Date of Award
Master of Science (MS)
Dr. Mohammed Daqaq, Committee Chair
Dr. Gang Li
Dr. Lonny Thompson
Most of the previous research studies that discuss the inﬂuence of surface tension on the nonlinear planar sloshing of incompressible ﬂuids in rectangular containers focused on the deep water scenario where internal resonances among the sloshing modes of the ﬂuid column cannot be easily activated. Very few, if any, have investigated how surface tension inﬂuences the dynamics of the surface waves in the vicinity of an internal resonance. To ﬁll this gap in the current knowledge, this thesis aims at investigating the inﬂuence of surface tension on the nonlinearity of the sloshing modes and the potential activation of internally-resonant multi-mode sloshing motions. The thesis addresses only weak surface tension eﬀects by assuming a 90◦ contact angle between the ﬂuid and the containers side walls and free slipping at the contact line. To achieve the thesis objectives, we develop a nonlinear model governing the dy-namics of the system assuming an inviscid, incompressible, and irrotational ﬂuid sloshing inside a rectangular container. We obtain an approximate analytical solution of the model using perturbation methods, namely the method of multiple scales, for the free and forced surface response. We utilize the resulting solution to study the inﬂuence of the bond number and the ratio between the ﬂuid height and the container’s width on the modal frequencies. We use the resulting understanding to construct a map in the design parameters’ space to highlight regions of possible nonlinear internal resonances among the sloshing modes up to ﬁfth mode. Subsequently, we study the inﬂuence of surface tension on the eﬀective non-linearity of the sloshing modes away from any internal resonances. We also investigate the inﬂuence of surface tension on the response of the sloshing waves near internal resonances of the two-to-one type. Finally, we study the inﬂuence of surface tension on the primary resonance behavior of the sloshing modes with and without a two-to-one internal resonance energy pump. Results indicate that surface tension has a dramatic inﬂuence on the re-gions where internal resonances can be activated and on the softening/hardening nonlinear characteristics of a given sloshing mode.
Xu, Yawen, "Influence of Surface Tension on the Nonlinear Planar Sloshing of Incompressible Fluids in Rectangular Containers" (2016). All Theses. 2429.