Jet-edge interaction: linear and non-linear frequency-selection mechanisms

Abstract

We consider a round turbulent jet grazing a rectangular plate angled at $45^\circ$. Through sound pressure measurements, the tonal dynamics associated with jet-edge interaction are explored in a parameter space comprising jet Mach number, $M_j$, and plate radial position, $R/D$. A variety of spectral signatures are observed and classified. The classification - based on analysis of power-spectral density and bicoherence, and on the resonance model proposed by Jordan et al. (2018) - comprises: broadband spectra; tonal spectra associated with purely linear frequency-selection mechanisms; tonal spectra associated with both linear and non-linear frequency selection. The classification identifies regions in the parameter space ($M_j$, $R/D$); and clarifies mechanisms underpinning regime changes. The linear frequency selection (LFS) regime comprises multiple tones, with no evidence of triad interaction. A regime involving non-linear frequency selection emerges from this state, with the strong amplification of one LFS tone, which then generates multiple harmonics. Intermediate regimes are identified involving weaker, non-harmonic triadic interactions where two LFS tones interact to generate a third tone. In addition to these mechanisms a mode-switching mechanism is identified at $M_j$ = 0.84 and shown to result from the cut-on of a new upstream-travelling wave at that Mach number. The mode-switch is found to be remarkably robust, occurring in a repeatable manner over a Mach-number increment of 0.01 regardless of whether the Mach number is increased or decreased (no hysteresis is observed).

Figures (27)

• Figure 1: Illustration of the installed-jet setup when viewed from above. Key variables are highlighted, and the microphone position is marked with a star.
• Figure 2: Feedback loop considered for the linear frequency-prediction model.
• Figure 3: Selected dispersion relation curves for $M_j$ 0.6, 0.65, 0.7, 0.75, 0.8, 0.82, 0.85, 0.9 where, for $M_j < 0.82$$k^{-}_{th}$ waves (cyan) are present and for $M_j \geq 0.82$$k^{-}_{d}$ (cyan), $k^{-}_{p}$ (red), and $k^{+}_{T}$ (green) waves are present.
• Figure 4: Illustration of saddle-point formation within the complex k-plane with arrows indicating the direction of increasing $St$.
• Figure 5: Broadband spectra for $(M_j,R/D) = (0.9,0.8)$.