Hierarchical multi-scale model reduction in the simulation of catalytic converters

This paper presents a methodology for multi-scale modelling using pre-computed data for the small scales. By pre-computing the required data at the micro- and meso-scales and storing them in a look-up table, these small-scale effects can be captured in a macro-scale model that executes with practicable execution times. The methodology is presented in the context of modelling a washcoated monolith reactor for the catalytic combustion of methane using a detailed multistep mechanistic model. The modelling is illustrated as a sequence of steps of increasing model simplification. In the first instance, only the reaction rates are pre-computed. Then the washcoat diffusion is included using a 2D axisymmetric model with a washcoat of uniform thickness, then with a non-symmetrical channel with a washcoat of non-uniform thickness. It is shown how a simple 1D single channel model can accurately account for the presence of a non-uniform washcoat. Finally, the external transport resistance is included in the pre-computation step, and it is shown that a simple one dimensional pseudo-homogeneous single channel model can be used provided the effective average rates are appropriately calculated. Execution times are shown to decrease by several orders of magnitude at minimal loss of solution accuracy. The use of pre-computed data allows for the inclusion of complex heat and mass transfer phenomena, as well as complex kinetics in full scale converter models at relatively small computational cost. The implementation of look-up tables into full scale CFD models is described, and optimal strategies proposed. (c) 2013 Elsevier Ltd. All rights reserved.