Modeling phase transition for compressible two-phase flows applied to metastable liquids
Modeling phase transition for compressible two-phase flows applied to metastable liquids
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DOI：
10.1016/j.jcp.2009.12.026
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发表时间：
2010-04
期刊：
影响因子：
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通讯作者：
A. Zein;M. Hantke;G. Warnecke
中科院分区：
文献类型：
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作者：
A. Zein;M. Hantke;G. Warnecke
两相流的七方程模型是一个完全的非平衡模型，每一相都有自己的压力、速度、温度等。每个性质的单一值，即平衡值，可以通过松弛方法得到。对于存在非保守项的平衡压力数值近似，该模型比其他简化模型具有更好的特点。本文对该模型进行了修正，加入了传热传质。我们通过温度和吉布斯自由能弛豫效应引入了传热传质。建立了新的松弛项模型，并提出了瞬时温度和吉布斯自由能趋向平衡松弛的新方法。对于这种松弛项的建模，我们的想法是利用这样的假设，即力学性质，压强和速度，比热性质，温度和吉布斯自由能弛豫快得多，吉布斯自由能弛豫时间与温度弛豫时间之比非常高。所有的弛豫过程都假定为瞬时的，即弛豫时间非常接近于零。温度和吉布斯自由能松弛只在界面处使用。通过这些修改，我们得到了一个新的模型，它能够处理过渡锋，蒸发锋，传热和传质发生的地方。这些锋面在系统中表现为额外的波。我们使用与Saurel等人相同的亚稳液体测试问题。张建军，张建军，张建军，等。亚稳流体相变模型的研究进展[j].流体力学学报，2008,34(2):557 - 557。我们得到了几乎相似的结果。计算结果与Simões-Moreira和Shepherd [J.R.]的实验结果进行了比较Simões-Moreira， J.E. Shepherd，过热十二烷的蒸发波，流体力学，[j].(1999): 63-86。达成了合理的协议。此外，我们还考虑了在零速度弛豫时间渐近极限下由七方程模型得到的单速度六方程模型。对传热传质采用了与六方程模型相同的方法，并与七方程模型的结果进行了比较。
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 Simões-Moreira and Shepherd [J.R. Simões-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.