Dynamic Liquid Slosh in Moving Containers
Liquid sloshing is known to strongly influence the directional dynamics and safety performance of highway tank vehicles in a highly adverse manner. Hydrodynamic forces and moments arising from liquid cargo oscillations in the tank under steering and/or braking maneuvers reduce the stability limit and controllability of the partially filled tank vehicles. While the transient fluid slosh within moving containers has been widely investigated, interactions between the sloshing cargo and the vehicle system dynamics have been addressed in only a few studies due to associated challenges. Furthermore, roll stability of heavy tank vehicles have been extensively studied in the absence of transient slosh induced forces and moments. This dissertation research aims at exploring the fluid slosh in moving containers through analytical methods and developing efficient models for simulating interactions of fluid slosh and vehicle dynamics. A comprehensive review of relevant studies reporting tank trucks accident data, tank design standards, and analysis methods of liquid sloshing in moving containers is initially performed and briefly summarized. The literature review provides not only the essential knowledge for developing an efficient method of analysis, but also demonstrates the needs for addressing limitations in the current standards so as to include effects of liquid sloshing dynamics in road tankers. An analytical model of two dimensional fluid slosh in horizontal cylindrical tanks subject to a lateral excitation is initially formulated assuming potential flows and linearized free surface boundary. For this purpose, the fluid domain in the Cartesian coordinates is transformed to the bipolar coordinates, where the Laplace equation could be solved using separation of variables. The resulting hydrodynamic pressure, free surface elevation, and slosh force and roll moment are compared with the reported experimental and numerical results to illustrate the range of applicability and limitations of the linear slosh theory. The results suggest that the linear theory can yield reasonably accurate predictions of non resonant lateral slosh in liquid transporting vehicles with significantly less computational effort than the CFD models. A multimodal model of fluid slosh is subsequently developed to study the effect of tank cross section on transient lateral slosh. Natural frequencies and modes of liquid slosh in tanks of different cross sections are obtained using a variational Ritz method, which are implemented into the multimodal model. The effect of transient liquid slosh and tank cross section on rollover stability limits of a tank vehicle is also investigated by integrating the fluid slosh model into a roll plane model of the suspended tank vehicle. The results are presented for four different tank cross sections: circular; elliptical; modified oval; and Reuleaux triangle. The results show that a tank cross section with lower overall center of mass and lower critical slosh length could yield enhanced roll stability limit under medium and high fill conditions. The multimodal method is also employed to investigate the effect of partial longitudinal baffles on the transient lateral slosh. Natural slosh frequencies and modes are computed using a boundary integral solution of the Laplace equation. The computational efficiency is significantly improved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials of the elements on the half free surface length. Damping due to the baffles is estimated from the energy dissipation rate. The results are presented for different designs/lengths of longitudinal baffles, namely, top mounted; bottom mounted; and center mounted baffles. It is shown that the multimodal method yields computationally efficient solutions of liquid slosh within moving baffled containers. The results suggest that a baffle is most effective and efficient when it pierces the free surface and partly submerged in the liquid. A three dimensional linear slosh model is further developed to study fluid motions under simultaneously applied lateral and longitudinal excitations, characterizing braking in a turn maneuver, using the multimodal method. Three dimensional Laplace equation is initially reduced to a two dimensional Helmholtz equation using separation of variables. A higher order boundary integral solution of the Helmholtz equation is then formulated to compute natural slosh frequencies and modes in a horizontal cylindrical tank of arbitrary cross section. The results obtained for a circular tank suggested rapid convergence of the natural slosh frequencies and hydrodynamic coefficients. The slosh forces and moments are also computed from the nonlinear analysis of liquid slosh in a tank under various lateral/longitudinal accelerations and fill ratios using the FLUENT software. Comparisons of the results obtained from the linear and nonlinear analyses revealed that the linear slosh theory yields reasonably accurate predictions of the peak slosh forces and moments under lateral/longitudinal accelerations of steady magnitudes of up to 0.3g/0.2g for a tank of aspect ratio of 2.4.