- Email: [email protected]
Heat transfer and pressure performance of a plain fin with radiantly arranged winglets around each tube in fin-and-tube heat transfer surface
International Journal of Heat and Mass Transfer 70 (2014) 734–744
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and pressure performance of a plain fin with radiantly arranged winglets around each tube in fin-and-tube heat transfer surface M.J. Li, W.J. Zhou, J.F. Zhang, J.F. Fan, Y.L. He, W.Q. Tao ⇑ Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy & Power Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 11 July 2013 Received in revised form 8 November 2013 Accepted 10 November 2013 Available online 12 December 2013 Keywords: Longitudinal vortex generator Fin-and-tube heat exchanger Wavy fin Field synergy principle Performance evaluation plot Waste heat recovery Numerical study
a b s t r a c t A radiantly arranged LVGs enhanced fin-and-tube structure is numerically investigated in this paper to enhance air side heat transfer. The arrangement of LVGs is totally different from existing publications. In the proposed structure there exist 12 winglets around each tube. The attack angles are 50, 50, 50, 50, 70 and 110°, respectively. The height ends of the winglets are further away from the tube, while the closed point ends of winglets are close to the tube wall. Heat transfer and pressure drop performance is compared with other three structures: an arc-shaped wavy fin-and-tube surface, a common-flowdown LVGs enhanced fin-and-tube surface and a plain plate fin-and-tube surface. The simulation results show that the 12 winglets form five local passages which can guide the moving fluid from the main flow to the tube wall, leading to some impinging effect or reducing the wake region behind the tube. The performance evaluation of the four structures is conducted by using the newly proposed ln (Nue/Nuo) vs. ln (fe/fo) plot based on energy saving. It is found that the proposed radiantly arranged LVGs enhanced finand-tube surface is the best. The field synergy principle is adopted to analyze the four structures and it is found that the domain averaged synergy angle of the proposed radiantly arranged LVGs enhanced structure is significantly less than that of other three cases. Finally characteristics of the proposed finand-tube surface with five tubes are investigated at five fin pitches and compared with the wavy structure of six tubes at the same other conditions. It is found that the proposed structure of five tubes can replace the wavy structure of six tubes. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Fin-and-tube heat exchangers are widely employed in industries such as heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems. Their efficiency directly determines the energy consumption of heat exchangers for both manufacturing and operating processes. Air is a common used working fluid in fin-andtube heat exchangers due to its cleanness and low cost, but the heat transfer capability of air is quite low, which leads to high thermal resistance on the air side of fin-and-tube heat exchanger. In typical applications, thermal resistance of the air side takes up over 90% of all [1], so the main approach for improvement of such heat exchangers is to enhance the air side heat transfer. Researchers have developed a lot of types of fin surfaces to enhance air-side heat transfer without introducing tremendous penalty of pressure drop and material consumption. Wavy fin and longitudinal vortex generator (LVG) are two usually employed enhancement techniques. The wavy structure periodically interrupts the growth of
⇑ Corresponding author. Tel.: +86 29 82669106. E-mail address: [email protected] (W.Q. Tao). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.024
the thermal boundary layers on the heat transfer surfaces and induces transverse vortex in wavy trough thus increasing fluid mixing and vortices. For the LVG enhanced fin surfaces, when fluid flows over LVG set at an appropriate attack angle, longitudinal vortices are generated [2] leading to the enhancement of heat transfer. In this paper a new-type arrangement of vortex generator will be proposed to enhance heat transfer of plain-fin surface and its performance is compared with an existing wavy fin surface. Hence, in the following previous studies on wavy and longitudinal vortex generator (LVG) enhanced fin surfaces will be briefly reviewed. In general, wavy or corrugated fins have different specific forms, including herringbone wavy fin, sinusoid or co-sinusoid wavy fin, v-shaped or triangular wavy fin, cambered corrugated fin, curved wavy fin and so on. Heat transfer and fluid flow characteristics of this fin configuration were reported in detail in literatures [3–5]. Jang and Chen [3] numerically investigated the effects of geometrical parameters especially the wavy angle on the triangular wavy fin performance, and concluded that the average Nusselt number Nu and friction factor f increase with the increase of wavy angle for equal wavy height. Savino et al. [4] identified that f always increases with the Reynolds number Re, while Nu increases significantly with Re only above a critical value of Re for herringbone
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
735
Nomenclature
Latin Symbols A air side heat transfer area Ac cross-section area at the inlet b1,b2,b3 lnCU, P, lnCU, 4p and lnCU, u cp specific heat L effective length of fin P pump power Pr Pr number qm mass flow rate T temperature u,v,w fluid velocity in x, y, and z direction
wavy fin. Furthermore, according to the study of [5], there exists an optimum fin pitch at which Nu is the maximum, and the increase of Re leads to the increase of Nu and the decrease of f. The above studies show that wavy fin will possess a satisfactory performance only at some certain circumstances like high inlet velocity and specific geometrical parameters. Longitudinal vortex generator is the fourth generation of enhanced measures [6]. In earlier studies, Jacobi and Shah [7] and Fiebig [8] gave thorough reviews of the development of LVG. Many kinds of generators in different shapes have been developed during the past two decays, such as wedge type, plough type, rectangular wing, delta winglet and so on. Among these types of LVGs triangular wing, rectangular wing, delta winglet and rectangular winglet are the most widely used ones [7]. Most of the typically used LVGs are summarized in [9]. Fiebig and his coworkers [10–12] made a great contribution to the development and application of LVG. They found that delta winglet has the best performance. So in this paper delta winglet generators are adopted, but the orientation and arrangement are different from all previous studies. Except the shape discussed above, the arrangement of LVGs is also an important factor influencing the comprehensive characteristics of enhanced surfaces. Chen et al. [13,14] employed punched winglet longitudinal vortex generators in staggered and inline arrangements to enhance heat transfer of oval tube heat exchanger, and found that winglets in staggered arrangement can bring larger heat transfer enhancement than in in-line arrangement. Torii et al. [15] referred to a pair of delta winglets as common-flow-up (in this winglets orientation flows between two adjacent winglets accelerate) and found it effective in reducing form drag and enhancing heat transfer of the wake region. Allison and Dally [16] also investigated common-flow-up winglets and found that the heat transfer of the winglet surface is 87% of a standard louver fin surface while the pressure drop is only 53%. Kwak et al. [17] and Biswas et al. [18] studied the common-flow-down configuration (in this winglets orientation flows between two adjacent winglets decelerate) and found it more effective for higher Re than for lower Re. He et al. [19] proposed a vortex generator array of ‘‘V’’ configuration inspired by the locomotion formation of bird and fish. The array is composed of two delta-winglet pairs placed at the attack angle of 10 degree or 30 degree. It is found that VG array with 30° is more efficient than two conventional single-pair designs at low Re representative of many HVAC&R applications. Fan et al. [20] combined LVGs with slotted protruding parallel strips and tried different variations of arrangement, finally substituted two tube-rows of the combined structure for an air-side wavy surface with three tube-rows.
Greek Symbols am modulus average intersection angle k thermal conductivity of fluid q density of fluid g dynamic viscosity Subscripts e enhanced fin o reference fin w wall
Researchers also conducted lots of studies on the effects of geometric parameters of LVGs. Wu and Tao [21] investigated geometric shape, size and the location of LVGs in a channel, and found that the overall Nu of the channel is higher with larger space between the LVG pair and larger area of LVG, and decreases with the LVG’s location away from the inlet of the channel. Lemouedda et al. [22] utilized a CFD analysis, response surface methodology and genetic algorithms to investigate the optimal attack angle of delta-winglet LVGs. They concluded that common-flow-up configuration shows better performance for the staggered arrangement, while common-flow-down is better for inline arrangement. Zeng et al. [23] studied and optimized the parameters of vortex-generator by the Taguchi method. They revealed that fin pitch has the greatest effect on the comprehensive performance, and then does the transverse tube pitch, attack angle, length of vortex generator, longitudinal tube pitch, and height of vortex generator. The friction factor and Nusselt number of heat transfer surface are almost independent of fin thickness and fin material. As far as the basic mechanism of enhancing heat transfer by LVG is concerned, it is often attributed to the disturbing of the thermal boundary layer, swirling and flow destabilization caused by LVG [2,7,8]. Wu and Tao [24,25] made comprehensive studies on this issue and their results definitely show that the fundamental reason that LVG can enhance heat transfer is the improvement of synergy between velocity and fluid temperature gradient. For more information of the recent developments and applications of LVG the review paper of [26] is recommended. The winglets adopted in the enhanced surfaces in open literatures are mostly placed in the line along the main flow direction, for either staggered or parallel arrangement. Considering that the flow passing a tube bank periodically changes its local direction: sometime towards the tube wall sometime leaving the tube wall, if we arrange individual winglet orientation to accommodate the local fluid flow direction, we may get some profits in enhancing heat transfer. The major goals of this paper is to find a more efficient structure to replace a wavy fin-and-tube surface already used in aircoolers widely adopted in air-conditioning equipment for clean air space in China. The present authors propose a new type of winglet orientation arrangement with 12 winglets being radiantly arranged around each tube. Considering that ‘common-flow-down’ structure of longitudinal vortex generator is one of the earliest and most representative LVG arrangements in literatures and the plain fin once was undoubtedly the most widely used fin in heat exchanger for its simple structure, we choose these four kinds of structure to make a comparison study in this paper. Numerical simulation is conducted and the results are compared with 3 referenced configurations (a corrugated fin in use, a conventional single-pair LVGs
736
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
placed at 45° (common-flow-down) enhanced fin and a plain plate fin with the same geometrical parameters) to illustrate that the proposed one possesses a satisfactory comprehensive performance. The influence of the winglets size is also investigated. The results are shown in an evaluation plot newly proposed by Fan et al. [27].
(a) Radiantly arranged LVGs enhanced fin
2. Physical and numerical models for simulated fin-and-tube heat transfer surface 2.1. Introduction to enhanced structures studied The schematic view of the proposed enhanced fin surface is partially shown in Fig. 1. As shown there we define x, y the streamwise and spanwise coordinates, respectively, and z the fin pitch direction. The entire heat transfer surface has five heat transfer units with each unit being composed of one tube and 12 surrounding winglets (see Fig. 2a). The delta winglets are punched out from the plain fin around each tube. The chord of the winglets l is 5 mm and will be optimized in Section 5.1. The number of attack angles, defined as the angle between the chord and the tube bank centerline, is 50, 50, 50, 50, 70 and 110°, respectively. These attack angles are obtained through some preliminary simulation for a better performance. The height of winglets hw is 2.425 mm. When punched out the delta winglets are just stuck perpendicular to the base surface and act as an obstacle to the coming flow, hence, can increase the disturbance of air flow. Since the delta winglet is punched from the plain fin, the thickness of the delta winglet is the same as the fin. The space between two neighboring winglets is not less than 1 mm for mechanical strength of the fin. The fin pitch Fp varies in different cases. Other geometric parameters are listed in Table 1. Apart from the proposed enhanced structure, we also take three referenced structure for comparison. Fig. 2b–d give the physical model of the three referenced structures studied in this paper. Fig. 2b is a collared wavy fin with 5 tubes in staggered arrangement, which is actually used in air-coolers. Further enhancement of heat transfer of the air-cooler is demanded in order to meet some practical requirements. The wavelength of the fin is 10.334 mm, the amplitude of the fin is 2 mm, and the diameter of the step is 18.0 mm. Fin pitch, fin thickness, tube diameter, transverse tube pitch and longitudinal tube pitch are identical with the proposed fin structure shown in Fig. 2a and Table 1; Fig. 2c shows a model with a common-flow-down arranged delta-winglet pair placed at the wake region of the tube. This structure is the most original arrangement of LVGs thus taken for comparison. The attack angle is 45° recommended by Fiebig and Chen [28]; Fig. 2d presents a plain fin-tube structure, which is the earliest fin-and-tube structure and still widely used now in industry. It’s worth pointing out further that the winglets configuration employed in this paper are different from that in open literatures in two ways. One difference indicated above is about the global arrangement of winglets: in conventional arrangement they are along the line of major flow direction, while in our arrangement
(b) Wavy fin
(c) Common-flow-down LVGs enhanced fin
(d) Plain plate fin Fig. 2. Physical model of the four simulated structures.
Table 1 Geometric dimensions of computational zone. Items
Dimensions (mm)
Fin thickness df Tube diameter Dc Transverse tube pitch Pt Longitudinal tube pitch Pl
0.115 13 27.5 15.875
they are grouped and winglets in each group are around a tube; the other is related to the orientation of the two ends (height end and its counterpart point end) of each winglet. Taking a pair of winglet arranged in common-flow-up pattern as an example, in the conventional arrangement the height end of each winglet is close to tube wall while its counterpart away from the tube wall (Fig. 3a); on the contrast, in the present arrangement the height end of the winglet is away from the tube wall while the point end is close the tube wall (Fig. 3b). 2.2. Computational domain Because of the obstruction of fin, the air velocity profile at the entrance of the channel is not uniform. So the computational domain has to be extended upstream by 2 the streamwise fin length to ensure a uniform velocity distribution at the domain inlet. With regard to the outlet, it is extended 10 the fin region to avoid recirculation and finally outflow boundary condition can be employed. The neighboring two fins’ center planes are chosen as the upper and lower boundaries of the computational domain due to the periodical repetition of the air channels in z direction in the whole fin-and-tube heat exchanger [20]. In the spanwise direction, the computational region is bounded by two adjacent center lines of tubes, also because of the periodicity in y-direction. 2.3. Physical assumptions and governing equations
Fig. 1. Schematic view of radiantly arranged winglets enhanced fin.
The inlet Reynolds number based on the outside tube diameter ranges from 1335 to 3116, and according to literatures [21,27,28] the flow is considered laminar and incompressible. The fluid flow
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
737
Boundary conditions in the y coordinate direction are: Tube region:
T w ¼ 280K; u ¼ m ¼ w ¼ 0;
ð4cÞ
Fin surface region:
u ¼ m ¼ w ¼ 0;
@T ¼0 @y
ð4dÞ
Fluid region:
@ m @w ¼ ¼ 0; @y @y
v ¼ 0;
@T ¼0 @y
ð4eÞ
All the top and bottom boundaries (z direction): periodic boundary conditions.
(a) Conventional common-flow-up 2.4. Numerical methods In the present study, the computational domain is discretized by non-uniform grids with software GAMBIT. The governing equations are discretized by the finite-volume method [29,30] and are solved using commercial code FLUENT (version 12). The temperatures in the solid fin surface and in the fluid are determined simultaneously, i.e., solved in the conjugated way. The convection terms for momentum and energy equations are discretized by QUICK scheme. The coupling between pressure and velocity is executed by SIMPLEC algorithm [30]. Iteration convergence is considered to be achieved, if following conditions are all satisfied: The residual of the continuity is less than 104. The residual of velocity component is less than 106. The residual of the energy is less than 108.
(b) Present common-flow-up Fig. 3. Two kinds of common-flow-up arranged LVGs.
3. Data reduction, grid independence examination and model validation and heat transfer are in steady state. The fluid thermophysical properties are constant. The heat transfer coefficient on the inner wall of the tube and the thermal conductivity of the tube wall are high enough, so the tube is assumed to be at constant temperature. Based on the foregoing assumptions, the governing equations of continuity, momentum and energy for three dimensional, constant material properties, laminar and steady forced convection flow can be described as follows: Continuity equation,
@ ðqui Þ ¼ 0 @xi
ð1Þ
@ @ @u ðqui uk Þ ¼ g k @xi @xi @xi
Total heat transfer rate:
U ¼ qm cp ðT out T in Þ
ð5Þ
The logarithmic mean temperature difference:
DT lg ¼
DT max DT min lnðDT max =DT min Þ
DT max ¼ maxðT w T in ; T w T out Þ
ð6Þ ð7Þ
The heat transfer coefficient :
Momentum equation,
Parameters used to evaluate and compare the performance of heat transfer surfaces are defined as follows:
@p ; @xk
h¼ k ¼ 1; 2; 3
ð2Þ
U
Nusselt number:
Energy equation,
@ @ @T ðqui TÞ ¼ C @xi @xi @xi
Nu ¼ ð3Þ
ð9Þ
m ¼ w ¼ 0; T in ¼ 305K
Re ¼
quin Dc g
ð10Þ
Pressure drop:
Dp ¼ pin pout
Boundary conditions in the x coordinate direction are: Domain inlet:
ð11Þ
The friction factor:
ð4aÞ
Domain outlet:
@u @ m @w @T ¼ ¼ ¼ ¼0 @x @x @x @x
hDc k
Reynolds number:
where C ¼ k=cp : Boundary conditions for the former equations are listed below:
u ¼ constantð1:5 3:5m=sÞ;
ð8Þ
ADT lg
f ¼1 2
ð4bÞ
Dp
Dc
qu2in L
ð12Þ
The Colburn j factor:
j ¼ Nu=ðRe Pr1=3 Þ
ð13Þ
738
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Table 2 Simulation results of different grid numbers.
4. Simulation results and discussion
Grid number
1.23 million,
1.97 million
2.65 million
Nu f
45.663 0.00360
47.453 0.00373
47.548 0.00382
In the above equations Tin and Tout are the values of mean air inlet and outlet cross-section of the fin zone, Tw is the tube wall temperature, Dc is the tube outside diameter, uin is the mean velocity at the inlet cross-section. The heat transfer coefficient h is defined in terms of the heat transfer rate U and the log-mean temperature difference, the heat transfer rate U is determined by the aid of FLUENT. Grid independence assessment is conducted with radiantly arranged LVGs enhanced fin at channel height of 10 fins per inch at 2.5 m/s. Three grid systems of 1.23 million, 1.97 million and 2.65 million are adopted. The predicted averaged Nusselt numbers for the three grid systems are shown in Table 2. The average Nusselt number difference between 1.97 million and 2.65 million spaced meshes is only 0.2%, thus the result of grid system 1.97 million meshes is regarded grid independent. Finally 1.97 million is used for radiantly arranged LVGs enhanced fin. The grid systems around each tube of the four types of fin-and-tube surfaces are shown in Fig. 4 In order to validate the computational model, numerical simulation is performed at the same geometric sizes and operating conditions as the test data provided in [31,32], which is a rectangular channel with a delta winglet pair of vortex generators in common-flow-down arrangement. The attack angle is 30°. The comparison of numerical and experimental results is provided in Fig. 5. The mean deviation is 6.5% and the maximum deviation is 13.4%. Here the mean deviation is defined as the average difference between the experiment result and the numerical value of this work. Such agreement between numerical and experimental results show the reliability of the model and method used in the present study.
4.1. Temperature distribution Fig. 6 shows temperature contour distribution in the middle plane of channel height direction for the four simulated cases at 2.5 m/s. The inlet air temperature is 305 K, and the tube temperature 280 K. The fin pitch is 10 fins per inch. It is well-known that the heat transfer in wake region is always weak owing to vortex and circulation. Hence, the wake region should be reduced as much as possible. From the figure the wake region is very obvious after each tube for the plain fin in Fig. 6a, while for the common-flowdown LVG enhanced fin and the wavy fin shown in Fig. 6b and c its size is reduced, and for the proposed structure in Fig. 6d it almost disappears. The local flow channel (passage) formed between the fifth winglet and sixth winglet for each tube in case D is beneficial to the reduction of wake region. In addition the local flow passages formed by the first to fourth pair of winglets can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall .The above two functions of the proposed arrangement of winglets make the fluid temperature distribution being much more uniform at each cross section in case D than other three cases, which also contributes to heat transfer enhancement [33]. It is also noticeable that the outlet temperature of case D is the lowest, which means the total heat transfer rate of the proposed fin is the highest. 4.2. Flow field Stagnation or wake region is always unfavorable in heat exchanger because in these zones fluid velocity is low, and foul is easy to deposit, leading to weak heat transfer. On the contrary, high velocity in zones with high temperature gradient is expected according to field synergy principle [31–34]. Fig. 7 presents the velocity contour distribution of the 4 types of structures at 2.5 m/s. In Fig. 7a there are large scope of wake region and highest velocity lies in the main flow; in Fig. 7b although velocity near the tube wall is improved, wake region is still obvious after the tubes;
(a) Radiantly arranged LVGs enhanced fin
(b) Wavy fin
(c) Common-flow-down LVGs enhanced fin
(d) Plain plate fin
Fig. 4. Grid system.
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
739
B; the corner vortex in the stagnation region of the winglet can be found on cross-section C and the partial enlarged view is shown in Fig. 8B; both of the two vortices disappear on cross-section D. The same development of vortices occurs for winglet B on cross-section C and D. These vortices lead to destabilization of the streamwise velocity and initiates higher disturbance [8]. This is also responsible for the pressure penalty. 4.3. Friction and heat transfer characteristics comparison
Fig. 5. Comparison of heat transfer coefficient between the computed results and experimental data of common-flow-down LVG pair in rectangular channel.
and in Fig. 7c wake region is reduced and velocity is also increased, but fluid gathers at the trough of the wavy fin and velocity is low consequently. In Fig. 7d, stagnant zones with low velocity and weak heat transfer are significantly reduced; vortices are generated by the winglets and the fluid field is much more disordered compared with other 3 cases. The velocity of fluid near the tube in Fig. 7d is also much higher than that in main flow. This is because the winglets construct convergent channels between each winglet and the tube wall so that air flowing through the channel is accelerated and directed rightly towards the tube wall. On the other hand, the 2 latter winglets enhance heat transfer in the wake region where velocity is low, and the 4 former ones guide the mainstream flow with high velocity toward the tube wall where the temperature gradient is great and largely broaden the area of improved heat transfer zones. All the above points contribute to intensify heat transfer in the channel with radiantly arranged LVGs. Fig. 8 shows the velocity vector on four cross-sections (the specific positions are marked in Fig. 1) perpendicular to the flow direction. It can be seen in the figure that winglets arranged as suggested in this paper can generate longitudinal vortices as well as the conventional ones. On the cross-section A there is no obvious vortex after winglet A; as the vortex develops the leading edge vortex arises due to separation along the leading edge on cross-section
Fig. 9a presents Nu number of the four configurations versus Re number and Fig. 9b provides friction factor f versus Re number of the four heat exchange surfaces. The Reynolds number ranges from about 1335 to 3116, corresponding to the inlet velocity from 1.5 m/ s to 3.5 m/s, which is the usual velocity range in HVAC & R systems. As can be expected, vortex generators not only enhance heat transfer but also cause additional pressure loss. In the figure, radiantly arranged LVGs enhanced fin has the highest Nu number compared with other three cases, but also the highest friction factor f. For example, at inlet velocity of 2.5 m/s, Nu of radiantly arranged LVGs enhanced fin is 16.7, 38.5 and 100.1% higher than wavy fin, common-flow-down LVGs enhanced fin and the plain plate fin, respectively, while the friction factor f is 19.4, 86.5 and 144.0% higher than the other three cases 4.4. Performance evaluation It is essential to determine whether the enhanced technique is economical and advisable in practical applications, with both heat transfer and pressure drop being increased compared with a referenced structure. Aiming at energy saving, Fan et al. [27] proposed a unified, easy and clear log–log plot for the performance comparison of enhanced techniques with a referenced structure under the most widely adopted three constraints: identical pumping power, identical pressure drop and identical mass flow rate of fluid. The derivation procedure is quite lengthy and can be found in detail in [27]. For the simplicity of presentation, it will not be repeated here. Only the major results and the understanding of the plot are described below for reader’s convenience. Based on some assumptions widely adopted in engineering practice, the ratio of enhanced heat transfer rate over that of the referenced structure, Qe/Qo, can be expressed as follows:
Unit: K
(a) Case A
(b) Case B
(c) Case C
(d) Case D Fig. 6. Temperature distribution of four cases.
740
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Unit: m/s
(a) Case A
(b) Case B
(c) Case C
(d) Case D Fig. 7. Velocity distribution of four cases.
Cross-section D
Unit: m/s
Cross-section C
Cross-section B
Cross-section A
(a) Longitudinal vortex on four cross-sections along x direction (See Fig. 1 for the positions of cross sections A,B,C and D)
(b) Partial enlarged view of vortices in cross-section (C) Fig. 8. Longitudinal vortices generated by winglets at different cross-sections along x direction.
C Q;i
, ki Qe Nue fe ¼ ¼ Qo Nuo Re fo Re
ði ¼ P; Dp; VÞ
ð14Þ
where for the identical pumping power (i = P), identical pressure drop (i = Dp) and identical flow rate (i = V) the exponent ki are:
kP ¼
m2 ; 3 þ m1
kDp ¼
m2 ; 2 þ m1
kV ¼ 1:0
ð15Þ
where m1 and m2 are exponents in correlations of f Rem1 and Nu Rem2 for the referenced structure respectively. Taking the logarithm of (14) and setting ln(Nue/Nuo)Re, ln(fe/fo)Re as the ordinate and abscissa, respectively, we get Eq. (16), which represents a straight line in such a coordinate system:
ln
Nue Nu0
¼ bi þ ki ln Re
fe f0 Re
ð16Þ
bi is the intercept and ki is the slope of straight line in log–log coordinate system. The constant bi takes the values of ln C Q ;P , ln C Q ;D p , and ln CQ,V for the three constraints, respectively. The two coordinates, ln(Nue/Nuo) and ln(fe/fo) divide a plan into four quadrants: in the first quadrant both Nue/Nuo and fe/fo are larger than 1, and it is the most frequently encountered situation; in the second quadrant, Nue/Nuo is larger than 1 while fe/fo less than 1. This is the most perfect situation, but no enhanced techniques developed so far can meet such condition; in the third quadrant both Nue/Nuo and fe/fo are less than 1, which sometimes can be
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
741
Fig. 10. Performance evaluation plot of three structures with wavy fin serving as baseline (Tin = 305 K, uin = 1.5, 2, 2.5, 3, 3.5 m/s, Tw = 280 K).
Fig. 9. Nu and f of the four structures at different Re numbers.
encountered in engineering; finally in the fourth quadrant, Nue/Nuo is less than 1 but fe/fo larger than 1. Enhanced techniques with such performance will never be adopted in practice. The first quadrant is divided into four regions by the three constraints: the first region, Region 1, is bounded by the abscissa and the constraint of identical pumping power whose straight line m2 slope kP ¼ 3þm . Any combination of Nue/Nuo and fe/fo within this re1 gion can enhance heat transfer but cannot save energy; the second region is bounded by the two constraints, identical pumping power m2 and identical pressure drop whose slope kDp ¼ 2þm . Techniques 1 whose values of Nue/Nuo and fe/fo are in this region can save energy under the identical pumping power constraint; the third region is bounded by the diagonal where Nue/Nuo = fe/fo and the constraint of identical pressure drop. In this region heat transfer is enhanced at the constraint of identical pressure drop; finally, in the fourth region, any combination of Nue/Nuo and fe/fo implies that the heat transfer enhanced ratio is larger than the ratio of friction factor at the same flow rate. Fig. 10 shows such a plot. The three straight lines corresponding to the three constraints are baselines. The application of this plot for evaluating performance of enhanced techniques is very clear. Each combination of fe/fo and corresponding Nue/Nuo can be represented by a point (hereafter, working point) in the figure. The third quadrant is also divided into 4 regions and the space below the baseline of a certain constraint
means the working points lie in area within which the heat transfer has deteriorated from view point of this constraint. In this study the wavy fin shown in Fig. 2b is taken as the reference. Actually the plain fin can serves as the reference in [27], but as indicated above in this paper we want to find out a more efficient structure to replace the wavy fin. By taking the wavy fin as reference in the log–log comparison plot [27] not only the advantage and disadvantage of the proposed structure can be clearly found, but also other two fins can be obviously presented. The performance comparisons of the three structures over wavy fin are shown in Fig. 10 by the points of square, circle and triangle, respectively. In the figure, each structure has five working points corresponding to inlet velocity of 1.5 m/s, 2 m/s, 2.5 m/s, 3 m/s, and 3.5 m/s from left to right, respectively. The five working points of the radiantly arranged LVGs enhanced fin lie almost on the ‘fixed flow’ line. This means the proposed fin has better performance than the wavy fin under ‘fixed pump power’ and ‘fixed pressure drop’ constraints, and nearly better under ‘fixed flow’ condition. That is under the same flow rate the enhanced ratio of heat transfer is nearly the same as the increased ratio of friction factor, a case which very hardly occurs for gas heat transfer enhancement. For example, for the off-set fin the heat transfer enhancement ratio over the friction increase ratio is only 0.8 [36]. For the plain fin and the common flow down LVGs, their working points are in the 3rd quadrant, which implies that compared with the wavy fin, the heat transfer is deteriorated and the friction factor is decreased, too. As shown in the figure for the ‘‘common-flow-down’’ LVGs the ratio of Nue/Nuo is much larger than friction factor ratio fe/fo, while for the plain plate these two ratios become closer. This indicates that the ‘common-flow-down’ fin has better performance than the plain plate fin. Thus it can be concluded that for the four structures compared the proposed radiantly arranged LVGs enhanced fin is the best, the wavy-fin is next, and then comes the common-flow-down LVGs enhanced fin, and the plain fin is the worst. 4.5. Field synergy principle analysis Field synergy principle (FSP) has been proved quite useful to explain the mechanism responsible for the heat transfer enhancement of many kinds of heat transfer surfaces in recent years. It states that reducing the intersection angle between velocity and temperature gradient can effectively enhance convective heat transfer. This concept was first put forward by Guo et al. in [34], later further enhanced in [35,37,38]. According to FSP, the local intersection angle between velocity and temperature gradient reflects local heat transfer intensity: the smaller the angle the better
742
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Fig. 11. Average intersection angles of four structures.
Fig. 13. Heat transfer rate and pressure drop of radiant LVGs enhanced fin with different fin pitches.
In this study the modulus average intersection angles are calculated by a self-developed UDF program with FLUENT. The numerical results of am vs. Re number is presented in Fig. 11. It can be seen from the picture that the average intersection angle of radiantly arranged LVGs enhanced fin is appreciably lower than that of the other three structures and ranks the smallest of all. The synergy degrees of wavy fin, common-flow-down LVG and plain plate fin then follow up in order. This tendency is just the opposite to that of Nu number. 5. Effect of winglet size and fin pitch on proposed structure
Fig. 12. Heat transfer rate and pressure drop of radiantly arranged LVGs enhanced fin with different winglet lengths.
the local heat transfer. For the entire heat transfer region the modulus average intersection angle, which is the most suitable determination method for the averaged synergy angle according to the meaning of synergy re-stated in [35], can be used to indicate the global synergy between velocity and temperature gradient, which reads [39]:
X j! u j jgradtji dV i am ¼ ai P !i j u ji jgradtji dV i
ð17Þ
Among many geometric parameters of fin-and-tube surfaces the fin pitch often is the most sensitive parameter to the performance [5]. For the proposed LVGs enhanced surface the attack angles of the winglets have been fixed, the height of winglet is affected by fin pitch; hence, the only parameter of LVG which can be easily changed is its length. In the following the effect of winglet size and fin pitch on proposed structure are presented. 5.1. Effect of winglet length The simulation results of the influence of the length of winglet are displayed in Fig. 12. The height of the LVGs is 2.425 mm (10 fins per inch); the studied chord length is 4 mm, 5 mm and 6 mm, respectively. Numerical simulation indicates that pressure
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
drop increases with the length of winglets, while heat transfer rate reaches its maximum value at a length of 5 mm. At 2.5 m/s heat transfer rate of the fin with 5 mm LVGs is 4.6% and 1.5% higher than 4 mm and 6 mm, respectively; while pressure drop is 16.3% and 8.35% (negative means less) higher than 4 mm and 6 mm.The reason can be described as below: the additional pressure drop of the winglet is mainly caused by its form drag, and the longer the winglet, the larger its form drag. With respect to heat transfer, as indicated above, winglets in the fin surface form a kind of channel which can direct fluid with higher velocity from the main flow towards the tube wall. Fluid near the centerline of the channel is then mixing with fluid near the wall where the temperature difference is higher so that the heat transfer is much more intensified. Numerical results show that such channel function is most effective when the winglet chord equals to 5 mm.
743
(3) Radiantly arranged winglets enhanced fin possesses the best comprehensive performance compared with other three structures studied in this paper according to the newly proposed performance evaluation plot; the average intersection angle is also the minimum of all, which reveals the essence why the proposed fin has the best performance. (4) The pressure drop of radiantly arranged LVGs enhanced fin increases with the length of LVG chord, while heat transfer rate reaches the maximum value at 5 mm, thus the proposed fin structure has an optimum performance at the chord length of 5 mm. (5) The total heat transfer rate of the proposed fin with five tubes are almost the same as that of way fin with six tubes, while the pressure drop of the proposed structure is lower than the wavy structure. So the proposed structure with 5tube can replace the wavy structure with 6-tube.
5.2. Effect of fin pitch Numerical study for the effect of fin pitch is conducted for the proposed structure of 5 tubes with five different fin numbers per inch: 12, 11, 10, 9 and 8, corresponding to fin pitch of 2.117 mm, 2.309 mm, 2.54 mm, 2.822 mm, and 3.175 mm, respectively. The height of the LVGs is selected according to the smallest channel height and takes the value of 2.002 mm. The results are compared with a wavy fin of six tubes at the same conditions to demonstrate whether the 6-tube wavy fin in use can be replaced by 5-tube proposed fin. The inlet velocity is 2.5 m/s. Fig. 13a and b present heat transfer rate and pressure drop of the 2 configurations. In Fig. 13a the heat transfer rate of radiantly arranged LVGs enhanced fin is a bit less than the wavy fin at larger fin pitch, while at smaller fin pitch heat transfer of the former gets equal or even a bit larger. The reason for such variation trend may be attributed to the relative effect of the height of the vortex generator. With the fixed height (2.002 mm) at larger fin pitches the height of the LVGs is a bit too small with respect to the channel, and can’t bring enough disturbances to the air flow; with the decreasing fin pitch the effect of disturbance gradually increases and finally leads to a higher heat transfer rate than that of the wavy fin. Thereupon there’s an intersection on the plot. In Fig. 13b pressure drop of radiantly arranged LVGs enhanced fin of five tubes is lower than that of wavy fin of six tubes at all fin pitches investigated. Therefore it can be concluded that based on the performance comparison shown in Fig. 10 and the comparison shown in Fig. 13 the radiantly arranged LVGs enhanced fin has a better comprehensive performance and the 5-tube with radiantly arranged LVGs enhanced fin can be used to replace the 6-tube wavy fin, reducing 1/6 of the use of material as well as the volume of the heat exchanger. 6. Conclusion A new arrangement of LVGs on the plain fin-and-tube surface is proposed and its heat transfer and fluid flow characteristics are simulated. Performance evaluation and comparison with other three structures are conducted. The effects of winglet length and fin pitch on the proposed structure are investigated. Conclusions are summarized as follows: (1) Radiantly arranged winglets on fin surface constitute several converging passages which can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall and reducing the wake region behind the tube. Both are beneficial to heat transfer enhancement. (2) Winglet with its height end in the upstream direction can generate longitudinal vortex as the conventional arrangement.
Acknowledgements This study was supported by the National Basic Key Research Program of China (973 Program) and the key project of the National Natural Science Foundation of China (51136004). References [1] C.C. Wang, J. Lo, Y.T. Lin, C.S. Wei, Flow visualization of annular and delta winglet vortex generators in fin-and-tube heat exchanger application, Int. J. Heat Mass Transfer 45 (18) (2002) 3803–3815. [2] M. Fiebig, Embedded vortices in internal flow: heat transfer and pressure loss enhancement, Int. J. Heat Fluid Flow 16 (5) (1995) 376–388. [3] J.Y. Jang, L.K. Chen, Numerical analysis of heat transfer and fluid flow in a three-dimensional wavy-fin and tube heat exchanger, Int. J. Heat Mass Transfer 40 (16) (1997) 3981–3990. [4] S. Savino, G. Comini, C. Nonino, Three-dimensional analysis of convection in two-dimensional wavy channels, Numer. Heat Transfer Part A 46 (9) (2004) 869–890. [5] Y.L. He, Y.B. Tao, J. Huang, Z.G. Wu, W.Q. Tao, Three-dimensional numerical study of wavy fin-and-tube heat exchangers and field synergy principle analysis, Int. J. Heat Mass Transfer 50 (5–6) (2007) 1163–1175. [6] A.E. Bergles, ExHFT for fourth generation heat transfer technology, Exp. Therm. Fluid Sci. 26 (2–4) (2002) 335–344. [7] A.M. Jacobi, R.K. Shah, Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress, Exp. Therm. Fluid Sci. 11 (3) (1995) 295–309. [8] M. Fiebig, Vortices, generators and heat transfer, Chem. Eng. Res. Des. 76 (2) (1998) 108–123. [9] C.C. Wang, J. Lo, Y.T. Lin, M.S. Liu, Flow visualization of wave-type vortex generators having inline fin-tube arrangement, Int. J. Heat Mass Transfer 45 (9) (2002) 1933–1944. [10] M. Fiebig, P. Kallweit, N. Mitra, S. Tiggelbeck, Heat transfer enhancement and drag by longitudinal vortex generators in channel flow, Exp. Therm. Fluid Sci. 4 (1) (1991) 103–114. [11] M. Fiebig, A. Valencia, N.K. Mitra, Wing-type vortex generators for fin-andtube heat exchangers, Exp. Therm. Fluid Sci. 7 (4) (1993) 287–295. [12] S. Tiggelbeck, N.K. Mitra, M. Fiebig, Comparison of wing-type vortex generators for heat transfer enhancement in channel flows, ASME J. Heat Transfer 116 (4) (1994) 880–885. [13] Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of a finned oval tube with punched longitudinal vortex generators in-line, Int. J. Heat Mass Transfer 41 (24) (1998) 4151–4166. [14] Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of finned oval tubes with staggered punched longitudinal vortex generators, Int. J. Heat Mass Transfer 43 (3) (2000) 417–435. [15] K. Torii, K. Kwak, K. Nishino, Heat transfer enhancement accompanying pressure-loss reduction with winglet-type vortex generators for fin-tube heat exchangers, Int. J. Heat Mass Transfer 45 (18) (2002) 3795–3801. [16] C. Allison, B. Dally, Effect of a delta-winglet vortex pair on the performance of a tube-fin heat exchanger, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5065– 5072. [17] K. Kwak, K. Torii, K. Nishino, Simultaneous heat transfer enhancement and pressure loss reduction for finned-tube bundles with the first or two transverse rows of built-in winglets, Exp. Therm. Fluid Sci. 29 (5) (2005) 625–632. [18] G. Biswas, N.K. Mitra, M. Fiebig, Heat transfer enhancement in fin-tube heatexchangers by winglet type vortex generators, Int. J. Heat Mass Transfer 37 (2) (1994) 283–291.
744
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
[19] J. He, L. Liu, A.M. Jacobi, Air-side heat-transfer enhancement by a new winglettype vortex generator array in a plain-fin round-tube heat exchanger, ASME J. Heat Transfer 132 (7) (2010) 071801-1–071801-9. [20] J.F. Fan, Y.L. He, W.Q. Tao, Application of combined enhanced techniques for design of highly efficient air heat transfer surface, Heat Transfer Eng. 33 (1) (2011) 52–62. [21] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a channel with longitudinal vortex generator. Part B: parametric study of major influence factors, Int. J. Heat Mass Transfer 51 (13–14) (2008) 3683–3692. [22] A. Lemouedda, M. Breuer, E. Franz, T. Botsch, A. Delgado, Optimization of the angle of attack of delta-winglet vortex generators in a plate-fin-and-tube heat exchanger, Int. J. Heat Mass Transfer 53 (23–24) (2010) 5386–5399. [23] M. Zeng, L.H. Tang, M. Lin, Q.W. Wang, Optimization of heat exchangers with vortex-generator fin by Taguchi method, Appl. Therm. Eng. 30 (13) (2010) 1775–1783. [24] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a rectangular channel with longitudinal vortex generator. Part A: verification of field synergy principle, Int. J. Heat Mass Transfer 51 (5–6) (2008) 1179–1191. [25] J.M. Wu, W.Q. Tao, Investigation of laminar convection heat transfer in finand-tube heat exchanger in aligned arrangement with longitudinal vortex generator from the viewpoint of field synergy principle, Appl. Therm. Eng. 27 (14–15) (2007) 2609–2617. [26] Y.L. He, Y.W. Zhang, Advances and outlooks of heat transfer enhancement by longitudinal vortex generators, Advances in Heat Transfer, vol. 44, Elsevier, Inc., New York, 2012, pp. 119–185. [27] J.F. Fan, W.K. Ding, J.F. Zhang, Y.L. He, W.Q. Tao, A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving, Int. J. Heat Mass Transfer 52 (1–2) (2009) 33–44. [28] M. Fiebig, Y. Chen, A. Grossegorgemann, N.K. Mitra, Conjugate heat transfer of a finned tube. Part B: heat transfer augmentation and avoidance of heat
[29] [30] [31]
[32] [33]
[34] [35]
[36] [37]
[38]
[39]
transfer reversal by longitudinal vortex generators, Numer. Heat Transfer Part A Appl. 28 (2) (1995) 147–155. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980. W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, Xi’an, 2001, pp. 220–221. J.M. Wu, Research on the enhancement of natural and forced convective heat transfer by longitudinal fins and by longitudinal vortex generator (Ph.D. thesis), Xi’an Jiaotong University, Xi’an, 2006. J.M. Wu, W.Q. Tao, Effect of longitudinal vortex generator on heat transfer in rectangular channels, Appl. Therm. Eng. 37 (5) (2012) 67–72. Z.Y. Guo, S.Q. Zhou, Z.X. Li, L.G. Chen, Theoretical analysis and experimental confirmation of the uniformity principle of temperature difference field in heat exchanger, Int. J. Heat Mass Transfer 45 (10) (2002) 2119–2127. Z.Y. Guo, D.Y. Li, B.X. Wang, A novel concept for convective heat transfer enhancement, Int. J. Heat Mass Transfer 41 (2) (1998) 2221–2225. Z.Y. Guo, W.Q. Tao, R.K. Shah, The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer, Int. J. Heat Mass Transfer 48 (9) (2005) 1797–1807. R.K. Shah, D.P. Seculik, Fundamentals of Heat Exchanger Design, John Wiley & Sons Inc., New York, 2003, p. 696. W.Q. Tao, Z.Y. Guo, B.X. Wang, Field synergy principle for enhancing convective heat transfer-its extension and numerical verifications, Int. J. Heat Mass Transfer 45 (18) (2002) 3849–3856. W.Q. Tao, Y.L. He, Q.W. Wang, Z.G. Qu, F.Q. Song, A unified analysis on enhancing single phase convective heat transfer with field synergy principle, Int. J. Heat Mass Transfer 45 (24) (2002) 4871–4879. J.J. Zhou, Research on the mechanisms of heat transfer enhancement and saving energy of compact heat exchanger surface and its optimization (Ph.D. thesis), Xi’an Jiaotong University, Xi’an, 2005.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and pressure performance of a plain fin with radiantly arranged winglets around each tube in fin-and-tube heat transfer surface M.J. Li, W.J. Zhou, J.F. Zhang, J.F. Fan, Y.L. He, W.Q. Tao ⇑ Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy & Power Engineering, Xi’an Jiaotong University, 28 Xianning West Road, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 11 July 2013 Received in revised form 8 November 2013 Accepted 10 November 2013 Available online 12 December 2013 Keywords: Longitudinal vortex generator Fin-and-tube heat exchanger Wavy fin Field synergy principle Performance evaluation plot Waste heat recovery Numerical study
a b s t r a c t A radiantly arranged LVGs enhanced fin-and-tube structure is numerically investigated in this paper to enhance air side heat transfer. The arrangement of LVGs is totally different from existing publications. In the proposed structure there exist 12 winglets around each tube. The attack angles are 50, 50, 50, 50, 70 and 110°, respectively. The height ends of the winglets are further away from the tube, while the closed point ends of winglets are close to the tube wall. Heat transfer and pressure drop performance is compared with other three structures: an arc-shaped wavy fin-and-tube surface, a common-flowdown LVGs enhanced fin-and-tube surface and a plain plate fin-and-tube surface. The simulation results show that the 12 winglets form five local passages which can guide the moving fluid from the main flow to the tube wall, leading to some impinging effect or reducing the wake region behind the tube. The performance evaluation of the four structures is conducted by using the newly proposed ln (Nue/Nuo) vs. ln (fe/fo) plot based on energy saving. It is found that the proposed radiantly arranged LVGs enhanced finand-tube surface is the best. The field synergy principle is adopted to analyze the four structures and it is found that the domain averaged synergy angle of the proposed radiantly arranged LVGs enhanced structure is significantly less than that of other three cases. Finally characteristics of the proposed finand-tube surface with five tubes are investigated at five fin pitches and compared with the wavy structure of six tubes at the same other conditions. It is found that the proposed structure of five tubes can replace the wavy structure of six tubes. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Fin-and-tube heat exchangers are widely employed in industries such as heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems. Their efficiency directly determines the energy consumption of heat exchangers for both manufacturing and operating processes. Air is a common used working fluid in fin-andtube heat exchangers due to its cleanness and low cost, but the heat transfer capability of air is quite low, which leads to high thermal resistance on the air side of fin-and-tube heat exchanger. In typical applications, thermal resistance of the air side takes up over 90% of all [1], so the main approach for improvement of such heat exchangers is to enhance the air side heat transfer. Researchers have developed a lot of types of fin surfaces to enhance air-side heat transfer without introducing tremendous penalty of pressure drop and material consumption. Wavy fin and longitudinal vortex generator (LVG) are two usually employed enhancement techniques. The wavy structure periodically interrupts the growth of
⇑ Corresponding author. Tel.: +86 29 82669106. E-mail address: [email protected] (W.Q. Tao). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.024
the thermal boundary layers on the heat transfer surfaces and induces transverse vortex in wavy trough thus increasing fluid mixing and vortices. For the LVG enhanced fin surfaces, when fluid flows over LVG set at an appropriate attack angle, longitudinal vortices are generated [2] leading to the enhancement of heat transfer. In this paper a new-type arrangement of vortex generator will be proposed to enhance heat transfer of plain-fin surface and its performance is compared with an existing wavy fin surface. Hence, in the following previous studies on wavy and longitudinal vortex generator (LVG) enhanced fin surfaces will be briefly reviewed. In general, wavy or corrugated fins have different specific forms, including herringbone wavy fin, sinusoid or co-sinusoid wavy fin, v-shaped or triangular wavy fin, cambered corrugated fin, curved wavy fin and so on. Heat transfer and fluid flow characteristics of this fin configuration were reported in detail in literatures [3–5]. Jang and Chen [3] numerically investigated the effects of geometrical parameters especially the wavy angle on the triangular wavy fin performance, and concluded that the average Nusselt number Nu and friction factor f increase with the increase of wavy angle for equal wavy height. Savino et al. [4] identified that f always increases with the Reynolds number Re, while Nu increases significantly with Re only above a critical value of Re for herringbone
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
735
Nomenclature
Latin Symbols A air side heat transfer area Ac cross-section area at the inlet b1,b2,b3 lnCU, P, lnCU, 4p and lnCU, u cp specific heat L effective length of fin P pump power Pr Pr number qm mass flow rate T temperature u,v,w fluid velocity in x, y, and z direction
wavy fin. Furthermore, according to the study of [5], there exists an optimum fin pitch at which Nu is the maximum, and the increase of Re leads to the increase of Nu and the decrease of f. The above studies show that wavy fin will possess a satisfactory performance only at some certain circumstances like high inlet velocity and specific geometrical parameters. Longitudinal vortex generator is the fourth generation of enhanced measures [6]. In earlier studies, Jacobi and Shah [7] and Fiebig [8] gave thorough reviews of the development of LVG. Many kinds of generators in different shapes have been developed during the past two decays, such as wedge type, plough type, rectangular wing, delta winglet and so on. Among these types of LVGs triangular wing, rectangular wing, delta winglet and rectangular winglet are the most widely used ones [7]. Most of the typically used LVGs are summarized in [9]. Fiebig and his coworkers [10–12] made a great contribution to the development and application of LVG. They found that delta winglet has the best performance. So in this paper delta winglet generators are adopted, but the orientation and arrangement are different from all previous studies. Except the shape discussed above, the arrangement of LVGs is also an important factor influencing the comprehensive characteristics of enhanced surfaces. Chen et al. [13,14] employed punched winglet longitudinal vortex generators in staggered and inline arrangements to enhance heat transfer of oval tube heat exchanger, and found that winglets in staggered arrangement can bring larger heat transfer enhancement than in in-line arrangement. Torii et al. [15] referred to a pair of delta winglets as common-flow-up (in this winglets orientation flows between two adjacent winglets accelerate) and found it effective in reducing form drag and enhancing heat transfer of the wake region. Allison and Dally [16] also investigated common-flow-up winglets and found that the heat transfer of the winglet surface is 87% of a standard louver fin surface while the pressure drop is only 53%. Kwak et al. [17] and Biswas et al. [18] studied the common-flow-down configuration (in this winglets orientation flows between two adjacent winglets decelerate) and found it more effective for higher Re than for lower Re. He et al. [19] proposed a vortex generator array of ‘‘V’’ configuration inspired by the locomotion formation of bird and fish. The array is composed of two delta-winglet pairs placed at the attack angle of 10 degree or 30 degree. It is found that VG array with 30° is more efficient than two conventional single-pair designs at low Re representative of many HVAC&R applications. Fan et al. [20] combined LVGs with slotted protruding parallel strips and tried different variations of arrangement, finally substituted two tube-rows of the combined structure for an air-side wavy surface with three tube-rows.
Greek Symbols am modulus average intersection angle k thermal conductivity of fluid q density of fluid g dynamic viscosity Subscripts e enhanced fin o reference fin w wall
Researchers also conducted lots of studies on the effects of geometric parameters of LVGs. Wu and Tao [21] investigated geometric shape, size and the location of LVGs in a channel, and found that the overall Nu of the channel is higher with larger space between the LVG pair and larger area of LVG, and decreases with the LVG’s location away from the inlet of the channel. Lemouedda et al. [22] utilized a CFD analysis, response surface methodology and genetic algorithms to investigate the optimal attack angle of delta-winglet LVGs. They concluded that common-flow-up configuration shows better performance for the staggered arrangement, while common-flow-down is better for inline arrangement. Zeng et al. [23] studied and optimized the parameters of vortex-generator by the Taguchi method. They revealed that fin pitch has the greatest effect on the comprehensive performance, and then does the transverse tube pitch, attack angle, length of vortex generator, longitudinal tube pitch, and height of vortex generator. The friction factor and Nusselt number of heat transfer surface are almost independent of fin thickness and fin material. As far as the basic mechanism of enhancing heat transfer by LVG is concerned, it is often attributed to the disturbing of the thermal boundary layer, swirling and flow destabilization caused by LVG [2,7,8]. Wu and Tao [24,25] made comprehensive studies on this issue and their results definitely show that the fundamental reason that LVG can enhance heat transfer is the improvement of synergy between velocity and fluid temperature gradient. For more information of the recent developments and applications of LVG the review paper of [26] is recommended. The winglets adopted in the enhanced surfaces in open literatures are mostly placed in the line along the main flow direction, for either staggered or parallel arrangement. Considering that the flow passing a tube bank periodically changes its local direction: sometime towards the tube wall sometime leaving the tube wall, if we arrange individual winglet orientation to accommodate the local fluid flow direction, we may get some profits in enhancing heat transfer. The major goals of this paper is to find a more efficient structure to replace a wavy fin-and-tube surface already used in aircoolers widely adopted in air-conditioning equipment for clean air space in China. The present authors propose a new type of winglet orientation arrangement with 12 winglets being radiantly arranged around each tube. Considering that ‘common-flow-down’ structure of longitudinal vortex generator is one of the earliest and most representative LVG arrangements in literatures and the plain fin once was undoubtedly the most widely used fin in heat exchanger for its simple structure, we choose these four kinds of structure to make a comparison study in this paper. Numerical simulation is conducted and the results are compared with 3 referenced configurations (a corrugated fin in use, a conventional single-pair LVGs
736
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
placed at 45° (common-flow-down) enhanced fin and a plain plate fin with the same geometrical parameters) to illustrate that the proposed one possesses a satisfactory comprehensive performance. The influence of the winglets size is also investigated. The results are shown in an evaluation plot newly proposed by Fan et al. [27].
(a) Radiantly arranged LVGs enhanced fin
2. Physical and numerical models for simulated fin-and-tube heat transfer surface 2.1. Introduction to enhanced structures studied The schematic view of the proposed enhanced fin surface is partially shown in Fig. 1. As shown there we define x, y the streamwise and spanwise coordinates, respectively, and z the fin pitch direction. The entire heat transfer surface has five heat transfer units with each unit being composed of one tube and 12 surrounding winglets (see Fig. 2a). The delta winglets are punched out from the plain fin around each tube. The chord of the winglets l is 5 mm and will be optimized in Section 5.1. The number of attack angles, defined as the angle between the chord and the tube bank centerline, is 50, 50, 50, 50, 70 and 110°, respectively. These attack angles are obtained through some preliminary simulation for a better performance. The height of winglets hw is 2.425 mm. When punched out the delta winglets are just stuck perpendicular to the base surface and act as an obstacle to the coming flow, hence, can increase the disturbance of air flow. Since the delta winglet is punched from the plain fin, the thickness of the delta winglet is the same as the fin. The space between two neighboring winglets is not less than 1 mm for mechanical strength of the fin. The fin pitch Fp varies in different cases. Other geometric parameters are listed in Table 1. Apart from the proposed enhanced structure, we also take three referenced structure for comparison. Fig. 2b–d give the physical model of the three referenced structures studied in this paper. Fig. 2b is a collared wavy fin with 5 tubes in staggered arrangement, which is actually used in air-coolers. Further enhancement of heat transfer of the air-cooler is demanded in order to meet some practical requirements. The wavelength of the fin is 10.334 mm, the amplitude of the fin is 2 mm, and the diameter of the step is 18.0 mm. Fin pitch, fin thickness, tube diameter, transverse tube pitch and longitudinal tube pitch are identical with the proposed fin structure shown in Fig. 2a and Table 1; Fig. 2c shows a model with a common-flow-down arranged delta-winglet pair placed at the wake region of the tube. This structure is the most original arrangement of LVGs thus taken for comparison. The attack angle is 45° recommended by Fiebig and Chen [28]; Fig. 2d presents a plain fin-tube structure, which is the earliest fin-and-tube structure and still widely used now in industry. It’s worth pointing out further that the winglets configuration employed in this paper are different from that in open literatures in two ways. One difference indicated above is about the global arrangement of winglets: in conventional arrangement they are along the line of major flow direction, while in our arrangement
(b) Wavy fin
(c) Common-flow-down LVGs enhanced fin
(d) Plain plate fin Fig. 2. Physical model of the four simulated structures.
Table 1 Geometric dimensions of computational zone. Items
Dimensions (mm)
Fin thickness df Tube diameter Dc Transverse tube pitch Pt Longitudinal tube pitch Pl
0.115 13 27.5 15.875
they are grouped and winglets in each group are around a tube; the other is related to the orientation of the two ends (height end and its counterpart point end) of each winglet. Taking a pair of winglet arranged in common-flow-up pattern as an example, in the conventional arrangement the height end of each winglet is close to tube wall while its counterpart away from the tube wall (Fig. 3a); on the contrast, in the present arrangement the height end of the winglet is away from the tube wall while the point end is close the tube wall (Fig. 3b). 2.2. Computational domain Because of the obstruction of fin, the air velocity profile at the entrance of the channel is not uniform. So the computational domain has to be extended upstream by 2 the streamwise fin length to ensure a uniform velocity distribution at the domain inlet. With regard to the outlet, it is extended 10 the fin region to avoid recirculation and finally outflow boundary condition can be employed. The neighboring two fins’ center planes are chosen as the upper and lower boundaries of the computational domain due to the periodical repetition of the air channels in z direction in the whole fin-and-tube heat exchanger [20]. In the spanwise direction, the computational region is bounded by two adjacent center lines of tubes, also because of the periodicity in y-direction. 2.3. Physical assumptions and governing equations
Fig. 1. Schematic view of radiantly arranged winglets enhanced fin.
The inlet Reynolds number based on the outside tube diameter ranges from 1335 to 3116, and according to literatures [21,27,28] the flow is considered laminar and incompressible. The fluid flow
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
737
Boundary conditions in the y coordinate direction are: Tube region:
T w ¼ 280K; u ¼ m ¼ w ¼ 0;
ð4cÞ
Fin surface region:
u ¼ m ¼ w ¼ 0;
@T ¼0 @y
ð4dÞ
Fluid region:
@ m @w ¼ ¼ 0; @y @y
v ¼ 0;
@T ¼0 @y
ð4eÞ
All the top and bottom boundaries (z direction): periodic boundary conditions.
(a) Conventional common-flow-up 2.4. Numerical methods In the present study, the computational domain is discretized by non-uniform grids with software GAMBIT. The governing equations are discretized by the finite-volume method [29,30] and are solved using commercial code FLUENT (version 12). The temperatures in the solid fin surface and in the fluid are determined simultaneously, i.e., solved in the conjugated way. The convection terms for momentum and energy equations are discretized by QUICK scheme. The coupling between pressure and velocity is executed by SIMPLEC algorithm [30]. Iteration convergence is considered to be achieved, if following conditions are all satisfied: The residual of the continuity is less than 104. The residual of velocity component is less than 106. The residual of the energy is less than 108.
(b) Present common-flow-up Fig. 3. Two kinds of common-flow-up arranged LVGs.
3. Data reduction, grid independence examination and model validation and heat transfer are in steady state. The fluid thermophysical properties are constant. The heat transfer coefficient on the inner wall of the tube and the thermal conductivity of the tube wall are high enough, so the tube is assumed to be at constant temperature. Based on the foregoing assumptions, the governing equations of continuity, momentum and energy for three dimensional, constant material properties, laminar and steady forced convection flow can be described as follows: Continuity equation,
@ ðqui Þ ¼ 0 @xi
ð1Þ
@ @ @u ðqui uk Þ ¼ g k @xi @xi @xi
Total heat transfer rate:
U ¼ qm cp ðT out T in Þ
ð5Þ
The logarithmic mean temperature difference:
DT lg ¼
DT max DT min lnðDT max =DT min Þ
DT max ¼ maxðT w T in ; T w T out Þ
ð6Þ ð7Þ
The heat transfer coefficient :
Momentum equation,
Parameters used to evaluate and compare the performance of heat transfer surfaces are defined as follows:
@p ; @xk
h¼ k ¼ 1; 2; 3
ð2Þ
U
Nusselt number:
Energy equation,
@ @ @T ðqui TÞ ¼ C @xi @xi @xi
Nu ¼ ð3Þ
ð9Þ
m ¼ w ¼ 0; T in ¼ 305K
Re ¼
quin Dc g
ð10Þ
Pressure drop:
Dp ¼ pin pout
Boundary conditions in the x coordinate direction are: Domain inlet:
ð11Þ
The friction factor:
ð4aÞ
Domain outlet:
@u @ m @w @T ¼ ¼ ¼ ¼0 @x @x @x @x
hDc k
Reynolds number:
where C ¼ k=cp : Boundary conditions for the former equations are listed below:
u ¼ constantð1:5 3:5m=sÞ;
ð8Þ
ADT lg
f ¼1 2
ð4bÞ
Dp
Dc
qu2in L
ð12Þ
The Colburn j factor:
j ¼ Nu=ðRe Pr1=3 Þ
ð13Þ
738
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Table 2 Simulation results of different grid numbers.
4. Simulation results and discussion
Grid number
1.23 million,
1.97 million
2.65 million
Nu f
45.663 0.00360
47.453 0.00373
47.548 0.00382
In the above equations Tin and Tout are the values of mean air inlet and outlet cross-section of the fin zone, Tw is the tube wall temperature, Dc is the tube outside diameter, uin is the mean velocity at the inlet cross-section. The heat transfer coefficient h is defined in terms of the heat transfer rate U and the log-mean temperature difference, the heat transfer rate U is determined by the aid of FLUENT. Grid independence assessment is conducted with radiantly arranged LVGs enhanced fin at channel height of 10 fins per inch at 2.5 m/s. Three grid systems of 1.23 million, 1.97 million and 2.65 million are adopted. The predicted averaged Nusselt numbers for the three grid systems are shown in Table 2. The average Nusselt number difference between 1.97 million and 2.65 million spaced meshes is only 0.2%, thus the result of grid system 1.97 million meshes is regarded grid independent. Finally 1.97 million is used for radiantly arranged LVGs enhanced fin. The grid systems around each tube of the four types of fin-and-tube surfaces are shown in Fig. 4 In order to validate the computational model, numerical simulation is performed at the same geometric sizes and operating conditions as the test data provided in [31,32], which is a rectangular channel with a delta winglet pair of vortex generators in common-flow-down arrangement. The attack angle is 30°. The comparison of numerical and experimental results is provided in Fig. 5. The mean deviation is 6.5% and the maximum deviation is 13.4%. Here the mean deviation is defined as the average difference between the experiment result and the numerical value of this work. Such agreement between numerical and experimental results show the reliability of the model and method used in the present study.
4.1. Temperature distribution Fig. 6 shows temperature contour distribution in the middle plane of channel height direction for the four simulated cases at 2.5 m/s. The inlet air temperature is 305 K, and the tube temperature 280 K. The fin pitch is 10 fins per inch. It is well-known that the heat transfer in wake region is always weak owing to vortex and circulation. Hence, the wake region should be reduced as much as possible. From the figure the wake region is very obvious after each tube for the plain fin in Fig. 6a, while for the common-flowdown LVG enhanced fin and the wavy fin shown in Fig. 6b and c its size is reduced, and for the proposed structure in Fig. 6d it almost disappears. The local flow channel (passage) formed between the fifth winglet and sixth winglet for each tube in case D is beneficial to the reduction of wake region. In addition the local flow passages formed by the first to fourth pair of winglets can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall .The above two functions of the proposed arrangement of winglets make the fluid temperature distribution being much more uniform at each cross section in case D than other three cases, which also contributes to heat transfer enhancement [33]. It is also noticeable that the outlet temperature of case D is the lowest, which means the total heat transfer rate of the proposed fin is the highest. 4.2. Flow field Stagnation or wake region is always unfavorable in heat exchanger because in these zones fluid velocity is low, and foul is easy to deposit, leading to weak heat transfer. On the contrary, high velocity in zones with high temperature gradient is expected according to field synergy principle [31–34]. Fig. 7 presents the velocity contour distribution of the 4 types of structures at 2.5 m/s. In Fig. 7a there are large scope of wake region and highest velocity lies in the main flow; in Fig. 7b although velocity near the tube wall is improved, wake region is still obvious after the tubes;
(a) Radiantly arranged LVGs enhanced fin
(b) Wavy fin
(c) Common-flow-down LVGs enhanced fin
(d) Plain plate fin
Fig. 4. Grid system.
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
739
B; the corner vortex in the stagnation region of the winglet can be found on cross-section C and the partial enlarged view is shown in Fig. 8B; both of the two vortices disappear on cross-section D. The same development of vortices occurs for winglet B on cross-section C and D. These vortices lead to destabilization of the streamwise velocity and initiates higher disturbance [8]. This is also responsible for the pressure penalty. 4.3. Friction and heat transfer characteristics comparison
Fig. 5. Comparison of heat transfer coefficient between the computed results and experimental data of common-flow-down LVG pair in rectangular channel.
and in Fig. 7c wake region is reduced and velocity is also increased, but fluid gathers at the trough of the wavy fin and velocity is low consequently. In Fig. 7d, stagnant zones with low velocity and weak heat transfer are significantly reduced; vortices are generated by the winglets and the fluid field is much more disordered compared with other 3 cases. The velocity of fluid near the tube in Fig. 7d is also much higher than that in main flow. This is because the winglets construct convergent channels between each winglet and the tube wall so that air flowing through the channel is accelerated and directed rightly towards the tube wall. On the other hand, the 2 latter winglets enhance heat transfer in the wake region where velocity is low, and the 4 former ones guide the mainstream flow with high velocity toward the tube wall where the temperature gradient is great and largely broaden the area of improved heat transfer zones. All the above points contribute to intensify heat transfer in the channel with radiantly arranged LVGs. Fig. 8 shows the velocity vector on four cross-sections (the specific positions are marked in Fig. 1) perpendicular to the flow direction. It can be seen in the figure that winglets arranged as suggested in this paper can generate longitudinal vortices as well as the conventional ones. On the cross-section A there is no obvious vortex after winglet A; as the vortex develops the leading edge vortex arises due to separation along the leading edge on cross-section
Fig. 9a presents Nu number of the four configurations versus Re number and Fig. 9b provides friction factor f versus Re number of the four heat exchange surfaces. The Reynolds number ranges from about 1335 to 3116, corresponding to the inlet velocity from 1.5 m/ s to 3.5 m/s, which is the usual velocity range in HVAC & R systems. As can be expected, vortex generators not only enhance heat transfer but also cause additional pressure loss. In the figure, radiantly arranged LVGs enhanced fin has the highest Nu number compared with other three cases, but also the highest friction factor f. For example, at inlet velocity of 2.5 m/s, Nu of radiantly arranged LVGs enhanced fin is 16.7, 38.5 and 100.1% higher than wavy fin, common-flow-down LVGs enhanced fin and the plain plate fin, respectively, while the friction factor f is 19.4, 86.5 and 144.0% higher than the other three cases 4.4. Performance evaluation It is essential to determine whether the enhanced technique is economical and advisable in practical applications, with both heat transfer and pressure drop being increased compared with a referenced structure. Aiming at energy saving, Fan et al. [27] proposed a unified, easy and clear log–log plot for the performance comparison of enhanced techniques with a referenced structure under the most widely adopted three constraints: identical pumping power, identical pressure drop and identical mass flow rate of fluid. The derivation procedure is quite lengthy and can be found in detail in [27]. For the simplicity of presentation, it will not be repeated here. Only the major results and the understanding of the plot are described below for reader’s convenience. Based on some assumptions widely adopted in engineering practice, the ratio of enhanced heat transfer rate over that of the referenced structure, Qe/Qo, can be expressed as follows:
Unit: K
(a) Case A
(b) Case B
(c) Case C
(d) Case D Fig. 6. Temperature distribution of four cases.
740
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Unit: m/s
(a) Case A
(b) Case B
(c) Case C
(d) Case D Fig. 7. Velocity distribution of four cases.
Cross-section D
Unit: m/s
Cross-section C
Cross-section B
Cross-section A
(a) Longitudinal vortex on four cross-sections along x direction (See Fig. 1 for the positions of cross sections A,B,C and D)
(b) Partial enlarged view of vortices in cross-section (C) Fig. 8. Longitudinal vortices generated by winglets at different cross-sections along x direction.
C Q;i
, ki Qe Nue fe ¼ ¼ Qo Nuo Re fo Re
ði ¼ P; Dp; VÞ
ð14Þ
where for the identical pumping power (i = P), identical pressure drop (i = Dp) and identical flow rate (i = V) the exponent ki are:
kP ¼
m2 ; 3 þ m1
kDp ¼
m2 ; 2 þ m1
kV ¼ 1:0
ð15Þ
where m1 and m2 are exponents in correlations of f Rem1 and Nu Rem2 for the referenced structure respectively. Taking the logarithm of (14) and setting ln(Nue/Nuo)Re, ln(fe/fo)Re as the ordinate and abscissa, respectively, we get Eq. (16), which represents a straight line in such a coordinate system:
ln
Nue Nu0
¼ bi þ ki ln Re
fe f0 Re
ð16Þ
bi is the intercept and ki is the slope of straight line in log–log coordinate system. The constant bi takes the values of ln C Q ;P , ln C Q ;D p , and ln CQ,V for the three constraints, respectively. The two coordinates, ln(Nue/Nuo) and ln(fe/fo) divide a plan into four quadrants: in the first quadrant both Nue/Nuo and fe/fo are larger than 1, and it is the most frequently encountered situation; in the second quadrant, Nue/Nuo is larger than 1 while fe/fo less than 1. This is the most perfect situation, but no enhanced techniques developed so far can meet such condition; in the third quadrant both Nue/Nuo and fe/fo are less than 1, which sometimes can be
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
741
Fig. 10. Performance evaluation plot of three structures with wavy fin serving as baseline (Tin = 305 K, uin = 1.5, 2, 2.5, 3, 3.5 m/s, Tw = 280 K).
Fig. 9. Nu and f of the four structures at different Re numbers.
encountered in engineering; finally in the fourth quadrant, Nue/Nuo is less than 1 but fe/fo larger than 1. Enhanced techniques with such performance will never be adopted in practice. The first quadrant is divided into four regions by the three constraints: the first region, Region 1, is bounded by the abscissa and the constraint of identical pumping power whose straight line m2 slope kP ¼ 3þm . Any combination of Nue/Nuo and fe/fo within this re1 gion can enhance heat transfer but cannot save energy; the second region is bounded by the two constraints, identical pumping power m2 and identical pressure drop whose slope kDp ¼ 2þm . Techniques 1 whose values of Nue/Nuo and fe/fo are in this region can save energy under the identical pumping power constraint; the third region is bounded by the diagonal where Nue/Nuo = fe/fo and the constraint of identical pressure drop. In this region heat transfer is enhanced at the constraint of identical pressure drop; finally, in the fourth region, any combination of Nue/Nuo and fe/fo implies that the heat transfer enhanced ratio is larger than the ratio of friction factor at the same flow rate. Fig. 10 shows such a plot. The three straight lines corresponding to the three constraints are baselines. The application of this plot for evaluating performance of enhanced techniques is very clear. Each combination of fe/fo and corresponding Nue/Nuo can be represented by a point (hereafter, working point) in the figure. The third quadrant is also divided into 4 regions and the space below the baseline of a certain constraint
means the working points lie in area within which the heat transfer has deteriorated from view point of this constraint. In this study the wavy fin shown in Fig. 2b is taken as the reference. Actually the plain fin can serves as the reference in [27], but as indicated above in this paper we want to find out a more efficient structure to replace the wavy fin. By taking the wavy fin as reference in the log–log comparison plot [27] not only the advantage and disadvantage of the proposed structure can be clearly found, but also other two fins can be obviously presented. The performance comparisons of the three structures over wavy fin are shown in Fig. 10 by the points of square, circle and triangle, respectively. In the figure, each structure has five working points corresponding to inlet velocity of 1.5 m/s, 2 m/s, 2.5 m/s, 3 m/s, and 3.5 m/s from left to right, respectively. The five working points of the radiantly arranged LVGs enhanced fin lie almost on the ‘fixed flow’ line. This means the proposed fin has better performance than the wavy fin under ‘fixed pump power’ and ‘fixed pressure drop’ constraints, and nearly better under ‘fixed flow’ condition. That is under the same flow rate the enhanced ratio of heat transfer is nearly the same as the increased ratio of friction factor, a case which very hardly occurs for gas heat transfer enhancement. For example, for the off-set fin the heat transfer enhancement ratio over the friction increase ratio is only 0.8 [36]. For the plain fin and the common flow down LVGs, their working points are in the 3rd quadrant, which implies that compared with the wavy fin, the heat transfer is deteriorated and the friction factor is decreased, too. As shown in the figure for the ‘‘common-flow-down’’ LVGs the ratio of Nue/Nuo is much larger than friction factor ratio fe/fo, while for the plain plate these two ratios become closer. This indicates that the ‘common-flow-down’ fin has better performance than the plain plate fin. Thus it can be concluded that for the four structures compared the proposed radiantly arranged LVGs enhanced fin is the best, the wavy-fin is next, and then comes the common-flow-down LVGs enhanced fin, and the plain fin is the worst. 4.5. Field synergy principle analysis Field synergy principle (FSP) has been proved quite useful to explain the mechanism responsible for the heat transfer enhancement of many kinds of heat transfer surfaces in recent years. It states that reducing the intersection angle between velocity and temperature gradient can effectively enhance convective heat transfer. This concept was first put forward by Guo et al. in [34], later further enhanced in [35,37,38]. According to FSP, the local intersection angle between velocity and temperature gradient reflects local heat transfer intensity: the smaller the angle the better
742
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
Fig. 11. Average intersection angles of four structures.
Fig. 13. Heat transfer rate and pressure drop of radiant LVGs enhanced fin with different fin pitches.
In this study the modulus average intersection angles are calculated by a self-developed UDF program with FLUENT. The numerical results of am vs. Re number is presented in Fig. 11. It can be seen from the picture that the average intersection angle of radiantly arranged LVGs enhanced fin is appreciably lower than that of the other three structures and ranks the smallest of all. The synergy degrees of wavy fin, common-flow-down LVG and plain plate fin then follow up in order. This tendency is just the opposite to that of Nu number. 5. Effect of winglet size and fin pitch on proposed structure
Fig. 12. Heat transfer rate and pressure drop of radiantly arranged LVGs enhanced fin with different winglet lengths.
the local heat transfer. For the entire heat transfer region the modulus average intersection angle, which is the most suitable determination method for the averaged synergy angle according to the meaning of synergy re-stated in [35], can be used to indicate the global synergy between velocity and temperature gradient, which reads [39]:
X j! u j jgradtji dV i am ¼ ai P !i j u ji jgradtji dV i
ð17Þ
Among many geometric parameters of fin-and-tube surfaces the fin pitch often is the most sensitive parameter to the performance [5]. For the proposed LVGs enhanced surface the attack angles of the winglets have been fixed, the height of winglet is affected by fin pitch; hence, the only parameter of LVG which can be easily changed is its length. In the following the effect of winglet size and fin pitch on proposed structure are presented. 5.1. Effect of winglet length The simulation results of the influence of the length of winglet are displayed in Fig. 12. The height of the LVGs is 2.425 mm (10 fins per inch); the studied chord length is 4 mm, 5 mm and 6 mm, respectively. Numerical simulation indicates that pressure
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
drop increases with the length of winglets, while heat transfer rate reaches its maximum value at a length of 5 mm. At 2.5 m/s heat transfer rate of the fin with 5 mm LVGs is 4.6% and 1.5% higher than 4 mm and 6 mm, respectively; while pressure drop is 16.3% and 8.35% (negative means less) higher than 4 mm and 6 mm.The reason can be described as below: the additional pressure drop of the winglet is mainly caused by its form drag, and the longer the winglet, the larger its form drag. With respect to heat transfer, as indicated above, winglets in the fin surface form a kind of channel which can direct fluid with higher velocity from the main flow towards the tube wall. Fluid near the centerline of the channel is then mixing with fluid near the wall where the temperature difference is higher so that the heat transfer is much more intensified. Numerical results show that such channel function is most effective when the winglet chord equals to 5 mm.
743
(3) Radiantly arranged winglets enhanced fin possesses the best comprehensive performance compared with other three structures studied in this paper according to the newly proposed performance evaluation plot; the average intersection angle is also the minimum of all, which reveals the essence why the proposed fin has the best performance. (4) The pressure drop of radiantly arranged LVGs enhanced fin increases with the length of LVG chord, while heat transfer rate reaches the maximum value at 5 mm, thus the proposed fin structure has an optimum performance at the chord length of 5 mm. (5) The total heat transfer rate of the proposed fin with five tubes are almost the same as that of way fin with six tubes, while the pressure drop of the proposed structure is lower than the wavy structure. So the proposed structure with 5tube can replace the wavy structure with 6-tube.
5.2. Effect of fin pitch Numerical study for the effect of fin pitch is conducted for the proposed structure of 5 tubes with five different fin numbers per inch: 12, 11, 10, 9 and 8, corresponding to fin pitch of 2.117 mm, 2.309 mm, 2.54 mm, 2.822 mm, and 3.175 mm, respectively. The height of the LVGs is selected according to the smallest channel height and takes the value of 2.002 mm. The results are compared with a wavy fin of six tubes at the same conditions to demonstrate whether the 6-tube wavy fin in use can be replaced by 5-tube proposed fin. The inlet velocity is 2.5 m/s. Fig. 13a and b present heat transfer rate and pressure drop of the 2 configurations. In Fig. 13a the heat transfer rate of radiantly arranged LVGs enhanced fin is a bit less than the wavy fin at larger fin pitch, while at smaller fin pitch heat transfer of the former gets equal or even a bit larger. The reason for such variation trend may be attributed to the relative effect of the height of the vortex generator. With the fixed height (2.002 mm) at larger fin pitches the height of the LVGs is a bit too small with respect to the channel, and can’t bring enough disturbances to the air flow; with the decreasing fin pitch the effect of disturbance gradually increases and finally leads to a higher heat transfer rate than that of the wavy fin. Thereupon there’s an intersection on the plot. In Fig. 13b pressure drop of radiantly arranged LVGs enhanced fin of five tubes is lower than that of wavy fin of six tubes at all fin pitches investigated. Therefore it can be concluded that based on the performance comparison shown in Fig. 10 and the comparison shown in Fig. 13 the radiantly arranged LVGs enhanced fin has a better comprehensive performance and the 5-tube with radiantly arranged LVGs enhanced fin can be used to replace the 6-tube wavy fin, reducing 1/6 of the use of material as well as the volume of the heat exchanger. 6. Conclusion A new arrangement of LVGs on the plain fin-and-tube surface is proposed and its heat transfer and fluid flow characteristics are simulated. Performance evaluation and comparison with other three structures are conducted. The effects of winglet length and fin pitch on the proposed structure are investigated. Conclusions are summarized as follows: (1) Radiantly arranged winglets on fin surface constitute several converging passages which can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall and reducing the wake region behind the tube. Both are beneficial to heat transfer enhancement. (2) Winglet with its height end in the upstream direction can generate longitudinal vortex as the conventional arrangement.
Acknowledgements This study was supported by the National Basic Key Research Program of China (973 Program) and the key project of the National Natural Science Foundation of China (51136004). References [1] C.C. Wang, J. Lo, Y.T. Lin, C.S. Wei, Flow visualization of annular and delta winglet vortex generators in fin-and-tube heat exchanger application, Int. J. Heat Mass Transfer 45 (18) (2002) 3803–3815. [2] M. Fiebig, Embedded vortices in internal flow: heat transfer and pressure loss enhancement, Int. J. Heat Fluid Flow 16 (5) (1995) 376–388. [3] J.Y. Jang, L.K. Chen, Numerical analysis of heat transfer and fluid flow in a three-dimensional wavy-fin and tube heat exchanger, Int. J. Heat Mass Transfer 40 (16) (1997) 3981–3990. [4] S. Savino, G. Comini, C. Nonino, Three-dimensional analysis of convection in two-dimensional wavy channels, Numer. Heat Transfer Part A 46 (9) (2004) 869–890. [5] Y.L. He, Y.B. Tao, J. Huang, Z.G. Wu, W.Q. Tao, Three-dimensional numerical study of wavy fin-and-tube heat exchangers and field synergy principle analysis, Int. J. Heat Mass Transfer 50 (5–6) (2007) 1163–1175. [6] A.E. Bergles, ExHFT for fourth generation heat transfer technology, Exp. Therm. Fluid Sci. 26 (2–4) (2002) 335–344. [7] A.M. Jacobi, R.K. Shah, Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress, Exp. Therm. Fluid Sci. 11 (3) (1995) 295–309. [8] M. Fiebig, Vortices, generators and heat transfer, Chem. Eng. Res. Des. 76 (2) (1998) 108–123. [9] C.C. Wang, J. Lo, Y.T. Lin, M.S. Liu, Flow visualization of wave-type vortex generators having inline fin-tube arrangement, Int. J. Heat Mass Transfer 45 (9) (2002) 1933–1944. [10] M. Fiebig, P. Kallweit, N. Mitra, S. Tiggelbeck, Heat transfer enhancement and drag by longitudinal vortex generators in channel flow, Exp. Therm. Fluid Sci. 4 (1) (1991) 103–114. [11] M. Fiebig, A. Valencia, N.K. Mitra, Wing-type vortex generators for fin-andtube heat exchangers, Exp. Therm. Fluid Sci. 7 (4) (1993) 287–295. [12] S. Tiggelbeck, N.K. Mitra, M. Fiebig, Comparison of wing-type vortex generators for heat transfer enhancement in channel flows, ASME J. Heat Transfer 116 (4) (1994) 880–885. [13] Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of a finned oval tube with punched longitudinal vortex generators in-line, Int. J. Heat Mass Transfer 41 (24) (1998) 4151–4166. [14] Y. Chen, M. Fiebig, N.K. Mitra, Heat transfer enhancement of finned oval tubes with staggered punched longitudinal vortex generators, Int. J. Heat Mass Transfer 43 (3) (2000) 417–435. [15] K. Torii, K. Kwak, K. Nishino, Heat transfer enhancement accompanying pressure-loss reduction with winglet-type vortex generators for fin-tube heat exchangers, Int. J. Heat Mass Transfer 45 (18) (2002) 3795–3801. [16] C. Allison, B. Dally, Effect of a delta-winglet vortex pair on the performance of a tube-fin heat exchanger, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5065– 5072. [17] K. Kwak, K. Torii, K. Nishino, Simultaneous heat transfer enhancement and pressure loss reduction for finned-tube bundles with the first or two transverse rows of built-in winglets, Exp. Therm. Fluid Sci. 29 (5) (2005) 625–632. [18] G. Biswas, N.K. Mitra, M. Fiebig, Heat transfer enhancement in fin-tube heatexchangers by winglet type vortex generators, Int. J. Heat Mass Transfer 37 (2) (1994) 283–291.
744
M.J. Li et al. / International Journal of Heat and Mass Transfer 70 (2014) 734–744
[19] J. He, L. Liu, A.M. Jacobi, Air-side heat-transfer enhancement by a new winglettype vortex generator array in a plain-fin round-tube heat exchanger, ASME J. Heat Transfer 132 (7) (2010) 071801-1–071801-9. [20] J.F. Fan, Y.L. He, W.Q. Tao, Application of combined enhanced techniques for design of highly efficient air heat transfer surface, Heat Transfer Eng. 33 (1) (2011) 52–62. [21] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a channel with longitudinal vortex generator. Part B: parametric study of major influence factors, Int. J. Heat Mass Transfer 51 (13–14) (2008) 3683–3692. [22] A. Lemouedda, M. Breuer, E. Franz, T. Botsch, A. Delgado, Optimization of the angle of attack of delta-winglet vortex generators in a plate-fin-and-tube heat exchanger, Int. J. Heat Mass Transfer 53 (23–24) (2010) 5386–5399. [23] M. Zeng, L.H. Tang, M. Lin, Q.W. Wang, Optimization of heat exchangers with vortex-generator fin by Taguchi method, Appl. Therm. Eng. 30 (13) (2010) 1775–1783. [24] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a rectangular channel with longitudinal vortex generator. Part A: verification of field synergy principle, Int. J. Heat Mass Transfer 51 (5–6) (2008) 1179–1191. [25] J.M. Wu, W.Q. Tao, Investigation of laminar convection heat transfer in finand-tube heat exchanger in aligned arrangement with longitudinal vortex generator from the viewpoint of field synergy principle, Appl. Therm. Eng. 27 (14–15) (2007) 2609–2617. [26] Y.L. He, Y.W. Zhang, Advances and outlooks of heat transfer enhancement by longitudinal vortex generators, Advances in Heat Transfer, vol. 44, Elsevier, Inc., New York, 2012, pp. 119–185. [27] J.F. Fan, W.K. Ding, J.F. Zhang, Y.L. He, W.Q. Tao, A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving, Int. J. Heat Mass Transfer 52 (1–2) (2009) 33–44. [28] M. Fiebig, Y. Chen, A. Grossegorgemann, N.K. Mitra, Conjugate heat transfer of a finned tube. Part B: heat transfer augmentation and avoidance of heat
[29] [30] [31]
[32] [33]
[34] [35]
[36] [37]
[38]
[39]
transfer reversal by longitudinal vortex generators, Numer. Heat Transfer Part A Appl. 28 (2) (1995) 147–155. S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980. W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, Xi’an, 2001, pp. 220–221. J.M. Wu, Research on the enhancement of natural and forced convective heat transfer by longitudinal fins and by longitudinal vortex generator (Ph.D. thesis), Xi’an Jiaotong University, Xi’an, 2006. J.M. Wu, W.Q. Tao, Effect of longitudinal vortex generator on heat transfer in rectangular channels, Appl. Therm. Eng. 37 (5) (2012) 67–72. Z.Y. Guo, S.Q. Zhou, Z.X. Li, L.G. Chen, Theoretical analysis and experimental confirmation of the uniformity principle of temperature difference field in heat exchanger, Int. J. Heat Mass Transfer 45 (10) (2002) 2119–2127. Z.Y. Guo, D.Y. Li, B.X. Wang, A novel concept for convective heat transfer enhancement, Int. J. Heat Mass Transfer 41 (2) (1998) 2221–2225. Z.Y. Guo, W.Q. Tao, R.K. Shah, The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer, Int. J. Heat Mass Transfer 48 (9) (2005) 1797–1807. R.K. Shah, D.P. Seculik, Fundamentals of Heat Exchanger Design, John Wiley & Sons Inc., New York, 2003, p. 696. W.Q. Tao, Z.Y. Guo, B.X. Wang, Field synergy principle for enhancing convective heat transfer-its extension and numerical verifications, Int. J. Heat Mass Transfer 45 (18) (2002) 3849–3856. W.Q. Tao, Y.L. He, Q.W. Wang, Z.G. Qu, F.Q. Song, A unified analysis on enhancing single phase convective heat transfer with field synergy principle, Int. J. Heat Mass Transfer 45 (24) (2002) 4871–4879. J.J. Zhou, Research on the mechanisms of heat transfer enhancement and saving energy of compact heat exchanger surface and its optimization (Ph.D. thesis), Xi’an Jiaotong University, Xi’an, 2005.