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) FSS to 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.
A study of the fluctuating wall pressure beneath a 2-d turbulent boundary layer was conducted in a water tunnel with Reynolds numbers, based on momentum thickness, ranging between 2,100 and 4,300. The boundary layer was perturbed with steady mild suction to assess the effect of upstream suction on the fluctuating wall pressure measured downstream of the suction slit. Wall pressure signatures were captured using a custom-fabricated piezoceramic array with d? values ranging between 64 and 107. Likewise, the velocity field was measured with a laser Doppler velocimeter with l? values ranging between 4.0 and 6.7 for the lowest and highest Reh investigated. Estimates of the wall pressure spectra revealed a noticeable hydrodynamic peak that scaled reasonably well with outer variables and with an average convective speed of 75% of the free stream velocity (based on unconditionally sampled pressure time series). Two boundary layer suction control cases were studied corresponding to suction rates of less then 30% of the boundary layer momentum. The findings reveal how only modest amounts of suction are needed to reduce upwards 50–60% of the hydrodynamic ridge.
To capture the full spectrum of the fluctuating wall pressure beneath a turbulent boundary layer (TBL) provides a unique challenge in transducer design. This paper discusses the design, construction and testing of an array of surface-mounted piezoelectric ceramic elements with the goal of having both the spatial resolution and the frequency bandwidth to accurately sense the low-frequency, low-wavenumber events beneath a TBL at moderately low Reynolds numbers. The array is constructed from twenty 1.27 cm tall prismatic rods with 0.18 cm × 0.16 cm cross-section made of Navy type II piezoelectric ceramic material. Calibration was performed by comparing the response of a Navy H56 precision-calibrated hydrophone to the outputs of each element on the array for a given input from a Navy J9 projector. The elements show an average sensitivity of −184 dB (re: 1 V μPa−1) and are assembled with a centre-to-centre spacing of 0.2 cm. Measurements of the fluctuating wall pressure below a 2d TBL with Reynolds numbers (based on momentum thickness) ranging from 2100 to 4300 show that the dimensions of the elements are between 64 and 107 viscous length units, respectively. A spatial and temporal footprint of the fluctuating wall pressure reveals convective speeds averaging 75% of the free stream velocity.
Surveys of both the static and dynamic wall pressure signatures on the interior surface of a subscale, cold-flow, and thrust-optimized parabolic nozzle are conducted during fixed nozzle pressure ratios corresponding to free shock separation and restricted shock separation states. The motive is to develop a better understanding for the sources of off-axis loads during the transient startup of overexpanded rocket nozzles. During free shock separation state, pressure spectra reveal frequency content resembling shock wave turbulent boundary-layer interaction. Presumably, when the internal flow is in restricted shock separation state, separation bubbles are trapped by shocks and expansion waves; interactions between the separated flow regions and the waves produce asymmetric pressure distributions. An analysis of the azimuthal modes reveals how the breathing mode encompasses most of the resolved energy and that the side load inducing mode is coherent with the response moment measured by strain gauges mounted upstream of the nozzle on a flexible tube. Finally, the unsteady pressure is locally more energetic during restricted shock separation, albeit direct measurements of the response moments indicate higher side load activity when in free shock separation state. It is postulated that these discrepancies are attributed to cancellation effects between annular separation bubbles.