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Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct
Author(s) -
Steck James E.,
Eversman Walter
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650160705
Subject(s) - duct (anatomy) , finite element method , propeller , wind tunnel , potential flow , velocity potential , mean flow , aeroacoustics , acoustics , engineering , mechanics , sound pressure , boundary value problem , physics , structural engineering , mathematics , turbulence , mathematical analysis , marine engineering , medicine , pathology
The recent interest in propeller noise generation, stimulated by development of new propeller types for commerical propjets, has generated a need for the ability of measure the noise characteristics of propellers. However, wind tunnel noise measurements are affected by reflections from the wind tunnel walls. Computer codes predicting the free‐field noise of a propeller and its noise field in a circular wind tunnel allow validating the use of wind tunnel measurements to predict free‐field noise characteristics. A wind tunnel contains flow which is uniform in the duct axial direction, but can vary in the radial direction. It can be shown that a third‐order differential equation governs the acoustic pressure field for such a duct containing radially sheared subsonic flow. This third‐order problem is then posed as a coupled pair of equations which are second‐order in terms of acoustic density and first‐order in terms of an artificial variable which represents the effects of the flow being sheared. It is shown that this form of the problem allows a natural extension of the existing numerical solution techniques for non‐sheared flow. The sheared flow problem is presented, and a finite element method is developed to yield a solution for propeller‐type acoustic forces. The finite element code and method are refined with numerical experiments, and results are presented for a specific propeller and duct geometry. Good agreement is shown between this method and an alternate approach to the sheared flow problem using a piecewise constant representation of the velocity in the boundary layer. This validates both the numerical methods.