An Efficient Analytical Solution of Blast Wave Problem in Real Gas Flow under the Influence of Dust-Laden Particles
Akmal Husain1, V. K. Singh2, Syed Aftab Haider3
1Akmal Husain*, Department of Mathematics, SoE University of Petroleum and Energy Studies (UPES), Dehradun, India.
2V. K Singh, Department of Applied Sciences, Institute of Engineering and Technology, Lucknow, India.
3Syed Aftab Haider, Department of Mathematics, Shia P. G. College, Lucknow, India.
Manuscript received on January 26, 2020. | Revised Manuscript received on February 05, 2020. | Manuscript published on February 30, 2020. | PP: 2490-2494 | Volume-9 Issue-3, February 2020. | Retrieval Number: C5746029320 /2020©BEIESP | DOI: 10.35940/ijeat.C5746.029320
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Abstract: In the present paper, we investigated the problem of the propagation of blast waves governed by a nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs), describing one-dimensional unsteady motion with generalized geometries in a real gas flow (van der Waals gas) in which the influence of the dust particles is significant. An efficient analytical approach has been used to the governing hyperbolic system with respect to the Rankine-Hugoniot (RH) conditions to obtain an exact solution in terms of flow parameters density, velocity and the pressure, which exhibits space-time dependence. Further, an analytical expression for the total energy influenced by real gas effects (consisting of non-ideal gas and small solid dust-laden particles) is derived. The results obtained significantly explore the effect of dust-laden particles on the propagation of blast waves in a van der Waals gas.
Keywords: Blast waves, Conservation laws, Dust-laden particles, Gas-dynamics, Rankine-Hugoniot jump conditions, Van der Waals gas