Flow Modeling in a Porous Cylinder with Regressing Walls Using Semi Analytical Approach

Abstract

In this paper, the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket
motors is presented. As usual, the cylindrical propellant grain of a solid rocket motor is modeled as a long tube with
one end closed at the headwall, while the other remains open. The cylindrical wall is assumed to be permeable so as
to simulate the propellant burning and normal gas injection. At first, the problem description and formulation are
considered. The Navier-Stokes equations for the viscous flow in a porous cylinder with regressing walls are reduced
to a nonlinear ODE by using a similarity transformation in time and space. Application of Differential Transformation
Method (DTM) as an approximate analytical method has been successfully applied. Finally the results have been
presented for various cases.