Nonlinear resonances of sloshing fluids: An ideal experiment to test data-driven approaches

  • Bäuerlein, Bastian (University of Bremen)
  • Avila, Kerstin (University of Bremen)

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Nonlinear resonances of sloshing liquids are notoriously difficult to predict and occur, for example, in tank ships transporting liquified natural gas or in rockets using cryogenic liquid fuel. Direct simulations of the Navier-Stokes equation are not feasible here, because the dynamics of the fluid has to be coupled to the dynamics of the structure itself (e.g. the bending modes of the rocket). Low-dimensional models capturing the key dynamics of the fluid resonances are therefore required. A key challenge is the modelling of the nonlinearity of the resonances with the characteristic bending to lower/higher frequencies of the response curve. Already at intermediate driving amplitudes this leads to at least two stable states at identical driving parameters and a region of hysteresis. In our sloshing experiment and at low driving amplitudes the dynamics obeys the Duffing equation, which describes one of the simplest nonlinear oscillators. By increasing the driving amplitude the dynamics departs from Duffing, which is first noticeable in the phase-lag between the driving and the sloshing. For further increasing driving amplitude a competition arises between flow states featuring e.g. a period three motion or wave breaking (Bäuerlein & Avila, 2021). The measurements are compared to a state-of-the-art multimodal sloshing model based on potential flow theory (Faltinsen & Timokha, 2009) and to the data-driven approach of the spectral submanifold theory (Cenedese et al., 2022) yielding an excellent agreement.