液体貯槽における有限振幅液面動揺に関する研究 : (その4)軸対称回転貯槽の場合の理論展開とその球形貯槽への適用

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In the foregoing papers^<1-3)>, the sloshing problem of the liquid in the cylindrical storage has been investigated from the view point of the nonlinear sloshing problem. Direct method based on the variational functional derived by J. C. Luke^<4)> has been applied for the potential flow problem, where the admissible function which satisfies the geometrical boundary conditions can be found from the set of the harmonic function. In the case of the spherical storage which is most spreadly used for the storage tanks next to the cylindrical ones, the above mentioned approach, however, can not be used because of the characteristics of the harmonic function for the spherical coordinate system. In the case of the general axisymmetric storage which consists of the generator with the arbitrary configulation, it is more difficult to get the objective admissible function. Some discretizing methods can be adopted for the general problem which contains the arbitrary boundary condition, for instance, finite element method, boundary integral method, finite difference method, and so on. Generally, the boundary integral approach can be said to be most suitable for the potential problems. In the present paper, the nonlinear oscillative problem of the perfect fluid in the axisymmetric storage which consists of the arbitrary shaped generator is treated. By applying the boundary integeral technique, the boundary value problem can be reduced into the simultaneous nonlinear algebraic equation which consists of both the unknown velocity potential on the free surface and the surface elevation. The normal mode technique is used for the effective reduction of the freedom of the unknowns and the harmonic balance method is also utilized for pursueing the stationary solutions. As the numerical example, both the cylindrical and the spherical storages are adopted, where the numerical results are minutely compared with the experimental results by the shaking table test. From the results, it is shown that some nonlinear sloshing resonances occur by the external excitation with the frequency in the neighborhood of the resonance point and, additionaly, the swirling phenomenon can be analyzed by treating as the bifurcational problem in the frequency-amplitude space.
社団法人日本建築学会の論文
1989-09-30

液体貯槽における有限振幅液面動揺に関する研究 : (その4)軸対称回転貯槽の場合の理論展開とその球形貯槽への適用

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