Application of parabolized stability equations to jet instabilities and the associated acoustic radiation
Abstract
Numerical approaches for predicting round jet instabilities and the associated noise radiation have been investigated. Classical inviscid Orr-Sommerfeld theory is first employed for parametric analysis of the jet instabilities. The solution from Orr-Sommerfeld theory is valid when the jet shear layer is thin. As the jet flow evolves downstream, the growing shear layer weakens the parallel flow assumption of the classical stability analysis and degrades the prediction of stability properties. A new numerical treatment called parabolized stability equations (PSE hereafter) has been developed for the prediction of jet instabilities. In this new method, the parallel flow assumption is relaxed to account to the slowly growing jet shear layer. In addition, by assuming streamwise slowly varying amplitude and wavenumber of the instability waves, the PSE theory simplifies the otherwise elliptic problem to a system of parabolic differential equations which is solvable by a space-marching procedure. This method has been applied to both incompressible and compressible jet flows and the resulting predictions have been compared to existing experiments and theories. A far-field noise prediction scheme has also been developed which makes use of the PSE solution. The method for noise prediction involves Fourier transforms and the method of stationary phase integration. Upon the application of these schemes to the classical wave equation, a closed-form solution for the radiated pressure field is obtained and the far-field noise distribution is predicted. The PSE solution provides the required inner boundary conditions for the far-field noise prediction.
Degree
Ph.D.
Advisors
Williams, Purdue University.
Subject Area
Aerospace materials|Mechanical engineering|Mechanics
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