Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions

Abstract

Abstract: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.

Phenomenological Thermodynamics of Irreversible Processes

“…C. Miller, W. Gray & C. Kees [ 57 ] “ Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions ”. Macro-scale models in continuum physics are based on certain averaging procedures and the avoidance of resolving the morphology of the distribution of the phases at the micro-scale.…”

An extension of Biot's theory with molecular influence based on mixture coupling theory: Mathematical model

“…Another challenge is the gap between microscale and macroscale (Lewis and Schrefler, 1987b): The hydro-mechanical coupling is at macroscale level, whereas the interaction between chemicals or/and thermal fields is on the microscale. Thermodynamically Constrained Averaging Theory (TCAT) of Gray and Miller (Gray and Miller, 2014;Gray et al, 2013;Miller et al, 2018) provides a rigorous way of bridging the gap. Mixture coupling theory develops another scope of the average method using non-equilibrium thermodynamics (Chen et al, 2016).…”