Whistling potential of throttling orifices and its connection to liquid rocket combustion instability

Orifice whistling is recently established as a cause of high frequency combustion instability in liquid rocket engines. The series of studies on the experimental thrust chamber, known as BKD, developed at the German Aerospace Center (DLR), were instrumental in identifying this phenomenon. BKD encountered an injector-driven thermo-acoustic instability caused by the self-excitation of the LOX injector. The throttle orifice in the LOX injector plays a vital role in the self-excitation through whistling. In this work, the impedance of the BKD throttling orifice is characterized with the motive to find its whistling range. The CFD approach based on solving the unsteady Reynolds Averaged Navier Stokes equations proposed by Lacombe et al. [1] is used for this characterization. We characterize the orifice at the weak and the strong coupling conditions reported in the literature. The orifice impedance is calculated in the range of 4 kHz to 15 kHz, covering the entire potential coupling range of LOX injector eigen modes. The impedance results show that the orifice character follows the whistling behavior of the “medium” orifices. The resistance turns negative in the Strouhal number range of $St=0.89$ - 1.2 for both the weak and strong operating conditions. When plotted against the frequency, the resistance at the strong coupling condition occurs close to the second longitudinal (2L) mode of the LOX injector, suggesting direct excitation of the injector through the orifice whistling. The coexistence of the 2L mode and the first transverse (1T) mode of the combustion chamber at the same frequency leads to combustion instability.