Investigation of sound field for a standing wave tube system with flow and with lateral Helmholtz resonator Ⅰ. Theoretical analysis

A lateral Helmholtz resonator added to a standing wave tube without flow has been validated as a method of noise reduction for combustion noise radiated from combustion channel of rockets or turbines. But in fact there is a flow with low velocity in the combustion channel. Therefore the theoretical analysis carried out is aimed at sound field of standing wave tube with flow and with lateral Helmholtz resonator. Certainly a relevant math-physical model should first be formulated. Here three key problems need to be solved: (1) To formulate the discontinuity condition at the joint between the standing wave tube and Helmholtz resonator in the case of flow. (2) To determine the acoustic impedance of Helmholtz resonator, considering the effects of flow, viscous and multihole. (3) To formulate the reflection condition at the end of the standing wave tube. Some formulas for analysis of the sound field in the tube with flow and with lateral Helmholtz resonator are deduced. These theoretical works have been validated by experiments.