基于耗散率最小的“盘点”脉管网络构形优化

以有限温差传热和流动阻力引起的最小耗散率和耗散数为优化目标,在圆盘总面积和脉管网络总体积给定的条件下,对圆盘区域内一级、二级和三级脉管网络进行构形优化,得到耗散率和耗散数最小的各级脉管网络最优构形.结果表明当参数B1?10??时,在相同无量纲质量流率M*(1?M*?102)下,耗散率最小和熵产率最小的一级脉管网络最优构形有明显区别.对于二级脉管网络,当无量纲质量流率在1?M*?102范围内时,传热耗散和流动耗散大小相当,此时脉管网络最优构形随质量流率变化显著.在相同脉管网络总体积和圆盘半径条件下,相同无量纲质量流率时,一级、二级和三级脉管网络最小耗散数性能几乎相同;当无量纲泵功率*5?10(?1,2,3)?i W i时,随着脉管级数的增大,脉管网络最小耗散数减小,此时增加脉管网络的复杂度有利于提高脉管网络的性能.此外,还以复合耗散率为优化目标对脉管性能进行优化.优化结果可从传热优化角度为脉管系统设计提供参考.

Constructal optimization for ＂disc-point＂ vascular networks based on minimum entransy dissipation rate

For the specified total area of the disc and total volume of the vascular network, the constructal optimizations of the first order, second order and third order vascular networks are carried out by taking the minimizations of the entransy dissipation rate and entransy dissipation number, caused by heat transfer with finite temperature difference and flow resistance, as optimization objectives. The optimal constructs for each order vascular network with minimum entransy dissipation rate and entransy dissipation number are obtained. The results show that when the parameter B1≥10^-4, for the same dimensionless mass flow rate M^＊（1≤M^＊≤10^2）, the optimal constructs of the first order vascular network based on the minimizations of entransy dissipation rate and entropy generation rate are obviously different. For the second order vascular network, when the dimensionless mass flow rate locates at the range of 1≤M^＊≤10^2, the magnitude orders of the entransy dissipations caused by heat transfer and flow resistance locate at the same level, and the optimal construct of the vascular network varies obviously with the change of the mass flow rate. For the same total volume of the vascular network and radius of the disc, when the dimensionless mass flow rates of the vascular networks are equal, the first order, second order and third order vascular networks almost exhibit the same performances of the entransy dissipation number; when the dimensionless pumping power satisfies Wi^＊〉10^5（i=l,2,3）, the minimum entransy dissipation number of the vascular network decreases with the increase in the order of the vascular network, and the performance of the vascular network can be improved by increasing the complexity of the vascular network in this case. Moreover, the performance of the vascular network is also optimized by taking complex index of entransy dissipation rate as optimization objective in this paper. The optimal results obtained in this paper can provide some guidelines for the designs of the vasculature from the point of view of heat transfer optimization.