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.     

Numerical analysis on heat transfer enhancement by longitudinal vortex based on field synergy principle

Three-dimensional numerical simulation results are presented for a fin-and-tube heat transfer surface with vortex generators. The effects of the Reynolds number (from 800 to 2 000) and the attack angle (30° and 45°) of a delta winglet vortex generator are examined. The numerical results are analyzed on the basis of the field synergy principle to explain the inherent mechanism of heat transfer enhancement by longitudinal vortex. The secondary flow generated by the vortex generators causes the reduction of the intersection angle between the velocity and fluid temperature gradients. In addition, the computational evaluations indicate that the heat transfer enhancement of delta winglet pairs for an aligned tube bank fin-and-tube surface is more significant than that for a staggered tube bank fin-and-tube surface. The heat transfer enhancement of the delta winglet pairs with an attack angle of 45° is larger than that with an angle of 30°. The delta winglet pair with an attack angle of 45° leads to an increase in pressure drop, while the delta winglet pair with the 30° angle results in a slight decrease. The heat transfer enhancement under identical pumping power condition for the attack angle of 30° is larger than that for the attack angle of 45° either for staggered or for aligned tube bank arrangement. Translated from Journal of Xi’an Jiao Tong University, 2006, 40(7): 757–761 [译自: 西安交通大学学报]     

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.     

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]     

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.     

开缝布置方式对开缝翅片管换热器 传热与阻力特性的影响

为了获得开缝布置方式对开缝翅片管换热器传热与阻力特性的影响规律,对5种不同翅片管换热器进行了数值模拟研究,并进行了模化试验验证。结果表明：增加开缝会提高翅片管换热器的传热性能,但阻力也随之增加;与开缝位置相比,开缝数量对开缝翅片管换热器传热与阻力特性的影响更大;在Re=4800~7500日时,开缝翅片管换热器综合流动传热性能 随着Re数的增大而增大;在5种翅片中,开缝翅片的综合流动传热性能高于普通平直翅片;数值模拟与试验结果偏差较小,采用数值模拟方法能够比较准确地分析开缝翅片管换热器的传热与阻力特性。     

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.     

Numerical study of fluid flow and heat transfer in a flat-plate channel with longitudinal vortex generators by applying field synergy principle analysis

Three dimensional numerical simulations are performed on laminar heat transfer and fluid flow characteristics of a flat-plate channel with longitudinal vortex generators (LVGs). The effects of two different shaped LVGs, rectangular winglet pair (RWP) and delta winglet pair (DWP) with two different configurations, common-flow-down (CFD) and common-flow-up (CFU), are studied. The numerical results indicate that the application of LVGs effectively enhances heat transfer of the channel. According to the performance evaluation parameter, (Nu/Nu₀)/(f/f₀), the channel with DWP has better overall performance than RWP; the CFD and CFU configurations of DWP have almost the same overall performance; the CFD configuration has a better overall performance than the CFU configuration for RWP. The basic mechanism of heat transfer enhancement by LVGs can be well described 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.     

Discussion on the convective heat transfer and field synergy principle

The convective “heat” transfer is actually mainly carried out by the motion of hotter or colder particles from one system into another system. Therefore, the best convective “heat” (strictly speaking, internal energy) transfer is the case where velocity vectors are always perpendicular to the isothermal surfaces (or isotherm in 2D cases). This conclusion has been named “field synergy principle”. In this paper, some field synergy exact solutions are presented to further develop the principle. The concrete physical meanings of the derived analytical solutions are analyzed. The method of separating variables with addition and other extraordinary approaches are adopted in the derivation.     

纵向涡发生器强化传热管的实验研究

介绍了一种高效强化传热管,沿传热管内壁轴向均匀排布三列成对的纵向涡发生器,在常壁温条件下进行加热空气在管内流动的冷却实验,研究强化传热管的传热和阻力特性。结果表明,在过渡流区管内置纵向涡发生器的强化传热大大增强,Nu增大为光管的2.02.3倍,阻力损失也相应有所增加,提出一种比较优化的发生器的形状设计,探讨了传热和阻力随设置间距变化的规律。     

倾斜封闭方腔内自然对流换热的场协同分析

采用场协同原理对倾斜封闭方腔内自然对流换热现象进行了研究。通过数值模拟获得了不同瑞利数(Ra=1~10~6)时倾斜封闭方腔内自然对流换热的协同关系,以及在一定Ra数下不同倾斜角φ对封闭方腔内自然对流换热的影响。结果表明:随着瑞利数Ra的增大,协同数Fc变小,其协同性越好。随着倾斜角φ的变化,当Ra≤10~3时,lg Fc的变化曲线近似呈现开口向上的抛物线型;当10~4≤Ra≤10~5时,lg Fc的变化曲线是单调的;当瑞利数Ra≥10~6时,lg Fc的变化曲线有2个极值和1个拐点。     

Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence of a balance between the entropy generation due to heat transfer and fluid friction. The entropy generation in a cross-flow HX with a new winglet-type convergent–divergent longitudinal vortex generator (CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regarding the overall system performance are presented. For the HX flow lengths and CDLVGs the optimization model was developed on the basis of the entropy generation minimization (EGM). It was found that increasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transfer irreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure to improve the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynolds number.     

A unified analysis on enhancing single phase convective heat transfer with field synergy principle

Numerical simulations were conducted to reveal the inherent relation between the filed synergy principle and the three existing mechanisms for enhancing single phase convective heat transfer. It is found that the three mechanisms, i.e., the decreasing of thermal boundary layer, the increasing of flow interruption and the increasing of velocity gradient near a solid wall, all lead to the reduction of intersection angle between velocity and temperature gradient. It is also revealed that at low flow speed, the fin attached a tube not only increases heat transfer surface but also greatly improves the synergy between the velocity and the temperature gradient.     

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.     

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.     

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.     

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.     

纵向涡强化竖直平板自然对流换热的实验研究

对纵向涡强化竖直平板自然对流换热进行了实验研究。结果表明，在一定的Rayleigh数范围内，直角三角翼纵向涡发生器的攻角、翼高、翼宽等几何参数是影响强化换热的主要因素。存在最佳攻角；宽高比一定时，翼高和翼宽的变化会影响换热的效果。发现在直角三角翼阵列中前排直角三角翼产生的纵向涡可以强化后排直角三角翼纵向涡的换热。将直角三角翼与矩形低肋换热表面的性能作了对比性实验，在其他条件相同的情况下，直角三角翼强化换热的效果优于矩形低肋。     

Flow visualization of annular and delta winlet vortex generators in fin-and-tube heat exchanger application

This study presents flow visualization and frictional results of enlarged fin-and-tube heat exchangers with and without the presence of vortex generators. Two types of vortex generators and a plain fin geometry were examined in this study. For plain fin geometry at Re=500, the horseshoe vortex generated by the tube row is not so pronounced, and the horseshoe vortex separates into two streams as it flows across the second row and consequently loses its vortical strength. This phenomenon may supports the “maximum phenomenon” in low Reynolds number region reported by previous studies. With the presence of annular vortex generator, the presence of a pair of longitudinal vortices formed behind the tube is seen. The strength of the counter-rotating vortices increases with the annular height and the strength of the longitudinal vortices is so strong that may swirl with the horseshoe vortices and other flow stream. For the same winlet height, the delta winlet shows more intensely vortical motion and flow unsteadiness than those of annular winlet. This eventually leads to a better mixing phenomenon. However, it is interesting to know that the corresponding pressure drops of the delta winlet are lower than those of annular winlet. Compared to the plain fin geometry, the penalty of additional pressure drops of the proposed vortex generators is relatively insensitive to change of Reynolds number.