Constructal entropy generation rate minimization for asymmetric vascular networks in a disc-shaped body

Abstract Based on constructal theory, the vascular networks with asymmetric pairing in a disc-shaped body are optimized by taking the minimizations of the dimensionless entropy generation rate and dimensionless entropy generation ratio as optimization objectives, respectively. The results show that there exist optimal tube lengths and angles which lead to the minimum dimensionless entropy generation rate and dimensionless entropy generation ratio of the vascular networks with two and three levels of asymmetric pairing, respectively. The optimal constructs of the vascular networks based on asymmetric and symmetric designs are different. For the specified heat flow per unit length on each tube surface, when the number of outlets N = 24 and the dimensionless mass flow rate M 1 ∗ = 10 - 2 , the dimensionless entropy generation rate with two levels of pairing based on asymmetric design is decreased by 7.80% than that based on symmetric design; when the number of outlets N = 24 and the dimensionless pumping power W 2 ∗ = 1 , the dimensionless entropy generation rate with three levels of pairing based on asymmetric design is decreased by 6.78% than that based on symmetric design. Moreover, the performance improvements of the vascular networks with asymmetric design can also be found for the specified heat flux on each tube surface. The optimization results of the vascular networks based on minimum flow resistance are special cases of those based on minimum entropy generation rate in this paper.

[1]  Adrian Bejan,et al.  Heterogeneous porous media as multiscale structures for maximum flow access , 2006 .

[2]  Kee-Hyeon Cho,et al.  Hydraulic-thermal performance of vascularized cooling plates with semi-circular cross-section , 2012 .

[3]  Arun S. Mujumdar,et al.  Flow and thermal characteristics of offset branching network , 2010 .

[4]  J. Ordonez,et al.  Constructal dendritic geometry and the existence of asymmetric bifurcation , 2006 .

[5]  A. Bejan.  Constructal Law: Optimization as Design Evolution , 2015 .

[6]  C D Murray,et al.  The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Adrian Bejan,et al.  Design with constructal theory , 2008 .

[8]  Lingen Chen,et al.  Constructal entropy generation rate minimization of line-to-line vascular networks with convective heat transfer , 2013 .

[9]  Lingai Luo,et al.  Heat and Mass Transfer Intensification and Shape Optimization , 2013 .

[10]  Adrian Bejan,et al.  Vascularization with trees matched canopy to canopy: Diagonal channels with multiple sizes , 2008 .

[11]  Adrian Bejan,et al.  Vascular structures for volumetric cooling and mechanical strength , 2010 .

[12]  A. Bejan.  Shape and Structure, from Engineering to Nature , 2000 .

[13]  Adrian Bejan,et al.  Vascularized materials: Tree-shaped flow architectures matched canopy to canopy , 2006 .

[14]  Simone Moretti,et al.  Fin Shape Thermal Optimization Using Bejan's Constructal Theory , 2011, Fin Shape Thermal Optimization Using Bejan's Constructal Theory.

[15]  Adrian Bejan,et al.  Thermodynamic optimization of tree-shaped flow geometries , 2006 .

[16]  Adrian Bejan,et al.  Design in Nature , 2012 .

[17]  Adrian Bejan,et al.  Thermodynamic optimization of tree-shaped flow geometries with constant channel wall temperature , 2006 .

[18]  A. Bejan,et al.  Constructal law of design and evolution: Physics, biology, technology, and society , 2013 .

[19]  A. Bejan,et al.  Vascularization for cooling and mechanical strength , 2011 .

[20]  Adrian Bejan,et al.  Networks of channels for self-healing composite materials , 2006 .

[21]  C. Elphick,et al.  Constructal Theory: From Engineering to Physics, and How Flow Systems Develop Shape and , 2006 .

[22]  Jianchao Cai,et al.  Symmetry is not always prefect , 2010 .

[23]  Fengrui Sun,et al.  Constructal entropy generation rate minimization for X-shaped vascular networks , 2015 .

[24]  Louis Gosselin,et al.  Emergence of asymmetry in constructal tree flow networks , 2005 .

[25]  Adrian Bejan,et al.  Thermodynamic Optimization of Flow Geometry in Mechanical and Civil Engineering , 2001 .

[26]  Adrian Bejan,et al.  Transient cooling response of smart vascular materials for self-cooling , 2009 .

[27]  A. Bejan,et al.  Constructal theory of generation of configuration in nature and engineering , 2006 .

[28]  A. Bejan,et al.  Vascularization with trees that alternate with upside-down trees , 2007 .

[29]  Chen Lingen.  Progress in study on constructal theory and its applications , 2012 .

[30]  A. Bejan,et al.  Fluid flow and heat transfer in vascularized cooling plates , 2010 .

[31]  J. Hansen,et al.  Shape and Structure , 2001 .