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.     

Experimental and numerical study of convective heat transfer and fluid flow in twisted oval tubes

Twisted oval tube heat exchanger is a type of heat exchanger aims at decreasing the pressure drop of the shell side. In the present study, heat transfer and pressure drop performances of twisted oval tube have been studied experimentally and numerically. The experimental study of the twisted oval tube shows that heat transfer process can be enhanced but also with an increasing of pressure drop when compared with the smooth round tube. The effects of geometrical parameters on the performance of the twisted oval tube have been analyzed numerically. The result reveals that the heat transfer coefficient and friction factor both increase with the increasing of axis ratio a/b, while both decrease with the increasing of twist pitch length P. The influence of a/b and P on the overall performance of the twisted oval tubes are also studied. Aiming at obtaining the heat transfer enhancement mechanism of the twisted oval tube, secondary flow, total velocity and temperature distributions of flow section are given. From the analysis it can be concluded that the emergence of twist in the twisted oval tube results in secondary flow. It exists in the form of spiral flow when a/b is big, but in the form of up and down when a/b is small. It is this secondary flow that changes the total velocity and temperature distributions of the twisted oval tube when compared with a smooth oval tube with the same sectional geometric parameters. Then the synergy angle between velocity vector and temperature gradient is reduced and the heat transfer process is enhanced.     

纵向涡强化换热的优化设计及机理分析

对带纵向涡发生器的椭圆管翅片换热器空气侧表面的换热和流动特性进行了三维数值模拟.深入分析了纵向涡对流场和温度场的影响,并通过场协同原理揭示了纵向涡强化换热的根本机理,即减小了速度和温度梯度之间的夹角,改善了速度场和温度场的协同性.在此基础上,对纵向涡发生器的布置位置(上游布置和下游布置)和纵向涡发生器的攻角α(15°,30°,45°,60°)进行了优化设计.结果表明:当纵向涡发生器布置于换热管下游时,具有更好的强化换热能力;在纵向涡发生器采用下游布置的前提下,当纵向涡发生器的攻角α=30°时,具有最佳的强化换热能力.     

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 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.     

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.     

Numerical study on laminar convection heat transfer in a rectangular channel with longitudinal vortex generator. Part A: Verification of field synergy principle

This study presents numerical computation results on laminar convection heat transfer in a rectangular channel with a pair of rectangular winglets longitudinal vortex generator punched out from the lower wall of the channel. The effect of the punched holes and the thickness of the rectangular winglet pair to the fluid flow and heat transfer are numerically studied. It is found that the case with punched holes has more heat transfer enhancement in the region near to the vortex generator and lower average flow frictional coefficient compared with the case without punched holes. The thickness of rectangular winglet can cause less heat transfer enhancement in the region near to the vortex generator and almost has no significant effect on the total pressure drop of the channel. The effects of Reynolds number (from 800 to 3000), the attack angle of vortex generator (15°, 30°, 45°, 60° and 90°) were examined. The numerical results were analyzed from the viewpoint of field synergy principle. It was found that the essence of heat transfer enhancement by longitudinal vortex can be explained very well by the field synergy principle, i.e., when the second flow generated by vortex generators results in the reduction of the intersection angle between the velocity and fluid temperature gradient, the heat transfer in the present channels will be enhanced. Longitudinal vortices (LVs) improve the synergy between velocity and temperature field not only in the region near LVG but also in the large downstream region of longitudinal vortex generator. So LVs enable to enhance the global heat transfer of channel. Transverse vortices (TVs) only improve the synergy in the region near VG. So TVs can only enhance the local heat transfer of channel.     

Field synergy principle for enhancing convective heat transfer--its extension and numerical verifications

The concept of enhancing parabolic convective heat transfer by reducing the intersection angle between velocity and temperature gradient is reviewed and extended to elliptic fluid flow and heat transfer situation. Five examples of elliptic flow are provided to show the validity of the new concept (field synergy principle). Two further examples are supplemented to demonstrate the importance of the concept in the design of the enhanced surfaces.     

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.     

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.     

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.     

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.     

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

Three-dimensional numerical simulations of the laminar flow and heat transfer of water in silicon microchannels with non-circular cross-sections (trapezoidal and triangular) were performed. The finite volume method was used to discretize the governing equations. Numerical results were compared with experimental data available in the literature, and good agreements were achieved. The effects of the geometric parameters of the microchannels were investigated, and the variations of Nusselt number with Reynolds number were discussed from the field synergy principle. The simulation results indicate that when the Reynolds numbers are less than 100, the synergy between velocity and temperature gradient is much better than the case with Reynolds number larger than 100. There is an abrupt change in the intersection angle between velocity and temperature gradient around Re=100. In the low Reynolds number region the Nusselt number is almost proportional to the Reynolds number, while in the high Reynolds number region, the increasing trend of Nusselt number with Reynolds number is much more mildly, which showed the applicability of the field synergy principle. In addition, for the cases studied the fully developed Nusselt number for the microchannels simulated increases with the increasing Reynolds number, rather than a constant.     

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.     

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.     

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.     

Lattice Boltzmann method simulation of backward-facing step on convective heat transfer with field synergy principle

The lattice Boltzmann method (LBM) is applied to simulate the two-dimensional incompressible steady low Reynolds number backward-facing step flows. In order to restrict the approach to the two-dimensional flow, the largest Reynolds number chosen was Re = 200. To increase the uniformity of the radial temperature profile for fluid flow in channel and consequently to enhance the heat transfer, the inserted square blockage is used and investigated numerically. In addition, the field synergy principle is also applied to demonstrate that an interruption within fluid results in decreased intersection angle between the velocity and temperature gradient. The numerical results of velocity and temperature field agree well with the available experimental and numerical results.     

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.     

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.     

Numerical study on laminar convection heat transfer in a channel with longitudinal vortex generator. Part B: Parametric study of major influence factors

This paper presents the influences of main parameters of longitudinal vortex generator (LVG) on the heat transfer enhancement and flow resistance in a rectangular channel. The parameters include the location of LVG in the channel, geometric sizes and shape of LVG. Numerical results show that the overall Nusselt number of channel will decrease with the LVGs’ location away from the inlet of the channel, and decrease too with the space between the LVG pair decreased. The location of LVG has no significant influence on the total pressure drop of channel. With the area of LVG increased, the average Nusselt number and the flow loss penalty of channel, especially when β = 45° will increase. With the area of LVG fixed, increasing the length of rectangular winglet pair vortex generator will bring about more heat transfer enhancement and less flow loss increase than that increasing the height of rectangular winglet pair vortex generator. With the same area of LVG, delta winglet pair is more effective than rectangular winglet pair on heat transfer enhancement of channel, and delta winglet pair-b is more effective than delta winglet pair-a. Delta winglet pair-a results in a higher pressure drop, the next is rectangular winglet pair and the last is delta winglet-b. The increase of heat transfer enhancement is always accompanied with the decrease of field synergy angle between the velocity and temperature gradient when the parameters of LVG are changed. This confirms again that the field synergy is the fundamental mechanism of heat transfer by longitudinal vortex. The laminar heat transfer of the channel with punched delta winglet pair is experimentally and numerically studied in the present paper. The numerical result for the average heat transfer coefficient of the channel agrees well with the experimental result, indicating the reliability of the present numerical predictions.