Numerical predictions of tuned liquid tank structural systems

Abstract

A fully nonlinear 2-D σ -transformed finite difference solver has been developed based on inviscid flow equations in rectangular tanks. The fluid equations are coupled to a linear elastic support structure. Nonoverturning sloshing motions are simulated during structural vibration cycles at and outside resonance. The wave tank acts as a tuned liquid damper (TLD). The TLD response is highly nonlinear when large liquid sloshing occurs. The solver is valid at any water depth except for small depth when shallow water waves and viscous effects would become important. Results of liquid sloshing induced by horizontal base excitations are presented for small to steep nonbreaking waves at tank aspect ratios, depth to length, h/b of 0.5, 0.25 and 0.125, representing deep to near shallow water cases. The effectiveness of the TLD is discussed through predictions of coupling frequencies and response of the tank-structural system for different tank sizes and mass ratios between fluid and structure. An effective tank-structural system typically displays two distinct frequencies with reduced structural response (e.g., h / b = 0.5 ). These eigenfrequencies differ considerably from their noninteracting values. Hardening or softening spring behavior of the fluid, known to be present in solutions of pure sloshing motion in tanks, does not exists in the coupled system response. Strongest interactions occur with only one dominating sloshing mode when the nth sloshing frequency is close to the natural frequency of the structure, as the mass ratio between fluid and structure μ → 0 . Inclusion of higher modes reduces the efficiency of the TLD. Good agreement is achieved between the numerical model and a first-order potential theory approximation outside the resonance region when the unsteady sloshing motions remain small. When the free-surface amplitudes become large in the coupled system, the numerical peaks are larger and the troughs become lower as time evolves (typical nonlinear effects) compared to the linear solution. Nonlinearities were found to reduce the system displacement significantly, e.g., system resonance shifted to beating response, compared to linear predictions. It was also found that the system response is extremely sensitive to small changes in forcing frequency. In conclusion, if strong interaction exists, the coupled system exhibits nonlinearity in structural and free-surface response, but the coupled eigenfrequencies compare well with the linear predictions. Furthermore, the solver removes the need for free-surface smoothing for the cases considered herein (maximum wave steepness of 1.2). The numerical model provides a quick and accurate way of determining system eigenfrequencies which can be hard to identify and interpret in physical experiments.