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Journal articles on the topic 'Equation of state, carbon, shock waves'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Nannan, Nawin R., Corrado Sirianni, Tiemo Mathijssen, Alberto Guardone, and Piero Colonna. "The admissibility domain of rarefaction shock waves in the near-critical vapour–liquid equilibrium region of pure typical fluids." Journal of Fluid Mechanics 795 (April 14, 2016): 241–61. http://dx.doi.org/10.1017/jfm.2016.197.

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Application of the scaled fundamental equation of state of Balfour et al. (Phys. Lett. A, vol. 65, 1978, pp. 223–225) based upon universal critical exponents, demonstrates that there exists a bounded thermodynamic domain, located within the vapour–liquid equilibrium region and close to the critical point, featuring so-called negative nonlinearity. As a consequence, rarefaction shock waves with phase transition are physically admissible in a limited two-phase region in the close proximity of the liquid–vapour critical point. The boundaries of the admissibility region of rarefaction shock waves are identified from first-principle conservation laws governing compressible flows, complemented with the scaled fundamental equations. The exemplary substances considered here are methane, ethylene and carbon dioxide. Nonetheless, the results are arguably valid in the near-critical state of any common fluid, namely any fluid whose molecular interactions are governed by short-range forces conforming to three-dimensional Ising-like systems, including, e.g. water. Computed results yield experimentally feasible admissible rarefaction shock waves generating a drop in pressure from 1 to 6 bar and pre-shock Mach numbers exceeding 1.5.

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2

Elperin, I., O. Igra, and G. Ben-Dor. "Analysis of Normal Shock Waves in a Carbon Particle-Laden Oxygen Gas." Journal of Fluids Engineering 108, no. 3 (September 1, 1986): 354–59. http://dx.doi.org/10.1115/1.3242586.

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The propagation of a normal shock wave into a quiescent oxygen gas seeded with carbon particles is studied. Due to the elevated postshock temperature the carbon particles ignite and burn until they disappear. For evaluating the effect of the burning carbon particles on the postshock-wave flow field, i.e., the relaxation zone, the conservation equations for a steady one-dimensional reactive suspension flow are formulated and solved numerically. The solution was repeated for a similar inert suspension flow. Comparing the two solutions revealed that the carbon burning has a major effect on the suspension properties in the relaxation zone and on the eventually reached postshock equilibrium state. For example, much higher temperatures and velocities are obtained in the reactive suspension while the pressure is lower than in a similar inert case. Longer relaxation zones are obtained for the reactive suspension.

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3

Nagayama, Kunihito. "Grueneisen Equation of State and Shock Waves." REVIEW OF HIGH PRESSURE SCIENCE AND TECHNOLOGY 4, no. 2 (1995): 118–27. http://dx.doi.org/10.4131/jshpreview.4.118.

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4

Khishchenko, K. V. "Equation of state for indium in shock waves." Journal of Physics: Conference Series 1385 (November 2019): 012002. http://dx.doi.org/10.1088/1742-6596/1385/1/012002.

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5

Gu, Yuan, Sizu Fu, Jiang Wu, Songyu Yu, Yuanlong Ni, and Shiji Wang. "Equation of state studies at SILP by laser-driven shock waves." Laser and Particle Beams 14, no. 2 (June 1996): 157–69. http://dx.doi.org/10.1017/s0263034600009915.

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The experimental progress of laser equation of state (EOS) studies at Shanghai Institute of Laser Plasma (SILP) is discussed in this paper. With a unique focal system, the uniformity of the laser illumination on the target surface is improved and a laser-driven shock wave with good spatial planarity is obtained. With an inclined aluminum target plane, the stability of shock waves are studied, and the corresponding thickness range of the target of laser-driven shock waves propagating steadily are given. The shock adiabats of Cu, Fe, SiO2 are experimentally measured. The pressure in the material is heightened remarkably with the flyer increasing pressure, and the effect of the increasing pressure is observed. Also, the high-pressure shock wave is produced and recorded in the experimentation of indirect laser-driven shock waves with the hohlraum target.

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6

Lifits, S. A., S. I. Anisimov, and J. Meyer-ter-Vehn. "Shock Waves produced by Impulsive Load: Equation of State Effects." Zeitschrift für Naturforschung A 47, no. 3 (March 1, 1992): 453–59. http://dx.doi.org/10.1515/zna-1992-0301.

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Abstract A numerical study of the flow after impulsive load of a plane material surface is carried out. It is shown that the flow is asymptotically self-similar provided one can neglect the cold components in the equation of state. In this case the effective exponent s(t) = d l n (X s) / d ln(t), derived from the shock trajectory Xs (t) does not depend on the initial pressure pulse and approaches the exponent α of the self-similar problem for time t →∞. For equations of state containing a cold pressure term, s (t) is larger than α and changes non-monotonically with time. Some features of the flow related to the presence of cold components in pressure and internal energy are discussed.

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7

Abdulazeem, Mohamed. "Condensed media shock waves and detonations: equation of state and performance." High Temperatures-High Pressures 30, no. 4 (1998): 387–422. http://dx.doi.org/10.1068/htrt121.

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8

Khishchenko, K. V. "Equation of state for potassium in shock waves at high pressures." Journal of Physics: Conference Series 946 (January 2018): 012082. http://dx.doi.org/10.1088/1742-6596/946/1/012082.

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9

Khishchenko, Konstantin V. "Equation of State for Bismuth at High Energy Densities." Energies 15, no. 19 (September 26, 2022): 7067. http://dx.doi.org/10.3390/en15197067.

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The purpose of this work is to describe the thermodynamic properties of bismuth in a broad scope of mechanical and thermal effects. A model of the equation of state in a closed form of the functional relationship between pressure, specific volume, and specific internal energy is developed. A new expression is proposed for the internal energy of a zero-temperature isotherm in a wide range of compression ratios, which has asymptotics to the Thomas–Fermi model with corrections. Based on the new model, an equation of state for bismuth in the region of body-centered cubic solid and liquid phases is constructed. The results of calculating the thermodynamic characteristics of these condensed phases with the new EOS are compared with the available experimental data for this metal in waves of shock compression and isentropic expansion. The parameters of shock waves in air obtained earlier by unloading shock-compressed bismuth samples are reconsidered. The newly developed equation of state can be used in modeling various processes in this material at high energy densities.

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10

Kouremenos, D. A., and K. A. Antonopoulos. "Real gas normal shock waves with the redlich-kwong equation of state." Acta Mechanica 76, no. 3-4 (March 1989): 223–33. http://dx.doi.org/10.1007/bf01253581.

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11

Harris, S. E. "Sonic shocks governed by the modified Burgers' equation." European Journal of Applied Mathematics 7, no. 2 (April 1996): 201–22. http://dx.doi.org/10.1017/s0956792500002291.

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In this paper, we investigate the evolution of N-waves in a medium governed by the modified Burgers' equation. It is shown that the general behaviour when the nonlinearity is of arbitrary odd integer order is the same as for the cubic case. For an N-wave of zero mean displacement, a shock is formed immediately to prevent a multi-valued solution and a second shock is formed at later times. At a finite time, the second shock satisfies a sonic condition and this state persists. The Taylor-type shock structure ceases to be the appropriate description, and instead we have a shock which matches only algebraically to the outer wave on one side. At a larger time still, the other shock is affected but the two shocks remain distinct until the wave dies under linear mechanisms. The behaviour of N-waves of non-zero mean is also examined and it is shown that in some cases, a purely one-signed profile remains.

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12

Cho, Heyrim, Daniele Venturi, and George E. Karniadakis. "Statistical analysis and simulation of random shocks in stochastic Burgers equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2171 (November 8, 2014): 20140080. http://dx.doi.org/10.1098/rspa.2014.0080.

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We study the statistical properties of random shock waves in stochastic Burgers equation subject to random space–time perturbations and random initial conditions. By using the response–excitation probability density function (PDF) method and the Mori–Zwanzig (MZ) formulation of irreversible statistical mechanics, we derive exact reduced-order equations for the one-point and two-point PDFs of the solution field. In particular, we compute the statistical properties of random shock waves in the inviscid limit by using an adaptive (shock-capturing) discontinuous Galerkin method in both physical and probability spaces. We consider stochastic flows generated by high-dimensional random initial conditions and random additive forcing terms, yielding multiple interacting shock waves collapsing into clusters and settling down to a similarity state. We also address the question of how random shock waves in space and time manifest themselves in probability space. The proposed new mathematical framework can be applied to different conservation laws, potentially leading to new insights into high-dimensional stochastic dynamical systems and more efficient computational algorithms.

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13

GUNDLACH, C., and R. J. LEVEQUE. "Universality in the run-up of shock waves to the surface of a star." Journal of Fluid Mechanics 676 (April 8, 2011): 237–64. http://dx.doi.org/10.1017/jfm.2011.42.

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We investigate the run-up of a shock wave from inside to the surface of a perfect fluid star in equilibrium and bounded by vacuum. Near the surface we approximate the fluid motion as plane-symmetric and the gravitational field as constant. We consider the ‘hot’ equation of state P = (Γ − 1)ρe and its ‘cold’ (fixed entropy, barotropic) form P = K0ρΓ (the latter does not allow for shock heating). We numerically find that the evolution of generic initial data approaches universal similarity solutions sufficiently near the surface, and we explicitly construct these similarity solutions. The two equations of state show very different behaviour because shock heating becomes the dominant effect when it is allowed. In the barotropic case, the fluid velocity behind the shock approaches a constant value, while the density behind the shock approaches a power law in space, as the shock approaches the surface. In the hot case with shock heating, the density jumps by a constant factor through the shock, while the sound speed and fluid velocity behind the shock diverge in a whiplash effect. We tabulate the similarity exponents as a function of the equation of state parameter Γ and the stratification index n∗.

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14

Kraus, Evgeny. "The Calculation of Elastic Modulus Behind Strong Shock Waves." Siberian Journal of Physics 4, no. 4 (December 1, 2009): 79–90. http://dx.doi.org/10.54362/1818-7919-2009-4-4-79-90.

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In the paper the approach for calculation of mechanical characteristics of materials behind strong shock waves is realized in the frame of uniform system of the few-parametric equation of state [1]. For the considered materials a comprehensive comparison of theoretical computational results with available at high energy density experimental data is carried out and good agreement of the results is obtained

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15

CONSTANTIN, C., E. DEWALD, C. NIEMANN, D. H. H. HOFFMANN, S. UDREA, D. VARENTSOV, J. JACOBY, U. N. FUNK, U. NEUNER, and A. TAUSCHWITZ. "Cold compression of solid matter by intense heavy-ion-beam-generated pressure waves." Laser and Particle Beams 22, no. 1 (March 2004): 59–63. http://dx.doi.org/10.1017/s0263034604221115.

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Experimental investigations of heavy-ion-generated shock waves in solid, multilayered targets were performed by applying a Schlieren and a laser-deflection technique. Shock velocity and the corresponding pressures, temporal and spatial density profiles inside the material compressed by multiple shock waves, and details of the shock dynamics were determined. Important for equation-of-state and phase transition studies, such experiments extend their relevance to inertial confinement fusion and astrophysical fundamental research.

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16

Nellis, W. J., A. C. Mitchell, F. H. Ree, M. Ross, N. C. Holmes, R. J. Trainor, and D. J. Erskine. "Equation of state of shock‐compressed liquids: Carbon dioxide and air." Journal of Chemical Physics 95, no. 7 (October 1991): 5268–72. http://dx.doi.org/10.1063/1.461665.

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17

Neff, S., and R. Presura. "Simulation of shock waves in flyer plate impact experiments." Laser and Particle Beams 28, no. 4 (October 14, 2010): 539–45. http://dx.doi.org/10.1017/s0263034610000595.

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AbstractIn this paper we present a newly developed one-dimensional hydrodynamic simulation code and use it to determine the shock evolution in flyer plate impact experiments. The code is Lagrangian with artificial viscosity and uses shock Hugoniot data in its equation-of-state calculations instead of SESAME data tables. First shock calculations for transparent targets show a good agreement with theoretical predictions, making the code suitable for designing future flyer impact experiments at the Nevada Terawatt Facility.

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18

Bugaev, K. A., M. I. Gorenshtein, and V. I. Zhdanov. "Relativistic shock waves in the presence of regions with anomalous equation of state." Theoretical and Mathematical Physics 80, no. 1 (July 1989): 767–75. http://dx.doi.org/10.1007/bf01015315.

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19

Ozaki, N., K. A. Tanaka, T. Ono, K. Shigemori, M. Nakai, H. Azechi, T. Yamanaka, et al. "GEKKO/HIPER-driven shock waves and equation-of-state measurements at ultrahigh pressures." Physics of Plasmas 11, no. 4 (April 2004): 1600–1608. http://dx.doi.org/10.1063/1.1650845.

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20

Khudainazarov, Sherzod, Burkhon Donayev, and B. Ashirov. "Propagation of a spherical wave in elastoplastic medium with complex equations of state." E3S Web of Conferences 264 (2021): 02041. http://dx.doi.org/10.1051/e3sconf/202126402041.

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The propagation of a spherical wave in the soil is solved in an analytically inverse way for soils with more complex equations of state. The results are obtained to propagate a spherical shock wave in soil with a more complex equation of state for the shape change in the medium. The study shows that taking into account the nonlinear elastic shock waves of the annular stress leads to an increase compared to the elastic medium. Note that in using a complicated equation of state of the soil, a spherical shock wave propagates in the soil, behind the front of which, in the disturbance region, the medium is unloaded.

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21

Ng, A., D. Parfeniuk, L. Da Silva, and P. Celliers. "Laser-driven shock wave experiments at the University of British Columbia." Laser and Particle Beams 4, no. 3-4 (August 1986): 555–67. http://dx.doi.org/10.1017/s0263034600002238.

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A review of recent laser-driven shock wave experiments at the University of British Columbia is presented. These include emissivity and reflectivity measurements on target rear surfaces when the shock wave emerges as well as measurements of the trajectories of shock propagation in initially transparent targets irradiated by temporally tailored laser pulses. The rear surface measurements allowed us to study the equation of state and electron conductivity of dense plasmas while coalescence of shock waves was evident in the trajectory of shock waves driven by a shaped pulse.

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22

Congy, T., G. A. El, and M. A. Hoefer. "Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves." Journal of Fluid Mechanics 875 (July 26, 2019): 1145–74. http://dx.doi.org/10.1017/jfm.2019.534.

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A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

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23

Tytarenko, P. V., and V. I. Zhdanov. "Existence and stability of shock waves in relativistic hydrodynamics with general equation of state." Physics Letters A 240, no. 6 (April 1998): 295–300. http://dx.doi.org/10.1016/s0375-9601(97)00973-0.

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24

Niu, Yang-Yao. "A Simulation of the Liquid Shock and Cavitation Based on a Multi-Equation Model." International Journal of Computational Methods 13, no. 04 (July 4, 2016): 1641010. http://dx.doi.org/10.1142/s0219876216410103.

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In this paper, an unsteady preconditioning formulation for multi-phase flows with arbitrary equation of state based on the approximated Riemann solver is developed for multi-phase flows at all speed. This paper considers a homogeneous two-phase multi-equation mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature-dependent hybrid equation of state. Benchmark test cases, including one-dimensional (1D) condensation shock in the cavitated nozzle and two-dimensional (2D) cavitated blunt body problem, demonstrate accurate capturing of interfaces, shock waves and cavitation zones.

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25

Anisimov, S. I., and V. A. Kravchenko. "Shock Wave in Condensed Matter Generated by Impulsive Load." Zeitschrift für Naturforschung A 40, no. 1 (January 1, 1985): 8–13. http://dx.doi.org/10.1515/zna-1985-0104.

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A shock wave in condensed matter generated by impulsive load ("shock loading") is considered. A self-similar solution of the problem is presented. The media are described by the equation-of-state of the Mie-Grüneisen type. Values of the self-similarity exponent and the profiles of gas-dynamical variables have been calculated. The problem of generation of shock waves by ultra-short laser pulses is discussed.

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26

YOSHIDA, Masatake. "Study of Equation of State Using Laser-Induced Shock-Wave Compression: Generation and Properties of Laser-Induced Shock Waves." Journal of Plasma and Fusion Research 80, no. 6 (2004): 427–31. http://dx.doi.org/10.1585/jspf.80.427.

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27

Crandall, L. E., J. R. Rygg, D. K. Spaulding, M. F. Huff, M. C. Marshall, D. N. Polsin, R. Jeanloz, et al. "Equation-of-state, sound speed, and reshock of shock-compressed fluid carbon dioxide." Physics of Plasmas 28, no. 2 (February 2021): 022708. http://dx.doi.org/10.1063/5.0039967.

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28

Lukyanov, A. A. "An equation of state of a carbon-fibre epoxy composite under shock loading." European Physical Journal B 74, no. 1 (February 2, 2010): 35–45. http://dx.doi.org/10.1140/epjb/e2010-00043-4.

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29

Konyukhov, A. V., P. R. Levashov, A. P. Likhachev, and I. L. Iosilevskii. "Instability of relativistic shock waves: numerical study on the basis of model equation of state." Vestnik Ob"edinennogo instituta vysokikh temperatur 3, no. 2 (2019): 43–49. http://dx.doi.org/10.33849/2019208.

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30

Zhdanov, V. I., and P. V. Tytarenko. "Criterion for existence of shock waves in relativistic magnetohydrodynamics with a general equation of state." Physics Letters A 235, no. 1 (October 1997): 71–75. http://dx.doi.org/10.1016/s0375-9601(97)00549-5.

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31

Konyukhov, A. V., A. P. Likhachev, P. R. Levashov, and I. L. Iosilevskiy. "Instability of relativistic shock waves: Numerical study on the basis of model equation of state." Journal of Physics: Conference Series 1147 (January 2019): 012024. http://dx.doi.org/10.1088/1742-6596/1147/1/012024.

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32

Bossi, Simone, Tom A. Hall, Mohammed Mahdieh, Dimitri Batani, Michel Koenig, Jothy Krishnan, Alessandra Benuzzi, Jean Michel Boudenne, and Thorsten Lower. "Determination of the color temperature in laser-produced shocks." Laser and Particle Beams 15, no. 4 (December 1997): 485–93. http://dx.doi.org/10.1017/s0263034600011071.

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Experimental results on the determination of the color temperature in shock waves produced with lasers are presented. The method is based on imaging the target rear side in two different spectral windows and on using phased zone plates to produce high-quality shocks. The shock velocity is also measured, allowing, with the use of the equation of state, the real shock temperature to be deduced and compared with the measured color temperature.

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33

Kharab, Abdelwahab, and Jamal Benbourenane. "Early response of soils to violent disturbances." International Journal of Applied Mathematical Research 6, no. 2 (April 9, 2017): 39. http://dx.doi.org/10.14419/ijamr.v6i2.3612.

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A one-dimensional model dealing with underground explosions as experienced in areas such as mining or excavations is presented. When an explosion in a typical soil medium occurs, soil material is displaced and shock waves propagate in the soil medium. Soil is considered as a floating, ideally locking material. In this paper, the speed of propagation for the shock waves is analyzed, and results are given. The Mie-Gruneisen equation of state is used to find the pressure as a function of the density. Results with the present model yield an efficient and comprehensive means to analyze speed of waves in a sandy medium.

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34

GUARDONE, ALBERTO, CALIN ZAMFIRESCU, and PIERO COLONNA. "Maximum intensity of rarefaction shock waves for dense gases." Journal of Fluid Mechanics 642 (December 23, 2009): 127–46. http://dx.doi.org/10.1017/s0022112009991716.

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Modern thermodynamic models indicate that fluids consisting of complex molecules may display non-classical gasdynamic phenomena such as rarefaction shock waves (RSWs) in the vapour phase. Since the thermodynamic region in which non-classical phenomena are physically admissible is finite in terms of pressure, density and temperature intervals, the intensity of RSWs is expected to exhibit a maximum for any given fluid. The identification of the operating conditions leading to the RSW with maximum intensity is of paramount importance for the experimental verification of the existence of non-classical phenomena in the vapour phase and for technical applications taking advantage of the peculiarities of the non-classical regime. This study investigates the conditions resulting in an RSW with maximum intensity in terms of pressure jump, wave Mach number and shock strength. The upstream state of the RSW with maximum pressure drop is found to be located along the double-sonic locus formed by the thermodynamic states associated with an RSW having both pre- and post-shock sonic conditions. Correspondingly, the maximum-Mach thermodynamic and maximum-strength loci locate the pre-shock states from which the RSW with the maximum wave Mach number and shock strength can originate. The qualitative results obtained with the simple van der Waals model are confirmed with the more complex Stryjek–Vera–Peng–Robinson, Martin–Hou and Span–Wagner equations of state for selected siloxane and perfluorocarbon fluids. Among siloxanes, which are arguably the best fluids for experiments aimed at the generation and measurement of an RSW, the state-of-the-art Span–Wagner multi-parameter equation of state predicts a maximum wave Mach number close to 1.026 for D6 (dodecamethylcyclohexasiloxane, [O-Si-(CH3)2]6). Such value is well within the capacity of the measurement system of a newly built experimental set-up aimed at the first-ever demonstration of the existence of RSWs in dense vapours.

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35

HENDERSON, LE ROY F., and RALPH MENIKOFF. "Triple-shock entropy theorem and its consequences." Journal of Fluid Mechanics 366 (July 10, 1998): 179–210. http://dx.doi.org/10.1017/s0022112098001244.

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For a convex equation of state, a general theorem on shock waves is proved: a sequence of two shocks has a lower entropy than a single shock to the same final pressure. We call this the triple-shock entropy theorem. This theorem has important consequences for shock interactions. In one dimension the interaction of two shock waves of the opposite family always results in two outgoing shock waves. In two dimensions the intersection of three shocks, such as a Mach configuration, must have a contact. Moreover, the state behind the Mach stem has a higher entropy than the state behind the reflected shock. For the transition between a regular and Mach reflection, this suggests that the von Neumann (mechanical equilibrium) criterion would be preferred based on thermodynamic stability, i.e. maximum entropy subject to the system constraint that the total specific enthalpy is fixed. However, to explain the observed hysteresis of the transition we propose an analogy with phase transitions in which locally stable wave patterns (regular or Mach reflection) play the role of meta-stable thermodynamic states. The hysteresis effect would occur only when the transition threshold exceeds the background fluctuations. The transition threshold is affected by flow gradients in the neighbourhood of the shock intersection point and the background fluctuations are due to acoustic noise. Consequently, the occurrence of hysteresis is sensitive to the experimental design, and only under special circumstances is hysteresis observed.

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36

Arora, Rajan. "ASYMPTOTICAL SOLUTIONS FOR A VIBRATIONALLY RELAXING GAS." Mathematical Modelling and Analysis 14, no. 4 (December 31, 2009): 423–34. http://dx.doi.org/10.3846/1392-6292.2009.14.423-434.

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Using the weakly non‐linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a vibrationally relaxing gas with Van der Waals equation of state. The transport equations for the amplitudes of resonantly interacting waves are derived. The evolutionary behavior of non‐resonant wave modes culminating into shock waves is also studied.

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37

Saenz, J. A., B. D. Taylor, and D. S. Stewart. "Asymptotic calculation of the dynamics of self-sustained detonations in condensed phase explosives." Journal of Fluid Mechanics 710 (August 31, 2012): 166–94. http://dx.doi.org/10.1017/jfm.2012.358.

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AbstractWe use the weak-curvature, slow-time asymptotics of detonation shock dynamics (DSD) to calculate an intrinsic relation between the normal acceleration, the normal velocity and the curvature of a lead detonation shock for self-sustained detonation waves in condensed phase explosives. The formulation uses the compressible Euler equations for an explosive that is described by a general equation of state with multiple reaction progress variables. The results extend an earlier asymptotic theory for a polytropic equation of state and a single-step reaction rate model discussed by Kasimov (Theory of instability and nonlinear evolution of self-sustained detonation waves. PhD thesis, University of Illinois Urbana-Champaign, Urbana, Illinois) and by Kasimov & Stewart (Phys. Fluids, vol. 16, 2004, pp. 3566–3578). The asymptotic relation is used to study the dynamics of ignition events in solid explosive PBX-9501 and in porous PETN powders. In the case of porous or powdered explosives, two composition variables are used to represent the extent of exothermic chemical reaction and endothermic compaction. Predictions of the asymptotic formulation are compared against those of alternative DSD calculations and against shock-fitted direct numerical simulations of the reactive Euler equations.

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38

Jahan, Sharmin, Booshrat E. Sharmin, Nure Alam Chowdhury, Abdul Mannan, Tanu Shree Roy, and A. A. Mamun. "Electrostatic Ion-Acoustic Shock Waves in a Magnetized Degenerate Quantum Plasma." Plasma 4, no. 3 (August 26, 2021): 426–34. http://dx.doi.org/10.3390/plasma4030031.

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A theoretical investigation has been carried out to examine the ion-acoustic shock waves (IASHWs) in a magnetized degenerate quantum plasma system containing inertialess ultra-relativistically degenerate electrons, and inertial non-relativistic positively charged heavy and light ions. The Burgers equation is derived by employing the reductive perturbation method. It can be seen that under the consideration of non-relativistic positively charged heavy and light ions, the plasma model only supports the positive electrostatic shock structure. It is also observed that the charge state and number density of the non-relativistic heavy and light ions enhance the amplitude of IASHWs, and the steepness of the shock profile is decreased with ion kinematic viscosity. The findings of our present investigation will be helpful in understanding the nonlinear propagation of IASHWs in white dwarfs and neutron stars.

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39

Chashechkin, Yuli D. "Singular perturbed components of flows – linear precursors of shock waves." Mathematical Modelling of Natural Phenomena 13, no. 2 (2018): 17. http://dx.doi.org/10.1051/mmnp/2018020.

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A comparative analysis of the infinitesimal symmetries of various well-known systems of governing equations used for mathematical descriptions of flows and waves in fluids has shown that only the basic system of equations, including the empirical equation of state and the partial differential equations of mass, momentum, energy and matter transport, is characterized by a ten-parameter Galilean transformation group. An analysis of the complete solutions of the linearized system of fundamental equations for weakly dissipating media reveals a wide class of previously unknown singularly perturbed solutions supplementing well investigated regular solutions describing propagating waves. Fine flow components, whose geometry is typical for internal boundary layers that supplement the wave fields exist both at the boundaries and inside the volume of the liquid, are classified as linear precursors of shock waves. The calculated pattern of periodic internal waves beams covered with high-gradient envelopes agrees with data from independently performed experiments on measurements and visualization of the fine structure of linear and nonlinear waves in continuously stratified media.

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Temporal, M., S. Atzeni, D. Batani, M. Koenig, A. Benuzzi, and B. Faral. "Design of absolute equation of state measurements in optically thick materials by laser-driven shock waves." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 415, no. 3 (October 1998): 668–73. http://dx.doi.org/10.1016/s0168-9002(98)00445-8.

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Wang, Jinhuan, Yicheng Pang, and Yu Zhang. "Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 3-4 (May 26, 2019): 461–73. http://dx.doi.org/10.1515/ijnsns-2018-0263.

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AbstractIn this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

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NADIM, A., D. GOLDMAN, J. J. CARTMELL, and P. E. BARBONE. "A PHASE-PLANE DESCRIPTION OF NONLINEAR TRAVELING WAVES IN BUBBLY LIQUIDS." Journal of Computational Acoustics 07, no. 02 (June 1999): 71–82. http://dx.doi.org/10.1142/s0218396x99000072.

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One-dimensional traveling wave solutions to the fully nonlinear continuity and Euler equations in a bubbly liquid are considered. The elimination of velocity from the two equations leaves a single nonlinear algebraic relation between the pressure and density profiles in the mixture. On assuming the bubbles to have identical size and taking the volume fraction of bubbles in the medium to be small, an equation of state which relates the mixture pressure to the density and its first two material time-derivatives is derived. When this equation of state is linearized and combined with the laws of conservation of mass and momentum, a nonlinear, second-order, ordinary differential equation is obtained for the density as a function of the single traveling wave coordinate. A phase-plane analysis of this equation reveals the existence of two fixed points, one of which is a saddle and the other a node. A single trajectory connects the two fixed points and corresponds to a traveling shock wave solution when the Mach number of the wave, defined as the ratio of traveling wave speed to the low-frequency speed of sound in the bubbly liquid, exceeds unity. The analysis provides a qualitative explanation of the oscillations behind shocks seen in experiments on bubbly liquids.

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Gojani, A. B., and Kazuyoshi Takayama. "Experimental Determination of Shock Hugoniot for Water, Castor Oil, and Aqueous Solutions of Sodium Chloride, Sucrose and Gelatin." Materials Science Forum 566 (November 2007): 23–28. http://dx.doi.org/10.4028/www.scientific.net/msf.566.23.

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Shock waves are indispensable tools for medical applications, and hence their interactions with human tissue become one of the most important basic research topics. In this paper, the determination of shock Hugoniot curves for liquids that can model human tissue, namely water, castor oil, and aqueous solutions of sodium chloride, sucrose and gelatin, at 10 and 20 weight percent are presented. Underwater shock waves were generated by ignition of 10 mg silver azide pellets and time variations of over-pressures were measured and simultaneously the shock speed was measured by the time of flight technique. Then shock Hugoniot curves were obtained, by assuming the Tait type equation of state, to relate the estimated density and measured pressure values. Results show in the cases of aqueous solutions that increasing amount of additives into water causes only a very minute decrease in the compressibility of the solution. This difference was more pronounced in the case of sodium chloride, less for gelatin, and almost none for sucrose aqueous solution.

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Koroleva, M. R., O. V. Mishchenkova, V. A. Tenenev, and T. Raeder. "Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State." Nelineinaya Dinamika 17, no. 1 (2021): 119–38. http://dx.doi.org/10.20537/nd210109.

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The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

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OZAKI, Norimasa, Kazuo A. TANAKA, Takatoshi ONO, Kikuo TAKAMATSU, Keiji NAGAI, Keisuke SHIGEMORI, Mitsuo NAKAI, Noriaki MIYANAGA, Hiroshi AZECHI, and Tatsuhiko YAMANAKA. "Characterization of GEKKO/HIPER-Driven Shock Waves for Equation-of-State Experiments in Ultra-High-Pressure Regime." Journal of Plasma and Fusion Research 80, no. 6 (2004): 486–91. http://dx.doi.org/10.1585/jspf.80.486.

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Yang, Li, Huizhao Wang, Minghua Chi, Xiangguo Zeng, Yuntian Wang, and Ping Zhao. "Molecular Dynamics Study on Hugoniot State and Mie–Grüneisen Equation of State of 316 Stainless Steel for Hydrogen Storage Tank." Materials 16, no. 2 (January 9, 2023): 628. http://dx.doi.org/10.3390/ma16020628.

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To promote the popularization and development of hydrogen energy, a micro-simulation approach was developed to determine the Mie–Grüneisen EOS of 316 stainless steel for a hydrogen storage tank in the Hugoniot state. Based on the combination of the multi-scale shock technique (MSST) and molecular dynamics (MD) simulations, a series of shock waves at the velocity of 6–11 km/s were applied to the single-crystal (SC) and polycrystalline (PC) 316 stainless steel model, and the Hugoniot data were obtained. The accuracy of the EAM potential for Fe–Ni–Cr was verified. Furthermore, Hugoniot curve, cold curve, Grüneisen coefficient (γ), and the Mie–Grüneisen EOS were discussed. In the internal pressure energy-specific volume (P-E-V) three-dimensional surfaces, the Mie–Grüneisen EOSs show concave characteristics. The maximum error of the calculation results of SC and PC is about 10%. The results for the calculation deviations of each physical quantity of the SC and PC 316 stainless steel indicate that the grain effect of 316 stainless steel is weak under intense dynamic loads, and the impact of the grains in the cold state increases with the increase in the volume compression ratio.

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Zhu, Qingyong, Jinkun Zheng, and Junjun Sun. "Fractal characteristics of surface roughness and their effects on laser shock waves." AIP Advances 12, no. 12 (December 1, 2022): 125021. http://dx.doi.org/10.1063/5.0133174.

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The Weierstrass–Mandelbrot function model was used to simulate the rough topography of a target surface, and the fractal theory was used to study the fractal characteristics of the target surface topography, which is the self-similarity of surface topography. The 3D fluid dynamics governing equations of the laser-supported detonation plasma flow field in Cartesian coordinates are given and discretized by a high-order difference scheme. The equation of state of plasma under different conditions is considered, and a new method of flux splitting is introduced to carry out numerical simulations. The numerical results of plasma pressure, density, temperature, and velocity at different times and different surface roughnesses are obtained, which show the evolvement of the ablative plasma. The simulated results show that a rough surface can obviously affect the propagation velocity of the detonation wave near the wall. In addition, the waveform is also destroyed, forming a broken waveform.

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SALHI, MEROUANE. "Numerical investigation of the thermal-caloric imperfections on entropy enhancement across normal shock waves." High Temperatures-High Pressures 48, no. 4 (2020): 285–308. http://dx.doi.org/10.32908/hthp.v48.689.

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Changes in flow properties across a normal shock wave are calculated for a real gas, thus giving us a better affinity to the real behavior of the waves. The purpose of this work is to develop shock-wave theory under the gaseous imperfections. Expressions are developed for analyzing the supersonic flow of such a thermally and calorically imperfect gas. The effects of molecular size and intermolecular attraction forces are used to correct a state equation, focusing on determination of the impact of upstream stagnation parameters on a normal shock wave. Flow through a shock wave in air is investigated to find a general form for normal shock waves. At Mach numbers greater than 2.0, the temperature rise is considerably below, and hence the density rise is well above, that predicted assuming ideal gas behavior. It is shown that caloric imperfections in air have an appreciable effect on the parameters developed in the processes considered. Computation of errors between the present model based on real gas theory and a perfect gas model shows that the influence of the thermal and caloric imperfections associated with a real gas is important.

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de la Cruz-Hernández, Manuel E., and Sergio Mendoza. "Full analytical ultrarelativistic 1D solutions of a planar working surface." Monthly Notices of the Royal Astronomical Society 507, no. 2 (July 30, 2021): 1827–35. http://dx.doi.org/10.1093/mnras/stab2158.

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ABSTRACT We show that the 1D planar ultrarelativistic shock tube problem with an ultrarelativistic polytropic equation of state can be solved analytically for the case of a working surface, i.e. for the case when an initial discontinuity on the hydrodynamical quantities of the problem form two shock waves separating from a contact discontinuity. The procedure is based on the extensive use of the Taub jump conditions for relativistic shock waves, the Taub adiabatic, and performing Lorentz transformations to present the solution in a system of reference adequate for an external observer at rest. The solutions are found using a set of very useful theorems related to the Lorentz factors when transforming between systems of reference. The energy dissipated inside the working surface is relevant for studies of light curves observed in relativistic astrophysical jets and so, we provide a full analytical solution for this phenomenon assuming an ultrarelativistic periodic velocity injected at the base of the jet.

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FORTOV, V. E., D. BATANI, A. V. KILPIO, I. K. KRASYUK, I. V. LOMONOSOV, P. P. PASHININ, E. V. SHASHKOV, A. YU SEMENOV, and V. I. VOVCHENKO. "The spall strength limit of matter at ultrahigh strain rates induced by laser shock waves." Laser and Particle Beams 20, no. 2 (April 2002): 317–20. http://dx.doi.org/10.1017/s0263034602202232.

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New results concerning the process of dynamic fracture of materials (spallation) by laser-induced shock waves are presented. The Nd-glass laser installations SIRIUS and KAMERTON were used for generation of shock waves with pressure up to 1 Mbar in plane Al alloy targets. The wavelengths of laser radiation were 1.06 and 0.53 μm, the target thickness was changed from 180 to 460 μm, and the laser radiation was focused in a spot with a 1-mm diameter on the surface of AMg6M aluminum alloy targets. Experimental results were compared to predictions of a numerical code which employed a real semiempirical wide-range equation of state. Strain rates in experiments were changed from 106 to 5 × 107 s−1. Two regimes of spallation were evidenced: the already known dynamic regime and a new quasi-stationary regime. An ultimate dynamic strength of 80 kbar was measured. Finally, experiments on targets with artificial spall layers were performed showing material hardening due to shock-wave compression.

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