Considering the excellent transport performance of treelike networks and the effect of roughness on fluid flow in a microchannel, the present work studied the optimization of a symmetric treelike roughened network with minimum hydraulic resistance under constant total channel base volume. It was found that there is an optimal base diameter ratio β_m of channels at two successive branching levels that minimizes the hydraulic resistance of the network. The β_m value increases with increasing average roughness height. A larger β_m value is needed to minimize the hydraulic resistance of the network with larger branching number N, branching level m, and channel length ratio γ, because the increases in N, m, and γ reduce the channel diameter and magnify the influence of roughness on the fluid flow.

中文翻译：

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具有均匀粗糙度的层流分形树状微通道网络的优化

考虑到树状网络的优异传输性能和粗糙度对微通道中流体流动的影响，本工作研究了在恒定总通道基体积下具有最小水力阻力的对称树状粗糙网络的优化。发现在两个连续的分支水平上有一个最佳的通道基础直径比β _m，它使网络的水力阻力最小化。的β_米随着平均粗糙度高度值增加。需要较大的β _m值来最小化具有较大分支数N、分支水平m和通道长度比的网络的水力阻力。γ，因为N、m和γ的增加会减小通道直径并放大粗糙度对流体流动的影响。