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Higher moments of the velocity distribution function in dense-gas shocks. (English) Zbl 1163.76387
Summary: Large-scale molecular dynamics simulations of a \(M_{s} = 4.3\) shock in dense argon (\(\rho = 532\) kg/m\(^3\), \(T = 300\) K) and a \(M_{s} = 3.6\) shock in dense nitrogen \((\rho = 371\) kg/m\(^3\), \(T = 300\) K) have been performed. Results for moments (up to order 10) of the velocity distribution function are shown. The excess even moments of the shock-normal velocity component (i.e., in the direction of shock propagation) are positive for most parts of the shock wave, but become negative towards the hot side of the shock before reverting back to zero. The even excess moments of the shock-parallel velocities and the odd moments of the shock-normal velocity do not change signs within the shock. The magnitude of the excess moments increases with the order of the moment, i.e., the higher moments correspond less and less to those of a Maxwell-Boltzmann distribution.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
74A25 Molecular, statistical, and kinetic theories in solid mechanics
Software:
Moldy
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[1] Cercignani, C., The Boltzmann equation and its applications, (1988), Springer New York · Zbl 0646.76001
[2] Elliott, J.P., Validity of navier – stokes relation in a shock-wave, Canadian journal of physics, 53, 6, 583-586, (1975)
[3] Cohen, E.G.D., Fifty years of kinetic theory, Physica A, 194, 1-4, 229-257, (1993)
[4] Holian, B.L.; Hoover, W.G.; Moran, B.; Straub, G.K., Shock-wave structure via non-equilibrium molecular-dynamics and navier – stokes continuum mechanics, Physical review A, 22, 6, 2798-2808, (1980)
[5] Salomons, E.; Mareschal, M., Usefulness of the Burnett description of strong shock waves, Physical review letters, 69, 2, 269-272, (1992)
[6] Kum, O.; Hoover, W.G.; Hoover, C.G., Temperature maxima in stable two-dimensional shock waves, Physical review E, 56, 1, 462-465, (1997)
[7] Yen, S.M., Temperature overshoot in shock waves, Physics of fluids, 9, 7, 1417-1418, (1966)
[8] Holway, L.H., Temperature overshoots in shock waves, Physics of fluids, 8, 10, 1905-1906, (1965)
[9] Salwen, H.; Grosch, C.E.; Ziering, S., Extension of the Mott-Smith method for a one-dimensional shock wave, Physics of fluids, 7, 2, 180-189, (1964) · Zbl 0122.20302
[10] Macpherson, A.K., Formation of shock waves in a dense gas using a molecular-dynamics type technique, Journal of fluid mechanics, 45, 601-621, (1971) · Zbl 0213.53101
[11] Horowitz, J.; Woo, M.; Greber, I., Molecular dynamics simulation of a piston-driven shock wave, Physics of fluids (gallery of fluid motion), 7, 9, S6, (1995)
[12] Woo, M.; Greber, I., Molecular dynamics simulation of piston-driven shock wave in hard sphere gas, AIAA journal, 37, 2, 215-221, (1999)
[13] Tokumasu, T.; Matsumoto, Y., Dynamic molecular collision (DMC) model for rarefied gas flow simulations by the DSMC method, Physics of fluids, 11, 7, 1907-1920, (1999) · Zbl 1147.76515
[14] Refson, K., Moldy: a portable molecular dynamics simulation program for serial and parallel computers, Computer physics communications, 126, 3, 310-329, (2000) · Zbl 1040.81501
[15] Murthy, C.S.; O’Shea, S.F.; McDonald, I.R., Electrostatic interactions in molecular crystals-lattics dynamics of solid nitrogen and carbon dioxide, Molecular physics, 50, 3, 531-541, (1983)
[16] Vrabec, J.; Stoll, J.; Hasse, H., A set of molecular models for symmetric quadrupolar fluids, Journal of physical chemistry B, 105, 48, 12126-12133, (2001)
[17] Mott-Smith, H.M., The solution of the Boltzmann equation for a shock wave, Physical reviews, 82, 11, 885-892, (1951) · Zbl 0043.40703
[18] McQuarrie, D.A., Statistical mechanics, (1976), HarperCollins Publishers New York
[19] Span, R.; Lemmon, E.W.; Jacobsen, R.T.; Wagner, W.; Yokozeki, A., A reference equation of state for the thermodynamic properties of nitrogen for temperatures from 63.151 to 1000K and pressures to 2200mpa, Journal of physical and chemical reference data, 29, 6, 1361-1433, (2000)
[20] Tegeler, C.; Span, R.; Wagner, W., A new equation of state for argon covering the fluid region for temperatures from the melting line to 700K at pressures up to 1000mpa, Journal of physical and chemical reference data, 28, 3, 779-850, (1999)
[21] Schmidt, B., Electron beam density measurements in shock waves in argon, Journal of fluid mechanics, 39, 361-373, (1969)
[22] Ohr, Y.G., Improvement of the Grad 13 moment method for strong shock waves, Physics of fluids, 13, 7, 2105-2114, (2001) · Zbl 1184.76404
[23] Cercignani, C.; Frezzotti, A.; Grosfils, P., The structure of an infinitely strong shock wave, Physics of fluids, 11, 9, 2757-2764, (1999) · Zbl 1149.76336
[24] Muntz, E.P.; Harnett, L.N., Molecular velocity distribution function measurements in a normal shock wave, Physics of fluids, 12, 10, 2027-2035, (1969)
[25] Robben, F.; Talbot, L., Measurement of rotational distribution function of nitrogen in a shock wave, Physics of fluids, 9, 4, 653-662, (1966)
[26] Holtz, T.; Muntz, E.P., Molecular velocity distribution-functions in an argon normal shock-wave at Mach-7, Physics of fluids, 26, 9, 2425-2436, (1983)
[27] Bird, G.A., The velocity distribution function within a shock wave, Journal of fluid mechanics, 30, 479-487, (1967)
[28] Perlmutter, M., Model sampling applied to the normal shock problem, (), 327-330
[29] Bird, G.A., Aspects of structure of strong shock waves, Physics of fluids, 13, 5, 1172-1177, (1970)
[30] Yen, S.M.; Ng, W., Shock-wave structure and intermolecular collision laws, Journal of fluid mechanics, 65, 127-144, (1974), +2 plates · Zbl 0344.76049
[31] Yen, S.M., Numerical solution of the nonlinear Boltzmann equation for nonequilibrium gas flow problems, Annual review of fluid mechanics, 16, 67-97, (1984) · Zbl 0595.76077
[32] Bird, G.A., Perception of numerical methods in rarefied gas dynamics, (), 211-226
[33] Erwin, D.A.; Pham-Van-Diep, G.C.; Muntz, E.P., Nonequilibrium gas-flows - 1. A detailed validation of Monte-Carlo direct simulation for monatomic gases, Physics of fluids A - fluid dynamics, 3, 4, 697-705, (1991) · Zbl 0735.76050
[34] Muntz, E.P.; Erwin, D.A.; Pham-Van-Diep, G.C., A review of the kinetic detail required for accurate predictions of normal shock waves, (), 198-206
[35] Bird, G.A., Molecular gas dynamics and the direct simulation of gas flows, Oxford engineering science series, vol. 42, (1994), Clarendon Press Oxford · Zbl 0709.76511
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