Multi-scale models coupling

Franco, A. A., Barthe, B., RouUlon, L., and Lemaire, 0.2009. Mechanistic investigations of NOj impact on ORR in PEM fuel cells A coupled experimental and multi-scale modeling approach. ECS Transactions 25 1595-1604. 

The "variational type of multi-scale CFD, here, refers to CFD with meso-scale models featuring variational stability conditions. This approach can be exemplified by the coupling of the EMMS model (Li and Kwauk, 1994) and TFM, where the EMMS/matrix model (Wang and Li, 2007) at the subgrid level is applied to calculate a structure-dependent drag force. 

The EMMS model was proposed for the time-mean behavior of fluidized beds on the reactor scale. A more extensive application of the EMMS model to gas-solid flow is through its coupling with the two-fluid CFD approaches, which brings about an EMMS-based multi-scale CFD framework for gas—solid flow. For this purpose, Yang et al. (2003) introduced an acceleration, a, into the EMMS model to account for the... 

Different scales presented in Figure 3-1 are related to different approximation levels. For an overview of conventional molecular modelling methods, (see e.g.1-3). Bridging the above mentioned disparate time scales for the description of biologically relevant collective motions requires hierarchical, multi-scale approaches. In practice, to describe real complex (bio)molecular or material systems and processes various models have to be coupled to each other. Selected coupling mechanisms will be briefly reviewed. 

In all of the above cases, a strong non-linear coupling exists between reaction and transport at micro- and mesoscales, and the reactor performance at the macroscale. As a result, the physics at small scales influences the reactor and hence the process performance significantly. As stated in the introduction, such small-scale effects could be quantified by numerically solving the full CDR equation from the macro down to the microscale. However, the solution of the CDR equation from the reactor (macro) scale down to the local diffusional (micro) scale using CFD is prohibitive in terms of numerical effort, and impractical for the purpose of reactor control and optimization. Our focus here is how to obtain accurate low-dimensional models of these multi-scale systems in terms of average (and measurable) variables. 

In a staged multi-scale approach, the energetics and reaction rates obtained from these calculations can be used to develop coarse-grained models for simulating kinetics and thermodynamics of complex multi-step reactions on electrodes (for example see [25, 26, 27, 28, 29, 30]). Varying levels of complexity can be simulated on electrodes to introduce defects on electrode surfaces, composition of alloy electrodes, distribution of alloy electrode surfaces, particulate electrodes, etc. Monte Carlo methods can also be coupled with continuum transport/reaction models to correctly describe surfaces effects and provide accurate boundary conditions (for e.g. see Ref. [31]). In what follows, we briefly describe density functional theory calculations and kinetic Monte Carlo simulations to understand CO electro oxidation on Pt-based electrodes. 

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