The central difficulty is geometric. When the ratio of blade chord to rotor arm length is not small, the curvature of the flow around a rotating blade changes the aerodynamic coefficients compared with those measured or computed in a uniform stream. Researchers have known since the pioneering work of Migliore and colleagues in 1980 that a symmetric airfoil in curved flow behaves, in terms of lift and moment, much like a cambered airfoil at a non-zero incidence in straight flow, an effect captured by the concepts of virtual camber and virtual incidence. Later work by Akimoto and co-authors in 2013 formalized this with a bidirectional conformal mapping, and studies by Rainbird and Bianchini confirmed the phenomenon experimentally and numerically. What has been missing, the new paper argues, is a complete and consistent treatment that works for every blade attachment point, every pitch angle, and all the way up to stall.

The team’s approach is deliberately economical. The correction models are allowed only one input: the standard aerodynamic coefficients of the airfoil in uniform flow, here obtained from wall-resolved computational fluid dynamics of a NACA0015 airfoil at a high Reynolds number of 6.0 million. Everything else is an analytical modification of those coefficients, expressed through the classic analogy with potential flow along curved streamlines. For the normal force and the aerodynamic moment, the authors extend known models so that they cover all possible attachment points of the blade to the rotor arm and remain valid up to stall, a regime where many earlier formulations broke down. Crucially, they show that the precise form of the correction matters: a seemingly natural alternative formula would predict stall angles several degrees away from those found in the reference simulations.

The most striking conceptual advance concerns the tangential force, the component along the direction of blade travel that ultimately determines how much torque, and therefore power, a vertical-axis turbine produces. The authors demonstrate that the potential flow analogy, which works well for the normal force and moment, is fundamentally flawed for this component. A straight potential flow past a cambered airfoil produces only a normal force and a moment, whereas an inviscid flow past a rotating airfoil also carries a tangential force. Their new model derives this inviscid tangential force from a simple physical requirement: because the flow is inviscid, the moment at the root of the rotating arm must be exactly zero, which forces the tangential force to compensate for the aerodynamic moment. Inviscid simulations confirmed this condition numerically, and the parasitic drag from viscosity is then added on top.

Validation came in two stages. First, the team compared their corrected coefficients against wall-resolved CFD of a NACA0015 airfoil rotating with a chord-to-radius ratio of 2/7, a deliberately severe case in which curvature effects are strong. They tested the full range of pitch angles up to the two stall angles, which are themselves shifted asymmetrically by the curvature, and for two attachment points: mid-chord and quarter-chord. The agreement was close throughout. For the unpitched mid-chord case, for example, the model predicted a normal force coefficient of about minus 0.454 against a measured value of minus 0.431, and incorporating a small correction for the deformed-airfoil moment brought the moment predictions into even tighter alignment with the reference data.

The second stage moved to a full unsteady turbine configuration: a single-blade vertical-axis turbine with the same NACA0015 profile, operating at a tip speed ratio of 3.25, the value at which power production is maximized and at which the flow does not separate dynamically at any point in the rotation cycle. To simulate this efficiently, the authors implemented their corrected models in an actuator line method, a moderate-fidelity technique that replaces the meshed blade with equivalent volumetric forces in the Navier-Stokes equations. This bypasses the need to resolve the thin boundary layers on the blade surface, cutting the mesh from roughly 328,000 cells in the wall-resolved reference to about 37,000 cells in the actuator line simulation, while still reproducing realistic loads and wake behavior.

The genuinely novel ingredient is the enforcement of the aerodynamic moment. A standard actuator line distributes forces over a Gaussian kernel centered on the blade, but it cannot impose a pure moment. The team solved this by replacing the moment with an annular force field, a swirling distribution of forces around the control point that produces the same net torque without any net force. This field is then integrated analytically over the same two-dimensional template of grid cells used for the forces, guaranteeing that the moment is fully transmitted to the flow solver regardless of the chosen kernel size. The result is an actuator line that imposes both the aerodynamic forces and the aerodynamic moment, and the authors show that the two must be treated consistently: if the moment is not enforced, the inviscid part of the tangential force must be ignored, and if the moment is enforced, that force component must be included.

The comparisons against the wall-resolved reference simulation were favorable across the entire rotation cycle. The cycle-averaged coefficients for the normal force, tangential force and moments agreed well, and the predicted power coefficient tracked the reference closely, with the corrected actuator line substantially outperforming an uncorrected version. When the actuator line was centered at the blade attachment point at mid-chord, the upstream half of the cycle was reproduced with excellent accuracy, eliminating a small shift in the peak power coefficient that appeared when the line was centered at the quarter-chord aerodynamic center instead. Small discrepancies persisted in the downstream half of the cycle, where the blade flies through its own wake and the effective angle of attack becomes harder to predict, but the overall agreement gives the authors confidence in the framework.

The implications reach well beyond a single test case. Because the corrections require nothing more than standard uniform-flow airfoil data, any actuator line user can apply them to an existing turbine model simply by knowing the chord-to-radius ratio and the blade attachment geometry. The moment-enforcement technique also opens the door to simulating cambered blades, which carry an intrinsic aerodynamic moment even in straight flow, and to multi-turbine cluster simulations that would be computationally prohibitive with wall-resolved methods. The authors note that their models are currently limited to flows without fast unsteady effects or dynamic stall, and that extending them to thicker airfoils and to the combined effects of curvature and thickness are natural next steps. For a technology whose commercial fortunes depend on cheap, trustworthy simulation, the ability to capture curved-flow aerodynamics accurately at a fraction of the computational cost may prove a decisive enabler for the next generation of vertical-axis wind, river and tidal energy systems.

Subject of Research: Flow curvature correction models and actuator line simulation of vertical-axis turbine aerodynamics

Article Title: Improved modeling of flow curvature effects and actuator line method with aerodynamic moment, with application to vertical-axis turbines

Article References: Winckelmans, G., Rochefort, P., Villeneuve, T., Trigaux, F., Duponcheel, M., & Dumas, G. (2026). Improved modeling of flow curvature effects and actuator line method with aerodynamic moment, with application to vertical-axis turbines. Wind Energy Science, 11(9), 3615-3651. https://doi.org/10.5194/wes-11-3615-2026

Image Credits: AI Generated

DOI: 10.5194/wes-11-3615-2026

Keywords: vertical-axis turbines, flow curvature, actuator line method, aerodynamic moment, NACA0015 airfoil, virtual camber, CFD, wind energy, turbine simulation, tangential force, potential flow, tip speed ratio

A team of researchers from the Massachusetts Institute of Technology, Princeton University, Queen’s University, and Penn State University believes it has found a way around that problem. In a new open access paper published in PNAS Nexus, the group describes a series of experiments conducted in a pressurized wind tunnel, a facility that allows scaled-down turbines to reproduce the flow physics of full-size machines operating in the open atmosphere. By raising the air pressure inside the tunnel, the researchers dramatically increased the density of the air, and with it the inertia of the flow around their model turbine, closing a gap between laboratory experiments and field conditions that has hampered wind energy research for decades.

The logic behind the approach rests on a principle known as dynamic similarity. A small turbine spinning in ordinary air does not behave like a giant machine standing in a windy plain, because the balance of inertial and aerodynamic forces is different at different scales. But when the air in the test chamber is pressurized, it becomes far denser, and the scaled model suddenly experiences forces that mirror those acting on a much larger turbine. In the new study, the team used a turbine measuring just 15 centimeters in diameter, but at pressures of up to 240 atmospheres the air density increased by a factor of 100 to 220 times. According to lead author John Kurelek, an assistant professor at Queen’s University, that means the experiments effectively tested a turbine that is, all else being equal, 15 to 20 meters in diameter, with the capability of reaching the equivalent of 35 meters.

The motivation for this experimental paradigm comes in part from the frustrations of field research. Michael Howland, MIT’s Jeffrey Cheah Career Development Professor and a senior figure in the project, has spent years developing models to simulate wind farm performance and to increase power output. In 2022, he demonstrated that accounting for the wake of individual turbines when controlling an entire wind farm could significantly boost electricity production. But that work demanded a lengthy and costly field campaign in which turbines at a real wind farm were intentionally misaligned with the wind for months, temporarily lowering the farm’s output, in order to understand how misalignment affects performance.

Wind energy, Howland explains, sits at a unique intersection of environmental flow, mechanics, aerodynamics, and meteorology, and that makes controlled experimentation extraordinarily difficult. Researchers want to isolate the effect of a single change, but wind farms operate in chaotic, turbulent environments where the weather is constantly evolving and turbines must react to conditions beyond anyone’s control. This complexity has left engineers uncertain about how precisely changes in the alignment between wind and turbine, or variations in the turbine’s tip speed relative to the wind, alter the power a machine produces. Many predictive models in use today are built on the assumption that turbines always face perfectly perpendicular to the wind, an assumption that is almost never true in the real world, even for modern turbines that continuously adjust their orientation in response to rapid directional shifts in the wind.

That uncertainty is exactly what the pressurized experiments were designed to resolve. Marcus Hultmark, a professor at Princeton University whose laboratory pioneered the study of scaled turbines in pressurized wind tunnels, notes that researchers have long debated which models best describe the output of wind farms, but without reliable experimental data to compare against, the field has struggled to advance. The new paper, he says, attempts to do both: settle questions about turbine performance and provide the missing experimental benchmark. Over several weeks of testing, the team ran the model turbine through a systematic series of operating conditions, varying its alignment with the wind and its control strategy to isolate how each factor influences power production.

The results carry direct implications for the economics of wind energy. The researchers found that power output could be significantly increased by adjusting the turbine’s tip speed based on its misalignment angle with the wind, a control strategy that is rarely employed at wind farms today but that could deliver performance gains at minimal added cost. Kurelek describes this as the clearest output of the experiments: new power maximums become achievable when a turbine is misaligned with the wind, simply through changes to the tip speed. Combined with optimization of the turbine’s alignment relative to the wind and the blade pitch angles, which control the airfoil’s angle of attack, the researchers estimate that such improvements could yield tens of thousands of dollars per turbine every year in additional revenue.

The experiments also served a second, equally important purpose: validating a new predictive model. Howland and his colleagues developed what they call a unified wind turbine model, building on previous work that produced a more general aerodynamic theory for wind turbines. The model simulates turbine performance across operating conditions without relying on the empirical corrections that have historically been baked into wind power models. Before running the experiments, Kurelek sent the dimensions of the wind tunnel and turbine setup to Howland, who used them to calculate the expected aerodynamics, forces, and power production. The close agreement between prediction and measurement marks the first experimental validation of the unified momentum model’s predictions about how turbines should be controlled under misalignment to achieve maximum power production.

One of the most striking features of the validated model is its computational efficiency. According to Howland, the model is fast enough to run on ordinary laptop computers, which means engineers designing and operating wind turbines anywhere in the world can use it to test different turbine designs and wind farm control strategies without access to supercomputers. That accessibility could accelerate the adoption of the control strategies identified in the study, allowing existing wind farms to be retuned for higher output rather than waiting for new hardware to be installed. Because the approach improves and validates the models that feed directly into wind turbine control protocols, its immediate impact applies to the vast installed base of turbines already generating power today.

Beyond the immediate gains, the researchers see the pressurized wind tunnel as a way to fill a persistent void in wind energy research. Howland describes a massive gap between idealized theoretical and simulation models on one side and full-scale testing in extremely complicated field environments on the other, a gap that he says nothing else currently fills except these pressurized experiments. By enabling high-throughput, controlled experiments that achieve the right physics in a time-efficient and low-cost manner, the technique could allow researchers to investigate a wide range of previously unanswered questions about turbine aerodynamics, wake behavior, and farm-level control. The work, supported in part by the Natural Sciences and Engineering Research Council of Canada, the National Science Foundation, and the MIT-GE Vernova Alliance, suggests that the path to more wind power may run not only through bigger turbines and new installations, but through smarter operation of the machines already turning in the wind.

Subject of Research: Pressurized wind tunnel experiments validating wind turbine aerodynamic models and control strategies for increased wind farm power output

Article Title: Pressurized experiments could help wind farms generate more power

Article References: Pressurized experiments could help wind farms generate more power. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: wind energy, wind turbines, pressurized wind tunnel, dynamic similarity, aerodynamics, wake modeling, turbine control, tip speed ratio, blade pitch, PNAS Nexus, MIT, renewable energy