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The radiated noise from isotropic turbulence revisited
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Lilley, Geoffrey M. |
| Copyright Year | 1993 |
| Description | The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's 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 Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 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 Tij retarded-time 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 Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions. |
| File Size | 2981562 |
| Page Count | 62 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19940019883 |
| Archival Resource Key | ark:/13960/t3wt3m22d |
| Language | English |
| Publisher Date | 1993-12-01 |
| Access Restriction | Open |
| Subject Keyword | Fluid Mechanics And Heat Transfer High Reynolds Number Stress Tensors Numerical Analysis Covariance Flow Distribution Aerodynamic Noise Isotropic Turbulence Mach Number Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
