Transient wall pressures in an overexpanded and large area ratio nozzle

Abstract

Surveys of the fluctuating wall pressure were conducted on a sub-scale parabolic-contour rocket nozzle to infer an understanding of the flow and shock structure pattern during fixed and transient operations of the nozzle. During start-up, the nozzle is highly overexpanded, which results in unsteady wall pressure signatures driven by shock foot unsteadiness. Wall pressure data are first analyzed using spatial Fourier transformations to extract the azimuthal modes during various operating states. A time-frequency analysis of the temporal azimuthal mode coefficients is then used to characterize the time-dependent spectral behavior of the wall pressure signatures during start-up. For both fixed and transient operations of the nozzle, the axisymmetric breathing mode (m = 0) comprises most of the resolved energy. As for the transient operations alone, slight deviations in ramp rate are shown to considerably influence the amount of unsteadiness that the nozzle wall is exposed to, even though the general spectral and temporal features remain similar. In particular, increased ramp rates result in increased wall pressure intensity. Secondly, three major low-frequency events (f ≲ 400 Hz) were observed during start-up and are attributed to: (1) \(\hbox{FSS} \rightarrow \hbox{RSS}\) transition, (2) the passing of the reattachment line from the first separation bubble, and (3) the ‘end-effects regime’. The last of these refers to a condition where a trapped separation bubble opens intermittently to ambient at the nozzle lip.