## Dynamic stall

Transient aerodynamics have another facet, called "dynamic stall". Dynamic stall or stall hysteresis is a dynamic effect which occurs on aerofoils if the angle of attack changes more rapidly than the air flow around the blade (or blade element) can adjust. Dynamic stall was shown to occur under a variety of inflow conditions, including turbulence, tower shadow, and yawed flow [100]. The result is aerofoil lift and drag coefficients which depend not only on the instantaneous angle of attack (quasi-steady aerodynamics assumption), but also on the recent angle of attack history. In particular, the lift and drag coefficients depend on the angle of attack as well as its first time derivative. These changes can produce hysteresis loops which, in turn, lead to cyclic pressure loadings that are not predictable from conventional lift and drag data obtained at steady angles of attack. Fig. 2.3 (from Leishman & Beddoes [157]) shows a typical rotating blade dynamic stall measurement compared to 2-D wind tunnel data.

Figure 2.3: Typical dynamic stall behavior of the lift coefficient Ci of a fictive aerofoil as function of the angle of attack a compared with 2-D wind tunnel data. Solid curve: 2-D wind tunnel data, dashed curve: Dynamic stall.

1 |
Flow reversals within boundary layer, Formation of a vortex |

2 |
Vortex detaches and moves over aerofoil surface |

3 |
Vortex passes trailing edge, full stall develops |

4 |
Reattachment of flow |

Figure 2.3: Typical dynamic stall behavior of the lift coefficient Ci of a fictive aerofoil as function of the angle of attack a compared with 2-D wind tunnel data. Solid curve: 2-D wind tunnel data, dashed curve: Dynamic stall.

Increased excitation of the blade structural dynamic modes becomes a possibility during dynamic stall. In case of torsionally soft rotor blades, severe stall may even excite the blade torsion mode at its natural frequency, leading to a dynamic instability known as stall-flutter [157].

Now that the structural dynamic modeling has reached a good level of maturity (see Section 2.3.2), it is also required that the relatively simple quasi-steady representation for the aerodynamics of stall regulated wind turbines is replaced by more accurate, but still computationally efficient, models that incorporate the unsteady behavior of the blade sections. At present it is possible to model dynamic stall in considerable detail, and accuracy using Computational Fluid Dynamics (CFD) methods. For example, numerical solutions to the unsteady Navier-Stokes equations are becoming increasingly feasible [277]. Unfortunately, these solutions are extremely complex, implying that implementation in a design code would exceed the practical limits of the computational power.

In order to include the unsteady behavior in the design codes, it is thus necessary to make use of semi-empirical models. Such models describe the sectional force coefficients in terms of angle of attack and some time derivatives in differential equation form allowing straightforward implementation in the aerodynamic routines based on the blade element momentum theory. The CFD methods can be used to check the validity of these models.

Prior to 1988 dynamic stall was not incorporated in wind turbine design codes [100] although most wind turbines were stall regulated. At present, the unsteady aerodynamics with a length scale of the order of the chord length are modeled in five ways in the state-of-the-art design codes, i.e. Beddoes [157] (or Beddoes-Leishman), Gormont [89, 103] (or Boeing-Vertol Gamma Function), ONERA [216, 217, 293], SIMPLE [192], and Stig 0ye [206]. All models are semi-empirical in nature, and require some a priori knowledge of aerofoil characteristics. In Molenaar [190] it is shown by comparing hysteresis loops calculated for an oscillating NACA-0012 aerofoil (where "00" means zero camber implying a symmetrical aerofoil, and "12" indicates a maximum thickness to chord ratio of 12%) that no preference for either of the mentioned dynamic stall models exists.

This conclusion is confirmed by e.g. Bierbooms [10], Snel [266], and Yeznasni et al. [322]. Hansen [99], on the other hand, reports that the Gormont model is able to predict the correct hysteresis loop when the two empirical constants are known a priori. The main cause for the observed differences is that dynamic stall depends on such a large number of parameters (including aerofoil geometry, pitching frequency, Mach number, Reynolds number). This implies that the phenomenon is difficult to analyze. Research is continuing to explore the most accurate and practical method to implement this aspect of unsteady aerodynamics. Riziotis et al. [237], for example, suggests to use the more advanced vortex models to check and calibrate the semi-empirical models.

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