interball-1 has observed the magnetopause at an unusually large standoff distance. The observed motion of the magnetopause and bow shock will be compared with model predictions. This set of observations provide an excellent test case for the behavior of gas dynamic and MHD models under extreme conditions.

Szabo, Adam↗

NASA NTRS1999

Shock Wave Dynamics in Weakly Ionized Plasmas

An investigation of the dynamics of shock waves in weakly ionized argon plasmas has been performed using a pressure ruptured shock tube. The velocity of the shock is observed to increase when the shock traverses the plasma. The observed increases cannot be accounted for by thermal effects alone. Possible mechanisms that could explain the anomalous behavior include a vibrational/translational relaxation in the nonequilibrium plasma, electron diffusion across the shock front resulting from high electron mobility, and the propagation of ion-acoustic waves generated at the shock front. Using a turbulence model based on reduced kinetic theory, analysis of the observed results suggest a role for turbulence in anomalous shock dynamics in weakly ionized media and plasma-induced hypersonic drag reduction.

Johnson, Joseph A., III↗

NASA NTRS1999

Accuracy Study of the Space-Time CE/SE Method for Computational Aeroacoustics Problems Involving Shock Waves

The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.

Wang, Xiao Yen↗

NASA NTRS1994

Structure, Shape and Movement of the Termination Shock

In this paper we review current ideas concerning the morphology and dynamics of the heliospheric termination shock. The mean distance of the shock is expected to lie somewhere in the range 50-200 AU, and should vary with latitude, depending on mean latitude variation of the dynamical pressure of the solar wind. The shock is expected to move in response to variation in upstream solar wind conditions, so that at any particular instant the termination shock will resemble a distorted asymmetric balloon with some parts moving inward and others moving outward. The simplest model of the shock is that of an infinitely thin gasdynamic or magnetohydrodynamic shock wave, which moves inward or outward at speeds of approximately 100 kilometers per second. The structure and motion of the shock will be strongly modified if an appreciable fraction of the incident solar wind energy goes into acceleration of energetic particles, specifically the anomalous cosmic rays.

Barnes, Aaron↗

NASA NTRS1995

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗

NASA NTRS1996

The Physics of Molecular Shocks in Star-Forming Regions

Molecular shocks are produced by the impact of the supersonic infall of gas and dust onto protostars and by the interaction of the supersonic outflow from the protostar with the circumstellar material. Infalling gas creates an accretion shock around the circumstellar disk which emits a unique infrared spectrum and which processes the interstellar dust as it enters the disk. The winds and jets from protostars also impact the disk, the infalling material, and the ambient molecular cloud core creating shocks whose spectrum and morphology diagnose the mass loss processes of the protostar and the orientation and structure of the star forming system. We discuss the physics of these shocks, the model spectra derived from theoretical models, and comparisons with observations of H2O masers, H2 emission, as well as other shocks tracers. We show the strong effect of magnetic fields on molecular shock structure, and elucidate the chemical changes induced by the shock heating and compression.

Hollenbach, David↗

NASA NTRS1997

Analysis of Emission Spectra from Arc-jet Shock Layer Flows

This paper reports computational comparisons with experimental studies of a nonequilibrium blunt body shock layer in a high enthalpy arc-jet wind tunnel at NASA Ames Research Center. The primary objective of this work is to investigate the existence of a thermochemical equilibrium region in the shock layer. The existence of such an equilibrium region is of interest for following reasons: (1) to understand the equilibration process behind the shock in an arc-jet flow environment; (2) to interpret measured surface heat transfer data for purpose of determining surface catalytic efficiency, and (3) to determine the total enthalpy from the spectroscopic measurements. The paper will present an analysis of the experimental data obtained in the arc-jet wind tunnel. Experimental data includes measurements of emission spectra of radiation emanating from a shock layer formed in front of a 6-inch flat-faced cylinder. The measurements, obtained using a two dimensional CCD camera mounted on a spectrograph, provide spatially resolved spectra along the stagnation streamline of the model. Computational analysis includes simulation of nonequilibrium flow in the arc-jet facility (flow in the conical nozzle and shock layer in front of a flat-faced cylinder) using 2-D/axisymmetric Navier-Stokes codes and prediction of the radiation spectra from the axisymmetric flowfield using NEQAIR radiation code. Various line-of-sight averaged flow properties such as vibrational and rotational temperatures, species number densities within the shock layer are deduced from the experimental spectra. Comparison of the computed and experimental line-of-sight averaged flow properties provides assessment of thermochemical equilibration processes in an arc-jet shock layer.

Gokcen, T.↗

NASA NTRS1998

Theory of the Shape of the Heliospheric Termination Shock: Axial Symmetry

The heliospheric termination shock must exhibit asymmetry in its shape, due in part to internal latitude variations in the solar wind, and in part to the special directions defined by the external interstellar flow and/or the galactic magnetic field. This asymmetry shows up naturally in numerical simulations of the interaction between the heliosphere and local interstellar medium. However, to date only one analytical treatment of the theory has appeared, which discussed the modification of the shock shape due to solar wind latitude variations in the presence of spherically symmetric outer boundary conditions. In the present report, we discuss an extension and generalization of this theory to an axially symmetric gasdynamic system, in which departure from spherical symmetry may be due either to internal solar wind variations or to the directional properties of the external interstellar medium. It is shown that for steady flow the post-shock region is characterized by an infinite set of quantities that are conserved along streamlines; among these invariants are the stagnation pressure and a quantity closely related to vorticity. Moreover, for a given latitude profile of the (supersonic) solar wind, the geometry of the termination shock uniquely determines the valued of these invariants at the points where the streamlines emerge from the shock. A self-consistent solution of the problem thus requires a match between the shock geometry and distant boundary conditions. The theory is applied to give estimates of termination-shock asymmetry for various internal and external conditions.

Barnes, Aaron↗

NASA NTRS2003

Experimentally Shock-loaded Anhydrite: Unit-Cell Dimensions, Microstrain and Domain Size from X-Ray Diffraction

Cretaceous Tertiary (K/T) boundary is traditionally associated with one of the most dramatic mass extinctions in the Earth history. A number of killing mechanisms have been suggested to contribute to the widespread extinctions of Cretaceous biota at this boundary, including severe, global deterioration of the atmosphere and hydrosphere from the shock-induced release of CO2 and SO(x) from carbonate- and sulfate-bearing target rocks, respectively. Recently carried out calculations revealed that the global warming caused by CO2 release was considerably less important than the cooling due to SO(x) gases release during the Chicxulub impact event. Considering apparent potential importance of the response of sulfates to the shock metamorphism, relative lack of the data on shock behavior of sulfates as well as some general difficulties encountered during thermodynamic modeling of the shock-induced CO2 loss from carbonates we subjected anhydrite to a series of shock experiments designed for complete recovery of the shocked material. We report here on the detail X-ray diffraction analysis of seven samples that were subjected to experimental shock-loading from 10 to 65 GPa.

Skala, R.↗

NASA NTRS2003

Shock Heating and Subsequent Cooling of Basaltic Shergottites: The Cases for QUE94201 and Dhofar 378

Shock metamorphism is one of the most fundamental processes in the history of Martian meteorites. Especially, shergottites experienced strong shock effects (>30 GPa) most likely when they were ejected from Mars. "Maskelynitization" of plagioclase and formation of shock melts are major effects due to this severe shock. QUE94201 (QUE) and Dhofar 378 (DHO) are basaltic shergottites that are mainly composed of pyroxene and plagioclase glass. These two shergottites suffered severe shock, which generated abundant impact melt and vesiculated flow textures. In spite of similar degrees of shock between two meteorites, they are distinct in several mineralogical aspects. In this abstract, we discuss their differences to understand differences in their shock heating and subsequent cooling histories.

Mikouchi, T.↗

NASA NTRS2004

Volatile Behavior in Lunar and Terrestrial Basalts During Shock: Implications for Martian Magmas

The amount of water in martian magmas has significant ramifications for the martian atmosphere-hydrosphere cycle. Large D-enrichments have been observed in kaersutitic amphiboles in Zagami, Chassigny and Shergotty meteorites (delta-D values up to 4400 per mil) suggesting that substantial amounts of H escaped Mars in its past. Furthermore, martian meteorites with inclusions of biotite and apatite imply possible origins in a hydrous mantle. However, whether martian magmas ever possessed considerable proportions of water remains controversial and unclear. The H-content of mica and amphibole melt inclusions has been found to be low, while bulk-rock H2O content is also low ranging from 0.013 to 0.035 wt. % in Shergotty. Hydrous martian magmas were considered responsible for light lithophile element (LLE) zoning patterns observed in Nakhlite and Shergottite pyroxenes. Since LLEs, such as Li and B, partition into aqueous fluids at temperatures greater than 350 C, workers interpreted Li-B depletions in pyroxene rims as evidence that supercritical fluid exsolution occurred during magma degassing. In that many martian basalts experienced substantial shock (15-45 GPa) it is possible that the magmatic volatile record preserved in martian basalts has been disturbed. Previous shock experiments suggest that shock processes may effect water content and H/D. To better understand the possible effects of shock on this volatile record, we are studying the redistribution of volatile elements in naturally and experimentally shocked basalts. Here, we report the initial results from shocked basalts associated with the Lonar Crater, India and an experimentally shocked lunar basalt.

Chaklader, Johny↗

NASA NTRS2004

High-Pressure Minerals in Meteorites: Constraints on Shock Conditions and Duration

The objective of this research was to better understand the conditions and duration of shock metamorphism in meteorites through microstructural and microanalytical characterization of high-pressure minerals. A) Continue to investigate the mineralogy and microstructures of melt-veins in a suite of chondritic samples ranging from shock grades S3 through S6 to determine how the mineral assemblages that crystallize at high-pressure and are related to shock grade. B) Investigate the chemical, mineralogical, and microstructural heterogeneities that occur across melt veins to interpret crystallization histories. C) Use static high-pressure experiments to simulate crystallization of melt veins for mineralogical and textural comparisons with the melt veins of naturally shocked samples. D) Characterize the compositions and defect microstructures of polycrystalline ringwoodite, wadsleyite, majorite, (Mg,Fe)Si03-ilmenite and (Mg,Fe)SiO3-perovskite in S6 samples to understand the mechanisms of phase transformations that occur during shock. These results will combined with kinetic data to constrain the time scales of kinetic processes. E) Investigate the transformations of metastable high-pressure minerals back to low- pressure forms to constrain post-shock temperatures and estimates of the peak shock pressure. Of these objectives, we have obtained publishable data on A, B and D. I am currently doing difficult high-pressure melting and quench experiments on an L chondrite known as Mbale. These experiments will provide additional constraints on the mineral assemblages that are produced during rapid quench of an L chondrite at pressures of 16 to 25 GPa. Results from published or nearly published research is presented below. Lists of theses, dissertations and publications are given below.

Sharp, Thomas G.↗