Asymmetric forcing of convectively unstable transverse jets

The present paper explores the effect of asymmetric and helical excitation of the flow about the exit plane of a jet injected perpendicularly into crossflow. Both acetone planar laser-induced fluorescence and stereo particle image velocimetry were used to quantify transverse jet response at relatively high jet-to-crossflow momentum flux ratios ($J=61$ and 41), which in the absence of external excitation produced a highly penetrating jet with a naturally convectively unstable upstream shear layer (USL) and asymmetric cross-sectional shape. For various excitation conditions, in some cases involving complete clockwise or clockwise perturbations and, in other cases, localized perturbations, alterations in the spectral character of the USL were observed, including lock-in to the applied frequency and quasiperiodicity involving applied and natural frequencies. For forcing frequencies and amplitudes producing lock-in, asymmetric excitation was found to accelerate USL vorticity roll-up and improved mean symmetry in the jet cross section. With these alterations in jet structure, molecular mixing between jet and crossflow fluid was improved in both center plane and cross-sectional planes of the transverse jet. Proper orthogonal decomposition analysis applied to the images revealed 2D and 3D mode coefficient plots with interesting topological features. In many cases, these phase diagrams revealed attractor like shapes, especially when excitation frequencies and amplitudes produced lock-in of the USL, suggesting that with further study, such topologies could be used as characteristic signatures for mixing optimization and low-order model development.

Figure 1

Schematic of the flush injected transverse jet and associated vortical flow structures. Orientation of coordinate axes $x, y, z$, jet upstream shear layer trajectory $s$, and jet centerline trajectory $s_c$ are shown. Adapted from Ref. [7].

Figure 2

Low velocity wind tunnel and associated experimental diagnostics for hot-wire anemometry, acetone PLIF, and stereo PIV.

Figure 3

Speaker configuration and numbering convention associated with external asymmetric forcing, where crossflow acts in the positive $x$ direction. Operation of speakers in the sequence 2-1-4-3 created clockwise excitation (a), and 2-3-4-1 created counterclockwise jet excitation (b).

Figure 4

Spectral characteristics of vertical velocity disturbances along the USL coordinate $s/D$ for the unforced JICF, including discrete power spectra and spectral contour maps, respectively, for $J=61$ [(a), (b)] and $J=41$ [(c), (d)].

Figure 5

Hot-wire-based vertical velocity spectra at $s/D=2.0$ for the JICF at $J=61$ and $\text{Re}=2300$, with and without four speaker clockwise and counterclockwise asymmetric forcing, at various forcing frequencies $f_f$ and pressure perturbation amplitudes. At $s/D=2.0, f_o\approxeq 1725$ Hz. (a) $f_f=1000$ Hz, ${\mathrm{P}}^{\prime }=0.065$ Pa, (b) $f_f=1000$ Hz, ${\mathrm{P}}^{\prime }$= 0.19 Pa, (c) $f_f=1600$ Hz, ${\mathrm{P}}^{\prime }=0.15$ Pa, (d) $f_f=1900$ Hz, ${\mathrm{P}}^{\prime }=0.15$ Pa, (e) $f_f=2600$ Hz, ${\mathrm{P}}^{\prime }=0.15$ Pa, (f) $f_f=3500$ Hz, and ${\mathrm{P}}^{\prime }=2.0$ Pa.

Figure 6

Hot-wire-based vertical velocity spectra at $s/\mathrm{D}=2.0$ for the JICF at $J=61$ and $\text{Re}=2300$, with and without one- and two- speaker upstream forcing, at two different forcing frequencies $f_f$ and pressure perturbation amplitudes. At $s/D=2.0, f_o\approxeq 1725$ Hz. (a) $f_f$ = 1900 Hz, P′= 0.15 Pa and (b) $f_f$ = 2300 Hz, P′ = 0.28 Pa.

Figure 7

Map of the USL response to external forcing at various forcing frequencies, modalities and perturbation amplitudes P', measured at shear layer location $s/D=2.0$. Green colored symbols represent 1:1 lock-in of the USL, blue symbols represent quasiperiodic behavior of the USL power spectra, and red symbols represent no significant response of the USL to forcing (a) 4-speaker, (b) Upstream (2 and 1-speaker), (c) Downstream, (2 and 1-speaker), and (d) All conditions.

Figure 8

Instantaneous center line and mean cross-sectional PLIF images in the $y/\mathrm{D}-z/\mathrm{D}$ plane for the $J=61$ JICF with $f_o\approx 1600-1900$ Hz. Shown are cases for unforced conditions (a) and 875 Hz excitation of all four speakers in the clockwise (b) and counterclockwise (c) directions, corresponding to QP and LI response of the USL, respectively.

Figure 9

Mean PLIF images in the cross-sectional $y/\mathrm{D}-z/\mathrm{D}$ plane for the $J=61$ JICF with localized excitation, each at amplitude $P^{\prime }=0.15$ Pa, and in all cases corresponding to lock-in [50]. (a)–(c) show $f_f=1600$ Hz excitation in the upstream region and (d), (e) show $f_f=1900$ Hz excitation in the downstream region.

Figure 10

Map of USL response, with representative mean cross-sectional jet PLIF images at $x/D=10.5$, to various speaker operational configurations: (a) All four speakers, (b) local upstream forcing, and (c) local downstream forcing. Symbols correspond to the legend in Fig. 7, where conditions are identified as LI (green), QP (blue), and NSR (red).

Figure 11

Unmixedness in center plane ($U_{c,xz}$) and cross-sectional ($U_{yz}$) planes for $J=61$ at various excitation conditions: (a) Four-speaker operation at frequencies at or below the fundamental range and (b) four-speaker operation at frequencies at or above the fundamental range. Circles represent forcing cases with the most symmetric cross section. Select mean jet cross-sectional PLIF images are inset.

Figure 12

Unmixedness in (a), (c) center plane ($U_{c,xz}$) and the (b), (d) cross-sectional ($U_{yz}$) planes for $J=61$ at localized excitation conditions at $f_f=1600$ Hz and P'= 0.15 Pa corresponding to upstream excitation (a), (b) and downstream excitation (c), (d). Circles represent forcing cases with the most symmetric cross section. Select mean jet cross sectional PLIF images are inset.

Figure 13

Instantaneous simultaneous PLIF/PIV imaging of the $J=41$ JICF. Data shown for scaled vorticity ${\omega }_y/(U_j/D)$ and scaled jet fluid concentration $C/C_o$ in the center-plane view for the (a) unforced case and (b), (c) subject to directional forcing with excitation $f_f=1600$ Hz and P'= 0.15 Pa.

Figure 14

Instantaneous simultaneous PLIF/PIV imaging of the $J=41$ JICF. Data shown for scaled vorticity ${\omega }_x/(U_j/D)$ and scaled jet fluid concentration $C/C_o$ for the $x/D=0$ cross-sectional view (a) unforced case, and (b), (c) jet subject to clockwise and counterclockwise directional forcing with excitation $f_f=1600$ Hz and P'= 0.15 Pa.

Figure 15

PLIF and PIV POD mode structures extracted from instantaneous images of the unforced $J=41$ JICF in (a), (b) center-plane view; (c), (d) upstream cross-sectional view at $x/D=-0.4$; (e), (f) jet center cross-sectional view at $x/D=0$. Percentage of total kinetic energy (KE) or scalar fluctuation energy (SE) contributed by each mode is indicated. The color bar in each image represents the mode scaled by its own norm and the mean jet velocity at the jet exit $U_j$.

Figure 16

PLIF POD mode structures from instantaneous center-plane images of the $J=61$ JICF for (a) unforced conditions and four-speaker forcing at $f_f=1000$ Hz and P'= 0.65 Pa, under (b) clockwise and (c) counter-clockwise operation. Percentage of total scalar fluctuation energy (SE) by each mode is indicated. The color bar in each image represents the mode scaled by its own norm and the mean jet velocity at the jet exit $U_j$.

Figure 17

PLIF POD mode coefficient plots extracted from instantaneous centerplane images of the $J=61$ JICF: (a) Unforced; four-speaker excitation at $f_f=1000$ Hz and 0.65 Pa for CW and CCW orientations (b), (c) and at $f_f=1750$ Hz and 0.10 Pa for CW and CCW orientations (d), (e).

Figure 18

PLIF POD mode coefficient plots extracted from instantaneous center-plane images of the $J=61$ JICF: Four-speaker excitation at $f_f=2300$ Hz and 0.42 Pa for (a) CW and (b) CCW orientations, and at $f_f=1600$ Hz and 0.075 Pa for (c) CW and (d) CCW orientations.

Figure 19

PLIF POD mode coefficient plots extracted from instantaneous center-plane images of the $J=61$ JICF: One-speaker excitation at $f_f=1600$ Hz and 0.15 Pa for speakers positioned (a) right upstream, (b) left upstream, (c) right downstream, and (d) left downstream; and at $f_f=2300$ Hz and 0.28 Pa for speakers positioned (e) right upstream and (f) left upstream.