Institute of Mathematics for Industry

Seminar



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Application of Helical Vortex Solutions to Determine Wind Turbine Tip Loss


Hold Date 2016-09-15 16:00~2016-09-15 17:30

Place Lecture Room M W1-C-512, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker David Wood (SERC/ENMAX Professor of Renewable Energy, University of Calgary, Canada)

Abstract:
The talk will discuss two related problems of Blade-Element-Momentum-Theory (BEMT) for horizontal axis wind turbines, both connected to the analytical solution for the flow induced by helical vortices. For many years, it was believed that this solution was first derived by the American scientist Hardin in 1982, but recently the work of the Japanese aerodynamicist Kawada in 1935 was rediscovered. The first problem is the determination of the tip loss, used in BEMT to account for the finite number of blades on a real turbine. Currently, tip loss is approximated by a simple expression due to Prandtl, but this formulation is not accurate over the full operating range of a wind turbine. In 1939 Kawada made two important contributions to this problem  which were subsequently forgotten for nearly 80 years. Kawada's work will be used to develop a more accurate alternative to Prandtl's formula that is almost as simple to implement. The second problem is the effect of the azimuthal variation of the flow in the wake of the rotor which give rise to nonlinear terms in the equations for axial and angular momentum. Kawada's  contributions allow these terms to be accurately determined for the first time. It will be shown that they contribute significantly at some operating conditions.