Application of Spinning Mode Theory to Submersible Vehicle Propellers

Abstract

The pressure distribution on a propeller generates periodic pressure fluctuations in the surroundings, and consequently discrete frequency noise. If the propeller is enclosed in a rigid cylindrical duct, spinning mode theory [J. M. Tyler and T. G. Sofrin, “Axial Flow Compressor Noise Studies,” Trans. SAE (1961)], which has been used successfully to combat noise in jet engine compressors, can be applied. An arbitrary pressure distribution at the propeller is decomposed into radial and circumferential modes by Fourier analysis. Solution of the wave equation shows that modes spinning around the duct at speeds greater than the speed of sound propagate undiminished through the duct, while those spinning at lower speeds decay exponentially. The decay rate is related to the geometry and speed of the propeller. Numerical examples for a submersible vehicle propeller show that the SPL of primary modes produced by the ducted propeller alone can be reduced to negligible levels. Some interference modes arising from interactions between the propeller and stationary supports will propagate undiminished.