Constructal Optimization for Tree-Shaped Fluid Networks in a Disc-Shaped Area Subjected to the Surface Area Constraint

Abstract

Constructal optimization of tree-shaped fluid networks in a disc-shaped area are re-performed by taking total pressure drop as optimization objective subjected to total tube surface area constraint (i.e., total tube wall material constraint). Two kinds of flow regimes in the tubes, i.e., fully developed laminar and turbulent flows, are considered. The results show that there exist optimal angles of tubes which lead to the minimum pressure drop between center and rim of disc for both fully developed laminar and turbulent flows. For fully developed laminar flow in tubes and total tube surface area constraint, the optimal number of the central tubes (D 0 tubes) is 2 for the one and the higher levels of pairing in the tree-shaped fluid networks, and the optimal angle (β 1) of the central and one level tubes (D 0 and D 1 tubes) is 48.72°. The optimal angles of the tree-shaped fluid network with new level of pairing are the same as the corresponding optimal angles of the tree-shaped fluid network with the last level of pairing. Transitions of fluid network from structure with no pairings to that with one pairing, from structure with one pairing to that with two pairings, from structure with two pairings to that with three pairings and from structure with three pairings to that with four pairings occur at a number of outlets on the rim of the disc, 4, 8, 16 and 32, respectively. The tree-shaped fluid networks with fully developed turbulent flow in the tubes subjected to the total tube volume and surface area constraints are also further optimized. Moreover, the optimal constructs of the tree-shaped fluid networks subjected to tube surface area constraint are obviously different from those subjected to tube volume constraint, and the optimization results obtained can provide different guidelines for the designs of practical tree-shaped fluid networks.