A study of sound field in a standing wave tube with flow and lateral Helmholtz resonator I. Theoretical analysis

A lateral Helmholtz resonator added to a standing wave tube without flow has been verified as a new method of noise reduction for combustion noise radiated from combustion channel of rockets or turbine machines. But in fact there is a flow with low velocity in the combustion channel. Therefore the theoretical analysis carried out by this paper is aimed at sound field of standing wave tube with flow and lateral Helmholtz resonator. Certainly a mathematic and physical problem should be formulated and solved. There are three key problems solved by the paper: (1) to formulate the discontinuity condition at the joint between the standing wave tube and Helmholtz resonator in the case of flow. (2) to formulate the acoustic impedance of Helmholtz resonator, considering the effects of flow, viscous and multihole. (3) to formulate the refection condition at the end of the standing wave tube. The theoretical works above have been verified by experiments.