Dynamic Stall and Stall Delay
It has been explained in Chapter 9 how the phenomenon of dynamic stall can give rise to large unsteady blade airloads that can limit the performance of a rotor system. While dynamic stall is a well-known unsteady flow problem found on wind turbines, the foregoing discussion has emphasized that unsteady airloads will be produced even in the absence of dynamic stall. These effects manifest as both amplitude and phase changes in the blade airloads compared to what would be obtained under quasi-steady conditions. Both circulatory and noncirculatory contributions to the airloads are, of course, always involved (see Chapter 8).
A prerequisite to predicting dynamic stall and its onset is to predict adequately the unsteady airloads under attached flow conditions. Despite its apparent simplicity compared to the stalled case, however, this is a nontrivial problem for which the development of general models that are valid for the turbine environment is still a major challenge. Currently, dynamic stall must be modeled using more parsimonious, semi-empirical models, for which a number of different approaches have been developed for helicopter applications (see Section 9.5) and adapted for wind turbine use. Many modem wind turbine analyses use the method developed by Leishman & Beddoes (1989), which has been modified and popularized by Pierce & Hansen (1995). However, while often giving good results, these models are not strictly predictive tools and can really only be used confidently for conditions that are not too much different from the conditions under which the models were originally validated.
The problem of dynamic stall is of particular importance on wind turbines because the large unsteady airloads that are produced (see Fig. 13.19) can cause structural damage – see Shipley et al. (1994). However, the power output from a wind turbine can be regulated deliberately by promoting stall, either by pitch regulation or through airfoil design (see Section 13.9). An example is shown in Fig. 13.28 where the onset of stall creates much turbulence over the blade and in the downstream wake. Unfortunately the prediction of dynamic stall has not yet been very successful on wind turbines. While part of the problem is the imprecise modeling of the delayed onset of flow separation resulting from unsteady aerodynamic effects, there are also subtle 3-D effects unique to the rotating environment that seem particularly pronounced on wind turbines.
In summary, the effects underlying the problem of dynamic stall can be divided into two areas: 1. Unsteady pressure gradient reduction effects on the blade, which give rise to delays or lags in the development of the 3-D boundary layer compared to that obtained under quasi-steady conditions; and 2. Coupled influences of the centrifugal and Coriolis effects acting on the boundary layer in the rotating flow environment (i. e., a radial flow effect). In general it is fair to say that a better integrated modeling capability for dynamic stall depends on gaining a much better understanding of the physics governing the 3-D boundary layer developments on rotating blades, both with wind turbines and helicopter rotors.
Several experimental and modeling studies have provided some insight into 3-D effects on rotating blades operating near stall – see Young and Williams (1972), Madsen &
Christensen (1990), Snel (1991), Narramore & Vermeland (1992), Dwyer & McCroskey (1971), Robinson et al. (1999), and Schreck et al. (2000, 2001). The first observations of the phenomenon are often attributed to Himmelskamp (1950). The motivation is clear, in that when stall occurs existing performance methods tend to predict power outputs that are lower than those actually measured. From an order of magnitude analysis of the 3-D boundary layer equations applied to a rotating flow environment, Snel (1991) has speculated that the Coriolis acceleration terms can act to alleviate adverse pressure gradients and so may delay the onset of flow separation and stall, but see also Corten (2000) for a critique of this analysis. The Coriolis and centripetal acceleration terms can be seen in a modified form of the boundary layer equations (see Section 7.3.2) first given by Fogarty (1951):
3 и dw
——- b — =0
Эх 3 z
ди ди 9 1 dp 3 2u
и—– b v——- fi x =—————- b v—- (x momentum),
Эх 3z p Эх dzl
3 и dv 2 1 fy? d2v
и—– 1- w—— H 2fiw — fi x =———— b v—- (y momentum),
Эх 3z P dy 3zz
where x is chordwise, у is spanwise, and z is normal to the blade. The Q2x terms are centripetal accelerations and the 2Q, u term is a Coriolis acceleration. Fogarty (1951) has calculated the radial or spanwise development of the boundary layer flow on the blade and has shown that for helicopter rotors these effects are small, except near the inboard part of the blade. It is here, however, where the blades of wind turbines (because of their design) tend to exhibit much higher values of lift coefficients compared to a helicopter rotor, and so the effects of radial flow can be more important here. Experimental results have shown increases in sectional maximum lift coefficients significantly beyond what would be expected based on using 2-D static airfoil characteristics. The helicopter rotor experiments of Dwyer & McCroskey (1971) also suggest favorable effects on the spanwise development of the boundary layer, which tend to delay the onset of flow separation to a higher blade section AoA and thus serve to increase the maximum thrust of the rotor system.
Similar observations have been found using CFD methods such as in the work of Narramore (1992), although confidence in these types of analyses to represent fully stalled flows is not yet high enough. As a result, approximate methods have been developed to model the observed 3-D “stall delay” effects – see Corrigan (1994) and Du & Selig (1998). A rigorous approach is still lacking because these models have not been validated under unsteady conditions or for situations where dynamic stall may occur. It has been shown in Chapter 9 that dynamic stall is fundamentally different to the phenomenon of static stall, so this is clearly an area where much further research is necessary if better 3-D models of unsteady airfoil behavior representing stall are to be developed and used confidently for rotor airloads predictions in either helicopter rotor or wind turbine work. To model these more general 3-D effects, the complexity of the models must usually be increased and parameters added. One must be cautious though that modeling accuracy is not obtained at the expense of the parsimony that is necessary to use these models in design analyses, or to destroy confidence in predictions – see page 808 for a discussion of this point.