Screeching supersonic jet

Temperature contours on a centerplane cross section taken from a snapshot of the screeching jet. Time histories of pressure were recorded at probe locations indicated by circles and .

Screech is a component of supersonic jet noise that is connected to the presence of a train of shock cells within the jet column. For a turbulent jet, the unsteady shear layers interact with the shocks to create sound. While this process is generally broadbanded, screech is a special case of shock-noise that arises from the creation of a feedback loop between the upstream-propagating part of the acoustic field and the generation of new disturbances at the nozzle lip. This self-sustaining feedback loop leads to an extremely loud (narrow-banded) screech tone at a specific fundamental frequency. The presence of a tonal process embedded in an otherwise broadbanded turbulent flow makes the screeching jet an excellent test case for the sparsity-promoting DMD method. The objective of the developed method is to extract the entire coherent screech feedback loop from the turbulent data and to describe the screech mechanism with as few modes as possible.

Power spectra of pressure corresponding to the measurement locations indicated in top figure. While both spectra peak at Strouhal number St approx 0.3 , the spectrum at location 2 (circles) is more broadbanded than at location 1 (crosses).

The three-dimensional DMD mode associated with the dominant frequency (that corresponds to the fundamental frequency of the screech tone, St approx 0.3 ). A red isosurface of perturbation pressure is shown together with a blue isosurface of the perturbation dilatation. An animation of this flow field is available below.

Dependence of the absolute value of the DMD amplitudes alpha_i on (a) the frequency and (b,c) the real part of the corresponding DMD eigenvalues mu_i . Plot (c) represents a zoomed version of plot (b) and it focuses on the amplitudes that correspond to lightly damped eigenvalues.

(a) The sparsity level hbox{{bf{card}}} , (alpha) and (b) the performance loss $% , Pi_{mathrm{loss}} ; mathrel{mathop:}= ; 100 , sqrt{J (alpha) / J (0)}$ of the optimal vector of amplitudes alpha resulting from the sparsity-promoting DMD algorithm.

Eigenvalues resulting from the standard DMD algorithm (circles) along with the subset of N_z eigenvalues selected by the sparsity-promoting DMD algorithm (crosses). In plots (b) and (c), the dashed curves identify the unit circle.

Dependence of the absolute value of the amplitudes alpha_i on the frequency (imaginary part) of the corresponding eigenvalues mu_i . The results are obtained using the standard DMD algorithm (circles) and the sparsity-promoting DMD algorithm (crosses) with N_z DMD modes.

Performance loss, $% , Pi_{mathrm{loss}} ; mathrel{mathop:}= ; 100 , sqrt{J (alpha) / J (0)}$ , of the optimal vector of amplitudes alpha resulting from the sparsity-promoting DMD algorithm with N_z DMD modes.

Animation

This animation was generated by Joseph W. Nichols at the Center for Turbulence Research, Stanford University.

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