Thermodynamic optimization of geometry in engineering flow systems

This review draws attention to an emerging body of work that relies on global thermodynamic optimization in the pursuit of flow system architecture. Exergy analysis establishes the theoretical performance limit. Thermodynamic optimization (or entropy generation minimization) brings the design as closely as permissible to the theoretical limit. The design is destined to remain imperfect because of constraints (finite sizes, times, and costs). Improvements are registered by spreading the imperfection (e.g., flow resistances) through the system. Resistances compete against each other and must be optimized together. Optimal spreading means spatial distribution, geometric form, topology, and geography. System architecture springs out of constrained global optimization. The principle is illustrated by simple examples: the optimization of dimensions, spacings, and the distribution (allocation) of heat transfer surface to the two heat exchangers of a power plant. Similar opportunities for deducing flow architecture exist in more complex systems for power and refrigeration. Examples show that the complete structure of heat exchangers for environmental control systems of aircraft can be derived based on this principle.     

Constructal tree-shaped flow structures

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.     

Entropy flow,entropy generation,exergy flux,and optimal absorbing temperature in radiative transfer between parallel plates

Taking nonequilibrium radiative heat transfer between two surfaces as an example, the nonequilibrium thermodynamics of radiation is studied and discussed. The formulas of entropy flow, entropy generation, exergy flux, and optimal temperature of absorbing surface for maximum exergy output are derived. The result is a contribution to the thermodynamic analysis and optimization of solar energy utilization and can be applied in more complex radiative heat transfer cases.     

Entropy flow, entropy generation, exergy flux, and optimal absorbing temperature in radiative transfer between parallel plates

Taking nonequilibrium radiative heat transfer between two surfaces as an example, the nonequilibrium thermodynamics of radiation is studied and discussed. The formulas of entropy flow, entropy generation, exergy flux, and optimal temperature of absorbing surface for maximum exergy output are derived. The result is a contribution to the thermodynamic analysis and optimization of solar energy utilization and can be applied in more complex radiative heat transfer cases.     

Thermodynamic optimization of geometric structure in the counterflow heat exchanger for an environmental control system

This paper shows that the internal geometric configuration of a component can be deduced by optimizing the global performance of the installation that uses the component. The example chosen is the counterflow heat exchanger that serves as condenser in a vapor-compression-cycle refrigeration system for environmental control of aircraft. The optimization of global performance is achieved by minimizing the total power requirement or the total entropy generation rate. There are three degrees of freedom in the heat exchanger configuration, which is subjected to two global constraints: total volume, and total volume (or weight) of wall-material. Numerical results show how the optimal configuration responds to changes in specified external parameters such as refrigeration load, fan efficiency, and volume and weight. In accordance with constructal theory and design [1], it is shown that the optimal configuration is robust: major features such as the ratio of diameters and the flow length are relatively insensitive to changes in the external parameters.     

Comprehensive exergy analysis of a ground-source heat pump system for both building heating and cooling modes

This paper presents a comprehensive exergy analysis of three circuits and whole system of a ground-source heat pump (GSHP) for both building heating and cooling modes. The purpose is to search out the key potential energy saving components. The analytical formulae of exergy loss, exergy efficiency, exergy loss ratio, exergy loss coefficient and thermodynamic perfect degree are derived, respectively. The results show that these exergy indexes should be used integratively, and in the whole system the location of maximum exergy loss ratio is the compressor, while the location of minimum exergy efficiency and thermodynamic perfect degree is the ground heat exchanger, so that the compressor and the ground heat exchanger should be primarily improved. The results also indicate that the exergy loss of a GSHP system for building heating mode is bigger than that of cooling mode, and the exergy efficiency of a whole GSHP system is obviously lower than those of its components for both building heating and cooling modes. Therefore, a comprehensive exergy analysis of a GSHP should be paid more attention to. The results may provide guidelines for the design and optimization of GSHP systems.     

构形理论:广义热力学优化的新方向之一

回顾了构形理论的产生与发展过程，指出其是广义热力学优化发展的一个新方向；阐明了热力学优化过程中运用该理论对装置进行优化的重要作用；综述了该理论拓展应用于传热、流体流动、干燥、交通运输、管网以及经济决策等领域现状；介绍了自然界中各种形式的系统和组织(生命体和非生命系统)，其结构均源自于要达到整体性能最优目的这一深刻命题；指出了构形理论与场协同理论结合进行研究是下一步的发展方向。     

基于能级概念的火用经济学计价策略

正确合理地对火用流计价,确定从燃料到产品(火用)流的转换过程中费用形成及变化过程,是实现能量系统的(火用)经济学分析和优化的关键之一.将能级的概念引入热经济学计价体系,把供入能流按能级拆分,依据能级相近最大化相供的原则,解决能量取出与供入间的对应问题,提出了基于能级相近最大化相供的(火用)流计价策略,以减少求解过程中所涉及的未知变量数,说明产品(火用)流存在时的附加方程引入情况.最后以典型的热电联产系统(CGAM系统)的(火用)经济分析优化中(火用)流计价为例,介绍了该计价方法的应用.     

Dynamic multi-objective optimization applied to a solar-geothermal multi-generation system for hydrogen production,desalination, and energy storage

The design of optimal energy systems is vital to achieving global environmental and economic targets. In the design of solar-geothermal multi-generation systems, most previous investigations have relied on the static multi-objective optimization approach (SMOA), which may leave considerable room for improvement under certain conditions. In this numerical study, the optimal condition at which to operate a solar-geothermal multi-generation system – which can simultaneously produce hydrogen, fresh water, electricity, and heat, along with storing energy ? is determined via a dynamic multi-objective optimization approach (DMOA). Optimization is performed using a combination of NSGA-II and TOPSIS, and the results are benchmarked against those of SMOA. The decision variables include the solar area, geothermal water extraction mass flow, and hydrogen storage pressure. The objective functions include the production of electricity, heat, hydrogen, and fresh water, along with the exergy and energy efficiencies and the payback period. It is found that when compared with SMOA, DMOA can significantly improve all the objective functions. The annual production of electricity, heat, hydrogen, and fresh water increases by 14.4, 16.1, 13.5, and 14.3%, respectively, while the average annual exergy and energy efficiencies increase by 5.2 and 3.0%, respectively. The use of DMOA also reduces the payback period from 5.56 to 4.43 years, with a 4.4% reduction in hydrogen storage pressure. This shows that compared with a static approach such as SMOA, DMOA can improve the exergy and energy efficiencies, economic viability, and safety of a solar-geothermal multi-generation system.     

Investigation of potential of improvement of helical coils based on avoidable and unavoidable exergy destruction concepts

An inevitable problem challenges heat exchanger designers is that the heat transfer augmentation in a thermal system is always achieved at the expense of an increase in pressure loss. Thus, the trade-off by choosing the most proper configuration and best flow condition has become the critical problem for design work. The brief survey on literature shows that optimal Reynolds number of laminar forced convection in a helical tube, was specified based on minimum entropy generation. Therefore, the present study analyzes the thermodynamic potential of improvement for steady, laminar, fully developed, forced convection in a helical coiled tube subjected to uniform wall temperature based on the concept of avoidable and unavoidable exergy destruction. The influence of various parameters such as coil curvature ratio, dimensionless inlet temperature difference, dimensionless passage length of the coil, and fluid properties on avoidable exergy destruction have been investigated for water as working fluid. Results show considerable potential of thermodynamic optimization of helical coil tubes. In addition, a relation for determining the amount of optimum Dean Number is proposed for the range considered in the present study.     

Determining the optimal pinch point temperature difference of evaporator for waste heat recovery

From the perspective of exergy recovery, the pinch point temperature difference (PPTD) of evaporator for waste heat recovery has been optimized by exergo-economic principle using the annual net profit per transferred heat load as objective function. And for comparison, another criterion, the annual total cost per transferred heat load from the view of exergy destruction, is introduced. Taking organic fluid R600a as an example, the effects of thermodynamic and economic parameters on the optimal PPTD are examined. It is found that the optimal PPTD is closely related to the total investment costs of evaporator. Different trends on the optimal PPTD are provided with the variations of thermodynamic and economic parameters. And the flow exergy loss has little impact on the optimal PPTD of evaporator. The optimal PPTD from the perspective of exergy recovery is larger than that from the view of exergy destruction.     

Thermodynamic optimization of tree-shaped flow geometries

In this paper we optimize the performance of several classes of simple flow systems consisting of T- and Y-shaped assemblies of ducts, channels and streams. In each case, the objective is to identify the geometric configuration that maximizes performance subject to several global constraints. Maximum thermodynamic performance is achieved by minimization of the entropy generated in the assemblies. The boundary conditions are fixed heat flow per unit length and uniform and constant heat flux. The flow is assumed laminar and fully developed. Every geometrical detail of the optimized structure is deduced from the constructal law. Performance evaluation criterion is proposed for evaluation and comparison of the effectiveness of different tree-shaped design heat exchangers. This criterion takes into account and compare the entropy generated in the system with heat transfer performance achieved.     

Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams

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.     

Thermodynamic evaluation of hydrogen and electricity cogeneration coupled with very high temperature gas-cooled reactors

Hydrogen production using thermal energy, derived from nuclear reactor, can achieve large-scale hydrogen production and solve various energy problems. The concept of hydrogen and electricity cogeneration can realize the cascade and efficient utilization of high-temperature heat derive for very high temperature gas-cooled reactors (VHTRs). High-quality heat is used for the high-temperature processes of hydrogen production, and low-quality heat is used for the low-temperature processes of hydrogen production and power generation. In this study, two hydrogen and electricity cogeneration schemes (S1 and S2), based on the iodine-sulfur process, were proposed for a VHTR with the reactor outlet temperature of 950 °C. The thermodynamic analysis model was established for the hydrogen and electricity cogeneration. The energy and exergy analysis were conducted on two cogeneration systems. The energy analysis can reflect the overall performance of the systems, and the exergy analysis can reveal the weak parts of the systems. The analysis results show that the overall hydrogen and electricity efficiency of S1 is higher than that of S2, which are 43.6% and 39.2% at the hydrogen production rate of 100 mol/s, respectively. The steam generators is the components with the highest exergy loss coefficient, which are the key components for improving the system performance. This study presents a theoretical foundation for the subsequent optimization of hydrogen and electricity cogeneration coupled with VHTRs.     

Constructal design of nanofluids

We develop a constructal approach that is capable of finding constructal microstructure of nanofluids for constructal system performance. The approach converts the inverse problem of optimizing the microstructure for the best system performance into a forward one by first specifying a type of microstructures and then optimizing system performance with respect to the available freedom within the specified type of microstructures. The approach is applied to constructal design of nanofluids with any branching level of tree-shaped nanostructures in a circular disc with uniform heat generation. The constructal configuration and constructal system thermal resistance have some elegant universal features for both cases of given aspect ratio of the periphery sectors and given the total number of slabs in the periphery sectors, respectively. While our focus is on the constructal design and optimization of nanofluids microstructure, the methodologies and results are equally valid for other problems such as heat conduction optimization for cooling a disc-shaped area.     

Constructal theory of global circulation and climate

The constructal law states that every flow system evolves in time so that it develops the flow architecture that maximizes flow access under the constraints posed to the flow. Earlier applications of the constructal law recommended it as a self-standing law that is distinct from the second law of thermodynamics. In this paper, we develop a model of heat transport on the earth surface that accounts for the solar and terrestrial radiation as the heat source and heat sink and with natural convection loops as the transport mechanism. In the first part of the paper, the constructal law is invoked to optimize the latitude of the boundary between the Hadley and the Ferrel cells, and the boundary between the Ferrel and the Polar cells. The average temperature of the earth surface, the convective conductance in the horizontal direction as well as other parameters defining the latitudinal circulation also match the observed values. In the second part of the paper, the constructal law is invoked in the analysis of atmospheric circulation at the diurnal scale. Here the heat transport is optimized against the Ekman number. Even though this second optimization is based on very different variables than in the first part of the paper, it produces practically the same results for the earth surface temperature and the other variables. The earth averaged temperature difference between day and night was found to be approximately 7 K, which matches the observed value. The accumulation of coincidences between theoretical predictions and natural flow configuration adds weight to the claim that the constructal law is a law of nature.     

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.     

Economic optimization of shell and tube heat exchanger based on constructal theory

In this paper, the new approach of constructal theory has been employed to design shell and tube heat exchangers. Constructal theory is a new method for optimal design in engineering applications. The purpose of this paper is optimization of shell and tube heat exchangers by reduction of total cost of the exchanger using the constructal theory. The total cost of the heat exchanger is the sum of operational costs and capital costs. The overall heat transfer coefficient of the shell and tube heat exchanger is increased by the use of constructal theory. Therefore, the capital cost required for making the heat transfer surface is reduced. Moreover, the operational energy costs involving pumping in order to overcome frictional pressure loss are minimized in this method. Genetic algorithm is used to optimize the objective function which is a mathematical model for the cost of the shell and tube heat exchanger and is based on constructal theory. The results of this research represent more than 50% reduction in costs of the heat exchanger.     

Thermodynamic optimization of heat‐transfer equipment configuration in an environmental control system

In this paper, we show that many features of a heat transfer installation can be deduced from the maximization of the global performance of the greater system that employs the installation. The heat transfer installation is a series of two cross‐flow heat exchangers. The greater system is the environmental control system (ECS) of an aircraft. The global performance objective is the minimization of the total thermodynamic irreversibility of the ECS. Several architectural features are deduced from principle: the relative position of the two heat exchangers, their relative sizes, and all the geometric aspect ratios of the two heat exchanger cores. We find that the optimized architecture is insensitive (robust) to changes in some of the external parameters. Robustness is a useful feature because it simplifies the design work. Furthermore, one design that is built can be expected to function at near‐optimal levels when the external parameters change. The application of this method of topology optimization to more complex systems is discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Constructal design of salt‐gradient solar pond fields

Salt‐gradient solar ponds (SGSPs) are water bodies that capture and accumulate large amounts of solar energy. The design of an SGSP field has never been analyzed in terms of studying the optimal number of solar ponds that must be built to maximize the useful energy that can be collected in the field, or the most convenient way to connect the ponds. In this paper, we use constructal design to find the optimal configuration of an SGSP field. A steady‐state thermal model was constructed to estimate the energy collected by each SGSP, and then a complementary model was developed to determine the final temperature of a defined mass flow rate of a fluid that will be heated by heat exchangers connected to the solar ponds. By applying constructal design, four configurations for the SGSP field, with different surface area distribution, were evaluated: series, parallel, mixed series‐parallel and tree‐shaped configurations. For the study site of this investigation, it was found that the optimal SGSP field consists of 30 solar ponds of increasing surface area connected in series. This SGSP field increases the final temperature of the fluid to be heated in 22.9%, compared to that obtained in a single SGSP. The results of this study show that is possible to use constructal theory to further optimize the heat transfer of an SGSP field. Experimental results of these configurations would be useful in future works to validate the methodology proposed in this study. Copyright © 2016 John Wiley & Sons, Ltd.