有限要素法による流出渦の解析

概要

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A satisfactory theoretical explanation of outflow vortices at intakes of a hydraulic system has never been made, because there are many complex factors involved such as the irregularity and the instability of the flow. From the mathematical standpoint, the nonlinearity of the boundary conditions and the ambiguity of the free surface make the problems more difficult to deal with. Moreover, the flow is unsteady and unstably rotational. In the present paper, a variational principle is applied to a flow with a free surface under gravity. Numerical analysis of the outflow vortex by the combined use of the Finite Element Method and the Newton-Raphson Method is carried out for the determination of the circulation γ giving a stable vortex. It is assumed that the flow is axisymmetric, steady, incompressible and irrotational throughout the whole flow field and uniform at the far-upstream and far-downstream boundaries. By the theory thus obtained, the nonlinear problem of analyzing the outflow vortices has been shown to be numerically solvable. The disadvantage of the Finite Difference Method, "the difficulty of treating the natural boundary, " has been overcome and we can discuss the problems concerning the growth, decay, and instability of the outflow vortices.
山梨大学の論文