Date of Award

2014

Document Type

Thesis

Degree Name

Master of Science in Engineering (MSE)

Department

Mechanical and Aerospace Engineering

Committee Chair

Kader Frendi

Committee Member

Sarma Rani

Committee Member

Robert A. Frederick, Jr.

Subject(s)

Modal analysis., Combustion., Electro-acoustics.

Abstract

A linear, modal analysis-based analytical method has been presented to predict the longitudinal, transverse, as well as the mixed acoustic modes in two-dimensional (2-D) cartesian ducts with discontinuities in the cross-sectional area. Two duct configurations are investigated involving one and two discontinuities in the cross-sectional area. The effects of mean flow, cross-sectional area ratio, as well as of the different types of boundary conditions on duct acoustic modes are investigated. The various boundary conditions considered at the duct inlet and outlet include: closed-closed for cases without mean flow; open-open for cases with and without mean flow; and open-choked for cases with mean flow. Acoustically consistent matching conditions have been developed. A rigorous and detailed parametric study was undertaken involving the variation of cross-sectional area ratio and mean inflow Mach number. Acoustic modal frequencies were determined for the first six longitudinal modes, the first transverse mode, as well as for the mixed longitudinal-transverse mode. It is demonstrated that the mean flow significantly influences the modal frequencies even at low Mach numbers (~0.1). A novel method to incorporate the effects of non-uniform mean velocity profiles into the modal analysis framework is developed. Two different mean velocity profiles viz. parabolic and turbulent mean velocity profiles and their impact on the acoustics of the duct are studied and shown to be negligible. A detailed investigation of the ``edge conditions" and its effect on the linear modal analysis has been undertaken.

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