Numerical modeling of the shock and detonation waves interaction with particles on microlevel

I. A. Bedarev

Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 2, pp. 172-192.

Résumé

A computational technology has been developed for direct modeling of the interaction of shock and detonation waves with a set of particles at the microlevel, taking into account the thermal and velocity relaxation of the particles. The simulation of the shock and detonation waves passage through a system of particles with their different mutual location is carried out. Detailed shock-wave patterns of the gas flow in the vicinity of the particles are obtained. The influence of the particles location on their drag coefficient is studied. It is shown that in the case of particles located perpendicular to the flow, the flow regime has an insignificant effect on the drag coefficient, and in the case of particles located along the flow, their mutual influence is preserved at a large distance. Dynamics of heat transfer during the passage of a shock wave through particles is determined and the influence of the mutual location of particles on the dynamics of heat exchange is revealed. In the calculations of the detonation wave-particles interaction, the possibility of detonation failure at particles volume fraction close to the concentrations obtained in modeling at the macrolevel was discovered.

Détail

Keywords: shock waves, detonation waves, velocity and thermal relaxation of particles, numerical simulation.

Bibliographie

[1] Kuznetsov O.M, Stulov V.P., “Supersonic flow around two spheres with a line of centers across the stream”, Aerodynamics of the entrance of bodies into the atmospheres of the planets, ed. G.F. Telenin, Moscow State University, Moscow, 1983, 12–16 (In Russ.)

[2] Lyagushin E.E., Stulov V.P., Yushkov A.Yu., “Experimental study of the interaction of shock waves in the flow around two cylinders”, Investigation of gas dynamics and heat transfer of complex flows of homogeneous and multiphase media, ed. V.P. Stulov, Moscow State University, Moscow, 1990, 26–29 (In Russ.)

[3] Blagosklonov V.I., Kuznetsov V.M., Minailos A.N., Stasenko A.L., Chekhovskii V.F., “Interaction of hypersonic multiphase flows”, Journal of Applied Mechanics and Technical Physics, 20:5 (1979), 571–578 | DOI

[4] Andreev A.A., Kholodov A.S., “On three-dimensional supersonic flow past blunt bodies when interference is present”, USSR Computational Mathematics and Mathematical Physics, 29:1 (1989), 103–107 | DOI | MR | Zbl

[5] Dubrovina I.A., Stulov V.P., “Determination of the greatest distance of the aerodynamic interaction of a pair of spheres and cylinders in a supersonic flow”, Bulletin of Moscow University. Series 1. Mathematics and Mechanics, 1989, no. 5, 46–49 (In Russ.)

[6] Zhdan I.A., Stulov V.P., Stulov P.V., “Aerodynamic interaction of two bodies in a supersonic flow”, Doklady Physics, 49:5 (2004), 315–317 | DOI

[7] N. A. Artem'eva, V. V. Shuvalov, “Interaction of shock waves during the passage of a disrupted meteoroid through the atmosphere”, Shock waves, 5:6 (1996), 359–367 | DOI | Zbl

[8] Zhdan I.A., Stulov V.P., Stulov P.V., “Characteristic elements of a fractured solid in supersonic flow”, Doklady Physics, 49:11 (2004), 680–682 | DOI

[9] Zhdan I.A., Stulov V.P., Stulov P.V., Turchak L.I., “Drag coefficients for bodies of meteorite-like shapes”, Solar System Research, 41:6 (2007), 505–508 | DOI

[10] H. Naiman, D. D. Knight, “The effect of porosity on shock interaction with a rigid, porous barrier”, Shock Waves, 16:4 (2007), 321–337 | DOI | Zbl

[11] Barri N.G., “Aerodynamic interaction of meteor-body fragments: The collimation effect”, Doklady Physics, 54:9 (2009), 423–425 | DOI

[12] Maksimov F.A., “Supersonic flow of bodies system”, Computer Research and Modeling, 5:6 (2013), 969–980 (In Russ.)

[13] Guvernyuk S.V., Maksimov F.A., “Supersonic flow past a flat lattice of cylindrical rods”, Computational Mathematics and Mathematical Physics, 56:6 (2016), 1012–1019 | DOI | DOI | MR | Zbl

[14] B. W. Skews, M. A. Draxl, L. Felthun, M. W. Seitz, “Shock wave trapping”, Shock Waves, 8:1 (1998), 23–28 | DOI | Zbl

[15] Boiko V.M., Klinkov K.V., Poplavskii S.V., “Collective bow shock ahead of a transverse system of spheres in a supersonic flow behind a moving shock wave”, Fluid Dynamics, 39:2 (2004), 330–338 | DOI | Zbl

[16] Boiko V.M., Kiselev V.P., Kiselev S.P., Papyrin A.N., Poplavskii S.V., Fomin V.M., “Interaction of a shock wave with a cloud of particles”, Combustion, Explosion and Shock Waves, 32:2 (1996), 191–203 | DOI | MR

[17] J. D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart, “Unsteady effects in dense, high speed, particle laden flows”, International Journal of Multiphase Flow, 61 (2014), 1–13 | DOI

[18] D. Igra, J. Falcovitz, “Lift and drag on a sphere above ground by a sliding shock”, Proceedings of the Institution of Mechanical Engineers. Part G. Journal of Aerospace Engineering, 226:5 (2012), 550–560 | DOI

[19] P. Sridharan, T. L. Jackson, J. Zhang, S. Balachandar, “Shock interaction with one-dimensional array of particles in air”, Journal of Applied Physics, 117 (2015), 1–18 | DOI

[20] P. Sridharan, T. L. Jackson, J. Zhang, S. Balachandar, S. Thakur, “Shock interaction with deformable particles using a constrained interface reinitialization scheme”, Journal of Applied Physics, 119 (2016), 1–18 | DOI

[21] L. T. Zhang, H. H. Shi, C. Wang, R. L. Dong, H. X. Jia, X. N. Zhang, S. Y. Yue, “Aerodynamic characteristics of solid particles’ acceleration by shock waves”, Shock Waves, 21 (2011), 243–252 | DOI

[22] R. R. Nourgaliev, T. N. Dinh, L. Nguyen, T. G. Theofanous, “Treatment of particle collisions in direct numerical simulations of high speed compressible flows”, Proceedings of IUTAM Symposium on Computational Approaches to Disperse Multiphase Flow, eds. S. Balachandar, A. Prosperetti, Springer, Dordrecht, 2006, 247–259 | DOI

[23] C. Lu, S. Sambasivan, A. Kapahi, H. S. Udaykumar, “Multiscale modeling of shock interaction with a cloud of particles using an artificial neural network for model representation”, Procedia IUTAM, 3 (2012), 25–52 | DOI

[24] Bedarev I.A., Fedorov A.V., Fomin V.M., “Numerical analysis of the flow around a system of bodies behind the shock wave”, Combustion, Explosion, and Shock Waves, 48:4 (2012), 446–454 | DOI

[25] Bedarev I.A., Fedorov A.V., “Computation of wave interference and relaxation of particles after passing of a shock wave”, Journal of Applied Mechanics and Technical Physics, 56:5 (2015), 750–760 | DOI

[26] Bedarev I.A., Fedorov A.V., “Direct simulation of the relaxation of several particles behind transmitted shock waves”, Journal of Engineering Physics and Thermophysics, 90:2 (2017), 423–429 | DOI

[27] Bedarev I.A., Fedorov A.V., Rylova K.V., “Application of detailed and reduced kinetic schemes for the description of detonation of diluted hydrogen-air mixtures”, Combustion, Explosion and Shock Waves, 51:5 (2015), 528–539 | DOI

[28] V. M. Boiko, K. V. Klinkov, S. V. Poplavski, “On a mechanism of intraphase interaction in nonrelaxing two-phase flow”, Procedings of 11th International Conference on Methods of Aerophysical Research, ICMAR'2002 (Novosibirsk, 28 June — 3 July, 2002), Novosibirsk, 2002, 24–27

[29] I. A. Bedarev, A. V. Fedorov, “Mathematical modeling of the detonation wave and inert particles interaction at the macro and micro levels”, Journal of Physics: Conference Series, 894:1 (2017), 012008 | DOI