Numerical study of the propagation of a small shock wave intensity from a homogeneous gas to an electrically charged dusty environment

D. A. Tukmakov ; A. A. Ahunov

Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 257-269.

Résumé

The paper is devoted to numerical modeling of the process of propagation of a low-intensity shock wave from a pure gas into an inhomogeneous medium, which is a gas suspension of solid particles. Computational experiments considered both electric neutral and charged suspensions of solid particles. In the mathematical model used in the work, the conservation of the momentum components of the carrier medium was described by the system of Navier-Stokes equations for a compressible gas in a two-dimensional formulation. When describing the interaction of the carrier and the dispersed phase of the gas suspension, the Stokes law, Archimedes' principle, the virtual masses force were considered, interphase heat transfer was also taken into account. For the dispersed component of the mixture, a complete hydrodynamic system of equations of motion was solved. It included the equation of continuity, the equation of conservation of momentum and energy. The system of equations of the mathematical model, supplemented by boundary conditions, was solved by an explicit finite-difference method of the second order of accuracy. In the numerical model, an algorithm for suppressing numerical oscillations was also used. Numerical modeling showed that the presence of an electric charge in the dispersed component of the mixture affects the movement of the dispersed component and, due to interfacial interaction, the gas flow. As a result of numerical calculations, it was found that an increase in particle size leads to a significant increase in interfacial velocity slip. It was determined that the intensity of the velocity slip between the carrier and the dispersed phases in an electrically charged dusty medium occurs in the direction of increasing the specific Coulomb force. While in an electrically neutral gas suspension, the growth of velocity slip occurs in the direction of motion of the shock wave.

Détail

Keywords: multiphase media, shock waves, Coulomb force, interfacial interaction, numerical simulation.

Bibliographie

[1] Nigmatulin R. I., Dinamika mnogofaznykh sred, v. 1, Nauka, 1987, 464 pp.

[2] Kutushev A. G., Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshkoobraznykh sredakh, Nedra, Sankt-Peterburg, 2003, 284 pp.

[3] Kisilev S. G., Ruev G. A., Trunev A. P., Fomin V. F., Shavaliev M. Sh., Udarno-volnovye protsessy v dvukhkomponentnykh i dvukhfaznykh sredakh, Nauka, Novosibirsk, 1992, 261 pp.

[4] Fedorov A. V., Fomin V. M., Khmel T. A., Volnovye protsessy v gazovzvesyakh chastits metallov, Novosibirsk, 2015, 301 pp.

[5] Sadin D. V., “TVD-skhema dlya zhestkikh zadach volnovoi dinamiki geterogennykh sred negiperbolicheskogo nekonservativnogo tipa”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 56:12 (2016), 2098–2109 | DOI | MR | Zbl

[6] Fedorov A. V., Mikhailov A. L., Finyushin S. A., Kalashnikov D. A., Chudakov E. A., Butusov E. I., Gnutov I. S., “Registratsiya parametrov mnozhestvennogo otkola i vnutrennei struktury oblaka chastits pri udarnovolnovom nagruzhenii metallov”, Zhurnal eksperimentalnoi i teoreticheskoi fiziki, 149:4 (2016), 792–795

[7] Varaksin Yu. A., Protasov M. V., Yatsenko V. P., “Analiz mekhanizmov osazhdeniya tverdykh chastits na stenki kanalov”, Teplofizika vysokikh temperatur, 2013, no. 5, 738–746 | DOI

[8] Verevkin A. A., Tsirkunov Yu. M., “Techenie dispersnoi primesi v sople Lavalya i rabochei sektsii dvukhfaznoi giperzvukovoi udarnoi truby”, Prikladnaya mekhanika i tekhnicheskaya fizika, 49:5 (291) (2008), 102–113

[9] Glazunov A. A., Dyachenko N. N., Dyachenko L. I., “Chislennoe issledovanie techeniya ultradispersnykh chastits oksida alyuminiya v sople raketnogo dvigatelya tverdogo topliva”, Teplofizika i aeromekhanika, 2013, no. 1, 81–88

[10] Zhuoqing A., Jesse Z., “Correlating the apparent viscosity with gas-solid suspension flow in straight pipelines”, Powder Technology, 345 (2019), 346–351 | DOI

[11] Tadaa Y., Yoshioka S., Takimoto A., Hayashi Y., “Heat transfer enhancement in a gas-solid suspension flow by applying electric field”, International Journal of Heat and Mass Transfer, 93 (2016), 778–787 | DOI

[12] Jaiswal S., Hall T., LeBlanc S., Mukherjee R., Thomas E., “Effect of magnetic field on the phase transition in a dusty plasma”, Physics of Plasmas, 2017 | DOI | MR

[13] Mazumder M. K., Wankum D. L., Sims R. A., “Influence of powder properties on the performance of electrostatic coating process”, J. Electrostat., 40 (1997), 369–374 | DOI

[14] Zinchenko S. P., Tolmachev G. N., “O nakoplenii produktov raspyleniya segnetoelektricheskoi misheni v plazme tleyuschego vysokochastotnogo razryada”, Prikladnaya fizika, 2012, no. 5, 53–56

[15] Dikalyuk A. S., Surzhikov S. T., “Chislennoe modelirovanie razrezhennoi pylevoi plazmy v normalnom tleyuschem razryade”, Teplofizika vysokikh temperatur, 50:5 (2012), 611–619

[16] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Izdatelstvo “Drofa”, M., 2003, 784 pp.

[17] Salyanov F. A., Osnovy fiziki nizkotemperaturnoi plazmy, plazmennykh apparatov i tekhnologii, Nauka, M., 1997, 240 pp.

[18] Tukmakov A. L., Tukmakov D. A., “Generatsiya akusticheskogo vozmuscheniya dvizhuscheisya zaryazhennoi gazovzvesyu”, Inzhenerno-fizicheskii zhurnal, 2018, no. 5, 1–7

[19] Tukmakov A. L., Kashapov N. F., Tukmakov D. A., Fazlyiyakhmatov M. G., “Protsess osazhdeniya zaryazhennoi polidispersnoi gazovzvesi na poverkhnost plastiny v elektricheskom pole”, Teplofizika vysokikh temperatur, 56:4 (2018), 498–502 | DOI | MR

[20] Tukmakov D. A., “Chislennoe modelirovanie kolebanii elektricheski zaryazhennoi geterogennoi sredy, obuslovlennykh mezhkomponentnym vzaimodeistviem”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 27:3 (2019), 73–85

[21] Fletcher C. A., Computation Techniques for Fluid Dynamics, Springer-Verlang, Berlin, 1988, 502 pp. | MR

[22] Muzafarov I. F., Utyuzhnikov S. V., “Primenenie kompaktnykh raznostnykh skhem k issledovaniyu nestatsionarnykh techenii szhimaemogo gaza”, Matematicheskoe modelirovanie, 5:3 (1993), 74–83 | MR | Zbl

[23] Krylov V. I., Bobkov V. V., Monastyrnyi P. I., Vychislitelnye metody, v. 2, Nauka, M., 1977, 401 pp. | MR

[24] Tukmakov A. L., “Chislennoe modelirovanie akusticheskikh techenii pri rezonansnykh kolebaniyakh gaza v zakrytoi trube”, Izvestiya vysshikh uchebnykh zavedenii. Aviatsionnaya tekhnika, 2006, no. 4, 33–36

[25] Gubaidullin D. A. Tukmakov D. A., “Chislennoe issledovanie evolyutsii udarnoi volny v gazovzvesi s uchetom neravnomernogo raspredeleniya chastits”, Matematicheskoe modelirovanie, 26:10 (2014), 109–119 | Zbl

[26] Nigmatulin R. I., Gubaidullin D. A., Tukmakov D. A., “Udarno-volnovoi razlet gazovzvesei”, Doklady akademii nauk, 466:4 (2016), 418–421 | DOI | MR

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