Dynamic stall on helicopter rotors
[1][2] Unlike fixed-wing aircraft, of which the stall occurs at relatively low flight speed, the dynamic stall on a helicopter rotor emerges at high airspeeds or/and during manoeuvres with high load factors of helicopters, when the angle of attack(AOA) of blade elements varies intensively due to time-dependent blade flapping, cyclic pitch and wake inflow.
For example, during forward flight at the velocity close to VNE, velocity, never exceed, the advancing and retreating blades almost reach their operation limits whereas flows are still attached to the blade surfaces.
The effect of dynamic stall limits the helicopter performance in several ways such as: The visualization is considered a vivid method to better understand the aerodynamic principle of the dynamic stall on a helicopter rotor, and the investigation generally starts from the analysis of the unsteady motion on 2D airfoil (see Blade element theory).
Flow separation is less likely to happen on the upper airfoil surface with a larger value of AoA than the latter, which can increase the maximum lift coefficient to a certain extent.
Three primary unsteady phenomena have been identified to contribute to the delay in the onset of flow separation under unsteady condition:[3] The development process of dynamic stall on 2D airfoil can be summarized in several stages:[8][9] Although the unsteady mechanism of idealized 2D experiments has already been studied comprehensively, the dynamic stall on a rotor presents strong three-dimensional character differences.
According to a well-collected in-flight data by Bousman,[11] the generation location of the DSV is "tightly grouped", where lift overshoots and large nose-down pitching moments are featured and can be classified into three groups.
The increasing of the mean value of AoA leads to more evident flow separation, higher overshoots of lift and pitch moment, and larger airloads hysteresis, which may ultimately result in deep dynamic stall.
suggests a delay of the onset of flow separation at higher AoA, and a reduction of airloads overshoots and hysteresis is secured because of the increase of the kinematic induced camber effect.
As is shown in the figure, for a cambered airfoil, the lift stall is delayed and the maximum nose-down pitch moment is significantly reduced.
[13] The sweep angle of the flow to a blade element for a helicopter in forward flight can be significant.
It is defined as the radial component of the velocity relative to the leading edge of the blade: Based on experimental data, a sweep angle of 30° is able to delay the onset of stall to a higher AoA thanks to the convection of the leading-edge vortex at a lower velocity and reduce the varying rate of lift, pitch moment, and the scale of hysteresis loops.
[14] As the figure suggests, the effect of Reynolds numbers seems to be minor, with a low value of reduced frequency k=0.004, stall overshoot is minimal and most of the hysteresis loop is attributable to a delay in reattachment, rather than vortex shedding.
[8] Lorber et al.[15] found that at the outermost wing station, the existence of the tip vortex gives both the steady and unsteady lift and pitching moment hysteresis loops a more nonlinear quasi-steady behaviour due to an element of steady vortex-induced lift, while for the rest of the wing stations where oscillations below stall, there is no particular difference from 2-D cases.
During forward flight, the blade element of a rotor will encounter a time-varying incident velocity, leading to additional unsteady aerodynamic characters.
With regard to the latter method, because of the sophisticated flow field during the process of the dynamic stall, the full Navier-Stokes equations and proper models are adopted, and some promising results have been presented in the literature.
Furthermore, this method is also sometimes too computationally costly for research purposes as well as the pre-design of a helicopter rotor.
On the other hand, to date some semi-empirical models have shown their capability of providing adequate precision, which contains sets of linear and nonlinear equations, based on classical unsteady thin-airfoil theory and parameterized by empirical coefficients.
Therefore, a large number of experimental results are demanded to correct the empirical coefficients, and it is foreseeable that these models cannot be generally adapted to a wide range of conditions such as different airfoils, Mach numbers, and so on.
Here, two typical semi-empirical methods are presented to give insights into the modelling of dynamic stall.
The model was initially developed by Gross&Harris[22] and Gormont,[23] the basic idea is as follows: The onset of dynamic stall is assumed to occur at
function is empirical, depends on geometry and Mach number and is different for lift and pitching moment.
The airloads coefficients are constructed from static data using an equivalent angle of attack
derived from Theodorsen's theory at the appropriate reduced frequency of the forcing and a reference angle
[27] The model consists of three distinct sub-systems for describing the dynamic stall physics:[3] One significant advantage of the model is that it uses relatively few empirical coefficients, with all but four at each Mach number being derived from static airfoil data.
