Particle swarm algorithm shapes aeroelastic small wind turbine blades

Engineers have long known that a wind turbine blade is not a rigid object: as air flows over it, the blade bends and twists, and that deformation feeds back into the airflow itself. A new study has now taken that two-way conversation between fluid and structure and placed it directly inside an automated design loop, using a multi-objective particle swarm optimization (MOPSO) algorithm to reshape a small-scale horizontal axis wind turbine blade. The result, reported in Advances in Aerodynamics, is an optimized flexible blade that delivers a 12.5% improvement in aerodynamic performance, a 7.15% reduction in weight, and a 22% reduction in blade tip displacement compared with the baseline design.

The research, conducted by Mohamadmahdi Falahi and Negar Nabatian, focuses on small wind turbines, which are increasingly attractive for urban and residential settings where strong winds are unreliable. Although medium and large turbines produce more power, they need relatively high wind velocities to do so, conditions that are not available everywhere. Small-scale turbines can serve as a reliable energy source at low wind speeds if they are properly sized and installed at suitable locations, with common applications including electricity generation stored in batteries, power supply for water pumps, and even powering wireless sensors that monitor building performance.

What sets this work apart from much of the earlier literature is the coupling of a two-way fluid–structure interaction (FSI) simulation with the optimization algorithm. Previous studies cited by the authors largely relied on one-way FSI approaches, in which aerodynamic loads drive structural analysis but the resulting deformation does not alter the flow. In the present study, the partitioned FSI approach was implemented using ANSYS CFX for the fluid domain and the Transient Structural module of ANSYS Mechanical for the structural domain, with variables transferred implicitly at a non-conformal interface through ANSYS system coupling with conservative interpolation.

The numerical setup was built for accuracy. The fluid simulation solved the Navier–Stokes equations with the k-ω SST turbulence model, using a velocity inlet of 6 m/s, an outlet pressure of 0 Pa, and no-slip conditions on the blade and hub walls, while the upper boundary was a free-slip wall. A mesh with 1.88 million elements proved sufficient, with the maximum dimensionless wall distance y+ kept below one to resolve the viscous sublayer. To reduce computational cost, one-third of the domain was modeled with a periodic boundary condition, and element sizes were locally reduced near the leading and trailing edges rather than refined uniformly. The time step of 0.053 milliseconds corresponds to roughly one degree of blade rotation per step, and to 225 steps per cycle of the baseline blade’s first bending mode frequency of 83.8 Hz, ensuring adequate temporal resolution for the structural dynamics.

The optimization problem was defined with 19 design variables: chord and twist distributions at eight spanwise sections of a 7.5 cm baseline blade built from NACA 0012 airfoils, the blade root radius, the tip speed ratio, and the blade material chosen from a list of candidates. The objectives were to maximize the power coefficient and minimize blade mass, formulated as a minimization of (1 − Cp) and the blade weight. Constraints included a requirement that chord and twist distributions decrease monotonically from root to tip, a limit on tip deflection to prevent blade–tower collision with a safety factor of 1.1, a minimum separation between the blade’s natural frequency and the third harmonic of the rotor rotation frequency to avoid resonance, and a maximum stress below the material’s yield stress divided by a safety factor of 1.1.

MOPSO was chosen over alternatives such as genetic algorithms because of its computational efficiency, requiring fewer function evaluations, and its suitability for continuous optimization problems. In the algorithm, each candidate solution is a particle moving through the search space, guided by its personal best position and the global best found by the swarm. The inertia weight starts high to promote exploration and is gradually reduced to enhance convergence, while a higher global learning coefficient than the personal coefficient was employed to accelerate convergence. Mutation with a decreasing probability helps maintain a well-distributed Pareto front, and archive leaders are managed through a deletion probability to prevent solutions from clustering in a single area. In each iteration, the design variables are stored in a Journal file, the FSI simulation runs, and the resulting parameters feed an Excel file that the algorithm uses to determine the particles’ next positions.

Before optimization, the model was validated. The predicted power coefficient at various tip speed ratios and wind speeds agreed closely with a previously validated study, with a mean error of less than 1%, and structural results for power, tip deflection, and stress at 12 m/s and a tip speed ratio of 5 also showed good agreement. The Pareto front revealed the trade-off between aerodynamic efficiency and blade weight, and from the subset of designs improving both objectives, the optimized blade was selected. Notably, although E-glass fiber and epoxy resin would provide less tip deformation due to their higher modulus of elasticity, the optimal material in the final solution was ABS M30, chosen for its lower density, which reduces blade weight while still satisfying the safety requirements.

The geometric changes explain much of the performance gain. Increasing the root diameter raises the moment of inertia and therefore the blade’s stiffness, limiting deflections relative to the baseline. The optimized chord lengths decrease near the root and tip regions, which reduces mass, while the twist angles increase at the root and decrease slightly toward mid-span, raising the local angle of attack and producing higher torque. Streamline analysis showed that the baseline blade developed a separation zone near the root because of an undesirable high angle of attack, which reduced efficiency by increasing drag and decreasing lift; this wake zone is absent in the optimized blade thanks to the increased twist angles of the first sections. The vorticity field showed significant vortex reduction behind the root and hub of the optimized blade, and weaker tip vortices with shorter vortex tubes, which decreases the interaction of tip wakes between blades. The pressure distribution near the tip is also more uniform in the optimized blade, whereas the baseline blade showed higher gradients between the pressure and suction sides that increase mechanical load and deformation.

The two-way FSI analysis also captured the dynamic aeroelastic behavior that one-way approaches miss. Blade deformation in the flapwise and edgewise directions induces oscillatory velocity and alters the twist distribution, changing the apparent angle of attack, while the oscillatory flapwise deflection adds a component to the apparent wind speed. The interaction between the blade’s oscillatory motion and the tip wake causes variations in the apparent angle of attack and relative wind speed that affect the velocity distribution at the blade tip. Although the induced velocity influence on aerodynamic performance is small, it creates a phase difference between the rigid and flexible blades. At the minimum deflection state, the maximum velocity on the suction side increased by 0.2 m/s due to the higher angle of attack, and the pressure difference was higher in the maximum deflection state. The turbine power for the flexible blade was approximately one percent lower than that of the rigid case, an effect the authors attribute to blade aeroelasticity, with a significant change in pressure coefficient observed near the leading edge when deflection twist reduced the apparent angle of attack.

The authors conclude that coupling two-way FSI with the optimization algorithm can lead to a more realistic and structurally safer wind turbine design, because real-world vibrations from complex operating conditions influence aerodynamic performance and loading. The 22% reduction in tip deflection, along with the lower stress level of the optimized blade, indicates improved safety performance and the potential for a longer service life. The study is a numerical simulation of a small-scale blade validated against prior experimental data rather than a demonstration on a physical turbine, so its findings apply to the modeled configuration and conditions. Nevertheless, by showing that an optimization loop can account for the full aeroelastic feedback loop—rather than treating deformation as an afterthought—the work offers a template for designing small wind turbines that are lighter, more efficient, and structurally safer at the same time.

Subject of Research: Aeroelastic multi-objective optimization of a small-scale horizontal axis wind turbine blade using two-way fluid–structure interaction and a particle swarm algorithm

Article Title: Aeroelastic optimization of a small scale horizontal axis wind turbine using particle swarm algorithm

Article References: Falahi, M., & Nabatian, N. (2026). Aeroelastic optimization of a small scale horizontal axis wind turbine using particle swarm algorithm. Advances in Aerodynamics, 8(1), Article 28. https://doi.org/10.1186/s42774-026-00256-5

Image Credits: AI Generated

DOI: 10.1186/s42774-026-00256-5

Keywords: wind turbine, aeroelasticity, fluid-structure interaction, particle swarm optimization, blade design, small wind turbines, MOPSO, power coefficient, blade weight, tip deflection, CFD, ANSYS