A LINEAR THEORY OF VISCOUS LIQUID SLOSHING

The purpose of this study is to determine some of the hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank. An analytical technique together with a numerical solution method is presented that efficiently and accurately describes the sloshing phenomenon. A linear theory of viscous liquid sloshing is developed by solving a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. An approximate solution in function space is obtained by the truncation of infinite series. The boundary conditions are satisfied through the use of Fourier series expansions. It is shown that the no-slip condition at the side walls can also be treated in a least-squares sense.;This study is focused on the viscous dissipation since, today, our principal knowledge of this phenomenon is mainly based on the results of some experimental studies on free surface flows. An attempt is made here to study the effects of viscosity on liquid sloshing phenomenon. The dependency of viscous dissipation on the Reynolds and Froude numbers has been demonstrated for the range of parameters studied. Also, the influence of the tank aspect ratio on viscous dissipation has been explored.