The Radiated Noise from Isotropic Turbulence Revisited
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman 1952, was the first application of Lighthills Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthills stress tensor, T sub ij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the a2T sub ijat2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order T sub ij retarded-tune covariance is evaluated from the square of similar second-order covariance, which is assumed known. In this derivation no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical SimulationDNS results of both Sarkar and Hussaini1993 and Dubois1993, is compared with the re-evaluation of Proudmans original model. Theses tests are then with the sound power derived from a phenomenological model based on simple approximations to the retarded-timespace covariance of T sub xx.
- Fluid Mechanics