Modeling non-isothermal vertical sloshing via experimentally-driven Froude-dependent Nusselt number

This article outlines a novel experimental-based reduced-order modeling framework for non-isothermal vertical sloshing. The methodology is based on experiments carried out on a cylindrical tank with water as surrogate fluid for liquid hydrogen. The Nusselt number derived from the experimental measurements, a non-dimensional proxy for interface heat exchange, is first mapped onto the characteristics of the harmonic seismic excitation, including frequency and amplitude. Such dataset is then used to train a time-delay neural network model designed to predict the Nusselt number from the time-dependent Froude number, which represents the non-dimensional vertical velocity of the tank. This innovative approach enables the efficient identification of the Nusselt number across a broad range of operational parameters from a single experimental test. The time-dependent Nusselt number is then fed as input to a lumped-capacity model able to simulate the thermodynamic response of the sloshing fluid, showing reasonable agreement with experimental data.