Mathematical model for wave impact on vertical wall with multiple bottom-mounted baffles - Fadhlyya Arawaney, Abdul Ghani (2021)
Impacts of water wave onto structures have always been considered crucial to most researchers in fields that involve liquid impact problems especially when the wave is extremely brief and violent. Among the problems is liquid sloshing which is generally associated with an extremely brief impact with high peak pressure and large sloshing forces that may capsize any liquid-tanked vehicle when large overturning moments are generated. In this study, liquid sloshing in a partially filled rectangular container with liquid is considered and the wave impact on vertical wall with multiple bottom mounted baffles configurations is theoretically investigated. This study proposes a modified mathematical model of two bottom-mounted baffles in front of a vertical wall problem by extending the work of previous researchers in studying the single bottom-mounted baffle effect on the pressure impulse exerted onto the wall behind the baffle. Pressure impulse theory (time integral of pressure) is applied to simplify the equations of an ideal incompressible fluid notion and a two-dimensional mathematical model is proposed. Eigenfunction expansions obtained for each rectangular region via separation of variables satisfy the boundary conditions except on the impact region and at the matching line of each of the two-liquid regions which are then analytically integrated by applying basis function which creates a matrix system for the unknown coefficients. The formulated problems are coded using MATLAB software and the results are analysed by varying the size of the impact region, height of the baffles and distance of the baffles from the wall. The modified model has been first validated with Cooker’s model in order to apply the idea of pressure impulse theory. This study found out that the pressure impulse is increasing with the presence of the baffles in front of a vertical wall which agreed with the theoretical work done by the previous researchers though contradicts with the function of a baffle in reducing the sloshing wave slammed onto the wall. These results suggest that more factors and parameters such as ‘trapped’ pressure impulse and overtopping might need to be taken into consideration.