Azimuthal mode measurements of elliptic jets

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Abstract
A procedure to quantitatively measure the relative amplitudes of azimuthal modes in the acoustic field of an elliptic jet is presented. The work describes how the azimuthal modes in an elliptic jet can be represented by a linear combination of Mathieu function modes and how the amplitude coefficients of each individual mode can be determined through an orthogonal decomposition based on Mathieu functions. The modal decomposition is performed in an elliptic cylindrical coordinate system natural to the elliptic jet geometry. The procedure is first tested on an artificially excited, perfectly expanded Mach 1.5 elliptic jet with preferential varicose and flapping mode excitation of discrete frequencies. The excitation was provided with a four electrode glow discharge system with phase control of the individual electrodes. Following that, the procedure was applied to naturally excited Mach 1.5 jets with both air and a helium/air mixture as the jet working gas. The helium/air jets simulate the higher jet velocity and lower jet density of heated jets. The modal decomposition technique is verified by experiment, allowing significant differences to be identified in the azimuthal modal content as the jet simulated temperature is increased.