Genetic Algorithm Finds Perfect Spots for Plasma Actuators That Slash Drag by 55 Percent

A pair of plasma actuators placed at the trailing-edge corners of a square cylinder can cut aerodynamic drag by more than half and virtually eliminate the lift fluctuations that shake bluff bodies in a flowing stream. That is the central result of a new computational study published in Advances in Aerodynamics, in which researchers combined high-fidelity fluid simulations with a Kriging-enhanced genetic algorithm to search for the single best location for steady dielectric barrier discharge (DBD) plasma actuation. At the optimized placement of y/h = ±1, the time-averaged drag coefficient fell from a baseline of 1.44 to 0.6376, a 55.73 percent reduction, while the root-mean-square lift coefficient collapsed from 0.453 to 0.0087, a 98.08 percent suppression of oscillations.

The study, authored by Muhammad Hamza, Yi Yu, Fahad Nawaz and Xuanshi Meng, focuses on flow over a two-dimensional square cylinder at a Reynolds number of 200, a regime chosen deliberately. At this Reynolds number the flow develops laminar boundary layers and a well-organized, quasi-two-dimensional von Kármán vortex street, making it a widely accepted benchmark for evaluating plasma-based flow control. Unlike circular cylinders, where separation points shift with Reynolds number and surface conditions, the sharp corners of a square cylinder fix the separation locations geometrically, producing consistent turbulent wakes and periodic vortex shedding even at low Reynolds numbers. That predictability makes the square cylinder an ideal platform for systematically testing where an actuator should sit to intervene most effectively.

DBD plasma actuators are deceptively simple devices: an exposed electrode on a surface, a buried electrode beneath a dielectric layer, and, when a high-voltage alternating current is applied, a weakly ionized plasma region that generates a localized body force dragging the adjacent fluid along. Because they add momentum without moving parts or mass injection, and respond almost instantly, they have long attracted interest for controlling boundary layers and suppressing vortex shedding. The catch is that their effectiveness depends critically on where they are placed relative to the flow structures they are meant to control, and previous work had left a gap in systematic placement studies for square cylinders at low to moderate Reynolds numbers.

To close that gap, the team built their simulations on an OpenFOAM-based custom solver implementing the Suzen-Huang body-force model, which approximates the plasma charge density distribution without simulating the full plasma chemistry. The solver was validated against experimental data from Forte and colleagues and numerical results from Yousif and co-workers, showing strong agreement in the induced near-wall jet and velocity gradients. The plasma parameters were kept physically realistic: a charge density of 0.002 coulombs per cubic meter, a peak-to-peak voltage of 9 kilovolts, and an excitation frequency of 1 kilohertz. The actuation itself ran in steady mode, applying a continuous sinusoidal voltage that produces a nearly constant force field, rather than the pulsed duty-cycle mode that delivers time-dependent forcing.

The computational setup mirrored established benchmark configurations: a square cylinder of side 0.02 meters in a domain with a blockage ratio of 0.125, incompressible Navier-Stokes equations solved with a second-order upwind scheme for convection, Crank-Nicolson time integration, and the PIMPLE algorithm for pressure-velocity coupling. Grid independence tests across three mesh resolutions showed that 200 grid points per cylinder side were sufficient, with the Strouhal number at Reynolds number 100 shifting only from 0.133 to 0.132 on the finest grid. A time step of 0.0001 provided stable results, and near-wall resolution satisfied y+ < 1. Baseline simulations reproduced the periodic vortex shedding at Reynolds number 200 and matched experimental drag coefficient data from Okajima along with numerical results from Sohankar and Zhu, establishing a credible reference against which all controlled cases could be judged.

The optimization itself is where the study’s methodological ambition lies. Rather than brute-force scanning every possible actuator position, the researchers used Latin Hypercube Sampling to generate 15 initial actuator placements along the vertical edges of the cylinder, with a symmetric pair constrained so that the lower actuator mirrors the upper one. Each configuration was evaluated by computational fluid dynamics, and the results trained a Kriging surrogate model, a Gaussian process regression technique that interpolates sparse, expensive simulation data while quantifying its own uncertainty. The surrogate was benchmarked on the Branin test function, achieving a root mean square error of 0.0071 and a coefficient of determination of 1.0000 before being applied to the aerodynamic problem.

A genetic algorithm then evolved the actuator positions to minimize a composite fitness function combining the average drag coefficient with 0.4 times the root-mean-square lift coefficient, a weighting adopted from prior plasma control studies. The algorithm used tournament selection, blend crossover and Gaussian mutation, with a population of 100 evolving over up to 100 generations. Sensitivity analyses confirmed that the optimal fitness value of 0.6358 remained stable across different mutation probabilities, crossover rates and population sizes, though computational cost rose sharply, with runtime increasing 3.7-fold when generations expanded from 50 to 200 at a population of 200. Adaptive infill sampling, guided by the Expected Improvement criterion, added ten new simulation points per iteration in regions of high predictive uncertainty, steadily flattening the expected improvement until further sampling offered negligible gains.

The optimizer converged on a placement at (x1, y1) = (0.01, 0.01) and (x2, y2) = (0.01, −0.01) in physical coordinates, corresponding to the trailing-edge corners of the cylinder, expressed nondimensionally as y/h = ±1. The Kriging surrogate’s final accuracy was impressive: a mean absolute error of 0.0136 and root mean squared error of 0.0221 for drag, and errors of 0.0040 and 0.0056 for lift fluctuations, with coefficients of determination of 0.9918 and 0.9863 respectively and narrow 95 percent confidence intervals on the prediction errors. Notably, the trailing-edge solution emerged repeatedly across both initial samples and all infill points, suggesting a well-defined and robust optimum rather than a statistical fluke.

The flow physics behind the numbers is coherent. Time histories of the force coefficients showed that actuation at y/h = ±1 flattened the drag signal to a quasi-steady value and nearly eliminated lift oscillations, indicators that vortex shedding had been suppressed at its source. Power spectral density analysis at three wake probe points revealed that the dominant shedding frequency lost more than 45 decibels of energy at the near-wake locations, showing that the coherent, instability-driven wake had transitioned to a diffused, stabilized state. Time-averaged streamlines, velocity profiles, vorticity fields and turbulence intensity contours all told the same story: a contracted wake, a shrunken recirculation zone, faster momentum recovery and delayed vortex roll-up. The mechanism is that actuators sitting directly at the shear layer detachment points inject momentum exactly where the flow is most receptive, energizing the near-wall fluid and interrupting vortex formation before it begins.

Intermediate placements at y/h = ±0.6, ±0.7 and ±0.8 delivered only partial benefits. Positioned away from the natural separation points, they interacted with already-separated, vorticity-dominated flow, producing intermittent forcing and weaker control authority; residual shedding frequencies remained prominent in the spectra and recirculation bubbles persisted in the mean fields. The authors are candid about the study’s limits: the simulations are two-dimensional and laminar at Reynolds number 200, omitting three-dimensional effects, turbulent transition and spanwise instabilities relevant at higher Reynolds numbers, the plasma model assumes a steady charge distribution and neglects thermal and chemical effects, and only a single symmetric actuator pair was explored. Experimental validation using particle image velocimetry, hot-wire anemometry and force balance measurements is planned, along with extensions to three-dimensional flows, higher Reynolds numbers and multi-actuator configurations. Within those boundaries, the work demonstrates that pairing a validated plasma flow model with surrogate-assisted evolutionary optimization can find physically meaningful control strategies at a fraction of the computational cost of exhaustive search, a framework the authors argue is transferable to wings, vehicle rear-ends and other bluff-body geometries where drag and vortex-induced loads matter.

Subject of Research: Optimization of dielectric barrier discharge plasma actuator placement on a square cylinder for drag reduction and vortex shedding suppression using surrogate-assisted genetic algorithms

Article Title: Optimal placement of plasma actuators on a square cylinder for flow control using Kriging-enhanced genetic algorithm

Article References: Hamza, M., Yu, Y., Nawaz, F., & Meng, X. (2026). Optimal placement of plasma actuators on a square cylinder for flow control using Kriging-enhanced genetic algorithm. Advances in Aerodynamics, 8(1), Article 15. https://doi.org/10.1186/s42774-025-00239-y

Image Credits: AI Generated

DOI: 10.1186/s42774-025-00239-y

Keywords: plasma actuators, DBD plasma, flow control, drag reduction, square cylinder, vortex shedding, Kriging surrogate model, genetic algorithm, computational fluid dynamics, Reynolds number 200, aerodynamic optimization, wake stabilization