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Optimal structure of tree-like branching networks for fluid flow

Author

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  • Kou, Jianlong
  • Chen, Yanyan
  • Zhou, Xiaoyan
  • Lu, Hangjun
  • Wu, Fengmin
  • Fan, Jintu

Abstract

Tree-like branching networks are very common flow or transportation systems from natural evolution. In this study, the optimal structures of tree-like branching networks for minimum flow resistance are analyzed for both laminar and turbulent flow in both smooth and rough pipes. It is found that the dimensionless effective flow resistance under the volume constraint for different flows is sensitive to the geometrical parameters of the structure. The flow resistance of the tree-like branching networks reaches a minimum when the diameter ratio β∗ satisfies β∗=Nk, where, N is the bifurcation number N=2,3,4,… and k is a constant. For laminar flow, k=−1/3, which is in agreement with the existing Murray’s law; for turbulent flow in smooth pipes, k=−3/7; for turbulent flow in rough pipes, k=−7/17. These results serve as design guidelines of efficient transport and flow systems.

Suggested Citation

  • Kou, Jianlong & Chen, Yanyan & Zhou, Xiaoyan & Lu, Hangjun & Wu, Fengmin & Fan, Jintu, 2014. "Optimal structure of tree-like branching networks for fluid flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 527-534.
  • Handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:527-534
    DOI: 10.1016/j.physa.2013.08.029
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    Cited by:

    1. Kurian, Varghese & Narasimhan, Sridharakumar, 2023. "Analysis of potential flow networks: Variations in transport time with discrete, continuous, and selfish operation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    2. Zhu, Jianting, 2018. "Effective aperture and orientation of fractal fracture network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 27-37.

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