Self-induced sloshing excited by a horizontally injected plane jet

A self-induced free-surface oscillation termed self-induced sloshing was observed in a rectangular tank with a submerged and horizontally injected water jet. Self-induced sloshing is excited by the flow itself without any external force. Its behaviour was examined by experiment. The dominant frequency was found to be close to the first or second eigenvalue of fluid in a tank. The conditions of sloshing excitation were obtained for four tank geometries. They were called the 'sloshing condition, and defined in terms of inlet velocity and water level. Sloshing conditions were found to be strongly dependent on inlet velocity and tank geometry. A two-dimensional numerical simulation code was developed to simulate self-induced sloshing. The code was based on the boundary-fitted coordinate (BFC) method with height function. The numerical results were qualitatively verified by the experimental results, and were found to correlate well in terms of flow pattern, free-surface shape and sloshing conditions. In this study, sloshing growth was evaluated quantitatively using the simulation results. Oscillation energy supplied for the sloshing motion during a sloshing period (E-con) was calculated from simulation results. Sloshing growth was found to be strongly related to the sign and magnitude of E-con. The distribution of E-con showed that jet flow had a strong correlation with the sloshing growth. It was clarified that sloshing growth was primarily dependent on the spatial phase state of jet fluctuation. A governing parameter of self-induced sloshing, the modified Strouhal number St,, was proposed on the basis of numerical evaluations of oscillation energy. The value of St, suggests that one or two large vortices generated by jet fluctuations exist between the inlet and outlet during a sloshing period. When St, is approximately either 1 (first stage) or 2 (second stage), self-induced sloshing occurs consistently in all experimental cases. The dependence of sloshing on inlet velocity, water level and tank geometry was revealed using St, For several tank geometries, a sloshing mode shift or jet mode (stage) transition was found to occur due to changes in inlet jet velocity. The combination of sloshing mode and jet stage can determine the state of the self-induced sloshing. As a result of this study, we propose a new excitation mechanism of self-induced sloshing, represented by a simple feedback loop closed by sloshing motion and jet fluctuation. The overall physical oscillation mechanism of self-induced sloshing was clarified using this feedback loop.