Low-dimensional and data fusion techniques applied to a supersonic multistream single expansion ramp nozzle

Low-dimensional models of experimental and simulation data for a complex supersonic jet were fused to reconstruct time-dependent proper orthogonal decomposition (POD) coefficients. The jet consists of a multistream rectangular single expansion ramp nozzle, containing a core stream operating at Mach number $M_{j,1}=1.6$ and bypass stream at $M_{j,3}=1.0$ with an underlying deck. Proper orthogonal decomposition was applied to schlieren and particle image velocimetry data to acquire the spatial basis functions. These eigenfunctions were projected onto their corresponding time-dependent large-eddy simulation (LES) fields to reconstruct the temporal POD coefficients. This reconstruction was able to resolve spectral peaks that were previously aliased due to the slower sampling rates of the experiments. Additionally, dynamic mode decomposition was applied to the experimental and LES data sets and the spatiotemporal characteristics were compared to POD.

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Figure 1

Three-stream turbofan design by AFRL, WPAFB and GE.

Figure 2

Cross-sectional view of the idealized three-stream nozzle with aft deck installed at Syracuse University.

Figure 3

Anechoic chamber showing the schlieren setup and microphone arrays with axes.

Figure 4

Comparison of time-averaged experimental and numerical schlieren images.

Figure 5

Instantaneous snapshot of the experimental and LES numerical schlieren fields: (a) experimental schlieren field at an exposure of $3.75\times {10}^{-6}$ s, (b) LES density gradients, and (c) LES pressure gradients.

Figure 6

Time-averaged $u$ velocity of PIV and LES fields along the centerline plane ($z/D_h=0$): (a) PIV average $u$ velocity (m/s) and (b) LES average $u$ velocity (m/s).

Figure 7

The rms $u$ velocity of PIV and LES fields along the centerline plane ($z/D_h=0$): (a) PIV rms $u$ velocity (m/s) and (b) LES rms $u$ velocity (m/s).

Figure 8

Spatial POD eigenfunctions on the $x-y$ plane for the (a) schlieren experiment, (b) LES density gradients, and (c) LES pressure gradients.

Figure 9

Power spectral density of $a_n\left(t\right)$: (a) schlieren $a_n\left(t\right)$ spectra sampled at 50 kHz, (b) reconstructed $a_n\left(t\right)$ spectra using LES density gradients sampled at 405 kHz, and (c) reconstructed $a_n\left(t\right)$ spectra using LES pressure gradients sampled at 405 kHz.

Figure 10

The DMD frequencies of experimental and numerical schlieren fields: (a) schlieren experiment sampled at 50 kHz, (b) LES numerical schlieren using density gradients sampled at 405 kHz, and (c) LES numerical schlieren using pressure gradients sampled at 405 kHz.

Figure 11

The DMD spatial modes of experimental and numerical schlieren fields: (a) DMD spatial structure of the schlieren experiment, (b) DMD spatial structure of LES numerical schlieren using density gradients, and (c) DMD spatial structure of LES numerical schlieren using pressure gradients.

Figure 12

Spatial correlation between DMD and POD modes for experimental and LES numerical schlieren: (a) schlieren experiment, (b) LES numerical schlieren using density gradients, and (c) LES numerical schlieren using pressure gradients.

Figure 13

The PIV modes of the $u$ component.

Figure 14

The LES modes of the $u$ component.

Figure 15

Spatial correlation between LES and PIV POD modes.

Figure 16

Power spectral density of reconstructed $a_n\left(t\right)$ using LES $u$-velocity snapshots and the PIV spatial eigenfunction.

Figure 17

The DMD of the LES $u$ velocity field: (a) DMD frequencies of the LES $u$ velocity and (b) DMD spatial structure of the LES $u$ velocity.

Figure 18

Spatial correlation between the DMD and POD modes of the LES $u$-velocity field.