Predicting the Degree of Non-Equilibrium Reached During Rapid Depressurization of Liquids
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Non-equilibrium during rapid depressurization of liquids has been studied in several fields, from refrigeration systems [1, 2, 3] to rocket propulsion [4, 5] and for safety estimates for accidental releases of pressurized liquids [6, 7, 8, 9]. The non-equilibrium relates to phase change from liquid to vapor, which has a major impact on the flow (pressure, temperature, mass flows). It is therefore important to predict the degree of non-equilibrium reached during depressurization. Experiments for a range of different fluids (water [6, 7, 8, 3], CO2 [2, 3, 9], R-12 [1], nitrogen and oxygen [4]) shows that the amount of non-equilibrium reached during depressurization depends strongly on the initial temperature of the liquid, and less strongly on the rate at which the liquid is depressurized. Many models have been proposed based on classical nucleation theory (CNT) of bubbles to predict the degree of non-equilibrium that will be reached [2, 3, 6, 7, 8]. These model works well for warm initial temperatures of the liquid, close to the fluid’s critical point, but the models need corrections of several orders of magnitude at colder temperatures. In the present work, we instead assume that evaporation into trapped, pre-existing bubbles limits the non-equilibrium at colder conditions. By balancing the volume lost during depressurization due to liquid outflow, with the volume created due to evaporation into pre-existing bubbles, the experimental trend at cold conditions follows naturally. This new calculation method is denoted the volume balancing method, and an open-source example code is available at [10]. The volume balancing method is shown to fit well for both CO2 and water data, and depends on one free parameter related to the number of pre-existing bubbles in the system. This parameter could be kept constant for all initial temperatures tested.
