Miller Cass T, Gray William G, Kees Christopher E
Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599-7431, USA.
US Army Engineer Research and Development Center, Vicksburg, MS 39180-6199, USA.
Entropy (Basel). 2018 Apr 5;20(4):253. doi: 10.3390/e20040253.
The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows.
热力学约束平均理论（TCAT）是一种综合理论，用于构建基于热力学第二定律封闭的多相、多尺度模型层次结构。熵产生率根据耗散过程的通量和力的乘积来表示。TCAT的吸引人的特点包括在不同长度尺度上的一致性；跨尺度的热力学一致性；包含界面、公共曲线以及相；开发运动学方程以提供几何范围度量的封闭关系；以及一种结构化的模型构建方法。展示了TCAT方法的要素；说明了这些吸引人的特点中的每一个是如何从TCAT方法中产生的；并提供了对已构建的模型层次结构的综述。由于TCAT方法在数学上较为复杂，我们说明了如何通过利用该理论中可应用于广泛应用的现有组件来应用此方法。与完整推导相比，这可以大幅减少公式化工作，同时产生相同的结果。最后，我们注意到之前对偏差动能的忽视，偏差动能在缓慢的多孔介质流动中并不重要，我们制定了扩展该理论所需的方程，并评论了新组件特别有用的应用。这项工作应有助于使TCAT在应用中更易于使用，从而为湍流多相流等应用实现更高保真度的模型。
