Better Friction Factors and Nusselt Numbers for DPFs and When Not to Use Them at All

Edward  Bissett, Gamma Technologies

Edward J. Bissett, Margaritis Kostoglou, and Athanasios G. Konstandopoulos

It is common in the 1D modeling of DPF performance to use friction factors and Nusselt numbers from idealized 2D/3D channel flows with zero wall flow, thereby making the additional approximation that the actual velocity and scalar (temperature or species concentrations) profiles within the channel are little affected by nonzero wall flow. There is extensive related research in the filtration literature for the simpler geometries of circular tubes and parallel planes, that exposes much more complex and interesting effects as the wall Reynolds number, Rew, increases. Here we extend the essentials of these results to the higher-dimensional square channels of DPFs and provide the correct friction factors and Nusselt numbers for nonzero Rew. Furthermore, we confirm the existence of a limiting Rew, beyond which there is no fully-developed flow for the inlet DPF channels. That is, for fixed conditions and geometry, we cannot arbitrarily increase the flow rate and legitimately generate a friction factor for a 1D model as usual. We also discuss the practical ranges of Rew where this effect must be considered, its physical meaning from the filtration literature, and the subsequent implications for DPF modeling.

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