Fundamental investigations of the finite element solutions for acoustic propagation in ducts

Abstract

The question of convergence of three finite element algorithms for the modelling of acoustic transmission in ducts carrying a nonuniform mean flow is addressed. The details of each algorithm are stated and example calculations in uniform and nonuniform ducts are made and assessed for accuracy and convergence. The algorithm based on the assumption of irrotationality is found to be highly convergent. This algorithm is the one used in current turbo-fan inlet acoustic radiation codes. A theoretical analysis indicating convergence is supported by example calculations. Two additional algorithms which do not require irrotationality are found to be less convergent, and perhaps not convergent at all for certain severely sheared velocity profiles. No theoretical convergence criteria can presently be established for these algorithms and convergence difficulties are shown here by example. Included in this class of algorithms is the duct analysis program ADAM which is known to display apparently nonconvergent solutions in certain cases