Within this study an unsteady, two-dimensional interacting boundary layer method is presented for the incompressible flow around wind turbine rotor blade sections. The main approach is to divide the flow field in to two regions; the one in the vicinity of the surface where the viscosity is effective (so called boundary layer) and the one away from the surface where the flow can be assumed as inviscid. The solutions obtained from these two regions are matched with a quasi-simultaneous viscous-inviscid interaction scheme. For the viscous flow, unsteady integral boundary layer equations together with laminar and turbulent closure sets are solved employing a high-order quadrature-free discontinuous Galerkin method. Laminar to turbulent transition is modeled with the e N method. The potential flow is solved by using the linear-strength vortex panel method. It is shown that introducing the interaction scheme leads to non-conservative mechanisms in the system. The discontinuous Galerkin method is extended to handle these non-conservative flux terms. Furthermore it is shown that this numerical method achieves the designed order of accuracy for smooth problems. Results are presented for the individual numerical solution methods which are verified on various test cases and subsequently for the coupled system which is applied on a chosen test case. Evaluation of a laminar flow over an airfoil section is shown and the results (converged to a steady state solution) are compared with other numerical solutions as well as with the experimental data where available. It is shown that the results of the developed numerical solution method are in good agreement with the experimental data and other computational methods.

The current challenges in wind turbine aerodynamics simulations share a number of similarities with the challenges that the aerospace industry has faced in the past. Some of the current challenges in the aerospace aerodynamics community are also relevant for today's wind turbine aerodynamics community and vice versa. This paper sketches these similarities in broad strokes and points out the possibilities to revive solutions from the aerospace aerodynamics community from the 1960's onward that, with some modifications, can be applied to wind turbine aerodynamics problems. Opportunities are indicated where both the wind turbine and the aerospace aerodynamics communities can benefit from collaborative research. Nomenclature BEM = Blade-Element-Momentum CFD = Computational Fluid Dynamics Cp = Power coefficient CoE = Cost of Energy IBL = Integral Boundary Layer LES = Large Eddy Simulation RaNS = Reynolds-averaged Navier Stokes VII = Viscous-Inviscid Interaction λ = Tip speed ratio (rotor tip speed/wind speed)

SummaryThe ongoing trend in wind turbine development is towards larger rotors because of the resulting lower cost of energy. These large rotors lead to relatively flexible structures that are more susceptible to the unsteady aerodynamic loading occurring in normal operating conditions. An accurate prediction of these loadings is important for the design of an economically viable and technically reliable wind turbine. Simulation methods of wind turbine aerodynamics currently in use mainly fall into two categories: the first is the group of traditional low-fidelity engineering models and the second is the group of computationally expensive CFD methods based on the Navier-Stokes equations.For an engineering environment the search is for "medium fidelity" wind turbine simulation methods that bridge the gap between the computationally inexpensive low-fidelity methods and the computationally expensive CFD methods. The ultimate goal is a balanced mixture of higher accuracy of the representation of the physics and shorter simulation times for wind turbine aerodynamics simulation methods. This can be found in the combination of the theories for panel methods, integral boundary layer methods, strong viscous-inviscid coupling, and fluid structure interaction.The present study focuses on the development of the theory and the practical implementation of a fast multilevel integral transform in a computer program. We utilize this multilevel scheme in a low-order panel method. It is demonstrated that for the simulation of the wake flow of wind turbine rotors the computational burden is reduced from O(N 2 ) for a conventional panel method to O(N ) for the present method. This implies that the computational effort is reduced to grow linearly with problem size N , with N the number of panels.We consider the unsteady, incompressible flow around wind turbine rotors and assume the effects of viscosity to be confined to infinitesimal thin boundary layers and wake regions and assume irrotational flow elsewhere. These assumptions allows us to reduce the flow problem to the problem of solving the Laplace equation for a (scalar) velocity potential function. This makes it possible to reformulate the problem as an integral equation over the surface of the rotor and the wakes that emanate from the trailing edges of the rotating wind turbine blades.The mathematical model is discretized in the form of a low-order panel iii Multilevel Panel Method method. The implementation of the panel method is verified by considering the flow over a stationary ellipsoid in a uniform onset velocity field, the flow over a rotating ellipsoid in a fluid at rest, and by considering the flow over a high aspect ratio wing with elliptic planform with as cross-section a von Kármán-Trefftz airfoil. For the first two test cases the numerical results are compared with analytical solutions. The error in the velocity potential is shown to be O(h 2 ), with h a characteristic panel size. The third test case uses the analytical solution for the 2D von Kármán-Trefftz airfoil ...

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A fast multilevel integral transform method has been developed that enables the rapid analysis of unsteady inviscid flows around wind turbines rotors. A low order panel method is used and the new multi-level multi-integration cluster (MLMIC) method reduces the computational complexity for calculating the wake deformation downstream of the wind turbine rotor from O(N 2) for a conventional approach to O(N). The method discretizes the volume surrounding the configuration with cubes. Each cube contains a grid of nodes that are used in the interpolation of the Green's functions underlying the panel method. The formulation of the panel method is described concisely and verified using exact solutions for a tri-axial ellipsoid in uniform flow and for a rotating ellipsoid in air at rest. For these tests the panel method exhibits an error varying quadratically with panel size. The MLMIC fast multilevel method is described and its accuracy and O(N) computational speed are verified for some model problems. Surface pressure distributions obtained with the fast panel method are compared with results from the MEXICO wind tunnel experiment and with results from a state-of-the-art numerical simulation method based on the Reynolds-averaged Navier-Stokes (RaNS) equations. This work repositions panel methods in the computational landscape as valuable intermediate fidelity computational design method for wind turbine engineering.