Interaction and vectoring of parallel rectangular twin jets in a turbulent boundary layer

The ability to impart momentum while maintaining a zero net mass flux renders synthetic jet actuators attractive tools for a wide variety of applications. Implementation of a single synthetic jet actuator for large-scale operations is unrealistic and, as such, an array of actuators is usually desired during flow control processes. The added complexity of several synthetic jets in close proximity and the subsequent jet-jet interaction, in addition to interaction with the cross flow, represent an area of research yet to be fully explored. This paper encompasses a parametric study to investigate the interaction of a zero pressure gradient turbulent boundary layer (${\text{Re}}_{\tau }=1300$) with twin parallel synthetic jets, where the major axis of the rectangular orifices is aligned with the cross flow. Only the separation distance, $s$, and the phase difference, $\beta$, between the two orifices are varied. Geometrical parameters such as the orifice shape and aspect ratio ($\text{AR}=13$), as well as fluidic properties such as the jet Strouhal number ($\text{St}=2.3$) and the momentum coefficient ($C_{\mu }=0.16$) are kept constant throughout. Velocity fields acquired through stereoscopic particle image velocimetry (SPIV) measurements at five downstream locations indicate noticeable differences in the flow field and associated stresses. A limit in spacing is noted beyond which any subsequent increase results in the twin jets behaving as two independent synthetic jets. In comparison to a single synthetic jet in cross flow, the results demonstrate that twin jets operate at a specific phase difference and spacing can be equally, if not, more efficient for flow entrainment and momentum distribution.

Figure 1

Interactions between parallel synthetic jet actuators in quiescent flow, adapted from Luo and Xia [15] and Berk et al. [3]. (a) Enhancement mechanism which occurs in the absence of a phase difference between the two jets and (b) vectoring mechanism associated with the introduction of a phase difference.

Figure 2

(a) Schematic of synthetic jet actuator design in parallel twin-jet configuration: (1) Orifice exit, (2) cavity assembly, and (3) loudspeaker). (b) Twin jet actuation signal with applied phase difference and phase-locking trigger signal.

Figure 3

A schematic of the test facility is presented. (a) A view of the wind tunnel configuration with a zigzag trip at the leading edge, the major axis of the orifices aligned with the incoming flow, a flap at the trailing edge to control the position of the stagnation point and laser sheets and cameras for SPIV measurements (not to scale). (b) Spanwise averaged boundary layer profile of the unperturbed flow at $x/\delta =0$ (blue diamond) compared to a log law with coefficients $\kappa =0.384$ and $B=4.4$ (red line). This paper follows the convention that $x, y$, and $z$ are the streamwise, wall-normal, and spanwise directions with $U, V$, and $W$ being the corresponding velocities in those directions.

Figure 4

Boundary layer-subtracted streamwise velocity contour plots for twin jets evolving during the blowing part of the actuation cycle for $s/d=2$ (a)–(d), $s/d=6.5$ (e)–(h), and $s/d=13$ (i)–(l).

Figure 5

Vorticity-signed swirling strength contour plots for twin jets evolving during the blowing part of the actuation cycle for $s/d=2$ (a)–(d), $s/d=6.5$ (e)–(h), and $s/d=13$ (i)–(l), all at $\beta$ of $0^{\circ }$.

Figure 6

Vorticity-signed swirling strength contour plots demonstrating the influence of orifice spacing on the vectoring behavior of twin jets in cross flow for $s/d=2$ (a)–(d) and $s/d=13$ (e)–(h), all at $\beta$ of ${778}^{\circ }$ and $x/\delta =0$.

Figure 7

Variation of (a) vectoring angle and (b) yawing offset, with streamwise location for differing phase difference between the twin jets.

Figure 8

Variation of the normalized intergrated turbulent kinetic energy with streamwise location as the phase difference between the jets is varied for (a) $s/d=2$, (b) $s/d=6.5$, and (c) $s/d=13$.

Figure 9

Variation of the spanwise and time averaged total shear stress as the phase difference and orifice spacing between the twin jets is changed.