Nonlinear acoustic response of stand-off tubes used in acoustic pressure measurements—Part II: Analysis

Abstract

Rocket engine combustion instabilities, which lead to rapid engine failure through enhanced heat transfer rates and high-cycle fatigue, continue to be the most serious concern facing engine designers. Experimental testing and pressure measurements remains the best approach to determine the susceptibility of an engine design to acoustically coupled combustion instabilities. But, the harsh, high-temperature environment requires remotely mounting dynamic pressure transducers to the engine’s main chamber using “sense-tubes.” Experiments reveal that the acoustic response of the sense-tube is highly nonlinear due to the area-contraction at the connection point between the engine and sense-tube. This nonlinearity leads to large discrepancies between the combustor's actual and the remotely measured acoustic amplitudes. Our aim was to develop an accurate, nonlinear sense-tube acoustic response model including steady flow effects. Therefore, the governing equation for the area-contraction pressure drop was approximated using a Fourier based technique to develop expressions for the steady and acoustic pressure drop across the area change. The acoustic pressure drop model was then incorporated into a response model for the tube. Measurements of the acoustic response of the area-contraction without mean flow agree well with predictions of the developed model.