Constructal Law of Vascular Trees for Facilitation of Flow

Abstract

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.

Constructal design of horizontal fins to improve the performance of phase change material rectangular enclosures

“…Many researchers throughout the world have invoked constructal law for better engineering [21,22]. This direction is called constructal design and with it not only better configurations are sought but also better strategies for generating the geometry are looked for.…”

Theoretical Analysis of the Vascular System and its Relation to Adrian Bejan's constructal Theory

“…[ii] [25][26][27] . Recently, based on the constructual law applied to vascular systems, an evolution parameter E V , defined as the ratio of the global flow conductance of the evolving configuration on the global conductance of the configuration with least imperfection, has been proposed to quantity the evolutionary value of the network configuration with regard to the configuration of least imperfection, as predicted by the constructal law 27 .…”

“…According to the constructal theory, the reason is that the type of stress that the water flow exerts on the river bed is similar to the type of stress that the blood flow or the air flow exerts on the vascular network and the bronchial network, respectively 24,27,28 . The same laws determine the systems of inanimate and animate flows.…”

“…If we take the examples of the hydrological and vascular networks, the constructal theory says that the similarities in the structure of these networks are explained by the fact that their construction responds to the same type of constraints that lead to the overall optimization of the system 24,27,28 . In these two cases, the system of constraints seems to shape the network dynamically.…”

Toward an optimal design principle in symmetric and asymmetric tree flow networks

“…The phenomenon of generation of flow configuration is ubiquitously in animate and inanimate systems, both in small and large scale systems (Pries et al, 1995;Bejan, 2000;Losa et al, 2002;Lorente and Bejan and, 2008;Lorthois and Cassot, 2010;Flores et al 2013;Razavi et al, 2014;Lorenzini et al, 2014;Miguel, 2006Miguel, , 2013aSchwen et al 2015). Tree-shaped flow networks are commonplace in fluid dynamics systems and a topic of much current interest in many fields of science and technology (Pries et al, 1995;Bejan, 2000;Losa et al, 2002;Bejan and Lorente, 2008;Miguel, 2013b).…”