The stream-function formulation of the potential flow solver has been modified to include new boundary conditions of an airfoil with arbitrary rotational velocity and center of rotation. As now, the reference frame is rotating, a change in the computation of pressure coefficient has to be made. The method of computing the surface velocities of the airfoil is also modified, as the original code was incompatible with the new modifications. A result is shown in Figure 2, where the pressure distribution of a NACA0015 airfoil computed by XFOIL is compared to the U2DIVA benchmark, for a chord-to-radius ratio of 0.2 and a mounting location at half the chord. The inviscid solution showed that no cumulative differences between the computed pressure distribution and the benchmark larger than 10% have been found (i.e. between the lift coefficients). It is assumed that with the modified potential flow solver, the viscous calculations can be left untouched and should perform as before. As there are no viscous benchmark solutions for rotating airfoils, this cannot be verified. A final investigation into airfoil optimization and turbine performance was performed with the newly modified version of XFOIL. Using optimized software based on a genetic algorithm, numerous different airfoils were generated and analyzed for their aerodynamic and structural properties. The optimizer scores each airfoil on two objectives, one to optimize the power output of the turbine and the other to maximize the area moment of inertia of the airfoil so as to obtain a blade which is as stiff as possible (Simão Ferreira,
VAN DER HORST
foil can simulate the chord-to-radius ratio, on which flow curvature effects depend. This provides for an excellent opportunity to implement in XFOIL.
Figure 3 - Power coefficient for optimized airfoils under varying operating conditions. 2015). The result is a whole range of optimized airfoils, varying from very aerodynamic and not so stiff, to structurally optimal and aerodynamically infeasible. Only the former are used in further investigations. Under the same circumstances, airfoils optimized for straight flow were compared to ones optimized while rotating. In this manner, one would be able to see if a power improvement could be obtained. Using software, the turbine power output over a range of operating conditions was simulated. Figure 3 shows the power coefficient calculated for three airfoils- the first is an airfoil optimized for straight flow, but simulated while rotating around its quarter chord. The latter two are airfoils optimized for rotating flows, one turning about the quarter chord and the other about the half chord location. As can be seen, up to a tip speed ratio of five, which is the region typical for a VAWT, at least one the airfoils optimized with the inclusion of flow curvature performs better. Even though the difference is small, the potential for power enhancement can be recognized. Although the above simulations lack some verification and surely need to be extended and improved, there are clear signs that the presented method can lead to improved tailored airfoil designs for vertical axis wind turbines. Including such a virtual modification of the rotating airfoil is currently not applied in the design process, but shows that increased turbine power output and efficiency can be obtained. This will not only aid in the proliferation of VAWTs, but of wind energy in general, hopefully solving our global energy crisis in the future.
The H-rotor arrangement of the vertical axis wind turbine.
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