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Constructal entransy dissipation rate minimization for X-shaped vascular networks

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Abstract

Combining with entransy theory, constructal designs of the X-shaped vascular networks (XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates (EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives (EDR minimization and entropy generation rate (EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate (DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network (HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number (EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

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Authors and Affiliations

  1. Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    HuiJun Feng & LinGen Chen

  2. School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    HuiJun Feng & LinGen Chen

  3. College of Power Engineering, Naval University of Engineering, Wuhan, 430033, China

    ZhiHui Xie

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  1. HuiJun Feng
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  2. LinGen Chen
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  3. ZhiHui Xie
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Correspondence to LinGen Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51506220, 51579244), the Natural Science Foundation of Hubei Province (Grant No. 2016CFB504), and the Independent Project of Naval University of Engineering (Grant No. 425317Q017).

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Feng, H., Chen, L. & Xie, Z. Constructal entransy dissipation rate minimization for X-shaped vascular networks. Sci. China Technol. Sci. 62, 2195–2203 (2019). https://doi.org/10.1007/s11431-018-9392-1

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