Problems of acoustic wave generation and propagation were developed with the intent of providing known solutions of these problems as a validation test for solutions generated by computational aeroacoustics methods. Many of these problems, called model or benchmark problems, could be solved in closed form or solved using standard numerical integration techniques. Both solutions followed from an analytic solution for the equations governing that particular benchmark problem. The present paper discusses the solution for a benchmark problem where an acoustic field is generated inside and outside of an unflanged circular duct by a single acoustic mode propagating from the source within the duct. The original solution to this problem was inaccurate and incomplete. Advances in the analytic techniques were used to solve the problem for both the acoustic field within the duct and the far-field directivity outside of the duct. The correct solutions for the variables specified in the benchmark problem statement were used to check the solutions of previous computational attempts to solve this problem. In addition, the NASA Broadband Aeroacoustic Stator Simulation code was used to solve for the acoustic field. Comparisons with the theoretical solution were made for the in-duct acoustic pressure, the far-field directivity, and the near-field acoustic pressure.
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