engleski

A Study of Potential Wind Flow Around Windmill Blades by the Boundary Element Method

The method for studying streamlines in the potential wind flow around windmill blades is presented. The components of wind velocity in the two-dimensional (plane) potential wind-flow model can be determined either as gradients of so-called velocity potential or stream function. Both functions satisfy Laplace's differential equation. Partial integration of Laplace's differential equation leads to integral equation that can be approximated with the system of linear equations by the application of the boundary element method. In the usual approach integral equation is developed based on property of velocity potential that satisfy Laplace's differential equation. The unknowns in corresponding linear equations system are values of velocity potential on the chosen set of points on the windmill blade surface, while wind velocity can be calculated as gradient of velocity potential. In the purpose to provide advance, the application of integral equation obtained by using stream function is presented. The benefit of this approach is that the tangential velocities of wind on the chosen set of points on the blade surface are directly obtained as the solution of corresponding linear equations system. Stream function can be calculated by integration of mentioned tangential velocities, while wind velocity in the any point of the space can be found as derivation of stream function. The problem arises from the fact that blade is in the stream that is definable as undisturbed only at enough far distance. Therefore, it is developed analytical solution of those integrals by which the boundary conditions corresponding to undisturbed wind-flow are integrated. Since in the proposed equations some integrals over boundary partially vanish, number of numerical operations is reduced, while a computer program becomes shorter.

potential wind flow; windmill blade; wind energy; streamlines; boundary element method

nije evidentirano