Fluctuating internal-kinetic energy exchanges in flows of fluids near a phase change

Abstract

This thesis is devoted to the study of unsteady energy exchanges in the vicinity of a phase change or between two different phases explored in three scenarios. First, the transfer function of the supersonic quasi-one dimensional flow of a single-phase non-ideal gas in a nozzle is investigated using linear and non-linear approaches. The possibility of exploiting near thermodynamic critical point (TCP) shock properties to confer a low-pass-filter behaviour to the nozzle on pressure and velocity fluctuations when prescribing an inlet entropy fluctuation is revealed. This is illustrated with siloxane D6 gas employing a multiparameter Span-Wagner equation of state to compute equilibrium properties and evaluate nozzle transfer functions which are contrasted with ideal gas predictions. Secondly, the interaction of an entropy perturbation with a two-dimensional bow shock, formed when a single-phase supersonic flow encounters a semi-circular obstacle, is investigated, with a van der Waals model representing a dense gas operating near the TCP, and compared to linear interaction analysis (LIA) for an isolated shock. Variations of refraction properties along the shock are shown to be exploitable for flow control and a noted departure from LIA prediction for incoming perturbation amplitudes greater than 5% of the base flow values is observed. Thirdly, energy exchanges between two different phase shallow-layers, representing the atmosphere and ocean, are investigated in the context of the 2022 Hunga Tonga-Hunga Ha’apai volcano eruption using a two-way coupled isentropic model. The linear properties are derived and show the disappearance of the ‘Proudman resonance’, occurring when atmospheric wave speed and oceanic gravity wave speed match, resulting in a finite atmosphere-to-ocean energy transfer and providing a low-cost predictive tool. Two-dimensional global numerical simulations show the predictive nature of the two-layer model for the Tonga event when simulating the atmospheric wave propagation provoked by the shock-induced energy injection in the atmosphere.