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NASA NTRS1954

Unsteady oblique interaction of a shock wave with a plane disturbance

Analysis is made of the flow field produced by oblique impingement of weak plane disturbances of arbitrary profile on a plane normal shock. Three types of disturbance are considered: (a) sound wave propagating in the gas at rest into which the shock moves; (b) sound wave overtaking the shock from behind,(The sound wave reflects as a sound wave, and a stationary vorticity wave is produced); (c) an incompressible vorticity wave stationary in the gas ahead of the shock. The incident wave refracts as a stationary vorticity wave, and either a sound wave or attenuating pressure wave is also produced. Computations are presented for the first two types of incident wave, over the range of incidence angles, for shock Mach numbers of 1, 1.5, and infinity.

Moore, Franklin K↗

NASA NTRS1984

Electron-rich particle events and the production of gamma-rays by solar flares

The abundance of electrons of 5-50 MeV energies relative to protons of similar energy has been determined in a total of 49 particle events of apparently solar origin during the year 1980. Most events with high electron abundances appear to have been produced by flares which also produced observable fluxes of gamma-rays. The overall distribution of abundances is consistent with that measured in 1968-1970 at similar energies, but is systematically lower in electron content than abundance distributions measured at lower energies. Electron-rich particle events have harder electron spectra than more normal events, and are never accompanied by strong interplanetary shocks. Therefore, an investigation is conducted to decide whether observations are consistent with models in which energetic particles are accelerated by a shock produced at the flare site. It is concluded that, in such models, the variable nature of the interplanetary particle events must reflect some fundamental but variable property of the shocks - possibly their direction of propagation. An outward moving shock may produce a particle event in interplanetary space whereas a shock directed toward the sun may produce a flux of particles in the lower solar atmosphere which generate the gamma-radiation.

Evenson, P.↗

NASA NTRS1977

An implicit shock-fitting scheme for unsteady transonic flow computations

The alternating-direction implicit scheme developed by NASA Ames for unsteady transonic flows has been modified to include a shock-fitting algorithm as well as an analytically stretched coordinate system. The shock-fitting procedure treats shock waves as discontinuities normal to the free stream. Improvements in shock position and the unsteady pressure distributions are obtained by this modification. The various types of shock motion observed experimentally by Tijdeman are well simulated in calculations using the modified computational scheme. The method of detecting shock wave formation and the procedure for fitting a moving shock wave are illustrated. Results for a pulsating parabolic arc airfoil and for an NACA 64A006 airfoil with oscillating quarter-chord flap are presented and discussed.

Yu, N. J.↗

NASA NTRS2006

A Magnetohydrodynamic Boost for Relativistic Jets

We have performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field may change the properties of the shock interface between the tenuous, overpressured jet (V(sub j) (sup z)) flowing tangentially to a dense external medium. Magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A poloidal magnetic field (B(sup z)), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to a larger Lorentz factors than those obtained in the pure-hydrodynamic case. In contrast, a strong toroidal magnetic field (B(sup y)), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case, but to a lesser extent than found for the poloidal case due to the fact that the velocity component normal to the shock interface is now much smaller. Overall, the acceleration efficiency in the toroidal case is less than that of the poloidal case but both geometries still result in higher Lorentz factors than the pure-hydrodynamic case. Thus, the presence and relative orientation of a magnetic field in relativistic jets can have a significant influence on the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).

Mizuno, Yosuke↗

NASA NTRS2003

Magnetized Plasma Expansion and its Interaction with a Plasma Stream

Expansion of magnetized plasma in the magnetic field of a solenoid is studied by means of simulations using a 3-dimensional hybrid code. The plasma expands against a high- density and slow plasma stream (PS). The expansion causes inflation of the magnetic field; near the solenoid the magnetic field variation with increasing distance (r) remains as B(alpha)r(sup -3), but at farther distances B(alpha)r(sup -p), where the exponent p is found in the range 0.5 approx. less than p approx. less than 1.2 forming a plateau in the magnetic field distribution B(r). At the start of injection of plasma from the ends of the solenoid, the PS interacts with the solenoid magnetic field and creates a bow shock at a distance where the Larmor radius (r(sub il)) of the PS ions in the solenoid magnetic field nearly equals the scale length (L) of B(r), that is, r(sub il) approx. L = (B(sup -1)dB L /dr)(sup -1). As the injected plasma accumulates in the solenoid magnetic field, it expands inflating the magnetic field and the bow shock moves outward. The speed of the expansion front and the shock progressively decreases and eventually a stand-off occurs when the PS dynamic pressure is eventually balanced by the magnetic and kinetic pressures of the expanding plasma and the inflating magnetic field. The inflating field shows wave-like behavior, with considerable structures in the field and current distributions.

Singh, Nagendra↗

NASA NTRS1993

Termination shock - Solar cycle variations of location and speed

Plasma and magnetic field data from Voyagers 1 and 2 over an 11-year period (1978-1988) together with a one-fluid MHD model are used to study the motion of the termination shock. The observed large fluctuations in solar wind parameters cause variations in the speed, in the jump conditions, and in the location of the termination shock. If the interstellar stagnation pressure is equivalent to a magnetic field of 0.5 nT plus draping enhancements, the termination shock moves between 88 AU and 102 AU. The location of the termination shock is anticorrelated with the sunspot number. The termination shock is very strong with pressure ratios of a few thousands, the fast Mach number is about 12, and the plasma beta ratio jumps from about 0.1 to about 14. During the declining phase of the solar cycle, the shock speed is often greater than or comparable to the spacecraft speed. If the crossing of the termination shock by a spacecraft occurs during the declining phase, the spacecraft will cross the termination shock 3 or more times over a period of about 4 years.

Whang, Y. C.↗

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 NTRS2007

A Magnetohydrodynamic Boost for Relativistic Jets

We performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. Simulation results show that the presence of a magnetic field changes the properties of the shock interface between the tenuous, overpressured jet (V^z j) flowing tangentially to a dense external medium. We find that magnetic fields can lead to more efficient acceleration of the jet, in comparison to the pure-hydrodynamic case. A "poloidal" magnetic field (B^z), tangent to the interface and parallel to the jet flow, produces both a stronger outward moving shock and a stronger inward moving rarefaction wave. This leads to a large velocity component normal to the interface in addition to acceleration tangent to the interface, and the jet is thus accelerated to larger Lorentz factors than those obtained in the pure-hydrodynamic case. Likewise, a strong "toroidal" magnetic field (B^y), tangent to the interface but perpendicular to the jet flow, also leads to stronger acceleration tangent to the shock interface relative to the pure-hydrodynamic case. Thus. the presence and relative orientation of a magnetic field in relativistic jets can significant modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).

Mizuno, Yosuke↗

NASA NTRS1986

Configurations of corotating shocks in the outer heliosphere

Configurations of corotating shocks in the outer heliosphere are computed on the assumption that the shocks move at constant speeds between collisions. The basic physical process is the interaction of a forward shock with a reverse shock. The points at which this interaction takes place are determined algebraically in terms of the initial shock positions and speeds. Between the points at which the shocks interact, the shocks have the form of Archimedian spirals. Shock configurations are determined for the case of two corotating shock pairs originating at 2.5 AU and for a single shock pair at 2.5 AU. In both cases the heliosphere is divided into several distinct regions distinguished by the number of times the particles have passed through a shock. Since the shock strengths decrease when a forward shock interacts with a reverse shock, corotating shocks are expected to be weaker at larger distances from the sun.

Burlaga, L. F.↗

NASA NTRS2011

Analysis of Exhaust Plume Effects on Sonic Boom for a 59-Degree Wing Body Model

Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions are due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analyses showed how the shock wave formed at the nozzle lip interacted with the nozzle boat-tail expansion wave. The nozzle lip shock moved with increasing nozzle pressure ratio (NPR) and reduced the nozzle boat-tail expansion. Lip shock movement caused a favorable change in the observed pressure signature. These results were applied to a simplified supersonic vehicle geometry with no inlets and no tail, in which the goal was to demonstrate how under-expanded nozzle operation reduced the sonic boom signature by twelve percent. A secondary goal was to demonstrate the use of the Cart3D inviscid code for off-body pressure signatures including the nozzle plume effect.

Castner, Raymond S.↗

NASA NTRS1988

ISEE studies of the quasi-parallel bow shock

ISEE-1 and-2 plasma and magnetic field observations are used to examine several encounters with brief magnetic pulsations in the quasi-parallel region of the earth's bow shock. The two-spacecraft timing of the magnetic field signature is examined to see if the pulsation encounters are nested (as for back and forth motion of the shock over the spacecraft) or simply time-shifted (as for a structure convected anti-sunward across the spacecraft). Examples of both types of signatures are found, some within minutes of each other, suggesting that at least some pulsations probably originate from the growth and steepening of upstream waves but may eventually be able to stand in the upstream flow, perhaps becoming part of the shock surface itself. The possibility that some of the pulsations may simply be brief encounters with the moving shock is also not ruled out.

Thomsen, M. F.↗

NASA NTRS1982

Spectrophotometry of the Cygnus Loop

New spectrophotometry for 17 filaments in the Cygnus Loop are presented. A wide variety of spectral properties is observed within the remnant. Comparisons with published shock models indicate significant differences between the models and observations with the range of observed line intensities not well described by models with varying shock velocity. Interference-filter photographs of the remnant's northeastern, northwestern, and western nebulae in H-alpha + N II, S II, O III, and O I show radial variations of line emission intensity with a scale much larger than that expected from a shock moving through a uniform medium. It is suggested that the emission variations and apparent ionization structure are the result of the shock front encountering an inhomogeneous interstellar medium.

Fesen, R. A.↗

NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. The paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third-order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation is quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows, Kristine R.↗

NASA NTRS1994

Computing unsteady shock waves for aeroacoustic applications

The computation of unsteady shock waves, which contribute significantly to noise generation in supersonic jet flows, is investigated. This paper focuses on the difficulties of computing slowly moving shock waves. Numerical error is found to manifest itself principally as a spurious entropy wave. Calculations presented are performed using a third order essentially nonoscillatory scheme. The effect of stencil biasing parameters and of two versions of numerical flux formulas on the magnitude of spurious entropy are investigated. The level of numerical error introduced in the calculation in quantified as a function of shock pressure ratio, shock speed, Courant number, and mesh density. The spurious entropy relative to the entropy jump across a static shock decreases with increasing shock strength and shock velocity relative to the grid, but is insensitive to Courant number. The structure of the spurious entropy wave is affected by the choice of flux formulas and algorithm biasing parameters. The effect of the spurious numerical waves on the calculation of sound amplification by a shock wave is investigated. For this class of problem, the acoustic pressure waves are relatively unaffected by the spurious numerical phenomena.

Meadows,, Kristine r.↗

NASA NTRS1974

Boundary-layer development and transition due to free-stream exothermic reactions in shock-induced flows

A study of the effect of free-stream thermal-energy release from shock-induced exothermic reactions on boundary-layer development and transition is presented. The flow model is that of a boundary layer developing behind a moving shock wave in two-dimensional unsteady flow over a shock-tube wall. Matched sets of combustible hydrogen-oxygen-nitrogen mixtures and inert hydrogen-nitrogen mixtures were used to obtain transition data over a range of transition Reynolds numbers from 1,100,000 to 21,300,000. The heat-energy is shown to significantly stabilize the boundary layer without changing its development character. A method for application of this data to flat-plate steady flows is included.

Hall, J. L.↗

NASA NTRS2018

Overview of Recent EAST Testing, Modeling & Analysis

Shock Layer Radiation at NASA Ames - Background: Complex aerothermal and thermochemical phenomena of planetary entry define convective and radiative heating. A spacecraft's TPS (Thermal Protective System) mitigates heat transfer to substructure. Successful TPS design relies on verifiable characterization of these phenomena in the anticipated flight environment. - Approach: EAST (Electric Arc Shock Tube) [facility at Ames] simulates high-enthalpy, real-gas phenomena encountered by hypersonic vehicles entering planetary atmospheres by spectrally imaging the flow behind a moving shock wave. - Goal: Validate aerothermal models (DPLR (Data Parallel Line Relaxation Code) and NEQAIR (Nonequilibrium Radiative Transport and Spectra Program)), inform model improvements, reduce uncertainty and quantify design uncertainties. - Recent Relevant Projects: MSL (Mars Science Laboratory) & Mars 2020, InSight, OSIRIS-REx (Origins Spectral Interpretation Resource Identification Security Regolith Explorer), Orion EFT-1 (Exploration Flight-1) and EM-1 (Exploration Mission-1) and New Frontiers.

Brandis, Aaron↗

NASA NTRS1985

Cometary kilometric radio waves and plasma waves correlated with ion pick-up effect at Comet Halley

Bow-shock movements at Comet Halley are inferred from the discrete spectra of the cometary kilometric radiation (30-195 kHz); the observed emissions can be interpreted as being generated and propagating from the moving shock. The shock motion is possibly associated with the time variation of the solar wind and cometary outgassing. It is concluded that these plasma wave phenomena are manifestations of ion pick-up processes, which occur even in a remote region 7 million to 10 million km from the cometary nucleus.

Oya, H.↗

NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗