Shock formation in small-data solutions to 3D quasilinear wave equations

CERN Document Server

Speck, Jared

2016-01-01

In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he prov...

2-Shock layered tuning campaign

Science.gov (United States)

Masse, Laurent; Dittrich, T.; Khan, S.; Kyrala, G.; Ma, T.; MacLaren, S.; Ralph, J.; Salmonson, J.; Tipton, R.; Los Alamos Natl Lab Team; Lawrence Livermore Natl Lab Team

2016-10-01

The 2-Shock platform has been developed to maintain shell sphericity throughout the compression phase of an indirect-drive target implosion and produce a stagnating hot spot in a quasi 1D-like manner. A sub-scale, 1700 _m outer diameter, and thick, 200 _m, uniformly Silicon doped, gas-filled plastic capsule is driven inside a nominal size 5750 _m diameter ignition hohlraum. The hohlraum fill is near vacuum to reduce back-scatter and improve laser/drive coupling. A two-shock pulse of about 1 MJ of laser energy drives the capsule. The thick capsule prevents ablation front feed-through to the imploded core. This platform has demonstrated its efficiency to tune a predictable and reproducible 1-D implosion with a nearly round shape. It has been shown that the high foot performance was dominated by the local defect growth due to the ablation front instability and by the hohlraum radiation asymmetries. The idea here is to take advantage of this 2-Shock platform to design a 1D-like layered implosion and eliminates the deleterious effects of radiation asymmetries and ablation front instability growth. We present the design work and our first experimental results of this near one-dimensional 2-Shock layered design. This work was performed under the auspices of the Lawrence Livermore National Security, LLC, (LLNS) under Contract No. DE-AC52-07NA27344.

Entropy jump across an inviscid shock wave

Science.gov (United States)

Salas, Manuel D.; Iollo, Angelo

1995-01-01

The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

Computations of slowly moving shocks

International Nuclear Information System (INIS)

Karni, S.; Canic, S.

1997-01-01

Computations of slowly moving shocks by shock capturing schemes may generate oscillations are generated already by first-order schemes, but become more pronounced in higher-order schemes which seem to exhibit different behaviors: (i) the first-order upwind (UW) scheme which generates strong oscillations and (ii) the Lax-Friedrichs scheme which appears not to generate any disturbances at all. A key observation is that in the UW case, the numerical viscosity in the shock family vanishes inside the slow shock layer. Simple scaling arguments show the third-order effects on the solution may no longer be neglected. We derive the third-order modified equation for the UW scheme and regard the oscillatory solution as a traveling wave solution of the parabolic modified equation for the perturbation. We then look at the governing equation for the perturbation, which points to a plausible mechanism by which postshock oscillations are generated. It contains a third-order source term that becomes significant inside the shock layer, and a nonlinear coupling term which projects the perturbation on all characteristic fields, including those not associated with the shock family. 5 refs., 8 figs

Budget of Turbulent Kinetic Energy in a Shock Wave Boundary-Layer Interaction

Science.gov (United States)

Vyas, Manan A.; Waindim, Mbu; Gaitonde, Datta V.

2016-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Quantities present in the exact equation of the turbulent kinetic energy transport were accumulated and used to calculate terms like production, dissipation, molecular diffusion, and turbulent transport. The present results for a turbulent boundary layer were validated by comparison with direct numerical simulation data. It was found that a longer development domain was necessary for the boundary layer to reach an equilibrium state and a finer mesh resolution would improve the predictions. In spite of these findings, trends of the present budget match closely with that of the direct numerical simulation. Budgets for the SBLI region are presented at key axial stations. These budgets showed interesting dynamics as the incoming boundary layer transforms and the terms of the turbulent kinetic energy budget change behavior within the interaction region.

Shock timing measurements in DT ice layers

Science.gov (United States)

Robey, H. F.; Celliers, P. M.; Moody, J. D.; Sater, J.; Parham, T.; Kozioziemski, B.; Dylla-Spears, R. J.; Ross, J. S.; Lepape, S.; Ralph, J. E.; Berzak Hopkins, L. F.; Kroll, J. J.; Yoxall, B. E.; Hamza, A. V.; Boehly, T. R.; Nikroo, A.; Landen, O. L.; Edwards, M. J.

2013-10-01

Shock timing experiments on the National Ignition Facility (NIF) are routinely conducted using the keyhole target geometry, in which the strength and timing of multiple shocks are measured in a liquid-deuterium (D2) filled capsule interior. These targets have recently been modified to improve the surrogacy to ignition implosions by replacing the standard, continuous liquid D2 capsule fill with a deuterium-tritium (DT) ice layer with a central DT gas fill. These experiments remove any possible material surrogacy difference between D2 and DT as well as incorporating the physics of multiple shock release and recompression events from an ice layer of finite thickness, an effect that is absent in the liquid-filled targets. Experimental results and comparisons with numerical simulation are presented. Prepared by LLNL under Contract DE-AC52-07NA27344.

First-order partial differential equations

CERN Document Server

Rhee, Hyun-Ku; Amundson, Neal R

2001-01-01

This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

Science.gov (United States)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

Science.gov (United States)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Heat-flow equation motivated by the ideal-gas shock wave.

Science.gov (United States)

Holian, Brad Lee; Mareschal, Michel

2010-08-01

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

Transonic shock wave. Boundary layer interaction at a convex wall

NARCIS (Netherlands)

Koren, B.; Bannink, W.J.

1984-01-01

A standard finite element procedure has been applied to the problem of transonic shock wave – boundary layer interaction at a convex wall. The method is based on the analytical Bohning-Zierep model, where the boundary layer is perturbed by a weak normal shock wave which shows a singular pressure

Experimental research on crossing shock wave boundary layer interactions

Science.gov (United States)

Settles, G. S.; Garrison, T. J.

1994-10-01

An experimental research effort of the Penn State Gas Dynamics Laboratory on the subject of crossing shock wave boundary layer interactions is reported. This three year study was supported by AFOSR Grant 89-0315. A variety of experimental techniques were employed to study the above phenomena including planar laser scattering flowfield visualization, kerosene lampblack surface flow visualization, laser-interferometer skin friction surveys, wall static pressure measurements, and flowfield five-hole probe surveys. For a model configuration producing two intersecting shock waves, measurements were made for a range of oblique shock strengths at freestream Mach numbers of 3.0 and 3.85. Additionally, measurements were made at Mach 3.85 for a configuration producing three intersecting waves. The combined experimental dataset was used to formulate the first detailed flowfield models of the crossing-shock and triple-shock wave/boundary layer interactions. The structure of these interactions was found to be similar over a broad range of interaction strengths and is dominated by a large, separated, viscous flow region.

Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

Science.gov (United States)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan

2016-01-01

The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

Inaccuracy caused by the use of thermodynamic equation inside shock wave front

International Nuclear Information System (INIS)

Sano, Yukio; Abe, Akihisa; Tokushima, Koji; Arathoon, P.

1998-01-01

The aim of this study is to examine the difference between shock temperatures predicted by an equation for temperature inside a steady wave front and the Walsh-Christian equation. Calculations are for yttria-doped tetragonal zirconia, which shows an elastic-plastic and a phase transition: Thus the shock waves treated are multiple structure waves composed of one to three steady wave fronts. The evaluated temperature was 3350K at the minimum specific volume of 0.1175 cm 3 /g (or maximum Hugoniot shock pressure of 140GPa) considered in the present examination, while the temperature predicted by the Walsh-Christian equation under identical conditions was 2657K. The cause of the large temperature discrepancy is considered to be that the present model treats nonequilibrium states inside steady waves

Nonequilibrium effects on shock-layer radiometry during earth entry.

Science.gov (United States)

Arnold, J. O.; Whiting, E. E.

1973-01-01

Radiative enhancement factors for the CN violet and N2(+) first negative band systems caused by nonequilibrium thermochemistry in the shock layer of a blunt-nosed vehicle during earth entry are reported. The results are based on radiometric measurements obtained with the aid of a combustion-driven shock tube. The technique of converting the shock-tube measurements into predictions of the enhancement factors for the blunt-body case is described, showing it to be useful for similar applications of other shock-tube measurements.

Test of a new heat-flow equation for dense-fluid shock waves.

Science.gov (United States)

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

Notes on the Prediction of Shock-induced Boundary-layer Separation

Science.gov (United States)

Lange, Roy H.

1953-01-01

The present status of available information relative to the prediction of shock-induced boundary-layer separation is discussed. Experimental results showing the effects of Reynolds number and Mach number on the separation of both laminar and turbulent boundary layer are given and compared with available methods for predicting separation. The flow phenomena associated with separation caused by forward-facing steps, wedges, and incident shock waves are discussed. Applications of the flat-plate data to problems of separation on spoilers, diffusers, and scoop inlets are indicated for turbulent boundary layers.

Titan atmospheric composition by hypervelocity shock layer analysis

International Nuclear Information System (INIS)

Nelson, H.F.; Park, C.; Whiting, E.E.

1989-01-01

The Cassini Mission, a NASA/ESA cooperative project which includes a deployment of probe into the atmosphere of Titan, is described, with particular attention given to the shock radiometer experiment planned for the Titan probe for the analysis of Titan's atmosphere. Results from a shock layer analysis are presented, demonstrating that the mole fractions of the major species (N2, CH4, and, possibly Ar) in the Titan atmosphere can be successfully determined by the Titan-probe radiometer, by measuring the intensity of the CN(violet) radiation emitted in the shock layer during the high velocity portion of the probe entry between 200 and 400 km altitude. It is shown that the sensitivity of the CN(violet) radiation makes it possible to determine the mole fractions of N2, CH4, and Ar to about 0.015, 0.003, and 0.01, respectively, i.e., much better than the present uncertainties in the composition of Titan atmosphere. 29 refs

Laser-driven shock-wave propagation in pure and layered targets

International Nuclear Information System (INIS)

Salzmann, D.; Eliezer, S.; Krumbein, A.D.; Gitter, L.

1983-01-01

The propagation properties of laser-driven shock waves in pure and layered polyethylene and aluminum slab targets are studied for a set of laser intensities and pulse widths. The laser-plasma simulations were carried out by means of our one-dimensional Lagrangian hydrodynamic code. It is shown that the various parts of a laser-driven compression wave undergo different thermodynamic trajectories: The shock front portion is on the Hugoniot curve whereas the rear part is closer to an adiabat. It is found that the shock front is accelerated into the cold material till troughly-equal0.8tau (where tau is the laser pulse width) and only later is a constant velocity propagation attained. The scaling laws obtained for the pressure and temperature of the compression wave in pure targets are in good agreement with those published in other works. In layered targets, high compression and pressure were found to occur at the interface of CH 2 on Al targets due to impedance mismatch but were not found when the layers were reversed. The persistence time of the high pressure on the interface in the CH 2 on Al case is long enough relative to the characteristic times of the plasma to have an appreciable influence on the shock-wave propagation into the aluminum layer. This high pressure and compression on the interface can be optimized by adjusting the CH 2 layer thickness

Interaction of a conical shock wave with a turbulent boundary layer

Science.gov (United States)

Teh, S. L.; Gai, S. L.

The paper reports an investigation on the interaction of an incident conical shock wave with a turbulent boundary layer. Although a conical shock theoretically creates a hyperbolic shock trace on the flat plate, the line joining all the experimental interaction origins takes a different form due to varying upstream influence. The existence of strong pressure gradients in the spanwise direction after the shock leads to the boundary-layer twist. A model based on the upstream influence of the shock when combined with McCabe's secondary-flow theory showed separation to occur at an external flow deflection of 11.8 deg. The oil flow measurements however show this to occur at 9.2 deg. This discrepancy is of the same order as that found by McCabe. Detailed data involving Schlieren and shadowgraph photography, surface-flow visualization, and surface-pressure measurements are presented.

A Coordinate Transformation for Unsteady Boundary Layer Equations

Directory of Open Access Journals (Sweden)

Paul G. A. CIZMAS

2011-12-01

Full Text Available This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also proposed. The unsteady boundary layer equations are subsequently derived. In addition, the boundary layer equations are derived using a time linearization approach and assuming harmonically varying small disturbances.

Transonic Shock-Wave/Boundary-Layer Interactions on an Oscillating Airfoil

Science.gov (United States)

Davis, Sanford S.; Malcolm, Gerald N.

1980-01-01

Unsteady aerodynamic loads were measured on an oscillating NACA 64A010 airfoil In the NASA Ames 11 by 11 ft Transonic Wind Tunnel. Data are presented to show the effect of the unsteady shock-wave/boundary-layer interaction on the fundamental frequency lift, moment, and pressure distributions. The data show that weak shock waves induce an unsteady pressure distribution that can be predicted quite well, while stronger shock waves cause complex frequency-dependent distributions due to flow separation. An experimental test of the principles of linearity and superposition showed that they hold for weak shock waves while flows with stronger shock waves cannot be superimposed.

Uncertainty Assessments of 2D and Axisymmetric Hypersonic Shock Wave - Turbulent Boundary Layer Interaction Simulations at Compression Corners

Science.gov (United States)

Gnoffo, Peter A.; Berry, Scott A.; VanNorman, John W.

2011-01-01

This paper is one of a series of five papers in a special session organized by the NASA Fundamental Aeronautics Program that addresses uncertainty assessments for CFD simulations in hypersonic flow. Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission relevant conditions at Mach 7 and Mach 14 are defined for a pre-compression ramp of a scramjet powered vehicle. Three compression angles are defined, the smallest to avoid separation losses and the largest to force a separated flow engaging more complicated flow physics. The Baldwin-Lomax and the Cebeci-Smith algebraic models, the one-equation Spalart-Allmaras model with the Catrix-Aupoix compressibility modification and two-equation models including Menter SST, Wilcox k-omega 98, and Wilcox k-omega 06 turbulence models are evaluated. Each model is fully defined herein to preclude any ambiguity regarding model implementation. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model form uncertainty. A set of coarse grained uncertainty metrics are defined to capture essential differences among turbulence models. Except for the inability of algebraic models to converge for some separated flows there is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shock-turbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new, grid-converged solutions presented here. This value is consistent with existing results in a literature review of hypersonic shock-turbulent-boundary-layer interactions by Roy and Blottner and with more recent computations of MacLean.

Anti-diffusive radiation flow in the cooling layer of a radiating shock

International Nuclear Information System (INIS)

McClarren, Ryan G.; Paul Drake, R.

2010-01-01

This paper shows that for systems with optically thin, hot layers, such as those that occur in radiating shocks, radiation will flow uphill: radiation will flow from low to high radiation energy density. These are systems in which the angular distribution of the radiation intensity changes rapidly in space, and in which the radiation in some region has a pancaked structure, whose effect on the mean intensity will be much larger than the effect on the scalar radiation pressure. The salient feature of the solution to the radiative transfer equation in these circumstances is that the gradient of the radiation energy density is in the same direction as the radiation flux, i.e. radiation energy is flowing uphill. Such an anti-diffusive flow of energy cannot be captured by a model where the spatial variation of the Eddington factor is not accounted for, as in flux-limited diffusion models or the P 1 equations. The qualitative difference between the two models leads to a monotonic mean intensity for the diffusion model whereas the transport mean intensity has a global maximum in the hot layer. Mathematical analysis shows that the discrepancy between the diffusion model and the transport solution is due to an approximation of exponential integrals using a simple exponential.

Complete equation of state for shocked liquid nitrogen: Analytical developments

International Nuclear Information System (INIS)

Winey, J. M.; Gupta, Y. M.

2016-01-01

The thermodynamic response of liquid nitrogen has been studied extensively, in part, due to the long-standing interest in the high pressure and high temperature dissociation of shocked molecular nitrogen. Previous equation of state (EOS) developments regarding shocked liquid nitrogen have focused mainly on the use of intermolecular pair potentials in atomistic calculations. Here, we present EOS developments for liquid nitrogen, incorporating analytical models, for use in continuum calculations of the shock compression response. The analytical models, together with available Hugoniot data, were used to extrapolate a low pressure reference EOS for molecular nitrogen [Span, et al., J. Phys. Chem. Ref. Data 29, 1361 (2000)] to high pressures and high temperatures. Using the EOS presented here, the calculated pressures and temperatures for single shock, double shock, and multiple shock compression of liquid nitrogen provide a good match to the measured results over a broad range of P-T space. Our calculations provide the first comparison of EOS developments with recently-measured P-T states under multiple shock compression. The present EOS developments are general and are expected to be useful for other liquids that have low pressure reference EOS information available.

Simulation of shock-induced bubble collapse using a four-equation model

Science.gov (United States)

Goncalves, E.; Hoarau, Y.; Zeidan, D.

2018-02-01

This paper presents a numerical study of the interaction between a planar incident shock wave with a cylindrical gas bubble. Simulations are performed using an inviscid compressible one-fluid solver based upon three conservation laws for the mixture variables, namely mass, momentum, and total energy along with a supplementary transport equation for the volume fraction of the gas phase. The study focuses on the maximum pressure generated by the bubble collapse. The influence of the strength of the incident shock is investigated. A law for the maximum pressure function of the Mach number of the incident shock is proposed.

A systematic comparison of two-equation Reynolds-averaged Navier-Stokes turbulence models applied to shock-cloud interactions

Science.gov (United States)

Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.

2017-07-01

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

A transport equation for the evolution of shock amplitudes along rays

Directory of Open Access Journals (Sweden)

Giovanni Russo

1991-05-01

Full Text Available A new asymptotic method is derived for the study of the evolution of weak shocks in several dimension. The method is based on the Generalized Wavefront Expansion derived in [1]. In that paper the propagation of a shock into a known background was studied under the assumption that shock is weak, i.e. Mach Number =1+O(ε, ε ≪ 1, and that the perturbation of the field varies over a length scale O(ε. To the lowest order, the shock surface evolves along the rays associated with the unperturbed state. An infinite system of compatibility relations was derived for the jump in the field and its normal derivatives along the shock, but no valid criterion was found for a truncation of the system. Here we show that the infinite hierarchy is equivalent to a single equation that describes the evolution of the shock along the rays. We show that this method gives equivalent results to those obtained by Weakly Nonlinear Geometrical Optics [2].

Multi-layer protective armour for underwater shock wave mitigation

Directory of Open Access Journals (Sweden)

Ahmed Hawass

2015-12-01

The strain gauge data and displacement sensors results showed that the multi-layer plates have higher level of underwater shock wave mitigation than the triple aluminum plates with strain and deflection of nearly 50%.

Hypersonic Shock Wave Computations Using the Generalized Boltzmann Equation

Science.gov (United States)

Agarwal, Ramesh; Chen, Rui; Cheremisin, Felix G.

2006-11-01

Hypersonic shock structure in diatomic gases is computed by solving the Generalized Boltzmann Equation (GBE), where the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively [1]. The computational framework available for the standard Boltzmann equation [2] is extended by including both the rotational and vibrational degrees of freedom in the GBE. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with internal degrees of freedom: (1) a large velocity domain is needed for accurate numerical description of the distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 energy levels are needed for accurate representation of the rotational spectrum of the gas. Our methodology addresses these problems, and as a result the efficiency of calculations has increased by several orders of magnitude. The code has been validated by computing the shock structure in Nitrogen for Mach numbers up to 25 including the translational and rotational degrees of freedom. [1] Beylich, A., ``An Interlaced System for Nitrogen Gas,'' Proc. of CECAM Workshop, ENS de Lyon, France, 2000. [2] Cheremisin, F., ``Solution of the Boltzmann Kinetic Equation for High Speed Flows of a Rarefied Gas,'' Proc. of the 24th Int. Symp. on Rarefied Gas Dynamics, Bari, Italy, 2004.

On the Unsteadiness of a Transitional Shock Wave-Boundary Layer Interaction Using Fast-Response Pressure-Sensitive Paint

Science.gov (United States)

Lash, E. Lara; Schmisseur, John

2017-11-01

Pressure-sensitive paint has been used to evaluate the unsteady dynamics of transitional and turbulent shock wave-boundary layer interactions generated by a vertical cylinder on a flat plate in a Mach 2 freestream. The resulting shock structure consists of an inviscid bow shock that bifurcates into a separation shock and trailing shock. The primary features of interest are the separation shock and an upstream influence shock that is intermittently present in transitional boundary layer interactions, but not observed in turbulent interactions. The power spectral densities, frequency peaks, and normalized wall pressures are analyzed as the incoming boundary layer state changes from transitional to fully turbulent, comparing both centerline and outboard regions of the interaction. The present study compares the scales and frequencies of the dynamics of the separation shock structure in different boundary layer regimes. Synchronized high-speed Schlieren imaging provides quantitative statistical analyses as well as qualitative comparisons to the fast-response pressure sensitive paint measurements. Materials based on research supported by the U.S. Office of Naval Research under Award Number N00014-15-1-2269.

Transonic shock wave. Turbulent boundary layer interaction on a curved surface

NARCIS (Netherlands)

Nebbeling, C.; Koren, B.

1988-01-01

This paper describes an experimental investigation of a transonic shock wave - turbulent boundary layer interaction in a curved test section, in which the flow has been computed by a 2-D Euler flow method. The test section has been designed such that the flow near the shock wave on the convex curved

Converging shock flows for a Mie-Grüneisen equation of state

Science.gov (United States)

Ramsey, Scott D.; Schmidt, Emma M.; Boyd, Zachary M.; Lilieholm, Jennifer F.; Baty, Roy S.

2018-04-01

Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. The remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.

Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression

International Nuclear Information System (INIS)

Zheng, J.; Gu, Y. J.; Chen, Z. Y.; Chen, Q. F.

2010-01-01

Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter Γ range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to ∼6 km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.

Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression

Science.gov (United States)

Zheng, J.; Gu, Y. J.; Chen, Z. Y.; Chen, Q. F.

2010-08-01

Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter Γ range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to ˜6km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.

Time-resolved stereo PIV measurements of shock-boundary layer interaction on a supercritical airfoil

Energy Technology Data Exchange (ETDEWEB)

Hartmann, Axel; Klaas, Michael; Schroeder, Wolfgang [RWTH Aachen University, Institute of Aerodynamics, Aachen (Germany)

2012-03-15

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave-boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 x 10{sup 6} are analyzed regarding the origin and nature of the unsteady shock-boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa. (orig.)

Thermodynamically Based Equation of State for Shock Wave Studies : Application to the Design of Experiments on Tin

International Nuclear Information System (INIS)

Buy, Francois; Voltz, Christophe; Llorca, Fabrice

2006-01-01

This work is devoted to the evaluation of complex behavior of metals under shock wave loading. It presents a methodology for the design of specific experiments performed for validation of models and the evaluation of a multiphase equation of state for tin. This material has been selected because of the numerous works completed during the past years on its equation of state. We focus on the solid diagram which presents two solid phases. A thermodynamically based equation of state is developed which gives the opportunity to search for singularities which could be activated under particular shock wave loading. In the temperature -- pressure diagram, the superimposed Hugoniot and release paths make apparent a double shock, release shock configurations. We propose the design and the VISAR results of a calibrated shock -- reshock test for investigating the validity and the efficiency of the model for predicting the thermodynamical state of tin (phases mixing, temperature...). Comparison between numerical and experimental data shows the good accuracy of the results given by the EOS

RANS Modeling of Benchmark Shockwave / Boundary Layer Interaction Experiments

Science.gov (United States)

Georgiadis, Nick; Vyas, Manan; Yoder, Dennis

2010-01-01

This presentation summarizes the computations of a set of shock wave / turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock / boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Three turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Shear Stress Transport wavenumber-angular frequency two-equation model, and an explicit algebraic stress wavenumber-angular frequency formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.!

Shock-wave structure based on the Navier-Stokes-Fourier equations

Science.gov (United States)

Uribe, F. J.; Velasco, R. M.

2018-04-01

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.

High pressure generation by laser driven shock waves: application to equation of state measurement; Generation de hautes pressions par choc laser: application a la mesure d'equations d'etat

Energy Technology Data Exchange (ETDEWEB)

Benuzzi, A

1997-12-15

This work is dedicated to shock waves and their applications to the study of the equation of state of compressed matter.This document is divided into 6 chapters: 1) laser-produced plasmas and abrasion processes, 2) shock waves and the equation of state, 3) relative measuring of the equation of state, 4) comparison between direct and indirect drive to compress the target, 5) the measurement of a new parameter: the shock temperature, and 6) control and measurement of the pre-heating phase. In this work we have reached relevant results, we have shown for the first time the possibility of generating shock waves of very high quality in terms of spatial distribution, time dependence and of negligible pre-heating phase with direct laser radiation. We have shown that the shock pressure stays unchanged as time passes for targets whose thickness is over 10 {mu}m. A relative measurement of the equation of state has been performed through the simultaneous measurement of the velocity of shock waves passing through 2 different media. The great efficiency of the direct drive has allowed us to produce pressures up to 40 Mbar. An absolute measurement of the equation of state requires the measurement of 2 parameters, we have then performed the measurement of the colour temperature of an aluminium target submitted to laser shocks. A simple model has been developed to infer the shock temperature from the colour temperature. The last important result is the assessment of the temperature of the pre-heating phase that is necessary to know the media in which the shock wave propagates. The comparison of the measured values of the reflectivity of the back side of the target with the computed values given by an adequate simulation has allowed us to deduce the evolution of the temperature of the pre-heating phase. (A.C.)

Advances in NIF Shock Timing Experiments

Science.gov (United States)

Robey, Harry

2012-10-01

Experiments are underway to tune the shock timing of capsule implosions on the National Ignition Facility (NIF). These experiments use a modified cryogenic hohlraum geometry designed to precisely match the performance of ignition hohlraums. The targets employ a re-entrant Au cone to provide optical access to multiple shocks as they propagate in the liquid deuterium-filled capsule interior. The strength and timing of all four shocks is diagnosed with VISAR (Velocity Interferometer System for Any Reflector). Experiments are now routinely conducted in a mirrored keyhole geometry, which allows for simultaneous diagnosis of the shock timing at both the hohlraum pole and equator. Further modifications are being made to improve the surrogacy to ignition hohlraums by replacing the standard liquid deuterium (D2) capsule fill with a deuterium-tritium (DT) ice layer. These experiments will remove any possible surrogacy difference between D2 and DT as well as incorporate the physics of shock release from the ice layer, which is absent in current experiments. Experimental results and comparisons with numerical simulation are presented.

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

Science.gov (United States)

Hall, J. L.

1974-01-01

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.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

Science.gov (United States)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Shock Wave Propagation in Layered Planetary Interiors: Revisited

Science.gov (United States)

Arkani-Hamed, J.; Monteux, J.

2017-12-01

The end of the terrestrial planet accretion is characterized by numerous large impacts. About 90% of the mass of a large planet is accreted while the core mantle separation is occurring, because of the accretionary and the short-lived radio-isotope heating. The characteristics of the shockwave propagation, hence the existing scaling laws are poorly known within the layered planets. Here, we use iSALE-2D hydrocode simulations to calculate shock pressure in a differentiated Mars type body for impact velocities of 5-20 km/s, and impactor sizes of 100-400 km. We use two different rheologies for the target interior, an inviscid model ("no-stress model") and a pressure and damage-dependent strength model ("elaborated model"). To better characterize the shock pressure within the whole mantle as a function of distance from the impact site, we propose the following distribution: (1) a near field zone larger than the isobaric core that extends to 7-15 times the projectile radius into the target, where the peak shock pressure decays exponentially with increasing distance, (2) a far field zone where the pressure decays with distance following a power law. The shock pressure decreases more rapidly with distance in the near field for the elaborated model than for the no-stress model because of the influence of acoustic fluidization and damage. However to better illustrate the influence of the rheology on the shock propagation, we use the same expressions to fit the shock pressure with distance for both models. At the core-mantle boundary, CMB, the peak shock pressure jumps as the shock wave enters the core. We derived the boundary condition at CMB for the peak shock pressure. It is less sensitive to the impact velocity or the impactor size, but strongly depends on the rheology of the planet's mantle. Because of the lower shock wave velocity in the core compared to that in the mantle, the refracted shockwave propagates toward the symmetry axis of the planet, and the shock

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

Science.gov (United States)

Vyas, Manan A.; Yoder, Dennis A.; Gaitonde, Datta V.

2018-01-01

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae

Science.gov (United States)

Marek, A.; Janka, H.-T.; Müller, E.

2009-03-01

We present two-dimensional (axisymmetric) neutrino-hydrodynamic simulations of the long-time accretion phase of a 15 M_⊙ progenitor star after core bounce and before the launch of a supernova explosion, when non-radial hydrodynamic instabilities like convection occur in different regions of the collapsing stellar core and the standing accretion shock instability (SASI) leads to large-amplitude oscillations of the stalled shock with a period of tens of milliseconds. Our simulations were performed with the Prometheus-Vertex code, which includes a multi-flavor, energy-dependent neutrino transport scheme and employs an effective relativistic gravitational potential. Testing the influence of a stiff and a soft equation of state for hot neutron star matter, we find that the non-radial mass motions in the supernova core impose a time variability on the neutrino and gravitational-wave signals with larger amplitudes, as well as higher frequencies in the case of a more compact nascent neutron star. After the prompt shock-breakout burst of electron neutrinos, a more compact accreting remnant produces higher neutrino luminosities and higher mean neutrino energies. The observable neutrino emission in the SASI sloshing direction exhibits a modulation of several ten percent in the luminosities and around 1 MeV in the mean energies with most power at typical SASI frequencies between roughly 20 and 100 Hz. The modulation is caused by quasi-periodic variations in the mass accretion rate of the neutron star in each hemisphere. At times later than ~50-100 ms after bounce, the gravitational-wave amplitude is dominated by the growing low-frequency (⪉200 Hz) signal associated with anisotropic neutrino emission. A high-frequency wave signal results from nonradial gas flows in the outer layers of the anisotropically accreting neutron star. Right after bounce such nonradial mass motions occur due to prompt post-shock convection in both considered cases and contribute mostly to the early

Thermal shock behavior of toughened gadolinium zirconate/YSZ double-ceramic-layered thermal barrier coating

International Nuclear Information System (INIS)

Zhong, Xinghua; Zhao, Huayu; Zhou, Xiaming; Liu, Chenguang; Wang, Liang; Shao, Fang; Yang, Kai; Tao, Shunyan; Ding, Chuanxian

2014-01-01

Highlights: • Gd 2 Zr 2 O 7 /YSZ DCL thermal barrier coating was designed and fabricated. • The Gd 2 Zr 2 O 7 top ceramic layer was toughened by addition of nanostructured 3YSZ. • Remarkable improvement in thermal shock resistance of the DCL coating was achieved. - Abstract: Double-ceramic-layered (DCL) thermal barrier coating system comprising of toughened Gadolinium zirconate (Gd 2 Zr 2 O 7 , GZ) as the top ceramic layer and 4.5 mol% Y 2 O 3 partially-stabilized ZrO 2 (4.5YSZ) as the bottom ceramic layer was fabricated by plasma spraying and thermal shock behavior of the DCL coating was investigated. The GZ top ceramic layer was toughened by addition of nanostructured 3 mol% Y 2 O 3 partially-stabilized ZrO 2 (3YSZ) to improve fracture toughness of the matrix. The thermal shock resistance of the DCL coating was enhanced significantly compared to that of single-ceramic-layered (SCL) GZ-3YSZ composite coating, which is believed to be primarily attributed to the two factors: (i) the increase in fracture toughness of the top ceramic layer by incorporating nanostructured YSZ particles and (ii) the improvement in strain tolerance through the utilization of 4.5YSZ as the bottom ceramic layer. In addition, the failure mechanisms are mainly attributed to the still low fracture toughness of the top ceramic layer and oxidation of the bond-coat

On the Nonlinear Dynamics of a Tunable Shock Micro-switch

Science.gov (United States)

Azizi, Saber; Javaheri, Hamid; Ghanati, Parisa

2016-12-01

A tunable shock micro-switch based on piezoelectric excitation is proposed in this study. This model includes a clamped-clamped micro-beam sandwiched with two piezoelectric layers throughout the entire length. Actuation of the piezoelectric layers via a DC voltage leads to an initial axial force in the micro-beam and directly affects on its overall bending stiffness; accordingly enables two-side tuning of both the trigger time and threshold shock. The governing motion equation, in the presence of an electrostatic actuation and a shock wave, is derived using Hamilton's principle. We employ the finite element method based on the Galerkin technique to obtain the temporal and phase responses subjected to three different shock waves including half sine, triangular and rectangular forms. Subsequently, we investigate the effect of the piezoelectric excitations on the threshold shock amplitude and trigger time.

Noncoplanar magnetic fields at collisionless shocks: A test of a new approach

International Nuclear Information System (INIS)

Gosling, J.T.; Winske, D.; Thomsen, M.F.

1988-01-01

Within the foot and ramp of a fast mode collisionless shock the magnetic field rotates out of the plane of coplanarity defined by the upstream magnetic field and the shock normal. As previously noted (Goodrich and Scudder, 1984), the sense of this rotation is such as to reduce the cross-shock potential drop when measured in the deHoffman-Teller frame relative to that measured in the normal incidence frame. From a consideration of the requirement that there be zero current in the coplanarity plane downstream of the shock, Jones and Ellison (1987) have argued that the field rotation and potential drop difference are a consequence of unequal ion and electron masses, and have derived an expression for the spatial integral of the noncoplanar field component in terms of the electron current within the shock layer. Moreover, by assuming that the ion current within the shock layer is negligible compared to the electron current, they derive equations which predict the magnitude of both the field rotation and the potential drop difference in terms of upstream quantities and the field jump at the shock. We have tested their equations with ISEE 1 and 2 plasma and field measurements at the Earth's bow shock and by means of numerical simulations. We find substantial support for their suggestion that the field rotation and thus also the frame dependence of the potential drop are fundamentally a consequence of unequal ion and electron masses. Further, for subcritical shocks (low Mach number) one can neglect the ion current to predict both the sign and the magnitude of the field rotation and potential drop difference. However, at supercritical shocks (high Mach numbers) the ion current associated with reflected, gyrating ions cannot be neglected, and the final equations of Jones and Ellison seriously underestimate the magnitude of the field rotation and the potential drop difference at these shocks

Effects of micro-ramps on a shock wave/turbulent boundary layer interaction

NARCIS (Netherlands)

Blinde, P.L.; Humble, R.A.; Van Oudheusden, B.W.; Scarano, F.

2009-01-01

Stereoscopic particle image velocimetry is used to investigate the effects of micro-ramp sub-boundary layer vortex generators, on an incident shock wave/boundary layer interaction at Mach 1.84. Single- and double-row arrangements of micro-ramps are considered. The micro-ramps have a height of 20% of

Validation of the activity expansion method with ultrahigh pressure shock equations of state

Science.gov (United States)

Rogers, Forrest J.; Young, David A.

1997-11-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter.

Initial layer theory and model equations of Volterra type

International Nuclear Information System (INIS)

Bijura, Angelina M.

2003-10-01

It is demonstrated here that there exist initial layers to singularly perturbed Volterra equations whose thicknesses are not of order of magnitude of 0(ε), ε → 0. It is also shown that the initial layer theory is extremely useful because it allows one to construct the approximate solution to an equation, which is almost identical to the exact solution. (author)

Nonaligned shocks for discrete velocity models of the Boltzmann equation

Directory of Open Access Journals (Sweden)

J. M. Greenberg

1991-05-01

Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.

Thin-Layer Solutions of the Helmholtz and Related Equations

KAUST Repository

Ockendon, J. R.

2012-01-01

This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.

Shock timing measurements and analysis in deuterium-tritium-ice layered capsule implosions on NIF

Energy Technology Data Exchange (ETDEWEB)

Robey, H. F.; Celliers, P. M.; Moody, J. D.; Sater, J.; Parham, T.; Kozioziemski, B.; Dylla-Spears, R.; Ross, J. S.; LePape, S.; Ralph, J. E.; Dewald, E. L.; Berzak Hopkins, L.; Kroll, J. J.; Yoxall, B. E.; Hamza, A. V.; Landen, O. L.; Edwards, M. J. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States); Hohenberger, M.; Boehly, T. R. [Laboratory for Laser Energetics, Rochester, New York 14623 (United States); Nikroo, A. [General Atomics, San Diego, California 92196 (United States)

2014-02-15

Recent advances in shock timing experiments and analysis techniques now enable shock measurements to be performed in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility (NIF). Previous measurements of shock timing in inertial confinement fusion implosions [Boehly et al., Phys. Rev. Lett. 106, 195005 (2011); Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] were performed in surrogate targets, where the solid DT ice shell and central DT gas were replaced with a continuous liquid deuterium (D2) fill. These previous experiments pose two surrogacy issues: a material surrogacy due to the difference of species (D2 vs. DT) and densities of the materials used and a geometric surrogacy due to presence of an additional interface (ice/gas) previously absent in the liquid-filled targets. This report presents experimental data and a new analysis method for validating the assumptions underlying this surrogate technique. Comparison of the data with simulation shows good agreement for the timing of the first three shocks, but reveals a considerable discrepancy in the timing of the 4th shock in DT ice layered implosions. Electron preheat is examined as a potential cause of the observed discrepancy in the 4th shock timing.

Shock timing measurements and analysis in deuterium-tritium-ice layered capsule implosions on NIF

Science.gov (United States)

Robey, H. F.; Celliers, P. M.; Moody, J. D.; Sater, J.; Parham, T.; Kozioziemski, B.; Dylla-Spears, R.; Ross, J. S.; LePape, S.; Ralph, J. E.; Hohenberger, M.; Dewald, E. L.; Berzak Hopkins, L.; Kroll, J. J.; Yoxall, B. E.; Hamza, A. V.; Boehly, T. R.; Nikroo, A.; Landen, O. L.; Edwards, M. J.

2014-02-01

Recent advances in shock timing experiments and analysis techniques now enable shock measurements to be performed in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility (NIF). Previous measurements of shock timing in inertial confinement fusion implosions [Boehly et al., Phys. Rev. Lett. 106, 195005 (2011); Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] were performed in surrogate targets, where the solid DT ice shell and central DT gas were replaced with a continuous liquid deuterium (D2) fill. These previous experiments pose two surrogacy issues: a material surrogacy due to the difference of species (D2 vs. DT) and densities of the materials used and a geometric surrogacy due to presence of an additional interface (ice/gas) previously absent in the liquid-filled targets. This report presents experimental data and a new analysis method for validating the assumptions underlying this surrogate technique. Comparison of the data with simulation shows good agreement for the timing of the first three shocks, but reveals a considerable discrepancy in the timing of the 4th shock in DT ice layered implosions. Electron preheat is examined as a potential cause of the observed discrepancy in the 4th shock timing.

Shock timing measurements and analysis in deuterium-tritium-ice layered capsule implosions on NIF

International Nuclear Information System (INIS)

Robey, H. F.; Celliers, P. M.; Moody, J. D.; Sater, J.; Parham, T.; Kozioziemski, B.; Dylla-Spears, R.; Ross, J. S.; LePape, S.; Ralph, J. E.; Dewald, E. L.; Berzak Hopkins, L.; Kroll, J. J.; Yoxall, B. E.; Hamza, A. V.; Landen, O. L.; Edwards, M. J.; Hohenberger, M.; Boehly, T. R.; Nikroo, A.

2014-01-01

Recent advances in shock timing experiments and analysis techniques now enable shock measurements to be performed in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility (NIF). Previous measurements of shock timing in inertial confinement fusion implosions [Boehly et al., Phys. Rev. Lett. 106, 195005 (2011); Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] were performed in surrogate targets, where the solid DT ice shell and central DT gas were replaced with a continuous liquid deuterium (D2) fill. These previous experiments pose two surrogacy issues: a material surrogacy due to the difference of species (D2 vs. DT) and densities of the materials used and a geometric surrogacy due to presence of an additional interface (ice/gas) previously absent in the liquid-filled targets. This report presents experimental data and a new analysis method for validating the assumptions underlying this surrogate technique. Comparison of the data with simulation shows good agreement for the timing of the first three shocks, but reveals a considerable discrepancy in the timing of the 4th shock in DT ice layered implosions. Electron preheat is examined as a potential cause of the observed discrepancy in the 4th shock timing

Control of a shock wave-boundary layer interaction using localized arc filament plasma actuators

Science.gov (United States)

Webb, Nathan Joseph

Supersonic flight is currently possible, but expensive. Inexpensive supersonic travel will require increased efficiency of high-speed air entrainment, an integral part of air-breathing propulsion systems. Although mixed compression inlet geometry can significantly improve entrainment efficiency, numerous Shock Wave-Boundary Layer Interactions (SWBLIs) are generated in this configuration. The boundary layer must therefore develop through multiple regions of adverse pressure gradient, causing it to thicken, and, in severe cases, separate. The associated increase in unsteadiness can have adverse effects on downstream engine hardware. The most severe consequence of these interactions is the increased aerodynamic blockage generated by the thickened boundary layer. If the increase is sufficient, it can choke the flow, causing inlet unstart, and resulting in a loss of thrust and high transient forces on the engine, airframe, and aircraft occupants. The potentially severe consequences associated with SWBLIs require flow control to ensure proper operation. Traditionally, boundary layer bleed has been used to control the interaction. Although this method is effective, it has inherent efficiency penalties. Localized Arc Filament Plasma Actuators (LAFPAs) are designed to generate perturbations for flow control. Natural flow instabilities act to amplify certain perturbations, allowing the LAFPAs to control the flow with minimal power input. LAFPAs also have the flexibility to maintain control over a variety of operating conditions. This work seeks to examine the effectiveness of LAFPAs as a separation control method for an oblique, impinging SWBLI. The low frequency unsteadiness in the reflected shock was thought to be the natural manifestation of a Kelvin-Helmholtz instability in the shear layer above the separation region. The LAFPAs were therefore placed upstream of the interaction to allow their perturbations to convect to the receptivity region (near the shear layer origin

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Validation of the activity expansion method with ultrahigh pressure shock equations of state

International Nuclear Information System (INIS)

Rogers, F.J.; Young, D.A.

1997-01-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. copyright 1997 The American Physical Society

Validation of the activity expansion method with ultrahigh pressure shock equations of state

Energy Technology Data Exchange (ETDEWEB)

Rogers, F.J.; Young, D.A. [Physics Department, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)

1997-11-01

Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}

Assessment of CFD Capability for Hypersonic Shock Wave Laminar Boundary Layer Interactions

OpenAIRE

Mehrnaz Rouhi Youssefi; Doyle Knight

2017-01-01

The goal of this study is to assess CFD capability for the prediction of shock wave laminar boundary layer interactions at hypersonic velocities. More specifically, the flow field over a double-cone configuration is simulated using both perfect gas and non-equilibrium Navier–Stokes models. Computations are compared with recent experimental data obtained from measurements conducted in the LENS XX (Large Energy National Shock Expansion Tunnel Version 2) at the Calspan University of Buffalo Rese...

A computational study on oblique shock wave-turbulent boundary layer interaction

Science.gov (United States)

Joy, Md. Saddam Hossain; Rahman, Saeedur; Hasan, A. B. M. Toufique; Ali, M.; Mitsutake, Y.; Matsuo, S.; Setoguchi, T.

2016-07-01

A numerical computation of an oblique shock wave incident on a turbulent boundary layer was performed for free stream flow of air at M∞ = 2.0 and Re1 = 10.5×106 m-1. The oblique shock wave was generated from a 8° wedge. Reynolds averaged Navier-Stokes (RANS) simulation with k-ω SST turbulence model was first utilized for two dimensional (2D) steady case. The results were compared with the experiment at the same flow conditions. Further, to capture the unsteadiness, a 2D Large Eddy Simulation (LES) with sub-grid scale model WMLES was performed which showed the unsteady effects. The frequency of the shock oscillation was computed and was found to be comparable with that of experimental measurement.

Entropy Generation Across Earth's Bow Shock

Science.gov (United States)

Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;

Effects of non-adiabatic walls on shock/boundary-layer interaction using direct numerical simulations

Science.gov (United States)

Volpiani, Pedro S.; Bernardini, Matteo; Larsson, Johan

2017-11-01

The influence of wall thermal conditions on the properties of an impinging shock wave interacting with a turbulent supersonic boundary layer is a research topic that still remains underexplored. In the present study, direct numerical simulations (DNS) are employed to investigate the flow properties of a shock wave interacting with a turbulent boundary layer at free-stream Mach number M∞ = 2.28 with distinct wall thermal conditions and shock strengths. Instantaneous and mean flow fields, wall quantities and the low-frequency unsteadiness are analyzed. While heating contributes to increase the extent of the interaction zone, wall cooling turns out to be a good candidate for flow control. The distribution of the Stanton number shows a good agreement with prior experimental studies and confirms the strong heat transfer and complex pattern within the interaction region. Numerical results indicate that the changes in the interaction length are mainly linked to the incoming boundary layer as suggested in previous studies (Souverein et al., 2013 and Jaunet et al., 2014). This work was supported by the Air Force Office of Scientific Research, Grant FA95501610385.

Color surface-flow visualization of fin-generated shock wave boundary-layer interactions

Science.gov (United States)

Lu, F. K.; Settles, G. S.

1990-03-01

Kerosene-lampblack mixtures with addition of a ground colored chalk were used in an experiment on visualizing surface flows of swept shock boundary-layer interactions. The results show that contrasting colors intensify the visualization of different regions of the interaction surface, and help the eye in following the fine streaks to locate the upstream influence. The study confirms observations of the separation occurring at shock strength below accepted values. The superiority of the reported technique over the previous monochrome technique is demonstrated.

Investigation of 3D Shock-Boundary Layer Interaction: A Combined Approach using Experiments, Numerical Simulations and Stability Analysis

Science.gov (United States)

2015-12-02

layer , the non-reflecting boundary condition suggested by Poinsot and Lele is adopted.38 On the flat – plate surface, the no-penetration (v = 0) and the no...Introduction Shock-wave boundary layer interactions (SBLIs) occur in most supersonic flight applications and have been the subject of many studies...generator plate is emulated to create an oblique shock that impinges on the boundary layer causing separation. This is similar to the experimental

Shock equation of state of 6LiH to 1.1 TPa

Science.gov (United States)

Lazicki, A.; London, R. A.; Coppari, F.; Erskine, D.; Whitley, H. D.; Caspersen, K. J.; Fratanduono, D. E.; Morales, M. A.; Celliers, P. M.; Eggert, J. H.; Millot, M.; Swift, D. C.; Collins, G. W.; Kucheyev, S. O.; Castor, J. I.; Nilsen, J.

2017-10-01

Using laser-generated shock waves, we have measured pressure, density, and temperature of LiH on the principal Hugoniot between 260 and 1100 GPa (2.6-11 Mbar) and on a second-shock Hugoniot up to 1400 GPa to near fivefold compression, extending the maximum pressure reached in non-nuclear experiments by a factor of two. We observe the onset of metal-like reflectivity consistent with temperature-induced ionization of the Li 2s electron, and no sign of additional changes in ionization up to the maximum pressure. Our measurements are in good agreement with gas gun, Z-machine, and underground test data and are accurately described by quantum molecular dynamics simulations. The results confirm the validity of equation of state models built on an average-atom description of the electron-thermal contribution to the free energy and a density-dependent Grüneisen parameter to describe shock response of LiH over this pressure range.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

Science.gov (United States)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

Modeling of the plasma generated in a rarefied hypersonic shock layer

International Nuclear Information System (INIS)

Farbar, Erin D.; Boyd, Iain D.

2010-01-01

In this study, a rigorous numerical model is developed to simulate the plasma generated in a rarefied, hypersonic shock layer. The model uses the direct simulation Monte Carlo (DSMC) method to treat the particle collisions and the particle-in-cell (PIC) method to simulate the plasma dynamics in a self-consistent manner. The model is applied to compute the flow along the stagnation streamline in front of a blunt body reentering the Earth's atmosphere at very high velocity. Results from the rigorous DSMC-PIC model are compared directly to the standard DSMC modeling approach that uses the ambipolar diffusion approximation to simulate the plasma dynamics. It is demonstrated that the self-consistent computation of the plasma dynamics using the rigorous DSMC-PIC model captures many physical phenomena not accurately predicted by the standard modeling approach. These computations represent the first assessment of the validity of the ambipolar diffusion approximation when predicting the rarefied plasma generated in a hypersonic shock layer.

Passive shock wave/boundary layer control of wing at transonic speeds

Directory of Open Access Journals (Sweden)

Ling Zhou

2017-11-01

Full Text Available At supercritical conditions a porous strip (or slot strip placed beneath a shock wave can reduce the drag by a weaker lambda shock system, and increase the buffet boundary, even may increase the lift. Passive shock wave/boundary layer control (PSBC for drag reduction was conducted by SC(2-0714 supercritical wing, with emphases on parameter of porous/slot and bump, such as porous distribution, hole diameter, cavity depth, porous direction and so on. A sequential quadratic programming (SQP optimization method coupled with adjoint method was adopted to achieve the optimized shape and position of the bumps. Computational fluid dynamics (CFD, force test and oil test with half model all indicate that PSBC with porous, slot and bump generally reduce the drag by weaker lambda shock at supercritical conditions. According to wind tunnel test results for angle of attack of 2° at Mach number M=0.8, the porous configuration with 6.21% porosity results in a drag reduction of 0.0002 and lift–drag ratio increase of 0.2, the small bump configuration results in a drag reduction of 0.0007 and lift–drag ratio increase of 0.3. Bump normally reduce drag at design point with shock wave position being accurately computed. If bump diverges from the position of shock wave, drag will not be easily reduced.

Analogy between soap film and gas dynamics. I. Equations and shock jump conditions

Energy Technology Data Exchange (ETDEWEB)

Wen, C.Y.; Lai, J.Y. [Department of Mechanical Engineering, Da-Yeh University, Chang-Hwa (Taiwan)

2003-01-01

The governing equations of compressible flows in soap films are formulated based on the very specific property equations of soap films. The basic normal shock relations and the Rankine-Hugoniot equation are derived for steady one-dimensional flows in soap films. The results are similar to those of compressible gases. The analogy between compressible flows in soap films and that in gases is discussed. On short time scales, the dynamic response of the film is characterized by the Marangoni elasticity, and soap films are shown to be analogous to compressible gases with a specific heat ratio of {gamma}=1.0. Results for Gibbs elasticity are also presented for reference, and no clear analogy to compressible gases is obtained. (orig.)

Modelling and nonlinear shock waves for binary gas mixtures by the discrete Boltzmann equation with multiple collisions

International Nuclear Information System (INIS)

Bianchi, M.P.

1991-01-01

The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation

A thin-shock-layer solution for nonequilibrium, inviscid hypersonic flows in earth, Martian, and Venusian atmospheres

Science.gov (United States)

Grose, W. L.

1971-01-01

An approximate inverse solution is presented for the nonequilibrium flow in the inviscid shock layer about a vehicle in hypersonic flight. The method is based upon a thin-shock-layer approximation and has the advantage of being applicable to both subsonic and supersonic regions of the shock layer. The relative simplicity of the method makes it ideally suited for programming on a digital computer with a significant reduction in storage capacity and computing time required by other more exact methods. Comparison of nonequilibrium solutions for an air mixture obtained by the present method is made with solutions obtained by two other methods. Additional cases are presented for entry of spherical nose cones into representative Venusian and Martian atmospheres. A digital computer program written in FORTRAN language is presented that permits an arbitrary gas mixture to be employed in the solution. The effects of vibration, dissociation, recombination, electronic excitation, and ionization are included in the program.

Shock Hugoniot and equations of states of water, castor oil, and aqueous solutions of sodium chloride, sucrose and gelatin

Science.gov (United States)

Gojani, A. B.; Ohtani, K.; Takayama, K.; Hosseini, S. H. R.

2016-01-01

This paper reports a result of experiments for the determination of reliable shock Hugoniot curves of liquids, in particular, at relatively low pressure region, which are needed to perform precise numerical simulations of shock wave/tissue interaction prior to the development of shock wave related therapeutic devices. Underwater shock waves were generated by explosions of laser ignited 10 mg silver azide pellets, which were temporally and spatially well controlled. Measuring temporal variation of shock velocities and over-pressures in caster oil, aqueous solutions of sodium chloride, sucrose and gelatin with various concentrations, we succeeded to determine shock Hugoniot curves of these liquids and hence parameters describing Tait type equations of state.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

Science.gov (United States)

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

State equations and stability of shock wave fronts in homogeneous and heterogeneous metallic medium

International Nuclear Information System (INIS)

Romain, Jean-Pierre

1977-01-01

This research thesis in physical sciences reports a theoretical and experimental study of some mechanical and thermodynamic aspects related to a shock wave propagation in homogeneous and heterogeneous metallic media: state equations, stability and instability of shock wave fronts. In the first part, the author reports the study of the Grueneisen coefficient for some metallic elements with known static and dynamic compression properties. The second part reports the experimental investigation of dynamic compressibility of some materials (lamellar Al-Cu compounds). The front shock wave propagation has been visualised, and experimental Hugoniot curves are compared with those deduced from a developed numeric model and other models. The bismuth Hugoniot curve is also determined, and the author compares the existence and nature of phase transitions obtained by static and dynamic compression

Geometrical shock dynamics for magnetohydrodynamic fast shocks

KAUST Repository

Mostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V.

2016-01-01

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press

Geometrical shock dynamics for magnetohydrodynamic fast shocks

KAUST Repository

Mostert, W.

2016-12-12

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press

Numerical simulation of shock initiation of Ni/Al multilayered composites

Energy Technology Data Exchange (ETDEWEB)

Sraj, Ihab; Knio, Omar M., E-mail: omar.knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, 144 Hudson Hall, Durham, North Carolina 27708 (United States); Specht, Paul E.; Thadhani, Naresh N. [School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive, Atlanta, Georgia 30332 (United States); Weihs, Timothy P. [Department of Materials Science and Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218 (United States)

2014-01-14

The initiation of chemical reaction in cold-rolled Ni/Al multilayered composites by shock compression is investigated numerically. A simplified approach is adopted that exploits the disparity between the reaction and shock loading timescales. The impact of shock compression is modeled using CTH simulations that yield pressure, strain, and temperature distributions within the composites due to the shock propagation. The resulting temperature distribution is then used as initial condition to simulate the evolution of the subsequent shock-induced mixing and chemical reaction. To this end, a reduced reaction model is used that expresses the local atomic mixing and heat release rates in terms of an evolution equation for a dimensionless time scale reflecting the age of the mixed layer. The computations are used to assess the effect of bilayer thickness on the reaction, as well as the impact of shock velocity and orientation with respect to the layering. Computed results indicate that initiation and evolution of the reaction are substantially affected by both the shock velocity and the bilayer thickness. In particular, at low impact velocity, Ni/Al multilayered composites with thick bilayers react completely in 100 ms while at high impact velocity and thin bilayers, reaction time was less than 100 μs. Quantitative trends for the dependence of the reaction time on the shock velocity are also determined, for different bilayer thickness and shock orientation.

Prediction of shock-layer ultraviolet radiation for hypersonic vehicles in near space

Directory of Open Access Journals (Sweden)

Niu Qinglin

2016-10-01

Full Text Available A systemic and validated model was developed to predict ultraviolet spectra features from the shock layer of near-space hypersonic vehicles in the “solar blind” band region. Computational procedures were performed with 7-species thermal non-equilibrium fluid mechanics, finite rate chemistry, and radiation calculations. The thermal non-equilibrium flow field was calculated with a two-temperature model by the finite volume technique and verified against the bow-shock ultra-violet (BSUV flight experiments. The absorption coefficient of the mixture gases was evaluated with a line-by-line method and validated through laboratory shock tube measurements. Using the line of sight (LOS method, radiation was calculated from three BSUV flights at altitudes of 38, 53.5 and 71 km. The investigation focused on the level and structure of ultraviolet spectra radiated from a NO band system in wavelengths of 200–400 nm. Results predicted by the current model show qualitative spatial agreement with the measured data. At a velocity of 3.5 km/s (about Mach 11, the peak absolute intensity at an altitude of 38 km is two orders of magnitude higher than that at 53.5 km. Under the same flight conditions, the spectra structures have quite a similar distribution at different viewing angles. The present computational model performs well in the prediction of the ultraviolet spectra emitted from the shock layer and will contribute to the investigation and analysis of radiative features of hypersonic vehicles in near space.

Investigation on Mie-Grüneisen type shock Hugoniot equation of state for concrete

Directory of Open Access Journals (Sweden)

M Katayama

2017-09-01

Full Text Available This paper ascertains that the bilinear shock Hugoniot equation of state (EOS can model the plasticizing process of the porous media like concrete material for high-velocity impact problems successfully. The negative slope of the bilinear Hugoniot for low particle velocity regime can simulate the process that the porosity of concrete may be compressed to form shock wave in concrete, through a series of numerical analyses over the investigation on the physical phenomena. The results of particle velocity for the concrete material are also discussed to be compared with those of non-porous aluminum alloy for 100 and 1000 m/s impact velocities. All the numerical simulations were carried out by applying the bilinear shock Hugoniot EOS to concrete which was linked to the binary object of a hydrocode: ANSYS Autodyn®[1−3] through a user’s subroutine.

An Experimental Study into the Scaling of an Unswept-Sharp-Fin-Generated Shock/Turbulent Boundary Layer Interaction.

Science.gov (United States)

1983-01-01

Influence Scaling of 2D and 3D Shock/Turbulent ioundary Layer Interactions at Compression Corners." AIM Paper 81-334, January 1981. 5. Kubota, H...generating 3D shock wave/boundary layer interactions 2 Unswept sharp fin interaction and coordinate system 3 Cobra probe measurements of Peake (4) at Mach 4...were made by two Druck 50 PSI transducers, each in- stalled in a computer-controlled 48-port Model 48J4 Scani- valve and referenced to vacuum. A 250

Dynamical behaviors of the shock compacton in the nonlinearly Schrödinger equation with a source term

International Nuclear Information System (INIS)

Yin, Jiuli; Zhao, Liuwei

2014-01-01

In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams

Gibberellic Acid-Induced Aleurone Layers Responding to Heat Shock or Tunicamycin Provide Insight into the N-Glycoproteome, Protein Secretion, and Endoplasmic Reticulum Stress

DEFF Research Database (Denmark)

Barba Espin, Gregorio; Dedvisitsakul, Plaipol; Hägglund, Per

2014-01-01

respond to gibberellic acid by secreting an array of proteins and provide a unique system for the analysis of plant protein secretion. Perturbation of protein secretion in gibberellic acid-induced aleurone layers by two independent mechanisms, heat shock and tunicamycin treatment, demonstrated overlapping...... and secretion, such as calreticulin, protein disulfide isomerase, proteasome subunits, and isopentenyl diphosphate isomerase. Sixteen heat shock proteins in 29 spots showed diverse responses to the treatments, with only a minority increasing in response to heat shock. The majority, all of which were small heat...... shock proteins, decreased in heat-shocked aleurone layers. Additionally, glycopeptide enrichment and N-glycosylation analysis identified 73 glycosylation sites in 65 aleurone layer proteins, with 53 of the glycoproteins found in extracellular fractions and 36 found in intracellular fractions...

Coronal mass ejection shock fronts containing the two types of intermediate shocks

International Nuclear Information System (INIS)

Steinolfson, R.S.; Hundhausen, A.J.

1990-01-01

Numerical solutions of the time-dependent, magnetohydrodynamic (MHD) equations in two dimensions are used to demonstrate the formation of both types of intermediate shocks in a single shock front for physical conditions that are an idealization of those expected to occur in some observed coronal mass ejections. The key to producing such a shock configuration in the simulations is the use of an initial atmosphere containing a magnetic field representative of that in a coronal streamer with open field lines overlying a region of closed field lines. Previous attempts using just open field lines (perpendicular to the surface) produced shock configurations containing just one of the two intermediate shock types. A schematic of such a shock front containing both intermediate shock types has been constructed previously based solely on the known properties of MHD shocks from the Rankine-Hugoniot equations and specific requirements placed on the shock solution at points along the front where the shock normal and upstream magnetic field are aligned. The shock front also contains, at various locations along the front, a hydrodynamic (nonmagnetic) shock, a switch-on shock, and a fast shock in addition to the intermediate shocks. This particular configuration occurs when the shock front speed exceeds the upstream (preshock) intermediate wave speed but is less than a critical speed defined in the paper (equation 1) along at least some portion of the shock front. A distinctive feature of the front is that it is concave upward (away from the surface) near the region where the field in the preshock plasma is normal to the front of near the central portion of the shock front

Model for Shock Wave Chaos

KAUST Repository

Kasimov, Aslan R.

2013-03-08

We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.

Nonequilibrium recombination after a curved shock wave

Science.gov (United States)

Wen, Chihyung; Hornung, Hans

2010-02-01

The effect of nonequilibrium recombination after a curved two-dimensional shock wave in a hypervelocity dissociating flow of an inviscid Lighthill-Freeman gas is considered. An analytical solution is obtained with the effective shock values derived by Hornung (1976) [5] and the assumption that the flow is ‘quasi-frozen’ after a thin dissociating layer near the shock. The solution gives the expression of dissociation fraction as a function of temperature on a streamline. A rule of thumb can then be provided to check the validity of binary scaling for experimental conditions and a tool to determine the limiting streamline that delineates the validity zone of binary scaling. The effects on the nonequilibrium chemical reaction of the large difference in free stream temperature between free-piston shock tunnel and equivalent flight conditions are discussed. Numerical examples are presented and the results are compared with solutions obtained with two-dimensional Euler equations using the code of Candler (1988) [10].

Cracking of a layered medium on an elastic foundation under thermal shock

Science.gov (United States)

Rizk, Abd El-Fattah A.; Erdogan, Fazil

1988-01-01

The cladded pressure vessel under thermal shock conditions which is simulated by using two simpler models was studied. The first model (Model 1) assumes that, if the crack size is very small compared to the vessel thickness, the problem can be treated as a semi-infinite elastic medium bonded to a very thin layer of different material. However, if the crack size is of the same order as the vessel thickness, the curvature effects may not be negligible. In this case it is assumed that the relatively thin walled hollow cylinder with cladding can be treated as a composite beam on an elastic foundation (Model 2). In both models, the effect of surface cooling rate is studied by assuming the temperature boundary condition to be a ramp function. The calculated results include the transient temperature, thermal stresses in the uncracked medium and stress intensity factors which are presented as a function of time, and the duration of cooling ramp. The stress intensity factors are also presented as a function of the size and the location of the crack. The problem is solved for two bonded materials of different thermal and mechanical properties. The mathematical formulation results in two singular integral equations which are solved numerically. The results are given for two material pairs, namely an austenitic steel layer welded on a ferritic steel substrate, and a ceramic coating on ferritic steel. In the case of the yielded clad, the stress intensity factors for a crack under the clad are determined by using a plastic strip model and are compared with elastic clad results.

Interactive boundary-layer calculations of a transonic wing flow

Science.gov (United States)

Kaups, Kalle; Cebeci, Tuncer; Mehta, Unmeel

1989-01-01

Results obtained from iterative solutions of inviscid and boundary-layer equations are presented and compared with experimental values. The calculated results were obtained with an Euler code and a transonic potential code in order to furnish solutions for the inviscid flow; they were interacted with solutions of two-dimensional boundary-layer equations having a strip-theory approximation. Euler code results are found to be in better agreement with the experimental data than with the full potential code, especially in the presence of shock waves, (with the sole exception of the near-tip region).

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

Assessment of CFD Capability for Hypersonic Shock Wave Laminar Boundary Layer Interactions

Directory of Open Access Journals (Sweden)

Mehrnaz Rouhi Youssefi

2017-04-01

Full Text Available The goal of this study is to assess CFD capability for the prediction of shock wave laminar boundary layer interactions at hypersonic velocities. More specifically, the flow field over a double-cone configuration is simulated using both perfect gas and non-equilibrium Navier–Stokes models. Computations are compared with recent experimental data obtained from measurements conducted in the LENS XX (Large Energy National Shock Expansion Tunnel Version 2 at the Calspan University of Buffalo Research Center (CUBRC. Four separate cases of freestream conditions are simulated to examine the models for a range of stagnation enthalpies from 5.44 MJ/kg to 21.77 MJ/kg and Mach numbers from 10.9 to 12.82.

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

Science.gov (United States)

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Alfven shock trains

International Nuclear Information System (INIS)

Malkov, M.A.; Kennel, C.F.; Wu, C.C.; Pellat, R.; Shapiro, V.D.

1991-01-01

The Cohen--Kulsrud--Burgers equation (CKB) is used to consider the nonlinear evolution of resistive, quasiparallel Alfven waves subject to a long-wavelength, plane-polarized, monochromatic instability. The instability saturates by nonlinear steepening, which proceeds until the periodic waveform develops an interior scale length comparable to the dissipation length; a fast or an intermediate shock then forms. The result is a periodic train of Alfven shocks of one or the other type. For propagation strictly parallel to the magnetic field, there will be two shocks per instability wavelength. Numerical integration of the time-dependent CKB equation shows that an initial, small-amplitude growing wave asymptotes to a stable, periodic stationary wave whose analytic solution specifies how the type of shock embedded in the shock train, and the amplitude and speed of the shock train, depend on the strength and phase of the instability. Waveforms observed upstream of the Earth's bowshock and cometary shocks resemble those calculated here

Application of pressure-sensitive paint in shock-boundary layer interaction experiments

OpenAIRE

Seivwright, Douglas L.

1996-01-01

Approved for public release; distribution is unlimited A new type of pressure transducer, pressure-sensitive paint, was used to obtain pressure distributions associated with shock-boundary layer interaction. Based on the principle of photoluminescence and the process of oxygen quenching, pressure-sensitive paint provides a continous mapping of a pressure field over a surface of interest. The data measurement and acquisition system developed for use with the photoluminescence sensor was eva...

The cosmic-ray shock structure problem for relativistic shocks

Science.gov (United States)

Webb, G. M.

1985-01-01

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Shock Isolation Elements Testing for High Input Loadings. Volume III. Mechanical Shock Isolation Elements.

Science.gov (United States)

SHOCK ABSORBERS ), (*GUIDED MISSILE SILOS, SHOCK ABSORBERS ), (*SPRINGS, (*SHOCK(MECHANICS), REDUCTION), TORSION BARS, ELASTOMERS, DAMPING, EQUATIONS OF MOTION, MODEL TESTS, TEST METHODS, NUCLEAR EXPLOSIONS, HARDENING.

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability Over Cones

Science.gov (United States)

Kara, Kursat; Balakumar, Ponnampalam; Kandil, Osama A.

2011-01-01

The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.

Structural characteristics of the shock-induced boundary layer separation extended to the leading edge

Science.gov (United States)

Tao, Y.; Liu, W. D.; Fan, X. Q.; Zhao, Y. L.

2017-07-01

For a better understanding of the local unstart of supersonic/hypersonic inlet, a series of experiments has been conducted to investigate the shock-induced boundary layer separation extended to the leading edge. Using the nanoparticle-based planar laser scattering, we recorded the fine structures of these interactions under different conditions and paid more attention to their structural characteristics. According to their features, these interactions could be divided into four types. Specifically, Type A wave pattern is similar to the classic shock wave/turbulent boundary layer interaction, and Type B wave configuration consists of an overall Mach reflection above the large scale separation bubble. Due to the gradual decrease in the size of the separation bubble, the separation bubble was replaced by several vortices (Type C wave pattern). Besides, for Type D wave configuration which exists in the local unstart inlet, there appears to be some flow spillage around the leading edge.

Shock waves in gas and plasma

International Nuclear Information System (INIS)

Niu, K.

1996-01-01

A shock wave is a discontinuous surface that connects supersonic flow with subsonic flow. After a shock wave, flow velocity is reduced, and pressure and temperature increase; entropy especially increases across a shock wave. Therefore, flow is in nonequilibrium, and irreversible processes occur inside the shock layer. The thickness of a shock wave in neutral gas is of the order of the mean free path of the fluid particle. A shock wave also appears in magnetized plasma. Provided that when the plasma flow is parallel to the magnetic field, a shock wave appears if the governing equation for velocity potential is in hyperbolic type in relation with the Mach number and the Alfven number. When the flow is perpendicular to the magnetic field, the Maxwell stress, in addition to the pressure, plays a role in the shock wave in plasma. When the plasma temperature is so high, as the plasma becomes collision-free, another type of shock wave appears. In a collision-free shock wave, gyromotions of electrons around the magnetic field lines cause the shock formation instead of collisions in a collision-dominant plasma or neutral gas. Regardless of a collision-dominant or collision-free shock wave, the fluid that passes through the shock wave is heated in addition to being compressed. In inertial confinement fusion, the fuel must be compressed. Really, implosion motion performs fuel compression. A shock wave, appearing in the process of implosion, compresses the fuel. The shock wave, however, heats the fuel more intensively, and it makes it difficult to compress the fuel further because high temperatures invite high pressure. Adiabatic compression of the fuel is the desired result during the implosion, without the formation of a shock wave. (Author)

Scattering for wave equations with dissipative terms in layered media

Directory of Open Access Journals (Sweden)

Mitsuteru Kadowaki

2011-05-01

Full Text Available In this article, we show the existence of scattering solutions to wave equations with dissipative terms in layered media. To analyze the wave propagation in layered media, it is necessary to handle singular points called thresholds in the spectrum. Our main tools are Kato's smooth perturbation theory and some approximate operators.

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

Santo, Daniele; Lannes, David

2017-01-01

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Equations of state and melting curve of boron carbide in the high-pressure range of shock compression

Energy Technology Data Exchange (ETDEWEB)

Molodets, A. M., E-mail: molodets@icp.ac.ru; Golyshev, A. A.; Shakhrai, D. V. [Russian Academy of Sciences, Institute for Problems in Chemical Physics (Russian Federation)

2017-03-15

We have constructed the equations of state for crystalline boron carbide B{sub 11}C (C–B–C) and its melt under high dynamic and static pressures. A kink on the shock adiabat for boron carbide has been revealed in the pressure range near 100 GPa, and the melting curve with negative curvature in the pressure range 0–120 GPa has been calculated. The results have been used for interpreting the kinks on the shock adiabat for boron carbide in the pressure range of 0–400 GPa.

High Frequency Measurements in Shock-Wave/Turbulent Boundary-Layer Interaction at Duplicated Flight Conditions, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Large amplitude, unsteady heating loads and steep flow gradients produced in regions of shock-wave/turbulent boundary-layer interaction (SWTBLI) pose a serious and...

High Frequency Measurements in Shock-Wave/Turbulent Boundary-Layer Interaction at Duplicated Flight Conditions, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — Large amplitude, unsteady heating loads and steep flow gradients produced in regions of shock-wave/turbulent boundary-layer interaction (SWTBLI) pose a serious and...

A multiple-scales model of the shock-cell structure of imperfectly expanded supersonic jets

Science.gov (United States)

Tam, C. K. W.; Jackson, J. A.; Seiner, J. M.

1985-01-01

The present investigation is concerned with the development of an analytical model of the quasi-periodic shock-cell structure of an imperfectly expanded supersonic jet. The investigation represents a part of a program to develop a mathematical theory of broadband shock-associated noise of supersonic jets. Tam and Tanna (1982) have suggested that this type of noise is generated by the weak interaction between the quasi-periodic shock cells and the downstream-propagating large turbulence structures in the mixing layer of the jet. In the model developed in this paper, the effect of turbulence in the mixing layer of the jet is simulated by the addition of turbulent eddy-viscosity terms to the momentum equation. Attention is given to the mean-flow profile and the numerical solution, and a comparison of the numerical results with experimental data.

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander; Petrova, Guergana

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

A general analytical equation for phase diagrams of an N-layer ferroelectric thin film with two surface layers

Energy Technology Data Exchange (ETDEWEB)

Lu, Z X; Teng, B H; Rong, Y H; Lu, X H; Yang, X [School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: phytbh@163.com

2010-03-15

Within the framework of effective-field theory with correlations, the phase diagrams of an N-layer ferroelectric thin film with two surface layers are studied by the differential operator technique based on the spin-1/2 transverse Ising model. A general analytical equation for the phase diagram of a ferroelectric thin film with arbitrary layer number as well as exchange interactions and transverse fields is derived, and then the effects of exchange interactions and transverse fields on phase diagrams are discussed for an arbitrary layer number N. Meanwhile, the crossover features, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for various parameters of an N-layer ferroelectric thin film with two surface layers are investigated. As a result, an N-independent common intersection point equation is obtained, and the three-dimensional curved surfaces for the crossover values are constructed. In comparison with the usual mean-field approximation, the differential operator technique with correlations reduces to some extent the ferroelectric features of a ferroelectric thin film.

On the wall-normal velocity of the compressible boundary-layer equations

Science.gov (United States)

Pruett, C. David

1991-01-01

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Shock dynamics induced by double-spot laser irradiation of layered targets

Directory of Open Access Journals (Sweden)

Aliverdiev Abutrab A.

2015-06-01

Full Text Available We studied the interaction of a double-spot laser beam with targets using the Prague Asterix Laser System (PALS iodine laser working at 0.44 μm wavelength and intensity of about 1015 W/cm2. Shock breakout signals were recorder using time-resolved self-emission from target rear side of irradiated targets. We compared the behavior of pure Al targets and of targets with a foam layer on the laser side. Results have been simulated using hydrodynamic numerical codes.

The internal propagation of fusion flame with the strong shock of a laser driven plasma block for advanced nuclear fuel ignition

International Nuclear Information System (INIS)

Malekynia, B.; Razavipour, S. S.

2013-01-01

An accelerated skin layer may be used to ignite solid state fuels. Detailed analyses were clarified by solving the hydrodynamic equations for nonlinear force driven plasma block ignition. In this paper, the complementary mechanisms are included for the advanced fuel ignition: external factors such as lasers, compression, shock waves, and sparks. The other category is created within the plasma fusion as reheating of an alpha particle, the Bremsstrahlung absorption, expansion, conduction, and shock waves generated by explosions. With the new condition for the control of shock waves, the spherical deuterium-tritium fuel density should be increased to 75 times that of the solid state. The threshold ignition energy flux density for advanced fuel ignition may be obtained using temperature equations, including the ones for the density profile obtained through the continuity equation and the expansion velocity for the r ≠ 0 layers. These thresholds are significantly reduced in comparison with the ignition thresholds at x = 0 for solid advanced fuels. The quantum correction for the collision frequency is applied in the case of the delay in ion heating. Under the shock wave condition, the spherical proton-boron and proton-lithium fuel densities should be increased to densities 120 and 180 times that of the solid state. These plasma compressions are achieved through a longer duration laser pulse or X-ray. (physics of gases, plasmas, and electric discharges)

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions are exactly preserved by the scheme and positivity preserving; that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers. The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces. © 2009 Society for Industrial and Applied Mathematics.

Effect of back-pressure forcing on shock train structures in rectangular channels

Science.gov (United States)

Gnani, F.; Zare-Behtash, H.; White, C.; Kontis, K.

2018-04-01

The deceleration of a supersonic flow to the subsonic regime inside a high-speed engine occurs through a series of shock waves, known as a shock train. The generation of such a flow structure is due to the interaction between the shock waves and the boundary layer inside a long and narrow duct. The understanding of the physics governing the shock train is vital for the improvement of the design of high-speed engines and the development of flow control strategies. The present paper analyses the sensitivity of the shock train configuration to a back-pressure variation. The complex characteristics of the shock train at an inflow Mach number M = 2 in a channel of constant height are investigated with two-dimensional RANS equations closed by the Wilcox k-ω turbulence model. Under a sinusoidal back-pressure variation, the simulated results indicate that the shock train executes a motion around its mean position that deviates from a perfect sinusoidal profile with variation in oscillation amplitude, frequency, and whether the pressure is first increased or decreased.

The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical?

International Nuclear Information System (INIS)

Wu, C.C.

1988-01-01

Contrary to the usual belief that MHD intermediate shocks are extraneous, the authors have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, he clarifies the differences between the conventional view and the results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms his results. In addition, the study shows that there exists a larger class of shocklike solutions in the time-dependent dissiaptive MHD equations than are given by the MHD Rankine-Hugoniot relations. it also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models

An experimental study of three-dimensional shock wave/boundary layer interactions generated by sharp fins

Science.gov (United States)

Lu, F. K.; Settles, G. S.; Bogdonoff, S. M.

1983-01-01

The interaction between a turbulent boundary layer and a shock wave generated by a sharp fin with leading edge sweepback was investigated. The incoming flow was at Mach 2.96 and at a unit Reynolds number of 63 x 10 to the 6th power 0.1 m. The approximate incoming boundary layer thickness was either 4 mm or 17 mm. The fins used were at 5 deg, 9 deg and 15 deg incidence and had leading edge sweepback from 0 deg to 65 deg. The tests consisted of surface kerosene lampblack streak visualization, surface pressure measurements, shock wave shape determination by shadowgraphs, and localized vapor screen visualization. The upstream influence lengths of the fin interactions were correlated using viscous and inviscid flow parameters. The parameters affecting the surface features close to the fin and way from the fin were also identified. Essentially, the surface features in the farfield were found to be conical.

Active flow control insight gained from a modified integral boundary layer equation

Science.gov (United States)

Seifert, Avraham

2016-11-01

Active Flow Control (AFC) can alter the development of boundary layers with applications (e.g., reducing drag by separation delay or separating the boundary layers and enhancing vortex shedding to increase drag). Historically, significant effects of steady AFC methods were observed. Unsteady actuation is significantly more efficient than steady. Full-scale AFC tests were conducted with varying levels of success. While clearly relevant to industry, AFC implementation relies on expert knowledge with proven intuition and or costly and lengthy computational efforts. This situation hinders the use of AFC while simple, quick and reliable design method is absent. An updated form of the unsteady integral boundary layer (UIBL) equations, that include AFC terms (unsteady wall transpiration and body forces) can be used to assist in AFC analysis and design. With these equations and given a family of suitable velocity profiles, the momentum thickness can be calculated and matched with an outer, potential flow solution in 2D and 3D manner to create an AFC design tool, parallel to proven tools for airfoil design. Limiting cases of the UIBL equation can be used to analyze candidate AFC concepts in terms of their capability to modify the boundary layers development and system performance.

The jumps of physical quantities at fast shocks under pressure anisotropy: theory versus observations at the bow shock

International Nuclear Information System (INIS)

Vogl, D.F.

2000-10-01

The interaction of the solar wind with magnetized planets leads to the formation of the so-called magnetosphere, a cavity generated by the geomagnetic field. The supersonic, superalfvenic, and magnetized solar wind flow interacting with blunt bodies produces a detached bow shock, separating the solar wind from the magnetosheath, the region between the shock wave and the magnetopause. On approach to a planetary obstacle, the solar wind becomes subsonic at the bow shock and then flows past the planet in the magnetosheath. At the bow shock, the plasma parameters and the magnetic field strength change from upstream to downstream, i.e., an increase of plasma density, temperature, pressure, and magnetic field strength, and a decrease of the velocity across the shock. In this PhD thesis we mainly concentrate on the variations of all physical quantities across the bow shock taking into account pressure anisotropy, which is an important feature in space plasma physics and observed by various spacecraft missions in the solar wind as well as in the magnetosheath. Dealing with anisotropic plasma conditions, one has to introduce the so-called pressure tensor, characterized by two scalar pressures, the pressure perpendicular (P p erp) and the pressure parallel (P p arallel) with respect to the magnetic field and in general one speaks of anisotropic conditions for P p erp is not P p arallel. Many spacecraft observations of the solar wind show P p arallel > P p erp, whereas observations of the magnetosheath show the opposite case, P p arallel p erp. Therefore, dissipation of kinetic energy into thermal energy plays an important role in studying the variations of the relevant physical quantities across the shock. It has to be mentioned that planetary bow shocks are good examples for fast MHD shock waves. Therefore, the basic equations for describing the changes across the shock can be obtained by integrating the MHD equations in conservative form. We note that these equations, the

Shock wave equation of state of powder material

OpenAIRE

Dijken, D.K.; Hosson, J.Th.M. De

1994-01-01

A model is proposed to predict the following quantities for powder materials compacted by shock waves: the pressure, the specific volume, the internal energy behind the shock wave, and the shock-wave velocity U-s. They are calculated as a function of flyerplate velocity u(p) and initial powder specific volume V-00. The model is tested on Cu, Al2024, and Fe. Calculated U-s vs u(p) curves agree well with experiments provided V-00 is smaller than about two times the solid specific volume. The mo...

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. II - Wall shear stress

Science.gov (United States)

Liou, M. S.; Adamson, T. C., Jr.

1980-01-01

Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.

Solution of the Dirichlet Problem for the Poisson's Equation in a Multidimensional Infinite Layer

Directory of Open Access Journals (Sweden)

O. D. Algazin

2015-01-01

Full Text Available The paper considers the multidimensional Poisson equation in the domain bounded by two parallel hyperplanes (in the multidimensional infinite layer. For an n-dimensional half-space method of solving boundary value problems for linear partial differential equations with constant coefficients is a Fourier transform to the variables in the boundary hyperplane. The same method can be used for an infinite layer, as is done in this paper in the case of the Dirichlet problem for the Poisson equation. For strip and infinite layer in three-dimensional space the solutions of this problem are known. And in the three-dimensional case Green's function is written as an infinite series. In this paper, the solution is obtained in the integral form and kernels of integrals are expressed in a finite form in terms of elementary functions and Bessel functions. A recurrence relation between the kernels of integrals for n-dimensional and (n + 2 -dimensional layers was obtained. In particular, is built the Green's function of the Laplace operator for the Dirichlet problem, through which the solution of the problem is recorded. Even in three-dimensional case we obtained new formula compared to the known. It is shown that the kernel of the integral representation of the solution of the Dirichlet problem for a homogeneous Poisson equation (Laplace equation is an approximate identity (δ-shaped system of functions. Therefore, if the boundary values are generalized functions of slow growth, the solution of the Dirichlet problem for the homogeneous equation (Laplace is written as a convolution of kernels with these functions.

Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

Directory of Open Access Journals (Sweden)

Boričić Zoran

2009-01-01

Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.

Finite difference method for inner-layer equations in the resistive MagnetoHydroDynamic stability analysis

International Nuclear Information System (INIS)

Tokuda, Shinji; Watanabe, Tomoko.

1996-08-01

The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)

A documentation of two- and three-dimensional shock-separated turbulent boundary layers

Science.gov (United States)

Brown, J. D.; Brown, J. L.; Kussoy, M. I.

1988-01-01

A shock-related separation of a turbulent boundary layer has been studied and documented. The flow was that of an axisymmetric turbulent boundary layer over a 5.02-cm-diam cylinder that was aligned with the wind tunnel axis. The boundary layer was compressed by a 30 deg half-angle conical flare, with the cone axis inclined at an angle alpha to the cylinder axis. Nominal test conditions were P sub tau equals 1.7 atm and M sub infinity equals 2.85. Measurements were confined to the upper-symmetry, phi equals 0 deg, plane. Data are presented for the cases of alpha equal to 0. 5. and 10 deg and include mean surface pressures, streamwise and normal mean velocities, kinematic turbulent stresses and kinetic energies, as well as reverse-flow intermittencies. All data are given in tabular form; pressures, streamwise velocities, turbulent shear stresses, and kinetic energies are also presented graphically.

The formation of shocks and fundamental solution of a fourth-order quasilinear Boussinesq-type equation

Science.gov (United States)

Galaktionov, Victor A.

2009-02-01

As a basic higher-order model, the fourth-order Boussinesq-type quasilinear wave equation (the QWE-4) \\[ \\begin{equation*}\\fl u_{tt} = -(|u|^n u)_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+, \\quad with\\ exponent\\ n > 0,\\end{equation*} \\] is considered. Self-similar blow-up solutions \\[ \\begin{eqnarray*}\\tqs\\tqs u_-(x,t)=g(z), \\quad\\, z=\\frac x{\\sqrt{T-t}},\\\\ where\\ g\\ solved\\ the\\ ODE\\ \\frac 14 g'' z^2 + \\frac 34 g'z = -(|g|^n g)^{(4)},\\end{eqnarray*} \\] are shown to exist that generate as t → T- discontinuous shock waves. The QWE-4 is also shown to admit a smooth (for t > 0) global 'fundamental solution' \\[ \\begin{eqnarray*}\\fl b_n(x,t)= t^{\\frac{2}{n+4}} F_n(y),\\ y = x/t^{\\frac{n+2}{n+4}},\\ such\\ that\\ b_{n}(x,0)= 0,\\ b_{nt}(x,0)= {\\delta}(x),\\end{eqnarray*} \\] i.e. having a measure as initial data. A 'homotopic' limit n → 0 is used to get b_0(x,t)= \\sqrt t \\, F_0(x/\\sqrt t) being the classic fundamental solution of the 1D linear beam equation \\[ \\begin{equation*}u_{tt} = -u_{xxxx} \\tqs in\\ \\mathbb{R} \\times \\mathbb{R}_+.\\end{equation*} \\

Augmentation of DAA Staggered – Solution Equations in Underwater Shock Problems for Singular Structural Mass Matrices

Directory of Open Access Journals (Sweden)

John A. DeRuntz Jr.

2005-01-01

Full Text Available The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA. Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equations, and the total pressure applied to the structural equations on its right hand side. By formally solving for the acceleration vector from the structural system and substituting it into its place in the DAA equations, the augmentation introduces a term involving the inverse of the structural mass matrix. However there exist at least two important classes of problems in which the structural mass matrix is singular. This paper develops a method to carry out the augmentation for such problems using a generalized inverse technique.

Measurement of high-pressure shock waves in cryogenic deuterium-tritium ice layered capsule implosions on NIF.

Science.gov (United States)

Robey, H F; Moody, J D; Celliers, P M; Ross, J S; Ralph, J; Le Pape, S; Berzak Hopkins, L; Parham, T; Sater, J; Mapoles, E R; Holunga, D M; Walters, C F; Haid, B J; Kozioziemski, B J; Dylla-Spears, R J; Krauter, K G; Frieders, G; Ross, G; Bowers, M W; Strozzi, D J; Yoxall, B E; Hamza, A V; Dzenitis, B; Bhandarkar, S D; Young, B; Van Wonterghem, B M; Atherton, L J; Landen, O L; Edwards, M J; Boehly, T R

2013-08-09

The first measurements of multiple, high-pressure shock waves in cryogenic deuterium-tritium (DT) ice layered capsule implosions on the National Ignition Facility have been performed. The strength and relative timing of these shocks must be adjusted to very high precision in order to keep the DT fuel entropy low and compressibility high. All previous measurements of shock timing in inertial confinement fusion implosions [T. R. Boehly et al., Phys. Rev. Lett. 106, 195005 (2011), H. F. Robey et al., Phys. Rev. Lett. 108, 215004 (2012)] have been performed in surrogate targets, where the solid DT ice shell and central DT gas regions were replaced with a continuous liquid deuterium (D2) fill. This report presents the first experimental validation of the assumptions underlying this surrogate technique.

Application of thin-layer Navier-Stokes equations near maximum lift

Science.gov (United States)

Anderson, W. K.; Thomas, J. L.; Rumsey, C. L.

1984-01-01

The flowfield about a NACA 0012 airfoil at a Mach number of 0.3 and Reynolds number of 1 million is computed through an angle of attack range, up to 18 deg, corresponding to conditions up to and beyond the maximum lift coefficient. Results obtained using the compressible thin-layer Navier-Stokes equations are presented as well as results from the compressible Euler equations with and without a viscous coupling procedure. The applicability of each code is assessed and many thin-layer Navier-Stokes benchmark solutions are obtained which can be used for comparison with other codes intended for use at high angles of attack. Reasonable agreement of the Navier-Stokes code with experiment and the viscous-inviscid interaction code is obtained at moderate angles of attack. An unsteady solution is obtained with the thin-layer Navier-Stokes code at the highest angle of attack considered. The maximum lift coefficient is overpredicted, however, in comparison to experimental data, which is attributed to the presence of a laminar separation bubble near the leading edge not modeled in the computations. Two comparisons with experimental data are also presented at a higher Mach number.

Exploratory laser-driven shock wave studies

International Nuclear Information System (INIS)

Solem, J.C.; Veeser, L.R.

1977-11-01

We show the results of a feasibility study for investigating shock structure and for measuring equation-of-state parameters using high-energy, short-pulse lasers. We discuss the temporal and spatial structure of the luminosity from laser-driven shock unloading in aluminum foils. We demonstrate that shock velocity can be measured by observing the time interval between shock emergence across two thicknesses and show data for shocks of 1.3 and 2.1 Mbar. The fact that we observe shock fronts cleanly breaking through steps as small as 3 μm indicates that the shock front thickness is very small in the few megabar region; this is the first experimental verification that these fronts are not more than a few micrometers thick. We present approximate measurements of free-surface velocity. Finally, we speculate on the use of these techniques to obtain detailed equation-of-state data

Parametric Study of Swept Impinging Oblique Shock/Boundary Layer Interactions

Science.gov (United States)

Doehrmann, Adam; Threadgill, James; Little, Jesse

2017-11-01

Modern high-speed vehicles have increasingly complex 3D geometries featuring: surface curvature, variable aspect ratio inlet ducts and swept bodies. Such distortion to the flow field necessitates a further understanding of swept 3D Shock/Boundary Layer Interactions (SBLIs), where various regimes of spanwise interaction development have been observed. A parametric experimental study of swept oblique impinging SBLIs has been conducted comparing cylindrical and conical interaction structures to that of swept compression ramps in previous work. This investigation examines five shock generators with 2D deflection of θ = 12 .5° and varying degrees of sweep (ψ = 10 .0° , 15 .0° , 22 .5° , 30 .0° , 40 .0°), with an incoming turbulent flow at Mach 2.3 and 3.0. Parametric characterization of surface oil-flow visualizations has shown that the inception length of the interaction follows a similar trend to that seen in swept compression ramps as sweep is varied, namely that it increases as sweep approaches a critical angle. However, this criteria disagrees with direct observations of separation and reattachment angles. Similarities in mean pressures profiles have also been assessed and analyzed with respect to the onset of a cylindrical/conical interaction. Supported by the Air Force Office of Scientific Research (FA9550-15-1-0430).

Compressible stability of growing boundary layers using parabolized stability equations

Science.gov (United States)

Chang, Chau-Lyan; Malik, Mujeeb R.; Erlebacher, Gordon; Hussaini, M. Y.

1991-01-01

The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

Heat transfer, velocity-temperature correlation, and turbulent shear stress from Navier-Stokes computations of shock wave/turbulent boundary layer interaction flows

Science.gov (United States)

Wang, C. R.; Hingst, W. R.; Porro, A. R.

1991-01-01

The properties of 2-D shock wave/turbulent boundary layer interaction flows were calculated by using a compressible turbulent Navier-Stokes numerical computational code. Interaction flows caused by oblique shock wave impingement on the turbulent boundary layer flow were considered. The oblique shock waves were induced with shock generators at angles of attack less than 10 degs in supersonic flows. The surface temperatures were kept at near-adiabatic (ratio of wall static temperature to free stream total temperature) and cold wall (ratio of wall static temperature to free stream total temperature) conditions. The computational results were studied for the surface heat transfer, velocity temperature correlation, and turbulent shear stress in the interaction flow fields. Comparisons of the computational results with existing measurements indicated that (1) the surface heat transfer rates and surface pressures could be correlated with Holden's relationship, (2) the mean flow streamwise velocity components and static temperatures could be correlated with Crocco's relationship if flow separation did not occur, and (3) the Baldwin-Lomax turbulence model should be modified for turbulent shear stress computations in the interaction flows.

Nonlinear Korteweg-de Vries-Burger equation for ion-acoustic shock waves in the presence of kappa distributed electrons and positrons

International Nuclear Information System (INIS)

Shah, Asif; Saeed, R

2011-01-01

The ion-acoustic shock waves are studied in electron-positron-ion plasma. The plasma system is composed of three components, specifically relativistic adiabatic ions, kappa distributed electrons and positrons. The Korteweg-de Vries-Burger equation is derived, solved analytically. The effects of plasma parameters on the shock strength and steepness are investigated. The numerical results are presented graphically for illustration. The results may have importance in non-thermal and relativistic plasmas of pulsar magnetosphere (Arons 2009 Astrophys. Space Sci. Library 357 373; Blasi and Amato arXiv:1007.4745V1 [astro-Ph.HE]).

SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLEFLUID’S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS

Directory of Open Access Journals (Sweden)

Nadjafikhah M.

2017-07-01

Full Text Available Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.

Influence of interface scattering on shock waves in heterogeneous solids

International Nuclear Information System (INIS)

Zhuang Shiming; Ravichandran, Guruswami; Grady, Dennis E.

2002-01-01

In heterogeneous media, the scattering due to interfaces between dissimilar materials play an important role in shock wave dissipation and dispersion. In this work the influence of interface scattering effect on shock waves was studied by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites. The experimental results (using VISAR and stress gauges) indicate that the rise time of the shock front decreases with increasing shock strength, and increases with increasing mechanical impedance mismatch between layers; the strain rate at the shock front increases by about the square of the shock stress. Experimental and numerical results also show that due to interface scattering effect the shock wave velocity in periodically layered composites decreases. In some cases the shock velocity of a layered heterogeneous composite can be lower than that of either of its components

Augmentation of DAA Staggered – Solution Equations in Underwater Shock Problems for Singular Structural Mass Matrices

OpenAIRE

DeRuntz Jr., John A.

2005-01-01

The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA). Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equa...

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. I - Pressure distribution

Science.gov (United States)

Messiter, A. F.

1980-01-01

Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.

Multi-fidelity numerical simulations of shock/turbulent-boundary layer interaction with uncertainty quantification

Science.gov (United States)

Bermejo-Moreno, Ivan; Campo, Laura; Larsson, Johan; Emory, Mike; Bodart, Julien; Palacios, Francisco; Iaccarino, Gianluca; Eaton, John

2013-11-01

We study the interaction between an oblique shock wave and the turbulent boundary layers inside a nearly-square duct by combining wall-modeled LES, 2D and 3D RANS simulations, targeting the experiment of Campo, Helmer & Eaton, 2012 (nominal conditions: M = 2 . 05 , Reθ = 6 , 500). A primary objective is to quantify the effect of aleatory and epistemic uncertainties on the STBLI. Aleatory uncertainties considered include the inflow conditions (Mach number of the incoming air stream and thickness of the boundary layers) and perturbations of the duct geometry upstream of the interaction. The epistemic uncertainty under consideration focuses on the RANS turbulence model form by injecting perturbations in the Reynolds stress anisotropy in regions of the flow where the model assumptions (in particular, the Boussinesq eddy-viscosity hypothesis) may be invalid. These perturbations are then propagated through the flow solver into the solution. The uncertainty quantification (UQ) analysis is done through 2D and 3D RANS simulations, assessing the importance of the three-dimensional effects imposed by the nearly-square duct geometry. Wall-modeled LES are used to verify elements of the UQ methodology and to explore the flow features and physics of the STBLI for multiple shock strengths. Financial support from the United States Department of Energy under the PSAAP program is gratefully acknowledged.

On Parametric Sensitivity of Reynolds-Averaged Navier-Stokes SST Turbulence Model: 2D Hypersonic Shock-Wave Boundary Layer Interactions

Science.gov (United States)

Brown, James L.

2014-01-01

Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.

Multi-layer protective armour for underwater shock wave mitigation

OpenAIRE

Ahmed Hawass; Hosam Mostafa; Ahmed Elbeih

2015-01-01

The effect of underwater shock wave on different target plates has been studied. An underwater shock wave generator (shock tube) was used to study the interactions between water and different constructed targets which act as shock wave mitigation. Target plates, composed of sandwich of two aluminum sheets with rubber and foam in between, were prepared and studied. For comparison, the target plates composed of triple aluminum sheets were tested. The study includes the testing of the selected p...

COLLISIONLESS ELECTRON–ION SHOCKS IN RELATIVISTIC UNMAGNETIZED JET–AMBIENT INTERACTIONS: NON-THERMAL ELECTRON INJECTION BY DOUBLE LAYER

International Nuclear Information System (INIS)

Ardaneh, Kazem; Cai, Dongsheng; Nishikawa, Ken-Ichi

2016-01-01

The course of non-thermal electron ejection in relativistic unmagnetized electron–ion shocks is investigated by performing self-consistent particle-in-cell simulations. The shocks are excited through the injection of a relativistic jet into ambient plasma, leading to two distinct shocks (referred to as the trailing shock and leading shock) and a contact discontinuity. The Weibel-like instabilities heat the electrons up to approximately half of the ion kinetic energy. The double layers formed in the trailing and leading edges then accelerate the electrons up to the ion kinetic energy. The electron distribution function in the leading edge shows a clear, non-thermal power-law tail which contains ∼1% of electrons and ∼8% of the electron energy. Its power-law index is −2.6. The acceleration efficiency is ∼23% by number and ∼50% by energy, and the power-law index is −1.8 for the electron distribution function in the trailing edge. The effect of the dimensionality is examined by comparing the results of three-dimensional simulations with those of two-dimensional simulations. The comparison demonstrates that electron acceleration is more efficient in two dimensions.

Converging cylindrical shocks in ideal magnetohydrodynamics

KAUST Repository

Pullin, D. I.

2014-09-01

We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R = √μ0/p0 I/(2π) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field then

Converging cylindrical shocks in ideal magnetohydrodynamics

International Nuclear Information System (INIS)

Pullin, D. I.; Mostert, W.; Wheatley, V.; Samtaney, R.

2014-01-01

We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R=√(μ 0 /p 0 ) I/(2 π) where I is the current, μ 0 is the permeability, and p 0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field

Converging cylindrical shocks in ideal magnetohydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Pullin, D. I. [Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125 (United States); Mostert, W.; Wheatley, V. [School of Mechanical and Mining Engineering, University of Queensland, Queensland 4072 (Australia); Samtaney, R. [Mechanical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

2014-09-15

We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R=√(μ{sub 0}/p{sub 0}) I/(2 π) where I is the current, μ{sub 0} is the permeability, and p{sub 0} is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The

Converging cylindrical shocks in ideal magnetohydrodynamics

KAUST Repository

Pullin, D. I.; Mostert, W.; Wheatley, V.; Samtaney, Ravi

2014-01-01

We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shock-jump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R = √μ0/p0 I/(2π) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field then

Statistics of peak overpressure and shock steepness for linear and nonlinear N-wave propagation in a kinematic turbulence.

Science.gov (United States)

Yuldashev, Petr V; Ollivier, Sébastien; Karzova, Maria M; Khokhlova, Vera A; Blanc-Benon, Philippe

2017-12-01

Linear and nonlinear propagation of high amplitude acoustic pulses through a turbulent layer in air is investigated using a two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Initial waves are symmetrical N-waves with shock fronts of finite width. A modified von Kármán spectrum model is used to generate random wind velocity fluctuations associated with the turbulence. Physical parameters in simulations correspond to previous laboratory scale experiments where N-waves with 1.4 cm wavelength propagated through a turbulence layer with the outer scale of about 16 cm. Mean value and standard deviation of peak overpressure and shock steepness, as well as cumulative probabilities to observe amplified peak overpressure and shock steepness, are analyzed. Nonlinear propagation effects are shown to enhance pressure level in random foci for moderate initial amplitudes of N-waves thus increasing the probability to observe highly peaked waveforms. Saturation of the pressure level is observed for stronger nonlinear effects. It is shown that in the linear propagation regime, the turbulence mainly leads to the smearing of shock fronts, thus decreasing the probability to observe high values of steepness, whereas nonlinear effects dramatically increase the probability to observe steep shocks.

Effect of the dynamic pressure on the shock wave structure in a rarefied polyatomic gas

Energy Technology Data Exchange (ETDEWEB)

Taniguchi, Shigeru, E-mail: taniguchi@stat.nitech.ac.jp; Sugiyama, Masaru, E-mail: sugiyama@nitech.ac.jp [Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555 (Japan); Arima, Takashi, E-mail: tks@stat.nitech.ac.jp [Center for Social Contribution and Collaboration, Nagoya Institute of Technology, Nagoya 466-8555 (Japan); Ruggeri, Tommaso, E-mail: tommaso.ruggeri@unibo.it [Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna, Bologna (Italy)

2014-01-15

We study the shock wave structure in a rarefied polyatomic gas based on a simplified model of extended thermodynamics in which the dissipation is due only to the dynamic pressure. In this case the differential system is very simple because it is a variant of Euler system with a new scalar equation for the dynamic pressure [T. Arima, S. Taniguchi, T. Ruggeri, and M. Sugiyama, Phys. Lett. A 376, 2799–2803 (2012)]. It is shown that this theory is able to describe the three types of the shock wave structure observed in experiments: the nearly symmetric shock wave structure (Type A, small Mach number), the asymmetric structure (Type B, moderate Mach number), and the structure composed of thin and thick layers (Type C, large Mach number)

A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

International Nuclear Information System (INIS)

Petitpas, Fabien; Franquet, Erwin; Saurel, Richard; Le Metayer, Olivier

2007-01-01

The relaxation-projection method developed in Saurel et al. [R. Saurel, E. Franquet, E. Daniel, O. Le Metayer, A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations, J. Comput. Phys. (2007) 822-845] is extended to the non-conservative hyperbolic multiphase flow model of Kapila et al. [A.K. Kapila, Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration to detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002-3024]. This model has the ability to treat multi-temperatures mixtures evolving with a single pressure and velocity and is particularly interesting for the computation of interface problems with compressible materials as well as wave propagation in heterogeneous mixtures. The non-conservative character of this model poses however computational challenges in the presence of shocks. The first issue is related to the Riemann problem resolution that necessitates shock jump conditions. Thanks to the Rankine-Hugoniot relations proposed and validated in Saurel et al. [R. Saurel, O. Le Metayer, J. Massoni, S. Gavrilyuk, Shock jump conditions for multiphase mixtures with stiff mechanical relaxation, Shock Waves 16 (3) (2007) 209-232] exact and approximate 2-shocks Riemann solvers are derived. However, the Riemann solver is only a part of a numerical scheme and non-conservative variables pose extra difficulties for the projection or cell average of the solution. It is shown that conventional Godunov schemes are unable to converge to the exact solution for strong multiphase shocks. This is due to the incorrect partition of the energies or entropies in the cell averaged mixture. To circumvent this difficulty a specific Lagrangian scheme is developed. The correct partition of the energies is achieved by using an artificial heat exchange in the shock layer. With the help of an asymptotic analysis this heat exchange takes a similar form as

A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

Science.gov (United States)

Petitpas, Fabien; Franquet, Erwin; Saurel, Richard; Le Metayer, Olivier

2007-08-01

The relaxation-projection method developed in Saurel et al. [R. Saurel, E. Franquet, E. Daniel, O. Le Metayer, A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations, J. Comput. Phys. (2007) 822-845] is extended to the non-conservative hyperbolic multiphase flow model of Kapila et al. [A.K. Kapila, Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration to detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002-3024]. This model has the ability to treat multi-temperatures mixtures evolving with a single pressure and velocity and is particularly interesting for the computation of interface problems with compressible materials as well as wave propagation in heterogeneous mixtures. The non-conservative character of this model poses however computational challenges in the presence of shocks. The first issue is related to the Riemann problem resolution that necessitates shock jump conditions. Thanks to the Rankine-Hugoniot relations proposed and validated in Saurel et al. [R. Saurel, O. Le Metayer, J. Massoni, S. Gavrilyuk, Shock jump conditions for multiphase mixtures with stiff mechanical relaxation, Shock Waves 16 (3) (2007) 209-232] exact and approximate 2-shocks Riemann solvers are derived. However, the Riemann solver is only a part of a numerical scheme and non-conservative variables pose extra difficulties for the projection or cell average of the solution. It is shown that conventional Godunov schemes are unable to converge to the exact solution for strong multiphase shocks. This is due to the incorrect partition of the energies or entropies in the cell averaged mixture. To circumvent this difficulty a specific Lagrangian scheme is developed. The correct partition of the energies is achieved by using an artificial heat exchange in the shock layer. With the help of an asymptotic analysis this heat exchange takes a similar form as

Enstrophy generation in a shock-dominated turbulence

International Nuclear Information System (INIS)

Miura, Hideaki.

1995-09-01

A mechanism of enstrophy generation is investigated numerically in a shock-dominated turbulence driven by a random external force which has only the compressible component. Enstrophy is generated, especially on collision of shock, as a pair of vortex tube of opposite sense of rotation behind curved shocks. The roles of various terms in enstrophy equation are clarified in enstrophy generation process. Generation of enstrophy is enhanced by strong alignment of each term of the enstrophy equation with the vorticity vector. (author)

CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave Boundary-Layer Interaction

Science.gov (United States)

Davis, David O.

2015-01-01

Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. The results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.

CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction

Science.gov (United States)

Davis, David Owen

2015-01-01

Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/ boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. These results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.

Experimental Study of Fillets to Reduce Corner Effects in an Oblique Shock-Wave/Boundary Layer Interaction

Science.gov (United States)

Hirt, Stefanie M.

2015-01-01

A test was conducted in the 15 cm x 15 cm supersonic wind tunnel at NASA Glenn Research Center that focused on corner effects of an oblique shock-wave/boundary-layer interaction. In an attempt to control the interaction in the corner region, eight corner fillet configurations were tested. Three parameters were considered for the fillet configurations: the radius, the fillet length, and the taper length from the square corner to the fillet radius. Fillets effectively reduced the boundary-layer thickness in the corner; however, there was an associated penalty in the form of increased boundary-layer thickness at the tunnel centerline. Larger fillet radii caused greater reductions in boundary-layer thickness along the corner bisector. To a lesser, but measureable, extent, shorter fillet lengths resulted in thinner corner boundary layers. Overall, of the configurations tested, the largest radius resulted in the best combination of control in the corner, evidenced by a reduction in boundary-layer thickness, coupled with minimal impacts at the tunnel centerline.

Numerical solution of the resistive magnetohydrodynamic boundary-layer equations

International Nuclear Information System (INIS)

Glasser, A.H.; Jardin, S.C.; Tesauro, G.

1983-10-01

Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Excellent agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical medthods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability

Nitro Stretch Probing of a Single Molecular Layer to Monitor Shock Compression with Picosecond Time-Resolution

Science.gov (United States)

Berg, Christopher; Lagutchev, Alexei; Fu, Yuanxi; Dlott, Dana

2011-06-01

To obtain maximum possible temporal resolution, laser-driven shock compression of a molecular monolayer was studied using vibrational spectroscopy. The stretching transitions of nitro groups bound to aromatic rings was monitored using a nonlinear coherent infrared spectroscopy termed sum-frequency generation, which produced high-quality signals from this very thin layer. To overcome the shock opacity problem, a novel polymer overcoat method allowed us to make the observation window (witness plate) a few micrometers thick. The high signal-to-noise ratios (>100:1) obtained via this spectroscopy allowed us to study detailed behavior of the shocked molecules. To help interpret these vibrational spectra, additional spectra were obtained under conditions of static pressures up to 10 GPa and static temperatures up to 1000 C. Consequently, this experiment represents a significant step in resolving molecular dynamics during shock compression and unloading with both high spatial and temporal resolution. Supported by the Stewardship Sciences Academic Alliance Program from the Carnegie-DOE Alliance Center under grant number DOE CIW 4-3253-13 and the US Air Force Office of Scientific Research under award number FAA9550-09-1-0163.

Composition of the earth's atmosphere by shock-layer radiometry during the PAET entry probe experiment.

Science.gov (United States)

Whiting, E. E.; Arnold, J. O.; Page, W. A.; Reynolds, R. M.

1973-01-01

A determination of the composition of the earth's atmosphere obtained from onboard radiometer measurements of the spectra emitted from the bow shock layer of a high-speed entry probe is reported. The N2, O2, CO2, and noble gas concentrations in the earth's atmosphere were determined to good accuracy by this technique. The results demonstrate unequivocally the feasibility of determining the composition of an unknown planetary atmosphere by means of a multichannel radiometer viewing optical emission from the heated atmospheric gases in the region between the bow shock wave and the vehicle surface. The spectral locations in this experiment were preselected to enable the observation of CN violet, N2(+) first negative and atomic oxygen emission at 3870, 3910, and 7775 A, respectively. The atmospheric gases were heated and compressed by the shock wave to a peak temperature of about 6100 K and a corresponding pressure of 0.4 atm. Complete descriptions of the data analysis technique and the onboard radiometer and its calibration are given.

A two-layer model for buoyant inertial displacement flows in inclined pipes

Science.gov (United States)

Etrati, Ali; Frigaard, Ian A.

2018-02-01

We investigate the inertial flows found in buoyant miscible displacements using a two-layer model. From displacement flow experiments in inclined pipes, it has been observed that for significant ranges of Fr and Re cos β/Fr, a two-layer, stratified flow develops with the heavier fluid moving at the bottom of the pipe. Due to significant inertial effects, thin-film/lubrication models developed for laminar, viscous flows are not effective for predicting these flows. Here we develop a displacement model that addresses this shortcoming. The complete model for the displacement flow consists of mass and momentum equations for each fluid, resulting in a set of four non-linear equations. By integrating over each layer and eliminating the pressure gradient, we reduce the system to two equations for the area and mean velocity of the heavy fluid layer. The wall and interfacial stresses appear as source terms in the reduced system. The final system of equations is solved numerically using a robust, shock-capturing scheme. The equations are stabilized to remove non-physical instabilities. A linear stability analysis is able to predict the onset of instabilities at the interface and together with numerical solution, is used to study displacement effectiveness over different parametric regimes. Backflow and instability onset predictions are made for different viscosity ratios.

Collisionless Electrostatic Shock Modeling and Simulation

Science.gov (United States)

2016-10-21

equations with piston -like boundary conditions gives a solution for the shock behavior. • Assumes cold upstream ions, therefore neglecting shock...temperature ratio (>10) – Wave Train Wavelength – Shock-Front Mach Number – Reflected Ion Beam Velocity Gathering Experiment Data – Double Plasma Device...experimental shock data. • Inconsistencies in published 1969 double -plasma device data hampered validation. Future Work: Extension to Moderately

Analytical extension of curved shock theory

Science.gov (United States)

Emanuel, G.

2018-03-01

Curved shock theory (CST) is limited to shock waves in a steady, two-dimensional or axisymmetric (2-Ax) flow of a perfect gas. A unique feature of CST is its use of intrinsic coordinates that result in an elegant and useful formulation for flow properties just downstream of a shock. For instance, the downstream effect of upstream vorticity, shock wave curvature, and the upstream pressure gradient along a streamline is established. There have been several attempts to extend CST, as mentioned in the text. Removal of the steady, 2-Ax, and perfect gas limitations, singly or in combination, requires an appropriate formulation of the shock wave's jump relations and the intrinsic coordinate Euler equations. Issues discussed include flow plane versus osculating plane, unsteady flow, vorticity, an imperfect gas, etc. The extension of CST utilizes concepts from differential geometry, such as the osculating plane, streamline torsion, and the Serret-Frenet equations.

Boundary layer phenomena for differential-delay equations with state-dependent time lags, I.

Science.gov (United States)

Mallet-Paret, John; Nussbaum, Roger D.

1992-11-01

In this paper we begin a study of the differential-delay equation \\varepsilon x'(t) = - x(t) + f(x(t - r)), r = r(x(t)) . We prove the existence of periodic solutions for 0equations. In a companion paper these results will be used to investigate the limiting profile and corresponding boundary layer phenomena for periodic solutions as ɛ approaches zero.

An analysis of the relaxation of laminar boundary layer on a flat plate after passage of an interface with application to expansion-tube flows

Science.gov (United States)

Gupta, R. N.

1972-01-01

The relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate in an expansion tube is analyzed. Several combinations of test gas and acceleration gas are considered. The problem is treated in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this lag is negligible. The time-dependent laminar-boundary-layer equations of a binary mixture of perfect gases are taken as the flow-governing equations. This coupled set of differential equations, written in terms of the Lam-Crocco variables, has been solved by a line-relaxation finite-difference techniques. The results presented include the Stanton number and the local skin-friction coefficient as functions of shock Mach number and the nondimensional distance-time variable. The results indicate that more than 95 percent of the test-gas boundary layer exists over a length, measured from the leading edge of the plate, equal to about three-tenths of the distance traversed by the interface in the free stream.

Control Volume Analysis of Boundary Layer Ingesting Propulsion Systems With or Without Shock Wave Ahead of the Inlet

Science.gov (United States)

Kim, Hyun Dae; Felder, James L.

2011-01-01

The performance benefit of boundary layer or wake ingestion on marine and air vehicles has been well documented and explored. In this article, a quasi-one-dimensional boundary layer ingestion (BLI) benefit analysis for subsonic and transonic propulsion systems is performed using a control volume of a ducted propulsion system that ingests the boundary layer developed by the external airframe surface. To illustrate the BLI benefit, a relationship between the amount of BLI and the net thrust is established and analyzed for two propulsor types. One propulsor is an electric fan, and the other is a pure turbojet. These engines can be modeled as a turbofan with an infinite bypass ratio for the electric fan, and with a zero bypass ratio for the pure turbojet. The analysis considers two flow processes: a boundary layer being ingested by an aircraft inlet and a shock wave sitting in front of the inlet. Though the two processes are completely unrelated, both represent a loss of total pressure and velocity. In real applications, it is possible to have both processes occurring in front of the inlet of a transonic vehicle. Preliminary analysis indicates that the electrically driven propulsion system benefits most from the boundary layer ingestion and the presence of transonic shock waves, whereas the benefit for the turbojet engine is near zero or negative depending on the amount of total temperature rise across the engine.

Flow-around modes for a rhomboid wing with a stall vortex in the shock layer

Science.gov (United States)

Zubin, M. A.; Maximov, F. A.; Ostapenko, N. A.

2017-12-01

The results of theoretical and experimental investigation of an asymmetrical hypersonic flow around a V-shaped wing with the opening angle larger than π on the modes with attached shockwaves on forward edges, when the stall flow is implemented on the leeward wing cantilever behind the kink point of the cross contour. In this case, a vortex of nonviscous nature is formed in which the velocities on the sphere exceeding the speed of sound and resulting in the occurrence of pressure shocks with an intensity sufficient for the separation of the turbulent boundary layer take place in the reverse flow according to the calculations within the framework of the ideal gas. It is experimentally established that a separation boundary layer can exist in the reverse flow, and its structure is subject to the laws inherent to the reverse flow in the separation region of the turbulent boundary layer arising in the supersonic conic flow under the action of a shockwave incident to the boundary layer.

Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

Science.gov (United States)

Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

2002-01-01

Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

Science.gov (United States)

Chapman, Dean R.; Fiscko, Kurt A.

1988-01-01

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Shock compression of strongly correlated oxides: A liquid-regime equation of state for cerium(IV) oxide

Science.gov (United States)

Weck, Philippe F.; Cochrane, Kyle R.; Root, Seth; Lane, J. Matthew D.; Shulenburger, Luke; Carpenter, John H.; Sjostrom, Travis; Mattsson, Thomas R.; Vogler, Tracy J.

2018-03-01

The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ =2.5 to 20 g /cm3 . The impact of on-site Coulomb interaction corrections +U on the equation of state (EOS) obtained from AIMD simulations was assessed by direct comparison with results from standard density functional theory simulations. Classical molecular dynamics (CMD) simulations were also performed to model atomic-scale shock compression of larger porous CeO2 models. Results from AIMD and CMD compression simulations compare favorably with Z-machine shock data to 525 GPa and gas-gun data to 109 GPa for porous CeO2 samples. Using results from AIMD simulations, an accurate liquid-regime Mie-Grüneisen EOS was built for CeO2. In addition, a revised multiphase SESAME-type EOS was constrained using AIMD results and experimental data generated in this work. This study demonstrates the necessity of acquiring data in the porous regime to increase the reliability of existing analytical EOS models.

Transport equation and shock waves

International Nuclear Information System (INIS)

Besnard, D.

1981-04-01

A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma

Modeling mode interactions in boundary layer flows via the Parabolized Floquet Equations

OpenAIRE

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanović, Mihailo R.

2017-01-01

In this paper, we develop a linear model to study interactions between different modes in slowly-growing boundary layer flows. Our method consists of two steps. First, we augment the Blasius boundary layer profile with a disturbance field resulting from the linear Parabolized Stability Equations (PSE) to obtain the modified base flow; and, second, we combine Floquet analysis with the linear PSE to capture the spatial evolution of flow fluctuations. This procedure yields the Parabolized Floque...

Development of Calculation Algorithm for ECCS Kinematic Shock

Energy Technology Data Exchange (ETDEWEB)

Lee, Seung-Chan; Yoon, Duk-Joo; Ha, Sang-Jun [KHNP-CRI, Daejeon (Korea, Republic of)

2014-10-15

The void fraction of inverted U-pipes in front of SI(Safety Injection) pumps impact on the pipe system of ECCS(Emergency Core Cooling Systems). This phenomena is called as 'Kinematic Shock'. The purpose of this paper is to achieve the more exactly calculation when the kinematic shock is calculated by simplified equation. The behavior of the void packet of the ECCS pipes is illustrated by the simplified (other name is kinematic shock equation).. The kinematic shock is defined as the depth of total length of void clusters in the pipes of ECCS when the void cluster is continually reached along the part of pipes in vertical direction. In this paper, the simplified equation is evaluated by comparing calculation error each other.]. The more exact methods of calculating the depth of the kinematic shock in ECCS is achieved. The error of kinematic shock calculation is strongly depended on the calculation search gap and the order of Taylor's expansion. From this study, to select the suitable search gap and the suitable calculation order, differential root method, secant method, and Taylor's expansion form are compared one another.

Optimal Growth in Hypersonic Boundary Layers

Science.gov (United States)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan

2016-01-01

The linear form of the parabolized linear stability equations is used in a variational approach to extend the previous body of results for the optimal, nonmodal disturbance growth in boundary-layer flows. This paper investigates the optimal growth characteristics in the hypersonic Mach number regime without any high-enthalpy effects. The influence of wall cooling is studied, with particular emphasis on the role of the initial disturbance location and the value of the spanwise wave number that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary-layer equations, mean flow solutions based on the full Navier-Stokes equations are used in select cases to help account for the viscous- inviscid interaction near the leading edge of the plate and for the weak shock wave emanating from that region. Using the full Navier-Stokes mean flow is shown to result in further reduction with Mach number in the magnitude of optimal growth relative to the predictions based on the self-similar approximation to the base flow.

Analysis of dimensionality effect on shock wave boundary layer interaction in laminar hypersonic flows

International Nuclear Information System (INIS)

John, Bibin; Surendranath, Srikanth; Natarajan, Ganesh; Kulkarni, Vinayak

2016-01-01

Highlights: • Leading edge bluntness based separation control has been analysed numerically for 2D and axi-symmetric flows. • Differential growth of entropy layer in the streamwise direction in these cases leads to different interaction with respective boundary layers. • Separation control is found possible for planar flows beyond a critical radius called as equivalent radius. • No equivalent radius has been noticed in axi-symmertric flows in the present studies due to thin entropy layer and lack of favourable pressure gradient. - Abstract: Present investigations are centered on passive control of shock wave boundary layer interaction (SWBLI) for double cone and double wedge configurations with leading edge bluntness. This study seeks the differences in the flow physics of SWBLI in case of two dimensional (2D) and axisymmetric flow fields. In-house developed second order accurate finite-volume 2D axisymmetric compressible flow solver is employed for these studies. It is observed that the idea of leading edge bluntness offers reduction in separation bubble for 2D flow fields, whereas it leads to enhanced separation zone in case of axisymmetric flow fields. Relevant flow physics is well explored herein using wall pressure profile and relative thicknesses of boundary layer and entropy layer. Thicker entropy layer and stronger favorable pressure gradient are found responsible for the possibility of separation control in case of 2D flow fields. Thin entropy layer due to three dimensional relieving effect and its swallowing by the boundary layer are attributed for higher separation bubble size in case of cone with range of radii under consideration.

First results of radiation-driven, layered deuterium-tritium implosions with a 3-shock adiabat-shaped drive at the National Ignition Facility

Energy Technology Data Exchange (ETDEWEB)

Smalyuk, V. A.; Robey, H. F.; Döppner, T.; Jones, O. S.; Milovich, J. L.; Bachmann, B.; Baker, K. L.; Berzak Hopkins, L. F.; Bond, E.; Callahan, D. A.; Casey, D. T.; Celliers, P. M.; Cerjan, C.; Clark, D. S.; Dixit, S. N.; Edwards, M. J.; Haan, S. W.; Hamza, A. V.; Hurricane, O. A.; Jancaitis, K. S. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); and others

2015-08-15

Radiation-driven, layered deuterium-tritium plastic capsule implosions were carried out using a new, 3-shock “adiabat-shaped” drive on the National Ignition Facility. The purpose of adiabat shaping is to use a stronger first shock, reducing hydrodynamic instability growth in the ablator. The shock can decay before reaching the deuterium-tritium fuel leaving it on a low adiabat and allowing higher fuel compression. The fuel areal density was improved by ∼25% with this new drive compared to similar “high-foot” implosions, while neutron yield was improved by more than 4 times, compared to “low-foot” implosions driven at the same compression and implosion velocity.

Ablative stabilization of Rayleigh-Taylor instabilities resulting from a laser-driven radiative shock

Science.gov (United States)

Huntington, C. M.; Shimony, A.; Trantham, M.; Kuranz, C. C.; Shvarts, D.; Di Stefano, C. A.; Doss, F. W.; Drake, R. P.; Flippo, K. A.; Kalantar, D. H.; Klein, S. R.; Kline, J. L.; MacLaren, S. A.; Malamud, G.; Miles, A. R.; Prisbrey, S. T.; Raman, K. S.; Remington, B. A.; Robey, H. F.; Wan, W. C.; Park, H.-S.

2018-05-01

The Rayleigh-Taylor (RT) instability is a common occurrence in nature, notably in astrophysical systems like supernovae, where it serves to mix the dense layers of the interior of an exploding star with the low-density stellar wind surrounding it, and in inertial confinement fusion experiments, where it mixes cooler materials with the central hot spot in an imploding capsule and stifles the desired nuclear reactions. In both of these examples, the radiative flux generated by strong shocks in the system may play a role in partially stabilizing RT instabilities. Here, we present experiments performed on the National Ignition Facility, designed to isolate and study the role of radiation and heat conduction from a shock front in the stabilization of hydrodynamic instabilities. By varying the laser power delivered to a shock-tube target with an embedded, unstable interface, the radiative fluxes generated at the shock front could be controlled. We observe decreased RT growth when the shock significantly heats the medium around it, in contrast to a system where the shock did not produce significant heating. Both systems are modeled with a modified set of buoyancy-drag equations accounting for ablative stabilization, and the experimental results are consistent with ablative stabilization when the shock is radiative. This result has important implications for our understanding of astrophysical radiative shocks and supernova radiative hydrodynamics [Kuranz et al., Nature Communications 9(1), 1564 (2018)].

An algebraic method to develop well-posed PML models Absorbing layers, perfectly matched layers, linearized Euler equations

International Nuclear Information System (INIS)

Rahmouni, Adib N.

2004-01-01

In 1994, Berenger [Journal of Computational Physics 114 (1994) 185] proposed a new layer method: perfectly matched layer, PML, for electromagnetism. This new method is based on the truncation of the computational domain by a layer which absorbs waves regardless of their frequency and angle of incidence. Unfortunately, the technique proposed by Berenger (loc. cit.) leads to a system which has lost the most important properties of the original one: strong hyperbolicity and symmetry. We present in this paper an algebraic technique leading to well-known PML model [IEEE Transactions on Antennas and Propagation 44 (1996) 1630] for the linearized Euler equations, strongly well-posed, preserving the advantages of the initial method, and retaining symmetry. The technique proposed in this paper can be extended to various hyperbolic problems

Model for Shock Wave Chaos

KAUST Repository

Kasimov, Aslan R.; Faria, Luiz; Rosales, Rodolfo R.

2013-01-01

: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation

Influence of shock waves from plasma actuators on transonic and supersonic airflow

Science.gov (United States)

Mursenkova, I. V.; Znamenskaya, I. A.; Lutsky, A. E.

2018-03-01

This paper presents experimental and numerical investigations of high-current sliding surface discharges of nanosecond duration and their effect on high-speed flow as plasma actuators in a shock tube. This study deals with the effectiveness of a sliding surface discharge at low and medium air pressure. Results cover the electrical characteristics of the discharge and optical visualization of the discharge and high-speed post-discharge flow. A sliding surface discharge is first studied in quiescent air conditions and then in high-speed flow, being initiated in the boundary layer at a transverse flow velocity of 50-950 m s-1 behind a flat shock wave in air of density 0.04-0.45 kg m-3. The discharge is powered by a pulse voltage of 25-30 kV and the electric current is ~0.5 kA. Shadow imaging and particle image velocimetry (PIV) are used to measure the flow field parameters after the pulse surface discharge. Shadow imaging reveals shock waves originating from the channels of the discharge configurations. PIV is used to measure the velocity field resulting from the discharge in quiescent air and to determine the homogeneity of energy release along the sliding discharge channel. Semicylindrical shock waves from the channels of the sliding discharge have an initial velocity of more than 600 m s-1. The shock-wave configuration floats in the flow along the streamlined surface. Numerical simulation based on the equations of hydrodynamics matched with the experiment showed that 25%-50% of the discharge energy is instantly transformed into heat energy in a high-speed airflow, leading to the formation of shock waves. This energy is comparable to the flow enthalpy and can result in significant modification of the boundary layer and the entire flow.

Factors influencing flow steadiness in laminar boundary layer shock interactions

Science.gov (United States)

Tumuklu, Ozgur; Levin, Deborah A.; Gimelshein, Sergey F.; Austin, Joanna M.

2016-11-01

The Direct Simulation Monte Carlo method has been used to model laminar shock wave boundary interactions of hypersonic flow over a 30/55-deg double-wedge and "tick-shaped" model configurations studied in the Hypervelocity Expansion Tube facility and T-ADFA free-piston shock tunnel, respectively. The impact of thermochemical effects on these interactions by changing the chemical composition from nitrogen to air as well as argon for a stagnation enthalpy of 8.0 MJ/kg flow are investigated using the 2-D wedge model. The simulations are found to reproduce many of the classic features related to Edney Type V strong shock interactions that include the attached, oblique shock formed over the first wedge, the detached bow shock from the second wedge, the separation zone, and the separation and reattachment shocks that cause complex features such as the triple point for both cases. However, results of a reacting air flow case indicate that the size of the separation length, and the movement of the triple point toward to the leading edge is much less than the nitrogen case.

Natural Rubber Modification For Upper Layer Of Rubberized Asphalt Paving Block AS Shock Absorber

OpenAIRE

Nasruddin, Nasruddin

2017-01-01

The research of rubber compounding modification for upper layer of rubberized asphalt paving block as shock absorber using natural rubber, styrene butadiene rubber (SBR) as synthetic rubber, fly ash as filler and also vegetable oil as plasticizer has been conducted. The research design was varying the filler Si-69, fly ash and palm oil. The five formulas A, B, C, D, and E designed by varying the amount of Si-69 (48.5; 50.75; 53.00; 55.25; and 57.50) phr; coal fly ash (4.75, 7.00, 9.25, 11.50 ...

MHD intermediate shock discontinuities: Pt. 1

International Nuclear Information System (INIS)

Kennel, C.F.; Blandford, R.D.; Coppi, P.

1989-01-01

Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic. (author)

An eddy-viscosity treatment of the unsteady turbulent boundary layer on a flat plate in an expansion tube

Science.gov (United States)

Gupta, R. N.; Trimpi, R. L.

1974-01-01

An analysis is presented for the relaxation of a turbulent boundary layer on a semiinfinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion tube flows. The flow-governing equations have been transformed into the Lamcrocco variables. The numerical results indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin-friction than a fully laminar boundary layer.

A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

KAUST Repository

Duru, Kenneth

2014-01-01

A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.

Model for shock wave chaos.

Science.gov (United States)

Kasimov, Aslan R; Faria, Luiz M; Rosales, Rodolfo R

2013-03-08

We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, xorder partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.

Nonlinear reflection of shock shear waves in soft elastic media.

Science.gov (United States)

Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël

2010-02-01

For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

Shock loading predictions from application of indicial theory to shock-turbulence interactions

Science.gov (United States)

Keefe, Laurence R.; Nixon, David

1991-01-01

A sequence of steps that permits prediction of some of the characteristics of the pressure field beneath a fluctuating shock wave from knowledge of the oncoming turbulent boundary layer is presented. The theory first predicts the power spectrum and pdf of the position and velocity of the shock wave, which are then used to obtain the shock frequency distribution, and the pdf of the pressure field, as a function of position within the interaction region. To test the validity of the crucial assumption of linearity, the indicial response of a normal shock is calculated from numerical simulation. This indicial response, after being fit by a simple relaxation model, is used to predict the shock position and velocity spectra, along with the shock passage frequency distribution. The low frequency portion of the shock spectra, where most of the energy is concentrated, is satisfactorily predicted by this method.

Mitigation of Adverse Effects Caused by Shock Wave Boundary Layer Interactions Through Optimal Wall Shaping

Science.gov (United States)

Liou, May-Fun; Lee, Byung Joon

2013-01-01

It is known that the adverse effects of shock wave boundary layer interactions in high speed inlets include reduced total pressure recovery and highly distorted flow at the aerodynamic interface plane (AIP). This paper presents a design method for flow control which creates perturbations in geometry. These perturbations are tailored to change the flow structures in order to minimize shock wave boundary layer interactions (SWBLI) inside supersonic inlets. Optimizing the shape of two dimensional micro-size bumps is shown to be a very effective flow control method for two-dimensional SWBLI. In investigating the three dimensional SWBLI, a square duct is employed as a baseline. To investigate the mechanism whereby the geometric elements of the baseline, i.e. the bottom wall, the sidewall and the corner, exert influence on the flow's aerodynamic characteristics, each element is studied and optimized separately. It is found that arrays of micro-size bumps on the bottom wall of the duct have little effect in improving total pressure recovery though they are useful in suppressing the incipient separation in three-dimensional problems. Shaping sidewall geometry is effective in re-distributing flow on the side wall and results in a less distorted flow at the exit. Subsequently, a near 50% reduction in distortion is achieved. A simple change in corner geometry resulted in a 2.4% improvement in total pressure recovery.

Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

Energy Technology Data Exchange (ETDEWEB)

Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp

2017-02-01

The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.

Shock waves in relativistic nuclear matter, I

International Nuclear Information System (INIS)

Gleeson, A.M.; Raha, S.

1979-02-01

The relativistic Rankine-Hugoniot relations are developed for a 3-dimensional plane shock and a 3-dimensional oblique shock. Using these discontinuity relations together with various equations of state for nuclear matter, the temperatures and the compressibilities attainable by shock compression for a wide range of laboratory kinetic energy of the projectile are calculated. 12 references

Double layers above the aurora

International Nuclear Information System (INIS)

Temerin, M.; Mozer, F.S.

1987-01-01

Two different kinds of double layers were found in association with auroral precipitation. One of these is the so-called electrostatic shock, which is oriented at an oblique angle to the magnetic field in such a way that the perpendicular electric field is much larger than the parallel electric field. This type of double layer is often found at the edges of regions of upflowing ion beams and the direction of the electric fields in the shock points toward the ion beam. The potential drop through the shock can be several kV and is comparable to the total potential needed to produce auroral acceleration. Instabilities associated with the shock may generate obliquely propagating Alfven waves, which may accelerate electrons to produce flickering auroras. The flickering aurora provides evidence that the electrostatic shock may have large temporal fluctuations. The other kind of double layer is the small-amplitude double layer found in regions of upward flowing in beams, often in association with electrostatic ion cyclotron waves. The parallel and perpendicular electric fields in these structures are comparable in magnitude. The associated potentials are a few eV. Since many such double layers are found in regions of upward flowing ion beams, the combined potential drop through a set of these double layers can be substantial

Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations

Science.gov (United States)

Kittell, D. E.; Yarrington, C. D.; Lechman, J. B.; Baer, M. R.

2018-05-01

A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.

Ion-acoustic shock waves with negative ions in presence of dust particulates

International Nuclear Information System (INIS)

Sarma, Arun; Nakamura, Y.

2009-01-01

Dust acoustics shock waves have been investigated experimentally in a homogeneous unmagnetized dusty plasma device containing negative ions. When the negative ion density larger than a critical concentration 'r c ' negative shock waves were observed instead of positive shock waves. Again when it is nearly equal to 'r c ' both positive and negative shock waves propagate. The experimental findings are compared with modified KdV-Burgers equation. The velocity of the shock waves are also measured and compared with the numerical integration of modified KdV-Burgers equation.

Evolution of disturbances in the shock layer on a flat plate in the flow of a mixture of vibrationally excited gases

Science.gov (United States)

Kirilovskiy, S. V.; Poplavskaya, T. V.; Tsyryulnikov, I. S.; Maslov, A. A.

2017-05-01

The results of the numerical and experimental investigations of the evolution of the disturbances in a hypersonic shock layer on a flat plate streamlined by a flow of the mixture of vibrationally excited gases are presented. The experimental study was conducted in the hot-shot high-enthalpy wind tunnel IT-302 of the ITAM SB RAS. The numerical simulation was carried out with the aid of the ANSYS Fluent package using the solution of the unsteady two-dimensional Navier-Stokes equations with the incorporation of the user-created modules and enabling the consideration of the vibrational non-equilibrium of the carbon dioxide molecules within the framework of the model of the two-temperature aerodynamics. It was obtained that an increase in the carbon dioxide concentration in the mixture with air leads to a reduction of the intensity of pressure disturbances on the surface. The efficiency (up to 20 %) of the method of sound absorbing coatings in the vibrationally excited flows of the mixture of the carbon dioxide and air has been shown.

Universal shocks in the Wishart random-matrix ensemble.

Science.gov (United States)

Blaizot, Jean-Paul; Nowak, Maciej A; Warchoł, Piotr

2013-05-01

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite N effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.

An engineering inviscid-boundary layer method for calculation of aerodynamic heating in the leeward region

International Nuclear Information System (INIS)

Dirin, M.M.; Karimian, S.M.H.; Maerefat, M.

2003-01-01

An engineering method has been modified for the prediction of aerodynamic heating of the hypersonic bodies in the leeward region. This is achieved using our proposed new method for determining streamlines in the leeward region. The modified form of Maslen's second order relation, which calculates pressure in the shock layer explicitly, is employed. The inviscid outer flow within the shock layer is first solved. The calculated solution, then, is used to determine the flow properties at the boundary layer edge and the orientation of the surface streamlines. Boundary layer equations, written in the streamline coordinates, are integrated along the surface to obtain the rate of heat transferred to the body surface. The present method is an inverse method in which the body shape is obtained according to the shape of the shock. In general, inviscid-boundary layer engineering methods calculate accurately the orientation of streamlines in the windward side only, and therefore they are not usually applicable in the leeward region. In the present study, a new method is proposed to determine the orientation of the surface streamlines in the leeward region. Using the present method, three-dimensional hypersonic flow is solved fast and easy all around a cone. The obtained results show that the corrections presented in this study extend excellently the application of the method to the leeward region. (author)

Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

International Nuclear Information System (INIS)

Masood, W.; Rizvi, H.

2011-01-01

Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the small amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.

On terminating Poisson processes in some shock models

Energy Technology Data Exchange (ETDEWEB)

Finkelstein, Maxim, E-mail: FinkelMI@ufs.ac.z [Department of Mathematical Statistics, University of the Free State, Bloemfontein (South Africa); Max Planck Institute for Demographic Research, Rostock (Germany); Marais, Francois, E-mail: fmarais@csc.co [CSC, Cape Town (South Africa)

2010-08-15

A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.

On terminating Poisson processes in some shock models

International Nuclear Information System (INIS)

Finkelstein, Maxim; Marais, Francois

2010-01-01

A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.

Broadband Shock Noise in Internally-Mixed Dual-Stream Jets

Science.gov (United States)

Bridges, James E.

2009-01-01

Broadband shock noise (BBSN) has been studied in some detail in single-flow jets and recently in dual-stream jets with separate flow exhaust systems. Shock noise is of great concern in these latter cases because of the noise created for the aircraft cabin by the underexpanded nozzle flow at cruise. Another case where shock noise is of concern is in the case of future supersonic aircraft that are expected to have bypass ratios small enough to justify internally mixed exhaust systems, and whose mission will push cycles to the point of imperfectly expanded flows. Dual-stream jets with internally mixed plume have some simplifying aspects relative to the separate flow jets, having a single shock structure given by the common nozzle pressure. This is used to separate the contribution of the turbulent shear layer to the broadband shock noise. Shock structure is held constant while the geometry and strength of the inner and merged shear layers are varying by changing splitter area ratio and core stream temperature. Flow and noise measurements are presented which document the efforts at separating the contribution of the inner shear layer to the broadband shock noise.

Shock/shock interactions between bodies and wings

Directory of Open Access Journals (Sweden)

Gaoxiang XIANG

2018-02-01

Full Text Available This paper examines the Shock/Shock Interactions (SSI between the body and wing of aircraft in supersonic flows. The body is simplified to a flat wedge and the wing is assumed to be a sharp wing. The theoretical spatial dimension reduction method, which transforms the 3D problem into a 2D one, is used to analyze the SSI between the body and wing. The temperature and pressure behind the Mach stem induced by the wing and body are obtained, and the wave configurations in the corner are determined. Numerical validations are conducted by solving the inviscid Euler equations in 3D with a Non-oscillatory and Non-free-parameters Dissipative (NND finite difference scheme. Good agreements between the theoretical and numerical results are obtained. Additionally, the effects of the wedge angle and sweep angle on wave configurations and flow field are considered numerically and theoretically. The influences of wedge angle are significant, whereas the effects of sweep angle on wave configurations are negligible. This paper provides useful information for the design and thermal protection of aircraft in supersonic and hypersonic flows. Keywords: Body and wing, Flow field, Hypersonic flow, Shock/shock interaction, Wave configurations

Shooting method for third order simultaneous ordinary differential equations with application to magnetohydrodynamic boundary layer

International Nuclear Information System (INIS)

Srivastava, A.C.; Hazarika, G.C.

1990-01-01

An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as the results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle. (author). 6 tabs., 7 refs

Effects of explosion-generated shock waves in ducts

International Nuclear Information System (INIS)

Busby, M.R.; Kahn, J.E.; Belk, J.P.

1976-01-01

An explosion in a space causes an increase in temperature and pressure. To quantify the challenge that will be presented to essential components in a ventilation system, it is necessary to analyze the dynamics of a shock wave generated by an explosion, with attention directed to the propagation of such a wave in a duct. Using the equations of unsteady flow and shock tube theory, a theoretical model has been formulated to provide flow properties behind moving shock waves that have interacted with various changes in duct geometry. Empirical equations have been derived to calculate air pressure, temperature, Mach number, and velocity in a duct following an explosion

Shock wave interaction with turbulence: Pseudospectral simulations

International Nuclear Information System (INIS)

Buckingham, A.C.

1986-01-01

Shock waves amplify pre-existing turbulence. Shock tube and shock wave boundary layer interaction experiments provide qualitative confirmation. However, shock pressure, temperature, and rapid transit complicate direct measurement. Computational simulations supplement the experimental data base and help isolate the mechanisms responsible. Simulations and experiments, particularly under reflected shock wave conditions, significantly influence material mixing. In these pseudospectral Navier-Stokes simulations the shock wave is treated as either a moving (tracked or fitted) domain boundary. The simulations assist development of code mix models. Shock Mach number and pre-existing turbulence intensity initially emerge as key parameters. 20 refs., 8 figs

An engineering method for interactive inviscid-boundary layers in three-dimensional hypersonic flows. Ph.D. Thesis - North Carolina State Univ., Raleigh

Science.gov (United States)

Riley, Christopher J.

1992-01-01

An engineering method has been developed that couples an approximate three dimensional inviscid technique with the axisymmetric analog and a set of approximate convective heating equations. The displacement effect on the boundary layer on the outer inviscid flow is calculated and included as a boundary condition in the inviscid technique. This accounts for the viscous interaction present at lower Reynolds numbers. The method is applied to blunted axisymmetric and three dimensional elliptic cones at angle of attack for the laminar hypersonic flow of a perfect gas. The method is applied to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates, pressures, and shock shapes that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes and viscous shock-layer equations. In addition, the inclusion of viscous interaction significantly improves results obtained at lower Reynolds numbers. The new technique represents a major improvement over current engineering aerothermal methods with only a modest increase in computational effort.

Bubble Dynamics and Shock Waves

CERN Document Server

2013-01-01

This volume of the Shock Wave Science and Technology Reference Library is concerned with the interplay between bubble dynamics and shock waves. It is divided into four parts containing twelve chapters written by eminent scientists. Topics discussed include shock wave emission by laser generated bubbles (W Lauterborn, A Vogel), pulsating bubbles near boundaries (DM Leppinen, QX Wang, JR Blake), interaction of shock waves with bubble clouds (CD Ohl, SW Ohl), shock propagation in polydispersed bubbly liquids by model equations (K Ando, T Colonius, CE Brennen. T Yano, T Kanagawa,  M Watanabe, S Fujikawa) and by DNS (G Tryggvason, S Dabiri), shocks in cavitating flows (NA Adams, SJ Schmidt, CF Delale, GH Schnerr, S Pasinlioglu) together with applications involving encapsulated bubble dynamics in imaging (AA Doinikov, A Novell, JM Escoffre, A Bouakaz),  shock wave lithotripsy (P Zhong), sterilization of ships’ ballast water (A Abe, H Mimura) and bubbly flow model of volcano eruptions ((VK Kedrinskii, K Takayama...

Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

Science.gov (United States)

Miyazaki, Yutaka; Tsuchiya, Takao

2012-07-01

The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

Flow control for oblique shock wave reflections

OpenAIRE

Giepman, R.H.M.

2016-01-01

Shock wave-boundary layer interactions are prevalent in many aerospace applications that involve transonic or supersonic flows. Such interactions may lead to boundary layer separation, flow unsteadiness and substantial losses in the total pressure. Flow control techniques can help to mitigate these adverse effects and stabilize the interaction. This thesis focuses on passive flow control techniques for oblique shock wave reflections on flat plates and presents experimental results for both la...

Attenuation of shock waves in copper and stainless steel

International Nuclear Information System (INIS)

Harvey, W.B.

1986-06-01

By using shock pins, data were gathered on the trajectories of shock waves in stainless steel (SS-304L) and oxygen-free-high-conductivity copper (OFHC-Cu). Shock pressures were generated in these materials by impacting the appropriate target with thin (approx.1.5 mm) flying plates. The flying plates in these experiments were accelerated to high velocities (approx.4 km/s) by high explosives. Six experiments were conducted, three using SS-304L as the target material and three experiments using OFHC-Cu as the target material. Peak shock pressures generated in the steel experiments were approximately 109, 130, and 147 GPa and in the copper experiments, the peak shock pressures were approximately 111, 132, and 143 GPa. In each experiment, an attenuation of the shock wave by a following release wave was clearly observed. An extensive effort using two characteristic codes (described in this work) to theoretically calculate the attenuation of the shock waves was made. The efficacy of several different constitutive equations to successfully model the experiments was studied by comparing the calculated shock trajectories to the experimental data. Based on such comparisons, the conclusion can be drawn that OFHC-Cu enters a melt phase at about 130 GPa on the principal Hugoniot. There was no sign of phase changes in the stainless-steel experiments. In order to match the observed attenuation of the shock waves in the SS-304L experiments, it was necessary to include strength effects in the calculations. It was found that the values for the parameters in the strength equations were dependent on the equation of state used in the modeling of the experiments. 66 refs., 194 figs., 77 tabs

Attenuation of shock waves in copper and stainless steel

Energy Technology Data Exchange (ETDEWEB)

Harvey, W.B.

1986-06-01

By using shock pins, data were gathered on the trajectories of shock waves in stainless steel (SS-304L) and oxygen-free-high-conductivity copper (OFHC-Cu). Shock pressures were generated in these materials by impacting the appropriate target with thin (approx.1.5 mm) flying plates. The flying plates in these experiments were accelerated to high velocities (approx.4 km/s) by high explosives. Six experiments were conducted, three using SS-304L as the target material and three experiments using OFHC-Cu as the target material. Peak shock pressures generated in the steel experiments were approximately 109, 130, and 147 GPa and in the copper experiments, the peak shock pressures were approximately 111, 132, and 143 GPa. In each experiment, an attenuation of the shock wave by a following release wave was clearly observed. An extensive effort using two characteristic codes (described in this work) to theoretically calculate the attenuation of the shock waves was made. The efficacy of several different constitutive equations to successfully model the experiments was studied by comparing the calculated shock trajectories to the experimental data. Based on such comparisons, the conclusion can be drawn that OFHC-Cu enters a melt phase at about 130 GPa on the principal Hugoniot. There was no sign of phase changes in the stainless-steel experiments. In order to match the observed attenuation of the shock waves in the SS-304L experiments, it was necessary to include strength effects in the calculations. It was found that the values for the parameters in the strength equations were dependent on the equation of state used in the modeling of the experiments. 66 refs., 194 figs., 77 tabs.

A radiating shock evaluated using Implicit Monte Carlo Diffusion

International Nuclear Information System (INIS)

Cleveland, M.; Gentile, N.

2013-01-01

Implicit Monte Carlo [1] (IMC) has been shown to be very expensive when used to evaluate a radiation field in opaque media. Implicit Monte Carlo Diffusion (IMD) [2], which evaluates a spatial discretized diffusion equation using a Monte Carlo algorithm, can be used to reduce the cost of evaluating the radiation field in opaque media [2]. This work couples IMD to the hydrodynamics equations to evaluate opaque diffusive radiating shocks. The Lowrie semi-analytic diffusive radiating shock benchmark[a] is used to verify our implementation of the coupled system of equations. (authors)

Properties and structure of a plasma non-neutral shock

International Nuclear Information System (INIS)

Hu Yemin; Hu Xiwei

2004-01-01

The shock is described by the Navier-Stokes equations of the electron and ion fluids, and coupled with Poisson's equation for the self-induced electric field. Profiles of the flow and electric variables in the weak or moderate shock front with or without current for different Debye lengths are presented. Comparison of profiles of flow and electric variables in the front for different heat flow modes is given

Direct measurements of wall shear stress by buried wire gages in a shock-wave boundary-layer interaction region

Science.gov (United States)

Murthy, V. S.; Rose, W. C.

1977-01-01

Detailed measurements of wall shear stress (skin friction) were made with specially developed buried wire gages in the interaction regions of a Mach 2.9 turbulent boundary layer with externally generated shocks. Separation and reattachment points inferred by these measurements support the findings of earlier experiments which used a surface oil flow technique and pitot profile measurements. The measurements further indicate that the boundary layer tends to attain significantly higher skin-friction values downstream of the interaction region as compared to upstream. Comparisons between measured wall shear stress and published results of some theoretical calculation schemes show that the general, but not detailed, behavior is predicted well by such schemes.

Various continuum approaches for studying shock wave structure in carbon dioxide

Science.gov (United States)

Alekseev, I. V.; Kosareva, A. A.; Kustova, E. V.; Nagnibeda, E. A.

2018-05-01

Shock wave structure in carbon dioxide is studied using different continuum models within the framework of one-temperature thermal equilibrium flow description. Navier-Stokes and Euler equations as well as commonly used Rankine-Hugoniot equations with different specific heat ratios are used to find the gas-dynamic parameters behind the shock wave. The accuracy of the Rankine-Hugoniot relations in polyatomic gases is assessed, and it is shown that they give a considerable error in the predicted values of fluid-dynamic variables. The effect of bulk viscosity on the shock wave structure in CO2 is evaluated. Taking into account bulk viscosity yields a significant increase in the shock wave width; for the complete model, the shock wave thickness varies non-monotonically with the Mach number.

Coupling Detonation Shock Dynamics in a Consistent Manner to Equations of State

Science.gov (United States)

Belfield, William

2017-06-01

In hydrocode simulations, detonating high explosives (HE) are often modelled using programmed burn. Each HE cell is assigned a ``burn time'' at which it should begin to behave as HE products in the subsequent simulation. Traditionally, these burn times were calculated using a Huygens construction to propagate the detonation wave at a constant speed corresponding to the planar Chapman-Jouguet (CJ) velocity. The Detonation Shock Dynamics (DSD) model improves upon this approach by treating the local detonation velocity as a function of wave curvature, reflecting that the detonation speed is not constant in reality. However, without alterations being made, this variable detonation velocity is inconsistent with the CJ velocity associated with the HE products equation of state (EOS). Previous work has shown that the inconsistency can be resolved by modifying the HE product EOS, but this treatment is empirical in nature and has only been applied to the JWL EOS. This work investigates different methods to resolve the inconsistency that are applicable both to JWL and to tabular HE product EOS, and their impact on hydrocode simulations.

Boundary layer phenomena for differential-delay equations with state-dependent time lags: III

Science.gov (United States)

Mallet-Paret, John; Nussbaum, Roger D.

We consider a class of singularly perturbed delay-differential equations of the form ɛ ẋ(t)=f(x(t),x(t-r)), where r= r( x( t)) is a state-dependent delay. We study the asymptotic shape, as ɛ→0, of slowly oscillating periodic solutions. In particular, we show that the limiting shape of such solutions can be explicitly described by the solution of a pair of so-called max-plus equations. We are able thereby to characterize both the regular parts of the solution graph and the internal transition layers arising from the singular perturbation structure.

Experimental Shock Transformation of Gypsum to Anhydrite: A New Low Pressure Regime Shock Indicator

Science.gov (United States)

Bell, Mary S.; Zolensky, Michael E.

2011-01-01

The shock behavior of gypsum is important in understanding the Cretaceous/Paleogene event and other terrestrial impacts that contain evaporite sediments in their targets (e.g., Mars Exploration Rover Spirit detected sulfate at Gusev crater, [1]). Most interest focuses on issues of devolatilization to quantify the production of SO2 to better understand its role in generating a temporary atmosphere and its effects on climate and biota [2,3]. Kondo and Ahrens [4] measured induced radiation emitted from single crystal gypsum shocked to 30 and 40 GPa. They observed greybody emission spectra corresponding to temperatures in the range of 3,000 to 4,000 K that are a factor of 2 to 10 times greater than calculated pressure-density energy equation of state temperatures (Hugoniot) and are high enough to melt gypsum. Chen et al. [5] reported results of shock experiments on anhydrite, gypsum, and mixtures of these phases with silica. Their observations indicated little or no devolatilization of anhydrite shocked to 42 GPa and that the fraction of sulfur, by mass, that degassed is approx.10(exp -2) of theoretical prediction. In another report of shock experiments on calcite, anhydrite, and gypsum, Badjukov et al. [6] observed only intensive plastic deformation in anhydrite shock loaded at 63 GPa, and gypsum converted to anhydrite when shock loaded at 56 GPa but have not experimentally shocked gypsum in a step-wise manner to constrain possible incipient transformation effects. Schmitt and Hornemann [7] shock loaded anhydrite and quartz to a peak pressure of 60 GPa and report the platy anhydrite grains were completely pseudomorphed by small crystallized anhydrite grains. However, no evidence of interaction between the two phases could be observed and they suggested that recrystallization of anhydrite grains is the result of a solid-state transformation. They concluded that significant decomposition of anhydrite requires shock pressures higher than 60 GPa. Gupta et al. [8

Evolution of wave patterns and temperature field in shock-tube flow

Science.gov (United States)

Kiverin, A. D.; Yakovenko, I. S.

2018-05-01

The paper is devoted to the numerical analysis of wave patterns behind a shock wave propagating in a tube filled with a gaseous mixture. It is shown that the flow inside the boundary layer behind the shock wave is unstable, and the way the instability develops fully corresponds to the solution obtained for the boundary layer over a flat plate. Vortical perturbations inside the boundary layer determine the nonuniformity of the temperature field. In turn, exactly these nonuniformities define the way the ignition kernels arise in the combustible mixture after the reflected shock interaction with the boundary layer. In particular, the temperature nonuniformity determines the spatial limitations of probable ignition kernel position relative to the end wall and side walls of the tube. In the case of low-intensity incident shocks the ignition could start not farther than the point of first interaction between the reflected shock wave and roller vortices formed in the process of boundary layer development. Proposed physical mechanisms are formulated in general terms and can be used for interpretation of the experimental data in any systems with a delayed exothermal reaction start. It is also shown that contact surface thickening occurs due to its interaction with Tollmien-Schlichting waves. This conclusion is of importance for understanding the features of ignition in shock tubes operating in the over-tailored regime.

Condensed matter at high shock pressures

International Nuclear Information System (INIS)

Nellis, W.J.; Holmes, N.C.; Mitchell, A.C.; Radousky, H.B.; Hamilton, D.

1985-01-01

Experimental techniques are described for shock waves in liquids: Hugoniot equation-of-state, shock temperature and emission spectroscopy, electrical conductivity, and Raman spectroscopy. Experimental data are reviewed and presented in terms of phenomena that occur at high densities and temperatures in shocked He, Ar, N 2 , CO, SiO 2 -aerogel, H 2 O, and C 6 H 6 . The superconducting properties of Nb metal shocked to 100 GPa (1 Mbar) and recovered intact are discussed in terms of prospects for synthesizing novel, metastable materials. Ultrahigh pressure data for Cu is reviewed in the range 0.3 to 6TPa (3 to 60 Mbar). 56 refs., 9 figs., 1 tab

Investigation of corner shock boundary layer interactions to understand inlet unstart

Science.gov (United States)

Funderburk, Morgan

2015-11-01

Inlet unstart is a detrimental phenomenon in dual-mode ramjet/scramjet engines that causes severe loss of thrust, large transient structural load, and potentially a loss of the aircraft. In order to analyze the effects that the corner shock boundary layer interaction (SBLI) has on initiating and perpetuating inlet unstart, a qualitative and quantitative investigation into mean and dynamic features of corner SBLI at various Mach numbers is made. Surface streakline visualization showed that the corner SBLI is highly three-dimensional with a dominant presence of corner separation vortex. Further, the peak r.m.s. pressure was located at the periphery of corner separation vortex, suggesting that the unsteady loading is caused by the corner vortex. Power spectral densities of wall-pressure fluctuations in the peak r.m.s. location were analyzed in order to characterize the dominant frequencies of oscillation of the flow structures and to unravel the dynamic interactions between them in order to expand the operating margin of future hypersonic air breathing vehicles.

30th International Symposium on Shock Waves

CERN Document Server

Sadot, Oren; Igra, Ozer

2017-01-01

These proceedings collect the papers presented at the 30th International Symposium on Shock Waves (ISSW30), which was held in Tel-Aviv Israel from July 19 to July 24, 2015. The Symposium was organized by Ortra Ltd. The ISSW30 focused on the state of knowledge of the following areas: Nozzle Flow, Supersonic and Hypersonic Flows with Shocks, Supersonic Jets, Chemical Kinetics, Chemical Reacting Flows, Detonation, Combustion, Ignition, Shock Wave Reflection and Interaction, Shock Wave Interaction with Obstacles, Shock Wave Interaction with Porous Media, Shock Wave Interaction with Granular Media, Shock Wave Interaction with Dusty Media, Plasma, Magnetohyrdrodynamics, Re-entry to Earth Atmosphere, Shock Waves in Rarefied Gases, Shock Waves in Condensed Matter (Solids and Liquids), Shock Waves in Dense Gases, Shock Wave Focusing, Richtmyer-Meshkov Instability, Shock Boundary Layer Interaction, Multiphase Flow, Blast Waves, Facilities, Flow Visualization, and Numerical Methods. The two volumes serve as a reference ...

Assessment of Computational Fluid Dynamics (CFD) Models for Shock Boundary-Layer Interaction

Science.gov (United States)

DeBonis, James R.; Oberkampf, William L.; Wolf, Richard T.; Orkwis, Paul D.; Turner, Mark G.; Babinsky, Holger

2011-01-01

A workshop on the computational fluid dynamics (CFD) prediction of shock boundary-layer interactions (SBLIs) was held at the 48th AIAA Aerospace Sciences Meeting. As part of the workshop numerous CFD analysts submitted solutions to four experimentally measured SBLIs. This paper describes the assessment of the CFD predictions. The assessment includes an uncertainty analysis of the experimental data, the definition of an error metric and the application of that metric to the CFD solutions. The CFD solutions provided very similar levels of error and in general it was difficult to discern clear trends in the data. For the Reynolds Averaged Navier-Stokes methods the choice of turbulence model appeared to be the largest factor in solution accuracy. Large-eddy simulation methods produced error levels similar to RANS methods but provided superior predictions of normal stresses.

Shock dynamics of weak imploding cylindrical and spherical shock waves with non-ideal gas effects

International Nuclear Information System (INIS)

Anand, R K

2013-01-01

The author (Anand 2012 Astrophys. Space Sci. 342 377–88) recently obtained jump relations across a shock front in non-ideal gas flow taking into consideration the equation of state for a non-ideal gas as given by Landau and Lifshitz. In this paper an analytical solution for one-dimensional adiabatic flow behind weak converging shock waves propagating in a non-ideal gas is obtained by using Whitham's (1974 Linear and Nonlinear Waves (New York: Wiley)) geometrical shock dynamics approach. The effects of an increase in (i) the propagation distance from the centre of convergence, (ii) the non-idealness parameter and (iii) the adiabatic index of the gas, on the shock velocity, pressure, density, particle velocity, adiabatic compressibility and the change in entropy across the shock front, are analyzed. The results provided a clear picture of whether and how the non-idealness parameter and the adiabatic index affect the flow field behind the imploding shock front. (paper)

Some recent advances of shock wave physics research at the Laboratory for Shock Wave and Detonation Physics Research

CERN Document Server

Jing Fu Qian

2002-01-01

Progress made in recent years on three topics that have been investigated at the Laboratory for Shock Wave and Detonation Physics Research are presented in this report. (1) A new equation of state (EOS) has been derived which can be used from a standard state to predict state variable change along an isobaric path. Good agreements between calculations for some representative metals using this new EOS and experiments have been found, covering a wide range from hundreds of MPa to hundreds of GPa and from ambient temperature to tens of thousands of GPa. (2) An empirical relation of Y/G = constant (Y is yield strength, G is shear modulus) at HT-HP has been reinvestigated and confirmed by shock wave experiment. 93W alloy was chosen as a model material. The advantage of this relation is that it is beneficial to formulate a kind of simplified constitutive equation for metallic solids under shock loading, and thus to faithfully describe the behaviours of shocked solids through hydrodynamic simulations. (3) An attempt...

Shock stand off Calculations for Hemisphere in Hypersonic Flows

International Nuclear Information System (INIS)

Hanif, M.; Ghaffar, A.; Bilal, S.; Zahir, S.; Khan, M.A.

2004-01-01

The shape and location of shock has been studied by solving the axi symmetric Navier Stokes Equations for a hemisphere in hypersonic flow. The effect of Mach number on shock stand-off distance has been investigated. It is found that the shock location varies with Mach number and the free stream conditions at a given nose radius. (author)

Formation of double layers: shocklike solutions of an mKdV-equation

International Nuclear Information System (INIS)

Raadu, M.A.; Chanteur, G.

1985-10-01

Small amplitude double layers (DLs) in a plasma with a suitable electron distribution may be identified with shocklike solutions of a modified Korteweg-deVries (mKdV) equation. A thought experiment for the formation of such DLs is specified to clarify the physical constraints and to demonstrate the emergence of a DL from an initial disturbance. A scattering formulation of the mKdV initial value problem may be diagonalised to give a pair of Schroedinger equations with a scattering potential satisfying the ordinary KdV equation. The initial value problem can then be treated using Khruslov's generalisation of the inverse scattering method which allows a difference in the asymptotic values of the potential. A necessary and sufficient condition for the emergence of a shocklike soliton (wave) train and of a finite number of isolated solitons may also be determined from the scattering properties of the initial potential. With 26 refs and 5 figures. (Author)

Parallel implementation of geometrical shock dynamics for two dimensional converging shock waves

Science.gov (United States)

Qiu, Shi; Liu, Kuang; Eliasson, Veronica

2016-10-01

Geometrical shock dynamics (GSD) theory is an appealing method to predict the shock motion in the sense that it is more computationally efficient than solving the traditional Euler equations, especially for converging shock waves. However, to solve and optimize large scale configurations, the main bottleneck is the computational cost. Among the existing numerical GSD schemes, there is only one that has been implemented on parallel computers, with the purpose to analyze detonation waves. To extend the computational advantage of the GSD theory to more general applications such as converging shock waves, a numerical implementation using a spatial decomposition method has been coupled with a front tracking approach on parallel computers. In addition, an efficient tridiagonal system solver for massively parallel computers has been applied to resolve the most expensive function in this implementation, resulting in an efficiency of 0.93 while using 32 HPCC cores. Moreover, symmetric boundary conditions have been developed to further reduce the computational cost, achieving a speedup of 19.26 for a 12-sided polygonal converging shock.

Cures for the shock instability: Development of a shock-stable Roe scheme

CERN Document Server

Kim, S S; Rho, O H; Kyu-Hong, S

2003-01-01

This paper deals with the development of an improved Roe scheme that is free from the shock instability and still preserves the accuracy and efficiency of the original Roe's Flux Difference Splitting (FDS). Roe's FDS is known to possess good accuracy but to suffer from the shock instability, such as the carbuncle phenomenon. As the first step towards a shock-stable scheme, Roe's FDS is compared with the HLLE scheme to identify the source of the shock instability. Through a linear perturbation analysis on the odd-even decoupling problem, damping characteristic is examined and Mach number-based functions f and g are introduced to balance damping and feeding rates, which leads to a shock-stable Roe scheme. In order to satisfy the conservation of total enthalpy, which is crucial in predicting surface heat transfer rate in high-speed steady flows, an analysis of dissipation mechanism in the energy equation is carried out to find out the error source and to make the proposed scheme preserve total enthalpy. By modif...

Effects of shock waves on Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Zhang Yongtao; Shu Chiwang; Zhou Ye

2006-01-01

A numerical simulation of two-dimensional compressible Navier-Stokes equations using a high-order weighted essentially nonoscillatory finite difference shock capturing scheme is carried out in this paper, to study the effect of shock waves on the development of Rayleigh-Taylor instability. Shocks with different Mach numbers are introduced ahead or behind the Rayleigh-Taylor interface, and their effect on the transition to instability is demonstrated and compared. It is observed that shock waves can speed up the transition to instability for the Rayleigh-Taylor interface significantly. Stronger shocks are more effective in this speed-up process

Pseudo-shock waves and their interactions in high-speed intakes

Science.gov (United States)

Gnani, F.; Zare-Behtash, H.; Kontis, K.

2016-04-01

In an air-breathing engine the flow deceleration from supersonic to subsonic conditions takes places inside the isolator through a gradual compression consisting of a series of shock waves. The wave system, referred to as a pseudo-shock wave or shock train, establishes the combustion chamber entrance conditions, and therefore influences the performance of the entire propulsion system. The characteristics of the pseudo-shock depend on a number of variables which make this flow phenomenon particularly challenging to be analysed. Difficulties in experimentally obtaining accurate flow quantities at high speeds and discrepancies of numerical approaches with measured data have been readily reported. Understanding the flow physics in the presence of the interaction of numerous shock waves with the boundary layer in internal flows is essential to developing methods and control strategies. To counteract the negative effects of shock wave/boundary layer interactions, which are responsible for the engine unstart process, multiple flow control methodologies have been proposed. Improved analytical models, advanced experimental methodologies and numerical simulations have allowed a more in-depth analysis of the flow physics. The present paper aims to bring together the main results, on the shock train structure and its associated phenomena inside isolators, studied using the aforementioned tools. Several promising flow control techniques that have more recently been applied to manipulate the shock wave/boundary layer interaction are also examined in this review.

Equation of state of laser-shocked compressed iron; Equation d'etat du fer comprime par choc laser

Energy Technology Data Exchange (ETDEWEB)

Huser, G

2004-01-01

This thesis enters the field of highly compressed materials equation of state studies. In particular, it focuses on the case of laser shock compressed iron. This work indeed aims at getting to the conditions of the earth's core, comprising a solid inner core and a liquid outer core. The understanding of phenomena governing the core's thermodynamics and the geodynamic process requires the knowledge of iron melting line locus around the solid-liquid interface at 3.3 Mbar. Several experiments were performed to that extent. First, an absolute measurement of iron Hugoniot was obtained. Following is a study of partially released states of iron into a window material: lithium fluoride (LiF). This configuration enables direct access to compressed iron optical properties such as reflectivity and self-emission. Interface velocity measurement is dominated by compressed LiF optical properties and is used as a pressure gauge. Using a dual wavelength reflectivity diagnostic, compressed iron electrical conductivity was estimated and found to be in good agreement with previous results found in geophysics literature. Self-emission diagnostic was used to measure temperature of partially released iron and revealed a solid-liquid phase transition at Mbar pressures. (author)

Internal energy relaxation in shock wave structure

International Nuclear Information System (INIS)

Josyula, Eswar; Suchyta, Casimir J.; Boyd, Iain D.; Vedula, Prakash

2013-01-01

The Wang Chang-Uhlenbeck (WCU) equation is numerically integrated to characterize the internal structure of Mach 3 and Mach 5 shock waves in a gas with excitation in the internal energy states for the treatment of inelastic collisions. Elastic collisions are modeled with the hard sphere collision model and the transition rates for the inelastic collisions modified appropriately using probabilities based on relative velocities of the colliding particles. The collision integral is evaluated by the conservative discrete ordinate method [F. Tcheremissine, “Solution of the Boltzmann kinetic equation for high-speed flows,” Comput. Math. Math. Phys. 46, 315–329 (2006); F. Cheremisin, “Solution of the Wang Chang-Uhlenbeck equation,” Dokl. Phys. 47, 487–490 (2002)] developed for the Boltzmann equation. For the treatment of the diatomic molecules, the internal energy modes in the Boltzmann equation are described quantum mechanically given by the WCU equation. As a first step in the treatment of the inelastic collisions by the WCU equation, a two- and three-quantum system is considered to study the effect of the varying of (1) the inelastic cross section and (2) the energy gap between the quantum energy states. An alternative method, the direct simulation Monte Carlo method, is used for the Mach 3 shock wave to ensure the consistency of implementation in the two methods and there is an excellent agreement between the two methods. The results from the WCU implementation showed consistent trends for the Mach 3 and Mach5 standing shock waves simulations. Inelastic contributions change the downstream equilibrium state and allow the flow to transition to the equilibrium state further upstream

Numerical study of shock waves in non-ideal magnetogasdynamics (MHD

Directory of Open Access Journals (Sweden)

Addepalli Ramu

2016-01-01

Full Text Available One-dimensional unsteady adiabatic flow of strong converging shock waves in cylindrical or spherical symmetry in MHD, which is propagating into plasma, is analyzed. The plasma is assumed to be non-ideal gas whose equation of state is of Mie–Gruneisen type. Suitable transformations reduce the governing equations into ordinary differential equations of Poincare type. In the present work, McQueen and Royce equations of state (EOS have been considered with suitable material constants and the spherical and cylindrical cases are worked out in detail to investigate the behavior and the influence on the shock wave propagation by energy input and β(ρ/ρ0, the measure of shock strength. The similarity solution is valid for adiabatic flow as long as the counter pressure is neglected. The numerical technique applied in this paper provides a global solution to the implosion problem for the flow variables, the similarity exponent α for different Gruneisen parameters. It is shown that increasing β(ρ/ρ0 does not automatically decelerate the shock front but the velocity and pressure behind the shock front increases quickly in the presence of the magnetic field and decreases slowly and become constant. This becomes true whether the piston is accelerated, is moving at constant speed or is decelerated. These results are presented through the illustrative graphs and tables. The magnetic field effects on the flow variables through a medium and total energy under the influence of strong magnetic field are also presented.

Condensed matter at high shock pressures

Energy Technology Data Exchange (ETDEWEB)

Nellis, W.J.; Holmes, N.C.; Mitchell, A.C.; Radousky, H.B.; Hamilton, D.

1985-07-12

Experimental techniques are described for shock waves in liquids: Hugoniot equation-of-state, shock temperature and emission spectroscopy, electrical conductivity, and Raman spectroscopy. Experimental data are reviewed and presented in terms of phenomena that occur at high densities and temperatures in shocked He, Ar, N/sub 2/, CO, SiO/sub 2/-aerogel, H/sub 2/O, and C/sub 6/H/sub 6/. The superconducting properties of Nb metal shocked to 100 GPa (1 Mbar) and recovered intact are discussed in terms of prospects for synthesizing novel, metastable materials. Ultrahigh pressure data for Cu is reviewed in the range 0.3 to 6TPa (3 to 60 Mbar). 56 refs., 9 figs., 1 tab.

Cosmic-ray acceleration at stellar wind terminal shocks

International Nuclear Information System (INIS)

Webb, G.M.; Forman, M.A.; Axford, W.I.

1985-01-01

Steady-state, spherically symmetric, analytic solutions of the cosmic-ray transport equations, applicable to the problem of acceleration of cosmic rays at the terminal shock to a stellar wind, are studied. The spectra, gradients, and flow patterns of particle modulated and accelerated by the stellar wind and shock are investigated by means of monoenergetic-source solutions at finite radius, as well as solutions with monoenergetic and power-law Galactic spectra. The solutions obtained apply in the test particle limit in which the cosmic rays do not modify the background flow. The solutions show a characteristic power-law momentum spectrum for accelerated particles and a more complex spectrum of particles that are decelerated in the stellar wind. The power-law spectral index depends on the compression ratio of the shock and on the modulation parameters characterizing propagation conditions in the upstream and downstream regions of the shock. Solutions of the transport equations for the total density N (integrated over all energies), pressure P/sub c/, and energy flux F/sub c/ of Galactic cosmic rays interacting with a stellar wind and shock are also studied. The density N(r) increases with radius r, and for strong shocks with large enough modulation parameters, there may be a significant enhancement of the pressure of weakly relativistic particles near the shock compared to the cosmic-ray background pressure P/sub infinity/. The emergent energy flux at infinity is of the order of 4π R 2 V 1 P/sub infinity/ (V 1 is wind velocity upstream of the shock, R is shock radius)

Shock waves in collective field theories for many particle systems

Energy Technology Data Exchange (ETDEWEB)

Oki, F; Saito, T [Kyoto Prefectural Univ. of Medicine (Japan); Shigemoto, K

1980-10-01

We find shock wave solutions to collective field equations for quantum mechanical many particle system. Importance of the existence of a ''tension'' working on the surface of the shock-wave front is pointed out.

The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

Energy Technology Data Exchange (ETDEWEB)

Giacalone, J. [Department of Planetary Sciences, University of Arizona, Tucson, AZ (United States)

2017-10-20

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean and an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.

DSMC Computations for Regions of Shock/Shock and Shock/Boundary Layer Interaction

Science.gov (United States)

Moss, James N.

2001-01-01

This paper presents the results of a numerical study of hypersonic interacting flows at flow conditions that include those for which experiments have been conducted in the Calspan-University of Buffalo Research Center (CUBRC) Large Energy National Shock (LENS) tunnel and the ONERA R5Ch low-density wind tunnel. The computations are made with the direct simulation Monte Carlo (DSMC) method of Bird. The focus is on Mach 9.3 to 11.4 flows about flared axisymmetric configurations, both hollow cylinder flares and double cones. The results presented highlight the sensitivity of the calculations to grid resolution, provide results concerning the conditions for incipient separation, and provide information concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Assessment of CFD capability for prediction of hypersonic shock interactions

Science.gov (United States)

Knight, Doyle; Longo, José; Drikakis, Dimitris; Gaitonde, Datta; Lani, Andrea; Nompelis, Ioannis; Reimann, Bodo; Walpot, Louis

2012-01-01

The aerothermodynamic loadings associated with shock wave boundary layer interactions (shock interactions) must be carefully considered in the design of hypersonic air vehicles. The capability of Computational Fluid Dynamics (CFD) software to accurately predict hypersonic shock wave laminar boundary layer interactions is examined. A series of independent computations performed by researchers in the US and Europe are presented for two generic configurations (double cone and cylinder) and compared with experimental data. The results illustrate the current capabilities and limitations of modern CFD methods for these flows.

Spectral fitting, shock layer modeling, and production of nitrogen oxides and excited nitrogen

Science.gov (United States)

Blackwell, H. E.

1991-01-01

An analysis was made of N2 emission from 8.72 MJ/kg shock layer at 2.54, 1.91, and 1.27 cm positions and vibrational state distributions, temperatures, and relative electronic state populations was obtained from data sets. Other recorded arc jet N2 and air spectral data were reviewed and NO emission characteristics were studied. A review of operational procedures of the DSMC code was made. Information on other appropriate codes and modifications, including ionization, were made as well as a determination of the applicability of codes reviewed to task requirement. A review was also made of computational procedures used in CFD codes of Li and other codes on JSC computers. An analysis was made of problems associated with integration of specific chemical kinetics applicable to task into CFD codes.

Electrical conductivity and equation of state of liquid nitrogen, oxygen, benzene, and 1-butene shocked to 60 GPa

International Nuclear Information System (INIS)

Hamilton, D.C.

1986-01-01

Measurements are reported for the electrical conductivity of liquid nitrogen (N 2 ), oxygen (O 2 ) and benzene (C 6 H 6 ), and Hugoniot equation of state of liquid 1-butene (C 4 H 8 ) under shock compressed conditions. The conductivity data span 7 x 10 -4 to 7 x 10 1 Ω -1 cm -1 over a dynamic pressure range 18.1 to 61.5 GPa and are discussed in terms of amorphous semiconduction models which include such transport phenomena as hopping, percolation, pseudogaps, and metallization. Excellent agreement is found between the equation-of-state measurements, which span a dynamic pressure range 12.3 to 53.8 GPa, and Ree's calculated values which assume a 2-phase mixture consisting of molecular hydrogen and carbon in a dense diamond-like phase. There is a 2-1/2 fold increase in the thermal pressure contribution over a less dense, stoichiometrically equivalent liquid. 90 refs., 48 figs., 8 tabs

Hydrogen-Helium shock Radiation tests for Saturn Entry Probes

Science.gov (United States)

Cruden, Brett A.

2016-01-01

This paper describes the measurement of shock layer radiation in Hydrogen/Helium mixtures representative of that encountered by probes entering the Saturn atmosphere. Normal shock waves are measured in Hydrogen-Helium mixtures (89:11% by volume) at freestream pressures between 13-66 Pa (0.1-0.5 Torr) and velocities from 20-30 km/s. Radiance is quantified from the Vacuum Ultraviolet through Near Infrared. An induction time of several centimeters is observed where electron density and radiance remain well below equilibrium. Radiance is observed in front of the shock layer, the characteristics of which match the expected diffusion length of Hydrogen.

Transient and steady-state flows in shock tunnels

Energy Technology Data Exchange (ETDEWEB)

Hannemann, K. [Deutsche Forschungsanstalt fuer Luft- und Raumfahrt e.V. (DLR), Goettingen (Germany); Jacobs, P.A. [Queensland Univ., Brisbane (Australia). Dept. of Mechanical Engineering; Thomas, A.; McIntyre, T.J. [Queensland Univ., Brisbane, QLD. (Australia). Dept. of Physics

1999-12-01

Due to the difficulty of measuring all necessary flow quantities in the nozzle reservoir and the test section of high enthalpy shock tunnels, indirect computational methods are necessary to estimate the required flow parameters. In addition to steady state flow computations of the nozzle flow and the flow past wind tunnel models it is necessary to investigate the transient flow in the facility in order to achieve a better understanding of its performance. These transient effects include the nozzle starting flow, the interaction of the shock tube boundary layers and the reflected shock, thermal losses in the shock reflection region and the developing boundary layers in the expanding section of the nozzle. Additionally, the nonequilibrium chemical and thermal relaxation models which are used to compute high enthalpy flows have to be validated with appropriate experimental data. (orig.)

Transient and steady-state flows in shock tunnels

Energy Technology Data Exchange (ETDEWEB)

Hannemann, K. (Deutsche Forschungsanstalt fuer Luft- und Raumfahrt e.V. (DLR), Goettingen (Germany)); Jacobs, P.A. (Queensland Univ., Brisbane (Australia). Dept. of Mechanical Engineering); Thomas, A.; McIntyre, T.J. (Queensland Univ., Brisbane, QLD. (Australia). Dept. of Physics)

1999-01-01

Due to the difficulty of measuring all necessary flow quantities in the nozzle reservoir and the test section of high enthalpy shock tunnels, indirect computational methods are necessary to estimate the required flow parameters. In addition to steady state flow computations of the nozzle flow and the flow past wind tunnel models it is necessary to investigate the transient flow in the facility in order to achieve a better understanding of its performance. These transient effects include the nozzle starting flow, the interaction of the shock tube boundary layers and the reflected shock, thermal losses in the shock reflection region and the developing boundary layers in the expanding section of the nozzle. Additionally, the nonequilibrium chemical and thermal relaxation models which are used to compute high enthalpy flows have to be validated with appropriate experimental data. (orig.)

A regularization of the Burgers equation using a filtered convective velocity

International Nuclear Information System (INIS)

Norgard, Greg; Mohseni, Kamran

2008-01-01

This paper examines the properties of a regularization of the Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as the convectively filtered Burgers (CFB) equation. A physical motivation behind the filtering technique is presented. An existence and uniqueness theorem for multiple dimensions and a general class of filters is proven. Multiple invariants of motion are found for the CFB equation which are shown to be shared with the viscous and inviscid Burgers equations. Traveling wave solutions are found for a general class of filters and are shown to converge to weak solutions of the inviscid Burgers equation with the correct wave speed. Numerical simulations are conducted in 1D and 2D cases where the shock behavior, shock thickness and kinetic energy decay are examined. Energy spectra are also examined and are shown to be related to the smoothness of the solutions. This approach is presented with the hope of being extended to shock regularization of compressible Euler equations

Theory of the corrugation instability of a piston-driven shock wave.

Science.gov (United States)

Bates, J W

2015-01-01

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Analysis of a cylindrical imploding shock wave

International Nuclear Information System (INIS)

Mishkin, E.A.; Fujimoto, Y.

1978-01-01

the self-similar solution of the gasdynamic equations of a strong cylindrical shock wave moving through an ideal gas, with γ = csub(p)/csub(v), is considered. These equations are greatly simplified following the transformation of the reduced velocity U 1 (xi) → U 1 = 1/2(γ + 1 ) (U + xi). The requirement of a single maximum pressure, dsub(xi)P = 0, leads to an analytical determination of the self-similarity exponent α(γ). For gases with γ = 2 + 3sup(1/2), this maximum ensues right at the shock front and the pressure distribution then decreases monotonically. The postulate of analyticity by Gelfand and Butler is shown to concur with the requirement dsub(xi)P 0. The saturated density of the gas left in the wake of the shock is computed and - U is shown to be the reduced velocity of sound at P = P sub(m). (author)

Dust acoustic shock wave at high dust density

International Nuclear Information System (INIS)

Ghosh, Samiran; Sarkar, Susmita; Khan, Manoranjan; Avinash, K.; Gupta, M. R.

2003-01-01

Dust acoustic (DA) shock wave at high dust density, i.e., the dust electroacoustic (DEA) or dust Coulomb (DC) shock wave has been investigated incorporating the nonadiabatic dust charge variation. The nonlinear DEA (DC) shock wave is seen to be governed by the Korteweg-de Vries Burger equation, in which the Burger term is proportional to the nonadiabaticity generated dissipation. It is seen that the shock strength decreases but after reaching minimum, it increases as the dust space charge density |q d n d | increases and the shock strength of DA wave is greater than that of DEA (DC) wave. Moreover the DEA (DC) shock width increases appreciably with increase mass m i of the ion component of the dusty plasma but for DA shock wave the effect is weak

Numerical simulation of diffuse double layer around microporous electrodes based on the Poisson–Boltzmann equation

International Nuclear Information System (INIS)

Kitazumi, Yuki; Shirai, Osamu; Yamamoto, Masahiro; Kano, Kenji

2013-01-01

Graphical abstract: - Highlights: • Diffuse double layers overlap with each other in the micropore. • The overlapping of the diffuse double layer affects the double layer capacitance. • The electric field becomes weak in the micropore. • The electroneutrality is unsatisfactory in the micropore. - Abstract: The structure of the diffuse double layer around a nm-sized micropore on porous electrodes has been studied by numerical simulation using the Poisson–Boltzmann equation. The double layer capacitance of the microporous electrode strongly depends on the electrode potential, the electrolyte concentration, and the size of the micropore. The potential and the electrolyte concentration dependence of the capacitance is different from that of the planner electrode based on the Gouy's theory. The overlapping of the diffuse double layer becomes conspicuous in the micropore. The overlapped diffuse double layer provides the mild electric field. The intensified electric field exists at the rim of the orifice of the micropore because of the expansion of the diffuse double layers. The characteristic features of microporous electrodes are caused by the heterogeneity of the electric field around the micropores

Parametric study of non-relativistic electrostatic shocks and the structure of their transition layer

Energy Technology Data Exchange (ETDEWEB)

Dieckmann, M. E. [Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam (Germany); Department of Science and Technology, Linkoeping University, SE-60174 Norrkoeping (Sweden); Ahmed, H.; Sarri, G.; Doria, D.; Kourakis, I.; Borghesi, M. [Centre for Plasma Physics, School of Mathematics and Physics, Queen' s University of Belfast, Belfast BT7 1NN (United Kingdom); Romagnani, L. [LULI, Ecole Polytechnique, CNRS, CEA, UPMC, 91128 Palaiseau (France); Pohl, M. [Institute of Physics and Astronomy, University of Potsdam, D-14476 Potsdam (Germany); DESY, D-15738 Zeuthen (Germany)

2013-04-15

Nonrelativistic electrostatic unmagnetized shocks are frequently observed in laboratory plasmas and they are likely to exist in astrophysical plasmas. Their maximum speed, expressed in units of the ion acoustic speed far upstream of the shock, depends only on the electron-to-ion temperature ratio if binary collisions are absent. The formation and evolution of such shocks is examined here for a wide range of shock speeds with particle-in-cell simulations. The initial temperatures of the electrons and the 400 times heavier ions are equal. Shocks form on electron time scales at Mach numbers between 1.7 and 2.2. Shocks with Mach numbers up to 2.5 form after tens of inverse ion plasma frequencies. The density of the shock-reflected ion beam increases and the number of ions crossing the shock thus decreases with an increasing Mach number, causing a slower expansion of the downstream region in its rest frame. The interval occupied by this ion beam is on a positive potential relative to the far upstream. This potential pre-heats the electrons ahead of the shock even in the absence of beam instabilities and decouples the electron temperature in the foreshock ahead of the shock from the one in the far upstream plasma. The effective Mach number of the shock is reduced by this electron heating. This effect can potentially stabilize nonrelativistic electrostatic shocks moving as fast as supernova remnant shocks.

Parametric study of non-relativistic electrostatic shocks and the structure of their transition layer

International Nuclear Information System (INIS)

Dieckmann, M. E.; Ahmed, H.; Sarri, G.; Doria, D.; Kourakis, I.; Borghesi, M.; Romagnani, L.; Pohl, M.

2013-01-01

Nonrelativistic electrostatic unmagnetized shocks are frequently observed in laboratory plasmas and they are likely to exist in astrophysical plasmas. Their maximum speed, expressed in units of the ion acoustic speed far upstream of the shock, depends only on the electron-to-ion temperature ratio if binary collisions are absent. The formation and evolution of such shocks is examined here for a wide range of shock speeds with particle-in-cell simulations. The initial temperatures of the electrons and the 400 times heavier ions are equal. Shocks form on electron time scales at Mach numbers between 1.7 and 2.2. Shocks with Mach numbers up to 2.5 form after tens of inverse ion plasma frequencies. The density of the shock-reflected ion beam increases and the number of ions crossing the shock thus decreases with an increasing Mach number, causing a slower expansion of the downstream region in its rest frame. The interval occupied by this ion beam is on a positive potential relative to the far upstream. This potential pre-heats the electrons ahead of the shock even in the absence of beam instabilities and decouples the electron temperature in the foreshock ahead of the shock from the one in the far upstream plasma. The effective Mach number of the shock is reduced by this electron heating. This effect can potentially stabilize nonrelativistic electrostatic shocks moving as fast as supernova remnant shocks.

Critical point anomalies include expansion shock waves

Energy Technology Data Exchange (ETDEWEB)

Nannan, N. R., E-mail: ryan.nannan@uvs.edu [Mechanical Engineering Discipline, Anton de Kom University of Suriname, Leysweg 86, PO Box 9212, Paramaribo, Suriname and Process and Energy Department, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft (Netherlands); Guardone, A., E-mail: alberto.guardone@polimi.it [Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Colonna, P., E-mail: p.colonna@tudelft.nl [Propulsion and Power, Delft University of Technology, Kluyverweg 1, 2629 HS Delft (Netherlands)

2014-02-15

From first-principle fluid dynamics, complemented by a rigorous state equation accounting for critical anomalies, we discovered that expansion shock waves may occur in the vicinity of the liquid-vapor critical point in the two-phase region. Due to universality of near-critical thermodynamics, the result is valid for any common pure fluid in which molecular interactions are only short-range, namely, for so-called 3-dimensional Ising-like systems, and under the assumption of thermodynamic equilibrium. In addition to rarefaction shock waves, diverse non-classical effects are admissible, including composite compressive shock-fan-shock waves, due to the change of sign of the fundamental derivative of gasdynamics.

Irreversible thermodynamics of overdriven shocks in solids

International Nuclear Information System (INIS)

Wallace, D.C.

1981-01-01

An isotropic solid capable of transporting heat and of undergoing dissipative plastic flow, is treated. The shock is assumed to be a steady wave, and any phase changes or macroscopic inhomogeneities which might be induced by the shock are neglected. Under these conditions it is established that for an overdriven shock, no solution is possible without heat transport, and when the heat transport is governed by the steady conduction equation, no solution is possible without plastic dissipation as well. Upper and lower bounds are established for the thermodynamic variables, namely the shear stress, temperature, entropy, plastic strain, and heat flux, as functions of compression through the shock

Analytical and numerical modelling of thermoviscous shocks in their interactions in nonlinear fluids including dissipation

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

2010-01-01

A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. The equation preserves the Hamiltonian structure of the fundamental fluid dynamical equations in the non dissipative limit. An exact...... thermoviscous shock solution is derived. This solution is, in an overall sense, equivalent to the Taylor shock solution of the Burgers equation. However, in contrast to the Burgers equation, the model equation considered here is capable to describe waves propagating in opposite directions. Studies of head...

Fast Near-Field Calculation for Volume Integral Equations for Layered Media

DEFF Research Database (Denmark)

Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav

2005-01-01

. Afterwards, the scattered electric field can be easily computed at a regular rectangular grid on any horizontal plane us-ing a 2-dimensional FFT. This approach provides significant speedup in the near-field calculation in comparison to a straightforward numerical evaluation of the ra-diation integral since......An efficient technique based on the Fast Fourier Transform (FFT) for calculating near-field scattering by dielectric objects in layered media is presented. A higher or-der method of moments technique is employed to solve the volume integral equation for the unknown induced volume current density...

A method for the approximate solutions of the unsteady boundary layer equations

International Nuclear Information System (INIS)

Abdus Sattar, Md.

1990-12-01

The approximate integral method proposed by Bianchini et al. to solve the unsteady boundary layer equations is considered here with a simple modification to the scale function for the similarity variable. This is done by introducing a time dependent length scale. The closed form solutions, thus obtained, give satisfactory results for the velocity profile and the skin friction to a limiting case in comparison with the results of the past investigators. (author). 7 refs, 2 figs

Supersonic flow. Pt. 5 Shock waves; Fondamenti fisici dei fasci molecolari supersonici. Pt 5 Onde di Shock

Energy Technology Data Exchange (ETDEWEB)

Sanna, G.; Tomassetti, G. [L`Aquila Univ. (Italy). Dipt. di Fisica

1998-02-01

The discontinuities in the flow fields (both tangential and shocks) are considered and the equations for the quantities conserved across them are written. The post-shock flow variables are expressed by the Mach number of the incident supersonic flow and its deflection angle operated by rigid wall. Normal and oblique shocks are considered and graphs and polar diagrams are introduced. Then the reflections of a shock wave operated by a rigid wall and by the boundary between a jet and a stagnating gas are analyzed. Finally, the interactions between two distinct shock waves are considered. [Italiano] Vengono considerate le discontinuita` (tangenziali e shocks) nei campi di flusso e sono scritte le equazioni per le quantita` che si conservano attraverso di esse. Le variabili del flusso oltre lo shock sono espresse in funzione del numero di Mach del flusso supersonico incidente e dell`angolo di deflessione di questo operato da una parete rigida. I casi di shock normale, obliquo e distaccato sono considerati e sono introdotti grafici vari e rappresentazioni polari. Sono quindi considerate le riflessioni di un fronte di shock da una parete rigida e dalla frontiera tra un gas in moto ed uno stagnante. Sono infine considerate le diverse interazioni tra due shock distinti.

Finsler-Geometric Continuum Dynamics and Shock Compression

Science.gov (United States)

2018-01-01

version of Finsler theory is newly applied to shock compression of this ceramic. An order parameter is linked simultaneously to densification and...set of algebraic equations that may be solved simultaneously (albeit, not in closed form) for the shock stress, order param- eter, entropy, and shock...δxa ⊗ dX A = ∂ϕ a(X, D, t) ∂X A δ δxa ⊗ dX A = ∂x(X, D, t) ∂X , FaA = ∂Aϕa = ∂Axa . (2.28) The inverse tangent mapping from spatial to referential

Micro-Ramp Flow Control for Oblique Shock Interactions: Comparisons of Computational and Experimental Data

Science.gov (United States)

Hirt, Stephanie M.; Reich, David B.; O'Connor, Michael B.

2012-01-01

Computational fluid dynamics was used to study the effectiveness of micro-ramp vortex generators to control oblique shock boundary layer interactions. Simulations were based on experiments previously conducted in the 15- by 15-cm supersonic wind tunnel at the NASA Glenn Research Center. Four micro-ramp geometries were tested at Mach 2.0 varying the height, chord length, and spanwise spacing between micro-ramps. The overall flow field was examined. Additionally, key parameters such as boundary-layer displacement thickness, momentum thickness and incompressible shape factor were also examined. The computational results predicted the effects of the microramps well, including the trends for the impact that the devices had on the shock boundary layer interaction. However, computing the shock boundary layer interaction itself proved to be problematic since the calculations predicted more pronounced adverse effects on the boundary layer due to the shock than were seen in the experiment.

Nonlinearity, Conservation Law and Shocks

Indian Academy of Sciences (India)

Almost all natural phenomena, and social and economic changes, .... reference moving with velocity c also by the same symbol x and ... abstract as can be seen from the publication of the book Shock Waves and Reaction Diffusion Equation.

29th International Symposium on Shock Waves

CERN Document Server

Ranjan, Devesh

2015-01-01

This proceedings present the results of the 29th International Symposium on Shock Waves (ISSW29) which was held in Madison, Wisconsin, U.S.A., from July 14 to July 19, 2013. It was organized by the Wisconsin Shock Tube Laboratory, which is part of the College of Engineering of the University of Wisconsin-Madison. The ISSW29 focused on the following areas: Blast Waves, Chemically Reactive Flows, Detonation and Combustion,  Facilities, Flow Visualization, Hypersonic Flow, Ignition, Impact and Compaction, Industrial Applications, Magnetohydrodynamics, Medical and Biological Applications, Nozzle Flow, Numerical Methods, Plasmas, Propulsion, Richtmyer-Meshkov Instability, Shock-Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shock Waves in Condensed Matter, Shock Waves in Multiphase Flow, as well as Shock Waves in Rarefield Flow. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 29 and individuals interes...

Measurement of the equation of state of porous materials through the use of shock waves generated by laser radiation; Mesure de l'equation d'etat de materiaux poreux a l'aide d'ondes de choc generees par laser

Energy Technology Data Exchange (ETDEWEB)

Philippe, F

2001-12-15

This work aims at measuring the equation of state of porous plastic materials in the view of their use in inertial confinement fusion. We have experimentally determined the shock polar curve of TMPTA (C{sub 15}H{sub 20}O{sub 6}) by the use of the impedance matching technique. This technique is based on the simultaneous measurement of the shock velocities in the 2 materials composing the target. The shock polar curve has been drawn for pressures ranging from 10 kbar to 3 Mbar and densities from 20 mg/cm{sup 3} to 1.1 g/cm{sup 3}. The use of a slit sweep camera to assess the propagation of the shock wave through the target has limited the accuracy of the technique to 10%. Experimental results match well data provided by the Sesame tables that are broadly used by hydrodynamic codes. Nevertheless the statistical distribution of experimental points seems to show a lower compressibility of the foam that might be attributed to a slight pre-heating process or to the effect of the foam micro-structure on the shock wave propagation. In order to improve the accuracy of the method, an attempt was made to use an active doppler interferometric diagnostic to measure shock wave velocities. It has been showed that the shock wave front in the foam is reflecting enough to make this method relevant if we can overcome the difficulty of a high luminous background. Despite that, we have succeeded in measuring with high accuracy, a point of the shock polar curve for 800 mg/cm{sup 3} dense TMPTA. (A.C.)

Partial differential equations

CERN Document Server

Evans, Lawrence C

2010-01-01

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

Shock structure in continuum models of gas dynamics: stability and bifurcation analysis

International Nuclear Information System (INIS)

Simić, Srboljub S

2009-01-01

The problem of shock structure in gas dynamics is analysed through a comparative study of two continuum models: the parabolic Navier–Stokes–Fourier model and the hyperbolic system of 13 moments equations modeling viscous, heat-conducting monatomic gases within the context of extended thermodynamics. When dissipative phenomena are neglected these models both reduce to classical Euler's equations of gas dynamics. The shock profile solution, assumed in the form of a planar travelling wave, reduces the problem to a system of ordinary differential equations, and equilibrium states appear to be stationary points of the system. It is shown that in both models an upstream equilibrium state suffers an exchange of stability when the shock speed crosses the critical value which coincides with the highest characteristic speed of the Euler's system. At the same time a downstream equilibrium state could be seen as a steady bifurcating solution, while the shock profile represents a heteroclinic orbit connecting the two stationary points. Using centre manifold reduction it is demonstrated that both models, although mathematically different, obey the same transcritical bifurcation pattern in the neighbourhood of the bifurcation point corresponding to the critical value of shock speed, the speed of sound

Rayleigh-Taylor stability for a shock wave-density discontinuity interaction

International Nuclear Information System (INIS)

Fraley, G.S.

1981-01-01

Shells in inertial fusion targets are typically accelerated and decelerated by two or three shocks followed by continuous acceleration. The analytic solution for perturbation growth of a shock wave striking a density discontinuity in an inviscid fluid is investigated. The Laplace transform of the solution results in a functional equation, which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is given by a gamma law. The four independent parameters of the solution are the gamma values on each side of the material interface, the density ratio at the interface, and the shock strength. The asymptotic behavior (for large distances and times) of the perturbation velocity is given. For strong shocks the decay of the perturbation away from the interface is much weaker than the exponential decay of an incompressible fluid. The asymptotic value is given by a constant term and a number of slowly decaying discreet frequencies. The number of frequencies is roughly proportional to the logarithm of the density discontinuity divided by that of the shock strength. The asymptotic velocity at the interface is tabulated for representative values of the independent parameters. For weak shocks the solution is compared with results for an incompressible fluid. The range of density ratios with possible zero asymptotic velocities is given

Focusing of Shear Shock Waves

Science.gov (United States)

Giammarinaro, Bruno; Espíndola, David; Coulouvrat, François; Pinton, Gianmarco

2018-01-01

Focusing is a ubiquitous way to transform waves. Recently, a new type of shock wave has been observed experimentally with high-frame-rate ultrasound: shear shock waves in soft solids. These strongly nonlinear waves are characterized by a high Mach number, because the shear wave velocity is much slower, by 3 orders of magnitude, than the longitudinal wave velocity. Furthermore, these waves have a unique cubic nonlinearity which generates only odd harmonics. Unlike longitudinal waves for which only compressional shocks are possible, shear waves exhibit cubic nonlinearities which can generate positive and negative shocks. Here we present the experimental observation of shear shock wave focusing, generated by the vertical motion of a solid cylinder section embedded in a soft gelatin-graphite phantom to induce linearly vertically polarized motion. Raw ultrasound data from high-frame-rate (7692 images per second) acquisitions in combination with algorithms that are tuned to detect small displacements (approximately 1 μ m ) are used to generate quantitative movies of gel motion. The features of shear shock wave focusing are analyzed by comparing experimental observations with numerical simulations of a retarded-time elastodynamic equation with cubic nonlinearities and empirical attenuation laws for soft solids.

A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism

Science.gov (United States)

Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi

2018-06-01

Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier-Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standard numerical flux, MUSCL, the usual Lagrange's polynomial and the conventional Runge-Kutta method. The scheme can compute a boundary layer accurately with a rational resolution and capture a stationary contact discontinuity sharply without inner points. And yet it is endowed with high resistance against shock anomalies (carbuncle phenomenon, post-shock oscillations, etc.). A good balance between high robustness and low dissipation is achieved by blending three types of numerical fluxes according to physical situation in an intuitively easy-to-understand way. The performance of the scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30-40% less than of that of the advanced scheme.

On linear relationship between shock velocity and particle velocity

International Nuclear Information System (INIS)

Dandache, H.

1986-11-01

We attempt to derive the linear relationship between shock velocity U s and particle velocity U p from thermodynamic considerations, taking into account an ideal gas equation of state and a Mie-Grueneisen equation of state for solids. 23 refs

Flow control for oblique shock wave reflections

NARCIS (Netherlands)

Giepman, R.H.M.

2016-01-01

Shock wave-boundary layer interactions are prevalent in many aerospace applications that involve transonic or supersonic flows. Such interactions may lead to boundary layer separation, flow unsteadiness and substantial losses in the total pressure. Flow control techniques can help to mitigate these

Electrical conductivity and equation of state of liquid nitrogen, oxygen, benzene, and 1-butene shocked to 60 GPa

Energy Technology Data Exchange (ETDEWEB)

Hamilton, D.C.

1986-10-08

Measurements are reported for the electrical conductivity of liquid nitrogen (N/sub 2/), oxygen (O/sub 2/) and benzene (C/sub 6/H/sub 6/), and Hugoniot equation of state of liquid 1-butene (C/sub 4/H/sub 8/) under shock compressed conditions. The conductivity data span 7 x 10/sup -4/ to 7 x 10/sup 1/ ..cap omega../sup -1/cm/sup -1/ over a dynamic pressure range 18.1 to 61.5 GPa and are discussed in terms of amorphous semiconduction models which include such transport phenomena as hopping, percolation, pseudogaps, and metallization. Excellent agreement is found between the equation-of-state measurements, which span a dynamic pressure range 12.3 to 53.8 GPa, and Ree's calculated values which assume a 2-phase mixture consisting of molecular hydrogen and carbon in a dense diamond-like phase. There is a 2-1/2 fold increase in the thermal pressure contribution over a less dense, stoichiometrically equivalent liquid. 90 refs., 48 figs., 8 tabs.

Kinematical Compatibility Conditions for Vorticity Across Shock Waves

Science.gov (United States)

Baty, Roy

2015-11-01

This work develops the general kinematical compatibility conditions for vorticity across arbitrary shock waves in compressible, inviscid fluids. The vorticity compatibility conditions are derived from the curl of the momentum equation using singular distributions defined on two-dimensional shock wave surfaces embedded in three-dimensional flow fields. The singular distributions are represented as generalized differential operators concentrated on moving shock wave surfaces. The derivation of the compatibility conditions for vorticity requires the application of second-order generalized derivatives and elementary tensor algebra. The well-known vorticity jump conditions across a shock wave are then shown to follow from the general kinematical compatibility conditions for vorticity by expressing the flow field velocity in vectorial components normal and tangential to a shock surface.

About perfectly adapted layers for the temporal resolution of Maxwell's equations

International Nuclear Information System (INIS)

Le Potier, Ch.

1995-01-01

The major obstacle encountered in diffraction problems is the limitation in place memory. One solution is to approach the Sommerfeld condition by taking into account absorbing boundary conditions on a boundary surface surrounding the studied object. Many authors have studied these problems, but, unfortunately, the implementation of absorbing boundary conditions of order greater than two for 3-dimensional non-structural meshes in the temporal case is a still unresolved problem to our knowledge. Another way is to add a dummy absorbent layer around the computational domain. J.P. Berenger has revived this method and considerably improved the resolution of the problems of time diffraction. His idea is to split the Maxwell equations in their anisotropic version in a layer surrounding the computational domain. On the other hand, J.Y. Wu introduced a new system of anisotropic equations in the frequency case. The author shows that this new system possesses the same properties as that of Berenger and this idea has been generalized to the temporal case with discretization in space by finite volumes in 3 dimensions for a structured or not structured mesh. The report also presents the implementation of these new methods in the SUMER-T code and the accuracy of these is compared with conventional absorbing boundary conditions [fr

Low-frequency electrostatic shock excitations in a multi-component dusty plasma

Energy Technology Data Exchange (ETDEWEB)

Ferdousi, M.; Miah, M.R.; Sultana, S.; Mamun, A.A., E-mail: mariyaferdousi@gmail.com [Department of Physics, Jahangirnagar University, Savar (Bangladesh)

2015-10-01

Dust-acoustic shock waves are investigated in a four-component plasma consisting of arbitrarily charged inertial dusts, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and electrons. The reductive perturbation technique is employed in order to derive the nonlinear time evolution Burgers-type equation. The properties of dust-acoustic shock waves are analysed via the solution of Burgers equation. It is observed that the basic features of dust-acoustic shock waves are significantly modified due to the influence of arbitrarily charged dusts, Maxwellian electrons, number density and temperatures of heavier and lighter ions, and dust kinematic viscosity. Both polarity (positive and negative potential) shock waves are also found to exists in the plasma under consideration in this manuscript. The findings of this investigation may be used in understanding the dust-acoustic wave properties in both laboratory and space plasmas. (author)

Low-frequency electrostatic shock excitations in a multi-component dusty plasma

International Nuclear Information System (INIS)

Ferdousi, M.; Miah, M.R.; Sultana, S.; Mamun, A.A.

2015-01-01

Dust-acoustic shock waves are investigated in a four-component plasma consisting of arbitrarily charged inertial dusts, Boltzmann distributed negatively charged heavy ions, positively charged light ions, and electrons. The reductive perturbation technique is employed in order to derive the nonlinear time evolution Burgers-type equation. The properties of dust-acoustic shock waves are analysed via the solution of Burgers equation. It is observed that the basic features of dust-acoustic shock waves are significantly modified due to the influence of arbitrarily charged dusts, Maxwellian electrons, number density and temperatures of heavier and lighter ions, and dust kinematic viscosity. Both polarity (positive and negative potential) shock waves are also found to exists in the plasma under consideration in this manuscript. The findings of this investigation may be used in understanding the dust-acoustic wave properties in both laboratory and space plasmas. (author)

Simulations of embedded lateral stress gauge profiles in shocked targets

International Nuclear Information System (INIS)

Winter, R E; Harris, E J

2008-01-01

In principle, stress gauges mounted to measure lateral stresses in a shocked matrix allow the shear strength of the material to be determined. However, interpreting the resistance profiles from lateral stress gauges is hindered by the fact that the stress field in the vicinity of the insulating layer in which the gauges are embedded can differ significantly from the stress field that would be generated in the sample if no gauge were present. A series of high resolution Eulerian hydrocode simulations have been run which suggest that the stresses in the insulating layer vary with distance and time in a way that depends on the thickness of the layer, the shock strength and the elastic and plastic properties of both the layer and the matrix. In particular, if the shock velocity in the matrix material is high the stress at a typical gauge position initially rises to a sharp peak then falls with time, but when the shock velocity in the matrix is low the stress rises relatively gradually throughout the time of interest. The shapes of the stress versus time profiles predicted by the hydrocode compare well with the results of lateral gauge experiments on several different materials. It is concluded that lateral gauges can be used to measure the dynamic strength of materials provided high resolution computer simulation is used to take account of the perturbation of the stress field in the shocked sample caused by the gauges

On the shock cell structure and noise of supersonic jets

Science.gov (United States)

Tam, C. K. W.; Jackson, J. A.

1983-01-01

A linear solution modeling the shock cell structure of an axisymmetric supersonic jet operated at off-design conditions is developed by the method of multiple-scales. The model solution takes into account the gradual spatial change of the mean flow in the downstream direction. Turbulence in the mixing layer of the jet has the tendency of smoothing out the sharp velocity and density gradients induced by the shocks. To simulate this effect, eddy viscosity terms are incorporated in the model. It is known that the interaction between the quasi-periodic shock cells and the downstream propagating large turbulence structures in the mixing layer of the jet is responsible for the generation of broadband shock associated noise. Experimentally, the dominant part of this noise has been found to originate from the part of the jet near the end of the potential core. Calculated shock cell spacing at the end of the jet core according to the present model is used to estimate the peak frequencies of the shock associated noise for a range of observation angles. Very favorable agreement with experimental measurements is found.

Thermal shock resistances of a bonding material of C/C composite and copper

International Nuclear Information System (INIS)

Kurumada, Akira; Oku, Tatsuo; Kawamata, Kiyohiro; Motojima, Osamu; Noda, Nobuaki; McEnaney, B.

1997-01-01

The purpose of this study is to contribute to the development and the safety design of plasma facing components for fusion reactor devices. We evaluated the thermal shock resistance and the thermal shock fracture toughness of a bonding material which was jointed a carbon-fiber-reinforced carbon composite (C/C composite) to oxygen-free copper. We also examined the microstructures of the bonding layers using a scanning electron microscope before and after thermal shock tests. The bonding material did not fracture during thermal shock tests. However, thermal cracks and delamination cracks were observed in the bonding layers. (author)

New test of bow-shock models of Herbig-Haro objects

International Nuclear Information System (INIS)

Raga, A.C.; Bohm, K.H.; Solf, J.; Max-Planck-Institut fuer Astronomie, Heidelberg, West Germany)

1986-01-01

Long-slit, high-resolution spectroscopy of the Herbig-Haro oject HH 32 has shown that the emission-line profiles in all four condensations A, B, C, and D show high- and low-velocity components. The spatial maxima of these two components are always arranged in a double-layer pattern, with the maximum of the high-velocity component 0.6-1.0 arcsecs closer to the central star (AS 353A) than the low-velocity maximum. A study of the emission-line profiles predicted from a model of a radiating bow shock shows that such a double-layer structure appears naturally for this type of flow. In this case both the high-velocity and the low-velocity components come from the post-shock gas, in agreement with the theoretical prediction that it should be very difficult to detect the pre-shock gas observationally. The present results agree qualitatively well with observations of HH 32, strengthening the case for a bow-shock interpretation of this Herbig-Haro object. It is shown that the double-layer effect will be more easily observable for bow shocks which move at a relatively large angle with respect to the plane of the sky (i.e., for Herbig-Haro objects which have large radial velocities). 31 references

Bifurcation parameters of a reflected shock wave in cylindrical channels of different roughnesses

Science.gov (United States)

Penyazkov, O.; Skilandz, A.

2018-03-01

To investigate the effect of bifurcation on the induction time in cylindrical shock tubes used for chemical kinetic experiments, one should know the parameters of the bifurcation structure of a reflected shock wave. The dynamics and parameters of the shock wave bifurcation, which are caused by reflected shock wave-boundary layer interactions, are studied experimentally in argon, in air, and in a hydrogen-nitrogen mixture for Mach numbers M = 1.3-3.5 in a 76-mm-diameter shock tube without any ramp. Measurements were taken at a constant gas density behind the reflected shock wave. Over a wide range of experimental conditions, we studied the axial projection of the oblique shock wave and the pressure distribution in the vicinity of the triple Mach configuration at 50, 150, and 250 mm from the endwall, using side-wall schlieren and pressure measurements. Experiments on a polished shock tube and a shock tube with a surface roughness of 20 {μ }m Ra were carried out. The surface roughness was used for initiating small-scale turbulence in the boundary layer behind the incident shock wave. The effect of small-scale turbulence on the homogenization of the transition zone from the laminar to turbulent boundary layer along the shock tube perimeter was assessed, assuming its influence on a subsequent stabilization of the bifurcation structure size versus incident shock wave Mach number, as well as local flow parameters behind the reflected shock wave. The influence of surface roughness on the bifurcation development and pressure fluctuations near the wall, as well as on the Mach number, at which the bifurcation first develops, was analyzed. It was found that even small additional surface roughness can lead to an overshoot in pressure growth by a factor of two, but it can stabilize the bifurcation structure along the shock tube perimeter.

Formation, structure, and stability of MHD intermediate shocks

International Nuclear Information System (INIS)

Wu, C.C.

1990-01-01

Contrary to the usual belief that MHD intermediate shocks are extraneous, the author has recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear wave steepening from continuous waves. In this paper, the formation, structure and stability of intermediate shocks in dissipative MHD are considered in detail. The differences between the conventional theory and his are pointed out and clarified. He shows that all four types of intermediate shocks can be formed from smooth waves. He also shows that there are free parameters in the structure of the intermediate shocks, and that these parameters are related to the shock stability. In addition, he shows that a rotational discontinuity can not exist with finite width, indicate how this is related to the existence of time-dependent intermediate shocks, and show why the conventional theory is not a good approximation to dissipative MHD solutions whenever there is rotation in magnetic field

Mars on Earth: Analog basaltic soils and particulates from Lonar Crater, India, include Deccan soil, shocked soil, reworked lithic and glassy ejecta, and both shocked and unshocked baked zones

Science.gov (United States)

Wright, S. P.

2017-12-01

"There is no perfect analog for Mars on Earth" [first line of Hipkin et al. (2013) Icarus, 261-267]. However, fieldwork and corresponding sample analyses from laboratory instrumentation (to proxy field instruments) has resulted in the finding of unique analog materials that suggest that detailed investigations of Lonar Crater, India would be beneficial to the goals of the Mars Program. These are briefly described below as Analog Processes, Materials, and Fieldwork. Analog Processes: The geologic history of Lonar Crater emulates localities on Mars with 1.) flood basaltic volcanism with interlayer development of 2.) baked zones or "boles" and 3.) soil formation. Of six flows, the lower three are aqueously altered by groundwater to produce a range of 4.) alteration products described below. The impact event 570 ka produced a range of 5.) impactites including shocked baked zones, shocked soils, and altered basalt shocked to a range of shock pressures [Kieffer et al., 1976]. Analog Materials: 65 Ma Deccan basalt contains augite and labradorite. Baked zones are higher in hematite and other iron oxides. Soil consists of calcite and organic matter. Several basalts with secondary alteration are listed here and these mirror alteration on Mars: hematite, chlorite, serpentine, zeolite, and palagonite, with varying combinations of these with primary igneous minerals. All of these materials (#1 through 4 above) are shocked to a range of shocked pressures to produce maskelynite, flowing plagioclase glass, vesiculated plagioclase glass, and complete impact melts. Shocked soils contain schlieren calcite amidst comminuted grains of augite, labradorite, and these glasses. Shocked baked zones unsurprisingly have a petrographic texture similar to hornfels, another product of contact metamorphism. Analog Fieldwork: The ejecta consists of two layers: 8 m of lithic breccia with unshocked and fractured basalts under a 1 m suevite consisting of all ranges of shock pressure described above

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

Science.gov (United States)

Tukhvatullina, R. R.; Frolov, S. M.

2018-03-01

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh-Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005-0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Comparison of Hydrocode Simulations with Measured Shock Wave Velocities

International Nuclear Information System (INIS)

Hixson, R. S.; Veeser, L. R.

2014-01-01

We have conducted detailed 1- and 2-dimensional hydrodynamics calculations to assess the quality of simulations commonly made to understand various shock processes in a sample and to design shock experiments. We began with relatively simple shock experiments, where we examined the effects of the equation of state and the viscoplastic strength models. Eventually we included spallation in copper and iron and a solid-solid phase transformation in iron to assess the quality of the damage and phase transformation simulations.

Application of an engineering inviscid-boundary layer method to slender three-dimensional vehicle forebodies

Science.gov (United States)

Riley, Christopher J.

1993-01-01

An engineering inviscid-boundary layer method has been modified for application to slender three-dimensional (3-D) forebodies which are characteristic of transatmospheric vehicles. An improved shock description in the nose region has been added to the inviscid technique which allows the calculation of a wider range of body geometries. The modified engineering method is applied to the perfect gas solution over a slender 3-D configuration at angle of attack. The method predicts surface pressures and laminar heating rates on the windward side of the vehicle that compare favorably with numerical solutions of the thin-layer Navier-Stokes equations. These improvements extend the 3-D capabilities of the engineering method and significantly increase its design applications.

Shock compression experiments on Lithium Deuteride (LiD) single crystals

Science.gov (United States)

Knudson, M. D.; Desjarlais, M. P.; Lemke, R. W.

2016-12-01

Shock compression experiments in the few hundred GPa (multi-Mbar) regime were performed on Lithium Deuteride single crystals. This study utilized the high velocity flyer plate capability of the Sandia Z Machine to perform impact experiments at flyer plate velocities in the range of 17-32 km/s. Measurements included pressure, density, and temperature between ˜190 and 570 GPa along the Principal Hugoniot—the locus of end states achievable through compression by large amplitude shock waves—as well as pressure and density of reshock states up to ˜920 GPa. The experimental measurements are compared with density functional theory calculations, tabular equation of state models, and legacy nuclear driven results that have been reanalyzed using modern equations of state for the shock wave standards used in the experiments.

Nonstandard jump functions for radically symmetric shock waves

International Nuclear Information System (INIS)

Baty, Roy S.; Tucker, Don H.; Stanescu, Dan

2008-01-01

Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function.

Shock compression of synthetic opal

International Nuclear Information System (INIS)

Inoue, A; Okuno, M; Okudera, H; Mashimo, T; Omurzak, E; Katayama, S; Koyano, M

2010-01-01

Structural change of synthetic opal by shock-wave compression up to 38.1 GPa has been investigated by using SEM, X-ray diffraction method (XRD), Infrared (IR) and Raman spectroscopies. Obtained information may indicate that the dehydration and polymerization of surface silanole due to high shock and residual temperature are very important factors in the structural evolution of synthetic opal by shock compression. Synthetic opal loses opalescence by 10.9 and 18.4 GPa of shock pressures. At 18.4 GPa, dehydration and polymerization of surface silanole and transformation of network structure may occur simultaneously. The 4-membered ring of TO 4 tetrahedrons in as synthetic opal may be relaxed to larger ring such as 6-membered ring by high residual temperature. Therefore, the residual temperature may be significantly high at even 18.4 GPa of shock compression. At 23.9 GPa, opal sample recovered the opalescence. Origin of this opalescence may be its layer structure by shock compression. Finally, sample fuse by very high residual temperature at 38.1 GPa and the structure closes to that of fused SiO 2 glass. However, internal silanole groups still remain even at 38.1 GPa.

Shock compression of synthetic opal

Science.gov (United States)

Inoue, A.; Okuno, M.; Okudera, H.; Mashimo, T.; Omurzak, E.; Katayama, S.; Koyano, M.

2010-03-01

Structural change of synthetic opal by shock-wave compression up to 38.1 GPa has been investigated by using SEM, X-ray diffraction method (XRD), Infrared (IR) and Raman spectroscopies. Obtained information may indicate that the dehydration and polymerization of surface silanole due to high shock and residual temperature are very important factors in the structural evolution of synthetic opal by shock compression. Synthetic opal loses opalescence by 10.9 and 18.4 GPa of shock pressures. At 18.4 GPa, dehydration and polymerization of surface silanole and transformation of network structure may occur simultaneously. The 4-membered ring of TO4 tetrahedrons in as synthetic opal may be relaxed to larger ring such as 6-membered ring by high residual temperature. Therefore, the residual temperature may be significantly high at even 18.4 GPa of shock compression. At 23.9 GPa, opal sample recovered the opalescence. Origin of this opalescence may be its layer structure by shock compression. Finally, sample fuse by very high residual temperature at 38.1 GPa and the structure closes to that of fused SiO2 glass. However, internal silanole groups still remain even at 38.1 GPa.

Shock compression of synthetic opal

Energy Technology Data Exchange (ETDEWEB)

Inoue, A; Okuno, M; Okudera, H [Department of Earth Sciences, Kanazawa University Kanazawa, Ishikawa, 920-1192 (Japan); Mashimo, T; Omurzak, E [Shock Wave and Condensed Matter Research Center, Kumamoto University, Kumamoto, 860-8555 (Japan); Katayama, S; Koyano, M, E-mail: okuno@kenroku.kanazawa-u.ac.j [JAIST, Nomi, Ishikawa, 923-1297 (Japan)

2010-03-01

Structural change of synthetic opal by shock-wave compression up to 38.1 GPa has been investigated by using SEM, X-ray diffraction method (XRD), Infrared (IR) and Raman spectroscopies. Obtained information may indicate that the dehydration and polymerization of surface silanole due to high shock and residual temperature are very important factors in the structural evolution of synthetic opal by shock compression. Synthetic opal loses opalescence by 10.9 and 18.4 GPa of shock pressures. At 18.4 GPa, dehydration and polymerization of surface silanole and transformation of network structure may occur simultaneously. The 4-membered ring of TO{sub 4} tetrahedrons in as synthetic opal may be relaxed to larger ring such as 6-membered ring by high residual temperature. Therefore, the residual temperature may be significantly high at even 18.4 GPa of shock compression. At 23.9 GPa, opal sample recovered the opalescence. Origin of this opalescence may be its layer structure by shock compression. Finally, sample fuse by very high residual temperature at 38.1 GPa and the structure closes to that of fused SiO{sub 2} glass. However, internal silanole groups still remain even at 38.1 GPa.

Absolute Hugoniot measurements from a spherically convergent shock using x-ray radiography

Science.gov (United States)

Swift, Damian C.; Kritcher, Andrea L.; Hawreliak, James A.; Lazicki, Amy; MacPhee, Andrew; Bachmann, Benjamin; Döppner, Tilo; Nilsen, Joseph; Collins, Gilbert W.; Glenzer, Siegfried; Rothman, Stephen D.; Kraus, Dominik; Falcone, Roger W.

2018-05-01

The canonical high pressure equation of state measurement is to induce a shock wave in the sample material and measure two mechanical properties of the shocked material or shock wave. For accurate measurements, the experiment is normally designed to generate a planar shock which is as steady as possible in space and time, and a single state is measured. A converging shock strengthens as it propagates, so a range of shock pressures is induced in a single experiment. However, equation of state measurements must then account for spatial and temporal gradients. We have used x-ray radiography of spherically converging shocks to determine states along the shock Hugoniot. The radius-time history of the shock, and thus its speed, was measured by radiographing the position of the shock front as a function of time using an x-ray streak camera. The density profile of the shock was then inferred from the x-ray transmission at each instant of time. Simultaneous measurement of the density at the shock front and the shock speed determines an absolute mechanical Hugoniot state. The density profile was reconstructed using the known, unshocked density which strongly constrains the density jump at the shock front. The radiographic configuration and streak camera behavior were treated in detail to reduce systematic errors. Measurements were performed on the Omega and National Ignition Facility lasers, using a hohlraum to induce a spatially uniform drive over the outside of a solid, spherical sample and a laser-heated thermal plasma as an x-ray source for radiography. Absolute shock Hugoniot measurements were demonstrated for carbon-containing samples of different composition and initial density, up to temperatures at which K-shell ionization reduced the opacity behind the shock. Here we present the experimental method using measurements of polystyrene as an example.

Viscous-shock-layer solutions with coupled radiation and ablation injection for earth entry

Science.gov (United States)

Gupta, Roop N.; Lee, Kam-Pui; Moos, James N.; Sutton, Kenneth

1990-01-01

Results are obtained for the forebody of a planetary exploration vehicle entering the earth's atmosphere. A viscous-shock-layer analysis is used assuming the flow to be laminar and in chemical equilibrium. Presented results include coupled radiation and ablation injection. This study further includes the effect of different transport and thermodynamic properties and radiation models. A Lewis number of 1.4 appears adequate for the radiation-dominated flows. Five velocities corresponding to different possible trajectory points at an altitude of 70 km have been further analyzed in detail. Sublimation and radiative equilibrium wall temperatures are employed for cases with and without coupled injection, respectively. For the cases analyzed here, the mass injection rates are small. However, the rates could become large if a lower altitude is used for aerobraking and/or the body size is increased. A comparison of the equilibrium results with finite-rate chemistry calculation shows the flowfield to be in chemical equilibrium.

Hugoniot-based equations of state for two filled EPDM rubbers

Science.gov (United States)

Pacheco, Adam; Dattelbaum, Dana; Orler, E.; Gustavsen, R.

2013-06-01

The shock response of silica filled and Kevlar filled ethylene-propylene-diene (EPDM) rubbers was studied using gas gun-driven plate impact experiments. Both materials are proprietary formulations made by Kirkhill-TA, Brea CA USA, and are used for ablative internal rocket motor insulation. Two types of experiments were performed. In the first, the filled-EPDM sample was mounted on the front of the projectile and impacted a Lithium Fluoride (LiF) window. The Hugoniot state was determined from the measured projectile velocity, the EPDM/LiF interface velocity (measured using VISAR) and impedance matching to LiF. In the second type of experiment, electromagnetic particle velocity gauges were embedded between layers of filled-EPDM. These provided in situ particle velocity and shock velocity measurements. Experiments covered a pressure range of 0.34 - 14 GPa. Hugoniot-based equations of state were obtained for both materials, and will be compared to those of other filled elastomers such as silica-filled polydimethylsiloxane and adiprene. Work performed while at Los Alamos National Laboratory.

Converging cylindrical magnetohydrodynamic shock collapse onto a power-law-varying line current

KAUST Repository

Mostert, W.

2016-03-16

We investigate the convergence behaviour of a cylindrical, fast magnetohydrodynamic (MHD) shock wave in a neutrally ionized gas collapsing onto an axial line current that generates a power law in time, azimuthal magnetic field. The analysis is done within the framework of a modified version of ideal MHD for an inviscid, non-dissipative, neutrally ionized compressible gas. The time variation of the magnetic field is tuned such that it approaches zero at the instant that the shock reaches the axis. This configuration is motivated by the desire to produce a finite magnetic field at finite shock radius but a singular gas pressure and temperature at the instant of shock impact. Our main focus is on the variation with shock radius, as, of the shock Mach number and pressure behind the shock as a function of the magnetic field power-law exponent, where gives a constant-in-time line current. The flow problem is first formulated using an extension of geometrical shock dynamics (GSD) into the time domain to take account of the time-varying conditions ahead of the converging shock, coupled with appropriate shock-jump conditions for a fast, symmetric MHD shock. This provides a pair of ordinary differential equations describing both and the time evolution on the shock, as a function of, constrained by a collapse condition required to achieve tuned shock convergence. Asymptotic, analytical results for and are obtained over a range of for general, and for both small and large . In addition, numerical solutions of the GSD equations are performed over a large range of, for selected parameters using . The accuracy of the GSD model is verified for some cases using direct numerical solution of the full, radially symmetric MHD equations using a shock-capturing method. For the GSD solutions, it is found that the physical character of the shock convergence to the axis is a strong function of . For μ≤0.816, and both approach unity at shock impact owing to the dominance of the strong

Laser shock processing on microstructure and hardness of polycrystalline cubic boron nitride tools with and without nanodiamond powders

International Nuclear Information System (INIS)

Melookaran, Roslyn; Melaibari, Ammar; Deng, Cheng; Molian, Pal

2012-01-01

Highlights: ► Laser shock waves hardened polycrystalline cubic boron nitride tools by up to 15%. ► Laser shock waves can build layer-by-layer of nanodiamond to form micro-diamond tools. ► Multiple laser shocks induce significant phase transitions in cBN and nanodiamond. -- Abstract: High amplitude, short duration shock waves created by a 1064 nm, 10 ns Q-switched Nd:YAG laser were used to increase the hardness as well as build successive layers of nanodiamond on sintered polycrystalline cubic boron nitride (PcBN) tools. Multiple scans of laser shocking were applied. Scanning electron microscopy, Raman spectroscopy, Tukon microhardness tester, and optical surface profilometer were used to evaluate the microstructure, phase change, Vicker’s microhardness and surface roughness. Results indicated that laser shock processing of plain PcBN changed the binder concentration, caused phase transition from cubic to hexagonal form, increased the hardness, and almost unaffected surface roughness. Laser shock wave sintering of nanodiamond powders on PcBN resulted in deagglomeration and layer-by-layer build-up of nanoparticles for a thickness of 30 μm inferring that a novel solid freeform technique designated as “shock wave induced freeform technique (SWIFT)” is being discovered for making micro-tools. Depending on the number of multiple laser shocks, the hardness of nanodiamond compact was lower or higher than that of PcBN. It is hypothesized that nanodiamond particles could serve as crack deflectors, increasing the fracture toughness of PcBN.

Shock diffraction in alumina powder

International Nuclear Information System (INIS)

Venz, G.; Killen, P.D.; Page, N.W.

1996-01-01

In order to produce complex shaped components by dynamic compaction of ceramic powders detailed knowledge of their response under shock loading conditions is required. This work attempts to provide data on release effects and shock attenuation in 1 μm and 5 μm α-alumina powders which were compacted to between 85 % and 95 % of the solid phase density by the impact of high velocity steel projectiles. As in previous work, the powder was loaded into large cylindrical dies with horizontal marker layers of a contrasting coloured powder to provide a record of powder displacement in the recovered specimens. After recovery and infiltration with a thermosetting resin the specimens were sectioned and polished to reveal the structure formed by the passage of the projectile and shock wave. Results indicate that the shock pressures generated were of the order of 0.5 to 1.4 GPa and higher, with shock velocities and sound speeds in the ranges 650 to 800 m/s and 350 to 400 m/s respectively

A shock absorber model for structure-borne noise analyses

Science.gov (United States)

Benaziz, Marouane; Nacivet, Samuel; Thouverez, Fabrice

2015-08-01

Shock absorbers are often responsible for undesirable structure-borne noise in cars. The early numerical prediction of this noise in the automobile development process can save time and money and yet remains a challenge for industry. In this paper, a new approach to predicting shock absorber structure-borne noise is proposed; it consists in modelling the shock absorber and including the main nonlinear phenomena responsible for discontinuities in the response. The model set forth herein features: compressible fluid behaviour, nonlinear flow rate-pressure relations, valve mechanical equations and rubber mounts. The piston, base valve and complete shock absorber model are compared with experimental results. Sensitivity of the shock absorber response is evaluated and the most important parameters are classified. The response envelope is also computed. This shock absorber model is able to accurately reproduce local nonlinear phenomena and improves our state of knowledge on potential noise sources within the shock absorber.

Experimental Study of Shock Generated Compressible Vortex Ring

Science.gov (United States)

Das, Debopam; Arakeri, Jaywant H.; Krothapalli, Anjaneyulu

2000-11-01

Formation of a compressible vortex ring and generation of sound associated with it is studied experimentally. Impulse of a shock wave is used to generate a vortex ring from the open end of a shock-tube. Vortex ring formation process has been studied in details using particle image Velocimetry (PIV). As the shock wave exits the tube it diffracts and expands. A circular vortex sheet forms at the edge and rolls up into a vortex ring. Far field microphone measurement shows that the acoustic pressure consists of a spike due to shock wave followed by a low frequency pressure wave of decaying nature, superimposed with high frequency pressure wave. Acoustic waves consist of waves due to expansion, waves formed in the tube during diaphragm breakage and waves associated with the vortex ring and shear-layer vortices. Unsteady evolution of the vortex ring and shear-layer vortices in the jet behind the ring is studied by measuring the velocity field using PIV. Corresponding vorticity field, circulation around the vortex core and growth rate of the vortex core is calculated from the measured velocity field. The velocity field in a compressible vortex ring differs from that of an incompressible ring due to the contribution from both shock and vortex ring.

Aeroheating Measurement of Apollo Shaped Capsule with Boundary Layer Trip in the Free-piston Shock Tunnel HIEST

Science.gov (United States)

Hideyuki, TANNO; Tomoyuki, KOMURO; Kazuo, SATO; Katsuhiro, ITOH; Lillard, Randolph P.; Olejniczak, Joseph

2013-01-01

An aeroheating measurement test campaign of an Apollo capsule model with laminar and turbulent boundary layer was performed in the free-piston shock tunnel HIEST at JAXA Kakuda Space Center. A 250mm-diameter 6.4%-scaled Apollo CM capsule model made of SUS-304 stainless steel was applied in this study. To measure heat flux distribution, the model was equipped with 88 miniature co-axial Chromel-Constantan thermocouples on the heat shield surface of the model. In order to promote boundary layer transition, a boundary layer trip insert with 13 "pizza-box" isolated roughness elements, which have 1.27mm square, were placed at 17mm below of the model geometric center. Three boundary layer trip inserts with roughness height of k=0.3mm, 0.6mm and 0.8mm were used to identify the appropriate height to induce transition. Heat flux records with or without roughness elements were obtained for model angles of attack 28º under stagnation enthalpy between H(sub 0)=3.5MJ/kg to 21MJ/kg and stagnation pressure between P(sub 0)=14MPa to 60MPa. Under the condition above, Reynolds number based on the model diameter was varied from 0.2 to 1.3 million. With roughness elements, boundary layer became fully turbulent less than H(sub 0)=9MJ/kg condition. However, boundary layer was still laminar over H(sub 0)=13MJ/kg condition even with the highest roughness elements. An additional experiment was also performed to correct unexpected heat flux augmentation observed over H(sub 0)=9MJ/kg condition.

Study of equation-of-state of dense helium

International Nuclear Information System (INIS)

Cai Lingcang; Zhang Lin; Xiang Shikai; Jing Fuqian

2001-01-01

Hugoniot EOS, shock temperature of gas helium plasma (the initial pressure is 1.2 MPa and the initial temperature is 293 K) are measured with the help of shock compression technique and transient radiation pyrometer. The experimental Hugoniot data are good agreement with the theoretical prediction by Saha equation pus Debye-Huckel correction

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2014-01-01

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

Sparse dynamics for partial differential equations.

Science.gov (United States)

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

2013-04-23

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Investigation of magnetic flux transport and shock formation in a staged Z-pinch

Science.gov (United States)

Narkis, J.; Rahman, H. U.; Wessel, F. J.; Beg, F. N.

2017-10-01

Target preheating is an integral component of magnetized inertial fusion in reducing convergence ratio. In the staged Z-pinch concept, it is achieved via one or more shocks. Previous work [Narkis et al., Phys. Plasmas 23, 122706 (2016)] found that shock formation in the target occurred earlier in higher-Z liners due to faster flux transport to the target/liner interface. However, a corresponding increase in magnitude of magnetic pressure was not observed, and target implosion velocity (and therefore shock strength) remained unchanged. To investigate other means of increasing the magnitude of transported flux, a Korteweg-de Vries-Burgers equation from the 1-D single-fluid, resistive magnetohydrodynamic equations is obtained. Solutions to the nondispersive (i.e., Burgers) equation depend on nondimensional coefficients, whose dependence on liner density, temperature, etc., suggests an increase in target implosion velocity, and therefore shock strength, can be obtained by tailoring the mass of a single-liner gas puff to a double-liner configuration. In the selected test cases of 1-D simulated implosions of krypton on deuterium, the peak Mach number increased from ˜ 5 to ˜ 8 . While a notable increase was seen, Mach numbers exceeding 10 (implosion velocities exceeding ˜25 cm/μs) are necessary for adequate shock preheating.

ShockWave science and technology reference library

CERN Document Server

2007-01-01

This book is the first of several volumes on solids in the Shock Wave Science and Technology Reference Library. These volumes are primarily concerned with high-pressure shock waves in solid media, including detonation, high-velocity impact, and penetration. Of the eight chapters in this volume three chapters survey recent, exciting experimental advances in - ultra-short shock dynamics at the atomic and molecular scale (D.S. More, S.D. Mcgrane, and D.J. Funk), - Z accelerator for ICE and Shock compression (M.D. Knudson), and - failure waves in glass and ceramics (S.J. Bless and N.S. Brar). The subsequent four chapters are foundational, and cover the subjects of - equation of state (R. Menikoff), - elastic-plastic shock waves (R. Menikoff), - continuum plasticity (R. M. Brannon), and - numerical methods (D. J. Benson). The last chapter, but not the least, describes a tour de force illustration of today’s computing power in - modeling heterogeneous reactive solids at the grain scale (M.R. Baer). All chapters a...

Vorticity generation and evolution in shock-accelerated density-stratified interfaces

International Nuclear Information System (INIS)

Yang, X.; Chern, I.; Zabusky, N.J.; Samtaney, R.; Hawley, J.F.

1992-01-01

The results of direct numerical simulations of inviscid planar shock-accelerated density-stratified interfaces in two dimensions are presented and compared with shock tube experiments of Haas [(private communication, 1988)] and Sturtevant [in Shock Tubes and Waves, edited by H. Gronig (VCH, Berlin, 1987), p. 89] . Heavy-to-light (''slow/fast or s/f) and light-to-heavy (''fast/slow,'' or f/s) gas interfaces are examined and early-time impulsive vorticity deposition and the evolution of coherent vortex structures are emphasized and quantified. The present second-order Godunov scheme yields excellent agreement with shock-polar analyses at early time. A more physical vortex interpretation explains the commonly used (i.e., linear paradigm) designations of ''unstable'' and ''stable'' for the f/s and s/f interfaces, respectively. The later time events are Rayleigh--Taylor like and can be described in terms of the evolution of a vortex layer (large-scale translation and rotation): asymmetric tip vortex ''roll-up'' and ''binding;'' layer ''instability;'' convective mixing; and baroclinic vorticity generation from secondary shock--interface interactions

28th International Symposium on Shock Waves

CERN Document Server

2012-01-01

The University of Manchester hosted the 28th International Symposium on Shock Waves between 17 and 22 July 2011. The International Symposium on Shock Waves first took place in 1957 in Boston and has since become an internationally acclaimed series of meetings for the wider Shock Wave Community. The ISSW28 focused on the following areas: Blast Waves, Chemically Reacting Flows, Dense Gases and Rarefied Flows, Detonation and Combustion, Diagnostics, Facilities, Flow Visualisation, Hypersonic Flow, Ignition, Impact and Compaction, Multiphase Flow, Nozzle Flow, Numerical Methods, Propulsion, Richtmyer-Meshkov, Shockwave Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shockwave Phenomena and Applications, as well as Medical and Biological Applications. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 28 and individuals interested in these fields.

Some techniques and results from high-pressure shock-wave experiments utilizing the radiation from shocked transparent materials

International Nuclear Information System (INIS)

McQueen, R.G.; Fritz, J.N.

1981-01-01

It has been known for many years that some transparent materials emit radiation when shocked to high pressures. This property was used to determine the temperature of shocked fused and crystal quartz, which in turn allowed the thermal expansion of SiO 2 at high pressure and also the specific heat to be calculated. Once the radiative energy as a function of pressure is known for one material it is shown how this can be used to determine the temperature of other transparent materials. By the nature of the experiments very accurate shock velocities can be measured and hence high quality equation of state data obtained. Some techniques and results are presented on measuring sound velocities from symmetrical impact of nontransparent materials using radiation emitting transparent analyzers, and on nonsymmetrical impact experiments on transparent materials. Because of special requirements in the later experiments, techniques were developed that lead to very high-precision shock-wave data. Preliminary results, using these techniques are presented for making estimates of the melting region and the yield strength of some metals under strong shock conditions

On Poor Separation in Magnetically Driven Shock Tube

DEFF Research Database (Denmark)

Chang, C.T.

1973-01-01

Observations made at steady-state running conditions in a magnetically driven shock tube, with parallel-plate electrodes, showed that for a given discharge voltage, sufficient separation between the shock and the current-sheet occurred only at relatively high discharge pressures. As a comparison......, poor separations were also noted in conventional diaphragm-type shock tubes running at low initial pressures. It is demonstrated that the observed poor separation can be explained by a mass leakage, instead of through the wall boundary layer, but through the current-sheet itself....

Chondrule destruction in nebular shocks

Energy Technology Data Exchange (ETDEWEB)

Jacquet, Emmanuel; Thompson, Christopher, E-mail: ejacquet@mnhn.fr [Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St George Street, Toronto, ON M5S 3H8 (Canada)

2014-12-10

Chondrules are millimeter-sized silicate spherules ubiquitous in primitive meteorites, but whose origin remains mysterious. One of the main proposed mechanisms for producing them is melting of solids in shock waves in the gaseous protoplanetary disk. However, evidence is mounting that chondrule-forming regions were enriched in solids well above solar abundances. Given the high velocities involved in shock models, destructive collisions would be expected between differently sized grains after passage of the shock front as a result of differential drag. We investigate the probability and outcome of collisions of particles behind a one-dimensional shock using analytic methods as well as a full integration of the coupled mass, momentum, energy, and radiation equations. Destruction of protochondrules seems unavoidable for solid/gas ratios ε ≳ 0.1, and possibly even for solar abundances because of 'sandblasting' by finer dust. A flow with ε ≳ 10 requires much smaller shock velocities (∼2 versus 8 km s{sup –1}) in order to achieve chondrule-melting temperatures, and radiation trapping allows slow cooling of the shocked fragments. Initial destruction would still be extensive; although re-assembly of millimeter-sized particles would naturally occur by grain sticking afterward, the compositional heterogeneity of chondrules may be difficult to reproduce. We finally note that solids passing through small-scale bow shocks around few kilometer-sized planetesimals might experience partial melting and yet escape fragmentation.

Study of the response of Zircaloy- 4 cladding to thermal shock during water quenching after double sided steam oxidation at elevated temperatures

Energy Technology Data Exchange (ETDEWEB)

Sawarn, Tapan K., E-mail: sawarn@barc.gov.in; Banerjee, Suparna; Kumar, Sunil

2016-05-15

This study investigates the failure of embrittled Zircaloy-4 cladding in a simulated loss of coolant accident condition and correlates it with the evolved stratified microstructure. Isothermal steam oxidation of Zircaloy-4 cladding at high temperatures (900–1200 °C) with soaking periods in the range 60–900 s followed by water quenching was carried out. The combined oxide + oxygen stabilized α-Zr layer thickness and the fraction of the load bearing phase (recrystallised α-Zr grains + prior β-Zr or only prior β-Zr) of clad tube specimens were correlated with the %ECR calculated using Baker-Just equation. Average oxygen concentration of the load bearing phase corresponding to different oxidation conditions was calculated from the average microhardness using an empirical correlation. The results of these experiments are presented in this paper. Thermal shock sustainability of the clad was correlated with the %ECR, combined oxide+α-Zr(O) layer thickness, fraction of the load bearing phase and its average oxygen concentration. - Highlights: • Response of the embrittled Zircaloy-4 clad towards thermal shock, simulated under LOCA condition was investigated. • Thermal shock sustainability of the clad was correlated with its evolved stratified microstructure. • Cladding fails at %ECR value ≥ 29. • To resist the thermal shock, clad should have load bearing phase fraction > 0.44 and average oxygen concentration < 0.69 wt%.

Shock compression parameters for a boron-loaded, silicone-rubber composite

International Nuclear Information System (INIS)

Gust, W.H.; Van Thiel, M.; Gathers, G.R.

1975-01-01

Hugoniot parameters under uniaxial-shock-wave-loading from 0.03 to 0.6 Mbar are presented for a composite with 70 wt percent boron loaded in a silicone-rubber matrix. The plot of shock velocity vs particle velocity was found to be nonlinear. Equations that describe fits of the data are presented. (U.S.)

Stability analysis of a boundary layer over a hump using parabolized stability equations

Energy Technology Data Exchange (ETDEWEB)

Gao, B; Park, D H; Park, S O, E-mail: sopark@kaist.ac.kr [Division of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Gusong-dong, Yusong-gu, Daejeon 305-701 (Korea, Republic of)

2011-10-15

Parabolized stability equations (PSEs) were used to investigate the stability of boundary layer flows over a small hump. The applicability of PSEs to flows with a small separation bubble was examined by comparing the result with DNS data. It was found that PSEs can efficiently track the disturbance waves with an acceptable accuracy in spite of a small separation bubble. A typical evolution scenario of Tollmien-Schlichting (TS) wave is presented. The adverse pressure gradient and the flow separation due to the hump have a strong effect on the amplification of the disturbances. The effect of hump width and height is also examined. When the width of the hump is reduced, the amplification factor is increased. The height of the hump is found to obviously influence the stability only when it is greater than the critical layer thickness.

Stability analysis of a boundary layer over a hump using parabolized stability equations

International Nuclear Information System (INIS)

Gao, B; Park, D H; Park, S O

2011-01-01

Parabolized stability equations (PSEs) were used to investigate the stability of boundary layer flows over a small hump. The applicability of PSEs to flows with a small separation bubble was examined by comparing the result with DNS data. It was found that PSEs can efficiently track the disturbance waves with an acceptable accuracy in spite of a small separation bubble. A typical evolution scenario of Tollmien-Schlichting (TS) wave is presented. The adverse pressure gradient and the flow separation due to the hump have a strong effect on the amplification of the disturbances. The effect of hump width and height is also examined. When the width of the hump is reduced, the amplification factor is increased. The height of the hump is found to obviously influence the stability only when it is greater than the critical layer thickness.

Evolution of scalar and velocity dynamics in planar shock-turbulence interaction

Science.gov (United States)

Boukharfane, R.; Bouali, Z.; Mura, A.

2018-01-01

Due to the short residence time of air in supersonic combustors, achieving efficient mixing in compressible turbulent reactive flows is crucial for the design of supersonic ramjet (Scramjet) engines. In this respect, improving the understanding of shock-scalar mixing interactions is of fundamental importance for such supersonic combustion applications. In these compressible flows, the interaction between the turbulence and the shock wave is reciprocal, and the coupling between them is very strong. A basic understanding of the physics of such complex interactions has already been obtained through the analysis of relevant simplified flow configurations, including propagation of the shock wave in density-stratified media, shock-wave-mixing-layer interaction, and shock-wave-vortex interaction. Amplification of velocity fluctuations and substantial changes in turbulence characteristic length scales are the most well-known outcomes of shock-turbulence interaction, which may also deeply influence scalar mixing between fuel and oxidizer. The effects of the shock wave on the turbulence have been widely characterized through the use of so-called amplification factors, and similar quantities are introduced herein to characterize the influence of the shock wave on scalar mixing. One of the primary goals of the present study is indeed to extend previous analyses to the case of shock-scalar mixing interaction, which is directly relevant to supersonic combustion applications. It is expected that the shock wave will affect the scalar dissipation rate (SDR) dynamics. Special emphasis is placed on the modification of the so-called turbulence-scalar interaction as a leading-order contribution to the production of mean SDR, i.e., a quantity that defines the mixing rate and efficiency. To the best of the authors' knowledge, this issue has never been addressed in detail in the literature, and the objective of the present study is to scrutinize this influence. The turbulent mixing of a

Measurement of the equation of state of porous materials through the use of shock waves generated by laser radiation; Mesure de l'equation d'etat de materiaux poreux a l'aide d'ondes de choc generees par laser

Energy Technology Data Exchange (ETDEWEB)

Philippe, F

2001-12-15

This work aims at measuring the equation of state of porous plastic materials in the view of their use in inertial confinement fusion. We have experimentally determined the shock polar curve of TMPTA (C{sub 15}H{sub 20}O{sub 6}) by the use of the impedance matching technique. This technique is based on the simultaneous measurement of the shock velocities in the 2 materials composing the target. The shock polar curve has been drawn for pressures ranging from 10 kbar to 3 Mbar and densities from 20 mg/cm{sup 3} to 1.1 g/cm{sup 3}. The use of a slit sweep camera to assess the propagation of the shock wave through the target has limited the accuracy of the technique to 10%. Experimental results match well data provided by the Sesame tables that are broadly used by hydrodynamic codes. Nevertheless the statistical distribution of experimental points seems to show a lower compressibility of the foam that might be attributed to a slight pre-heating process or to the effect of the foam micro-structure on the shock wave propagation. In order to improve the accuracy of the method, an attempt was made to use an active doppler interferometric diagnostic to measure shock wave velocities. It has been showed that the shock wave front in the foam is reflecting enough to make this method relevant if we can overcome the difficulty of a high luminous background. Despite that, we have succeeded in measuring with high accuracy, a point of the shock polar curve for 800 mg/cm{sup 3} dense TMPTA. (A.C.)

A Source-Term Based Boundary Layer Bleed/Effusion Model for Passive Shock Control

Science.gov (United States)

Baurle, Robert A.; Norris, Andrew T.

2011-01-01

A modeling framework for boundary layer effusion has been developed based on the use of source (or sink) terms instead of the usual practice of specifying bleed directly as a boundary condition. This framework allows the surface boundary condition (i.e. isothermal wall, adiabatic wall, slip wall, etc.) to remain unaltered in the presence of bleed. This approach also lends itself to easily permit the addition of empirical models for second order effects that are not easily accounted for by simply defining effective transpiration values. Two effusion models formulated for supersonic flows have been implemented into this framework; the Doerffer/Bohning law and the Slater formulation. These models were applied to unit problems that contain key aspects of the flow physics applicable to bleed systems designed for hypersonic air-breathing propulsion systems. The ability of each model to predict bulk bleed properties was assessed, as well as the response of the boundary layer as it passes through and downstream of a porous bleed system. The model assessment was performed with and without the presence of shock waves. Three-dimensional CFD simulations that included the geometric details of the porous plate bleed systems were also carried out to supplement the experimental data, and provide additional insights into the bleed flow physics. Overall, both bleed formulations fared well for the tests performed in this study. However, the sample of test problems considered in this effort was not large enough to permit a comprehensive validation of the models.

Two-fluid dusty shocks: simple benchmarking problems and applications to protoplanetary discs

Science.gov (United States)

Lehmann, Andrew; Wardle, Mark

2018-05-01

The key role that dust plays in the interstellar medium has motivated the development of numerical codes designed to study the coupled evolution of dust and gas in systems such as turbulent molecular clouds and protoplanetary discs. Drift between dust and gas has proven to be important as well as numerically challenging. We provide simple benchmarking problems for dusty gas codes by numerically solving the two-fluid dust-gas equations for steady, plane-parallel shock waves. The two distinct shock solutions to these equations allow a numerical code to test different forms of drag between the two fluids, the strength of that drag and the dust to gas ratio. We also provide an astrophysical application of J-type dust-gas shocks to studying the structure of accretion shocks on to protoplanetary discs. We find that two-fluid effects are most important for grains larger than 1 μm, and that the peak dust temperature within an accretion shock provides a signature of the dust-to-gas ratio of the infalling material.

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

Science.gov (United States)

Parker, L. N.; Zank, G. P.

2013-12-01

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Shock and Detonation Physics at Los Alamos National Laboratory

Energy Technology Data Exchange (ETDEWEB)

Robbins, David L [Los Alamos National Laboratory; Dattelbaum, Dana M [Los Alamos National Laboratory; Sheffield, Steve A [Los Alamos National Laboratory

2012-08-22

WX-9 serves the Laboratory and the Nation by delivering quality technical results, serving customers that include the Nuclear Weapons Program (DOE/NNSA), the Department of Defense, the Department of Homeland Security and other government agencies. The scientific expertise of the group encompasses equations-of-state, shock compression science, phase transformations, detonation physics including explosives initiation, detonation propagation, and reaction rates, spectroscopic methods and velocimetry, and detonation and equation-of-state theory. We are also internationally-recognized in ultra-fast laser shock methods and associated diagnostics, and are active in the area of ultra-sensitive explosives detection. The facility capital enabling the group to fulfill its missions include a number of laser systems, both for laser-driven shocks, and spectroscopic analysis, high pressure gas-driven guns and powder guns for high velocity plate impact experiments, explosively-driven techniques, static high pressure devices including diamond anvil cells and dilatometers coupled with spectroscopic probes, and machine shops and target fabrication facilities.

Structure of intermediate shocks and slow shocks in a magnetized plasma with heat conduction

International Nuclear Information System (INIS)

Tsai, C.L.; Wu, B.H.; Lee, L.C.

2005-01-01

The structure of slow shocks and intermediate shocks in the presence of a heat conduction parallel to the local magnetic field is simulated from the set of magnetohydrodynamic equations. This study is an extension of an earlier work [C. L. Tsai, R. H. Tsai, B. H. Wu, and L. C. Lee, Phys. Plasmas 9, 1185 (2002)], in which the effects of heat conduction are examined for the case that the tangential magnetic fields on the two side of initial current sheet are exactly antiparallel (B y =0). For the B y =0 case, a pair of slow shocks is formed as the result of evolution of the initial current sheet, and each slow shock consists of two parts: the isothermal main shock and the foreshock. In the present paper, cases with B y ≠0 are also considered, in which the evolution process leads to the presence of an additional pair of time-dependent intermediate shocks (TDISs). Across the main shock of the slow shock, jumps in plasma density, velocity, and magnetic field are significant, but the temperature is continuous. The plasma density downstream of the main shock decreases with time, while the downstream temperature increases with time, keeping the downstream pressure constant. The foreshock is featured by a smooth temperature variation and is formed due to the heat flow from downstream to upstream region. In contrast to the earlier study, the foreshock is found to reach a steady state with a constant width in the slow shock frame. In cases with B y ≠0, the plasma density and pressure increase and the magnetic field decreases across TDIS. The TDIS initially can be embedded in the slow shock's foreshock structure, and then moves out of the foreshock region. With an increasing B y , the propagation speed of foreshock leading edge tends to decrease and the foreshock reaches its steady state at an earlier time. Both the pressure and temperature downstreams of the main shock decrease with increasing B y . The results can be applied to the shock heating in the solar corona and

Efficient electron heating in relativistic shocks and gamma-ray-burst afterglow.

Science.gov (United States)

Gedalin, M; Balikhin, M A; Eichler, D

2008-02-01

Electrons in shocks are efficiently energized due to the cross-shock potential, which develops because of differential deflection of electrons and ions by the magnetic field in the shock front. The electron energization is necessarily accompanied by scattering and thermalization. The mechanism is efficient in both magnetized and nonmagnetized relativistic electron-ion shocks. It is proposed that the synchrotron emission from the heated electrons in a layer of strongly enhanced magnetic field is responsible for gamma-ray-burst afterglows.

Gamma-ray emission from internal shocks in novae

Science.gov (United States)

Martin, P.; Dubus, G.; Jean, P.; Tatischeff, V.; Dosne, C.

2018-04-01

Context. Gamma-ray emission at energies ≥100 MeV has been detected from nine novae using the Fermi Large Area Telescope (LAT), and can be explained by particle acceleration at shocks in these systems. Eight out of these nine objects are classical novae in which interaction of the ejecta with a tenuous circumbinary material is not expected to generate detectable gamma-ray emission. Aim. We examine whether particle acceleration at internal shocks can account for the gamma-ray emission from these novae. The shocks result from the interaction of a fast wind radiatively-driven by nuclear burning on the white dwarf with material ejected in the initial runaway stage of the nova outburst. Methods: We present a one-dimensional model for the dynamics of a forward and reverse shock system in a nova ejecta, and for the associated time-dependent particle acceleration and high-energy gamma-ray emission. Non-thermal proton and electron spectra are calculated by solving a time-dependent transport equation for particle injection, acceleration, losses, and escape from the shock region. The predicted emission is compared to LAT observations of V407 Cyg, V1324 Sco, V959 Mon, V339 Del, V1369 Cen, and V5668 Sgr. Results: The ≥100 MeV gamma-ray emission arises predominantly from particles accelerated up to 100 GeV at the reverse shock and undergoing hadronic interactions in the dense cooling layer downstream of the shock. The emission rises within days after the onset of the wind, quickly reaches a maximum, and its subsequent decrease reflects mostly the time evolution of the wind properties. Comparison to gamma-ray data points to a typical scenario where an ejecta of mass 10-5-10-4 M⊙ expands in a homologous way with a maximum velocity of 1000-2000 km s-1, followed within a day by a wind with a velocity values of which result in the majority of best-fit models having gamma-ray spectra with a high-energy turnover below 10 GeV. Our typical model is able to account for the main

A multi-phase equation of state for solid and liquid lead

International Nuclear Information System (INIS)

Robinson, C.M.

2004-01-01

This paper considers a multi-phase equation of state for solid and liquid lead. The thermodynamically consistent equation of state is constructed by calculating separate equations of state for the solid and liquid phases. The melt curve is the curve in the pressure, temperature plane where the Gibb's free energy of the solid and liquid phases are equal. In each phase a complete equation of state is obtained using the assumptions that the specific heat capacity is constant and that the Grueneisen parameter is proportional to the specific volume. The parameters for the equation of state are obtained from experimental data. In particular they are chosen to match melt curve and principal Hugoniot data. Predictions are made for the shock pressure required for melt to occur on shock and release

Nonlinearity, Conservation Law and Shocks

Indian Academy of Sciences (India)

However, genuine nonlinearity is always present in an ideal gas. The conservation form of the equation (25) brings in shocks which cut off the growing part of the amplitUde as shown in. Figure 15. Acknowledgements. The author sincerely thanks the two referees whose valuable comments led to an improvement of the ...

Ab Initio Studies of Shock-Induced Chemical Reactions of Inter-Metallics

Science.gov (United States)

Zaharieva, Roussislava; Hanagud, Sathya

2009-06-01

Shock-induced and shock assisted chemical reactions of intermetallic mixtures are studied by many researchers, using both experimental and theoretical techniques. The theoretical studies are primarily at continuum scales. The model frameworks include mixture theories and meso-scale models of grains of porous mixtures. The reaction models vary from equilibrium thermodynamic model to several non-equilibrium thermodynamic models. The shock-effects are primarily studied using appropriate conservation equations and numerical techniques to integrate the equations. All these models require material constants from experiments and estimates of transition states. Thus, the objective of this paper is to present studies based on ab initio techniques. The ab inito studies, to date, use ab inito molecular dynamics. This paper presents a study that uses shock pressures, and associated temperatures as starting variables. Then intermetallic mixtures are modeled as slabs. The required shock stresses are created by straining the lattice. Then, ab initio binding energy calculations are used to examine the stability of the reactions. Binding energies are obtained for different strain components super imposed on uniform compression and finite temperatures. Then, vibrational frequencies and nudge elastic band techniques are used to study reactivity and transition states. Examples include Ni and Al.

Hybrid simulation techniques applied to the earth's bow shock

Science.gov (United States)

Winske, D.; Leroy, M. M.

1985-01-01

The application of a hybrid simulation model, in which the ions are treated as discrete particles and the electrons as a massless charge-neutralizing fluid, to the study of the earth's bow shock is discussed. The essentials of the numerical methods are described in detail; movement of the ions, solution of the electromagnetic fields and electron fluid equations, and imposition of appropriate boundary and initial conditions. Examples of results of calculations for perpendicular shocks are presented which demonstrate the need for a kinetic treatment of the ions to reproduce the correct ion dynamics and the corresponding shock structure. Results for oblique shocks are also presented to show how the magnetic field and ion motion differ from the perpendicular case.

Model for calculating shock loading and release paths for multicomponent geologic media

International Nuclear Information System (INIS)

Butkovich, T.R.; Moran, B.; Burton, D.E.

1981-07-01

A model has been devised to calculate shock Hugoniots and release paths off the Hugoniots for multicomponent rocks containing silicate, carbonate, and water. Hugoniot equations of state are constructed from relatively simple measurements of rock properties including bulk density, grain density of the silicate component, and weight fractions of water and carbonate. Release paths off the composite Hugoniot are calculated by mixing release paths off the component Hugoniots according to their weight fractions. If the shock imparts sufficient energy to the component to cause vaporization, a gas equation of state is used to calculate the release paths. For less energetic shocks, the rock component will unload like a solid or liquid, taking into account the irreversible removal of air-filled porosity

Analytical solutions of hypersonic type IV shock - shock interactions

Science.gov (United States)

Frame, Michael John

An analytical model has been developed to predict the effects of a type IV shock interaction at high Mach numbers. This interaction occurs when an impinging oblique shock wave intersects the most normal portion of a detached bow shock. The flowfield which develops is complicated and contains an embedded jet of supersonic flow, which may be unsteady. The jet impinges on the blunt body surface causing very high pressure and heating loads. Understanding this type of interaction is vital to the designers of cowl lips and leading edges on air- breathing hypersonic vehicles. This analytical model represents the first known attempt at predicting the geometry of the interaction explicitly, without knowing beforehand the jet dimensions, including the length of the transmitted shock where the jet originates. The model uses a hyperbolic equation for the bow shock and by matching mass continuity, flow directions and pressure throughout the flowfield, a prediction of the interaction geometry can be derived. The model has been shown to agree well with the flowfield patterns and properties of experiments and CFD, but the prediction for where the peak pressure is located, and its value, can be significantly in error due to a lack of sophistication in the model of the jet fluid stagnation region. Therefore it is recommended that this region of the flowfield be modeled in more detail and more accurate experimental and CFD measurements be used for validation. However, the analytical model has been shown to be a fast and economic prediction tool, suitable for preliminary design, or for understanding the interactions effects, including the basic physics of the interaction, such as the jet unsteadiness. The model has been used to examine a wide parametric space of possible interactions, including different Mach number, impinging shock strength and location, and cylinder radius. It has also been used to examine the interaction on power-law shaped blunt bodies, a possible candidate for

Acceleration of Solar Energetic Particles at a Fast Traveling Shock in Non-uniform Coronal Conditions

Science.gov (United States)

Le Roux, J. A.; Arthur, A. D.

2017-09-01

Time-dependent solar energetic particle (SEP) acceleration is investigated at a fast, nearly parallel spherical traveling shock in the strongly non-uniform corona by solving the standard focused transport equation for SEPs and transport equations for parallel propagating Alfvén waves that form a set of coupled equations. This enables the modeling of self-excitation of Alfvén waves in the inertial range by SEPs ahead of the shock and its role in enhancing the efficiency of the diffusive shock acceleration (DSA) of SEPs in a self-regulatory fashion. Preliminary results suggest that, because of the highly non-uniform coronal conditions that the shock encounters, both DSA and wave excitation are highly time-dependent processes. Thus, DSA spectra of SEPs strongly deviate from the simple power-law prediction of standard steady-state DSA theory and initially strong wave excitation weakens rapidly. Consequently, the ability of DSA to produce high energy SEPs in the corona of ∼1 GeV, as observed in the strongest gradual SEP events, appears to be strongly curtailed at a fast nearly parallel shock, but further research is needed before final conclusions can be drawn.

Shock waves in helium at low temperatures

International Nuclear Information System (INIS)

Liepmann, H.W.; Torczynski, J.R.

1986-01-01

Results are reported from studies of the properties of low temperature He-4 using shock waves as a probe. Ideal shock tube theory is used to show that sonic speeds of Mach 40 are attainable in He at 300 K. Viscosity reductions at lower temperatures minimize boundary layer effects at the side walls. A two-fluid model is described to account for the phase transition which He undergoes at temperatures below 2.2 K, after which the quantum fluid (He II) and the normal compressed superfluid (He I) coexist. Analytic models are provided for pressure-induced shocks in He I and temperature-induced shock waves (called second sound) which appear in He II. The vapor-fluid interface of He I is capable of reflecting second and gasdynamic sound shocks, which can therefore be used as probes for studying phase transitions between He I and He II. 17 references

Equations of state of detonation products: ammonia and methane

Science.gov (United States)

Lang, John; Dattelbaum, Dana; Goodwin, Peter; Garcia, Daniel; Coe, Joshua; Leiding, Jeffery; Gibson, Lloyd; Bartram, Brian

2015-06-01

Ammonia (NH3) and methane (CH4) are two principal product gases resulting from explosives detonation, and the decomposition of other organic materials under shockwave loading (such as foams). Accurate thermodynamic descriptions of these gases are important for understanding the detonation performance of high explosives. However, shock compression data often do not exist for molecular species in the dense gas phase, and are limited in the fluid phase. Here, we present equation of state measurements of elevated initial density ammonia and methane gases dynamically compressed in gas-gun driven plate impact experiments. Pressure and density of the shocked gases on the principal Hugoniot were determined from direct particle velocity and shock wave velocity measurements recorded using optical velocimetry (Photonic Doppler velocimetry (PDV) and VISAR (velocity interferometer system for any reflector)). Streak spectroscopy and 5-color pyrometry were further used to measure the emission from the shocked gases, from which the temperatures of the shocked gases were estimated. Up to 0.07 GPa, ammonia was not observed to ionize, with temperature remaining below 7000 K. These results provide quantitative measurements of the Hugoniot locus for improving equations of state models of detonation products.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter.

Science.gov (United States)

Fovargue, Daniel E; Mitran, Sorin; Smith, Nathan B; Sankin, Georgy N; Simmons, Walter N; Zhong, Pei

2013-08-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model.

The shock formation distance in a bounded sound beam of finite amplitude.

Science.gov (United States)

Tao, Chao; Ma, Jian; Zhu, Zhemin; Du, Gonghuan; Ping, Zihong

2003-07-01

This paper investigates the shock formation distance in a bounded sound beam of finite amplitude by solving the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation using frequency-domain numerical method. Simulation results reveal that, besides the nonlinearity and absorption, the diffraction is another important factor that affects the shock formation of a bounded sound beam. More detailed discussions of the shock formation in a bounded sound beam, such as the waveform of sound pressure and the spatial distribution of shock formation, are also presented and compared for different parameters.

HIFiRE-1 Turbulent Shock Boundary Layer Interaction - Flight Data and Computations

Science.gov (United States)

Kimmel, Roger L.; Prabhu, Dinesh

2015-01-01

The Hypersonic International Flight Research Experimentation (HIFiRE) program is a hypersonic flight test program executed by the Air Force Research Laboratory (AFRL) and Australian Defence Science and Technology Organisation (DSTO). This flight contained a cylinder-flare induced shock boundary layer interaction (SBLI). Computations of the interaction were conducted for a number of times during the ascent. The DPLR code used for predictions was calibrated against ground test data prior to exercising the code at flight conditions. Generally, the computations predicted the upstream influence and interaction pressures very well. Plateau pressures on the cylinder were predicted well at all conditions. Although the experimental heat transfer showed a large amount of scatter, especially at low heating levels, the measured heat transfer agreed well with computations. The primary discrepancy between the experiment and computation occurred in the pressures measured on the flare during second stage burn. Measured pressures exhibited large overshoots late in the second stage burn, the mechanism of which is unknown. The good agreement between flight measurements and CFD helps validate the philosophy of calibrating CFD against ground test, prior to exercising it at flight conditions.

Analysis of turbulent boundary layers

CERN Document Server

Cebeci, Tuncer

1974-01-01

Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculati

Cavitation cluster dynamics in shock-wave lithotripsy: Part I

NARCIS (Netherlands)

Arora, M.; Junge, L.; Junge, L.; Ohl, C.D.

2005-01-01

The spatiotemporal dynamics of cavitation bubble growth and collapse in shock-wave lithotripsy in a free field was studied experimentally. The lithotripter was equipped with two independently triggerable layers of piezoceramics. The front and back layers generated positive pressure amplitudes of 30

Shock-jump conditions in a general medium: weak-solution approach

Science.gov (United States)

Forbes, L. K.; Krzysik, O. A.

2017-05-01

General conservation laws are considered, and the concept of a weak solution is extended to the case of an equation involving three space variables and time. Four-dimensional vector calculus is used to develop general jump conditions at a shock wave in the material. To illustrate the use of this result, jump conditions at a shock in unsteady three-dimensional compressible gas flow are presented. It is then proved rigorously that these reduce to the commonly assumed conditions in coordinates normal and tangential to the shock face. A similar calculation is also outlined for an unsteady three-dimensional shock in magnetohydrodynamics, and in a chemically reactive fluid. The technique is available for determining shock-jump conditions in quite general continuous media.

The acceleration of particles at propagating interplanetary shocks

Science.gov (United States)

Prinsloo, P. L.; Strauss, R. D. T.

2017-12-01

Enhancements of charged energetic particles are often observed at Earth following the eruption of coronal mass ejections (CMEs) on the Sun. These enhancements are thought to arise from the acceleration of those particles at interplanetary shocks forming ahead of CMEs, propagating into the heliosphere. In this study, we model the acceleration of these energetic particles by solving a set of stochastic differential equations formulated to describe their transport and including the effects of diffusive shock acceleration. The study focuses on how acceleration at halo-CME-driven shocks alter the energy spectra of non-thermal particles, while illustrating how this acceleration process depends on various shock and transport parameters. We finally attempt to establish the relative contributions of different seed populations of energetic particles in the inner heliosphere to observed intensities during selected acceleration events.

Structure of shocks in solids and liquids: Six reprints with an introduction

International Nuclear Information System (INIS)

Wallace, D.C.

1991-01-01

This monograph consists of six papers on the theory of shocks in solids and liquids, reprinted from Physical Review, together with an introduction summarizing the complete shock theory and its limitations. The shock theory of this monograph is based on the principles of irreversible thermodynamics, characterized as follows. First, in equilibrium thermodynamics, materials are required to pass through states which lie on the equilibrium surface. In irreversible thermodynamics, materials pass through nonequilibrium states, but only those states which are close to the equilibrium surface, specifically, those states for which the equilibrium properties of temperature and entropy are still reasonably well defined. To construct an irreversible thermodynamic theory it is necessary to define the variables which measure the departure from equilibrium, to express the effect of these variables by a modification of the equilibrium thermodynamic equations, and to write an equation for the (irreversible) entropy generation. These principles are applied to planar shocks in the reprints collected here

Algebraic quantity equations before Fisher and Pigou

OpenAIRE

Thomas M. Humphrey

1984-01-01

Readers of this Review are doubtlessly familiar with the famous equation of exchange, MV=PQ, frequently employed to analyze the price level effects of monetary shocks. One might think the algebraic formulation of the equation is an outgrowth of the 20th century tendency toward mathematical modeling and statistical testing. Indeed, textbooks typically associate the transaction velocity version of the equation with Irving Fisher and the alternative Cambridge cash balance version with A. C. Pigo...

High-order shock-fitted detonation propagation in high explosives

Science.gov (United States)

Romick, Christopher M.; Aslam, Tariq D.

2017-03-01

A highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich-von Neumann-Döring (ZND) detonation wave, and Taylor-Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m /s, which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott-Stewart-Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting

Numerical simulation of the interaction of charged particles with oblique magnetohydrodynamic shocks

International Nuclear Information System (INIS)

Chen, G.L.

1975-01-01

The motion of high energy charged particles in ideal oblique MHD shocks, characteristic of the interplanetary medium, has been studied extensively. The shock is treated as a plane surface across which the tangential component of magnetic field changes discontinuously. The orbits of charged particles can be solved exactly from Lorentz force equation and initial conditions of particles in each region, pre- and post-shock, separately. The essential procedure is to determine the crossings and that has been achieved by solving numerically for the times when the particle meets the shock. The position and velocity vectors are continuous across the shock. An ensemble of 1972 monoenergetic particles distributed isotropically in the shock frame are chosen to obtain collective results

About potential of double layer and boundary value problems for Laplace equation

International Nuclear Information System (INIS)

Aleshin, M.V.

1991-01-01

An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C 2 class presented by a boundary of the finite domain in R 3 ). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

Shock wave convergence in water with parabolic wall boundaries

International Nuclear Information System (INIS)

Yanuka, D.; Shafer, D.; Krasik, Ya.

2015-01-01

The convergence of shock waves in water, where the cross section of the boundaries between which the shock wave propagates is either straight or parabolic, was studied. The shock wave was generated by underwater electrical explosions of planar Cu wire arrays using a high-current generator with a peak output current of ∼45 kA and rise time of ∼80 ns. The boundaries of the walls between which the shock wave propagates were symmetric along the z axis, which is defined by the direction of the exploding wires. It was shown that with walls having a parabolic cross section, the shock waves converge faster and the pressure in the vicinity of the line of convergence, calculated by two-dimensional hydrodynamic simulations coupled with the equations of state of water and copper, is also larger

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

Science.gov (United States)

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

SHOCK-JR: a computer program to analyze impact response of shipping container

International Nuclear Information System (INIS)

Ikushima, Takeshi; Nakazato, Chikara; Shimoda, Osamu; Uchino, Mamoru.

1983-02-01

The report is provided for using a computer program, SHOCK-JR, which is used to analyze the impact response of shipping containers. Descriptions are the mathematical model, method of analysis, structures of the program and the input and output variables. The program solves the equations of motion for a one-dimensional, lumped mass and nonlinear spring model. The solution procedure uses Runge-Kutta-Gill and Newmark-β methods. SHOCK-JR is a revised version of SHOCK, which was developed by ORNL. In SHOCK-JR, SI dimension is used and graphical output is available. (author)

Shadowgraph studies of laser-assisted non-thermal structuring of thin layers on flexible substrates by shock-wave-induced delamination processes

Energy Technology Data Exchange (ETDEWEB)

Lorenz, Pierre, E-mail: pierre.lorenz@iom-leipzig.de [Leibniz-Institut für Oberflächenmodifizierung e. V., Permoserstraße 15, 04318 Leipzig (Germany); Smausz, Tomi [Department of Optics and Quantum Electronics, University of Szeged, H-6720 Szeged, Dóm tér 9 (Hungary); MTA-SZTE Research Group on Photoacoustic Spectroscopy, University of Szeged, H-6720 Szeged, Dóm tér 9 (Hungary); Csizmadia, Tamas [Department of Optics and Quantum Electronics, University of Szeged, H-6720 Szeged, Dóm tér 9 (Hungary); Ehrhardt, Martin; Zimmer, Klaus [Leibniz-Institut für Oberflächenmodifizierung e. V., Permoserstraße 15, 04318 Leipzig (Germany); Hopp, Bela [Department of Optics and Quantum Electronics, University of Szeged, H-6720 Szeged, Dóm tér 9 (Hungary)

2015-05-01

Highlights: • The shock-wave-induced film delamination (SWIFD) is a laser patterning process. • The SWIFD process of CIGS solar cells was studied by shadowgraph measurements. • The study presented that SWIFD allows the structuring of CIGS solar cells. • The dynamics of the delamination process was analyzed. - Abstract: The laser-assisted microstructuring of thin films especially for electronic applications without damaging the layers or the substrates is a challenge for the laser micromachining techniques. The laser-induced thin-film patterning by ablation of the polymer substrate at the rear side that is called ‘SWIFD’ – shock-wave-induced film delamination patterning has been demonstrated. This study focuses on the temporal sequence of processes that characterize the mechanism of this SWIFD process on a copper indium gallium selenide (CIGS) solar cell stacks on polyimide. For this purpose high-speed shadowgraph experiments were performed in a pump probe experimental set-up using a KrF excimer laser for ablating the rear side of the polyimide substrate and measuring the shock wave generation at laser ablation of the polymer substrate as well as the thin-film delamination. The morphology and size of the thin-film structures were studied by scanning electron microscopy (SEM). Furthermore, the composition after the laser treatment was analyzed by energy dispersive X-ray (EDX) spectroscopy. The shadowgraph experiments allow the time-dependent identification and evaluation of the shock wave formation, substrate bending, and delamination of the thin film in dependence on the laser parameters. These results will contribute to improve the physical understanding of the laser-induced delamination effect for thin-film patterning.

Relativistic shocks in the systems containing domains with anomalous equation of state and quark baryonic matter hadronization

International Nuclear Information System (INIS)

Bugaev, K.A.; Gorenshtejn, M.I.; Zhdanov, V.I.

1987-01-01

Theoretical basis for general stability criterion of relativistic shocks in baryonic matter is proposed. Different formulations of shock mechanical stability are considered and applied to the analysis of rarefaction shock hadronization transition. 13 refs.; 2 figs

On governing equations for crack layer propagation

Science.gov (United States)

Chudnovsky, A.; Botsis, J.

1988-01-01

Results of analysis on damage distribution of a crack layer, in a model material, supported the self-similarity hypothesis of damage evolution which has been adopted by the crack layer theory. On the basis of measurements of discontinuity density and the double layer potential technique, a solution to the crack damage interaction problem has been developed. Evaluation of the stress intensity factor illustrated the methodology. Analysis of experimental results showed that Arrhenius type constitutive relationship described very well the expansion of the active zone of a crack layer.

Transverse jet-cavity interactions with the influence of an impinging shock

International Nuclear Information System (INIS)

Zare-Behtash, H.; Lo, K.H.; Kontis, K.; Ukai, T.; Obayashi, S.

2015-01-01

Highlights: • Experimental study of shock-jet-cavity in a supersonic freestream is conducted. • Shock impingement at the cavity leading edge lifts the shear layer, encouraging momentum transfer. • Shock impingement close to the jet location increases the number of smaller turbulent structures. - Abstract: For high-speed air breathing engines, fuel injection and subsequent mixing with air is paramount for combustion. The high freestream velocity poses a great challenge to efficient mixing both in macroscale and microscale. Utilising cavities downstream of fuel injection locations, as a means to hold the flow and stabilise the combustion, is one mechanism which has attracted much attention, requiring further research to study the unsteady flow features and interactions occurring within the cavity. In this study we combine the transverse jet injection upstream of a cavity with an impinging shock to see how this interaction influences the cavity flow, since impinging shocks have been shown to enhance mixing of transverse jets. Utilising qualitative and quantitative methods: schlieren, oilflow, PIV, and PSP the induced flowfield is analysed. The impinging shock lifts the shear layer over the cavity and combined with the instabilities generated by the transverse jet creates a highly complicated flowfield with numerous vertical structures. The interaction between the oblique shock and the jet leads to a relatively uniform velocity distribution within the cavity

Two-temperature hydrodynamics of laser-generated ultrashort shock waves in elasto-plastic solids

International Nuclear Information System (INIS)

Ilnitsky, Denis K; Migdal, Kirill P; Khokhlov, Viktor A; Inogamov, Nail A; Petrov, Yurii V; Anisimov, Sergey I; Zhakhovsky, Vasily V; Khishchenko, Konstantin V

2014-01-01

Shock-wave generation by ultrashort laser pulses opens new doors for study of hidden processes in materials happened at an atomic-scale spatiotemporal scales. The poorly explored mechanism of shock generation is started from a short-living two-temperature (2T) state of solid in a thin surface layer where laser energy is deposited. Such 2T state represents a highly non-equilibrium warm dense matter having cold ions and hot electrons with temperatures of 1-2 orders of magnitude higher than the melting point. Here for the first time we present results obtained by our new hybrid hydrodynamics code combining detailed description of 2T states with a model of elasticity together with a wide-range equation of state of solid. New hydro-code has higher accuracy in the 2T stage than molecular dynamics method, because it includes electron related phenomena including thermal conduction, electron-ion collisions and energy transfer, and electron pressure. From the other hand the new code significantly improves our previous version of 2T hydrodynamics model, because now it is capable of reproducing the elastic compression waves, which may have an imprint of supersonic melting like as in MD simulations. With help of the new code we have solved a difficult problem of thermal and dynamic coupling of a molten layer with an uniaxially compressed elastic solid. This approach allows us to describe the recent femtosecond laser experiments.

Modeling shock waves in an ideal gas: combining the Burnett approximation and Holian's conjecture.

Science.gov (United States)

He, Yi-Guang; Tang, Xiu-Zhang; Pu, Yi-Kang

2008-07-01

We model a shock wave in an ideal gas by combining the Burnett approximation and Holian's conjecture. We use the temperature in the direction of shock propagation rather than the average temperature in the Burnett transport coefficients. The shock wave profiles and shock thickness are compared with other theories. The results are found to agree better with the nonequilibrium molecular dynamics (NEMD) and direct simulation Monte Carlo (DSMC) data than the Burnett equations and the modified Navier-Stokes theory.

PIV tracer behavior on propagating shock fronts

International Nuclear Information System (INIS)

Glazyrin, Fyodor N; Mursenkova, Irina V; Znamenskaya, Irina A

2016-01-01

The present work was aimed at the quantitative particle image velocimetry (PIV) measurement of a velocity field near the front of a propagating shock wave and the study of the dynamics of liquid tracers crossing the shock front. For this goal, a shock tube with a rectangular cross-section (48  ×  24 mm) was used. The flat shock wave with Mach numbers M  =  1.4–2.0 propagating inside the tube channel was studied as well as an expanding shock wave propagating outside the channel with M  =  1.2–1.8 at its main axis. The PIV imaging of the shock fronts was carried out with an aerosol of dioctyl sebacate (DEHS) as tracer particles. The pressures of the gas in front of the shock waves studied ranged from 0.013 Mpa to 0.1 MPa in the series of experiments. The processed PIV data, compared to the 1D normal shock theory, yielded consistent values of wake velocity immediately behind the plain shock wave. Special attention was paid to the blurring of the velocity jump on the shock front due to the inertial particle lag and peculiarities of the PIV technique. A numerical algorithm was developed for analysis and correction of the PIV data on the shock fronts, based on equations of particle-flow interaction. By application of this algorithm, the effective particle diameter of the DEHS aerosol tracers was estimated as 1.03  ±  0.12 μm. A number of different formulations for particle drag were tested with this algorithm, with varying success. The results show consistency with previously reported experimental data obtained for cases of stationary shock waves. (paper)

An Iterative Method for Solving of Coupled Equations for Conductive-Radiative Heat Transfer in Dielectric Layers

Directory of Open Access Journals (Sweden)

Vasyl Chekurin

2017-01-01

Full Text Available The mathematical model for describing combined conductive-radiative heat transfer in a dielectric layer, which emits, absorbs, and scatters IR radiation both in its volume and on the boundary, has been considered. A nonlinear stationary boundary-value problem for coupled heat and radiation transfer equations for the layer, which exchanges by energy with external medium by convection and radiation, has been formulated. In the case of optically thick layer, when its thickness is much more of photon-free path, the problem becomes a singularly perturbed one. In the inverse case of optically thin layer, the problem is regularly perturbed, and it becomes a regular (unperturbed one, when the layer’s thickness is of order of several photon-free paths. An iterative method for solving of the unperturbed problem has been developed and its convergence has been tested numerically. With the use of the method, the temperature field and radiation fluxes have been studied. The model and method can be used for development of noncontact methods for temperature testing in dielectrics and for nondestructive determination of its radiation properties on the base of the data obtained by remote measuring of IR radiation emitted by the layer.

Stability of mixing layers

Science.gov (United States)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

A computational method for oleo-acoustics, application to hydraulic shock absorbers

NARCIS (Netherlands)

B. Koren (Barry); P.F.M. Michielsen (Paul); J.-W. Kars; P. Wesseling

1995-01-01

textabstractTo predict high-frequency oil-flow phenomena in hydraulic-shock-absorber designs, a mathematical-physical model is proposed. The model consists of the 2-D unsteady Euler equations in axial-symmetric coordinates and an appropriate equation of state for oil. The main topic of the paper is

Modeling boundary-layer transition in DNS and LES using Parabolized Stability Equations

Science.gov (United States)

Lozano-Duran, Adrian; Hack, M. J. Philipp; Moin, Parviz

2016-11-01

The modeling of the laminar region and the prediction of the point of transition remain key challenges in the numerical simulation of boundary layers. The issue is of particular relevance for wall-modeled large eddy simulations which require 10 to 100 times higher grid resolution in the thin laminar region than in the turbulent regime. Our study examines the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate, yet computationally efficient treatment of the growth of disturbances in the pre-transitional flow regime. The PSE captures the nonlinear interactions that eventually induce breakdown to turbulence, and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the point of transition is the solution of the Navier-Stokes equations, it provides a natural inflow condition for large eddy and direct simulations by avoiding unphysical transients. We show that in a classical H-type transition scenario, a combined PSE/DNS approach can reproduce the skin-friction distribution obtained in reference direct numerical simulations. The computational cost in the laminar region is reduced by several orders of magnitude. Funded by the Air Force Office of Scientific Research.

Improvement of an installation to generate shock waves

Energy Technology Data Exchange (ETDEWEB)

1974-04-29

An installation to generate a shock wave in a fluid layer is described. A water projectile is moved at a high velocity. It leaves behind an underpressure in which the adjacent water implodes, therby generating the desired shock wave. The installation is characterized by a tube-shaped hull in which a piston can move freely. One side of the hull is connected to the pressure-generator chamber of the piston. (6 claims)

The laminar boundary layer equations

CERN Document Server

Curle, N

2017-01-01

Thorough introduction to boundary layer problems offers an ordered, logical presentation accessible to undergraduates. The text's careful expositions of the limitations and accuracy of various methods will also benefit professionals. 1962 edition.

Molecular origins of anisotropic shock propagation in crystalline and amorphous polyethylene

Science.gov (United States)

O'Connor, Thomas C.; Elder, Robert M.; Sliozberg, Yelena R.; Sirk, Timothy W.; Andzelm, Jan W.; Robbins, Mark O.

2018-03-01

Molecular dynamics simulations are used to analyze shock propagation in amorphous and crystalline polyethylene. Results for the shock velocity Us are compared to predictions from Pastine's equation of state and hydrostatic theory. The results agree with Pastine at high impact velocities. At low velocities the yield stress becomes important, increasing the shock velocity and leading to anisotropy in the crystalline response. Detailed analysis of changes in atomic order reveals the origin of the anisotropic response. For shock along the polymer backbone, an elastic front is followed by a plastic front where chains buckle with a characteristic wavelength. Shock perpendicular to the chain backbone can produce plastic deformation or transitions to different orthorhombic or monoclinic structures, depending on the impact speed and direction. Tensile loading does not produce stable shocks: Amorphous systems craze and fracture while for crystals the front broadens linearly with time.

Observation of shock transverse waves in elastic media.

Science.gov (United States)

Catheline, S; Gennisson, J-L; Tanter, M; Fink, M

2003-10-17

We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger's equation, shows good agreement.

Relaxation of an unsteady turbulent boundary layer on a flat plate in an expansion tube

Science.gov (United States)

Gurta, R. N.; Trimpi, R. L.

1974-01-01

An analysis is presented for the relaxation of a turbulent boundary layer on a semi-infinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion-tube flows. The flow-governing equations have been transformed into the Crocco variables, and a time-similar solution is presented in terms of the dimensionless distance-time variable alpha and the dimensionless velocity variable beta. An eddy-viscosity model, similar to that of time-steady boundary layers, is applied to the inner and outer regions of the boundary layer. A turbulent Prandtl number equal to the molecular Prandtl number is used to relate the turbulent heat flux to the eddy viscosity. The numerical results, obtained by using the Gauss-Seidel line-relaxation method, indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin friction than a laminar boundary layer. The results also give a fairly good estimate of the local skin friction and heat transfer for near steady-flow conditions.

Numerical modelling of two-layer shallow water flow in microtidal salt-wedge estuaries: Finite volume solver and field validation

Directory of Open Access Journals (Sweden)

Krvavica Nino

2017-03-01

Full Text Available A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Q-scheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor λi was chosen correctly, the agreement between numerical results and field observations was satisfactory.

The boundary integral equations method for analysis of high-frequency vibrations of an elastic layer

Czech Academy of Sciences Publication Activity Database

Sorokin, S.; Kolman, Radek; Kopačka, Ján

2017-01-01

Roč. 87, č. 4 (2017), s. 737-750 ISSN 0939-1533 R&D Projects: GA ČR(CZ) GA16-03823S; GA MŠk(CZ) EF15_003/0000493 Institutional support: RVO:61388998 Keywords : an elastic layer * symmetric and skew-symmetric waves * the Green’s matrix * boundary integral equations * eigen frequencies Subject RIV: BI - Acoustics OBOR OECD: Acoustics Impact factor: 1.490, year: 2016 https://link.springer.com/article/10.1007/s00419-016-1220-y

Stress relaxation of shear in metals during shock loading

International Nuclear Information System (INIS)

Glazyrin, V.P.; Platova, T.M.

1988-01-01

Constructed determining equation, taking into account stress relaxation of shear, was used to calculate the evolution of plane shock waves of primary and secondary compression in metals. Values of shear stress and viscosity coefficient were

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

Science.gov (United States)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Tandem shock wave cavitation enhancement for extracorporeal lithotripsy

Science.gov (United States)

Loske, Achim M.; Prieto, Fernando E.; Fernández, Francisco; van Cauwelaert, Javier

2002-11-01

Extracorporeal shock wave lithotripsy (ESWL) has been successful for more than twenty years in treating patients with kidney stones. Hundreds of underwater shock waves are generated outside the patient's body and focused on the kidney stone. Stones fracture mainly due to spalling, cavitation and layer separation. Cavitation bubbles are produced in the vicinity of the stone by the tensile phase of each shock wave. Bubbles expand, stabilize and finally collapse violently, creating stone-damaging secondary shock waves and microjets. Bubble collapse can be intensified by sending a second shock wave a few hundred microseconds after the first. A novel method of generating two piezoelectrically generated shock waves with an adjustable time delay between 50 and 950 µs is described and tested. The objective is to enhance cavitation-induced damage to kidney stones during ESWL in order to reduce treatment time. In vitro kidney stone model fragmentation efficiency and pressure measurements were compared with those for a standard ESWL system. Results indicate that fragmentation efficiency was significantly enhanced at a shock wave delay of about 400 and 250 µs using rectangular and spherical stone phantoms, respectively. The system presented here could be installed in clinical devices at relatively low cost, without the need for a second shock wave generator.

Laser Structuring of Thin Layers for Flexible Electronics by a Shock Wave-induced Delamination Process

Science.gov (United States)

Lorenz, Pierre; Ehrhardt, Martin; Zimmer, Klaus

The defect-free laser-assisted structuring of thin films on flexible substrates is a challenge for laser methods. However, solving this problem exhibits an outstanding potential for a pioneering development of flexible electronics. Thereby, the laser-assisted delamination method has a great application potential. At the delamination process: the localized removal of the layer is induced by a shock wave which is produced by a laser ablation process on the rear side of the substrate. In this study, the thin-film patterning process is investigated for different polymer substrates dependent on the material and laser parameters using a KrF excimer laser. The resultant structures were studied by optical microscopy and white light interferometry (WLI). The delamination process was tested at different samples (indium tin oxide (ITO) on polyethylene terephthalate (PET), epoxy-based negative photoresist (SU8) on polyimide (PI) and indium tin oxide/copper indium gallium selenide/molybdenum (ITO/CIGS/Mo) on PI.

Multiple spacecraft observations of interplanetary shocks: characteristics of the upstream ulf turbulence

International Nuclear Information System (INIS)

Russell, C.T.; Smith, E.J.; Tsurutani, B.T.; Gosling, J.T.; Bame, S.J.

1982-01-01

All interplanetary shocks observed by ISEE-3 and either ISEE-1 or ISEE-2 or both in 1978 and 1979 are examined for evidence of upstream waves. In order to characterize the properties of these shocks it is necessary to determine accurate shock normals. We invert an overdetermined set of equations to obtain shock normals, velocities and error estimates for all these shocks. Tests of the method indicate it is quite reliable. Using these normals we then calculate the Mach number and angle between the interplanetary magnetic field and the shock normal for each shock. These parameters allow us to separate the upstream waves into two classes: whistler-mode precursors which occur at low Mach numbers and upstream turbulence whose amplitude at Mach numbers greater than 1.5 is controlled by the angle of the field to the shock normal. The former waves are right-hand circularly polarized and quite monochromatic. The latter waves are more linearly polarized and have a broadband featureless spectrum

CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave/Boundary-Layer Interaction

Science.gov (United States)

Davis, David O.

2015-01-01

Experimental investigations of specific flow phenomena, e.g., Shock Wave Boundary-Layer Interactions (SWBLI), provide great insight to the flow behavior but often lack the necessary details to be useful as CFD validation experiments. Reasons include: 1.Undefined boundary conditions Inconsistent results 2.Undocumented 3D effects (CL only measurements) 3.Lack of uncertainty analysis While there are a number of good subsonic experimental investigations that are sufficiently documented to be considered test cases for CFD and turbulence model validation, the number of supersonic and hypersonic cases is much less. This was highlighted by Settles and Dodsons [1] comprehensive review of available supersonic and hypersonic experimental studies. In all, several hundred studies were considered for their database.Of these, over a hundred were subjected to rigorous acceptance criteria. Based on their criteria, only 19 (12 supersonic, 7 hypersonic) were considered of sufficient quality to be used for validation purposes. Aeschliman and Oberkampf [2] recognized the need to develop a specific methodology for experimental studies intended specifically for validation purposes.

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz

2014-04-24

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.

Generalized conjugate-gradient methods for the Navier-Stokes equations

Science.gov (United States)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Assessment of UF6 Equation of State

Energy Technology Data Exchange (ETDEWEB)

Brady, P; Chand, K; Warren, D; Vandersall, J

2009-02-11

A common assumption in the mathematical analysis of flows of compressible fluids is to treat the fluid as a perfect gas. This is an approximation, as no real fluid obeys the perfect gas relationships over all temperature and pressure conditions. An assessment of the validity of treating the UF{sub 6} gas flow field within a gas centrifuge with perfect gas relationships has been conducted. The definition of a perfect gas is commonly stated in two parts: (1) the gas obeys the thermal equation of state, p = {rho}RT (thermally perfect), and, (2) the gas specific heats are constant (calorically perfect). Analysis indicates the thermally perfect assumption is valid for all flow conditions within the gas centrifuge, including shock fields. The low operating gas pressure is the primary factor in the suitability of the thermally perfect equation of state for gas centrifuge computations. UF{sub 6} is not calorically perfect, as the specific heats vary as a function of temperature. This effect is insignificant within the bulk of the centrifuge gas field, as gas temperatures vary over a narrow range. The exception is in the vicinity of shock fields, where temperature, pressure, and density gradients are large, and the variation of specific heats with temperature should be included in the technically detailed analyses. Results from a normal shock analysis incorporating variable specific heats is included herein, presented in the conventional form of shock parameters as a function of inlet Mach Number. The error introduced by assuming constant specific heats is small for a nominal UF{sub 6} shock field, such that calorically perfect shock relationships can be used for scaling and initial analyses. The more rigorous imperfect gas analysis should be used for detailed analyses.

Converging shocks in elastic-plastic solids.

Science.gov (United States)

Ortega, A López; Lombardini, M; Hill, D J

2011-11-01

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the

A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

Science.gov (United States)

Raychaudhuri, D.

2007-01-01

The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

Thermophysical properties of liquid carbon dioxide under shock compressions: quantum molecular dynamic simulations.

Science.gov (United States)

Wang, Cong; Zhang, Ping

2010-10-07

Quantum molecular dynamics were used to calculate the equation of state, electrical, and optical properties of liquid carbon dioxide along the Hugoniot at shock pressures up to 74 GPa. The principal Hugoniot derived from the calculated equation of state is in good agreement with experimental results. Molecular dissociation and recombination are investigated through pair correlation functions and decomposition of carbon dioxide is found to be between 40 and 50 GPa along the Hugoniot, where nonmetal-metal transition is observed. In addition, the optical properties of shock compressed carbon dioxide are also theoretically predicted along the Hugoniot.

Self-similar solutions for implosion and reflection of strong and weak shocks in a plasma

International Nuclear Information System (INIS)

Desai, B.N.; Chavda, L.K.

1980-06-01

We present an improved approximation scheme for finding approximate solutions in analytic form to the self-similar equations of gas dynamics. The method gives better agreement with exact results not only for the weak shocks which were considered previously but also for strong shocks for which the previous method gave poor results. We have considered various shock configurations in spherical and cylindrical geometries. (author)

ASYMPTOTIC STEADY-STATE SOLUTION TO A BOW SHOCK WITH AN INFINITE MACH NUMBER

Energy Technology Data Exchange (ETDEWEB)

Yalinewich, Almog; Sari, Re’em [Racah Institute of Physics, the Hebrew University, 91904, Jerusalem (Israel)

2016-08-01

The problem of a cold gas flowing past a stationary obstacle is considered. We study the bow shock that forms around the obstacle and show that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The profiles of the hydrodynamic variables in the interior of the shock are obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force on the obstacle is also calculated. Finally, we use these results to model the bow shock around an isolated neutron star.

Shock wave attenuation in a micro-channel

Science.gov (United States)

Giordano, J.; Perrier, P.; Meister, L.; Brouillette, M.

2018-05-01

This work presents optical measurements of shock wave attenuation in a glass micro-channel. This transparent facility, with a cross section ranging from 1 mm× 150 μm to 1 mm× 500 μm, allowed for the use of high-speed schlieren videography to visualize the propagation of a shock wave within the entire micro-channel and to quantify velocity attenuation of the wave due to wall effects. In this paper, we present the experimental technique and the relevant data treatment we have used to increase the sensitivity of shock wave detection. Then, we compared our experimental results for different channel widths, lengths, and shock wave velocities with the analytical model for shock attenuation proposed by Russell (J Fluid Mech 27(2):305-314, 1967), which assumes laminar flow, and by Mirels (Attenuation in a shock tube due to unsteady-boundary-layer action, NACA Report 1333, 1957) for turbulent flow. We found that these models are inadequate to predict the observed data, owing to the presence of fully developed flow which violates the basic assumption of these models. The data are also compared with the empirical shock attenuation models proposed by Zeitoun (Phys Fluids 27(1):011701, 2015) and Deshpande and Puranik (Shock Waves 26(4):465-475, 2016), where better agreement is observed. Finally, we presented experimental data for the flow field behind the shock wave from measurements of the Mach wave angle which shows globally decreasing flow Mach numbers due to viscous wall effects.

Study of Unsteady, Sphere-Driven, Shock-Induced Combustion for Application to Hypervelocity Airbreathing Propulsion

Science.gov (United States)

Axdahl, Erik; Kumar, Ajay; Wilhite, Alan

2011-01-01

A premixed, shock-induced combustion engine has been proposed in the past as a viable option for operating in the Mach 10 to 15 range in a single stage to orbit vehicle. In this approach, a shock is used to initiate combustion in a premixed fuel/air mixture. Apparent advantages over a conventional scramjet engine include a shorter combustor that, in turn, results in reduced weight and heating loads. There are a number of technical challenges that must be understood and resolved for a practical system: premixing of fuel and air upstream of the combustor without premature combustion, understanding and control of instabilities of the shock-induced combustion front, ability to produce sufficient thrust, and the ability to operate over a range of Mach numbers. This study evaluated the stability of the shock-induced combustion front in a model problem of a sphere traveling in a fuel/air mixture at high Mach numbers. A new, rapid analysis method was developed and applied to study such flows. In this method the axisymmetric, body-centric Navier-Stokes equations were expanded about the stagnation streamline of a sphere using the local similarity hypothesis in order to reduce the axisymmetric equations to a quasi-1D set of equations. These reduced sets of equations were solved in the stagnation region for a number of flow conditions in a premixed, hydrogen/air mixture. Predictions from the quasi-1D analysis showed very similar stable or unstable behavior of the shock-induced combustion front as compared to experimental studies and higher-fidelity computational results. This rapid analysis tool could be used in parametric studies to investigate effects of fuel rich/lean mixtures, non-uniformity in mixing, contaminants in the mixture, and different chemistry models.

RAPID COSMIC-RAY ACCELERATION AT PERPENDICULAR SHOCKS IN SUPERNOVA REMNANTS

Energy Technology Data Exchange (ETDEWEB)

Takamoto, Makoto; Kirk, John G., E-mail: mtakamoto@eps.s.u-tokyo.ac.jp, E-mail: john.kirk@mpi-hd.mpg.de [Max-Planck-Institut für Kernphysik, Postfach 103980, D-69029 Heidelberg (Germany)

2015-08-10

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio u{sub s} of the shock speed to the particle speed roughly equals the ratio 1/η of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy generated at these shocks, and find, for ηu{sub s} ≈ 1, that the spectral index softens by unity and the acceleration time increases by a factor of two compared to the standard result of the diffusive shock acceleration theory. These results provide a theoretical basis for the 30 year old conjecture that a supernova exploding into the wind of a Wolf–Rayet star may accelerate protons to an energy exceeding 10{sup 15} eV.

Experiments on ion-acoustic shock waves in a dusty plasma

International Nuclear Information System (INIS)

Nakamura, Y.

2002-01-01

Dust ion-acoustic shock waves have been investigated experimentally in a homogeneous unmagnetized dusty double-plasma device. An initial compressional wave with a ramp shape steepens to form oscillations at the leading part due to dispersion. The oscillation develops to a train of solitons when the plasma contains no dust grain. The wave becomes an oscillatory shock wave when the dust is mixed in the plasma and the density of the dust grains is smaller than a critical value. When the dust density is larger than the critical value, only steepening is observed at the leading part of the wave and a monotonic shock structure is observed. The velocity and width of the shock waves are measured and compared with results of numerical integrations of the modified Korteweg-de Vries-Burgers equation

Shock interactions with heterogeneous energetic materials

Science.gov (United States)

Yarrington, Cole D.; Wixom, Ryan R.; Damm, David L.

2018-03-01

The complex physical phenomenon of shock wave interaction with material heterogeneities has significant importance and nevertheless remains little understood. In many materials, the observed macroscale response to shock loading is governed by characteristics of the microstructure. Yet, the majority of computational studies aimed at predicting phenomena affected by these processes, such as the initiation and propagation of detonation waves in explosives or shock propagation in geological materials, employ continuum material and reactive burn model treatment. In an effort to highlight the grain-scale processes that underlie the observable effects in an energetic system, a grain-scale model for hexanitrostilbene (HNS) has been developed. The measured microstructures were used to produce synthetic computational representations of the pore structure, and a density functional theory molecular dynamics derived equation of state (EOS) was used for the fully dense HNS matrix. The explicit inclusion of the microstructure along with a fully dense EOS resulted in close agreement with historical shock compression experiments. More recent experiments on the dynamic reaction threshold were also reproduced by inclusion of a global kinetics model. The complete model was shown to reproduce accurately the expected response of this heterogeneous material to shock loading. Mesoscale simulations were shown to provide a clear insight into the nature of threshold behavior and are a way to understand complex physical phenomena.

An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium

Science.gov (United States)

Pepe, R.; Bonfiglioli, A.; D'Angola, A.; Colonna, G.; Paciorri, R.

2015-11-01

A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron-atom and atom-atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M

2012-09-12

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

KAUST Repository

Crosta, M; Trillo, S; Fratalocchi, Andrea

2012-01-01

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

General relativistic study of astrophysical jets with internal shocks

Science.gov (United States)

Vyas, Mukesh K.; Chattopadhyay, Indranil

2017-08-01

We explore the possibility of the formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry (θ = 0) in a Schwarzschild metric. We use two models for the jet geometry: (I) a conical geometry and (II) a geometry with non-conical cross-section. A jet with conical geometry has a smooth flow, while the jet with non-conical cross-section undergoes multiple sonic points and even standing shock. The jet shock becomes stronger, as the shock location is situated farther from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium, is that these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically, a jet with specific energy 1.8c2 will achieve a terminal speed of v∞ = 0.813c for jet with any geometry, where, c is the speed of light in vacuum. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is 40rg, then, in addition, a steady shock will form at rsh ˜ 7.5rg and compression ratio of R ˜ 2.7. Moreover, electron-proton jet seems to harbour the strongest shock. We will discuss possible consequences of such a scenario.

Microstructure Evolution and Impedance Spectroscopy Characterization of Thermal Barrier Coating Exposed to Gas Thermal-shock Environment

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CHEN Wen-long

2017-10-01

Full Text Available Gas thermal-shock experiment of thermal barrier coatings (TBCs was carried out in air up to 1250℃ in order to simulate the thermal cycling process of the engine blades during the start heating and shut down cooling. The growth of thermal growth oxide (TGO layer and microstructure evolution of YSZ layer during thermal cycling process were investigated systematically by electrochemical impedance spectroscopy testing and SEM. The results show that the thickness of TGO layer increases when increasing the frequency of thermal cycling, and the impedance response of middle frequencies is more and more remarkable. Meanwhile, initiation and growth of micro-cracks occur in YSZ layer during the gas thermal-shock experiment. The corresponding impedance characterization of YSZ layer after 100 cycles is similar to the as-sprayed sample, indicating that micro-cracks in short time could heal since the YSZ micro-cracks sinter at high temperature. But after 300 cycles, the impedance spectroscopy of YSZ layer is quite different to the as-sprayed sample, with the corresponding impedance of particle-gap of YSZ more and more remarkable with the increase of the thermal-shock times, indicating that non-healing micro-cracks form in the YSZ layer, which may be the main reason to induce the failure of YSZ layer.

Shock initiation sensitivity and Hugoniot-based equation of state of Composition B obtained using in situ electromagnetic gauging

International Nuclear Information System (INIS)

Gibson, L L; Bartram, B D; Sheffield, S A; Gustavsen, R L; Brown, G W; Sandstrom, M M; Giambra, A M; Dattelbaum, D M; Handley, C A

2014-01-01

A series of gas gun-driven plate impact experiments were performed on vacuum melt-cast Composition B to obtain new Hugoniot states and shock sensitivity (run-distance-to-detonation) information. The Comp B (ρ 0 = 1.713 g/cm 3 ) consisted of 59.5% RDX, 39.5% TNT, and 1% wax, with ∼ 6.5% HMX in the RDX. The measured Hugoniot states were found to be consistent with earlier reports, with the compressibility on the shock adiabat softer than that of a 63% RDX material reported by Marsh.[4] The shock sensitivity was found to be more sensitive (shorter run distance to detonation at a given shock input condition) than earlier reports for Comp B-3 and a lower density (1.68-1.69 g/cm 3 ) Comp B formulation. The reactive flow during the shock-to-detonation transition was marked by heterogeneous, hot spot-driven growth both in and behind the leading shock front.

Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

Science.gov (United States)

Hall, Philip; Bennett, James

1986-01-01

The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

Radiative relativistic shock adiabate

International Nuclear Information System (INIS)

Tsintsadze, L.N.; Nishikawa, K.

1997-01-01

The influences of thermal radiation on the state equation of shock waves, derived in the previous paper [L. N. Tsintsadze, Phys. Plasmas 2, 4462 (1995)], are studied and a series of relations of thermodynamic quantities that hold for shock waves are derived. It is shown that the presence of radiation can strongly change the compressibility of the plasma. It is well known that for polytropic gases the compressibility cannot change more than four times the initial value in the case of nonrelativistic temperatures. The numerical calculations show that there are no such restrictions, when the radiation energy exceeds the kinetic energy of the plasma. The ultrarelativistic temperature range is also covered in our numerical calculations. Also studied are the influences of the radiation on the PT and the TV diagrams. A significant modification due to radiation is found in every case studied. copyright 1997 American Institute of Physics

Characteristics of shock waves in neutrino-thick medium of collapsing stars

International Nuclear Information System (INIS)

Imshennik, V.S.; Murzina, M.V.

1989-01-01

Hugoniot relations for shock waves in neutrino-thick medium of colapsing stars are formulated. The equations obtained are solved numerically for rather wide range of shock wave velocities (D=(1,3,5)x10 9 cm/s) as well as for values of medium physical parameters against the shock wave front ( temperature T=(3,5,10)x1 -9 K; medium degree Θ 0 =n n /n p =10;100; at ρ 0 =10 11 g/cm 3 density).Presence of neutrino radiation is shown to result in matter essential deneutronization (up to Θ=10-30) at shock wave passage though contribution of leptonic component into the matter main characteristics (pressure, internal energy, temperature etc.) is rather small. 17 refs.; 3 figs.; 3 tabs

Report of 22nd International Symposium on Shock Waves; Dai 22 kai kokusai shogekiha symposium shusseki hokoku

Energy Technology Data Exchange (ETDEWEB)

Takayama, K. [Tohoku Univ., Sendai (Japan). Inst. of Fluid Science

1999-11-05

Outlined herein are the topics at the 22nd. International Symposium on Shock Waves, held in July 1999 in London. Prof. Takayama of Tohoku University gave an invited lecture on application of shock waves to medical area, stressing significance of shock waves on a human body. A total of 81 papers were presented from Japan. Number of Japanese papers and number of Japanese attendees both accounted for approximately 25%. The themes of these papers are centered by behavior of shock waves (e.g., propagation, reflection, and diffraction), extreme supersonic flows, interference between shock wave and boundary layer, aerodynamics (e.g., interference between vortex and shock wave), numerical simulation of shock wave phenomena, development of a new shock wave tube and measurement method, researches on elementary steps in chemical reactions, shock wave phenomena in condensed media and multi-phase media, shock wave noise produced while a high-speed train is running in a tunnel, and application of shock waves to industrial and medical areas. Japan contributes much to the application to medical area, and a method dispensing with injection is reported. Japan's aerospace-related researches include interference between shock wave and boundary layer, in which the real gas effect is taken into consideration, designs for protection from heat during the re-entry into the atmosphere, and construction of the world largest free-piston type wind tunnel. (NEDO)

Assessment of thermodynamic parameters of plasma shock wave

International Nuclear Information System (INIS)

Vasileva, O V; Isaev, Yu N; Budko, A A; Filkov, A I

2014-01-01

The work is devoted to the solution of the one-dimensional equation of hydraulic gas dynamics for the coaxial magneto plasma accelerator by means of Lax-Wendroff modified algorithm with optimum choice of the regularization parameter artificial viscosity. Replacement of the differential equations containing private derivatives is made by finite difference method. Optimum parameter of regularization artificial viscosity is added using the exact known decision of Soda problem. The developed algorithm of thermodynamic parameter calculation in a braking point is proved. Thermodynamic parameters of a shock wave in front of the plasma piston of the coaxial magneto plasma accelerator are calculated on the basis of the offered algorithm. Unstable high-frequency fluctuations are smoothed using modeling and that allows narrowing the ambiguity area. Results of calculation of gas dynamic parameters in a point of braking coincide with literary data. The chart 3 shows the dynamics of change of speed and thermodynamic parameters of a shock wave such as pressure, density and temperature just before the plasma piston

Energetic magnetospheric protons in the plasma depletion layer

International Nuclear Information System (INIS)

Fuselier, S.A.

1992-01-01

Interplanetary magnetic field draping against the Earth's dayside subsolar magnetopause creates a region of reduced plasma density and increased magnetic field called the plasma depletion layer. In this region, leakage of energetic ions from the Earth's magnetosphere onto magnetic field lines in the plasma depletion layer can be studied without interference from ions accelerated at the Earth's quasi-parallel bow shock. Active Magnetospheric Particle Tracer Experiment/Charge Composition Explorer (AMPTE/CCE) observations for 13 plasma depletion layer events are used to determine the characteristics of energetic protons between a few keV/e and ∼100keV/e leaked from the magnetosphere. Results indicate that the leaked proton distributions resemble those in the magnetosphere except that they have lower densities and temperatures and much higher velocities parallel (or antiparallel) and perpendicular to the magnetic field. Compared to the low-energy magnetosheath proton distributions present in the depletion layer, the leaked energetic proton distributions typically have substantially higher flow velocities along the magnetic field indicate that the leaked energetic proton distributions to contribute to the energetic proton population seen upstream and downstream from the quasi-parallel bow shock. However, their contribution is small compared to the contribution from acceleration of protons at the bow shock because the leaked proton densities are on the order of 10 times smaller than the energetic proton densities typically observed in the vicinity of the quasi-parallel bow shock

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

Science.gov (United States)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).

Effect of losses on acceleration of energetic particles by diffusive scattering through shock waves

International Nuclear Information System (INIS)

Voelk, H.J.; Morfill, G.E.; Forman, M.A.

1981-01-01

The effect of local losses on the acceleration of energetic particles by shocks is discussed considering both energy losses of individual particles and damping processes for the scattering hydromagnetic waves. The calculations are all time asymptotic and steady state. For locally plane and infinitely extended shocks, the requirement for acceleration is that the loss time exceed the acceleration time. The resulting modifications of the spatial structure and of the momentum dependence of the cosmic-ray distribution are described. For acceleration to be a local effect within the Galaxy, the local scattering mean free path must be small compared to the effective overall galactic mean free path as deduced from the cosmic-ray escape time. The required strengths of the scattering wave fields are such that neutral molecular clouds do not allow acceleration; in a partially ionized, warm interstellar medium, quite large shock strengths are needed. Such strong shock discontinuities are surrounded by an ionization layer within which Alfven wave damping is presumably negligible. Given the spatial extent of the layer for strong shocks propagating into neutral interstellar clouds, the possibility of localized diffusive acceleration is investigated. The estimated strength and extent of the scattering region is not large enough to confine acceleration within the layer. Rather, it will extend across the whole cloud, whose integrated losses then determine the efficiency

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

Science.gov (United States)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

A volume-filtered formulation to capture particle-shock interactions in multiphase compressible flows

Science.gov (United States)

Shallcross, Gregory; Capecelatro, Jesse

2017-11-01

Compressible particle-laden flows are common in engineering systems. Applications include but are not limited to water injection in high-speed jet flows for noise suppression, rocket-plume surface interactions during planetary landing, and explosions during coal mining operations. Numerically, it is challenging to capture these interactions due to the wide range of length and time scales. Additionally, there are many forms of the multiphase compressible flow equations with volume fraction effects, some of which are conflicting in nature. The purpose of this presentation is to develop the capability to accurately capture particle-shock interactions in systems with a large number of particles from dense to dilute regimes. A thorough derivation of the volume filtered equations is presented. The volume filtered equations are then implemented in a high-order, energy-stable Eulerian-Lagrangian framework. We show this framework is capable of decoupling the fluid mesh from the particle size, enabling arbitrary particle size distributions in the presence of shocks. The proposed method is then assessed against particle-laden shock tube data. Quantities of interest include fluid-phase pressure profiles and particle spreading rates. The effect of collisions in 2D and 3D are also evaluated.

Upwind algorithm for the parabolized Navier-Stokes equations

Science.gov (United States)

Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.

1989-01-01

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

Strong shock wave and areal mass oscillations associated with impulsive loading of planar laser targets

International Nuclear Information System (INIS)

Velikovich, A.L.; Schmitt, A.J.; Metzler, N.; Gardner, J.H.

2003-01-01

When a rippled surface of a planar target is irradiated with a short (subnanosecond) laser pulse, the shock wave launched into the target and the mass distribution of the shocked plasma will oscillate. These oscillations are found to be surprisingly strong compared, for example, to the case when the laser radiation is not turned off but rather keeps pushing the shock wave into the target. Being stronger than the areal mass oscillations due to ablative Richtmyer-Meshkov instability and feedout in planar targets, which have recently been observed at the Naval Research Laboratory (NRL) [Aglitskiy et al., Phys. Plasmas 9, 2264 (2002)], these oscillations should therefore be directly observable with the same diagnostic technique. Irradiation of a target with a short laser pulse represents a particular case of an impulsive loading, a fast release of finite energy in a thin layer near the surface of a target. Renewed interest to the impulsive loading in the area of direct-drive laser fusion is due to the recent proposals of using a short pulse prior to the drive pulse to make the target more resistant to laser imprint and Rayleigh-Taylor growth. Impulsive loading produces a shock wave that propagates into the target and is immediately followed by an expansion wave, which gradually reduces the shock strength. If the irradiated surface is rippled, then, while the shock wave propagates through the target, its modulation amplitude grows, exceeding the initial ripple amplitude by a factor of 2 or more. The oscillating areal mass reaches the peak values that exceed the initial mass modulation amplitude (density times ripple height) by a factor of 5-7 or more, and reverses its phase several times after the laser pulse is over. The oscillatory growth is more pronounced in fluids with higher shock compressibility and is probably related to the Vishniac's instability of a blast wave. Frequency of the oscillations is determined by the speed of sound in the shocked material, and

Particle Acceleration and Radiative Losses at Relativistic Shocks

Science.gov (United States)

Dempsey, P.; Duffy, P.

A semi-analytic approach to the relativistic transport equation with isotropic diffusion and consistent radiative losses is presented. It is based on the eigenvalue method first introduced in Kirk & Schneider [5]and Heavens & Drury [3]. We demonstrate the pitch-angle dependence of the cut-off in relativistic shocks.

The size effects upon shock plastic compression of nanocrystals

Science.gov (United States)

Malygin, G. A.; Klyavin, O. V.

2017-10-01

For the first time a theoretical analysis of scale effects upon the shock plastic compression of nanocrystals is implemented in the context of a dislocation kinetic approach based on the equations and relationships of dislocation kinetics. The yield point of crystals τy is established as a quantitative function of their cross-section size D and the rate of shock deformation as τy ɛ2/3 D. This dependence is valid in the case of elastic stress relaxation on account of emission of dislocations from single-pole Frank-Read sources near the crystal surface.

Soliton shock wave fronts and self-similar discontinuities in dispersion hydrodynamics

International Nuclear Information System (INIS)

Gurevich, A.V.; Meshcherkin, A.P.

1987-01-01

Nonlinear flows in nondissipative dispersion hydrodynamics are examined. It is demonstrated that in order to describe such flows it is necessary to incorporate a new concept: a special discontinuity called a ''self-similar'' discontinuity consisting of a nondissipative shock wave and a powerful slow wave discontinuity in regular hydrodynamics. The ''self similar discontinuity'' expands linearly over time. It is demonstrated that this concept may be introduced in a solution to Euler equations. The boundary conditions of the ''self similar discontinuity'' that allow closure of Euler equations for dispersion hydrodynamics are formulated, i.e., those that replace the shock adiabatic curve of standard dissipative hydrodynamics. The structure of the soliton front and of the trailing edge of the shock wave is investigated. A classification and complete solution are given to the problem of the decay of random initial discontinuities in the hydrodynamics of highly nonisothermic plasma. A solution is derived to the problem of the decay of initial discontinuities in the hydrodynamics of magnetized plasma. It is demonstrated that in this plasma, a feature of current density arises at the point of soliton inversion

A model for the electrical double layer combining integral equation techniques with quantum density functional theory

International Nuclear Information System (INIS)

Luque, N.B.; Woelki, S.; Henderson, D.; Schmickler, W.

2011-01-01

Highlights: · We augment a double-layer model based on integral equations by calculating the interaction parameters with the electrode from quantum density functional theory · Explicit model calculations for Ag(1 1 1) in aqueous solutions give at least qualitatively good results for the particle profiles · Ours is the only method which allows the calculation of capacity-charge characteristics. · We obtain reasonable values for the Helmholtz (inner-layer) capacity. - Abstract: We have complemented the singlet reference interaction site model for the electric double layer by quantum chemical calculations for the interaction of ions and solvents with an electrode. Specific calculations have been performed for an aqueous solution of NaCl in contact with a Ag(1 1 1) electrode. The particle profiles near the electrode show the specific adsorption of Cl - ions, but not of Na + , and are at least in qualitative agreement with those obtained by molecular dynamics. Including the electronic response of the silver surface into the model results in reasonable capacity-charge characteristics.

Implementation of compact finite-difference method to parabolized Navier-Stokes equations

International Nuclear Information System (INIS)

Esfahanian, V.; Hejranfar, K.; Darian, H.M.

2005-01-01

The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

Structure of slow shocks in a magnetized plasma with heat conduction