Control Volume Analysis of Rectangular Ducts with Arbitrary Mean-Flow, Transverse Wall Impedances, and Temperature Discontinuity

Abstract

Combustion instabilities (CIs) are a consistent and ubiquitous problem for industrial burners, rockets, and gas turbines. Reduced order acoustic models are often used to analyze combustion instabilities. Typically, reduced order models incorporate a few important parameters based on the application and are limited in complexity by design. Combining a small number of parameters quickly causes the underlying equations to become untenable, necessitating the use of numerical methods, computational models, and experimentation. Therefore, reduced order models which include many relevant parameters that are still computationally inexpensive are desirable. This thesis proposes a linear control volume analysis (CVA) based around the assumptions of linear acoustics and planar acoustic wave propagation. Transverse wall impedance, axial mean-flow, and transverse mean flow are explicitly accounted for in the derivation. The resulting governing equation imbeds three-dimensional information from the transverse wall impedance, axial mean flow, and transverse mean flow into a plane wave solution. Thus, the effects of transverse wall impedance, axial mean-flow, and transverse mean flow can be investigated directly. The governing equation developed from the CVA equation reduces to the classical analytical wave equation in one dimension when eliminating the wall impedances and mean flow. The CVA is applied to two duct acoustic problems: a closed – closed duct and a constant mass flow-rate – nozzle duct. These application problems include the effects of transverse wall impedance, axial mean-flow, transverse mean-flow, and temperature.