21. Comparing Analytical and Numerical Solutions for Fluid–Structure Problems with Free Surface Conditions: A Study on Tuned Liquid Dampers and Tuned Liquid Column Dampers

This paper presents a finite element analysis of sloshing in 3D water tanks using a pressure-based Eulerian approach. The fluid domain is discretized by isoperimetric elements (FLUID220) that exhibit a quadratic pressure behavior and are used for modeling the fluid domain. Three examples (a rectangular cavity, a square-tuned liquid column damper (TLCD), and a bidirectional-tuned liquid multicolumn damper (TMLCD)) were modeled with rigid contours and a free surface to study uncoupled liquid reservoirs. Free vibration and harmonic analysis were performed to determine dynamic parameters of the three cases. For the rectangular cavity, the numerical results are compared to analytical solutions and previous numerical and experimental studies. The numerical solutions present acceptable relative error (inferior to 0.2% relative error) when compared to analytical solutions. For the TLCD example, the numerical results were validated using experimental results and previous numerical studies, presenting acceptable errors (6% relative error). For the third case, the modal results were compared to the analytic solution and previous works returning an error of 2.75 and 3.14% relative to the experimental values and the harmonic analysis presented a reduction of 44.88% in the amplitude of displacement of the system, thus validating this approach of analysis in the development of this kind of device.