Dynamic coupling in sloshing systems with multiple baffles.

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When you walk with a cup of coffee, the coffee can slosh back and forth in the cup, and in some cases, spill on the floor. The reason this happens is because as the cup moves in our hand that motion imparts a force on the coffee, causing it to move, while the motion of the coffee imparts its own hydrodynamic force on the wall of the cup, causing the cup itself to move. This dynamic sloshing motion, if we don't stop walking to let it damp out or move our arm in a specific manner to nullify the coffee motion, is destabilizing and hence leads to the coffee being spilt. This coupled phenomena does not necessarily have to be undesirable, and in some cases this process can be used to an advantage. Once such case is in tuned liquid dampers (TLDs), which are large containers of fluid attached to springs, which are placed within high-rise buildings. When these buildings oscillate back and forth due to either high winds or an earthquake, the TLD is forced to move back and forth essentially transferring the energy of the moving building into the fluid. Therefore the understanding of such dynamic sloshing problems is of great practical interest.The introduction of rigid baffles to the dynamic sloshing system can be a useful addition, as these baffles (rigid screens or plates) modify the natural frequency of the system, making it possible to tune the system in such a way as to reduce the motion of the fluid carrying vessel, putting more of the system energy into the fluid. This proposal investigates the introduction of porous and non-porous baffles in two simplified dynamic sloshing problems to identify just how these natural frequencies are modified, and whether it can be modified to coincide with an internal resonance of the system. Such resonances are particularly interesting because they are pathways for energy transfer between modes, and hence all the energy of a moving vessel could be transferred to the fluid (and vice versa) at such a resonance.This project aims to construct a novel, fast and efficient numerical scheme to simulate the motion of a coupled sloshing system where rigid impermeable baffles are inserted on the side walls of a rectangular vessel, which is restricted to oscillate in one horizontal space dimension. The scheme is novel because it incorporates conformal mappings from complex analysis to map the unknown position of the fluid surface to a line, along which the solution can be found. Therefore all the information about the baffle positions and shape is contained in the mapping itself. While the determination of this mapping is non-trivial, its existence makes a seeming intractable problem tractable. The second part of this project focuses on the effect of porous baffles on the system natural frequency. We investigate how the system frequency varies as the porosity (amount of fluid which can pass though) of the baffles vary.