Relativistic shock structure.
Relativistic theory for plane shock wave in ionized hydrogen
SHOCK WAVE↗
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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 For this reason it is no longer valid to treat the shock wave as a discontinuous jump and it becomes necessary to compute through the shock wave itself.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.↗
Theoretical and experimental aspects of the shock structure problem.
Numerical solution of Bhatnagar-Gross-Krook model for shock wave structure problem, noting Chapman-Enskog approximation
KROOK EQUATION↗
Shock associated noise of inverted-profile coannular jets. II - Condition for minimum noise. III - Shock structure and noise characteristic
The generation of noise by the shock-turbulence interaction with shock cells in an inverted-profile coannular jet with nozzle exit velocity aligned with the jet axis is investigated analytically, interpreting the optical measurements of Tanna et al. (1985). The noise-intensity minimum at slightly supersonic primary-flow velocities is related to the weakness of the primary-stream shock-cell structure and the lack of such a pattern in the outer fan stream. The discrepancies between this finding and those of Dosanjh et al. (1977 and 1978) are attributed to nozzle design, the definition of minimum noise, and different interpretative approaches. A first-order shock-cell model is then developed to derive formulas for the peak frequencies and the scaling of noise intensity. The results of computations using these formulas are presented in graphs and found to be in good agreement with the experimental data.
Tam, C. K. W.↗
Observations of large-amplitude MHD waves in Jupiter's foreshock in connection with a quasi-perpendicular shock structure
Plasma and magnetic field observations performed onboard the Voyager 2 spacecraft have been used to investigate Jupiter's foreshock. Large-amplitude waves have been detected in association with the quasi-perpendicular structure of the Jovian bow shock, thus proving that the upstream turbulence is not a characteristic signature of the quasi-parallel shock.
Bavassano-Cattaneo, M. B.↗
Testing continuum descriptions of low-Mach-number shock structures
Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier-Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater that 1.2, the Burnett predictions are more accurate than the Navier-Stokes results. Temperature-density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.
Pham-Van-diep, Gerald C.↗
Comparison of experimental and computational shock structure in a transonic compressor rotor
Measurement of passage shock strength in a transonic compressor rotor using a gas fluorescent technique revealed an unexpected variation in shock strength in the radial direction. An axisymmetric idealization would normally predict that the passage shock strength would gradually weaken when moving radially inward until disappearing at the sonic radius. However, the measurements indicated a sharp peak in strength at the nominal sonic radius. Blade boundary layer separation originating at this point accounts for about one half of the total rotor losses. A numerical computation of the three-dimensional inviscid flow, using time-marching techniques, has accurately predicted in general the radial and tangential variations in passage shock strength and in particular the sharp pressure peak at the nominal sonic radius. The overall shock strength was somewhat overpredicted, but this overprediction may be the result of boundary layer separation in the experiment. This paper presents comparisons between the optical density measurements and computational results and in addition a short analytical discussion which demonstrates that the sharp shock strength rise may occur in many transonic compressor rotors.
Haymann-Haber, G.↗
Shock structure in classical magnetohydrodynamics
How the structure of coplanar MHD fast and slow shocks depends upon the relative magnitudes of the dissipation coefficients contained in classical magnetohydrodynamics is examined. An asymptotic method is used in which the scale lengths for resistivity, thermal conduction, and viscosity are widely separated, and the qualitative dependence of the shock solutions upon the ordering of the scales is studied. Upper limit Mach numbers for both fast and slow shocks are defined at which resistivity and thermal conduction taken together can provide all the shock dissipation and at which viscosity is not needed.
Kennel, Charles F.↗
Shock structure for the seven-equation, two-phase continuum-mixture model
Not Available
5-equation reduced model↗
Relativistic magnetosonic shock waves in synchrotron sources - Shock structure and nonthermal acceleration of positrons
The theoretical properties of relativistic, transverse, magnetosonic collisionless shock waves in electron-positron-heavy ion plasmas of relevance to astrophysical sources of synchrotron radiation are investigated. Both 1D electromagnetic particle-in-cell simulations and quasi-linear theory are used to examine the spatial and kinetic structure of these nonlinear flows. A new process of shock acceleration of nonthermal positrons, in which the gyrating reflected heavy ions dissipate their energy in the form of collectively emitted, left-handed magnetosonic waves which are resonantly absorbed by the positrons immediately behind the ion reflection region, is described. Applications of the results to the termination shocks of pulsar winds and to the termination shocks of jets emanating from the AGN are outlined.
Hoshino, Masahiro↗
Drop Interactions with the Conical Shock Structure Generated by a Mach 4.5 Projectile
This work presents measurements of liquid drop deformation and breakup time behind approximately conical shock waves and evaluates the predictive capabilities of low-order models and correlations developed using planar shock experiments. A conical shock was approximated by firing a bullet at Mach 4.5 past a vertical column of water drops with a mean initial diameter of $192$ $\mu$m. The time-resolved drop position and maximum transverse dimension were characterized using backlit stereo images taken at 500 kHz. The gas density and velocity fields experienced by the drops were estimated using a Reynolds-averaged Navier–Stokes simulation of the bullet. Classical correlations predict drop breakup times and deformation in error by a factor of 3 or more. The Taylor analogy breakup (TAB) model predicts deformed drop diameters that agree within the confidence bounds of the ensemble-averaged experimental values using a dimensionless constant $C$ 2 = $2$ compared to the accepted value $C$ 2 = $2/3$. In conclusion, results demonstrate existing correlations are inadequate for predicting the drop response to the three-dimensional relaxation of the flowfield downstream of a conical-like shock and suggest the TAB model results represent a path toward improved predictions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Three-dimensional shock structure in a transonic flutter cascade
Rapid double-pulse holography was employed to obtain detailed, two-dimensional images of the shock forming during simulated flutter in a transonic flowfield. The experiment comprised a linear cascade of airfoils externally oscillated in torsion and viewed tangentially at the shock surface. Three biconvex airfoils were subjected to harmonic pitching motion about the midchord axis at a frequency of 0.53 while immersed in a Mach 0.81 flow. Failure to produce observable shocks led to use of choked flow with a Mach number near one, of which 50 holograms were taken. The images revealed a narrow shock surface with a spanwise variation in the shock properties. The method is concluded to be useful for examining transonic flowfield shocks in the presence of airfoil flutter.
Boldman, D. R.↗
Cosmic ray decreases and shock structure: A multispacecraft study
We examine greater than 60-MeV/amu ion data from three spacecraft (IMP 8 and Helios 1 and 2) at the time of a number of short term (less than 20-day duration) cosmic ray decreases (greater than 1 GeV) detected by ground-based neutron monitors in the years 1976 to 1979. The multispacecraft data allow us to investigate the structure of the modulation region and in particular the relative importance, as a function of location, of the shock and shock driver (ejecta) in causing the reduction in particle densities. Although the shocks contributing to cosmic ray decrease often have particle enhancements associated with them in the greater than 60-meV/amu data, this is not the case for three of the events discussed in this paper where a shock-associated decrease is also evident. Whereas the shock can cause an increase or decrease at low (i.e., less than neutron monitor) energies, the reduction of particle densities in the driver, if it is intercepted, is usually evident at all energies. Thus the overall shape of a decrease at greater than 60 MeV/amu depends primarily on whether the ejecta is intercepted. We find that the particle density inside ejecta increases with increasing radical distance from the Sun. In many of the events in this study, entry and exit of ejecta are accompanied by abrupt changes in the decrease and recovery rates which indicate that the effect of the ejecta is local. In contrast, the effect of the shock lasts many days after the shock has passed by and is evident at large angular distances from the longitude of the solar source, i.e., the effect of the shock is nonlocal. Within 1 AU there seems to be no radial dependence of the shock effect. One cosmic ray decrease seen at Earth, which had an unusual profile, can be understood if the median plane of the ejecta was inclined to the ecliptic.
Cane, H. V.↗
Three-dimensional structured shocks in AM Herculis-type systems. II - Cyclotron emission from ridge-shaped emission regions
The properties of cyclotron emission from accretion shocks in AM Herculis binaries are studied which result from nonuniform accretion onto linearly extended regions on the surface of the magnetic white dwarf. The resulting ridge-shaped postshock structures yield cyclotron spectra with prominent harmonic features over a wide range of viewing aspects, even for high total accretion rates, in contrast to what has been found previously for axisymmetric accretion shocks.
Wu, Kinwah↗
Monte Carlo simulation of steady state shock structure including cosmic ray mediation and particle escape
Both hydrodynamic calculations (Drury and Volk, 1981, and Axford et al., 1982) and kinetic simulations imply the existence of thermal subshocks in high-Mach-number cosmic-ray-mediated shocks. The injection efficiency of particles from the thermal background into the diffusive shock-acceleration process is determined in part by the sharpness and compression ratio of these subshocks. Results are reported for a Monte Carlo simulation that includes both the back reaction of accelerated particles on the inflowing plasma, producing a smoothing of the shock transition, and the free escape of particles allowing arbitrarily large overall compression ratios in high-Mach-number steady-state shocks. Energy spectra and estimates of the proportion of thermal ions accelerated to high energy are obtained.
Ellison, D. C.↗
Shock structure and noise of supersonic jets in simulated flight to Mach 0.4
Measured jet plume static pressure distributions and far-field acoustic spectra are presented for underexpanded jets in simulated flight up to a Mach number of 0.4. A gradual stretching of the downstream shock cells is found as the Mach number increases, with no perceptible change in the shock strength. There appears to be little effect of flight on the broadband shock noise amplitudes, and the small changes in its peak frequency for the same emission angle are correlated with the slightly longer shock cells in flight. The larger changes in the broadband peak frequency found at the same angle in wind tunnel coordinates are attributable to convection. Jet mixing noise production decreases significantly with increasing flight speed.
Norum, Thomas D.↗
The Shock Structure of Supernova Remnant IC443
We present and discuss ISO observations of IC443, a supernova remnant interacting with a molecular cloud. An SWS spectrum centered on molecular hydrogen clump R10E (RA(2000) = 6 17 7.6, Decl(2000) = 22 25 34.6) is dominated by strong [SiII] (34 microns) emission and the pure rotational transitions of molecular hydrogen ranging from 0-0 S(1) to 0-0 S(13). Fits to these H$-2$ lines imply a large column (approx. 7E19 cm$ {-2)$) of warm (T approx. 700 K) gas and an ortho/para ratio for hydrogen near 3. LWS Fabry-Perot spectra of [OI] (63 microns) and [CII] (158 microns) at positions R10E and C (RA(2000) = 6 17 42.8, Decl(2000) = 22 21 38.1) find broad (approx. 75 km/s), blue-shifted (-40 km/s) line profiles; their similarity strongly suggests a common, shock-generated origin for these two lines. The surprisingly large [CII]/[OI] ratio (approx. 0.1 to 0.2) confirms previous observations with the Kuiper Airborne Observatory. These [CII] and [OI] line intensities, the [SiII] intensity (above), and LWS grating measurements of OH (119 microns) and [OI] (145 microns) are all readily fit by a single, fast J-shock model. Although the [OI] (63) emission can alternatively be produced by a slow C-shock, this ensemble of lines can not be produced by such a shock and provides strong evidence for the existence of a J-shock. A 24-arcmin strip map shows that this far-infrared line emission is spatially correlated with the H$-2$ 1-0 S(1) emission, which most likely arises in an associated C-shock. In addition to this spatially correlated shock emission, the strip map identifies extended [CII] and [OI] emission with a significantly larger line ratio (approx. 0.6); this 'background' component is compared with current J-shock, C-shock, photo-dissociation region (PDR), and X-ray dissociation region (XDR) models in an effort to explain its origin.
Haas, Michael R.↗
SHOCK STRUCTURE AND THE LEADING EDGE PROBLEM
Rarefied gas dynamics - low density flow near leading edge of flat plate in hypersonic stream
HYPERSONIC FLOW↗