Numerical Investigation of Boundary-Layer Height and Actuation-Parameter Effects of a Circular Synthetic Jet Actuator in Crossflow

TL;DR

This study addresses how a circular synthetic jet actuator (SJA) behaves in crossflow as the blowing ratio $C_B$, stroke ratio $L^+$, and boundary-layer height ratio $D^+$ are varied independently. Using 3D URANS simulations with a Womersley-driven neck inlet in OpenFOAM, nine cases spanning $0.85<C_B<1.7$, $10.6<L^+<21.3$, and $2.1<D^+<8$ are analyzed to map vortex-structure development, near-wall momentum modification, and surface-shear responses. Key findings show that actuation frequency primarily controls vortex packing and penetration, boundary-layer height modulates near-wall coherence and spanwise reach, and there is a trade-off in mean-flow response between near-wall momentum gains and far-field deficits; these insights identify practical operating envelopes for SJA-based separation control in low-$Re$ boundary layers and guide array design for broad spanwise authority with efficient energy use.

Abstract

Three-dimensional unsteady numerical simulations are performed to investigate the effects of blowing ratio $C_B$ ($0.85 < \overline{U}_j/U_\infty < 1.7$), stroke ratio $L^+$ ($10.6 < \overline{U}_j /(fd) < 21.3$), and boundary-layer height ratio $D^+$ ($2.1<δ/d<8.0$) on circular synthetic jet actuator (SJA) performance in crossflow. Nine cases are examined at constant free-stream velocity $U_\infty$, with systematic independent variation of averaged jet velocity $\overline{U}_j$, actuation frequency $f$ ($200$-$400~\mathrm{Hz}$), and boundary-layer momentum thickness Reynolds number ($170<Re_θ<740$) to isolate the individual effects of these parameters on a circular-nozzle SJA with fixed nozzle diameter $d$ in crossflow. Instantaneous vortical structures exhibited tilted vortex rings with a trailing vortex pair at low actuation frequency; closely packed expelled vortical structures for higher frequency SJAs, and the largest boundary-layer height ratio induced hairpin-like vortices. Near-wall tertiary vortices, which promote downwash and increase wall shear stress, remain coherent longer and have extended spanwise coverage for low $D^+$. Time-averaged boundary-layer profiles and skin-friction distributions reveal that SJAs with low to moderate $D^+$ have the greatest potential for separation control, maintaining increased near-wall momentum over extended streamwise distances.

Figures (16)

• Figure 1: Schematic of a synthetic jet actuator in crossflow during the expulsion cycle.
• Figure 2: Schematic of vortex structures formed by a synthetic jet actuator in boundary-layer crossflow: (a) hairpin vortex (HV), or (b) tilted vortex ring (VR) with trailing vortex pair (TVP) and near-wall tertiary vortices (TV).
• Figure 3: Computational domain and boundary conditions for the SJA in crossflow.
• Figure 4: Mesh configuration: (a) symmetry-plane view (partial length shown) and (b) zoomed view of the jet exit.
• Figure 5: Boundary-layer profiles for the three inlets, compared with analytical/experimental dataroach1992 at similar Reynolds numbers.