Spectral-Element/Kirchhoff Method for Fan-Tone Directivity Calculations

A Kirchhoff integral method is coupled to a spectral-element radiation solver for efficient computations of fan-tone directivities at arbitrary distances from a turbofan inlet. The Kirchhoff algorithm accurately constructs the acoustic solution at specified locations in the farfield by processing near-field data supplied by the spectral-element solver. This allows the use of a much smaller spectral-element domain concentrated near the engine that is not required to encompass the specified directivity radius. The use of a smaller computational domain translates into a reduction in overall CPU time and/or an increase in the frequency limit of the code. This paper presents a detailed description of the theory, implementation, and validation of the Kirchhoff algorithm. Numerical studies are performed to address the following issues: 1) optimal placement of the Kirchhoff integration surface in the presence of a locally non-uniform mean-flow; 2) impact of a partially opened Kirchhoff surface on the accuracy of the predicted directivity. The spectralelement/Kirchhoff system is further demonstrated by computing inlet radiation directivities up to a radius of 150 feet for practical engine power conditions and frequencies.