The research, published in the journal Results in Engineering, was carried out by Maziyar Moghtadaeifar, Ramin Farzadi, and Majid Bazargan, who built their design around a radical idea that has been gathering momentum in wind engineering: the J-shaped airfoil. A conventional blade cross-section, such as the standard NACA0021 profile used here as a baseline, is a closed teardrop shape. A J-shaped airfoil takes that profile and simply removes part of the pressure side, the face of the blade that faces away from the turbine’s rotation axis, leaving a hollow, scoop-like section bounded by a wall just one millimeter thick. The opening begins at the point of maximum thickness and runs all the way to the trailing edge, transforming the blade into something between a wing and a curved trough.

That hollow matters. When wind sweeps across a J-shaped blade, air circulates inside the concave cavity, and the resulting changes in pressure distribution alter how lift and drag act on the rotor. Earlier experimental and numerical work had shown that such profiles can improve self-starting, because the open cavity behaves somewhat like a drag device at low speeds, but often at a cost to peak efficiency. The innovation in the new study is to combine this profile with a helical configuration: three blades, each twisted sixty degrees around the rotation axis, mounted on a rotor with a radius of 0.99 meters and a height of 1.15 meters. Helical blades smooth the torque output because some section of some blade is always optimally positioned relative to the wind, reducing the violent fluctuations that plague straight-bladed designs and making the rotor less dependent on the angle at which it happens to have stopped.

To test the concept, the team ran three-dimensional unsteady Reynolds-averaged Navier-Stokes simulations using the shear-stress transport k-omega turbulence model, a combination that previous validation studies have identified as among the most accurate for capturing the complex, separated flows around vertical-axis rotors, including the transient phenomenon of dynamic stall. The computational domain stretched thirty-two rotor radii downstream and twelve radii in the other directions, with a blockage ratio of just 1.61 percent, and a sliding-mesh cylinder carried the spinning blades. The researchers verified their setup against published experimental data for two different variable-pitch turbines, then ran careful mesh and time-step independence studies, refining the grid until the cycle-averaged torque coefficient changed by less than one percent and settling on a time step of half a degree of rotation per step.

The first headline result concerns how the J-shaped profile itself performs. Across low and medium tip speed ratios, the ratio of blade speed to wind speed that governs rotor behavior, the J-shaped helical turbine outperformed a geometrically identical machine with conventional NACA0021 blades. At a tip speed ratio of 1.11, for example, the J-shaped rotor produced a torque coefficient 26.59 percent higher than the full-profile machine, with the advantage concentrated in the upwind passage between azimuth angles of thirty and one hundred twenty degrees, where dynamic stall dominates. The cavity appears to reshape the internal flow structure in a way that enlarges the pressure difference between the two sides of the blade, and the first torque peak shifts to a later azimuth angle and grows taller. Averaged across all the operating conditions examined, the profile swap alone was worth roughly a ten percent improvement in torque.

But the J-shape carried a hidden liability that emerged at high speed. At a tip speed ratio of 1.77, the open-tipped J-shaped turbine’s performance collapsed, falling more than fifty percent below the conventional rotor. The culprit was the blade tip. Because the J-profile is hollow, vortices do not merely shed from the tip the way they do on a solid wing; they can leak out through the open cavity itself, spilling high-energy flow and destroying the pressure difference the blade depends on. Tip vortices, the swirling structures that form wherever lift-generating surfaces end abruptly, are a familiar efficiency tax on all rotors, but the open J-section makes the leakage far more damaging precisely when the turbine is spinning fast enough to generate its best power.

The team’s fix was disarmingly simple: cap the tips. They added thin NACA0021-shaped plates, one millimeter thick, to both ends of each blade, sealing the hollow section like lids on a tube. The effect was enormous. At the problematic tip speed ratio of 1.77, the caps boosted the torque coefficient by roughly 122 percent compared with the uncapped J-shaped turbine, lifting it about eight percent above even the conventional full-profile machine. Averaged over all five tip speed ratios studied, from 0.44 to 1.77, the caps raised the J-shaped turbine’s torque coefficient by about 46 percent, and the capped J-shaped design beat the conventional helical turbine by about 48 percent overall. In power-coefficient terms, obtained by multiplying torque by tip speed ratio, the capped machine dominated across the operating range.

By slicing each blade into twenty sections along its height and tracking the torque of each, the researchers traced exactly where the gains came from. At a mid-range tip speed ratio of 1.33, the upwind half of the rotor improved by just over twenty percent with caps installed, while the downwind half gained a more modest eight percent, with the largest benefits near the tips themselves. Flow visualizations revealed the mechanism: without caps, the vortex forming inside the blade’s concave cavity escapes outward over the open edge; with caps in place, the vortex is redirected toward the trailing edge, and pressure builds inside the cavity, strengthening the force that drives rotation. The caps essentially convert a leaking bucket into a sealed one, letting the J-profile’s pressure advantage accumulate instead of draining away through the blade ends.

Perhaps most important for the urban applications that motivate this whole line of research, the capped design starts better. The team held the rotor stationary in a seven-meter-per-second wind and computed the starting torque at azimuth angles from zero to 105 degrees in fifteen-degree increments. The capped J-shaped turbine beat the conventional helical rotor at every single angle, with improvements ranging from about four percent to a striking 46.6 percent at ninety degrees, and an average gain of roughly 21.5 percent across all positions. For a technology whose central weakness has always been the dead zone where lift-based rotors cannot overcome their own drag, a design that simultaneously raises efficiency, smooths torque, and strengthens self-starting is a meaningful step forward. The authors caution that they fixed the cut ratio and cap thickness rather than optimizing them, so further gains may remain on the table. But the message of the study is clear: sometimes the path to better wind energy is not a bigger machine or a fancier material, but a hollow blade with its ends sealed shut, turning the city’s messy gusts into cleaner, steadier power.

Subject of Research: Aerodynamic performance and self-starting behavior of a helical J-shaped vertical-axis wind turbine with capped blade tips

Article Title: Aerodynamic performance and self-starting characteristics of a novel helical J-shaped vertical-axis wind turbine with blade-tip caps

Article References: Moghtadaeifar, M., Farzadi, R., & Bazargan, M. (2026). Aerodynamic performance and self-starting characteristics of a novel helical J-shaped vertical-axis wind turbine with blade-tip caps. Results in Engineering, 32, Article 113308. https://doi.org/10.1016/j.rineng.2026.113308

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113308

Keywords: vertical-axis wind turbine, J-shaped airfoil, helical blades, blade-tip caps, tip vortices, self-starting torque, CFD simulation, URANS, SST k-omega, dynamic stall, urban wind energy, power coefficient

The concept of a variable-diameter rotor is not new. Engineers have flirted with the idea since at least the late 1960s, when early studies explored the Trac variable diameter rotor concept, followed by Air Force Flight Dynamics Laboratory studies in the 1970s and wind tunnel tests of a variable-diameter tiltrotor model in the 1990s. The appeal is straightforward: a rotor that can extend its diameter in hover gains lift efficiency, while retracting the blades in forward flight or high-speed cruise reduces drag, noise, and structural loads. More recent work has shown that combining variable rotor radius with variable rotational speed can significantly improve helicopter performance, and that span morphing can expand a rotorcraft’s usable flight envelope. Yet almost all previous analyses treated the morphing process itself as quasi-steady, assuming the aerodynamics simply track the geometric change. The new study challenges that assumption head-on.

Xiayang Zhang, Chencheng Gao, Wei Li, Bo Wang, Jiachen Yang, and Qijun Zhao developed a computational fluid dynamics framework specifically built to capture the physics of diameter morphing as it happens. The method solves the unsteady Reynolds-averaged Navier–Stokes equations, the workhorse equations of practical aerodynamics that describe how momentum, mass, and energy evolve in a turbulent flow with time-averaged turbulence modeling. Crucially, the team coupled these equations with a moving-embedded grid method, an overset grid approach in which separate mesh systems around each blade move, overlap, and exchange information with a background mesh. This allows the blades to slide spanwise, extending or retracting their tips, while the simulation continues to resolve the wake, the tip vortices, and the flow between blades without remeshing the entire domain at every instant.

Before trusting the method on morphing rotors, the researchers validated it against a well-studied benchmark: a rotor undergoing a rapid ramp change in collective pitch, the same kind of transient that has been measured experimentally on full-scale helicopter rotors since the 1950s. Rapid blade-pitch increases are known to produce thrust responses that lag behind the control input, and the team’s comparative analysis confirmed that their unsteady aerodynamic method reproduces these dynamic behaviors. This validation step matters because the same lag, or hysteresis, between geometry change and aerodynamic response is precisely what the researchers set out to quantify for diameter morphing, and a method that could not capture pitch transients could not be trusted with span transients.

With the method verified, the team simulated the full three-dimensional flow field of a rotor during diameter morphing in both hover and forward flight. The simulations exposed a rich set of interactions. As the blades extend or retract, the tip vortices, the concentrated spirals of air shed from each blade tip that dominate rotor noise and vibration, move spanwise along with the blade geometry. This spanwise motion of the wake system couples with the flow along the blade itself, and in the midspan region, far from the tip where blade–vortex interaction is normally expected, the simulations revealed novel blade–vortex interaction and vortex–vortex interaction phenomena. In other words, the very act of changing the rotor’s diameter creates new collision patterns between blades and vortices that a fixed-diameter rotor never produces, with implications for loading, vibration, and acoustic signatures that designers must now account for.

The study also quantified how the parameters of the morphing maneuver itself, rather than just the final geometry, control the aerodynamic outcome. The amplitude of the diameter change, how far the rotor extends or retracts, exhibits a broadly linear relationship with rotor thrust, a reassuringly simple rule of thumb for control engineers. The speed of the change is a different story: the faster the diameter morphs, the more unsteady the flow field becomes, with overshoots in the unsteady loads that temporarily exceed the values associated with either the starting or ending diameter. This overshoot response is an aerodynamic inertia effect, analogous to the way a rapid pitch increase on a conventional rotor produces a thrust spike before the induced velocity field catches up. For an intelligent variable-diameter rotor, it means the actuation system and the blade structure must be designed to tolerate transient loads well above the steady-state design loads.

Perhaps the most practically significant finding concerns the pattern of the diameter change. The researchers found that the morphing trajectory, the specific time history by which the diameter varies, affects both the peak magnitude and the phase of the aerodynamic loads. Moreover, the aerodynamic response is not symmetric: extending the diameter and retracting it produce different degrees of load change, a clear signature of hysteresis in which the flow field remembers its history. Similar hysteretic aerodynamic characteristics have been documented on variable-sweep morphing wings, and the new results extend that picture to rotating systems, where centrifugal and rotational effects add further complexity. The asymmetry means that a morphing schedule optimized for extension cannot simply be reversed for retraction.

The implications reach well beyond conventional helicopters. Variable-diameter concepts are being studied for tiltrotors, ducted fans in urban air mobility vehicles, quadcopters with variable speed and geometry, and even large wind turbines under adaptive rotor programs. As electric vertical-takeoff-and-landing aircraft crowd the design space, the ability to trade hover efficiency against cruise drag by reshaping the rotor in flight is one of the most promising levers for extending range and reducing noise. The Nanjing team’s results provide engineering guidance for exactly this design problem: how fast to morph, how far to morph, and which morphing patterns minimize the unsteady load penalties while achieving the desired performance change. Their conclusions suggest that morphing strategies should be treated as dynamic aerodynamic maneuvers in their own right, not merely as transitions between static configurations.

The work, supported by the National Natural Science Foundation of China and the State Key Laboratory of Helicopter Aeromechanics, arrives as computational power finally makes it feasible to resolve the full unsteady flow field of a morphing rotor rather than relying on simplified wake models. What the simulations reveal is that a rotor in the act of changing shape is a genuinely distinct aerodynamic object, governed by coupling between spanwise flow and tip vortices, by transient overshoots, and by history-dependent loads. For the engineers hoping to build rotors that breathe, extending to lift and contracting to cruise, the message of this study is clear: the transition is where the physics lives, and mastering it will determine whether morphing rotors deliver their promised revolution in flight efficiency.

Subject of Research: Unsteady aerodynamic characteristics of variable-diameter morphing rotors analyzed with CFD

Article Title: Aerodynamic Analysis of Rotor During Diameter Morphing Process

Article References: Zhang, X., Gao, C., Li, W., Wang, B., Yang, J., & Zhao, Q. (2026). Aerodynamic Analysis of Rotor During Diameter Morphing Process. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01237-0

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01237-0

Keywords: variable-diameter rotor, rotorcraft, CFD, unsteady aerodynamics, blade–vortex interaction, tip vortices, morphing aircraft, hysteresis, URANS, helicopter performance, urban air mobility, overset grids