Abstract
In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.
Highlights
Direct acoustic response measurements in combustion devices such as solid and liquid rocket engines remain the best way to identify thermo-acoustic instabilities
The nearest sensors to the area contraction were placed 2.4 and 5.4 tube diameters from the sample for the standing wave tube (SWT) and extension tube (EXT) sections, respectively, which exceeds the 2 diameters outlined in ASTM E1050-19.7 This configuration allows for subtraction of the influence of the downstream components, thereby isolating the effects of the area contraction, as described in Kawell et al
Impedance tube measurements are highly sensitive to errors in phase between the microphones; a calibration procedure was implemented as outlined in ASTM E1050-19.7 An absolute static pressure transducer and thermocouple were used for measuring the pressure and temperature inside the SWT to determine the air density, which is especially critical in the cases with flow
Summary
Direct acoustic response measurements in combustion devices such as solid and liquid rocket engines remain the best way to identify thermo-acoustic instabilities. The high heat and corrosive gasses contained within combustion chambers make them inhospitable to pressure transducers; sense-lines are often used to offset the sensor from this harsh environment. By employing a sense-line for pressure measurements, an area contraction is created at the connection point between the sense-line and the combustion chamber. This area contraction has an associated complex acoustic impedance to acoustic driving, thereby modifying both the amplitude and phase of the pressure response measured by the sensors in the sense-line. Purge flow of an inert gas is often introduced into the sense-line to further protect the sensors from high temperatures, introducing additional complications toward understanding the measured pressure
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