Constructal tree-shaped flow structures (original) (raw)

Multiscale optimization of flow distribution by constructal approach

China Particuology, 2005

Constructal approach is a recent concept allowing to generate and optimize multi-scale structures, in particular, branching structures, connecting a microscopic world to a macroscopic one, from an engineer's point of view. Branching morphologies are found in many types of natural phenomena, and may be associated to some kind of optimization, expressing the evolutionary adaptation of natural systems to their environment. In a sense, the constructal approach tries to imitate this morphogenesis while short-cutting the trial-and-error of nature.

Svelteness, freedom to morph, and constructal multi-scale flow structures

International Journal of Thermal Sciences, 2005

This paper reviews recent progress on constructal theory and design. The emphasis is on the development of multi-scale, nonuniformly distributed flow structures that offer increased compactness (e.g., heat transfer density). Examples are counterflow heat exchangers with tree-shaped hot and cold streams, and tree architectures on a disc. Every flow system has a property called svelteness (Sv), which is the ratio between its external (global) length scale and its internal length scale (V 1/3 ), where V is the volume occupied by all the ducts. Emphasis is placed on the development of simple strategies for decreasing the computational cost required by the development of such structures. The generation of multi-scale flow configurations is a process that can be projected on a diagram having global performance on the abscissa and degrees of freedom on the ordinate. This process rules the development (evolution) of all flow configurations for systems with global objective, global constraints and freedom to morph.

Tree-shaped flow structures designed by minimizing path lengths

International Journal of Heat and Mass Transfer, 2002

This paper outlines a direct route to the construction of effective tree-shaped flow structures. Dendritic flow structures dominate the design of natural and engineered flow systems, especially in thermal and fluid systems. The starting point is the optimization of the shape of each elemental area or volume, such that the length of the flow path housed by the element is

Novel Geometrical Approach to Designing Flow Channels

Volume 3: 38th Design Automation Conference, Parts A and B, 2012

Many natural systems that transport heat, energy or fluid from a distributed volume to a single flow channel exhibit an analogous appearance to trees (examples include bronchial tubes, watersheds, lightening, and blood vessels). Several authors have proceeded with analytical methods to develop fractal or pseudo-fractal designs analogous to these natural instances. This implicates an implicit belief in some designers that there is an optimal attribute to this 'tree-like' appearance. A novel explanation for the appearance of these systems is presented in this paper. Natural systems follow the path of least resistance; or in other words, minimize transport effort. Effort is required to overcome all forms of friction (an unavoidable consequence of motion). Therefore effort minimization is analogous to transport distance (path length) minimization. Effort due to friction will be integrated over the total transport distance. Leveraging this observation a simple, geometric explanation for the emergent 'tree-like' architecture of many natural systems is now achievable. Note that this 'tree' effect occurs when most of the flow volume exhibits diffusion, with a small percentage of interdigitated high flow velocity channels. One notable application of our novel method, path length analysis, is the automated creation of cooling channel networks for heat generating micro-chips. As a demonstration, this path length analysis method was used to develop a significantly more efficient channel configuration (by 14%) than the state of the art for conductive microchip cooling. An extensive array of finite element models confirms the performance of this novel configuration.

Tree-shaped flow structures with local junction losses

International Journal of Heat and Mass Transfer, 2006

This paper is a fundamental study of the effect of junction losses on the optimized geometry of tree-shaped flows. Several classes of flows are investigated systematically in a T-shaped construct with fixed internal and external size: laminar with non-negligible entrance and junction losses, and turbulent in tubes with smooth and rough walls. It is shown that in all cases junction losses have a sizeable effect on optimized geometry when Sv 2 < 10, where the svelteness Sv is a global property of the entire flow system: Sv = external length scale/ internal length scale. The relationship between the global Sv and the slenderness of individual channels is discussed. The study shows that, in general, the duct slenderness decreases as the tree architecture becomes finer and more complex. In conclusion, miniaturization pushes flow architectures not only toward the smaller, finer and more complex, but also toward the domain in which junction losses must be taken into account in the optimization of geometry.

The effect of size on efficiency: Power plants and vascular designs

International Journal of Heat and Mass Transfer, 2011

In this paper we use thermodynamics to show why larger flow systems are more efficient than smaller flow systems. This trend is visible across the board, from power generation and refrigeration, to vascular design and animal design. The reason is that larger systems have larger flow passages and heat transfer surfaces, and do not strangle the flow of the currents that must flow. Three fundamental examples show how to predict this trend: a power plant with fluid friction and finite heat transfer area, a vascular body with building blocks optimized at every level of assembly, and a vascular body designed based on a ductpairing algorithm. The examples show that the performance improves as the size increases, and that the architecture changes with the size. These constructal-design features constitute the basis for scaling up and scaling down the configurations of flow systems, from desktop models to life size installations.

Constructal theory of energy-system and environment flow configurations

International Journal of Exergy, 2005

This paper outlines the place occupied by the constructal law in thermodynamics, and provides a vision of the future development of energy engineering as a transdisciplinary science of systems of systems. Natural and man-made flow systems do not exist in isolation. The optimal balance between engineered flow systems and their surroundings is achieved through the optimal distributing of thermodynamic imperfections. The paper traces the development of constructal theory from a principle of maximisation of flow access in morphing configurations to engineering discoveries, such as optimal internal spacings, tree-shaped flow networks, machine flight, and multi-scale flow structures for maximal heat transfer density. The introduction of constructal theory and design in thermodynamics education is also discussed.

The constructal law and the thermodynamics of flow systems with configuration

International Journal of Heat and Mass Transfer, 2004

In this paper we develop an analytical and graphical formulation of the constructal law of maximization of flow access in systems with heat and fluid flow irreversibilities and freedom to change configuration. The flow system has global performance (e.g., minimization of global flow resistance) and global properties, or constraints (e.g., overall size, and total duct volume). The infinity of possible flow structures occupies a region of the two-dimensional domain of ''global performance versus freedom to morph''. This region of ''nonequilibrium flow structures'' is bounded by a line representing the best flow structures that are possible when the freedom to morph is limited. The best of all such structures are the ''equilibrium flow structures'': here the performance level is the highest, and it does not change even though the flow architecture can change with maximum freedom. The universality of this graphical and analytical presentation is illustrated with examples of flow structures from three classes: flow between two points, flow between a circle and its center, and flow between one point and an area. In sum, this paper presents an analytical and graphical formulation of the constructal principle of generation of flow architecture. The place of this new and self-standing principle in the greater framework of thermodynamics is outlined.