**APA**

**In-text citation:** (Bulat et al., 2016)

**Reference:** Bulat, P. V., Volkov, K. N., & Ilyina, T. Y. (2016). Interaction of a Shock Wave with a Cloud of Particles. *International Electronic Journal of Mathematics Education, 11*(8), 2949-2962.

**AMA**

**In-text citation:** (1), (2), (3), etc.

**Reference:** Bulat PV, Volkov KN, Ilyina TY. Interaction of a Shock Wave with a Cloud of Particles. *INT ELECT J MATH ED*. 2016;11(8), 2949-2962.

**Chicago**

**In-text citation:** (Bulat et al., 2016)

**Reference:** Bulat, Pavel V., Konstantin N. Volkov, and Tamara Y. Ilyina. "Interaction of a Shock Wave with a Cloud of Particles". *International Electronic Journal of Mathematics Education* 2016 11 no. 8 (2016): 2949-2962.

**Harvard**

**In-text citation:** (Bulat et al., 2016)

**Reference:** Bulat, P. V., Volkov, K. N., and Ilyina, T. Y. (2016). Interaction of a Shock Wave with a Cloud of Particles. *International Electronic Journal of Mathematics Education*, 11(8), pp. 2949-2962.

**MLA**

**In-text citation:** (Bulat et al., 2016)

**Reference:** Bulat, Pavel V. et al. "Interaction of a Shock Wave with a Cloud of Particles". *International Electronic Journal of Mathematics Education*, vol. 11, no. 8, 2016, pp. 2949-2962.

**Vancouver**

**In-text citation:** (1), (2), (3), etc.

**Reference:** Bulat PV, Volkov KN, Ilyina TY. Interaction of a Shock Wave with a Cloud of Particles. INT ELECT J MATH ED. 2016;11(8):2949-62.

# Abstract

The problem of reducing the likelihood of detonation and explosion during saturation of a gas or liquid flow with the cloud of particles is considered. The tasks, associated with the formation of particles clouds, dust lifting behind a travelling shock wave, ignition of particles in high-speed and high-temperature gas flows are adjoined to these problems. The conditions of excitation and propagation of detonation waves are determined for the purpose of their initiation, prevention, suppression or damping. A review of existing methods for modeling of two-phased flows is provided. The mathematical model of shock wave interaction with the cloud of solid particles is discussed, and numerical method is briefly described. The numerical simulation of interaction between a supersonic flow and a cloud of particles being in motionless state at the initial time is performed. Calculations are carried out taking into account the influence that the particles cause on the flow of carrier gas.