Normal shock waves in a compressible fluid.
Fundamental relations for normal shock wave behavior in compressible fluid for classical and hydromagnetic cases
NORMAL SHOCK WAVE↗
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Flight test measurements and analysis of sonic boom phenomena near the shock wave extremity
A NASA flight test program conducted during the summer and fall of 1970 was devoted to investigating sonic boom phenomena near caustics formed by steady flight near the threshold Mach number, during accelerations, and at the lateral extremes of the ground carpet. The vertical extent of the shock waves attached to near-sonic airplanes was also studied. The flights were conducted over the 1500 ft instrumented BREN tower so that vertical surveys through the shock waves were measured. These data on caustic phenomena near the shock wave extremity were analyzed in detail and compared with theoretical results. Amplifications of shock wave strength varied from 2 to 5 during longitudinal accelerations, from 1 to 1.8 during steady threshold Mach number flight, and up to 3 for small inadvertent accelerations during flight near the threshold Mach number.
Haglund, G. T.↗
Radiative transfer effects on reflected shock waves. II - Absorbing gas.
Radiative cooling effects behind a reflected shock wave are calculated for an absorbing-emitting gas by means of an expansion procedure in the small density ratio across the shock front. For a gray gas shock layer with an optical thickness of order unity or less the absorption integral is simplified by use of the local temperature approximation, whereas for larger optical thicknesses a Rosseland diffusion type of solution is matched with the local temperature approximation solution. The calculations show that the shock wave will attenuate at first and then accelerate to a constant velocity. Under appropriate conditions the gas enthalpy near the wall may increase at intermediate times before ultimately decreasing to zero. A two-band absorption model yields end-wall radiant-heat fluxes which agree well with available shock-tube measurements.
Su, F. Y.↗
Augmented shock wave fracture/severance of materials
The present invention related generally to severing materials, and more particularly to severing or weakening materials through explosively induced, augmented shock waves. Explosive cords are placed in grooves on the upper surface of the material to be severed or weakened. The explosive cords are initiated simultaneously to introduce explosive shock waves into the material. These shock waves progress toward the centerline between the explosive cords and the lower surface of the material. Intersecting and reflected waves produce a rarefaction zone on the centerline to fail the material in tension. A groove may also be cut in the lower surface of the material to aid in severing or weakening the material.
Schimmel, Morry L.↗
The carbon dioxide chaperon efficiency for the reaction H + O2 + M yields HO2 + M from ignition delay times behind reflected shock waves
Ignition delay times for stoichiometric hydrogen-oxygen in argon with and without carbon dioxide were measured behind reflected shock waves. A 20-reaction kinetic mechanism models the measured hydrogen-oxygen delay times over the temperature range 950 to 1300 K. The chaperon efficiency for carbon dioxide determined for the hydrogen-oxygen carbon dioxide mixture was 7.0. This value is in agreement with literature values but much less than a recent value obtained from flow tube experiments. Delay times measured behind a reflected shock wave were about 20% longer than those measured behind incident shock waves. The kinetic mechanism successfully modeled the high-pressure data of Skinner and the hydrogen-air data of Stack. It is suggested that the lowest temperature points for the hydrogen-air data of Slack are unreliable and that the 0.27-atm data may illustrate a case where vibrational relaxation of nitrogen is important. The reaction pathway HO2 yields H2O2 yields OH yields H was required to model the high-pressure data of Skinner. The successful modeling of the stoichiometric hydrogen-air data demonstrates the appropriateness of deriving kinetic models from data for gas mixtures highly diluted with argon. The technique of reducing a detailed kinetic mechanism to only the important reactions for a limited range of experimental data may render the mechanism useless for other test conditions.
Brabbs, Theodore A.↗
Far-Infrared Water Emissions from Magnetohydrodynamic Shock Waves
Nondissociative, magnetohydrodynamic, C-type shock waves are expected to be a prodigious source of far-infrared water emissions in dense interstellar regions. We have constructed a model to calculate the farinfrared H20 line spectra that emerge from such shocks. Using the best estimates currently available for the radiative cooling rate and the degree of ion-neutral coupling within the shocked gas, we modeled the temperature structure of MHD shocks using standard methods in which the charged and neutral particles are treated separately as two weakly coupled, interpenetrating fluids. Then we solved the equations of statistical equilibrium to find the populations of the lowest 179 and 170 rotational states of ortho- and para-H2O We have completed an extensive parameter study to determine the emergent H2O line luminosities as a function of preshock density in the range n(H2) equals 10(exp 4) - 10(sup 6.5)/cc and shock velocity in the range upsilon(sub s) = 5 - 40 km/ s. We find that numerous rotational transitions of water are potentially observable using the Infrared Space Observatory and the Submillimeter Wave Astronomy Satellite and may be used as diagnostics of the shocked gas. We have also computed the rotational and ro-vibrational emissions expected from H2, CO, and OH, and we discuss how complementary observations of such emissions may be used to further constrain the shock conditions. In common with previous studies, we come close to matching the observed H2, and high-J CO emissions from the Orion-KL star-forming region on the basis of a single shock model. We present our predictions for the strengths of H2O line emission from the Orion shock, and we show how our results may be scaled to other regions where molecular shocks are likely to be present.
Kaufman, Michael J.↗
Shock waves in the solar wind and geomagnetic storms.
Shock waves in solar wind and magnetic storms, deriving equations governing shock, ambient and driver gas velocities
SOLAR WIND↗
Collisionless shock waves in high beta plasmas. I, II.
Collisionless shock waves in plasmas with high beta parameter, discussing Alfven wave turbulence, firehose instability, dissipation and structure
PLASMA INSTABILITY↗
Transmission of singularities through a shock wave and the sound generation
The interaction of a plane shock wave of finite strength with a vortex line, point vortex, doublet or quadrupole of weak strength is studied. Based upon the physical condition that a free vortex line cannot support a pressure difference, rules are established which define the change of the linear intensity of the segment of the vortex line after its passage through the shock. The rules for point vortex, doublet, and quadrupole are then established as limiting cases. These rules can be useful for the construction of the solution of the entire flow field and for its physical interpretation. However, the solution can be obtained directly by the technique developed for shock diffraction problems. Explicit solutions and the associated sound generation are obtained for the passage of a point vortex through the shock wave.
Ting, L.↗
Shock waves in a beta Doradus model
The accumulation of observational evidence and interpretation supports the conclusion that beta Doradus has running shock waves in its atmosphere. It is the work by Hutchinson with its predictions for the phases of the shock waves that prompted this author to construct a numerical hydrodynamical model for the atmosphere of beta Doradus. A short description of the procedure of the calculation follows. The results for the beta Doradus model contain a comparison with the observations. It is of particular interest to verify that the atmosphere contains multiple shock waves as suggested by Hutchinson for the ultraviolet observations.
Hill, S. J.↗
On Reflection of Shock Waves from Boundary Layers
Measurements are presented at Mach numbers from about 1.3 to 1.5 of reflection characteristics and the relative upstream influence of shock waves impinging on a flat surface with both laminar and turbulent boundary layers. The difference between impulse and step waves is discussed and their interaction with the boundary layer is compared. General considerations on the experimental production of shock waves from wedges and cones and examples of reflection of shock waves from supersonic shear layers are also presented.
Liepmann, H W↗
The role of plasma wave turbulence in the formation of shock waves in collisionless plasmas
A data set containing measurements for approximately 100 shock crossings was compiled, and plasma wave profiles were plotted in conjunction with magnetic field data. Three emissions analyzed include upstream electron plasma oscillations, ion acoustic noise, and low frequency electromagnetic noise. The data demonstrate that the observed waves are consistent with generation by the kinetic cross-field streaming instability. Reanalysis of shock overshoots prompted by the presence of plasma feet upstream of nominally subcritical shocks leads to the conclusion that no firm evidence exists for a sharp subcritical supercritical transition. Electron plasma oscillations persist up to the ramps of subcritical shocks and begin decaying at the front edge of the feet of supercritical shocks. Their intensity is anticorrelated with the amplitude of the foot ion acoustic noise. Wave measurements support the predicted predominance of lower hybrid-like modes over ion acoustic noise in the production of resistive (plasma) heating. Evidence for variable shock normal angles is seen upstream from nominally quasiparallel shocks. The first cases of very strong electron heating observed at the terrestrial bow shock were discovered.
Mellott, M. M.↗
Collapse and fragmentation of molecular cloud cores. 2: Collapse induced by stellar shock waves
The standard scenario for low-mass star formation involves 'inside-out' collapse of a dense molecular cloud core following loss of magnetic field support through ambipolar diffusion. However, isotopic anomalies in presolar grains and meteoritical inclusions imply that the collapse of the presolar cloud may have been triggered by a stellar shock wave. This paper explores 'outside-in' collapse, that is, protostellar collapse initiated directly by the compression of quiescent dense cloud cores impacted by relatively slow stellar shock waves. A second-order accurate, gravitational hydrodynamics code has been used to study both the spherically symmetrical and three-dimensional evolution of initially centrally condensed, isothermal, self-gravitating, solar-mass cloud cores that are struck by stellar shock waves with velocities up to 25 km/s and postshock temperatures of 10 to 10,000 K. The models show that such mild shock waves do not completely shred and destroy the cloud, and that the dynamical ram pressure can compress the cloud to the verge of self-gravitational collapse. However, compression caused by a high postshock temperature is a considerably more effective means of inducing collapse. Shock-induced collapse produces high initial mass accretion rates (greater than 10(exp -4) solar mass/yr in a solar-mass cloud) that decline rapidly to much lower values, depending on the presence (approximately 10(exp -6) solar mass/yr) or absence (approximately 10(exp -8) to 10(exp -7) solar mass/yr) of an infinite reservoir of mass. Stellar mass accretion rates approximately 10(exp -7) solar mass/yr have been previously inferred from the luminosities of T Tauri stars; balanced mass accretion (stellar rate = envelope rate) at approximately 10(exp -7) solar mass/yr could then be possible if accretion occurs from a finite mass reservoir. Fluid tracers are used to determine what fraction of the stellar shock material is incorporated into the resulting protostellar object and disk; roughly half the impinging material is injected into the collapsing cloud core when there is a high postshock temperature. The models are consistent with a scenario where an AGB star wind triggered the collapse of the presolar cloud while injecting about 0.01 solar mass of matter derived from the AGB star envelope, as has been separately inferred on the basis of nucleosynthesis calculations.
Boss, Alan P.↗
Energetic solar flare particles and interplanetary shock waves
Estimates from hard X-ray measurements show that for many flares the bulk of the flare energy is released in the form of approximately 10-100-keV energy electrons. The interaction of these electrons with the solar atmosphere can produce the optical, UV, EUV, and radio emissions observed during the flare impulsive phase. In addition, explosive heating and evaporation of the chromosphere by these electrons can produce the roughly 10 million K soft X-ray plasma. For the large solar flares which produce interplanetary shock waves, the accelerated approximately 10-100-keV electron population may produce the heating and mass motion required for mass ejection and the formation of the shock wave. The shock wave can in turn accelerate ions and electrons to higher energy as it travels through the corona and interplanetary medium.
Lin, R. P.↗
Holographic flow visualization of time-varying shock waves
Rapid-double-exposure, diffuse-illumination holography is evaluated analytically and experimentally as a flow visualization method for time-varying shock waves. Conditions are determined that minimize the distance (localization error) between the surface or curve of interference-fringe localization and the shock surface. Treated specifically are the cases of shock waves in a transonic compressor rotor for which there is laser anemometer data for comparison and shock waves in a flutter cascade.
Decker, A. J.↗
Structure of ion acoustic solitons and shock waves in a two-component plasma.
Time-independent solitary waves and shocks are investigated in a two-component plasma using a fluid model and kinetic theory. It is found that very small concentrations of a light ion can drastically alter the structure, changing the potential maximum by an order of magnitude. For a fixed Mach number, a critical density ratio of light to heavy ions is found at which the potential maximum changes discontinuously from a value large enough to reflect the light ions to one which allows them to traverse the shock front and enter the downstream flow. The downstream oscillatory structure normally seen in a shock is completely quenched by dissipation due to light ion reflection at concentrations of 3-8% He in an Ar plasma for typical electron to ion temperature ratios and Mach number values.
White, R. B.↗
The physical mechanisms of subcritical collisionless shock-wave formation
The key process in shock wave formation is related to energy dissipation, and the nature of the operative dissipation mechanism determines the basic character of the resulting shock. In the case of collisionless plasmas, the primary problem consists in the identification of the processes which can provide the necessary dissipation in relatively short spatial scale lengths. The present investigation is concerned with the various collisionless dissipation mechanisms which can operate in weak shocks, taking into account the effects of different mechanisms on shock structure. Particular attention is given to a restricted class of quasi-perpendicular low beta low Mach number shocks. Such shocks are traditionally called 'laminar shocks'. Resistive shocks are considered along with subcritical shocks observed with the aid of the ISEE spacecraft.
Mellott, M. M.↗
Interaction of metallic powders with a shock wave through an oxidizing atmosphere.
Light output of shock wave interacting with metallic powder in oxidizing atmosphere
SHOCK WAVE INTERACTION↗