Energy dissipation in sloshing waves in a rolling rectangular tank — III. Results and applications |
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| Authors: | Zeki Demirbilek |
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| Institution: | Research and Development Department, Conoco Inc., Ponca City, OK 74603, U.S.A. |
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| Abstract: | The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated. |
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