Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers with Various Fin Types

Transcription

1 CHAPTER 7 Air-Side Heat Transfer and Friction Characteristics of Fin-and-Tube Heat Exchangers with Various Fin Types L.B. Wang 1, M. Zeng 2, L.H. Tang 2 & Q.W. Wang 2 1 Department of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu, China. 2 Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi an Jiaotong University, Xi an, Shaanxi, China. Abstract Tube bank fin heat exchangers have widespread applications, they are transferring enormous amounts of energy, and also consuming very large amount of mechanical energy. Because the dominant thermal resistance in such heat exchangers is usually on the air side in practical applications, and therefore the use of the fin surfaces on the air side is very common to effectively improve their overall thermal performance. Energy costs and environmental considerations continue to motivate attempts to derive better performance over the existing designs. As a result, during the past few years, there are also many investigations to the slit fin pattern and to the longitudinal vortex generator fins. Because it involves a huge cost and a strenuous work to compare the heat transfer performances of these fin patterns, up to now there are no enough data to summarize the comparisons thoroughly. However, there are a few reported results now available to make a brief summary on the airside performances of the various fin patterns with aims to provide information for some readers to utilize the available data, to find the work need to be done further, and find out new fin pattern having good heat transfer performance. Therefore, in this chapter the heat transfer performances of five fin patterns of circular tube bank fin heat exchangers are compared. In addition, the heat transfer performances of three fin patterns of flat tube bank fin heat exchangers are also compared. Three sets of criteria, namely, the identical mass flow rate, pressure drop, and the identical pumping power, are used in judging. The results show that for the circular tube bank fin heat exchangers, with the Reynolds number ranging from 4,000 to 10,000, doi: / /007

2 212 EMERGING TOPICS IN HEAT TRANSFER at high Reynolds numbers, the slit fin offers best heat transfer performance; for the flat tube bank fin heat exchangers, the fin with vortex generators has a better heat transfer performance than the fin punched rhombic formation and the louver fin; naphthalene heat mass transfer analogy method can be used to screen the fin pattern with a required accuracy; for the circular tube bank fin heat exchangers, further optimization and experimental comparisons of the fin pattern with vortex generators to the slit fin pattern should be carried out to identify the one with better heat transfer performance. Keywords: Evaluation criteria; fi n-and-tube heat exchanger; fi n patterns; performance. 1 Introduction Tube bank fin heat exchangers are used in a broad range of applications including industrial and chemical processes, air conditioners for domestic or industrial applications, and automotive radiators. These heat exchangers mostly use three types of the tubes, namely, circular tube, flat tube, and oval tube as shown in Fig. 1. The basic design consists of a stack of closely spaced fins through which tubes have been inserted, and this configuration has changed little since their introduction over 40 years ago [1]. Because of their widespread applications, they are transferring enormous amounts of energy, and also consuming very large amount of mechanical energy. As global energy consumption is has a negative impact on the environment and causes depletion of our existing fuel stocks, energy utilizations have come under close scrutiny. Heat exchangers are an integral component of the dissemination of energy and their effectiveness is becoming crucial to our lifestyle sustainability. Energy costs and environmental considerations continue to motivate attempts to derive better performance over the existing designs. The dominant thermal resistance in such heat exchangers is usually on the air side in practical applications, and therefore the use of the fin surfaces on the air side is very common to effectively improve their overall thermal performance. Figure 1: Tube bank fin heat exchangers with different types of the tube.

3 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 213 The most simple fin pattern of these heat exchangers is plain fin. For circular tube bank plain fin geometry, McQuiston [2], Gray and Webb [3], and Wang et al. [4 6] established extensive data and correlations of the heat transfer performance. For flat tube bank plain fin heat exchangers, Kays and London [1], Wang et al. [7, 8] and Kylikof [9] contributed much to the data and the correlations. For oval tube bank plain fin heat exchangers, Kays and London [1], Matos et al. [10] and Saboya and Sparrow [11] contributed much to the data and the correlations. It was found that in most cases, the plain fin is not enough to decrease the air-side thermal resistance. Therefore, many fin patterns have been invented in the past years. These have evolved from wavy fins to slit fins and presently louver fins are widely used. However, in general, modifications to the fin surface have resulted in an increase in pressure drop with little improvement in heat transfer performance [12]. During the past few years, the crimped spiral fin was addressed by Nuntaphan et al. [13, 14]. There are also many investigations to the slit fin pattern [15 18] and to the longitudinal vortex generator fins [7, 8, 19 28]. Because it involves a huge cost and strenuous work to compare the heat transfer performances of these fin patterns, up to now there are no enough data to summarize the comparisons thoroughly. However, there are a few reported results now available to make a brief summary on the air-side performances of the various fin patterns. This may provide information for some readers to utilize the available data, to find the work need to be done further, and find out new fin pattern having good heat transfer performance. The following pages are divided into two parts. In first part, the heat transfer performance of the fin patterns of circular tube bank fin heat exchangers is compared; in the second part, the heat transfer performance of fin patterns of flat tube bank fin heat exchangers is compared. In the comparing processes, three sets of criteria (i.e. the identical mass flow rate, pressure drop and the identical pumping power) are used. 2 Heat Transfer Performances of the Fin Patterns for Circular Tube In this section, the fin-side heat transfer performances of five fin patterns as shown in Fig. 2 for circular tube are summarized. The geometrical details of these fin patterns are presented in Table 1. The experimental details to obtain the heat transfer performances of the aforementioned fin patterns [27] will not be repeated here, but in order to use these data conveniently and correctly, it is necessary to declare the process of data reduction again. The average value of the inlet and outlet temperatures of air side is used to evaluate the thermal properties of air. The total heat transfer coefficient, UA product, is calculated from the following relationship: UA = Q ave /Δ t m (1)

4 214 EMERGING TOPICS IN HEAT TRANSFER (a) Crimped spiral fin (b) Plain fin (c) Slit fin (d) Vortex-generator fin (e) Mixed fin Figure 2: Fin configurations. Table 1: Geometric dimensions of fin-and-tube heat exchangers. Name Type D i D o D c F p P t P l s w s l s h V l V h α N P12 Plain S12 Slit V12 Vortex VSM12 Mixed SP12 Spiral Note: 1. Fin thicknesses of all test samples are 0.3 mm; 2. VSM12 is mixed by front 6-row vortex-generator fin and rear 6-row slit fin. where Δt m is the logarithmic-mean temperature difference, defined by Δt m = ( ts tin ) ( ts tout ) ts tin ln t t s out (2) where t in is the inlet temperature of air, t out is the outlet temperature, and t s is the saturated temperature of steam at the corresponding pressure. The overall heat transfer resistance can be defined as Do Do 1 = + ln + (3) UA h h A 2 l A D h A o o o w w i i i

5 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 215 In eqn (3), h o is the finned surface efficiency, which may be written in terms of the fin efficiency h, fin surface area A f and total surface area A o, as follows: Af ho = 1 1 h A ( ) (4) o where A o = A f + A b, A f, and A b are the areas of the fin and base surface, respectively. h is calculated by the approximation method described by Schmidt [29] h= tanh( mrcw)/( mrc w) (5) where m = 2h o /( ld f f ) (6) w = ( R / r 1)[ log ( R / r )] (7) eq c e eq c R r eq c X M X L = 127. ( 03. ) 05. (8) r X c M 2 2 X = ( P/ 2) + P / 2 (9) L t X M= Pt/2 (10) The air-side heat transfer coefficient h o and the surface efficiency h o can be acquired by solving eqns (5) (10) using an iterative method. The heat transfer and friction characteristics of the heat exchanger are presented in the following dimensionless forms: Nu= h o D c /l (11) 1 ReD v D c max c/ (12) 1/3 j = Nu/( ReD Pr ) c (13) 2 f = ( 2ΔpDc L v max (14) where v max is the velocity at the minimum free flow area, v max = v fr /σ. The term σ is the ratio of the minimum flow area to frontal area. Figures 3 and 4 show Nu, Δp, j factor and f factor with air frontal velocity for various fin patterns. In these figures, P12 stands for plain fin with N = 12, S12 stands for slit fin with N = 12, V12 stands for vortex-generator fin with N = 12, VSM12 stands for mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin with N = 12, and SP12 stands for spiral fin with N = 12, respectively. Both Nusselt number and Δp increase with increasing air frontal velocity, and both j factor and f factor decrease with the increase of air frontal velocity. In Fig. 3, the Nusselt number of SP12 is the highest among the five fins at the same frontal velocity, and that of S12 takes the second place, while that of P12 is the lowest. By contrast, Fig. 5 shows that j factor of SP12 is the highest among these fins at the

6 216 EMERGING TOPICS IN HEAT TRANSFER Figure 3: Nu and Δp for 12-row tested samples. Figure 4: j and f for 12-row tested samples. same frontal velocity, and that of P12 is the lowest. From Fig. 3, Δp of SP12 is the highest, while Δp of P12 is the lowest. The f factor of SP12 is obviously the highest among these fins at the same frontal velocity in Fig. 4. In a sense, these results can be expected, because the enhancement of heat transfer is usually penalized by the increase of pressure drop. The correlations for heat transfer and friction factors can be expressed as follows: c2 Nu= c 1 Re D f cre c c = 3 D c 4 (15)

7 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 217 Figure 5: Fin patterns for flat tube: (a) fin with punched vortex generators and (b) fin with punched rhombic formation. The corresponding correlations for five different fin patterns in the present study are shown in Tables 2 and 3. These correlations can be referred to engineering applications or further researches such as optimization or prediction. The heat exchanger with crimped spiral fin provides the highest Nusselt number associated with the highest pressure drop. Accordingly, it is essential to compare Table 2: The correlations of Nusselt number. Name Range of Re Dc Nu = f(re) Maximum relative error P12 4,000 10, Nu = 0.080Re Dc 6.4% S12 4,000 10, Nu = 0.057Re Dc 4.6% V12 4,000 10, Nu = 0.094Re Dc 4.0% VSM12 4,000 10, Nu = 0.076Re Dc 3.6% SP12 4,000 10,000 Nu = 0.069Re % Table 3: The correlations of friction factor. Name Range of Re Dc f = f(re) Maximum relative error P12 4,000 10, f = Re Dc 4.9% S12 4,000 10, f = Re Dc 2.5% V12 4,000 10, f = Re Dc 3.3% VSM12 4,000 10, f = 6.15 Re Dc 2.9% SP12 4,000 10,000 f = 4.31 Re %

8 218 EMERGING TOPICS IN HEAT TRANSFER the heat transfer enhancement performance of the test heat exchangers. In the present study, the identical mass flow rate criteria, the identical pumping power criteria, and the identical pressure drop criteria are used. These criteria were successfully adopted by Yu and Tao [30] and Wang et al. [31]. Based on the constant properties assumption, the formulations of these criteria are given as: a. Identical mass flow rate criteria: ( ReA / D ) = ( ReA / D ) (16) c c b. Identical pumping power criteria: c. Identical pressure drop criteria: 3 c p c c c p ( fre A / D ) = ( fre A / D ) (17) c c c p ( fre / D ) = ( fre / D ) (18) where the subscripts of p and c refer to plain finned tube (P12) and enhanced finned tubes (S12 V12 VSM12, or SP12), respectively. Under the condition of same temperature difference between the fluid and the wall, the ratio of heat transfer rate between the enhanced finned tubes and the plain finned tube may be formulated as follows: Φ Φ c p Nu( Re) A / D c = c Nu( Re) A / Dc p (19) where Nu(Re) represents the experimental correlation of Nusselt number versus Reynolds number. The comparison results are shown in Fig. 6, where the Reynolds number of plain fin heat exchanger is taken as the x coordinate. It can be clearly seen that S12, V12, and VSM12 have better heat transfer performances than P12, while SP12 has worse performance than P12. V12 offers the best heat transfer performance when Re Dc is less than about 4,500 under identical mass flow rate criteria, or when Re Dc is less than about 4,500 under identical pumping power criteria, or when Re Dc is less than about 5,000 under identical pressure drop criteria. However, when Re Dc is larger than about 4,500 under identical mass flow rate criteria, or when Re Dc is larger than about 6,000 under identical pumping power criteria, or when Re Dc is larger than about 6,700 under identical pressure drop criteria, the performance of S12 is the best. At low Reynolds numbers, the boundary layer of airflow is thick. The structure of winglet-type VGs makes VGs be able to destroy the boundary layer more effectively and provide better airflow mixed than the slit fin, and therefore, the winglet-type VGs perform better at low Reynolds numbers. However, at high Reynolds numbers, the boundary layer of airflow becomes thin, and the slit fin disturbs the airflow stronger and provides better airflow mixed than that of the winglet-type VGs. Therefore, with the increase of Re, the ratio F c /F p for vortex generator decreases, while that for slit fin is quite the opposite.

9 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 219 Figure 6: Φc/Φp comparisons for 12-row. For the slit fin, the fin with delta-wing vortex generators, and the mixed fin (front vortex-generator fin and rear slit fin) at hand, the mixed fin has better performance than the fin with delta-wing vortex generators, and the slit fin offers best heat transfer performance at high Reynolds numbers. 3 Heat Transfer Performances of the Fin Patterns for Flat Tube In this section, the fin-side heat transfer performances of two fin patterns as shown in Fig. 5 for circular tube are summarized. The geometrical details of these fin patterns are presented in Table 4. These fin patterns are manufactured, and then assembled into a kind of heat exchangers shown in Fig. 7 with the same fin space (having the same fin numbers, thus having the same heat transfer area). Table 4: Geometric dimensions of fin-and-tube heat exchangers. Name Type a T p S 1 S 2 B H R δ α N V1 Vortex generators R2 Rhombic formation

10 220 EMERGING TOPICS IN HEAT TRANSFER The heat transfer performances of these heat exchangers were obtained by experimental method reported in [28]. The experimental results of Nu and f on the fin side are shown in Fig. 8. The correlations of the data are presented in Tables 5 and 6. In order to compare the heat transfer performances of V1 and R2, the identical mass flow rate criteria, the identical pumping power criteria, and the identical pressure drop criteria as mentioned in above section are used. The results are presented in Fig. 9. Figure 7: Heat exchangers of flat tube bank fin used in experiments. Figure 8: Heat exchangers of flat tube bank fin used in experiments.

11 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 221 Table 5: The correlations of Nusselt number. Name Range of Re a Nu = f(re a ) Maximum relative error V1 1,360 2, Nu = Re a 6.4% R2 1,330 2, Nu = Re a 4.6% Table 6: The correlations of friction factor. Name Range of Re a f = f(re a ) Maximum relative error V1 1,360 2, f = Re a 4.9% R2 1,330 2, f = Re a 2.5% It is easy to see that V1 is much better than R2 at three identical conditions. For the same mass flow rate, the heat transfer of V1 is larger than that of R2 with an amount of 2%, but the pressure drop decreases 30%. At the same pumping power, the heat transfer of V1 is larger than that of R2 with an amount of 10%. Under the condition of the pressure drop, the heat transfer of V1 is larger than that of R2 with 15%. It is very hard to manufacture the fin patterns having variable parameters, and thus we used naphthalene heat mass transfer analogy method [32] in the model as Figure 9: Comparisons of heat transfer performances of V1 and R2 exchangers.

12 222 EMERGING TOPICS IN HEAT TRANSFER shown in Fig. 10 to obtain the correlations of flat tube bank fin with vortex generators [7 8, 23, 33 38]. As shown in Fig. 10a, the flow passages walled with flat tube and plates (to model the fins) mounted with VGs are presented. Two plates with 6 mm thickness shown in Fig. 10b and one plate with same thickness shown in Fig. 10c are used in test channel. On the plate shown in Fig. 10b, there is a void region marked with abcd on which we put the experimentally measured plates, which are presented in Figure 10: Experimental setup: (a) flow passages; (b) measured plate supporting; (c) plate constructing flow passage; (d) fin surface I; (e) fin surface II; (f) flat tube cast from naphthalene.

13 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 223 Fig. 10d named with fin surface I and Fig. 10e named with fin surface II. One of the surfaces of experimentally measured plates is cast from naphthalene. The depth of naphthalene is about one half of the plate thickness. VGs are mounted on the fin surface I and the back surface of fin surface II. Fin surfaces I and II are arranged face to face, as Fig. 10a shows, so that fin surface II can be used for modeling the back side surface of the fin mounted with VGs. The stakes with 8 mm width and 4, 5, and 6 mm heights are used to set up the fin spacing (T p ). Two flat tubes cast from naphthalene shown in Fig. 10f are put in the regions labeled with B in Fig. 10a to measure the sublimation of flat tubes. Other flat tubes and plates except the parts of fin surface I and fin surface II serve only to model the fluid mechanics of the tubes and fins in a fin and tube heat exchanger, and do not participate directly in the mass transfer process. The geometrical parameters are S1 = 40 mm, S2 = 55 mm, b = 46.3 mm, and a = 6.3 mm. As shown in Fig. 5a, the leading points of first VG pair are on the line tangent to the flat tube and two tube widths apart. The leading points of second VG pair are located on the mid line of the flat tube with the same width apart as that of the first pair. The geometry of VG is a delta winglet as shown Fig. 5a with the base-side edge length twice the trailing edge length. Experiments are carried out for parameter combinations of three attack angles (a = 25, 35, and 45 ), three relative heights of VG (H/T p = 0.6, 0.8, and 0.975), three types of fin spacing (T p = 4, 5, and 6 mm), and including three types of tube arrangement. The preparation of naphthalene plates is as follows: First, the naphthalene plates (fin surfaces I and II) are cast in a specially designed mold. The surface of the cast plates had a high quality of flatness and smoothness. Second, VGs are manufactured with copper plate of 0.8 mm thickness by a line milling method, and then the VGs are mounted at the given positions on the fin surface I and fin surface II by quick-drying glue. With special care, ensure the use of this glue does not damage the naphthalene surface. Finally, each cast plate is sealed in a special glass container and placed in a temperature-controlled experimental room having temperature fluctuation less than ± 0.1 C for a period of about 24 hours before a test run. Measurements of the surface contour of the naphthalene plates before and after a test run are made with a sensitive dial gauge with the resolution of 1 μm. The dial gauge is mounted on a fixed strut that hangs over a movable coordinate table. The coordinate table enables the surface to be independently traversed in two directions in the horizontal plane. The traversing is controlled by a micrometer head and can be read with a resolution of 0.05 mm. The sublimation depth on the plate is measured on the entire surface and a symmetrical mass transfer is obtained in some pre-test experiments. In the formal experiments, only half of fin surfaces I and II are measured (hatched areas in Fig. 10d and e) due to symmetry. The total measured points are 3,300 on the half fin surface I or II. The interval of any two neighboring points is 1 mm in both the streamwise direction (y) and spanwise direction (x). The average mass transfer is measured with a precision balance capable of discriminating to within 0.1 mg for specimens having a mass up to 200 g. A volumetric flow meter is used to measure the flow with precision of 0.1/3,600 m 3 /s. The temperature of air entering the test section is sensed

14 224 EMERGING TOPICS IN HEAT TRANSFER by a precision grade laboratory thermometer, which can be read to 0.1 C. A digital timer is used to measure the duration of a test run as well as the time required for setting up the experiment and for executing the surface contour measurements. The pressure drops are measured by a micropressure gauge with a precision of 0.2 mm water column. More details analysis of experimental uncertainty are discussed in [7, 8]. The results obtained by the experiments are local and averaged Sherwood numbers, which indicate the mass transfer characteristics. Thus, after obtaining the local and average Sherwood number [7], the analogy between heat and mass transfers is used to determine the local and average Nusselt number by where Sc and Nu are defined as Nu=Sh(Pr/Sc) n (20) Sc = 2. 28( T ) (21) Nu = a D/ l (22) According to the suggestion of Goldstein [32] n = 0.4 is adopted in this study. The Reynolds number and the friction factor are defined as follows: Re= r umax D/ m (23) f =Δ pd ( L rv 2 / 2 ) (24) where vmax= Q Amin and D= 4( S1 a) Tp ( 2( S1 a) + 2Tp). The more detailed reports of serials investigations can be found in Gao et al. [33] for the effect of the height of vortex generators, Ke et al. [34] for the effect of the attack angle of vortex generators, Shi et al. [35] for the effect of the fin space, and Zhang et al. [36, 37] for the effect of vortex generator position. Here, we only introduce the effect of transversal tube pitch on the local heat transfer and average heat transfer characteristics [38]. The local Nu a distributions on the surface II for three different S 1 /S 2 values are presented in Fig 11a c, respectively. These figures reveal that ahead of the second row of VGs, Nu a is small. This characteristic means that the vortices generated by the first row of VGs mounted on the surface I will need space to develop. These vortices can reach the fin surface II and have some effect on Nu a of the surface II. Starting from the second row of VGs, there is a region with large Nu a around the tube. This indicates that the vortices near the surface II is intensified by the second row VGs. The stream-wise axis of the core of vortices is nearly in line with the second row of tube for case of S 1 /S 2 = 0.582, the region with large Nu a is broken by this tube, see Fig. 11a. Nu a on the surface II is small around the second row of tube indicates the interactions of vortices generated by the tube and VGs of first and second rows decrease the heat transfer enhancement around this tube for the max

15 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 225 Figure 11: Comparison of local Nu a distribution on fin surface I: (a) Re a = 1,119, S 1 /S 2 = 0.528, (b) Re a = 1,121, S 1 /S 2 = 0.727, (c) Re a = 1,090, S 1 /S 2 = case of S 1 /S 2 = For this configuration, heat transfer enhancement is deteriorated around the third row tube because of the intensified unfavorable interactions of the vortices generated by VGs, the tubes upstream, and the VGs downstream. Here the interactions between vortices mean the vortices generated at different positions increase or decrease the amplitude of the same velocity component in a given point. If more rigorous definition is used, interactions mean the increase or decrease of the cross-averaged absolute vortex flux in main flow direction. Unfavorable interactions of vortices mean they decrease the amplitude of velocity components. It is found that unlike for the case of S 1 /S 2 = 0.582, for cases of S 1 /S 2 = and S 1 /S 2 = 0.727, starting from the second row VGs, there are clear regions with large Nu a beside the tubes, see Figs 11b and c. The width of the region with large Nu a is increased with increasing of S 1 /S 2. As shown in Figs 12a c, on fin surface I, the heat transfer enhancement is appreciable, especially around the tube. The heat transfer enhancement becomes weak in the region far from the tube for S 1 /S 2 = The distributions of Nu a around the first tube row are similar for three cases of S 1 /S 2. In the region of the second tube row, it is found that the effect of the vortices generated upstream on Nu a can penetrate far downstream. It is found that the vortices generated by VGs located around the first tube row has counter rotation direction as the vortices generated by the VGs located around the second tube row. If the tube center lining the main flow direction of the first-tube row and the second-tube row are too close,

16 226 EMERGING TOPICS IN HEAT TRANSFER Figure 12: Comparison of local Nu distribution on fin surface II: (a) Re a = 1,119, S 1 / S 2 = 0.528, (b) Re a = 1,121, S 1 /S 2 = 0.727, (c) Re a = 1,090, S 1 /S 2 = the interactions of these vortices with counter rotation direction reduce the amplitude of velocity components and hence deteriorate heat transfer enhancement. Because of increase in the intensity of vortices interactions with counter rotation direction for small S 1 /S 2, there is no clear region with large Nu a near the end of the third tube row. For large S 1 /S 2, for example S 1 /S 2 = 0.969, with less interactions of vortices, two clear regions in which the Nu a is enhanced are observed. At different S 1 /S 2, the comparison of span-averaged Nu a distribution in the stream direction on fin surfaces I and II is presented in Fig. 13. In this experiment, we used the same size of VG, considering the fin with different S 1 /S 2 will have different area of heat transfer, and in this figure we added the span-averaged Nu a of smooth fin for reference. The heat transfer enhancement can be compared with these reference data. As shown in Fig. 13a, for S 1 /S 2 = 0.582, it is clear that VGs can enhance heat transfer efficiently, in most regions, Nu a on surface I is larger than that on surface II. When S 1 /S 2 = 0.727, within relative large region, Nu a on II is larger than Nu a on I around the first and the second tube rows. However, when S 1 /S 2 = 0.969, Nu a on II is larger than Nu a on I around the third tube row. Interactions of vortices will decrease heat transfer enhancement for small S 1 /S 2 case. For the case of S 1 /S 2 = 0.969, there is enough space for vortices generated upstream to develop, and there is less intensity of interactions between vortices, the Nu a on II has a larger value than Nu a on I downstream. If we refer to Fig. 13c, because the centerlines in main flow direction of the first tube row and the second tube row are far away, it is clear that the vortices generated by VGs around the first row are unlikely to interact with vortices generated by VGs around the second row

17 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 227 Figure 13: Comparison of span-averaged Nu a on the fin surfaces I and II for different S 1 /S 2. tube. If compared with the reference data, from Fig. 13, the heat transfer enhancement by VGs is different for the three cases studied. The larger heat transfer enhancement comes from the case of S 1 /S 2 = The smaller heat transfer enhancement occurred for a case of S 1 /S 2 = These results can be explained by the interactions of vortices generated by VGs explained previously. The interactions of vortices affect the heat transfer on surfaces with and without VGs. The average Nu a and f a for parameters at a = 35, T p = 5 mm, and H = 4 mm is presented as a function of Re a for various transversal tube pitch in Fig. 14. Nu a increases with increasing Re a for all cases of different transversal tube pitch. The friction factor decreases with increasing Re a.

18 228 EMERGING TOPICS IN HEAT TRANSFER Figure 14: Effects of S 1 /S 2 on average Nu a and f a at different Re a. For different S 1 /S 2, it is clear that the large value of S 1 /S 2 will have small value of Nu a and f a at the same Re a. If all of data obtained by the experiments are correlated with considering of T p, θ, H, and S 1 /S 2, the following correlations can be obtained: T p H a S Nua= Rea ( ) ( ) ( ) ( ) (25) a T o 45 S p 2 f a = Re a Tp a H Tp a S1 S (26) 500 < Re a < 4,100, 25 q 45, T p /a The maximum deviation of data is 12.3%. The maximum deviations are 7.6% and 8.3% for Nusselt number and friction factor, respectively. The correlation obtained through mass transfer, that is, eqns (25) and (26), are validated through the experimental method carried out in [28], and the difference between mass transfer and real heat exchanger performance is shown in Fig. 15.

19 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 229 Figure 15: Effects of S 1 /S 2 on average Nu a and f a at different Re a. Comparing the air-side average Nusselt number and the friction factor obtained by the naphthalene sublimation technique with that obtained by the experiments of the real heat exchanger, one can note that small differences exist for both Nu a Re a and f a Re a, as shown in Fig. 15. The experimental results of naphthalene sublimation technique via the heat/mass transfer analogy is in a good agreement with experimental data of the real heat exchanger on the air side. The maximal difference for Nu a is 6.63%, and for f a is 4.48%. This indicates that although two kinds of experiments have different thermal boundary conditions, one is an isothermal condition and the other is a mixed condition, yet, at the Reynolds numbers studied, the results indicate that the heat/mass transfer coefficient obtained using the naphthalene sublimation technique at an isothermal condition can be applied to the mixed thermal boundary condition. Our further studies show the reason is that at the present configuration and the fin material, the fin efficiency is larger than 0.8, and thus the thermal boundary effect is only limited below 5% [39]. The aforementioned facts show correlations (25) and (26) have a required accuracy. Up to now, for flat-tube bank fin heat exchangers, the heat transfer performance of the fan with vortex generators have not been compared with the louver fin pattern thoroughly. Fortunately, Allison and Dally [26] carried out investigations in comparing a special fin with one par vortex generators to a special louver fin of flat tube bank fin heat exchanger. It was found that the test of a full-scale coil with flow-up delta-winglet geometry exhibited 87% of the capacity of the louver fin surface. By contrast, it showed a substantially lower pressure drop to approximately 53% of the louver surface. Allison and Dally claimed that the configuration studied appears to be the best arrangement yet published in the literature, and in many applications the capacity deficit can be compensated for by an increase in coil face area, and the resulting fan energy consumption is only 54% of that of the equivalent louver fin surface.

20 230 EMERGING TOPICS IN HEAT TRANSFER 4 Conclusion Based on limited data available on various fin patterns that can be used for tube bank fin heat exchangers, a brief summary of heat transfer performances of these fin patterns is provided in this chapter. The main conclusion remarks are as follows: 1. For the circular tube bank fin heat exchangers, with the Reynolds number ranging from 4,000 to 10,000, at high Reynolds numbers, the slit fin offers best heat transfer performance. 2. For the flat tube bank fin heat exchangers, the fin with vortex generators has a better heat transfer performance than the fin punched rhombic formation and the louver fin. 3. Naphthalene heat mass transfer analogy method can be used to screen the fin pattern with a required accuracy. 4. For the circular tube bank fin heat exchangers, further optimization and experimental comparisons of the fin pattern with vortex generators to the slit fin pattern should be carried out to make sure it has better heat transfer performance. Acknowledgments This work is supported by National Natural Science Foundation of China (Grant Nos and ) and the National Basic Research Program of China (973 Program, No. 2012CB720402). Nomenclature a a width of flat tube, mm A area, m 2 A fr air frontal area, m 2 A min minimum flow area, m 2 A o total surface area, m 2 B length of flat tube, mm c 1, c 2, c 3, c 4 coefficient of formulation D hydraulic diameter of fin side channel, mm D c fin collar outside diameter, D c = D o +2d, mm D i inside diameter of tube, mm D o outside diameter of tube, mm F p fin pitch, mm F s fin spacing, mm f, f a friction factor f pd v 2 Δ c/( r max L ) 2, fa= 2Δ pd /( rv max L) H heat transfer coefficient, W.m 2.K 1

21 AIR-SIDE HEAT TRANSFER AND FRICTION CHARACTERISTICS 231 H height of vortex generator, mm j Colburn factor L length of fin, mm m mass flow rate, kg.s 1 N number of tube rows n constant Nu,Nu a Nusselt number, Nu=h D c /λ, Nu a =h D e /λ P12 abbreviation of plain fin with N=12 P l longitudinal tube pitch, mm P t transverse tube pitch, mm Q heat transfer rate, W, or volume flow rate, m 3 /s R length of rhombic formations, mm R2 fin pattern with punched rhombic formation r c fin collar outside radius, D c /2, mm Re, Re Dc, Re a Reynolds number, Re=r v D o /µ, Re Dc =r v D c /µ, Re Dc =r v D/µ S 1 longitudinal tube pitch, mm S 2 transverse tube pitch, mm S12 abbreviation of slit fin with N = 12 Sc Schmidt number Sh Sherwood number s l length of slit, mm s h height of slit or spiral fin, mm s w width of slit, mm T temperature, K T p fin spacing, mm U overall heat transfer coefficient, W.m 2.K 1 V velocity, m.s -1 V1 fin pattern with punched vortex generators V12 abbreviation of vortex-generator fin with N = 12 v fr air frontal velocity, m.s 1 V h height of vortex generator, mm V l length of vortex generator, mm VSM12 abbreviation of mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin Greek symbols Δt Δp F d a logarithmic mean temperature difference, K pressure drop, Pa heat transfer rate, W fin thickness, mm angle of attack, deg

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