Acoustic Analysis of Solid Rocket Motor Cavities by a Finite Element Method

Adaptation of NASTRAN program to solve acoustic mode problems of solid rocket motor cavities by finite element method.

This paper describes an approach to the solution of acoustic modes in a cavity containing both axisymmetric regions and evenly spaced radial slots. A finite element approach is used with degrees of freedom taken as the harmonic coefficients in a Fourier expansion of the pressure. If the assumptions are made that the radial slots are evenly spaced around the circumference and that the circumferential pressure gradient within each slot is negligible, the equations for the harmonic coefficients become uncoupled. Formulas are derived by which the finite element stiffness and mass matrices may be computed. In addition, special terms are derived to account for rapid expansion of the flow in the opening between the slots and the circular cavity. Results are given for three operational solid rocket motors having four, six, and twelve radial slots respectively. Comparisons with other analytic results and with experimental results are given where these data are available.