The research team, led by Shantanu Purohit together with Haoyuan Sun, Andrea Sciacchitano and Wei Yu, used a porous disk as a stand-in for an operating turbine. Porous disks have long served as wind turbine analogues because, when their porosity is tuned to match the thrust coefficient of a real rotor, they reproduce the essential far-wake characteristics of a spinning machine without the complexity of rotating blades. The team 3D printed a uniform disk of 10 centimeters in diameter with a porosity of 0.6, yielding a thrust coefficient of approximately 0.69, a value consistent with the porosity-to-thrust relationships established in prior literature.

The genuinely novel element was the inflow. To generate wind veer in the laboratory, the researchers installed a bank of twisted NACA 0014 airfoil vanes at the exit of the open-jet W-tunnel. Because the vanes were twisted in opposite directions above and below the disk centerline, the flow emerged with an angle of attack that varied linearly with height, producing a total direction change of roughly 10 or 20 degrees across the disk. Flow characterization without the disk confirmed that the generated veer profiles closely matched the idealized linear profiles used in atmospheric simulations, with turbulence intensity remaining below 2.5 percent across the disk area in the veered cases.

Measuring the three-dimensional wake required a demanding diagnostic technique. The team employed high-resolution stereoscopic particle image velocimetry, using two sCMOS cameras viewing a laser-illuminated plane from different angles to reconstruct all three velocity components. Smoke particles of roughly one micrometer seeded the flow, and the researchers captured 100 vector fields at each measurement plane, mapping wake cross-sections at four downstream stations and streamwise evolution across three overlapping fields of view. This full-field view was essential because, under the combined action of yaw and veer, the wake deforms in ways no single-component measurement could capture.

The results reveal a striking geometric transformation. Under uniform inflow and no yaw, the wake is nearly circular and symmetric, apart from a modest downward shift caused by the tower. When the disk is yawed by 30 degrees, the familiar curled, kidney-bean shape appears, produced by a counter-rotating vortex pair shed from the top and bottom edges of the disk that induces strong spanwise velocity and deflects the wake laterally. But when veer is introduced, the wake stretches into an ellipse, elongated along one lateral axis and compressed along the other, because the spanwise velocity points in opposite directions above and below the disk center. With 20 degrees of veer, the stretching becomes dramatic, and the wake thins into a narrow band.

When yaw and veer act together, the curled shape from yaw is superimposed on the elliptical stretching from veer, producing a complex three-dimensional wake topology. Crucially, as the magnitude of veer increases, it exerts dominant control over the wake shape, progressively overshadowing the influence of yaw. The vorticity measurements reinforce this picture: the background veer, which carries streamwise vorticity of opposite orientation to the upper vortex of the yawed disk, weakens the counter-rotating vortex pair, reducing both peak vorticity and circulation compared with uniform inflow. The vortex sheet also breaks down faster under veered conditions, with peak vertical vorticity disappearing within five disk diameters downstream rather than persisting beyond six.

To understand why veered wakes recover faster, the researchers performed a budget analysis of the streamwise momentum equation, decomposing wake recovery into contributions from lateral advection, vertical advection, and turbulent mixing through Reynolds stress divergence. Under uniform inflow, lateral advection of momentum dominates the recovery process, particularly for yawed disks. Under veered inflow, however, vertical advection becomes the leading mechanism, with its contribution approximately five times higher for the 20-degree veer case than for uniform inflow at three diameters downstream. The sharper velocity gradients created by the elliptical wake shape also enhance turbulent kinetic energy production along the wake edges, and turbulent transport then carries this energy into the wake core, re-energizing the deficit more rapidly.

The practical consequences emerge most clearly in the analysis of available power, a metric that integrates the cube of the streamwise velocity over the frontal projection of a hypothetical downstream rotor. For a turbine placed directly inline at five disk diameters behind the first, available power under 20-degree veer was 45 percent higher than under uniform inflow with no yaw. Combining veer with 30 degrees of yaw pushed the gain to 77 percent at that location, and up to 85 percent at seven diameters downstream. Yet the comparison that matters most for control engineers is subtler: under strong veer, adding yaw yielded only modest additional benefit, roughly 9 percent more available power at 30 degrees of yaw compared with no yaw under the same veered inflow, because the wake had already substantially recovered on its own.

This finding strikes at the heart of wake steering, the strategy of deliberately misaligning upstream turbines to deflect their wakes away from downstream neighbors. Wake steering performs best under low-turbulence conditions, which occur precisely at night in stable boundary layers, the same conditions under which wind veer is most pronounced. Field observations show veer occurring more than 70 percent of the time in offshore environments, with average gradients around 0.07 degrees per meter, meaning a 200-meter rotor routinely experiences roughly 18 degrees of direction change across its span. If veer alone already re-energizes the wake to a large degree, the marginal value of yawing upstream turbines diminishes, and control look-up tables that ignore veer risk suboptimal farm performance and unnecessary loading.

The study is not without limitations, which the authors discuss candidly. The vanes shed their own periodic wake structures that locally distort the inflow, and the discrete spacing of the vanes produces a wavy variation in veer angle across the span, unlike the spanwise-uniform veer of the real atmosphere. Future work will explore finer vane spacing, mesh screens to homogenize the flow, and the interaction between rotor rotation direction and veered inflow. Still, as the first experimental reproduction of wind veer in a wind tunnel, the study delivers validation data for high-fidelity simulations and a foundation for extending analytical wake models. Its central message is likely to resonate across the industry: the atmosphere itself, through the quiet rotation of wind direction with height, already performs a portion of the wake recovery that engineers have been trying to achieve with yaw.

Subject of Research: Experimental wind tunnel investigation of how wind veer affects the wakes of yawed and non-yawed porous disk turbine models

Article Title: Wind tunnel study of yawed porous discs subjected to veered inflow

Article References: Purohit, S., Sun, H., Sciacchitano, A., & Yu, W. (2026). Wind tunnel study of yawed porous discs subjected to veered inflow. Wind Energy Science, 11(9), 3671-3701. https://doi.org/10.5194/wes-11-3671-2026

Image Credits: AI Generated

DOI: 10.5194/wes-11-3671-2026

Keywords: wind energy, wind veer, wake steering, wind tunnel, porous disk, stereoscopic PIV, atmospheric boundary layer, turbine wake recovery, yaw control, turbulent kinetic energy, available power, Delft University of Technology

The research, published in the journal Aerospace Systems, was carried out by Pavel Makeev of the Department of Aeronautical Engineering at the Moscow Aviation Institute. The work revisits and modernizes a concept first embodied in the tail rotor scheme of the TsAGI-1EA, an experimental helicopter built in the Soviet Union in the 1930s. The idea is deceptively simple: instead of mounting a single multi-bladed rotor on one side of the tail boom, the coaxial tail rotor places a pair of two-bladed rotors on the same axis but on opposite sides of the boom, one to the right and one to the left. This arrangement gives the rotors a substantial axial separation along the axis of rotation, and it is precisely that separation, the study finds, that unlocks an aerodynamic benefit familiar from coaxial main rotor systems.

To evaluate the concept, Makeev used a free-wake model, a computational approach that tracks the vortical wake shed by each blade as it moves through the air rather than imposing a prescribed wake geometry. The free-wake method is particularly valuable for coaxial configurations, where the wake of one rotor travels directly into the path of the other and the resulting blade-vortex interactions strongly influence both performance and loads. The simulations focused on hovering flight, the aerodynamically demanding condition in which a rotor must generate maximum thrust for the least possible power, and the rotors were analyzed in isolation, without the complicating influences of the main rotor wake or the helicopter airframe.

The coaxial tail rotor was benchmarked against two established alternatives: the conventional four-bladed tail rotor used on serial production helicopters and the so-called scissors tail rotor, a promising design in which blade pairs are mounted at an angle to one another on the same hub. The baseline axial spacing between the rotational planes of the coaxial blade pairs was set at 0.8 rotor radii, a value chosen because it is approximately equal to the doubled side spacing of a conventional tail rotor relative to the helicopter’s longitudinal axis. Both co-rotating and counter-rotating versions of the coaxial pair were examined, along with two different control strategies: one in which both rotors operate at the same blade pitch angle, and one in which both rotors are trimmed to produce the same thrust.

The headline result concerns hover efficiency, conventionally measured by the Figure of Merit, a dimensionless ratio that compares the ideal power required to produce a given thrust with the actual power consumed. For the coaxial counter-rotating configuration with 0.8R axial spacing operating under the equal-thrust strategy, the Figure of Merit increased by up to 12.2 percent relative to the conventional four-bladed rotor, while power consumption fell by approximately nine percent. That is a substantial gain for a component whose aerodynamic losses translate directly into fuel burn and payload capacity. The equal-thrust control strategy consistently outperformed the equal-pitch strategy, indicating that allowing each rotor of the pair to find its own pitch while matching thrust output extracts more of the available aerodynamic benefit.

The direction of rotation mattered as well. Counter-rotating pairs, in which the upper and lower rotors spin in opposite directions, delivered better performance than co-rotating pairs. This finding echoes the established behavior of coaxial main rotors, where counter-rotation allows the swirling wake of one rotor to partially cancel the swirl of the other, reducing rotational losses in the slipstream and improving the distribution of induced velocity across the rotor disk. The study also documented the shapes of the rotor wakes, the detailed flow patterns, and both distributed and total aerodynamic characteristics, providing a physical picture of how the separated blade planes interact through their vortex systems.

Perhaps the most intriguing result concerns how the axial spacing between the two rotors shapes the benefit. Makeev extended the analysis across a range of spacings from 0.6R to 2.0R and found that the maximum increase in Figure of Merit, reaching 15.8 to 16.2 percent, occurs at spacings of 1.4R to 1.8R. Beyond that range, the positive effect begins to decline. This non-monotonic behavior suggests there is an optimal window in which the wake of one rotor is far enough from the other to avoid destructive interference yet close enough for the two vortex systems to interact favorably. In practical terms, the axial separation inherent in the coaxial tail rotor arrangement makes it possible to maximize the positive aerodynamic effect that has long been recognized in coaxial main rotor research, where high Figure of Merit values at hover have been documented since the 1990s.

The implications extend beyond raw efficiency. Because the coaxial arrangement places rotors on both sides of the tail boom, it offers the potential for increased yaw control authority, which is directly relevant to flight safety. Loss of tail rotor effectiveness, whether caused by main rotor wake interference, crosswind conditions, or low-speed maneuvering, remains a serious hazard, and a tail rotor with higher aerodynamic efficiency and greater thrust capability for the same power budget could enlarge the safety margin in precisely the flight regimes where conventional designs are most vulnerable. The concept also fits into a broader research effort spanning variable-speed tail rotors, advanced blade tip shapes, and optimized twist distributions, all aimed at squeezing more performance from this hardworking component.

Makeev is careful to frame the findings as preliminary. All results were obtained for an isolated tail rotor, and real helicopters present a far messier aerodynamic environment. The wake of the main rotor sweeps past the tail, the airframe sheds its own vortices, and in forward flight the tail rotor operates in oblique flow rather than in the clean axial conditions of hover. Two open tasks stand out: quantifying how the main rotor wake and airframe modify the coaxial tail rotor’s performance, and assessing the drag penalty of the coaxial hub assembly at forward flight, since two hubs and their linkages inevitably create more parasite drag than a single conventional hub. The final choice of parameters, the study concludes, must account for the specifics of the helicopter on which the concept is to be installed.

Even with those caveats, the study makes a compelling case that a design idea nearly a century old deserves a second look with modern computational tools. A tail rotor that delivers more than twelve percent better hover efficiency and nine percent lower power consumption, with the potential for stronger yaw control and improved safety, would be a meaningful advance for an industry under pressure to reduce fuel consumption and emissions. As eVTOL aircraft and next-generation helicopters bring coaxial configurations back into the mainstream, the coaxial tail rotor may find itself moving from a 1930s curiosity to a standard feature of tomorrow’s rotorcraft.

Subject of Research: Numerical analysis of the hover aerodynamic performance of a coaxial helicopter tail rotor using a free-wake model

Article Title: Numerical study of the aerodynamic performance of the coaxial tail rotor concept in hover

Article References: Numerical study of the aerodynamic performance of the coaxial tail rotor concept in hover. (n.d.). https://doi.org/10.1007/s42401-026-00549-z

Image Credits: AI Generated

DOI: 10.1007/s42401-026-00549-z

Keywords: helicopter, coaxial tail rotor, hover, free-wake model, aerodynamic performance, Figure of Merit, rotorcraft, tail rotor efficiency, blade-vortex interaction, yaw control, computational fluid dynamics, aerospace engineering