Multilevel panel method for wind turbine rotor flow simulations

Abstract

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 ...

Wind Turbine Aerodynamics from an Aerospace Perspective

“…The accuracy of the selected pressure transducers is well balanced to the prevailing dynamic pressure at the rotating tip of the turbine, whereas the accuracy of experimental pressure data decreases towards the hub. In addition to the results obtained by the ENSOLV numerical solution method the results obtained by a fast multilevel panel method 20,21 that models inviscid, incompressible flow are also shown. Other cases computed with the ENSOLV numerical solution method and compared with experimental data consist of a turbulent wake state (wind speed of 10 m/s, tip speed ratio of 10), a separated flow case (wind speed of 24.12 m/s, tip speed ratio of 4.2) and a standstill condition (wind speed of 29.92 m/s, tip speed ratio 0), the latter only being instructive for the assessment of aerodynamic loads predictions on the rotor in vane position.…”

“…Recent progress 20,21 in reducing the computational burden of the classical panel method for wind turbine applications makes this approach an attractive proposition. Figure 11 shows an example of achieved reductions in integral evaluation time for the newly developed multilevel panel method.…”

“…However, by that time the vast investments in numerical flow simulation methods based on the Euler equations, their successful application, and the prospect of extending the method to general viscous flows was the reason the project was abandoned for good. For wind turbine designs, where the trend is towards higher subsonic rotor tip speeds (currently ~100 m/s), this approach could be revived while keeping the computational costs limited through the use of the fast multilevel panel method 20,21 .…”

Fast Multilevel Panel Method for Wind Turbine Rotor Flow Simulations

“…Combining the normal velocity from boundary condition (11), the expression for the source strength (14), and the tangential velocity (15) gives an expression for the velocity at the surface, in the inertial coordinate system, as…”

“…The development of advanced multilevel algorithms provides a very significant alleviation of this computational burden. In our work 15 it has been proven that a practical solution can be developed that reduces this burden to O(N ) work. The significance of the multilevel method developed in this work is already illustrated in the same figure and its advantage for large problem sizes is obvious.…”