Volume Averaging Theory (VAT) has been used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of heat exchanger channel morphology. Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV, which could be evaluated using scaling suggested by VAT from the output of a CFD code. To get reasonable lower scale flow field and heat transfer solutions, the length of computational domain must be determined in advance. There-dimensional numerical simulations for laminar heat transfer and fluid flow characteristics of plain finned tube heat exchangers were performed. The effects of two factors, Reynolds number and tube row number, were examined. The Reynolds number based on the fin collar outside diameter varied from 500 to 6000 and the corresponding air frontal velocity was ranged from 0.38m/s to 4.6m/s. The cases with tube row number varying from 1 to 9 were tested numerically. Field synergy principle analysis was performed for the results, including the in-depth analysis of every REV, which gave a clear perspective of the variation of heat transfer performance with the tube rows. It is found that when the number of tube row N>4, the increasing trend of the intersection angle decreases and almost keep constant when N>6, which leads to the heat transfer approaching fully developed conditions. Simulations over the computational domain with a length of 5+2+2 REVs were recommended to obtain a reasonable local flow and heat transfer field, and then the VAT based closure formulas for drag resistance coefficient and heat transfer coefficient were integrated over the sixth and seventh REV to close the heat exchanger modeling based volume averaging theory.
Determining the Computational Domain Length to Obtain Closure for VAT Based Modeling by 3D Numerical Simulation and Field Synergy Analysis
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Zhou, F, Hansen, N, & Catton, I. "Determining the Computational Domain Length to Obtain Closure for VAT Based Modeling by 3D Numerical Simulation and Field Synergy Analysis." Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition. Volume 2: Biomedical and Biotechnology Engineering. Vancouver, British Columbia, Canada. November 12–18, 2010. pp. 593-602. ASME. https://doi.org/10.1115/IMECE2010-37561
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