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.     

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.     

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.     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

Field synergy principle analysis on fully developed forced convection in porous medium with uniform heat generation

In the presence of uniform heat source, the energy equation for forced convective heat transfer in porous medium between two parallel plates is solved for fully developed flow. Field synergy analysis is performed with emphasis on the intersection angle between the velocity vector and temperature gradient vector with the inclusion of heat generation. Maximum local intersection angle corresponds to location with the highest resistance to heat convection. Relationship between Nusselt number and field synergy for forced convection in the presence of heat generation is studied. It is necessary to define a modified intersection angle in order to compare the wall heat transfer coefficient for convective heat transfer processes with uniform heat source.     

加肋旋转对相变蓄热器蓄热性能的影响及场协同分析

建立加肋旋转的相变蓄热器模型,通过数值模拟研究不同转速下蓄热器的蓄热特性,并利用场协同理论进行相应的热分析。结果表明:加肋并旋转可显著提升相变蓄热器蓄热效果,缩短蓄热时间;通过提升转速可降低蓄热过程的场协同角,但过高的提升转速反而会使协同角增大,降低流动与换热协同性。从节能和场协同性角度综合考虑,不宜过高提升转速,转速控制在0.1~0.3 r/min的范围为最佳。     

Experimental verification of the field synergy principle

In this paper, the basic idea of the field synergy principle (FSP) is briefly reviewed and is validated experimentally by incompressible flow through a square duct with an imposed temperature difference between vertical walls and perfectly insulated on the horizontal walls. This creates a situation where the steamwise flow velocity is normal to the cross section temperature gradient. The experimental results show the independency of crosswise heat transfer rate on the steamwise flow velocity. Detailed discussion is provided to account for some minor deviation from the expected results of FSP.     

关于管内单相对流换热强化的极限问题

从场协同理论出发,分析了通道内表面全部为射流冲击换热表面时的极限换热率;将全射流冲击管内换热与普通流动管内换热进行了比较。给出了层流和紊流工况下全射流冲击换热可能达到的最大强化比。针对相同R e,分析得出:在层流充分发展段,全射流冲击通道的强化极限是16.9倍;在紊流充分发展段是3.5倍。综合现有各种通道内强化换热的研究结果进行比较,其换热率均低于全射流冲击管内换热率,其中层流工况以折流翅片式通道和交叉缩放椭圆管的换热率与极限换热率最为接近;紊流工况以内插螺旋丝强化管最为接近。     

Numerical study and field synergy analysis on CO selective methanation packed-bed reactor

Carbon monoxide selective methanation (CO-SMET) is one of the most efficient technologies for hydrogen purification and CO deep removal. This paper applies the field synergy principle for a deep understanding on the chemically reactive flow in a CO-SMET tubular reactor. The variation of CO conversion rate under different operating conditions is interpreted, at the first time, as relevant to the variation of the synergy angle between temperature and gas concentration fields. Sensitive analyses of the bed pressure, CO/CO₂ ratio, heat exchange modes, etc., are studied to obtain the profile of field synergy angle in the inlet gas temperature range of 373 K – 873 K. It is found that the region with synergy angles between 0° and 70° enhances the heat transfer between mass transfer and contributes the main output of CO conversion. This work provides a fundamental basis on the future optimal design of CO–SMET reactors.     

对流换热场协同理论的新视角

从能量方程出发，对过增元教授提出的对流换热场协同理论公式变形，得到另一种形式的速度场和温度场的协同关系。研究表明，除物性外对流的换热强度主要取决于与温度和速度积的散度，并通过例子对其进行了探讨。     

Field synergy principle in forced convection of plane Couette–Poiseuille flows with effect of thermal asymmetry

The field synergy principle is employed to analyze convection heat transfer enhancement which can be achieved by reducing the included angle between the velocity vector and the temperature gradient (synergy angle). The present study is aimed to scrutinize the relationship of the synergy angle and the field synergy number with other pertinent parameters in forced convection of plane Couette–Poiseuille flows with asymmetric heat-flux wall boundary conditions. This type of problem arises in various engineering processes, such as in the operation of extruders and in various lubrication problems. The variation of the velocity vector is governed by the moving plate velocity while the temperature gradient is affected by both the moving plate velocity and the asymmetrical heat fluxes at the wall boundaries. Analytical solutions are obtained and the effects of thermal asymmetries under the imposition of isoflux at the walls in Couette–Poiseuille flows are analyzed by adopting field synergy principle. The variations of synergy angle with different boundary conditions and the relationship between the Nusselt number and the synergy (coordination) number, are compared and analyzed. The thermal condition at the wall boundary, the variations of the moving plate velocity and the Peclet number are the essential parameters in the synergetic behavior of the system.     

基于场协同理论的超声波对强化换热影响

本研究分别对圆管、波节管和横纹管在Fluent软件中进行数值模拟,模拟了3种管型在紊流工况下的换热效果并对数值模拟所得到的结果用场协同的理论分析。结果表明:从场协同理论得出加入超声波会增强场的协同程度,增强换热管的换热效果;圆管、波节管、横纹管的场协同数则随着雷诺数的增加而减小;而努塞尔数和表面传热系数随着雷诺数的增加而增加,综合性能系数随着雷诺数的增加而增加,而效能评价系数会随着雷诺数的增加而减小。     

Numerical investigation and analysis of heat transfer enhancement in channel by longitudinal vortex based on field synergy principle

3-D numerical simulations were presented for laminar flow and heat transfer characteristics in a rectangular channel with vortex generators. The effects of Reynolds number (from 800 to 3 000), the attack angle of vortex generator (from 15° to 90°) and the shape of vortex generator were examined. The numerical results were analyzed based on the field synergy principle. It is found that the inherent mechanism of the heat transfer enhancement by longitudinal vortex can be explained by the field synergy principle, that is, the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient. The longitudinal vortex improves the field synergy of the large downstream region of longitudinal vortex generator (LVG) and the region near (LVG); however, transverse vortex only improves the synergy of the region near vortex generator. Thus, longitudinal vortex can enhance the integral heat transfer of the flow field, while transverse vortex can only enhance the local heat transfer. The synergy angle decreases with the increase of Reynolds number for the channel with LVG to differ from the result obtained from the plain channel, and the triangle winglet performs better than the rectanglar one under the same surface area condition. __________ Translated from Journal of Xi’an Jiaotong University, 2006, 40(9): 996–1000 [译自: 西安交通大学学报]     

Heat transfer and phase change of liquid in an inclined enclosure packed with unsaturated porous media

In this paper, we present a mathematical model to describe the simultaneous heat and mass transfer with liquid phase change in unsaturated porous media. Two-dimensional natural convective flow in an inclined rectangular enclosure with porous material unsaturated with fluid is analyzed numerically. The parameter variations are considered for the tilted angle, the aspect ratio and the Darcy–Rayleigh number. Local and global Nusselt numbers are presented as functions of those parameters. Compared with the saturated porous material, the heat transfer characters in the unsaturated case are discussed for the identical aspect ratio and Darcy–Rayleigh number, The discussion is also made for the field synergy of fluid velocity and heat flow in natural convection.     

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.     

Unified field synergy and heatline visualization of forced convection with thermal asymmetries

Forced convection between two parallel plates imposed with thermal asymmetric boundary condition is analyzed by employing a unified field synergy and heatline visualization technique. The heatline visualization is incorporated in the field synergy analysis through the introduction of an included angle between the heatline and the streamline, which is comparable to the well-established synergy angle of the field synergy principle. Inherently, both angles present the common intrinsic characteristics with each other. The heatline plot provides a more explicit visualization of heat flow in convection heat transfer compared to the isotherm plot, which is widely used in the existing field synergy study. Similar to the synergy angle, it is observed that the decrease of the included angle between the heatline and the streamline enhances the synergy between the heat and fluid flow, resulting in higher Nusselt number and field coordination number. The variations of the heat flux ratio induce changes on the field synergy of the flow due to the effects of thermal asymmetries, which concurrently alter the heatline patterns.     

Experimental study on friction factor and numerical simulation on flow and heat transfer in an alternating elliptical axis tube

This paper focuses on the experimental study on friction factor and the numerical simulation on the periodic fully developed fluid flow and heat transfer in an alternating elliptical axis tube (AEAT). The experimental results show that in the laminar flow regime fRe = 84.7, and the transition from laminar to turbulent flow occurs at an earlier Reynolds number about 1000. The predicted cycle average Nusselt numbers from the standard k–ε model and RNG k–ε model are quite close to each other, which are appreciably higher than that of elliptic tube and round tube. Heat transfer performance comparisons are made under identical pumping power constraint, showing the obvious superiority of AEAT over a round tubes. In addition, the complicated multi-longitudinal vortex structure of the flow is detected in detail from the numerical simulation results, which improves the synergy between velocity field and temperature gradient in a large extent, hence, greatly enhancing the convective heat transfer.     

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.     

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.     

Field-Synergy and Figure-of-Merit Analysis of Two Oxide–Water-Based Nanofluids' Flow in Heated Tubes

Field-synergy analysis is performed on the water–oxide nanofluid flow in circular heat sinks to examine the synergetic relation between the flow and temperature fields for heating processes. By varying the Reynolds number and the nanoparticle volume fraction, the convective heat transfer of nanofluid is investigated based on the field synergy number. For heating, the degree of synergy between the velocity and temperature fields of nanofluid flow deteriorates with the Reynolds number increase, leading to a decreased heat transfer performance of the nanofluid. By increasing the particle volume fraction, the degree of synergy between the velocity and temperature fields of the nanofluid flow can be intensified, thus going to convection heat transfer enhancement. After generating results, one can notice that the heat transfer enhancement is strongly dependent on nanoparticle type, Reynolds number, and volume fraction. The results are similar, even if the thermal conductivity of the two considered oxide nanoparticles are quite different. Additionally, a convenient figure of merit that is known as the Mouromtseff number was used as base of comparison, and the results indicated that the considered nanofluids can successfully replace water in specific applications for single-phase forced convection flow in a tube.