Numerical technologies for investigations of heterogeneous detonations of gas particle suspensions

T. A. Khmel ; A. V. Fedorov

Matematičeskoe modelirovanie, Tome 18 (2006) no. 8, pp. 49-63.

Résumé

The paper presents a review of some numerical technologies for investigation of shock wave and detonation processes in suspensions of gas and reactive particles in the frame of mechanics of heterogeneous media. Corrections of the TVD-schemes for fine-dispersed (in the frame of one-velocity two-temperature approach) and ultra-fine (equilibrium in velocities and temperatures) mixtures are introduced. The data of testing calculations and some results of numerical modeling of cellular detonations (on the model of aluminum suspension) are presented. A technology of parallel computations of detonation based on geometric principles is described. Linear dependence of acceleration on number of processors used is obtained in calculations on the complex MVS-1000.

Bibliographie

[1] Eckhoff R., Dust explosions in the process industries, Gulf Professional Publishing, Hardbound, 2003

[2] Nigmatulin R. I., Dinamika mnogofaznykh sred, Ch. 1, 2, Nauka, M., 1987

[3] Korobeinikov V. P., Markov V. V., Menshov I. S., “Chislennoe modelirovanie rasprostraneniya udarnykh voln po neodnorodnoi pylegazovoi smesi”, Dokl. AN SSSR, 290:4, (1986), 816–819

[4] Korobeinikov V. P., Markov V. V., Sizykh G. B., “Chislennoe reshenie dvumernykh nestatsionarnykh zadach o dvizhenii goryuchei pylegazovoi smesi”, Dokl. AN SSSR, 316:5 (1991), 1077–1081 | MR | Zbl

[5] Gelfand B. E., Gubanov A. V., Medvedev S. P., Timofeev E. I., Tsyganov S. A., “Udarnye volny pri razlete szhatogo ob'ema gazovzvesi tverdykh chastits”, Dokl. AN SSSR, 281:5 (1985), 1113–1116

[6] Gelfand B. E., Borisov A. A., Tsyganov S. A., “Modelirovanie voln razrezheniya pri detonatsii gazovykh smesei”, Fizika goreniya i vzryva, 25:1 (1989), 90–97

[7] Levin V. A., Tunik Yu. V., “Vzryvnoe initsiirovanie detonatsii v metanovozdushnoi gazovzvesi”, Khim. fizika protsessov goreniya i vzryva. Probl. goreniya i vzryva, Mater. 9 Vses. simp. po goreniyu i vzryvu (Suzdal, 19–24 noyab., 1989), Chernogolovka, 1989, 99–101

[8] Tunik Yu. V., “Global modelling of heat release during initiation and propagation of detonation and deflagration waves in methane-air-particle systems”, Shock Waves, 9:3 (1999), 173–179 | DOI | Zbl

[9] Borisov A. A., Khasainov B. A., Veisser B. i dr., “O detonatsii vzvesei alyuminiya v vozdukhe i kislorode”, Khimicheskaya fizika, 10:2 (1991), 250–272

[10] Varaksin A. Yu., Turbulentnye techeniya gaza s tverdymi chastitsami, Fizmatlit, M., 2003

[11] Smirnov N. N., “Gorenie i detonatsiya v mnogofaznykh sredakh, soderzhaschikh zhidkoe goryuchee”, Fizika goreniya i vzryva, 24:3 (1988), 84–94

[12] Smirnov N. N., Nikitin V. F., Legros J. C., “Ignition and combustion of turbulized dust-air mixtures”, Combustion and Flame, 123:1–2 (2000), 46–67 | DOI

[13] Mitrofanov V. V., Detonatsiya gomogennykh i geterogennykh sistem, Izd-vo In-ta gidrodinamiki im. M. A. Lavrenteva SO RAN, Novosibirsk, 2003 | MR

[14] Voronin D. V., Zhdan S. A., “Ob odnomernoi neustoichivosti detonatsionnykh voln v raspylakh”, Fizika goreniya i vzryva, 22:4 (1986), 92–98

[15] Zhdan S. A., Prokhorov E. S., “Initsiirovanie detonatsii v vakuum-vzvesi chastits geksogena”, Fizika goreniya i vzryva, 34:4 (1998), 65–71

[16] Zhdan S. A., Prokhorov E. S., “Detonatsiya vzvesi chastits geksogena, chastichno zapolnyayuschei tsilindricheskii kanal”, Fizika goreniya i vzryva, 35:4 (1999), 79–87

[17] Zhdan S. A., Prokhorov E. S., “Raschet yacheistoi struktury detonatsii raspylov v sisteme $\mathrm{H}_2$-$\mathrm{O}_2$”, Fizika goreniya i vzryva, 36:6 (2000), 111–112

[18] Kutateladze S. S., Nakoryakov V. E., Teplomassoobmen i volny v gazo-zhidkostnykh sistemakh, Nauka, Novosibirsk, 1984

[19] Kutushev A. G., Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshloobraznykh sredakh, Nedra, Sankt-Peterburg, 2003

[20] Gubaidullin A. A., Ivandaev A. I., Nigmatullin R. I., “Modifitsirovannyi metod “krupnykh chastits” dlya rascheta nestatsionarnykh volnovykh protsessov v mnogofaznykh dispersnykh sredakh”, Zhurnal vychisl. matematiki i mat. fiziki, 17:6 (1977), 1531–1544 | MR | Zbl

[21] Ivandaev A. I., Kutushev A. G., Rodionov S. P., “Matematicheskoe modelirovanie udarno-volnovykh protsessov v khimicheski-inertnykh i reagiruyuschikh polidispersnykh smesyakh gaza s tverdymi chastitsami”, Matem. modelirovanie, 7:12 (1995), 19–32 | Zbl

[22] Kutushev A. G., Rodionov S. P., “Ploskie detonatsionnye volny v gazovzvesyakh unitarnogo topliva s prostranstvenno-neodnorodnym raspredeleniem chastits”, Fizika goreniya i vzryva, 34:5 (1998), 103–110

[23] Medvedev A. E., Fedorov A. V., Fomin V. M., “Matematicheskoe modelirovanie vosplameneniya chastits metallov v vysokotemperaturnom potoke za udarnoi volnoi”, Fizika goreniya i vzryva, 18:3 (1982), 5–9

[24] Medvedev A. E., Fedorov A. V., Fomin V. M., “Opisanie vosplameneniya i goreniya smesei gaza i tverdykh chastits metodami mekhaniki sploshnoi sredy”, Fizika goreniya i vzryva, 20:2 (1984), 3–9

[25] Medvedev A. E., Fedorov A. V., Fomin V. M., “Issledovaniya adiabat geterogennoi dvukhfaznoi detonatsii”, Fizika goreniya i vzryva, 23:2 (1987), 115–121

[26] Fedorov A. V., Tetenov E. V., “Initsiirovanie geterogennoi detonatsii chastits, dispergirovannykh v kislorode”, Fizika goreniya i vzryva, 1992, no. 3, 83–89

[27] Fedorov A. V., Vesser B., Tetenov E. V., “Vosplamenenie chastits metallov pri realnom vzryve I, II”, Fizika goreniya i vzryva, 27:5 (1991), 16–28

[28] Fedorov A. V., “Struktura geterogennoi detonatsii chastits alyuminiya, dispergirovannykh v kislorode”, Fizika goreniya i vzryva, 28:3 (1992), 82–83

[29] Kazakov Yu. V., Fedorov A. V., Fomin V. M., “Raschet razleta szhatogo ob'ema gazovzvesi”, PMTF, 23:5 (1987), 139–144 | MR

[30] Kazakov Yu. V., Fedorov A. V., Fomin V. M., “Rezhimy normalnoi detonatsii v relaksiruyuschikh sredakh”, Fizika goreniya i vzryva, 25:1 (1989), 119–127 | MR

[31] Fedorov A. V. Fomin V. M., “Chislennoe issledovanie techenii kompozitnykh reagiruyuschikh gazovzvesei”, PMTF, 40:2 (1999), 128–136 | Zbl

[32] Fedorov A. V., Khmel T. A., “Tipy i ustoichivost detonatsionnykh techenii aerovzvesi alyuminiya v kislorode”, Fizika goreniya i vzryva, 32:2 (1996), 74–85

[33] Fedorov A. V., Khmel T. A., “Vzaimodeistvie detonatsionnykh voln i voln razrezheniya v aerovzvesi chastits alyuminiya v kislorode”, Fizika goreniya i vzryva, 33:2 (1997), 102–110

[34] Fomin V. M., Fedorov A. V., Boiko V. M. dr., “Volnovaya dinamika reagiruyuschikh i nereagiruyuschikh gazovzvesei”, Teplofizika i aeromekhanika, 4:2 (1997), 129–157 | MR

[35] Fedorov A. V., “Vosplamenenie gazovzvesei v rezhime vzaimodeistvuyuschikh kontinuumov”, Fizika goreniya i vzryva, 34:4 (1998), 57–64

[36] Fedorov A. V., Khmel T. A., “Opredelenie samopodderzhivayuschikhsya rezhimov neidealnoi detonatsii na modeli aerovzvesi chastits alyuminiya”, Fizika goreniya i vzryva, 34:5 (1998), 95–102

[37] Fedorov A. V., Fomin V. M., Khmel' T. A., “Non-equilibrium model of steady detonations in aluminum particle-oxygen suspensions”, Shock Waves, 9:5 (1999), 313–318 | DOI | Zbl

[38] Fedorov A. V., Khmel T. A., “Chislennoe modelirovanie udarno-volnovogo initsiirovaniya geterogennoi detonatsii aerovzvesi chastits alyuminiya”, Fizika gopeniya i vzpyva, 35:3 (1999), 81–88

[39] Fedorov A. V., Khmel T. A., “Chislennoe modelirovanie initsiirovaniya detonatsii pri vkhozhdenii udarnoi volny v oblako chastits alyuminiya”, Fizika goreniya i vzryva, 38:1 (2002), 114–122

[40] Fedorov A. V., Khmel T. A., “Vzaimodeistvie udarnoi volny s oblakom chastits alyuminiya v kanale”, Fizika goreniya i vzryva, 38:2 (2002), 89–98

[41] Khmel T. A., “Chislennoe modelirovanie dvumernykh detonatsionnykh techenii v gazovzvesi reagiruyuschikh tverdykh chastits”, Matem. modelirovanie, 16:6 (2004), 73–77 | Zbl

[42] Fedorov A. V., Khmel T. A., “Chislennoe modelirovanie formirovaniya yacheistoi geterogennoi detonatsii chastits alyuminiya v kislorode”, Fizika goreniya i vzryva, 41:4 (2005), 84–98

[43] Fedorov A. V., Khmel T. A., “Matematicheskoe modelirovanie detonatsionnykh protsessov v gazovzvesi chastits uglya”, Fizika goreniya i vzryva, 38:6 (2002), 103–112

[44] Khasainov B. A., Veyssiere B., “Initiation of detonation regimes in hybrid two-phase mixtures”, Shock Waves, 6 (1996), 9–15 | DOI

[45] Arfi P., Veyssiere B., Khasainov B. A., “Detonations of starch suspensions in gaseous $\mathrm{O}_2$/$\mathrm{N}_2$ and stoichiometric $\mathrm{H}_2$/$\mathrm{O}_2$ mixtures”, Combustion and Flame, 117:3 (1999), 477–492 | DOI

[46] Veyssiere B., Khasainov B. A., Arfi P., “Investigation of the detonation regimes in gaseous mixtures with suspended starch particles”, Shock Waves, 9:3 (1999), 165–172 | DOI | Zbl

[47] Khasainov B. A., Veyssiere B., Ingignoli W., “Numerical simulation of detonation cell structure in hydrogen-air mixture loaded by aluminum particles”, High-Speed Deflagration and Detonation. Fundamental and Control, eds. G. Roy et al., ELEX-KM Publishers, M., 2001, 163–174

[48] Veyssiere B., Bozier O., Khasainov B. A., “Effect of a suspension of magnesium particles on the detonation characteristics of methane-oxygen-nitrogen mixtures at elevated initial pressures”, Shock Waves, 12:3 (2002), 227–233 | DOI | Zbl

[49] Eidelman S., Yang X., “Detonation wave propagation in variable density multi-phase layers”, AIAA, 1992, 0346

[50] Ludwig T., Roth P., “Modeling of laminar combustion wave propagation in reactive gas/particle mixtures”, International Journal of Multiphase Flow, 23:1 (1997), 93–111 | DOI | Zbl

[51] Loth E., Sivier S., Baum J., “Dusty detonation simulations with adaptive unstructured finite elements”, AIAA Journal, 35:6 (1997), 1018–1024 | DOI | Zbl

[52] Tsuboi N., Hayashi A. K., Matsumoto Y., “Three-dimensional parallel simulation of cornstarch-oxygen two-phase detonation”, Shock Waves, 10:4 (2000), 277–285 | DOI | Zbl

[53] Benkiewicz K., Hayashi A. K., “Aluminum dust ignition behind reflected shock wave: two-dimensional simulations”, Fluid Dynamics Research, 30:5 (2002), 269–292 | DOI

[54] Benkiewicz K., Hayashi A. K., “Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement”, Shock Waves, 13 (2003), 385–402 | DOI

[55] Murray S. B., Zhang F., Thibault P. A., “Transition from Deflagration to Detonation in an End Multiphase Slug”, Progress in Astronautics and Aeronautics 94. Combustion and Flame, 114:1–2 (1998), 13–25

[56] Zhang F., Frost D. L., Thibault P. A., Murray S. B., “Explosive dispersal of solid particles”, Shock Waves, 10 (2001), 431–443 | DOI | Zbl

[57] Park J. S., Baek S. W., “Interaction of a moving shock wave with a two-phase reacting medium”, International Journal of Heat and Mass Transfer, 46:24 (2003), 4717–4732 | DOI | MR | Zbl

[58] Bielert, M. Sichel, “Numerical simulation of dust explosions in pneumatic conveyors”, Shock Waves, 9:2 (1999), 125–139 | DOI

[59] Chang E. J., Kailasanath K., “Shock wave interactions with particles and liquid fuel droplets”, Shock Waves, 12:4 (2003), 333–341 | DOI | Zbl

[60] Rogue X., Rodrigues G., Haas J. F., Saurel R., “Experimental and numerical investigation of the shock-induced fluidization of the particle bed”, Shock Waves, 8 (1998), 29–45 | DOI | Zbl

[61] Arienti M., Shepherd J. E., “A numerical study of detonation diffraction”, Journal of Fluid Mechanics, 529 (2005), 117–146 | DOI | MR | Zbl

[62] M. V. Papalexandris, “Numerical simulation of detonations in mixtures of gases and solid particles”, Journal of Fluid Mechanics, 507 (2004), 95–142 | DOI | MR | Zbl

[63] Kosinski P., Hoffmann A. C., “Mathematical modelling of dust explosions in interconnected vessels”, Nonlinear Analysis, 63:5–7, e1087–e1096 | Zbl

[64] Boiko V. M., Kiselev V. P., Kiselev S. P., Papyrin A. M., Poplavskii S. V., Fomin V. M., “O vzaimodeistvii udarnoi volny s oblakom chastits”, Fizika goreniya i vzryva, 32:2 (1996), 86–99

[65] Saito T., Marumoto M., Takayama K., “Numerical investigations of shock waves in gas-particle mixtures. Evaluation of numerical methods for dusty-gas shock wave phenomena”, Shock Waves, 13 (2003), 299–322 | DOI | Zbl

[66] Strauss W. A., “Investigation of the detonation of aluminum powder-oxygen mixtures”, AIAA Journal, 6:12 (1968), 1753–1761 | DOI

[67] Harten, “High resolution schemes for hyperbolic conservation laws”, J. of Computational Phys., 49:3 (1983), 357–393 | DOI | MR | Zbl

[68] Wang J. C. T., Widhopf G. F., “A High-Resolution TVD Finite Volume Scheme for the Euler Equations in Conservation Form”, AIAA Paper, 1987, 0538

[69] Roe P. L., “Approximate Riemann solvers, parameter vectors, and difference schemes”, Journal of Computational Physics, 43 (1981), 357–72 | DOI | MR

[70] Gentry R. A., Martin R. E., Daly B. J., “An Eulerian differencing method for unsteady compressible flow problems”, Journal of Computational Physics, 1 (1966), 87–118 | DOI | Zbl

[71] Rouch P., Vychislitelnaya gidrodinamika, Mir, M., 1980 | Zbl

[72] Montagne J. L., Yee H. C., Vinokur M., “Comparative study of high-resolution shock-capturing schemes for a real gas”, AIAA Journal, 27:10 (1989), 1332–1346 | DOI | MR

[73] Barthel H. O., “Predicted spacings in hydrogen-oxygen-argon detonations”, Physics of Fluids, 17:8 (1974), 1547–1553 | DOI

[74] Shpakovskii G. I., Serikova N. V., Programmirovanie dlya mnogoprotsessornykh sistem v standarte MPI, BGU, Minsk, 2002