Beyond actuator line arrays in active flow control studies: Lessons from a genetic algorithm approach

This study explores the problem of optimal spatial placement of microjet actuators for flow control in a canonical bluff body of relevance to the aerodynamics community, namely, the slanted cylinder with a slant angle of ${45}^{\circ }$. The solution found by a genetic algorithm whose goal function is to reduce aerodynamic drag (achieving 10.6% reduction at ${\text{Re}}_D=100000$) challenges the intuitive and, to date, most commonly followed de facto standard of using line arrays of steady microjet actuators to control a flow field. This study provides strong evidence that line arrays are not the optimal approach for active flow control of this bluff body wake, since most of the jets in the line array were neutrally, or even negatively, contributing to the goal function of drag reduction. Further observations of the flow physics with surface flow visualization and particle image velocimetry unveil two key mechanisms that were leveraged by this automated approach: First, a shrinkage of the separation bubble at the leading edge of the slanted surface appears to be strongly related to the very strong energization of the boundary layer just upstream of the separation due to microjets in crossflow being applied in tandem. Second, a wavelike perturbation that appears to be related to an increased wandering of the vortex pair formed in the far field of this wake is also observed. Although this study employed steady microjet actuators, the lessons learned can potentially be extended to other actuation mechanisms commonly used for active flow control. The results obtained demonstrate the spatial sensitivity problem is one that, despite its complexity and challenges in physical implementation, is worthwhile considering in active flow control studies.

Figure 1

(a) Model dimensions and simplified schematic of the internal mechanism used to actuate the microjets with control over every jexel. Blue and red coordinate systems mark the origin used in the Results section. (b) Schematic of the baseline flow field interrogated as learned from [42] and specific planes used in this study.

Figure 2

(a) Overview of the setup used for the reconfigurable jet array and (b) detail of the jexel viewed from inside of the model, showing how each group of four microjets are grouped in a cavity. (c) A summary of the progress the GA was able to achieve by starting with manually selected line array configurations. (d) The symmetric, “cleaned-up” configuration derived from the GA result.

Figure 3

Iterative jexel clean-up process when the best manually selected pattern is chosen as the starting point. Starting pattern consists of two line arrays of jexels (four line arrays of jets).

Figure 4

Comparison between the surface flow patterns generated at ${\text{Re}}_D=100000$ for baseline (a) and actuated cases (b), (c). Black and blue dots indicate position of the active microjets. Movie 1 in the Supplemental Material [48] clarifies directions given by arrows.

Figure 5

Comparison between boundary layer $V_z$ profiles as captured by a high-magnification PIV plane at $x=0$ (centerline, plane b5 in Fig. 1). Blue triangles indicate locations of the microjets closest to the center plane.

Figure 6

PIV fields of the separation bubble, observed at ${\text{Re}}_D=100000$ for baseline (a) and actuated cases (b), (c). Top row shows mean fields of streamwise velocity $V_z/V_{\infty }$ from 500 snapshots. In (d) a high-magnification PIV resolves the very small separation bubble present in the GA solution case. Highest energy POD modes (1–3) displayed in the subsequent subfigures, colored by velocity normal to the slanted surface ($V_n/V_{\infty }$).

Figure 7

Principal modes of the GA solution at ${\text{Re}}_D=100000$ when a larger PIV field is used, displaying a traveling wave pair.

Figure 8

Mean vorticity fields obtained from 500 SPIV fields at ${\text{Re}}_D=100000$ and $z/D=2$. Yellow stars indicate mean vortex core, whereas black dots indicate instantaneous vortex cores as found by peak ${\mathrm{\Gamma }}_1$. (b) Baseline and line array mean cores also shown to facilitate comparison between the results. Line array solution omitted due to its high similarity to the baseline field (a).

Figure 9

Two principal vorticity modes of the vortex pair for the three cases studied, acquired from 500 SPIV snapshots at $z/D=2$.