Physical quantity synergy in laminar flow field and its application in heat transfer enhancement

On the basis of field synergy principle for heat transfer enhancement, physical quantity synergy in laminar flow field of convective heat transfer is analyzed according to physical nature of convective heat transfer between fluid and solid wall. Synergy regulation among physical quantities is revealed by mathematical expressions reflecting mechanism of heat transfer enhancement. Characteristic of heat transfer enhancement, which is directly associated with synergy angles α, β and γ, is also analyzed. Numerical simulation is made to verify the principle of physical quantity synergy developed in the paper.     

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.     

Three-dimensional numerical study on fin-and-oval-tube heat exchanger with longitudinal vortex generators

Three-dimensional numerical study was performed for heat transfer characteristics and fluid flow structure of fin-and-oval-tube heat exchangers with longitudinal vortex generators (LVGs). For Re (based on the hydraulic diameter) ranges from 500 to 2500, it was found that the average Nu for the three-row fin-and-oval-tube heat exchanger with longitudinal vortex generators increased by 13.6–32.9% over the baseline case and the corresponding pressure loss increased by 29.2–40.6%. The results were analyzed on the basis of the field synergy principle to provide fundamental understanding of the relation between local flow structure and heat transfer augmentation. It was confirmed that the reduction of the intersection angle θ between the velocity field and the temperature field was one of the essential factors influencing heat transfer enhancement. Three geometrical parameters – placement of LVGs (upstream and downstream), angles of attack (α = 15°, 30°, 45° and 60°) and tube-row number (n = 2, 3, 4 and 5) – were also investigated for parameter optimization. The LVGs with placement of downstream, angles of attack α = 30° and minimum tube-row number provide the best heat transfer performance. The effects of the three geometrical parameters on heat transfer enhancement were also analyzed from the view point of the field synergy principle and it was found that the results can be well explained by the field synergy principle.     

Three-dimensional numerical study of wavy fin-and-tube heat exchangers and field synergy principle analysis

In this paper, 3-D numerical simulations were performed for laminar heat transfer and fluid flow characteristics of wavy fin-and-tube heat exchanger by body-fitted coordinates system. The effect of four factors were examined: Reynolds number, fin pitch, wavy angle and tube row number. The Reynolds number based on the tube diameter varied from 500 to 5000, the fin pitch from 0.4 to 5.2 mm, the wavy angle from 0° to 50°, and the tube row range from 1 to 4. The numerical results were compared with experiments and good agreement was obtained. The numerical results show that with the increasing of wavy angles, decreasing of the fin pitch and tube row number, the heat transfer of the finned tube bank are enhanced with some penalty in pressure drop. The effects of the four factors were also analyzed from the view point of field synergy principle which says that the reduction of the intersection angle between velocity and fluid temperature gradient is the basic mechanism for enhance convective heat transfer. It is found that the effects of the four factors on the heat transfer performance of the wavy fin-and-tube exchangers can be well described by the field synergy principle.     

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 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.     

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.     

NUMERICAL DESIGN OF EFFICIENT SLOTTED FIN SURFACE BASED ON THE FIELD SYNERGY PRINCIPLE

In this article, a numerical investigation of the flow and heat transfer in a three-row finned-tube heat exchanger is conducted with a three-dimensional laminar conjugated model. Four types of fin surfaces are studied; one is the whole plain plate fin, and the other three are of slotted type, called slit 1, slit 2, and slit 3. All four fin surfaces have the same global geometry dimensions. The three slotted fin surfaces have the same numbers of strips, which protrude upward and downward alternatively and are positioned along the flow direction according to the rule of “front coarse and rear dense.” The difference in the three slotted fins is in the degree of “coarse” and “dense” along the flow direction. Numerical results show that, compared to the plain plate fin, the three types of slotted fin all have very good heat transfer performance in that the percentage increase in heat transfer is higher than that in the friction factor. Among the three slotted fin surfaces, slit 1 behaves the best, followed by slit 2 and slit 3 in order. Within the Reynolds number range compared ( from 2,100 to 13,500), the Nusselt number of slit 1 is about 112–48% higher than that of the plain plate fin surface under the identical pumping constraint. An analysis of the essence of heat transfer enhancement is conducted from the field synergy principle, which says that the reduction of the intersection angle between the velocity and the temperature gradient is the basic mechanism for enhancing convective heat transfer. It is found that for the three comparison constraints the domain-average synergy angle of slit 1 is always the smallest, while that of the plain plate fin is the largest, with slit 2 and slit 3 being somewhat in between. The results of the present study once again show the feasibility of the field synergy principle and are helpful to the development of new types of enhanced heat transfer surfaces.     

Experimental and numerical investigation of thermal -hydraulic performance in wavy fin-and-flat tube heat exchangers

To the more deeply understand the enhancement heat transfer mechanism and optimization design for wavy fin-and-flat tube heat exchangers, three-dimensional numerical simulations and experimental investigation of air flow and heat transfer characteristics over the wavy fin heat exchangers are presented in this study. The numerical simulation results compared with the wind tunnel test data, the results show that the numerical simulation results are in good with the test. The experimental results show that, in the range of Re = 1000–5500, the standard k-ε mode (SST) is more suitable to predict the air flow and heat transfer of wavy fin. The waviness amplitude has the distinct effect on the heat transfer and pressure drop of wavy fin, while the wavy fin profile (Triangular, Sinusoidal and Triangular round corner) has little effect on the heat transfer performance. In additional, the enhancement heat transfer mechanism of wavy fin is explained in view of field synergy principle. Reduction the synergy angle between velocity and temperature gradient will induce to the heat transfer coefficients increase of wavy fin.     

CFD study on local fluid-to-wall heat transfer in packed beds and field synergy analysis

To reach the target of smaller pressure drop and better heat transfer performance, packed beds with small tube-to-particle diameter ratio (D/d _p<10) have now been considered in many areas. Fluid-to-wall heat transfer coefficient is an important factor determining the performance of this type of beds. In this work, local fluid- to-wall heat transfer characteristic in packed beds was studied by Computational Fluid Dynamics (CFD) at different Reynolds number for D/d _p=1.5, 3.0 and 5.6. The results show that the fluid-to-wall heat transfer coefficient is oscillating along the bed with small tube-to-particle diameter ratio. Moreover, this phenomenon was explained by field synergy principle in detail. Two arrangement structures of particles in packed beds were recommended based on the synergy characteristic between flow and temperature fields. This study provides a new local understanding of fluid-to-wall heat transfer in packed beds with small tube-to-particle diameter ratio.     

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.     

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]     

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.     

Investigation on laminar convection heat transfer in fin-and-tube heat exchanger in aligned arrangement with longitudinal vortex generator from the viewpoint of field synergy principle

3-D numerical simulation results are presented for laminar flow heat transfer of the fin-and-tube surface with vortex generators. The effects of Reynolds number (from 800 to 2000), the attack angle (30° and 45°) of delta winglet vortex generator are examined. The numerical results are analyzed from the viewpoint of field synergy principle. It is found that the inherent mechanism of heat transfer enhancement by longitudinal vortex can be explained by the field synergy principle, the second flow generated by the vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient. In addition, the heat transfer enhancement of delta winglet with the attack angle of 45° is larger than that of 30°, while the delta winglet with the attack angle of 45° results in an increase of the pressure drop, however, the delta winglet with the attack angle of 30° results in a slight decrease.     

3D numerical simulation on shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles – Part II: Simulation results of periodic model and comparison between continuous and noncontinuous helical baffles

In this paper, based on the simplified periodic model the performance predictions for heat exchanger with middle-overlapped helical baffles are carried out by 3D simulation for three different helix angles (30°, 40° and 50°), and the commercial codes of GAMBIT 2.3 and FLEUNT 6.3 are adopted in the simulation. It is found that the model average heat transfer coefficient per unit pressure drop of the 40° angle case is the largest, which is in qualitative agreement with the existing literature. The predicted average intersection angle of this case is the smallest, being consistent with the field synergy principle. The performance of periodic model with continuous helical baffle is also compared with that of the noncontinuous middle-overlapped helical baffles. It is found that the heat transfer coefficient per unit pressure drop of the noncontinuous middle-overlapped helical baffles is appreciably larger than that of the continuous helical baffle, indicating that the heat exchanger with noncontinuous middle-overlapped helical baffles has its advantage over the one with continuous helical baffle.     

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.     

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.     

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.     

Numerical study on a slit fin-and-tube heat exchanger with longitudinal vortex generators

A 3-D numerical simulation is performed on laminar heat transfer and flow characteristics of a slit fin-and-tube heat exchanger with longitudinal vortex generators. Heat transfer enhancement of the novel slit fin mechanism is investigated by examining the effect of the strips and the longitudinal vortices. The structure of the slit fin is optimized and analyzed with field synergy principle. The result coincides with the guideline ‘front coarse and rear dense’. The heat transfer and fluid flow characteristics of the slit fin-and-tube heat exchanger with longitudinal vortex generators are compared with that of the heat exchanger with X-shape arrangement slit fin and heat exchanger with rectangular winglet longitudinal vortex generators. It is found that the Colburn j-factor and friction factor f of the novel heat exchanger with the novel slit fin is in between them under the same Reynolds number, and the factor j/(f^1/3) of the novel heat exchanger increased by 15.8% and 4.2%, respectively.     

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.