W. J. Baars, Tinney, C. E., and Ruf, J. H., “Time-frequency analysis of rocket nozzle wall pressures during start-up transients,” 13th European Turbulence Conference, Journal of Physics: Conference Series, vol. 318, no. 092001, 2011.
Surveys of the fluctuating wall pressure were conducted on a sub-scale, thrust-optimized parabolic nozzle in order to develop a physical intuition for its Fourier-azimuthal mode behavior during fixed and transient start-up conditions. These unsteady signatures are driven by shock wave turbulent boundary layer interactions which depend on the nozzle pressure ratio and nozzle geometry. The focus however, is on the degree of similarity between the spectral footprints of these modes obtained from transient start-ups as opposed to a sequence of fixed nozzle pressure ratio conditions. For the latter, statistically converged spectra are computed using conventional Fourier analyses techniques, whereas the former are investigated by way of time-frequency analysis. The findings suggest that at low nozzle pressure ratios –where the flow resides in a Free Shock Separation state– strong spectral similarities occur between fixed and transient conditions. Conversely, at higher nozzle pressure ratios –where the flow resides in Restricted Shock Separation– stark differences are observed between the fixed and transient conditions and depends greatly on the ramping rate of the transient period. And so, it appears that an understanding of the dynamics during transient start-up conditions cannot be furnished by a way of fixed flow analysis.