Abstract
Underexpanded jets exhibit interactions between turbulent shear layers and shock-cell trains that yield complex phenomena that are absent in the more commonly studied perfectly expanded jets. We quantitatively analyze these mechanisms by considering the interplay between hydrodynamic (turbulence) and acoustic modes, using a validated large-eddy simulation. Using momentum potential theory (MPT) to achieve energy segregation, the following observations are made. The sharp gradients in fluctuations introduced by the shock-cell structure are captured mostly in the hydrodynamic mode, whose amplitude is an order of magnitude larger than the acoustic mode. The acoustic mode has a relatively smoother distribution, exhibiting a compact wavepacket form. Proper orthogonal decomposition (POD) identifies the third-to-sixth cells as the most dynamic structures. The imprint of shock cells is discernible in the nearfield of the acoustic mode, primarily along the sideline direction. Energy interactions that feed the acoustic mode remain compact in nature, facilitating a simple propagation technique for farfield noise prediction. The farfield sound spectra show peak directivity at 30 ∘ to the downstream axis. The POD modes of the acoustic component also identify two main energetic components in the wavepacket: one representative of the periodic internal structure and the other of intermittent downstream lobes. The latter component occurs at exactly the same frequency as, and displays high correlation with, the farfield peak noise spectra, making the acoustic mode a better predictor of the dynamics than velocity fluctuations.
Highlights
Supersonic jets occur in numerous industrial and military applications
A domain defined by 0 ≤ r ≤ 0.5 and 0 ≤ x ≤ 8 is chosen to plot its contours, since this region encompasses the strongest compression and expansion cells
We show the prediction capability of the acoustic mode based on information collected at r = 1.5, which is much closer to the axis than that employed with typical Ffowcs Williams-Hawkings approaches
Summary
Supersonic jets occur in numerous industrial and military applications. Among many features of interest in such jets are their mixing and acoustic properties. Any mismatch between the pressure at the jet exit and the ambient, i.e., imperfect expansion, yields compression and expansion cells in the jet plume, through which pressure equalization takes place. The focus of this paper is on an underexpanded jet, where the exit pressure is higher than the ambient. The initial flow outside the jet comprises an expansion, which is followed by alternating compression and expansion cells (shock cells). In modern commercial turbofan engines, underexpanded conditions exist in the fan stream at cruise conditions [1], giving rise to shock cells in the jet plume. At higher pressure differentials between the nozzle exit and the ambient [3], the oblique shocks constituting the shock-cells transform into a normal shock or Mach disc [4], making the flow downstream of it subsonic [5]. Extraction of plume characteristics of underexpanded jets have provided valuable insights into the thermal radiation properties of hot jets encountered in propulsion systems [6], relation between
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