Constructal theory is the view that the generation of “designedness” in nature is a universal (physics) phenomenon that can be based on principle (the constructal law): “For a finite-size flow system to persist in time (to live) its configuration must change in time so that it provides greater and greater access to its currents”. This principle predicts natural form across the board, from river basins to animal design, engineering and social dynamics. In this introduction to the theory we show examples of vascular designs at large and small scales and multi-objective flow configurations.
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This paper presents a series of examples in which the global performance of flow systems is optimized subject to global constraints. The flow systems are assemblies of ducts, channels and streams shaped as Ts, Ys and crosses. In pure fluid flow, thermodynamic performance maximization is achieved by minimizing the overall flow resistance encountered over a finite-size territory. In the case of more complex objectives such as the distribution of a stream of hot water over a territory, performance maximization requires the minimization of flow resistance and the leakage of heat from the entire network. Taken together, these examples show that the geometric structure of the flow system springs out of the principle of global performance maximization subject to global constraints. Every geometric detail of the optimized flow structure is deduced from principle. The optimized structure (design, architecture) is robust with respect to changes in some of the parameters of the system. The paper shows how the geometric optimization method can be extended to other fields, e.g., urban hydraulics and, in the future, exergy analysis and thermoeconomics.
This paper shows that the main geometric features of a flow component can be deduced from the thermodynamic optimization of the global performance of the largest flow system that incorporates the component. This approach represents a departure from the usual approach, where a flow component is optimized in isolation. The example chosen is the counterflow heat exchanger of the environmental control system (ECS) used on modern aircraft. The heat exchanger is fitted with a diffuser and a nozzle for the ram air, and the ECS runs on the boot strap air cycle, employing an additional compressor and turbine. Two heat transfer surface types are considered, finned and smooth parallel plates. Numerical results are reported for the external geometric aspect ratios of the heat exchanger, and for the plate-to-plate spacing of the smooth-plates model. It is shown that the optimized geometry for the core with finned surfaces is nearly the same as the optimized geometry for the core with smooth plates. Several of the optimized geometric features are robust with respect to changes in external parameters that vary from one application to the next. The method illustrated in this paper – the thermodynamic (constructal) optimization of flow geometry – is applicable to any system that runs on the basis of a limited amount of fuel (exergy) installed onboard, e.g., automobiles, ships, portable tools.
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: The objective of this research effort is to construct a purely theoretical foundation for the phenomenon of turbulent heat transfer. In this first annual report, the current methodology of theoretical research is reexamined critically. The report outlines in three self-standing units (papers) the new theoretical viewpoint that turbulence is the result of inviscid flow buckling. This viewpoint leads to first examples of theoretical prediction of turbulence parameters, for instance, the transition to turbulence, the flapping motion of turbulent jets, the frequency of vortex shedding and the meandering and mixing mechanism of thermal plumes. (Author)
This paper describes a comprehensive study of the natural convection phenomenon occurring inside a porous layer with both heat and mass transfer from the side. The natural circulation is driven by a combination of buoyancy effects due to both temperature and concentration variations. The first part of the study consists of an extensive series of numerical simulations conducted in the range 0.01 ⩽ Le ⩽ 100, 50 ⩽ Ra H ⩽ 104, − 5 ⩽ N ⩽ +3 and H/L = 1, where Le, Ra H , N and H/L are the Lewis number, Dareymodified Rayleigh number, buoyancy ratio and geometric aspect ratio of the porous layer. In the second part, the phenomenon is studied based on scale analysis : the chief conclusions of this part, namely, the order-ofmagnitude predictions for the overall heat and mass transfer rates and their respective domains of validity, are shown to be in agreement with the results produced by discrete numerical experiments. Furthermore, the scale analysis is used to sort out the many effects that influence the overall heat and mass transfer results of numerical experiments.
The optimum thermodynamic match between two streams at different temperatures is determined by maximizing the power generation (or minimizing the entropy generation) associated solely with the stream-to-stream interaction. Each stream experiences a change of phase. It is shown that the optimum is marked by an optimal ratio between the stream mass flow rates, and an optimal ratio between the two heat exchanger sizes when the total heat transfer area is fixed. The sensitivity of the optimum relative to the various physical parameters of the two-stream arrangement is documented systematically. The study shows that the optimum is “robust” relative to changes in several parameters such as the distribution of heat transfer coefficient along the hot-end heat exchanger, and the model used for the thermodynamic behavior of steam.
In this paper the optimization of fluid networks is based on the minimization of pumping power requirement. The total pipe network volume is constrained. It is shown that only in special cases the minimization of pumping power leads to the same architecture as the minimization of pressure drop or flow resistance. Fundamentals of fluid network optimization are developed for both spanning networks and networks where new non-consumer points are added (Gilbert–Steiner points). It is shown that networks with minimum pumping power must not contain loops. The influence of gravity on the optimization of flow configuration is also addressed. The principles developed in the paper are illustrated with an example representing a set of ten vertices to be connected with pipes. The paper provides designers with more effective basic tools for the conceptual design of fluid networks.
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Papers on convection in porous media continue to be published at the rate of over 100 per year. This indication of the continued importance of the subject, together with the wide acceptance of the first edition, has encouraged us to prepare an expanded second edition. We have retained the basic structure and most of the text of the first edition. With space considerations in mind, we have been selective in our choice of references, but nevertheless there are over 600 new references. We also made an effort to highlight new conceptual developments and engineering applications. In the introductory material, we judged that Chapters 2 and 3 needed little alteration (though there is a new Section 2.6 on other approaches to the topic), but our improved understanding of the basic modeling of flow through a porous medium has led to a number of changes in Chapter 1, both within the old sections and by the addition of a section on turbulence in porous media, and a section on fractured media, deformable media, and complex porous structures. In Chapter 4, on forced convection, we have added major new sections on compact heat exchangers, on heatlines for visualizing convection, and on constructal tree networks for the geometric minimization of the resistance to volume-to-point flows in heterogeneous porous media.
Here we report the heat and fluid flow characteristics of counterflow heat exchangers with tree-shaped line-to-line flow channels. The flow structures of the hot and cold sides are sequences of point-to-line trees that alternate with upside-down trees. The paper shows under what conditions the tree vascularization offers greater heat flow access than corresponding conventional designs with parallel single-scale channels. The analytical part is based on assuming fully developed laminar flow in every channel and negligible longitudinal conduction in the solid. The numerical part consists of simulations of three-dimensional convection coupled with conduction in the solid. It is shown that tree vascularization offers greater heat flow access (smaller global thermal resistance) than parallel channels when the number of pairing levels increases and the available pumping power or pressure drop is specified. When the solid thermal conductivity increases, the heat transfer effectiveness decreases because of the effect of longitudinal heat conduction. The nonuniformity in fluid outlet temperature becomes more pronounced when the number of pairing levels increases and the pumping power (or pressure drop number) increases. The nonuniformity in outlet fluid temperature decreases when the solid thermal conductivity increases.
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Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): ‘for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it’. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution ‘movie’ runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of ‘engine and brake’ designs.
