Designing biologically inspired leaf structures: computational geometric transport analysis of volume-to-point flow channels (original) (raw)
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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 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 Topological Approach to Designing Flow Channels
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. Commonly for natural and designed systems with this type of flow, the flow volume consists primarily of high resistance regimes with a smaller portion of interdigitated low resistance regions (flow channels). Perhaps, the most relevant design problem is cooling of a microchip. Since microchip performance is optimal at lower temperatures, bulk heat flow resistance for heat exiting the system should be minimized; therefore, it is critical to cleverly align the channel to maximize flow. Heat conduction from a microchip is typically simplified into heat conduction from a homogenously heat-generating plate. This simplified problem is used as a standard model with which engineering designers can compare the performance of various cooling configurations. Due to the apparent tree-fractal characteristics of empirically emerging systems (i.e. in nature), several authors have examined analogous, simplified fractal configurations. These fractal configurations appear to be the best solution in current publication. We present a novel topological analysis that provides insight into performance at a schematic level. This analysis leads to the development of a new configuration, leaflike, which outperforms the current state-of-the-art. Performance is compared among the configurations with two parallels analyses: an extensive series of finite element models, covering a broad combinatory array of material properties and heating conditions; and topological analysis of path length, or the average distance heat, energy or fluid, must travel through the substrate and channel media before exiting through the point flow channel. There is a strong correlative mapping between the two analyses. Finite element modeling is employed because it provides a fundamental mechanics approach to assessment of heat transfer behavior, while the path length analysis provides an intuitive and computationally affordable means to predict performance. Novel contributions of this work include a configuration for conductive cooling in a plate for VTP flow, superior to the state-of-the-art, and a topological analysis of VTP flow that provides a generalized metric of bulk flow resistance and a schematic level conceptualization of the mechanics of VTP flow. Future advancements of our research could include enhancing the algorithm to automatically parse geometry into channel segments from an image or other external representation and eventually to even generate a suitable channel from arbitrary substrate geometry.
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.
Optimization of tree-shaped flow distribution structures over a disc-shaped area
International Journal of Energy Research, 2003
In this paper, we review the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centred at O. This is a fundamental problem in energy engineering: the distribution of fluid, energy, electric power, etc., from points to surrounding areas. This problem is also fundamental in heat transfer and electronics cooling: how to bathe and cool with a single stream of coolant a disc-shaped area or volume that generates heat at every point. This paper outlines, first, a direct route to the construction of effective tree-shaped flow structures. The starting point is the optimization of the shape of each elemental area, such that the length of the flow path housed by the element is minimized. Proceeding towards larger and more complex structures}from elements to first constructs, second constructs, etc.}the paper develops tree-shaped flow structures between one point and a straight line, as an elemental problem, and a circle and its centre. We also consider the equivalent tree-shaped networks obtained by minimizing the pressure drop at every step of the construction, in accordance with geometric constraints. The construction method is applied to a fluid flow configuration with laminar fully developed flow. It is shown that there is little difference between the two methods. The minimal-length structures perform very close to the fully optimized designs. These results emphasize the robustness of optimized tree-shaped flows.
International Journal of Exergy, 2004
Constructal theory is applied to the cooling of a disc where heat is uniformly generated. The disc size and the total volume occupied by the ducts (distributing the flow from the centre to the periphery) are constrained. It is shown that when the objective is to minimise the global thermal resistance, the best design is the one built with radial ducts. On the other hand, the minimisation of the pumping power leads to tree-shaped structures. The results show that the two optimisation approaches, thermal and fluid-mechanical, generate results with nearly the same global performance. Yet, when the scale of the problem becomes smaller and smaller and dendritic flows perform better, demonstrating the usefulness and robustness of tree-shaped structures.
Tree-Shaped Flow Architectures: Strategies for Increasing Optimization Speed and Accuracy
Numerical Heat Transfer, Part A: Applications, 2005
This article is about novel applications of computational heat transfer and fluid dynamics: the optimization and design of complex tree-shaped flow structures for cooling high-density heat-generating volumes (e.g., electronics). The focus is on computational cost, and how to reduce it by devising effective strategies for identifying paths that lead to the optimal complex flow structure. The method is illustrated by considering dendritic architectures that connect with laminar fluid flow the center of a circle with points distributed equidistantly on the circle. Optimal architectures are pursued numerically based on several methods: the optimization of every geometric detail of the complex structure, the minimization of every duct length, and the optimization of every angle of bifurcation. It is shown that strategy leads to dramatic increases in optimization speed, and provides an effective albeit approximate description of the optimal complex flow structure.
Constructal tree-shaped flow structures
Applied Thermal Engineering, 2007
This paper is an introduction to a new trend in the conceptual design of energy systems: the generation of flow configuration based on the ''constructal'' principle that the global performance is maximized by balancing and arranging the various flow resistances (the irreversibilities) in a flow system that is free to morph. The paper focuses on distribution and collection, which are flows that connect one point (source, or sink) with an infinity of points (volume, area, curve). The flow configurations that emerge from this principle are tree-shaped, and the systems that employ them are ''vascularized''. The paper traces the most recent progress made on constructal vascularization. The direction is from large-scale applications toward microscales. The large-scale tree-shaped designs of electric power distribution systems and networks for natural gas and water are now invading small-scale designs such as fuel cells, heat exchangers and cooled packages of electronics. These flow configurations have several properties in common: freedom to morph, multiple scales, hierarchy, nonuniform (optimal) distribution of scales through the available volume, compactness and finite complexity.
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.