Meso-scale model

The final two chapters discuss modeling of PEFCs. Mukherjee and Wang provide an in-depth review of meso-scale modeling of two-phase transport, while Zhou et al. summarize both the simulation of electrochemical reactions on electrocatalysts and the transport of protons through the polymer electrolyte using atomistic simulation tools such as molecular dynamics and Monte Carlo techniques. 

Meso-Scale Modeling—The Key to Multi-Scale CFD Simulation... 

To meet the industrial demand for both large-scale computation and good predictability, the reasonable way out is not to simulate from the beginning of the micro-scale, but to use coarse-grid simulation with meso-scale modeling for the effects of structure. This kind of approach can be termed the "multi-scale CFD." It is entitled "multi-scale," not because the problem it solves is multi-scale, but because its meso-scale model contains multi-scale structure parameters. 

According to the choice of meso-scale models, we may divide the multi-scale CFD into two branches the "correlative" and the "variational," as named in Li and Kwauk (2003) and will be discussed in the following sections. 

The "correlative" multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a "multilevel" approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

Following the above approach, the correlative multi-scale CFD reduces the computation cost by transforming information over a range of scales into meso-scale models. With these works, it seems feasible to establish a numerical experiment facility to consider thoroughly the... 

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. 

MESO-SCALE MODELING—THE KEY TO MULTI-SCALE APPROACHES... 

Energy-minimization multi-scale (EMMS) model—a meso-scale model... 

Lu, B., EMMS-based Meso-Scale Model and Its Application in Simulating Gas-Solid Two-Phase Flows, Ph.D. thesis (in Chinese), Institute of Process Engineering, Chinese Academy of Sciences, Beijing (2009). 

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