Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “shock jumps”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

On the noncoplanarity of the magnetic field within a fast collisionless shock

Within the magnetic ramp of fast collisionless plasma shocks observed with spacecraft instruments and simulated numerically, the magnetic field undergoes an excursion out of the plane of coplanarity. This rotation is consistently in the direction such that the electrostatic potential jump across the shock, as measured in the de Hoffman-Teller frame of the reference (HTF), is about 2-6 times smaller than the electrostatic potential jump measured in the normal incidence frame. The preferred direction is consistent with a basic whistler mode transition between the upstream and downstream orientations. The potential jump in the HTF is considerably smaller than the change in bulk flow energy across the shock, confirming the recent suggestion that magnetic forces contribute importantly to the slowing of the plasma in that frame. A further consequence is that suprathermal particles leaking back into the upstream region across the shock do not gain much energy from the cross-shock electric field.

Thomsen, M. F.↗

An analytic treatment of the structure of the bow shock and magnetosheath

A theoretical examination of the jump conditions of the bow shock is used to investigate the influence of the solar wind magnetic fields on the structure of the parameters behind the bow shock. Through the assumption that the average values of the parameters along the radial direction in the magnetosheath are equal to their values just behind the bow shock, the influence of the direction of the solar wind magnetic fields on the average structure of the magnetosheath is determined. From this assumption, a zero-order formula for the thickness of the magnetosheath is deduced which satisfies the boundary conditions and conservation laws of mass and momentum flux. The theoretical estimate of the thickness is compared with satellite observations to check the assumption and select the optimum value of the polytropic exponent of the plasma gas.

Zhuang, H. C.↗

Comparison of characteristics and shock capturing methods with application to the space shuttle vehicle.

A critical appraisal is presented of a method-of-characteristics (MOC) and a shock-capturing technique (SCT) for calculating three-dimensional supersonic flow. Detailed comparisons are made for pointed and blunt-nosed bodies with a thick delta wing at angles of attack from 5 to 15 deg. The results show excellent agreement between the methods and with experiment. It is established that the SCT code yields accurate shock locations and jump conditions. The SCT code typically requires about three times as many mesh points as the MOC code in order to resolve the bow shock, but the total computation time is about the same. On a point for point basis, the SCT code is about four times faster than the MOC code.

Rakich, J. V.↗

Distant Bow Shock Observations by Explorer 33

Locations, orientations and magnetic field changes are given for 135 bow shock crossings at distances downstream from earth between 84 and 117 earth radii. The shock locations are dependent on the spacecraft trajectory and agree with locations calculated for the hypersonic analogue for a Mach number of 3.8. The shock normal vectors have been calculated using magnetic coplanarity. The average normal vectors have a greater inclination by approximately 17 + or - 5 deg from the symmetry axis than the Dryer and Heckman shock orientations for a 3.8 Mach number. Over a range of downstream distances from 60 to 115 earth radii, the median magnetic field magnitude jump across the shock changes from 1.90 to 1.70 times.

Mihalov, J. D.↗

Distant bow shock observations by Explorer 33

Locations, orientations and magnetic field changes are given for 135 bow shock crossings at distances downstream from earth between 84 and 117 earth radii. The shock locations bracket those calculated for the hypersonic analogue by Dryer and Heckman (1967) for a Mach number of 3.8. The shock normal vectors have been calculated using magnetic coplanarity. The average normal vectors have a greater inclination by about 17 plus or minus 5 deg from the symmetry axis than the Dryer and Heckman shock orientations for a 3.8 Mach number. Over a range of downstream distances from 60 to 115 earth radii, the median magnetic field magnitude jump across the shock changes from 1.90 to 1.70 times.

Mihalov, J. D.↗

Computation of nonlinear supersonic potential flow over three dimensional surfaces

A fully implicit three dimensional marching technique is presented for the computation of inviscid supersonic flows. The nonconservative full potential equation is solved on spherical cross flow planes using standard transonic SLOR techniques. The three dimensional bow shock is fitted as a boundary with isentropic jump conditions and embedded shocks are captured. Applications of these techniques are presented for three dimensional bodies, wings, and wing-body configurations and the computed solutions are compared to experimental pressure data. Zero lift wave drag calculations are also presented and compared with measurements to evaluate the accuracy of the present techniques.

Siclari, M. J.↗

Formation of slow shock pairs associated with coronal mass ejections

The formation of a forward-reverse slow shock pair in the solar corona is presently simulated by an MHD model that uses the Rankine-Hugoniot solution to calculate the flow-property jumps at all shock crossings. The shocks divide the solution-domain into several continuous flow regions whose respective governing characteristics are solved by the method of characteristics. The plasma impact compresses the plasma near the front of the coronal mass ejection (CME); as the CME-associated slow shock pair moves outwards in interplanetary space, it evolves into a pair of fast shocks. All three phenomena are eventually manifested in interplanetary space as a magnetic cloud accompanied by a fast shock pair, with a forward shock preceding the cloud and a reverse shock appearing either within or behind the cloud.

Whang, Y. V.↗

A Physical Relationship Between Electron-Proton Temperature Equilibration and Mach Number in Fast Collisionless Shocks

The analysis of Balmer-dominated optical spectra from nonradiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature at the blast wave is close to unity at v(s) approximate or smaller than 400 km s(-1) but declines sharply down to the minimum value of m(e) /m(p) dictated by the jump conditions at shock speeds exceeding 2000 km s(-1). We propose a physical model for the heating of electrons and ions in non-cosmic-ray-dominated, strong shocks (v(s) 400 km s(-1)) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the cosmic ray pressure gradient upstream from the shock. Our model predicts a nearly constant level of electron heating over a wide range of shock speeds, producing a relationship (T(e)/T(p))sub 0 proportional to v(-2/s) (proportional to M(-2)) that is fully consistent with the observations.

SNR(ONRADIATIVE SUPERNOVA REMNANTS)↗

A Strong Merger Shock in Abell 665

Deep (103 ks) Chandra observations of Abell 665 have revealed rich structures in this merging galaxy cluster, including a strong shock and two cold fronts. The newly discovered shock has a Mach number of M =3.0 +/- 0.6, propagating in front of a cold disrupted cloud. This makes Abell 665 the second cluster, after the Bullet cluster, where a strong merger shock of M is approximately 3 has been detected. The shock velocity from jump conditions is consistent with (2.7 +/- 0.7) × 10(exp 3) km s(exp −1). The new data also reveal a prominent southern cold front with potentially heated gas ahead of it. Abell 665 also hosts a giant radio halo. There is a hint of diffuse radio emission extending to the shock at the north, which needs to be examined with better radio data. This new strong shock provides a great opportunity to study the reacceleration model with the X-ray and radio data combined.

galaxies: clusters: general- galaxies: clisters; i↗

Shock interactions in the outer heliosphere

The results of recent simulations of the nonlinear evolution of the solar wind structures are reviewed, emphasizing theoretical development and the shock interactions model (SIM). Models which calculate jumps in flow properties across shocks without using exact Rankine-Hugoniot relations and models which do use them are addressed. The development of a computer code and some basic applications to the SIM are considered. Simulation results for the formation and propagation of forward-reverse shock pairs and the collision and merging of shocks are shown. Two studies which used the SIM to simulate nonlinear evolution of large-scale solar wind structures in the outer heliosphere are examined, and the SIM is then applied to study the heating of the solar wind in the outer heliosphere. The results support the hypothesis that shocks are mainly responsible for the heating of the solar wind plasma in the outer heliosphere at least up to 30 AU.

Whang, Y. C.↗

Computational fluid dynamics research in three-dimensional zonal techniques

Patched-grid algorithms for the analysis of complex configurations with an implicit, upwind-biased Navier-Stokes solver were investigated. Conservative and non-conservative approaches for performing zonal interpolations were implemented. The latter approach yields the most flexible technique in that it can handle both patched and overlaid grids. Results for a two-dimensional blunt body problem show that either approach yield accurate steady-state shock locations and jump conditions. In addition, calculations of the turbulent flow through a hypersonic inlet on a three-zone grid show that the numerical prediction is in good agreement with the experimental results. Through the use of a generalized coordinate transformation at the zonal interface between two or more blocks, the algorithm can be applied to highly stretched viscous grids and to arbitrarily-shaped zonal boundaries. Applications were made to the F-18 aircraft at subsonic, high-alpha conditions, in support of the NASA High-Alpha Research Program. The calculations were compared to ground-based and flight test experiments and were used as a guide to understanding the ground-based tests, which are laminar and transitional, and their relationship to flight. Calculations about a complete reconnaissance aircraft were also performed in order to further demonstrate the capability of the patched-grid algorithm.

Walters, Robert W.↗

Shock Waves in a Bose-Einstein Condensate

A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.

Kulikov, Igor↗

Siphon flows in isolated magnetic flux tubes. V - Radiative flows with variable ionization

Steady siphon flows in arched isolated magnetic flux tubes in the solar atmosphere are calculated here including radiative transfer between the flux tube and its surrounding and variable ionization of the flowing gas. It is shown that the behavior of a siphon flow is strongly determined by the degree of radiative coupling between the flux tube and its surroundings in the superadiabatic layer just below the solar surface. Critical siphon flows with adiabatic tube shocks in the downstream leg are calculated, illustrating the radiative relaxation of the temperature jump downstream of the shock. For flows in arched flux tubes reaching up to the temperature minimum, where the opacity is low, the gas inside the flux tube is much cooler than the surrounding atmosphere at the top of the arch. It is suggested that gas cooled by siphon flows contribute to the cool component of the solar atmosphere at the height of the temperature minimum implied by observations of the infrared CO bands at 4.6 and 2.3 microns.

Montesinos, Benjamin↗

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.↗

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.↗

Wave particle interactions in the foot of the Saturnian bow shock

Voyager 1 plasma wave data show that the quasi-perpendicular, supercritical bow shock of Saturn exhibits the same plasma wave phenomenology observed near Jupiter. Using a quasi-linear model developed for the Jovian bow shock, it is shown that plasma waves at Saturn can generate a significant portion of the totalelectron temperature jump measured across the shock. In this respect, Saturn's bow shock more closely resembles Jupiter's than the earth's, where plasma waves contribute negligibly to the total electron temperature jump.

Moses, S. L.↗

A numerical determination of the bow shock wave in transonic axisymmetric flow about blunt bodies

A numerical method was developed for calculating axisymmetric transonic (M greater than 1) flow about a blunt body; the bow shock wave location was investigated. A Rankine-Hugoniot jump was applied at the shock while relaxation on the isentropic equation of motion was used between shock and body. The shock wave is adjusted by a Newton type iteration scheme. Results are given for a sphere in the Mach number range 1.62 down to 1.02.

Jones, D. J.↗

Calculation of hypersonic shock structure using flux-split algorithms

There exists an altitude regime in the atmosphere that is within the continuum domain, but wherein the conventional Navier-Stokes equations cease to be accurate. The altitude limits for this so called continuum transition regime depend on vehicle size and speed. Within this regime the thickness of the bow shock wave is no longer negligible when compared to the shock stand-off distance and the peak radiation intensity occurs within the shock wave structure itself. For this reason it is no longer valid to treat the shock wave as a discontinuous jump and it becomes necessary to compute through the shock wave itself. To accurately calculate hypersonic flowfields, the governing equations must be capable of yielding realistic profiles of flow variables throughout the structure of a hypersonic shock wave. The conventional form of the Navier-Stokes equations is restricted to flows with only small departures from translational equilibrium; it is for this reason they do not provide the capability to accurately predict hypersonic shock structure. Calculations in the continuum transition regime, therefore, require the use of governing equations other than Navier-Stokes. Several alternatives to Navier-Stokes are discussed; first for the case of a monatomic gas and then for the case of a diatomic gas where rotational energy must be included. Results are presented for normal shock calculations with argon and nitrogen.

Eppard, W. M.↗