Decay of a Saw Tooth–profile in Two-phase-flows of Gas-particle Mixture

Abstract

Aim: To study the length and decay behavior of a saw tooth-profile in Two-Phase-Flows of gas-particle mixture and compare the analytical solution with numerical solution. Study Design: Progressive-wave approach is used to obtain asymptotic solution of the non linear system of partial differential equations governing two-phase flows of gas-particle-mixture in reacting gases, which governs the growth and decay of acceleration front. In preparation of graphs origin 7.5 is applied. Place of Study: Department of Mathematics & Astronomy, Lucknow University, Lucknow-226007, India. Methodology: Analytical and numerical method (Runge-Kutta method of fourth order) is used. Results: The evolution equation governs the growth and decay of acceleration front and its analytical solution is obtained. With help of this evolution equation length and decay behavior of saw –tooth profile is investigated. These results are compared numerically with help of Runge-Kutta method of fourth order. Numerical results shows that the applied numerical method is in good agreement for length of Saw-Tooth profile for cylindrical case. In case of decay behavior it is in good agreement with analytical one for plane and cylindrical case. Conclusion: We conclude that the applied method is in good agreement for length of Saw-Tooth profile of cylindrical case and for decay behavior of Saw-Tooth profile for plane and cylindrical case.