Analytical study on plate edge noise. (1st report, trailing edge noise caused by vorticity waves)

An analysis is performed on the trailing edge noise which is one of the mechanisms of noise generation in flow machines. An acoustic field is treated where a semi-infinite flat plate is placed parallel to the inviscid uniform flow with incident vorticity waves convected from the upstream direction. Applying the Wiener-Hopf technique, we obtain an exact solution to the sound pressure proportional to the amplitude of the incident vorticity wave without restriction of frequency or velocity. The calculated acoustic field, which varies with flow velocity, exhibits general features of the sound pressure level (SPL) in a cardioid pattern with the constant phase surface distorted by the main flow. The relationship between flow velocity and SPL is ascertained to be dependent on the 5th law at low Mach numbers. But the results show that such dependence does not hold at higher Mach numbers where the radiated noise level rises progressively as the flow velocity increases.