Experimental and Numerical Analysis of the Intermittentency in a Nozzle Overexpanded-Flow

TL;DR

This study investigates intermittent wall-pressure loads in a shock-separated, over-expanded nozzle by combining wind-tunnel experiments with a hybrid RANS/LES (DDES) simulation of a truncated TIC nozzle. Wavelet-based analysis reveals scale-by-scale intermittency, with bursts concentrated near the dominant first azimuthal mode, and both the time delays between bursts and their energy content exhibiting universal log-normal behavior across nozzle pressure ratios and wall locations. The results support a stochastic description of aerodynamic side-loads in over-expanded nozzle flows and demonstrate that the hybrid SA-based DDES captures the essential unsteady dynamics. Collectively, the work provides a physically grounded basis for reduced-order stochastic models of nozzle loads and connects to intermittency observations in subsonic and supersonic jets reported in the literature.

Abstract

The present work reports an investigation into the statistical properties of wall-pressure fluctuations in a highly over-expanded nozzle flow, characterized by significant shock-induced flow separation. This regime is extremely hazardous to rocket nozzles, as it leads to very high off-axis loads. The database under investigation has been obtained both experimentally and numerically by means of a hybrid RANS/LES simulation of the flow issuing from a sub-scale Truncated Ideal Contour (TIC) nozzle, fed with cold air and operating at a Reynolds number on the order of 10^6. The experimental campaign was conducted in the S150 supersonic wind tunnel at the Institut PPRIME in Poitiers. The degree of over-expansion is quantified by the nozzle pressure ratio (NPR). Pressure fluctuations are extracted from several probes positioned along the nozzle wall, considering different NPR values. The intermittent behavior is investigated using conditional statistics based on the wavelet transform, which demonstrates that the aerodynamic loads of the over-expanded jet consist of intermittent bursts rather than continuous variations. The wavelet analysis reveals scale-by-scale intermittency and, in particular, shows that the wall-pressure signals exhibit a significant degree of intermittency around the frequency associated with aerodynamic side-loads. The statistics of these intermittent events, in terms of the time delay between occurrences and in terms of their amplitude, are found to be weakly sensitive to NPRs and to locations along the nozzle wall and appear to follow a universal behaviour that can be modelled by a log-normal distribution. This finding may support the development of a stochastic model of the aerodynamic side-loads.

Figures (12)

• Figure 1: Experimental apparatus at PPRIME Institute.
• Figure 2: a) Instantaneous visualisation of the turbulent and shock structures at NPR=9 from : numerical Schlieren on a longitudinal view; b) experimental and numerical mean wall-pressure; c) experimental and numerical standard deviation of the wall-pressure signals along the streamwise direction.
• Figure 3: a) PSD's of the experimental and numerical wall-pressure signals at $x/L=0.85$ for $NPR=9$ b) Experimental PSD's of the first pressure azimuthal mode as a function of frequency at $x/L = 0.67$ for $NPR=6, 7.5, 9, 10.5$.
• Figure 4: Numerical PSD maps of the wall-pressure signals along the nozzle for the first three azimuthal modes at $NPR=9$: (a) $m = 0$, (b) $m = 1$, (c) $m = 2$.
• Figure 5: Scalograms of the experimental (a) and numerical (b) wall-pressure signals and corresponding LIM2 maps (c, d) at $x/L=0.67$ for NPR$=9$. The grey dashed lines indicate the characteristic frequency of the $m=1$ mode. The LIM2 maps only show values greater than 3.