# Trailing and Leading Edge Flaps for Load Alleviation and Structure Control

## Abstract

This chapter presents the results of numerical computations for a 10-MW wind turbine rotor equipped with the trailing and leading edge flaps. The aerodynamic loads on the rotor are computed using the Helicopter Multi-Block flow solver. The method solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. The trailing edge flap was located at 75%R, and the leading edge flap was located at 60%R, where R is the radius of the blade. The chapter is divided in the description of employed numerical methods, mesh convergence study, and the cases with trailing and leading edge flaps. Also, the chapter defines flap geometry, deformation and frequency of motion. The blade structure was assumed rigid for all presented cases. The comparison of the flap performance is conducted using non-dimensional parameters, and conclusions are drawn at the end of the chapter.

## Keywords

Wind Turbine Pitching Moment Flap Deflection Mesh Convergence Study Flap Angle## 7.1 Numerical Methods

The HMB3 code is a 3D multi-block structured solver for the 3D Navier-Stokes equations. HMB3 solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. The solver uses a cell-centred finite volume approach combined with an implicit dual-time method. Osher’s upwind scheme (Osher and Chakravarthy 1983) is used to resolve the convective fluxes, and MUSCL (Van Leer 1979) variable extrapolation is used to provide formally third-order accuracy on uniform grids. Central differencing (CD) spatial discretisation is used for the viscous terms. The non-linear system of equations that is generated as a result of the linearization is solved by integration in pseudo-time using a first-order backward difference method based on Jameson’s pseudo-time integration approach (Jameson 1991). A Generalised Conjugate Gradient (GCG) method is then used (Eisenstat et al. 1983) in conjunction with a Block Incomplete Lower-Upper (BILU) factorisation as a pre-conditioner. The HMB3 solver has a library of turbulence closures including several one- and two- equation models. Turbulence simulation is also possible using either the Large-Eddy or the Detached-Eddy simulation approach (Spalart et al. 1997). The solver was designed with parallel execution in mind and the MPI library along with a load-balancing algorithm are used to this end. The flow solver can be used in serial or parallel fashion for large-scale problems. Depending on the purposes of the simulations, steady and unsteady wind turbine CFD simulations can be performed in HMB3 using single or full rotor meshes generated using the ICEM-Hexa tool. Rigid or elastic blades can be simulated using static or dynamic computations. HMB3 allows for sliding meshes to simulate rotor-tower interaction (Steijl and Barakos 2008). Alternatively, overset grids can be used (Jarkowski et al. 2013). To account for low-speed flows, the Low-Mach Roe scheme (LM-Roe) developed by (Rieper 2011) is employed for wind turbine cases (Carrión et al. 2013).

The HMB3 CFD solver has so far been validated for several wind turbine cases, including the NREL Annex XX experiments (Gómez-Iradi et al. 2009), where the effect of the blades passing in front of the tower was captured. The pressure and PIV data of the MEXICO project (Carrión et al. 2014) have also been used for validation, where the wake was resolved on a fine mesh capable to capture and preserve the vortices downstream the rotor, which enabled the prediction of the onset of wake instabilities (Carrión et al. 2015).

*sin(ωt)*or

*cos(ωt)*. In this case the motion is described by a Fourier series of arbitrary number of harmonics. It must be noted here, that since only mean and maximum surfaces are known to the solver, the interpolation tends to shrink the flap slightly. To understand this behaviour, consider a 2D rod-like flap shown in Fig. 7.1. As can be seen, the linear interpolation tends to shrink the flap, but the effect is not pronounced for relatively small angles of deflection.

The computational mesh is updated at each time step after the deformation of the surface. The Trans-Finite Interpolation (TFI), described by Dubuc et al. (2000), is applied to the blocks attached to the deformed surface. The TFI interpolates the block face deformation from the edge deformations and then the full block deformation from the deformation of the block faces. The grid deformation uses a weighted approach to interpolate a face/block from the boundary vertices/surfaces respectively. The weight depends on the curvilinear coordinate divided by the length of the curve.

## 7.2 Numerical Parameters

^{3}, the dynamic viscosity of the air was μ = 1.8 × 10

^{−5}N s/m

^{2}, and the speed of sound was 340 m/s. Further, a fully turbulent flow was assumed with free-stream level of turbulence of 2.6 % and uniform inflow velocity distribution was set across the inflow boundary. The k-ω SST turbulence model was employed for all tests, unless otherwise stated. The

*y*

^{+}parameter was estimated based on the flat-plate boundary layer theory. For given Reynolds number, inflow velocity U

_{∞}, density ρ, dynamic viscosity μ and cord length c the

*y*

^{+}parameter was computed in the following steps:

- 1
Estimate the skin friction coefficient from Schlichting’s correlation:

- 2
Obtain the wall shear stress from the definition of C

_{f}:

- 3
Compute the friction velocity from:

- 4
Compute the

*y*^{+}parameter from the definition, where y is the employed spacing next to the wall:

For the presented cases with trailing and leading edge flaps, the inflow wind speed was set to 11.4 m/s, and the rotational speed of the rotor was set to 9.6 rpm, giving a tip speed ratio of 7.83.

## 7.3 Mesh Convergence Study

Computational conditions for the mesh convergence study

Parameter | Value |
---|---|

U | 11 m/s |

U | 82.437 m/s |

RPM | 8.836 |

Re | 34.817°×°10 |

M | 0.243 |

λ | 7.494 |

Pitch angle | 0° |

## 7.4 Computational Grid

^{−6}

*c*, where

*c = 6.206 m*is a maximum chord of the blade. The

*y*

^{+}parameter for this gird at rated conditions was 0.2. Figure 7.4b shows the surface grid on the blade for the 9.2 M cells grid.

## 7.5 Definition of the Flaps

*x*, and

*α*is providing the maximum deflection for given time instance. For the trailing edge flap \( {\xi}^{TE}=\left(x/c-{x}_0^{TE}\right)/\left(1-{x}_0^{TE}\right) \), and for the leading edge flap \( {\xi}^{LE}=\left({x}_0^{LE}-x/c\right)/\left({x}_0^{LE}\right) \), where

*x*

_{0}

^{ TE }and

*x*

_{0}

^{ LE }are the

*x*/

*c*locations of the hinge point for the trailing and leading edge flap, respectively; and

*c*is the local chord. From the equation for the shape function it follow that \( \eta \left(\xi \right)\in \left[0,\alpha \right] \). In principle, \( \alpha \equiv \alpha (t)={\alpha}_m \sin \left(\omega t\right) \), where

*α*

_{ m }. is the maximum value of deflection determined by the maximum deflection angle

*β*. Here, the maximum deflection was obtained as \( {\alpha}_m^{TE}=\left(1-{x}_0^{TE}\right) \tan \left(\beta \right) \) and \( {\alpha}_m^{LE}=\left({x}_0^{LE}\right) \tan \left(\beta \right) \) for trailing and leading edge flap, respectively. By denoting the point at which the flap starts with

*x*

_{0}, the process to compute flap deflection is as follows: For each point \( x>{x}_0 \), define \( \xi =\xi (x) \) based on the length along the chord line; compute point displacement

*α*based on the maximum deflection angle

*β*and time

*t*; compute shape function

*η*(

*ξ*); apply shape function and obtain deformed flap shape.

## 7.6 Results for the TE Flap

## 7.7 Results for the LE Flap

## 7.8 Comparison of the Performance

*α*as:

*T*

_{ F }) and driving (

*D*

_{ F }) forces are defined in Fig. 7.11, and were obtained from the surface pressure integration in the middle of the flap with the length of the section in radial direction \( \varDelta r=2.15m \). Note, that the geometrical pitch angle

*α*is defined in Bak et al. (2013), and is constant i.e. it does not change with the flap angle

*β*. Then, the forces and moment were non-dimensionalized as:

*U*and

*A*are the geometrical local inflow velocity and the local platform area, respectively. The inflow velocity is defined as:

*c*is the local chord in the middle of the flap.

*β*are compared in Fig. 7.12. As can be seen, the trailing edge flap significantly modifies all three non-dimensional coefficients. On the other hand, leading edge flap has the most pronounced effect on the pitching moment coefficient, and almost negligible (as compared to the TE flap) influence on the normal force coefficient. Further, the relative change and slope of the pitching moment coefficient is higher for the trailing edge flap. Finally, both flaps can change the tangential force coefficient, but the TE flap has higher hysteresis loop, as compared to the results for the LE flap.

## 7.9 Summary

The results showed a significant, but localized effect of the flap deflection on the distribution of the loads. The trailing edge flap can modify both thrust force and pitching moment, whereas trailing edge flap mostly affects the pitching moment. That suggests, that trailing edge flaps can be used to locally change aerodynamic loads on the blades, possibly eliminating the adverse effect of the blade passing in front of the tower. On the other hand the leading edge flap can be used to counter the additional pitching moment created by the deflection of the trailing edge flap.

## Notes

### Acknowledgments

Results were obtained using the EPSRC funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk). EPSRC grant no. EP/K000586/1.

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