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Modeling phase transition for compressible two-phase flows applied to metastable liquids

机译：建模应用于亚稳态液体的可压缩两相流的相变

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The seven-equation model for two-phase flows is a full non-equilibrium model, each phase has its own pressure, velocity, temperature, etc. A single value for each property, an equilibrium value, can be achieved by relaxation methods. This model has better features than other reduced models of equilibrium pressure for the numerical approximations in the presence of non-conservative terms. In this paper we modify this model to include the heat and mass transfer. We insert the heat and mass transfer through temperature and Gibbs free energy relaxation effects. New relaxation terms are modeled and new procedures for the instantaneous temperature and Gibbs free energy relaxation toward equilibrium is proposed. For modeling such relaxation terms, our idea is to make use of the assumptions that the mechanical properties, the pressure and the velocity, relax much faster than the thermal properties, the temperature and the Gibbs free energy, and the ratio of the Gibbs free energy relaxation time to the temperature relaxation time is extremely high. All relaxation processes are assumed to be instantaneous, i.e. the relaxation times are very close to zero. The temperature and the Gibbs free energy relaxation are used only at the interfaces. By these modifications we get a new model which is able to deal with transition fronts, evaporation fronts, where heat and mass transfer occur. These fronts appear as extra waves in the system. We use the same test problems on metastable liquids as in Saurel et al. [R. Saurel, F. Petitpas, R. Abgrall, Modeling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607 (2008) 313-350]. We have almost similar results. Computed results are compared to the experimental ones of Simes-Moreira and Shepherd [J.R. Simes-Moreira, J.E. Shepherd, Evaporation waves in superheated dodecane, J. Fluid Mech. 382 (1999) 63-86]. A reasonable agreement is achieved. In addition we consider the six-equation model with a single velocity which is obtained from the seven-equation model in the asymptotic limit of zero velocity relaxation time. The same procedure for the heat and mass transfer is used with the six-equation model and a comparison is made between the results of this model with the results of the seven-equation model.
机译：两相流动的七方程模型是一个完全的非平衡模型，每个相都有自己的压力，速度，温度等。每种特性的单个值即平衡值可以通过松弛方法来实现。对于存在非保守项的数值逼近，该模型具有比其他平衡压力简化模型更好的功能。在本文中，我们修改了该模型以包括热量和质量传递。我们通过温度和吉布斯自由能弛豫效应来插入传热和传质。对新的松弛项进行建模，并提出了瞬时温度和吉布斯自由能向平衡松弛的新程序。为了对此类松弛项建模，我们的想法是利用以下假设：机械特性，压力和速度比热特性，温度和吉布斯自由能以及吉布斯自由能的比率快得多。松弛时间到温度的松弛时间极高。假定所有松弛过程都是瞬时的，即松弛时间非常接近零。温度和吉布斯自由能弛豫仅在界面处使用。通过这些修改，我们得到了一个新模型，该模型能够处理发生传热和传质的过渡前沿，蒸发前沿。这些战线在系统中显示为多余的波浪。我们对亚稳态液体使用的测试问题与Saurel等人相同。 [R. Saurel，F。Petitpas，R。Abgrall，亚稳态液体的相变建模：在空化和闪蒸流动中的应用，J。Fluid Mech。 607（2008）313-350]。我们几乎有相似的结果。将计算结果与Simes-Moreira和Shepherd的实验结果进行比较[J.R. Simes-Moreira，J.E。Shepherd，过热十二烷中的蒸发波，J.Fluid Mech。 382（1999）63-86]。达成了合理的协议。另外，我们考虑具有零速度的六方程模型，该模型是在零速度弛豫时间的渐近极限中从七方程模型获得的。六方程模型使用相同的传热和传质程序，并将该模型的结果与七方程模型的结果进行比较。

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