SHOCK-WAVE PROFILES OVER ELLIPSOIDAL-NOSED BODIES IN HYPERSONIC FLOW
Shock-wave profiles over ellipsoidal-nosed bodies in hypersonic flow
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Shock-wave profiles over ellipsoidal-nosed bodies in hypersonic flow
Shock wave impingement effects on heat transfer on cylindrical leading edge
The region surrounding the Crab Nebula is searched for the existence of a shock wave with the imaging instruments of the Einstein Observatory. The search is complicated by the scattering of nebula and pulsar X-rays from the imperfectly polished surfaces of the telescope mirror, as well as from interstellar grains along the line of sight. Both of these effects lead to the appearance of X-ray emission, in the form of an X-ray halo, beyond the boundaries of the nebula filaments. It is shown that the size, shape, and intensity of the halo around the Crab Nebula, above the contribution of mirror scattering, is consistent with what is expected from the scattering from interstellar grains. The upper limit on the X-ray emission from a shock wave is about 1 percent of the total 0.5-4 keV luminosity of the Crab, or about 2 x 10 to the 35th ergs/sec (assuming a distance of 2.2 kpc). This figure applies to a shell whose angular radius is 9 arcminutes. The upper limit is smaller (larger) for a shell of larger (smaller) size. This upper limit is an order of magnitude or more below the flux of Cas A, Tycho, and Kepler SNRs, which are 2 to 3 times younger, but it is still above that of SN 1006.
Cold wall and multibody collision effects on reflection of imploding shock waves using Monte Carlo method and molecular dynamics
We have constructed models that predict the dynamic evolution and infrared (IR) emission of grains behind nonradiative shock waves. We present a self-consistent treatment of the effect of grain destruction and heating on the ionization structure and X-ray emission of the postshock gas. Incorporating thermal sputtering, collisional heating, and deceleration of grains in the postshock flow, we predict the IR and X-ray fluxes from the dusty plasma as a function of swept-up column density. Heavy elements such as C, O, Mg, S, Si and Fe are initially depleted from the gas phase but are gradually returned as the grains are destroyed. The injected neutral atoms require some time to 'catch up' with the ionization state of the ambient gas. The nonequilibrium ionization state and gradient in elemental abundances in the postshock flow produces characteristic X-ray signatures that can be related to the age of the shock and amount of grain destruction. We study the effects of preshock density and shock velocity on the X-ray and IR emission from the shock. We show that the effects of graindestruction on the X-ray spectra of shock waves are substantial. In particular, temperatures derived from X-ray spectra of middle-aged remnants are likely to be overestimated by approximately 15% if cosmic abundances are assumed. Due to the long timescales for grain destruction in X-ray gases over a wide range of temperatures, we suggest that future X-ray spectra studies of supernova remnants be based on depleted abundances instead of cosmic abundances. Our model predictions agree reasonably well with IRAS and Einstein IPC observations of the Cygnus Loop.
The intensity of shock-wave noise at the ground resulting from flights at Mach numbers to 2.0 and altitudes to 60,000 feet was measured. Meagurements near the ground track for flights of a supersonic fighter and one flight of a supersonic bomber are presented. Level cruising flight at an altitude of 60,000 feet and a Mach number of 2.0 produced sonic booms which were considered to be tolerable, and it is reasonable t o expect that cruising flight at higher altitudes will produce booms of tolerable intensity for airplanes of the size and weight of the test airplanes. The measured variation of sonic-boom intensity with altitude was in good agreement with the variation calculated by an equation given in NASA Technical Note D-48. The effect of Mach number on the ground overpressure is small between Mach numbers of 1.4 and 2.0, a result in agreement with the theory. No amplification of the shock-wave overpressures due to refraction effects was apparent near the cutoff Mach number. A method for estimating the effect of fligh-path angle on cutoff Mach number is shown. Experimental results indicate agreement with the method, since a climb maneuver produced booms of a much decreased intensity as compared with the intensity of those measured in level flight at about the same altitude and Mach number. Comparison of sound pressure levels for the fighter and bomber airp lanes indicated little effect of either airplane size or weight at an altitude of 40,000 feet.
An experimental and computational research program providing new knowledge of the heat transfer in swept-shock-wave/boundary-layer interactions is described. An equilibrium turbulent boundary layer on a flat plate is subjected to impingement by a swept planar shock wave generated by a sharp fin. Five different interactions with fin angles ranging from 10 to 20 deg at freestream Mach numbers of 3 and 4 produce a variety of interaction strengths ranging from weak to very strong. A foil heater generates a uniform heat flux over the flat plate surface, and miniature thin-film-resistance sensors are used to measure the local surface temperature. The heat convection equation is then solved for the heat transfer distribution within an interaction, yielding an uncertainty of about +/- 10%. These data are compared with numerical Navier-Stokes solutions that employ a k-epsilon turbulence model. A simple peak heat transfer correlation for fin interactions is suggested.
An asymptotic description is derived for the interaction of a weak normal shock wave and a turbulent boundary layer along a plane wall. In the case studied the nondimensional friction velocity is small in comparison with the nondimensional shock strength, and the shock wave extends well into the boundary layer. Analytical results are described for the local pressure distribution and wall shear, and a criterion for incipient separation is proposed. A comparison of predicted pressures with available experimental data includes the effect of longitudinal wall curvature.
The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
Combustion instability of solid propellants due to shock waves
Hydrodynamic variables in primary and reflected argon and nitrogen shock waves
Shock wave effects on generation of high infensity molecular beams by nozzles
Halley plasma electron parameters from 2.7 million km from the comet nucleus to the bow shock wave at 1.1 million km and beyond are surveyed. The features of the electron foreshock lying outside the shock to a distance of 230,000 km are described. It is a region of intense solar wind-comet plasma interaction in which energetic electrons are prominent. Several spikes of electrons whose energies extend to 2.5 keV appear in front of the shock. These energetic electrons may be accelerated in the same way electrons are accelerated at the Earth's bow shock to energies of 1 to 10 keV. The direction of the electron bulk flow direction changes abruptly between 1920 and 1922 UT, and the flow speed begins a sharp decline at the same time. It is suggested that the spacecraft entered the bow shock wave between 1920 and 1922 UT. Electron density variations at Halley are very much smaller than those at Giacobini-Zinner.
The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross (1961) which included both experimental schlieren pictures and theoretical calculations using Whitham's ray-shock theory and results of the present finite difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects which are not accounted for by the Euler equations.
Aerodynamic heating rates are calculated from time-dependent temperature measurements in the vicinity of shock-wave boundary-layer interactions due to conical compression ramps on an axisymmetric body. The data were acquired at the Ohio State University Aeronautical and Astronautical Research Laboratory and at the Air Force Flight Dynamics Laboratory at Mach numbers of 6 and 10. The model is a cylindrical body with a 10 deg conical nose. Conical ramps with half-angles of 10, 20, 25, 30, and 35 deg serve as shock-wave generators. Flowfield surveys are made in the vicinity of the ramp vertices, separation points, and reattachment points. Experimental results quantify temperature response and the resulting heat transfer rates as a function of ramp angle, Reynolds number and freestream Mach number. The temperature responses within the flowfield appear to be steady-state for all angles and all Reynolds numbers, and hence, the heat transfer rates appear to be steady-state.
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.
A detailed qualitative analysis of the processes leading to the explosive ignition of a reactive liquid droplet that is suspended in a gas-phase oxidizer and subjected to the passage of a shock wave, is presented. The interval of time between shock wave passage and ignition is described by identifying a two-stage process which consists of a period of relative reactive dormancy that is followed by a chemical induction period leading to the thermal explosion of reactant that has been stripped from the liquid drop, vaporized, and mixed with the gas-phase oxidizer. The results of first-order calculations based on this model are presented and compared with experimental data for diethlcyclohexane drops in oxygen.