Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Optimization principles for convective heat transfer

Optimization for convective heat transfer plays a significant role in energy saving and high-efficiency utilizing. We compared two optimization principles for convective heat transfer, the minimum entropy generation principle and the entransy dissipation extremum principle, and analyzed their physical implications and applicability. We derived the optimization equation for each optimization principle. The theoretical analysis indicates that both principles can be used to optimize convective heat-transfer process, subject to different objectives of optimization. The minimum entropy generation principle, originally derived from the heat engine cycle process, optimizes the convective heat-transfer process with minimum usable energy dissipation focusing on the heat–work conversion. The entransy dissipation extremum principle however, originally for pure heat conduction process, optimizes the heat-transfer process with minimum heat-transfer ability dissipation, and therefore is more suitable for optimization of the processes not involving heat–work conversion. To validate the theoretical results, we simulated the convective heat-transfer process in a two-dimensional foursquare cavity with a uniform heat source and different temperature boundaries. Under the same constraints, the results indicate that the minimum entropy production principle leads to the highest heat–work conversion while the entransy dissipation extremum principle yields the maximum convective heat-transfer efficiency.     

Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process

Based on theories of thermodynamics, the energy equation in terms of entransy in heat transfer process is introduced, which not only describes the change of entransy, but also defines the entransy consumption rate. According to the regularity of entransy change in heat transfer process and the effect of entransy consumption rate on the irreversibility of heat transfer process, it can be found that entransy is a state variable, from which a new expression for the second law of thermodynamics is presented. Then by setting entransy consumption rate and power consumption rate as optimization objective and constraint condition for each other, the Lagrange conditional extremum principle is used to deduce momentum equation, constraint equation and boundary condition for optimizing flow field of convective heat transfer, which are applied to simulate convective heat transfer coupling with energy equation in an enclosed cavity. Through the numerical simulation, the optimized flow field under different constraint conditions is obtained, which shows that the principle of minimum entransy consumption is more suitable than the principle of minimum entropy generation for optimizing convective heat transfer process.     

Application of Entransy Optimization to One-Stream Series-Wound and Parallel Heat Exchanger Networks

Entransy theory has developed in recent years to describe heat transfer behavior from another point of view. Entransy dissipation is proposed to evaluate the irreversibility of heat transfer and is used to optimize heat transfer processes. We apply this theory to the one-stream series-wound and parallel heat exchanger (HE) networks. The heat transfer optimization for the HE networks includes the distribution of the heat transfer area or heat load. The distribution of the cold fluid flow rate in parallel HE networks can also be optimized. For these problems, physical and mathematical models are set up, analyzed, and discussed with the entransy theory. It is found that the optimization objectives of these problems and the optimization directions of the extremum entransy dissipation principle are consistent. The optimized results for the distribution optimization problem with given heat load are in agreement with the uniformity principle of temperature difference field. Examples of simple one-stream HE networks are given; the distributions of the heat transfer area or heat load are optimized by the extremum entransy dissipation method.     

基于火积理论的螺旋折流板换热器的优化结构分析

为了比较平面螺旋折流板换热器和折面螺旋折流板换热器的传热和阻力性能,应用了换热器常用评价标准PEC准则和火积理论对两种换热器实验结果进行了分析,同时采用火积耗散极值原理对两种换热器的传热火积耗散率、阻力火积耗散率以及总火积耗散率进行了对比。结果表明:火积耗散理论分析换热器性能的结果与传统换热器评价标准PEC准则相符,说明了火积耗散理论的可靠性;折面螺旋折流板换热器的综合性能得到了有效的改进,火积耗散率也均优于原始结构,表明折面螺旋折流板换热器的性能得到较大改善;两种换热器传热火积耗散率值要远远大于阻力火积耗散率,约为阻力火积耗散率的一千余倍,说明传热损失为换热器的主要不可逆损失。     

Entransy flux of thermal radiation and its application to enclosures with opaque surfaces

Entransy is a new concept developed in recent years to measure the transport ability of heat at a temperature in conduction and convection. This paper develops the concept of entransy flux for thermal radiation in enclosures with opaque surfaces. The entransy balance equation and entransy dissipation function are derived. The minimum principle of radiative entransy loss is developed. The potentials and the heat fluxes distribution which meet the Stefan–Boltzmann’s law and the energy balance equation would make the radiative entransy loss minimum if the net heat flux of each surface or the thermal potentials of the surfaces are given. The extremum entransy dissipation principles (EEDP) for thermal radiation are developed. The minimum radiative entransy dissipation leads to the minimum average radiative thermal potential difference for prescribed total heat exchange and the maximum radiative entransy dissipation leads to the maximum heat exchange for prescribed average radiative thermal potential difference. The minimum and maximum principle can be concluded into the minimum thermal resistance principle (MTRP) for thermal radiation by defining the thermal resistance with the entransy dissipation. The EEDP or MTRP is proved to be reliable when they are used to optimize some radiative heat transfer problems, and a comparison is made between the minimum principle of entropy generation and the EEDP.     

Heat Transfer and Thermal Resistance Characteristics of Fin with Built-In Interrupted Delta Winglet Type

The heat transfer and fluid flow characteristics of a new type of fin with built-in interrupted delta winglets is studied in this paper by three-dimensional numerical simulation. In order to ensure reliability of numerical model, plate fin with common-flow-up delta winglets is firstly simulated. The comparison of numerical and experimental results shows a maximum deviation of 11.4% within the entire range of Reynolds number. The computational results show that heat transfer capacity and overall performance increase by 35–60% and 19–64%, respectively. The flow field visualization shows that the interrupted delta winglets can produce longitudinal vortices at the rear of delta winglets and reduce the wake zone behind the tube, so the proposed fin can enhance heat transfer accompanied by low pressure loss. The field synergy theory and entransy dissipation extremum principle are employed on analyzing the mechanism of heat transfer enhancement. The results indicate that enhancement heat transfer mechanism of interrupted delta winglets can be explained as the result of the decrease of synergy angle and reduction of the entransy dissipation.     

Thermo-Hydraulic Performance Evaluation,Field Synergy,and Entransy Dissipation Analysis for Hexagon-Like and Circular-Like Pin Finned Tube Bundles

In this paper, a comprehensive thermo-hydraulic performance evaluation for air flow across the hexagon-like and circular-like staggered pin finned tube bundle heat transfer surfaces has been numerically carried out by adopting the performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving. In addition, the simulation results have also been analyzed from the viewpoints of field synergy principle and entransy dissipation extreme principle. The results indicate that the heat transfers are all enhanced based on identical pressure drop for the hexagon-like and circular-like pin finned tube bundles within the inlet velocity range from 1 m/s to 10 m/s studied. Moreover, the circular-like pin finned tube bundle offers the lowest friction factor increase ratio for the same Nusselt number increase ratio. Furthermore, the synergy between velocity and fluid temperature gradient has been proved again, having inherent consistency with the dissipation of entransy.     

Field synergy analysis and optimization of the convective mass transfer in photocatalytic oxidation reactors

A convective mass transfer field synergy equation with a specific boundary condition for photocatalytic oxidation reactors developed based on the extremum principle of mass transfer potential capacity dissipation can be used to increase the field synergy between the velocity and contaminant concentration gradient fields over the entire fluid flow domain to enhance the convective mass transfer and increase the contaminant removal effectiveness of photocatalytic oxidation reactors. The solution of the field synergy equation gives the optimal flow field, having the best field synergy for a given viscous dissipation, which maximize the contaminant removal effectiveness. As an illustrative example, the field synergy analysis for laminar mass transfer in plate type reactors is presented. The analysis shows that generating multiple longitudinal vortex flow in the plate type reactor effectively enhances the laminar mass transfer. With the guide of the optimal velocity pattern, the discrete double-inclined ribs can be introduced in actual applications to generate the desired multi-longitudinal vortex flow, so as to enhance the laminar mass transfer, and consequently, improve the contaminant removal performance. The experimental result shows that the contaminant removal effectiveness for the discrete double-inclined ribs plate reactor is increased by 22% compared to the smooth plate reactor.     

An entransy dissipation-based optimization principle for building central chilled water systems

The recently developed entransy theory is introduced in this paper to tackle the heat transfer processes in building central chilled water systems so as to improve their energy efficiency. We first divide the irreversible heat transfer processes into four categories: (1) air mixing processes; (2) heat transfer processes between chilled water and air; (3) chilled water mixing processes; and (4) heat transfer processes between chilled water and refrigerant. The formulas of entransy dissipation rates for each irreversible process are derived, and then the total entransy dissipation rate in the whole chilled water systems is obtained, which connects the geometrical structures of each heat exchanger and the operating parameters of each fluid directly to the demands of users and the supply of refrigerating unit. Based on the formula of entransy dissipation rate together with the conditional extremum method in mathematics, two optimization equation groups are deduced theoretically. Simultaneously solving such equation groups will easily find the optimal central chilled water system with the highest energy efficiency. Finally, a simple building central chilled water system with two users is taken as an example to illustrate the applications of the newly proposed optimization principle.     

Field synergy analysis and optimization of decontamination ventilation designs

The field synergy principle has been validated to be an effective tool for enhancing convective heat transfer capability. Since convective mass transfer is analogous to convective heat transfer, the field synergy principle has been extended to convective mass transfer analyses to enhance the overall decontamination rate of indoor ventilation systems. According to the field synergy principle, the overall decontamination capability and the utilization efficiency of the air are both influenced by the synergy between the velocity vectors and the contaminant concentration gradients. Furthermore, in order to derive a method to improve the synergy based on the essence of convective mass transfer, the mass transfer potential capacity dissipation function is defined, and then the convective mass transfer field synergy equation is obtained by seeking the extremum of the mass transfer potential capacity dissipation function for a set of specified constraints. The convective mass transfer field synergy equation can be solved to find the optimized air velocity distribution to increase the field synergy and the overall decontamination capability. The optimized air velocity field provides guidance for optimizing ventilation system designs.     

A new approach to analysis and optimization of evaporative cooling system I: Theory

Using the analogy between heat and mass transfer processes, the recently developed entransy theory is extended in this paper to tackle the coupled heat and mass transfer processes so as to analyze and optimize the performance of evaporative cooling systems. We first introduce a few new concepts including the moisture entransy, moisture entransy dissipation, and the thermal resistance in terms of the moisture entransy dissipation. Thereinafter, the moisture entransy is employed to describe the endothermic ability of a moist air. The moisture entransy dissipation on the other hand is used to measure the loss of the endothermic ability, i.e. the irreversibility, in the coupled heat and mass transfer processes – this total loss is shown to consist of three parts: (1) the sensible heat entransy dissipation, (2) the latent heat entransy dissipation, and (3) the entransy dissipation induced by a temperature potential. Finally the new thermal resistance, defined as the moisture entransy dissipation rate divided by the squared refrigerating effect output rate, is recommended as an index to effectively reflect the performance of the evaporative cooling system. In the end, two typical evaporative cooling processes are analyzed to illustrate the applications of the proposed concepts.     

The forced air cooling heat dissipation performance of different battery pack bottom duct

Due to the requirement of the battery for the thermal management system, based on the coupling relationship between the velocity field and the thermal flow field of the field synergy principle, the flow paths of the forced air cooling system for different battery packs were analyzed. First, the thermodynamic parameters of the battery were collected through experiments and verified by simulation. Secondly, based on the collected thermodynamic parameters of the battery, the heat generation model of the battery, the heat conduction model of the gas, and the coupled heat dissipation model of the battery and air were established. Determine the boundary conditions, calculation methods and evaluation indicators required for simulation; Finally, based on four different driving conditions, the forced air cooling performance of the double “U” shape duct and double “1” type duct is simulated. Through the analysis of the results, the dual “U” air ducts have a more heat dissipation effect on the battery pack than the double “1” shape duct. The results conform to the definition of the field synergy principle for the coupling relationship between the velocity field and the heat flow field. Then research provide references for the design of battery packs and matching of cooling systems.     

基于火积理论的多级套管式相变蓄热系统优化

本文基于最小火积耗散热阻原理,在考虑相变材料导热热阻以及非稳态传热过程的基础上,对多级套管式相变蓄热系统的融化温度进行了数值优化,获得了最优融化温度分布。在此基础上,研究了相变材料导热系数和传热管长度对最优融化温度、火积耗散热阻和平均蓄热速率的影响。研究结果表明,与现有理论优化方法相比,本文提出的数值优化方法具有更好的适用性;优化后多级套管式相变蓄热系统可有效提高相变蓄热系统的平均蓄热速率,降低火积耗散热阻;随着相变材料导热系数增大和传热管长度增加,多级套管式相变蓄热系统最优融化温度的温差愈加明显,其强化传热性能呈上升趋势。     

Experimental performance comparison and trade-off among air-based precooling methods for postharvest apples by comprehensive multiscale thermodynamic analyses

Air-based precooling methods including room cooling and forced-air cooling were traditionally used for postharvest horticultural products. In this study, disturbed-air cooling with different layouts was proposed for the trade-off between room cooling with long cooling time and forced-air cooling with high energy consumption. Lab-scale experiments with 30 bins of postharvest apples were conducted using the aforementioned methods to measure the temperature history. Multiscale thermodynamic analyses from energy, entropy, exergy, and entransy perspectives were then performed. The time evolution of transient quantities and overall comparison of the trade-off performances were further discussed. The ventilation power and transformed heat became more significant respectively for the total energy consumption and heat load during the precooling processes. The rates of entropy generation, exergy destruction, and entransy dissipation reduced in consistent with the tendency of heat rejection from all bins. The major part of these losses was resulted by the ventilation for convective heat transfer between cold air and apples and became more significant during later stage of precooling processes. The middle-parallel disturbed-air cooling achieved the best trade-off between the lowest energy consumption for room cooling and the lowest maximum seven-eighths cooling time for forced-air cooling by respectively reaching 81.68% and 28.82% of the optimization potential. The best trade-off between the lowest thermodynamic loss for room cooling and the lowest heat transfer ability loss for forced-air cooling was also achieved by this method with around 55% to 62% optimization of the coefficients of performance, around 83% optimization of the entropy generation ratio, around 58% to 62% optimization of the exergy destruction ratio, and around 36% optimization of the entransy dissipation ratio.     

Field synergy optimization and enhanced heat transfer by multi-longitudinal vortexes flow in tube

The field synergy equation for steady laminar convection heat transfer was derived by conditional variation calculus based on the least dissipation of heat transport potential capacity. The optimum velocity field with the best heat transfer performance and least flow resistance increase can be obtained by solving the synergy equation. The numerical simulation of laminar convection heat transfer in a straight circular tube shows that the multi-longitudinal vortex flow in the tube is the flow pattern that enhances the heat transfer enormously. Based on this result, a novel enhanced heat transfer tube, the discrete double-inclined ribs tube (DDIR-tube), is developed. The flow field of the DDIR-tube is similar to the optimal velocity field. The experimental results show that the DDIR-tube has better comprehensive heat transfer performance than the current heat transfer enhancement tubes. The present work indicates that new heat transfer enhancement techniques could be developed according to the optimum velocity field.     

缩放管管外流动沸腾换热的数值模拟与场协同分析

本文利用FLUENT软件对制冷剂R134a在光管和缩放管水平管外沸腾传热进行了三维数值模拟,得到了其饱和泡状沸腾过程中体积含汽率的分布规律,并比较了它们的换热系数,结果表明:缩放管外侧能够很好地强化沸腾传热.此外,通过改变边界条件分析了质量流量、热流密度的变化对缩放管管外沸腾换热系数的影响.最后应用场协同理论,从局部换热角度分析其强化机理.研究表明:缩放管水平管外沸腾换热得到强化的原因是其凹槽前后的速度场与温度梯度场之间夹角更小,协同程度更好.     

A new approach to analysis and optimization of evaporative cooling system II: Applications

After introducing the concepts of moisture entransy, moisture entransy dissipation and thermal resistance based on moisture entransy dissipation (TRMED) in part I of this study, we further analyze several direct/indirect evaporative cooling processes based on the above concepts in this part. The nature of moisture entransy, moisture entransy dissipation and TRMED during evaporative cooling processes was reexamined. The results demonstrate that it is the moisture entransy, not the enthalpy, that represents the endothermic ability of a moist air, and reducing the entransy dissipation by both enlarging the thermal conductance of heat and mass transfer, and decreasing the temperature potential of the moist air, i.e. the difference between the dry-bulb temperature of moist air over its dew-point temperature, will result in a smaller system TRMED, and consequently a better evaporative cooling performance. Then, a minimum thermal resistance law for optimizing evaporative cooling systems is developed. For given mass flow rates of both moist air and water, with prescribed moist air and water conditions, minimizing the TRMED will actually lead to the most efficient evaporative cooling performance. Finally, the thermal conductance allocation for an indirect evaporative cooling system is optimized to illustrate the application of the proposed minimum thermal resistance law.     

Numerical investigations of curved square channel from the viewpoint of field synergy principle

A curved square channel in laminar flow is numerically investigated based on the classical Navier–Stokes equations from the viewpoint of the field synergy principle. The field synergy principle may accurately describe the curved channel has higher convective heat transfer rate in the case that the heat transfer surface is specified on the outer wall, rather than on the inner wall. The field synergy principle could also be responsible for that the curved channel can enhance the convective heat transfer significantly at the cost of the slight increase of the flow resistance. The field synergy number represents the degree of the synergy between the temperature gradient and the velocity vector, the higher field synergy number leads to the higher convective heat transfer rate under the same Reynolds number and Prandtl number. The field synergy number plays the same positive role in the convective heat transfer whether the fluid is heated or cooled.     

The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer

In this paper the concept of field synergy (coordination) principle is briefly introduced first, and then its numerical verification is presented. A dimensionless number, field synergy number Fc, is defined as an indication of the synergy degree between velocity and temperature field for the entire flow and heat transfer domain. It is found that for the ideal case, this number should equal one, and for most of the engineering heat transfer cases, its value is far from being equal to one, showing a large room for the heat transfer enhancement study. Then the applications of the principle are discussed, with focusing being paid on the application for developing new type of enhanced techniques. Three examples are provided to demonstrate the importance and feasibility of the field synergy principle.