Analytical Modeling of Fluid Sloshing in A 2D Rectangular Container with A Bottom-Mounted T-Shaped Baffle

An analytical procedure is presented to evaluate the fluid sloshing characteristics in a two-dimensional (2D) rectangular container with a bottom-mounted T-shaped baffle. The fluid region is divided into several sub-domains with hypothetical interfaces and the velocities and pressures of the fluid on adjacent interfaces should be identical. The separation of variables in conjunction with the superposition principle is employed to formulate the velocity potential of each sub-domain. The Fourier series expansion is used to derive the eigenvalue equation by substituting the velocity potential solutions into the free surface conditions and the continuity conditions on adjacent interfaces. Under the horizontal base excitation, the total velocity potential of fluid is decomposed of the impulsive and perturbed velocity potentials. The orthogonality of the sloshing modes is demonstrated by implementing Gauss formula. The dynamic response equation is established by incorporating the total velocity potential solution into the surface wave equation. Excellent agreements are achieved between the present results and those from the reported literature and finite element code. Numerical results are exhibited to reveal the effect of the baffle parameters and excitation frequency on sloshing characteristics and responses of liquid.