Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 8, 2015

Constructal vascularized structures

  • Erdal Cetkin
From the journal Open Engineering

Abstract

Smart features such as self-healing and selfcooling require bathing the entire volume with a coolant or/and healing agent. Bathing the entire volume is an example of point to area (or volume) flows. Point to area flows cover all the distributing and collecting kinds of flows, i.e. inhaling and exhaling, mining, river deltas, energy distribution, distribution of products on the landscape and so on. The flow resistances of a point to area flow can be decreased by changing the design with the guidance of the constructal law, which is the law of the design evolution in time. In this paper, how the flow resistances (heat, fluid and stress) can be decreased by using the constructal law is shown with examples. First, the validity of two assumptions is surveyed: using temperature independent Hess-Murray rule and using constant diameter ducts where the duct discharges fluid along its edge. Then, point to area types of flows are explained by illustrating the results of two examples: fluid networks and heating an area. Last, how the structures should be vascularized for cooling and mechanical strength is documented. This paper shows that flow resistances can be decreased by morphing the shape freely without any restrictions or generic algorithms.

References

[1] Bejan A., Lorente S., Design with constructal theory, Wiley, 2008. 10.1002/9780470432709Search in Google Scholar

[2] Aragon A.M., Wayer J.K., Geubelle P.H., Goldberg D.E., White S.R., Design of microvascular flow networks using multiobjective genetic algorithms, Comput. Methods Appl. Mech. Eng., 2008, 197, 4399–4410. 10.1016/j.cma.2008.05.025Search in Google Scholar

[3] Cho K.-H., Kim M.-H., Fluid flow characteristics of vascularized channel networks, Chem. Eng. Sci., 2010, 65, 6270–6281. 10.1016/j.ces.2010.09.020Search in Google Scholar

[4] Hamilton A.R., Sottos N.R., White S.R., Mitigation of fatigue damage in self-healing vascular materials, Polymer, 2012, 53, 5575–5581. 10.1016/j.polymer.2012.09.050Search in Google Scholar

[5] Williams H.R., Trask R.S.,Waever P.M., Bond I.P., Minimummass vascular networks in multifunctional materials, J. R. Soc. Interface, 2008, 5, 55–65. 10.1098/rsif.2007.1022Search in Google Scholar PubMed PubMed Central

[6] Lee J., Lorente S., Bejan A., Kim M., Vascular structures with flow uniformity and small resistance, Int. J. Heat Mass Transfer, 2009, 52, 1761–1768. 10.1016/j.ijheatmasstransfer.2008.09.027Search in Google Scholar

[7] Bejan A., Lorente S., The constructal law and the evolution of the design in nature, Phys. Life Rev., 2011, 8, 209–240. 10.1016/j.plrev.2011.05.010Search in Google Scholar PubMed

[8] Cetkin E., Lorente S., Bejan A., Vascularization for cooling and mechanical strength, Int. J. HeatMass Transfer, 2011, 54, 2774– 2781. 10.1016/j.ijheatmasstransfer.2011.02.061Search in Google Scholar

[9] Cetkin E., Lorente S., Bejan A., Hybrid grid and tree structures for cooling and mechanical strength, J. Appl. Phys., 2011, 110, 064910. 10.1063/1.3626062Search in Google Scholar

[10] Cetkin E., Lorente S., Bejan A., Vascularization for cooling a plate heated by a randomly moving source, J. Appl. Phys., 2012, 112, 084906. 10.1063/1.4759290Search in Google Scholar

[11] Bejan A., Advanced engineering thermodynamics, 2nd ed, Wiley, 1997. Search in Google Scholar

[12] Rocha L.A.O., Lorente S., Bejan A., Constructal law and the unifying principle of design, Springer, 2012. 10.1007/978-1-4614-5049-8Search in Google Scholar

[13] Bejan A., Zane J.P., Design in nature: How the constructal law governs evolution in biology, physics, technology and social organizations, Doubleday, 2012. Search in Google Scholar

[14] Bejan A., Merkx G.W., Constructal theory of social dynamics, Springer, 2007. 10.1007/978-0-387-47681-0Search in Google Scholar

[15] Bejan A., Shape and structure from engineering to nature, Cambridge University Press, 2000. Search in Google Scholar

[16] Reis A.H., Constructal theory: from engineering to physics, and howflowsystems develop shape and structure, Appl. Mec. Rev., 2006, 59, 269–282. 10.1115/1.2204075Search in Google Scholar

[17] Raja A.H., Basak T., Das S.K., Thermal performance of a multiblock heat exchanger designed on the basis of Bejan’s constructal theory, Int. J. HeatMass Transfer, 2008, 51, 3582–3594. 10.1016/j.ijheatmasstransfer.2007.10.027Search in Google Scholar

[18] Lorente S., Constructal view of electrokinetic transfer through porous media, J. Phys. D Appl. Phys.,2007, 40, 2941–2947. 10.1088/0022-3727/40/9/041Search in Google Scholar

[19] Chen Y., Cheng P., An experimental investigation on the thermal efficiency of fractal tree- like microchannel nets, Int. Comm. Heat Mass Transfer, 2005, 32, 931–938. 10.1016/j.icheatmasstransfer.2005.02.001Search in Google Scholar

[20] Reis A.H., Constructal view of scaling laws of river basins, Geomorphology, 2006, 78, 201–206. 10.1016/j.geomorph.2006.01.015Search in Google Scholar

[21] Muzychka Y.S., Constructal multi-scale design of compact micro-tube heat sinks and heat exchangers, Int. J. Thermal Sci., 2007, 46, 245–252. 10.1016/j.ijthermalsci.2006.05.002Search in Google Scholar

[22] Reis A.H., Miguel A.F., Aydin M., Constructal theory of flow architecture of lungs, Med. Phys., 2004, 31, 1135–1140. 10.1118/1.1705443Search in Google Scholar PubMed

[23] Azoumah Y., Mazet N., Neveu P., Constructal network for heat and mass transfer in a solid–gas reactive porous medium, Int. J. Heat Mass Transfer, 2004, 47, 2961–2970. 10.1016/j.ijheatmasstransfer.2004.03.022Search in Google Scholar

[24] Tondeur D., Luo L., Design and scaling laws of ramified fluid distributors by the constructal approach, Chem. Eng. Sci., 2004, 59, 1799–1813. 10.1016/j.ces.2004.01.034Search in Google Scholar

[25] Miguel A.F., Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions, J. Theoretical Biol. 2006, 242, 954–961. Search in Google Scholar

[26] Zhou S., Chen L., Sun F., Optimization of constructal volumepoint conduction with variable cross section conducting path, Energy Convers. Manage., 2007, 48, 106–111. 10.1016/j.enconman.2006.05.007Search in Google Scholar

[27] Wechsatol W., Ordonez J.C., Kosaraju S., Constructal dendritic geometry and the existence of asymmetric bifurcations, J. Appl. Phys., 2006, 100, 113514. 10.1063/1.2388732Search in Google Scholar

[28] Wu W., Chen L., Sun F., On the area to point flow problem based on constructal theory, Energy Convers.Manage., 2007, 48, 101– 105. 10.1016/j.enconman.2006.05.009Search in Google Scholar

[29] Rocha L.A.O., Lorenzini E., Biserni C., Geometric optimization of shapes on the basis of Bejan’s Constructal theory, Int. Comm. Heat Mass Transfer, 2005, 32, 1281–1288. 10.1016/j.icheatmasstransfer.2005.07.010Search in Google Scholar

[30] Wu W., Chen L., Sun F., Heat-conduction optimization based on constructal theory, Appl. Energy, 2007, 84, 39–47. 10.1016/j.apenergy.2006.04.006Search in Google Scholar

[31] Beyene A., Peffley J., Constructal theory, adaptive motion, and their theoretical application to low-speed turbine design, J. Energy Eng., 2009, 135, 112–118. 10.1061/(ASCE)0733-9402(2009)135:4(112)Search in Google Scholar

[32] Lorenzini G., Rocha L.A.O., Constructal design of T–Y assembly of fins for an optimized heat removal, Int. J. HeatMass Transfer, 2009, 52, 1458–1463. 10.1016/j.ijheatmasstransfer.2008.09.007Search in Google Scholar

[33] Biserni C., Rocha L.A.O., Stanescu G., Lorenzini E., Constructal H-shaped cavities according to Bejan’s theory, Int. J. Heat Mass Transfer, 2007, 50, 2132–2138. 10.1016/j.ijheatmasstransfer.2006.11.006Search in Google Scholar

[34] Azoumah Y., Neveu P.,Mazet N., Optimal design of thermochemical reactors based on constructal approach, Aiche J., 2007, 53, 1257–1266. 10.1002/aic.11152Search in Google Scholar

[35] Zhou S., Chen L., Sun F., Constructal entropy generation minimization for heat andmass transfer in a solid–gas reactor based on triangular element, J. Phys. D Appl. Phys., 2007, 40, 3545– 3550. 10.1088/0022-3727/40/11/044Search in Google Scholar

[36] Reis A.H., Miguel A.F., Constructal theory and flowarchitectures in living systems, Thermal Sci., 2006, 10, 57–64. 10.2298/TSCI0601057RSearch in Google Scholar

[37] Carone M.J., Williams C.B., Allen J.K., Mistree F., An application of constructal theory in the multi-objective design of product platforms, ASME 2003 Design Engineering Technical Conferences and Computer and Information in Engineering Conference Chicago, Illinois USA, September 2-6, 2003. 10.1115/DETC2003/DTM-48667Search in Google Scholar

[38] Lorente S., Cetkin E., Bello-Ochende T., Meyer J.P., Bejan A., The constructal-law physics of why swimmers must spread their fingers and toes, J. Theor. Biol., 2012, 308, 141–146. 10.1016/j.jtbi.2012.05.033Search in Google Scholar PubMed

[39] Bejan A., Lorente S., The physics of spreading ideas, Int. J. Heat Mass Transfer, 2012, 55, 802–807. 10.1016/j.ijheatmasstransfer.2011.10.029Search in Google Scholar

[40] Bejan A., Jones E.C., Charles J.D., The evolution of speed in athletics: why the fastest runners are black and swimmers are white, Int. J. Design Nature, 2010, 5, 1–13. 10.2495/DNE-V5-N3-199-211Search in Google Scholar

[41] Bejan A., Why so many shapes resemble the golden ratio: vision, cognition, and locomotion as a single design in nature, Int. J. Design Nature Ecodyn., 2009, 4, 97–104. 10.2495/DNE-V4-N2-97-104Search in Google Scholar

[42] Rocha L.A.O., Isoldi L.A., Real M.V., dos Santos E.D., Correia A.L.G., Lorenzini G., Biserni C., Constructal design applied to the elastic buckling of thin plates with holes, Centr. Eur. J. Eng., 2013, 3, 475–483. 10.2478/s13531-013-0105-xSearch in Google Scholar

[43] Miguel A.F., An analytical approach for optimal design of heat sinks under forced convection, Centr. Eur. J. Eng., 2013, 3, 276– 284. 10.2478/s13531-012-0054-9Search in Google Scholar

[44] Cetkin E., Lorente S., Bejan A., Natural constructal emergence of vascular design with turbulent flow, J. Appl. Phys., 2010, 107, 114901. 10.1063/1.3430941Search in Google Scholar

[45] Bejan A., Lorente S., Yilbas B.S., Sahin A.Z., The effect of size on efficiency: power plants and vascular designs, Int. J. Heat Mass Transfer, 2011, 54, 1475–1481. 10.1016/j.ijheatmasstransfer.2010.11.045Search in Google Scholar

[46] Lorente S., Bejan A., Few large and many small: hierarchy in movement on earth, Int. J. Nature Ecodyn., 2010, 5, 254–267. 10.2495/DNE-V5-N3-254-267Search in Google Scholar

[47] Kim S., Lorente S., Bejan A., Miller W., Morse J., The emergence of vascular design in three dimensions, J. Appl. Phys., 2008, 103, 123511. 10.1063/1.2936919Search in Google Scholar

[48] Cetkin E., Lorente S., Bejan A., The steepest S curve of spreading and collecting flows: Discovering the invading tree, not assuming it, J. Appl. Phys., 2012, 111, 114903. 10.1063/1.4721657Search in Google Scholar

[49] Bejan A., Lorente S., Lee J., Unifying constructal theory of roots, canopies and forests, J. Theor. Biol., 2008, 254, 529–540. 10.1016/j.jtbi.2008.06.026Search in Google Scholar PubMed

[50] Bejan A., The constructal-laworigin of the wheel, size and skeleton in animal design, Am. J. Phys., 2010, 78, 692–699. 10.1119/1.3431988Search in Google Scholar

[51] Lorente S., Lee J., Bejan A., The flow of stresses concept: The analogy between mechanical strength and heat convection, Int. J. Heat Mass Transfer, 2010, 53, 2963–2968. 10.1016/j.ijheatmasstransfer.2010.03.038Search in Google Scholar

[52] Bhattacharje S., Grosshandler W.L., The formation of a wall jet near a high temperature wall under microgravity environment, ASME HTD, 1988, 96, 711–716. Search in Google Scholar

[53] Petrescu S., Comments on the optimal spacing of parallel plates cooled by forced convection, Int. J. HeatMass Transfer, 1994, 37, 1283. Search in Google Scholar

Received: 2014-9-2
Accepted: 2015-1-1
Published Online: 2015-6-8

©2015 Erdal Cetkin

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 28.4.2024 from https://www.degruyter.com/document/doi/10.1515/eng-2015-0017/html
Scroll to top button