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Analysis of the wind streaming around windmill's spade by boundary element method

Streaming around profile of spade must be defined in order to optimize the shape of the spade and it's position. Assuming the potential flow, velocity potential and stream function are determined as a solution of Laplace's differential equation which is governing differential equation of potential flow. Partial integration of Laplace's differential equation is needed to obtain the governing integral equation determining the velocity potential and stream function as function of boundary conditions. Governing integral equation yields to boundary integral equation, which solution (unknown boundary conditions) can be found by boundary element method. Once, when boundary conditions are determined, calculation of streamlines and velocities, that are function of boundary conditions are trivial and requires relatively small number of additional numerical operations. Boundary element method consists of dividing boundary into elements. It approximates the boundary integral equation with the system of linear equations. Very few linear equations are needed for very good approximation of results. The presented method exhibits fast convergence to a true value. Therefore, it is needed much less time for calculations then in using some other of the other numerical methods, such as finite element or finite difference method.

wind flow; windmill's spade; boundary element method

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