Integral Formulation of the Compressible Flowfield in Solid Rocket Motors

In this thesis, a semi-analytical formulation is provided for the rotational, steady, inviscid, compressible motion in a solid rocket motor that is modeled as a slender porous chamber. The analysis overcomes some of the deficiencies encountered in previous work on the subject. The method that we employ consists of reducing the problem’s mass, momentum, energy, ideal gas, and isentropic relations into a single integral equation that can be solved numerically. Furthermore, Saint-Robert’s power law is used to link the pressure to the sidewall mass injection rate. At the outset, results are presented for the axisymmetric and planar porous chambers and compared to two closed-form analytical solutions developed under one-dimensional and two-dimensional, isentropic flow conditions, in addition to experimental data. The comparison is carried out assuming either uniformly distributed mass flux or constant injection speed along the porous wall. Our amended formulation is shown to agree with the one-dimensional solution obtained for the case of uniform wall mass flux and with the asymptotic approximation for the constant wall injection speed.