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Experimental investigation of heat transfer and pressure drop in serrated finned tube banks with staggered layouts
Applied Thermal Engineering 37 (2012) 314e323
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation of heat transfer and pressure drop in serrated finned tube banks with staggered layouts Youfu Ma*, Yichao Yuan, Yuzheng Liu, Xiaohong Hu, Yan Huang College of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2011 Accepted 20 November 2011 Available online 28 November 2011
An experimental study was performed to investigate the heat transfer and pressure drop characteristics of serrated finned tube banks with staggered layouts. The influences of varied fin densities, transversal tube spacing and longitudinal tube spacing were presented. For a constant fin height, an increase in the fin density resulted in an increase in the Euler number, and a gradual decrease in the Nusselt number was observed as the Reynolds number increased. An increase in the transversal tube spacing corresponded to a significant reduction in the Euler number, whereas the Nusselt number essentially remained unchanged. The longitudinal tube spacing had an insignificant effect on the Nusselt and Euler numbers, and the optimum ratio of the transversal tube spacing to longitudinal tube spacing increased with an increase in the transversal tube spacing. Scaling of the tube spacing had little effect on the Nusselt number but had a significant influence on the Euler number. Finally, predictive correlations for Nusselt and Euler numbers were developed based on the data presented here, and comparisons between the test data from this paper and the predictive values from previously published correlations were performed. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Pressure drop Heat recovery steam generator Finned tube Serrated fin
1. Introduction Helical finned tubes are widely used in large-scale heat transfer equipment with flue gas emissions, such as combined cycle heat recovery steam generators (HRSGs) in power plants and waste heat boilers in chemical industries. For high-temperature applications, tubes and fins are normally made from carbon steel, and the fin assembly is welded to the tube surface. Due to restrictions in the required technical level of welding, early helical steel-finned tubes had an L-shaped fin-root (known as an L-foot fin) that was used to increase the welding area. With recent technical developments in high-frequency electric resistance welding techniques, stripshaped fins (called I-foot fins) can now be directly welded to a tube surface. Due to the poor ductility of steel, the manufacturing of solid steel fins consumes a large amount of energy in the winding process, and the fin height must be within the limits of radial deformation and fin-end rips. Hence, serrated helical steel-finned tubes emerged in industrial applications in the 1960s to overcome these defects related to solid fins. Compared to solid fins, serrated fins are easier to manufacture and have a larger finned ratio. Serrated fins can also exhibit a higher fin efficiency and heat
* Corresponding author. Tel.: þ86 021 55272320. E-mail addresses: [email protected], [email protected] (Y. Ma). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.11.037
transfer coefficient as a result of the better penetrativity and turbulent condition of the fin-side gas. However, the number of published experimental studies on the heat transfer and pressure drop characteristics of serrated helical finned tube banks is very limited. Among the available studies on serrated helical finned tube banks, many experiments have focused on comparisons between solid fins and serrated fins tube banks, such as Sparrow and Myrum [1], Zhuo et al. [2], Chen et al. [3] and Kawaguchi et al. [4,5]. In general, these studies found that serrated fins could increase the fin-side heat transfer coefficient by approximately 10e25% relative to solid fins, whereas the pressure drop is enhanced by approximately 10e15%. Moreover, Reid [6] compared two types of finned tubes while also considering the cost of finned tubes, and recommended to choose serrated finned tube when fin heights are greater than 12 mm. Early in the 1940s, Schryber and Brooklyn [7] presented heat transfer data for 3 L-foot serrated copper-finned tube banks. Subsequently, I-foot serrated steel-finned tube received widespread attention. For example, Weierman (1977) [8] reported pressure drop data for 6 tube banks and later compared the effects of square and equivalent triangle tube layouts on heat transfer and pressure drop through 2 tube banks [9]. Later, Hashizume [10], Zhuo et al. [2], Chen et al. [3] and Kawaguchi et al. [4,5,11,12] reported heat transfer and pressure drop data for I-foot serrated
Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323
finned tube banks with staggered layouts. In addition, Næss [13] also recently investigated L-foot serrated steel-finned tube. In contrast to the aforementioned experiments conducted in laboratory wind tunnels, Rabas et al. [14] and Martinez et al. [15,16] obtained measurements from an operating combined cycle HRSG and an economizer with a serrated finned tube bank, respectively. Heat transfer and pressure drop correlations are generally applicable and remain important topics in the study of serrated finned tube banks. In this regard, correlations developed by Weierman [17], who served at the Extended Surface Corporation Of America (ESCOA) Fin-tube Corporation, have been widely referenced, and ESCOA revised several correlation coefficients in 1979 [18]; however, the experimental data on which the ESCOA correlations were based have not been published. Nir [19] presented a set of correlations based on the collection of published experimental data available in 1991. Chen et al. [3], Kawaguchi et al. [11,12] and Næss [13] also presented correlations based on their experiments. For solid finned tube banks with staggered layouts, the heat transfer correlations presented by Briggs and Young [20] and the pressure drop correlations presented by Robinson and Briggs [21] have been widely recommended. These correlations are compared with the experimental data of this paper in a later section. When considering the multiform geometric factors of helical finned tubes, the fin height-spacing ratio (hf/sf) is essential for the formation of flow between fins and tubes [22]. For instance, the experimental results presented by Chen et al. [3] showed that the fin height-spacing ratio, within the range of 1.1e3.8, influenced the heat transfer and pressure drop by approximately 27% and 45%, respectively; within this same range, the heat transfer and pressure drop values predicted according to the ESCOA correlations [18] showed an alteration of 20% and 28%, respectively. In the above studies, the fin height-spacing ratio ranges of Chen et al. [3], Kawaguchi et al. [4,5,11,12] and Næss [13] were 1.1e3.8, 2.2e3.8 and 2.1e4.2, respectively. To our knowledge, the heat transfer and pressure drop data for serrated finned tube bank with higher fin height-spacing ratios were not reported. However, a higher fin height-spacing ratio is often preferred in combined cycle HRSGs due to the small quantity of fly ash in working flue gas. Therefore, four types of I-foot serrated finned tubes with different fin densities and fin height-spacing ratios ranging from 5.0 to 5.5 were investigated in this paper. Moreover, because serrated finned tube banks are typically arranged in staggered layouts [9], and non-equilateral triangular tube layouts are very common in practical applications, the effects of transversal and longitudinal tube spacing on the heat transfer and pressure drop of tube banks with staggered layouts were also investigated. 2. Experimental setup and data processing 2.1. Experimental setup Experiments were carried out in a circulating wind tunnel consisting of air circulation and cooling water systems, as shown in Fig. 1. Air was pulled using a draft fan, and the air flow rate was adjusted using an analog input on the fan. The air then passed through an electric heater that maintained the test section inlet temperature at approximately 180 C for all experiments. In the upstream wind tunnel of the test section, the hot air was passed through a calming section equipped with flow straighteners and several fine wire meshes to reduce the large-scale turbulence and to provide a uniform velocity profile at the test section entrance. The hot air then passed across the tube banks, and heat was transferred to the cooling water in the test section. Subsequently, the low-temperature air was directed to a wind box for measuring
315
Fig. 1. Schematic diagram of the experimental system.
the air flux and was then passed back to the draft fan to complete the air circulation cycle. To minimize the heat loss, all surfaces of the wind tunnel and test section were covered with thermal insulators. The inlet and outlet air temperatures were measured by placing fine wire meshes in the wind tunnel; sixteen thermocouples were attached to the meshes and spaced equally over the cross-sectional area. The air flow was determined using four nozzles, which were placed in the wind box and had various combinations of different diameters for varying the air flow. The air-side pressure drop across the tube banks was determined using measurements of the static pressure difference between the upstream and downstream sides of the tube banks, and each side consisted of four parallel connected pressure taps located around the test section circumference. A sketch of the test section is shown in Fig. 2. The test section width (i.e., the active tube length) was 400 mm, and the section height was 4.5 times the transversal tube spacing. The test section consisted of forty active tubes for heat transfer (four transversal and ten longitudinal tube rows), and ten dummy half-tubes were located at the section walls to obtain hydraulic similitude. As confirmed by most previous experiments on finned tube banks with cross flow, fully developed conditions for heat transfer and pressure drop were reached within four tube rows for staggered layouts. Hence, ten longitudinal tube rows were considered sufficient to obtain representative heat transfer and pressure drop data. City water was used as coolant in the tubes. A water tank was used to maintain a steady water level and thus sustain a steady water flux during the course of the experiments. In addition, an electric heater was placed inside the water tank to raise the temperature of the water to prevent moisture condensation on the fin side. The cooling water was pumped using a water pump, and the water flow was adjusted using a valve placed at the outlet pipe of the tube bank. In the test section, the cooling water was passed through a single tube, and the forty active tubes were connected in series to provide an overall cross-countercurrent arrangement for
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Fig. 2. Dimensions of the test section.
the air/water flow. The inlet and outlet water temperatures were measured using platinum resistance thermometers, and the water flow rate was measured using a turbine flowmeter. All of the meters, including the thermocouples, platinum resistance thermometers, differential pressure transmitters, turbine flowmeter and nozzles, were calibrated before use. During the experiments, all measured data were recorded at 5-s intervals for at least 15 min per experiment after stable operating conditions were ensured. Furthermore, the first experiment in each series was repeated at the end of a run to substantiate the repeatability. The air-side and water-side heat balance deviations were within 3% in all experiments.
2.3. Data processing The heat duty was calculated based on the measured mass flow rates and overall temperature changes, and the overall heat transfer coefficient was then calculated from Eq. (1) using the arithmetic average of the air-side and water-side heat duties.
K ¼
The testing tubes were commercially available tubes with I-foot fins, as shown in Fig. 3. The tubes and fins were made from carbon steel. The fin root was resistance-welded to the tubes, providing negligible thermal contact resistance between the fin and the outer surface of the tube. The outer diameter of the tube, fin thickness, fin height, segment width and segment height of do ¼ 38.1 mm, df ¼ 1 mm, hf ¼ 16 mm, ws ¼ 4 mm and hs ¼ 10 mm, respectively, remained constant for all testing tube banks. The main features of the testing tube banks are shown in Table 1, and the geometric variables are explained in Fig. 3. All finned tubes and tube spacing geometries were selected from several operating combined cycle HRSGs. A total of 12 tube banks were tested. Banks 1e4 consisted of tubes with different fin densities (i.e., varied fin pitch or spacing), but the tube spacing and other finned tube geometries were identical. Banks 4e12 consisted of tubes with different transversal or longitudinal tube spacing, but with identical finned tube geometries. Therefore, banks 1e4 were used to explore the effect of the fin height-spacing ratio (hf/sf) in the range of 5.0e5.5, and banks 4e12 were used to explore the effects of the relative transversal tube spacing (ST/do) in the range of 2.3e3.2, the relative longitudinal tube spacing (SL/do) in the range of 2.4e3.1 and the effects of the transversalelongitudinal tube spacing ratio (ST/SL) in the range of 0.75e1.30.
(1)
The fin-side heat transfer coefficient was determined using Eq. (2)
ao ¼
2.2. Testing tube banks
Q Ao $Dtm
1 dt Ao 1 Ao $ $ K kt Aav ai Ai
1
Ao At þ Ef Af
(2)
In Eq. (2), the tube-side heat transfer coefficient was calculated using the Gnielinski correlation [22] (valid for 2300 < Re<106, 0.6 < Pr<105 and l/d 1), and the fin efficiency was given by Eq. (3) as discussed below. To ensure the validity of using the Gnielinski correlation, fully turbulent flow was maintained on the tube side during the experiments in this paper, in which the corresponding flow conditions for water were 2 104 < Re<4 104, 4.0 < Pr<7.0 and l/d ¼ 12.5. Thus, the conditions for the use of the Gnielinski correlation were satisfied. In addition, the uncertainty in the tubeside heat transfer coefficient was estimated to be 10% according to the reported accuracy of the Gnielinski correlation, and therefore, the sensitivity of the fin-side heat transfer coefficient was approximately 5% for this paper. The appropriate fin efficiency, which compensates for the finite conductance of the fins according to Gardner [23], under the assumption of a uniform fin-side heat transfer coefficient, is expressed as:
Eth
h i tanh m hf þ df =2 ¼ where m ¼ m hf þ df =2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u u2ao d þ ws f t kf df ws
(3)
However, as pointed out by Hashizume [24], the heat transfer coefficient distribution is not uniform, yielding actual fin
Fig. 3. Geometric schematic of the serrated finned tube and tube bank with staggered layouts.
Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323 Table 1 Main geometry data for testing tube banks. Tube banks no.
ST [mm]
SL [mm]
do [mm]
Nf [fins/m]
hf [mm]
df [mm]
hs [mm]
ws [mm]
1 2 3 4 5 6 7 8 9 10 11 12
88 88 88 88 88 88 104 104 104 120 120 120
92 92 92 92 105 117 92 105 117 92 105 117
438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1
257 252 245 241 241 241 241 241 241 241 241 241
16 16 16 16 16 16 16 16 16 16 16 16
1 1 1 1 1 1 1 1 1 1 1 1
10 10 10 10 10 10 10 10 10 10 10 10
4 4 4 4 4 4 4 4 4 4 4 4
efficiencies that are lower than predicted by Eq. (3). In the analysis presented here, the empirical correction factor proposed by Weierman [17] was applied to the theoretical fin efficiency, as shown in Eq. (4). The magnitude of the correction introduced using Eq. (4) relative to the uncorrected value obtained using Eq. (3) was relatively small (less than approximately 1e5%) for all experiments.
Ef ¼ Eth ð0:9 þ 0:1Eth Þ
(4)
To represent the correlativity between the heat transfer or pressure drop and the fin-side flow conditions, the dimensionless norms, such as the Nusselt number, Prandtl number, Euler number and Reynolds number, were used in this paper. In the calculations of the above norms, the arithmetic mean temperature was used for the calculations of gas physical properties. The outer diameter of the tube was adopted as the characteristic length for the Reynolds and Nusselt numbers, and the gas mass flux in the narrowest crossflow area was adopted to calculate the characteristic velocity for the Reynolds and Euler numbers. Because the pressure drop of the gas across the tube banks was determined using measurements of the static pressure difference and the pressure drop data were recorded with simultaneously the heat transfer data, the dynamic pressure differences of the gas between the upstream and downstream sides of the tube banks should be considered in the determination of the real pressure drop of the tube banks. Because the gas was cooled in the tube banks, the measured static pressure drops were smaller relative to the real pressure drops of the gas. Therefore, the dynamic pressure differences between the upstream and downstream sides of the tube banks were added to the measured pressure drop in this paper to provide the resistance coefficients of the tube banks in the cold tests. Specifically, the rectified Euler number of each tube bank was 0.8e2.0% greater than that of the actual measurements. For the comparison of the overall thermalehydraulic performance of the tube banks, the Colburn-Fanning factor ratio (j/f), representing the heat transfer efficiency of a surface with a given resistance coefficient, was used for the tested tube banks. The definitions of the Colburn heat transfer factor and the Fanning friction factor are shown in the nomenclature. Based on the error analyses of the experiments in this paper, the maximum experimental uncertainties for the Nusselt and Euler numbers were 4.5% and 2.7%, respectively.
geometries but differed in their fin density (Fig. 4). The Nusselt numbers of banks 2, 3 and 4 were larger than that of bank 1 by approximately 3%, 4% and 5%, respectively, demonstrating a quantitative increase in the Nusselt numbers with decreasing fin density under the same Reynolds number. This result is qualitatively consistent with the corresponding results obtained for solid finned tube banks with staggered layouts and can be attributed to the enhanced action of gases penetrating into fin gaps due to a decrease in the fin heightespacing ratio or a decrease in the fin density with a constant fin height. In previous experiments on serrated finned tube banks, Chen [3] demonstrated an approximately 27% decrease in the Nusselt number with an increase in the fin heightespacing ratio from 1.1 to 3.8, which is consistent with the results obtained here using a fin height-spacing ratio range of 5.0e5.5. However, Kawaguchi [11] reported that an increase in the Nusselt number of approximately 7% corresponded to an increase in the fin height-spacing ratio from 2.2 to 3.8; Næss [13] presented a similar result when using two tube banks. These contradictory findings likely resulted from differences in the fin heights: a lower fin height (8.6 mme13 mm) was used by Kawaguchi [11] and Næss [13], and a higher fin height (15 mme16 mm) was used by Chen [3] and in the present study. Specifically, an increase in the fin height can enhance the gas turbulence due to the shape of the serrated fins, whereas there is no obvious effect on the gas penetrability when the fin height is relatively low; however, this effect is reversed when the fin height is relatively high. Banks 1e4 had identical fin heights, and therefore, this mechanism needed to be confirmed using additional experimental data for tube banks with various fin heights. As shown in Fig. 4, a smaller decrease in the Nusselt number due to differences in the fin density occurred as the Reynolds number increased; similar results were also observed for the solid finned tube banks [25]. This trend is mainly attributed to the thinning of the gas boundary layer such that the influence of the fin spacing on heat transfer tends to weaken with an increase in the Reynolds number. The Nusselt number for bank 1 was lower than that of bank 4 by 11e0% with Reynolds numbers increasing from 4000 to 30,000; at the same time, the total external surface area (Ao) of bank 1 was larger than that of bank 4 by approximately 8%. Thus, there is a minimum critical Reynolds number (Remc) for bank 1 below which the fin-side heat transfer quantity per meter (aoAoEo) is less than that of bank 4 under the same Reynolds number. This minimum critical Reynolds number was approximately 15,000
3. Results and discussion 3.1. Heat transfer 3.1.1. Effect of the fin density The effect of the fin density on the heat transfer performance is demonstrated using testing banks 1e4, which had identical
317
Fig. 4. Fin-side Nu vs. Re in terms of the various fin densities.
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when comparing banks 1 and 4, as shown in Fig. 5. According to the analysis, the minimum critical Reynolds number must decrease with an increase in the fin density difference of the compared tube banks; therefore, the minimum critical Reynolds number may be worthy of further attention in the case of a small fin density difference. 3.1.2. Effects of tube spacing The effects of tube spacing on heat transfer were demonstrated using testing banks 4e12, which had identical geometries but differed in their transversal and longitudinal tube spacing (Fig. 6). Changes in the transversal tube spacing resulted in a heat transfer difference of less than 3%, and therefore, the effects were negligible. In contrast, the longitudinal tube spacing had a greater effect on the heat transfer: the Nusselt numbers for the tube banks with SL ¼ 105 mm were always approximately 6% higher than those of the tube banks with SL ¼ 92 mm and SL ¼ 117 mm. Thus, for typical tube arrangements, the longitudinal tube spacing had a more distinct effect on the heat transfer, which was mainly due to the influence of the longitudinal tube spacing on the reflow region on the leeward side of the tube. Although the effect of the transversal tube spacing on heat transfer can be neglected in typical tube arrangements, as indicated by Kawaguchi [4,11] (ST/df ¼ 1.3e1.5) and corroborated in this paper (ST/df ¼ 1.3e1.7), the heat transfer would evidently decrease when the ratio of transversal tube spacing to fin tip diameter (ST/df) is greater than 2, as shown by Næss [13] (ST/df ¼ 2.04 and 2.09). This influence of the transversal tube spacing may mainly result from the clear increase in the free longitudinal flow (i.e., the bypass flow) in staggered tube banks, which would induce a marked increase in the stagnation flow regions on the windward side and the reflow regions on the leeward side of the tube. In the heat transfer correlation analysis for the finned tube banks in a cross flow configuration, the transversal-longitudinal tube spacing ratio (ST/SL) was usually used as a geometric factor for determining the influences of tube spacing. The comparison of banks 4e12 indicated that the optimum transversalelongitudinal tube spacing ratio for achieving the maximum heat transfer increased with an increase in the relative transversal tube spacing. These findings are distinct from prevailing views: the Nusselt number is expected to increase with an increase in the transversalelongitudinal tube spacing ratio, which is generally attributed to an increase in the average gas velocity or level of turbulence
Fig. 5. Fin-side heat transfer quantities per meter of finned tube vs. Re for banks 1 and 4.
Fig. 6. Fin-side Nu vs. Re in terms of the various tube spacing.
at the same Reynolds number (i.e., the Reynolds number is usually defined by the gas velocity in the narrowest flow area, and in most cases, the area is dependent on the transversal tube spacing). On the other hand, an increase in the transversal-longitudinal tube spacing ratio shortens the travel distance of the gas and also increases the proportion of free longitudinal flow; these effects tend to cause a decrease in the Nusselt number with an increase in the transversalelongitudinal tube spacing ratio. Therefore, the overall effect is that there must be an optimum transversallongitudinal tube spacing ratio for a certain relative transversal tube spacing to maximize heat transfer. However, there was only an approximately 6% variation in the Nusselt number with varied transversalelongitudinal tube spacing ratios in this paper, and thus, this type of active mechanism for the tube spacing needs to be confirmed by further experimental data. Testing bank 4 (ST/do ¼ 2.3, SD/do ¼ 2.7) could be considered an approximate scaled-down version of bank 12 (ST/do ¼ 3.1, SD/ do ¼ 3.5) with respect to the tube spacing with the shortest fin-tip clearance increasing from 18 mm to 50 mm. The comparison of banks 4 and 12 indicated that their heat transfer performances were almost identical. This result was corroborated by the work of Chen [3] in which the tube banks were arranged in an equilateral triangle configuration and the relative transversal tube spacing ranged from 2.0 to 3.1. Thus, the scaled tube spacing had a negligible effect on the heat transfer performance for serrated finned tube banks with approximate equilateral triangular layouts with the exception, based on reasonable deduction, of cases where the ratio of the transversal tube spacing to fin tip diameter is greater than 2. 3.1.3. Heat transfer correlations For the heat transfer correlation of this paper, the geometric factors of the fin heightespacing ratio and transversalelongitudinal tube spacing ratio, which have been adopted in most existing studies on solid or serrated finned tube banks, such as Briggs and Young [20], Weierman [17], Chen [3], Næss [13], were used to present the influences of the finned tube and tube layouts geometries. In contrast to the fin height-spacing ratio, the transversalelongitudinal tube spacing ratio often has a marginal effect on the heat transfer performance in common tube layouts, thus, its influence was presented in the heat transfer correlation using a constant exponent derived from the linear regression of heat transfer data, like the traditional processing method for the
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Reynolds number. However, in this study, the heat transfer value does not deviate in direct correlation with varied fin heightespacing ratios; in addition, the influences on the heat transfer tend to be weak when the fin height-spacing ratio is decreased, as confirmed in solid finned tube banks where the Nusselt number is independent of the fin spacing when the fin spacing is larger than 4.5 mm [25]. To present the composite effects of the fin heightspacing ratio, a special corrective factor (see Eq. (5)) was used in the heat transfer correlation based on the experimental data in this paper. In contrast with the typical approach for imposing a constant exponent on fin heightespacing ratio, this fin height-spacing ratio correction factor also took into account the decreased effect on the heat transfer as the Reynolds number increased. To address the influences of the gas physical properties, an analytic solution of 0.33 was used as a constant exponent on the Prandtl number. Thus, the heat transfer correlation for the serrated finned tube banks was presented as follows using a multiple linear regression analysis of the experimental data:
0 Nu ¼ 0:117Re
0:717
Pr
0:33 B
@0:6 þ 0:4e
1 250h =s Ref f
0:06 C ST A SL
Fig. 8. Fin-side Eu vs. Re in terms of the various fin densities.
(5)
The validated ranges for Eq. (5) are Re ¼ 4000e30,000, hf/ sf ¼ 5.0e5.5 and ST/SL ¼ 0.75e1.30. Eq. (5) has a 95% confidence interval of the standard deviation of 4.4%. The overall prediction accuracy is shown in Fig. 7. 3.2. Pressure drop 3.2.1. Effect of the fin density The effect of the fin density on the pressure drop characteristics was demonstrated using testing banks 1e4, which had identical geometries but differed in their fin density (Fig. 8). An increase in the fin density resulted in an increase in the Euler number under constant Reynolds number conditions. Specifically, the Euler numbers of bank 1, 2 and 3 were greater than that of bank 4 by approximately 8%, 6% and 2%, respectively. This observation is qualitatively consistent with the corresponding results for the solid finned tube banks with staggered layouts and is likely the result of additional frictional surface and stronger gas disturbance caused by the serrated fins as the fin density increases.
Fig. 7. Measured Nuexp vs. predicted Nucalc values calculated using Eq. (5).
In previous experiments on serrated finned tube banks, Chen [3] concluded that the Euler number increased by approximately 45% as the fin heightespacing ratio increased from 1.1 to 3.8; this finding is qualitatively consistent with the results of this paper for a fin heightespacing ratio range of 5.0e5.5, representing a proportional change in the Euler number of approximately 16% for each unit interval change in the fin height-spacing ratio. However, the results of Kawaguchi [12] appear to be conservative, showing an increase in the Euler number of only 4% as the fin heightespacing ratio was increased from 2.2 to 3.8. 3.2.2. Effects of tube spacing The effects of the tube spacing on the pressure drop characteristics were demonstrated using testing banks 4e12, which had identical geometries but differed in their transversal and longitudinal tube spacing (Fig. 9). As shown in Fig. 9, the transversal tube spacing had a significant influence on the pressure drop; specifically, the Euler numbers of the tube banks with ST ¼ 104 mm and ST ¼ 120 mm decreased by approximately 8% and 20%, respectively, relative to the tube banks with ST ¼ 88 mm. In addition, the longitudinal tube spacing had a modest influence on the pressure drop; specifically, the Euler numbers of the tube banks with
Fig. 9. Fin-side Eu vs. Re in terms of the various tube spacing.
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SL ¼ 105 mm and SL ¼ 117 mm decreased by approximately 1% and 5%, respectively, relative to the tube banks with SL ¼ 92 mm. Hence, the transversal tube spacing had a more distinct effect on the pressure drop than the longitudinal tube spacing in these reasonable tube arrangements. It is generally acknowledged that the pressure loss of the cross flow in tube banks with staggered layouts is the result of three main components: the flow around loss, the frictional loss and the loss due to gas volume expansion and contraction. Therefore, with an increase in the transversal tube spacing, the flow around loss may decrease due to the additional flow of gas across the tube bank in a similar manner as bypass flow. In addition, the loss due to gas volume expansion and contraction tends to decrease because the transversal free cross sectional area is less than the diagonal free cross sectional in typical tube arrangements. Moreover, an increase in the ratio of the free longitudinal flow also tends to reduce the frictional loss. Hence, the Euler number evidently decreases with an increase in the transversal tube spacing. With respect to the longitudinal tube spacing, an increase in the longitudinal tube spacing can increase the leeward reflow region, thus decreasing the flow around and frictional losses; however, the loss due to gas volume expansion and contraction may increase slightly because the Euler number generally decreases with an increase in the longitudinal tube spacing. As mentioned above, the tube spacing of banks 4 and 12 were approximately proportional in scale. The comparison of these two banks indicated that the Euler number of bank 12 (ST/do ¼ 3.1) was approximately 23% less than that of bank 4 (ST/do ¼ 2.3). Chen [3] presented a similar decrease of approximately 18% in equilateral triangular tube banks as the relative transversal tube spacing increased from 2.0 to 3.1. Thus, in contrast to its small effect on the heat transfer, the scaled tube spacing has a noticeable influence on the pressure drop. In addition, it is noteworthy that the tube spacing is also related to the compactness of the tube bank. 3.2.3. Pressure drop correlations The geometric factor of the fin height-spacing ratio was used to represent the influences of the finned tube geometries in the pressure drop correlation analysis in this paper. With respect to the tube spacing effects, the dimensionless geometric factors of the relative transversal tube spacing and relative longitudinal tube spacing were used because these factors influence the pressure drop to a varied extent. The pressure drop correlation for the serrated finned tube banks was presented using a multiple linear regression analysis of the experimental data as follows:
Eu ¼ 1:773Re
0:184
hf sf
!0:556
S1 do
0:673
S2 do
Fig. 10. Measured Euexp vs. predicted Eucalc values calculated using Eq. (6).
and only bank 7 showed a monotonically decreasing trend (Fig. 11). In general, the Reynolds number range corresponding to the higher Colburn-Fanning factor ratios was approximately 7000e10,000. Regarding the influences of the geometries, as shown in Fig. 11, an increase in the fin pitch and transversal tube spacing resulted in clear improvements in the Colburn-Fanning factor ratios of tube banks. However, the longitudinal tube spacing had a relatively small influence on the Colburn-Fanning factor ratios. More specifically, the Colburn-Fanning factor ratio for bank 4 was greater than that of bank 1 by approximately 28% due to an decrease in the fin density from 257 fins/m to 241 fins/m; the Colburn-Fanning factor ratio increased by approximately 25% as the transversal tube spacing increased from 88 mm to 120 mm with a constant longitudinal tube spacing. Although a larger fin pitch and transversal tube spacing may be helpful in improving the overall thermalehydraulic performance of the tube banks, these geometries also had a detrimental effect on the compactness of the tube banks. As far as the longitudinal tube spacing was concerned, the tube banks with SL ¼ 105 mm always had the highest Colburn-Fanning factor ratios with the same transversal tube spacing, the tube banks with SL ¼ 117 mm were the second highest and the tube banks with SL ¼ 92 mm showed the lowest ratio. This result
0:133 (6)
The validated ranges for Eq. (6) are Re ¼ 4000e30,000, hf/sf ¼ 5.0e5.5, ST/do ¼ 2.3e3.2 and SL/do ¼ 2.4e3.1. Eq. (6) has a 95% confidence interval of the standard deviation of 2.7%. The overall prediction accuracy is shown in Fig. 10.
3.3. Overall thermalehydraulic performances Various assessment criteria have been used previously to evaluate the overall performance of tube banks depending on the different desired goals, including the Colburn-Fanning factor ratio (j/f) that is mainly used for the assessment of the overall thermale hydraulic performance of finned tube banks. Fig. 11 shows the Colburn-Fanning factor ratios for the twelve tested tube banks. The Colburn-Fanning factor ratio of eleven tube banks increased initially and then gradually decreased as the Reynolds number increased,
Fig. 11. The overall thermalehydraulic performances of the tested tube banks.
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indicated that the Colburn-Fanning factor ratio increased initially and then showed a modest decrease as the longitudinal tube spacing increased, i.e., there were an optimum longitudinal tube spacing that resulted in a maximum Colburn-Fanning factor ratio for a given transversal tube spacing. However, the extent of effect of the longitudinal tube spacing was relatively small, as the greatest difference in Colburn-Fanning factor ratio at the same transversal tube spacing was approximately 7%. 3.4. Comparisons of the correlations 3.4.1. Comparison of the heat transfer correlations Fig. 12 shows a comparison between the heat transfer test data of banks 1e12 and the predicted values calculated using previously published correlations (identified here as Weierman1976 [17], ESCOA1979 [18], Nir1991 [19], Chen1998 [3], Kawaguchi2006 [11], Næss2010 [13] and Briggs1963 [20]). As shown in Fig. 12, the predicted Nusselt values from Weierman1976, ESCOA1979 and Næss2010 correlations deviated from the test data of banks 1e12 within the range of 10%, among which the ESCOA1979 heat transfer correlation showed the greatest degree of consistency with the test data as the standard deviations for each tube bank being less than 5%. The deviations of the predicted Nusselt values from the Chen1998 and Kawaguchi2006 correlations were in the range of 20%, whereas the predicted Nusselt values from Nir1991 correlation was approximately 45% less than the test data. The predicted Nusselt values from Briggs1963 correlation was approximately 35% less than the test data, which indicates that serrated finned tube banks have a superior heat transfer performance relative to solid finned tube banks, as confirmed by Zhuo [2] and Chen [3]. 3.4.2. Comparison of the pressure drop correlations Fig. 13 shows a comparison between the pressure drop test data of banks 1e12 and the predicted values calculated using previously published correlations (identified here as Weierman1976 [17], ESCOA1979 [18], Nir1991 [19], Chen1998 [3], Kawaguchi2006 [12], Næss2010 [13] and Robinson1966 [21]). As shown in Fig. 13, the predicted Euler values from ESCOA1979 correlation also had the greatest consistency with the test data, as the standard deviations for each tube bank were less than 10%. The predicted Euler values from Weierman1976 and Chen1998
Fig. 12. Comparison between the heat transfer test data and the predicted values calculated from previously published correlations.
Fig. 13. Comparison between the pressure drop test data and the predicted values calculated from previously published correlations.
correlations were greater than the test data by approximately 10e20% and Kawaguchi2006 correlation were also greater by approximately 50%. However, the predicted Euler values from Nir1991 and Næss2010 correlations were 2.5 times higher than the test data, and therefore, these predicted values are not displayed in Fig. 13. The predicted Euler values from Robinson1966 correlation lower initially and then was greater than the tested data as the Euler number increased (or the Reynolds number decreased), which indicates that the additional pressure drop induced by the serrated fins tends to increase as the Reynolds number increases; however, the Euler number differences between the test data from this paper and the predicted values from Robinson1966 correlation remain within 15% as the Reynolds number increases from 4000 to 30,000. 4. Conclusions A set of experiments was performed to evaluate the influence of the tube layout and fin density on the heat transfer, pressure drop and overall thermalehydraulic performance of serrated finned tube banks with staggered layouts. Based on the experimental results, the following conclusions were drawn. The Nusselt number ranged from showing no difference to decreasing up to 11% and the Euler number increased by approximately 8% as the fin heightespacing ratio increased from 5.0 to 5.5 while the Reynolds number was held constant. Because the extent of the effect of the fin density on heat transfer decreased as the Reynolds number increased, there must be a minimum critical Reynolds number for the tube bank with higher fin density that will avoid fin-side heat transfer per meter tube that is less than the tube bank with the lower fin density under the same Reynolds number. The transversal tube spacing had a negligible effect on the heat transfer over the spacing range used in the tested tube banks, whereas the pressure drop decreased by approximately 20% as the relative transversal tube spacing increased from 2.3 to 3.2. Variations in the longitudinal tube spacing had insignificant effects on the heat transfer and pressure drop (less than 6%) over the relative longitudinal tube spacing range of 2.4e3.1, and the optimum transversalelongitudinal tube spacing ratio that results in the maximum heat transfer increased as the relative transversal tube spacing increased. Moreover, scaling of the tube spacing had little
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effect on the heat transfer but had a significant influence on the pressure drop. With respect to the overall thermal-hydraulic performances of the tube banks, increases in the fin pitch and transversal tube spacing corresponded to an approximately 28% and 25% increase, respectively, in the Colburn-Fanning factor. As the longitudinal tube spacing increased, the Colburn-Fanning factor increased initially and then showed a modest decrease; thus, there must be an optimum longitudinal tube spacing for maximizing the Colburn-Fanning factor ratio for a given transversal tube spacing. However, the influence of the longitudinal tube spacing on the Colburn-Fanning factor ratio was relatively small (approximately 7%). Predictive correlations for the Nusselt and Euler numbers were developed based on the data presented here. In addition, comparisons between the tested data from this paper and the predicted values from previously published correlations were performed. The ESCOA1979 correlations showed the greatest degree of consistency with the experimental data. Nomenclature
Re sf SD
fin spacing, pfedf [m] diagonal tube spacing [m]
Ai Af At Ao cp,g df do Ef Eo Eth Eu f G hf hf/sf hs j j/f kf kg kt K l/d Nf Nr Nu pf Pr Q
relative diagonal tube spacing longitudinal tube spacing [m] relative longitudinal tube spacing transversal tube spacing [m] ratio of transversal tube spacing to fin tip diameter relative transversal tube spacing transversal-longitudinal tube spacing ratio
Greek symbols ai tube-side (internal side) heat transfer coefficient [W m2 K1] ao fin-side (external side) heat transfer coefficient [W m2 K1] rg density of gas [kg m3] df fin thickness [m] dt tube wall thickness [m] Dp pressure drop of gas [Pa] Dtm logarithmic mean temperature difference for countercurrent flow [ C] mg dynamic viscosity of gas [kg m1 s1] References
arithmetic average area of bare tube inside and outside surface [m2] tube inside surface area [m2] surface area of the fins, including the fin-ends surface [m2] net exposed inter-fins tube surface area [m2] total external heat transfer surface (including the fins surface), Af þ At [m2] gas specific heat at constant pressure [J kg1 K1] fin tip diameter [m] outer diameter of the tube [m] fin efficiency overall surface efficiency, (At þ Ef$Af)/Ao theoretical fin efficiency rg Dp Euler number, 2 > G Nr rg Dp Fanning fraction factor, 2 2 G Nr gas mass flux in the narrowest cross-flow area [kg m2 s1] fin height [m] fin height-spacing ratio segment height [m] Nu Colburn heat transfer factor, Re$Pr 1=3 Colburn-Fanning factor ratio thermal conductivity of fin material [W m1 K1] thermal conductivity of gas [W m1 K1] thermal conductivity of tube wall [W m1 K1] overall heat transfer coefficient [W m2 K1] ratio of tube length to tube inside diameter fin density [fins/m] number of longitudinal tube rows ao do Nusselt number, kg fin pitch [m] cp;g mg Prandtl number, kg heat duty [W] do G Reynolds number,
Aav
SD/do SL SL/do ST ST/df ST/do ST/SL
mg
[1] E.M. Sparrow, T.A. Myrum, Crossflow heat transfer for tubes with periodically interrupted annular fins, International Journal of Heat and Mass Transfer 28 (No.2) (1985) 509e512. [2] Zhuo Ning, Jiang Weiyuan, Wang Jian, et al., Heat transfer and flow resistance properties of helically segmented finned tube bank, Journal of University of Shanghai for Science and Technology 18 (No.1) (1996) 23e26. [3] Cheng Guibing, Chen Yuanguo, Experimental study on the heat transfer and flow resistance of serrated finned tube banks, Chinese Society of Engineering Thermophysics, Proceeding on Heat and Mass Transfer Academic Conference (1998) 47e52 Hefei. [4] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (comparison of the heat transfer characteristics between spiral fin and serrated fin), Heat Transfer Asian Research 34 (No.2) (2005) 120e133. [5] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (comparison of the pressure drop characteristics between spiral fin and serrated fin), Heat Transfer Asian Research 33 (No.7) (2004) 431e444. [6] D.R. Reid, J. Taborek, Selection criteria for plain and segmented fined tubes for heat recovery systems, Journal of Engineering for Gas Turbines and PowerTransactions of the ASME 116 (No.4) (1994) 406e410. [7] E.A. Schryber, N.Y. Brooklyn, Heat transfer coefficients and other data on individual serrated-finned surface, Transactions of the ASME 67 (No.8) (1945) 683e686. [8] C. Weierman, Pressure drop data for heavy-duty finned tubes, Chemical Engineering Progress 73 (No.2) (1977) 69e72. [9] C. Weierman, J. Taborek, W.J. Marner, Comparison of the performance of inline and staggered banks of tubes with segmented fins. AIChE symposium series, San Francisco, National Heat Transfer Conference, 15th, Heat Transfer, Research and Application. 74(No. 174) (1978) 39-46. [10] K. Hashizume, Heat transfer and pressure drop characteristics of finned tubes in cross flow, Heat Transfer Engineering 3 (No.2) (1981) 15e20. [11] K. Kawaguchi, K. Okui, T. Asai, et al., The heat transfer and pressure drop characteristics of the finned tube banks in forced convection (effects of fin height on heat transfer characteristics), Heat Transfer Asian Research 35 (No.3) (2006) 194e208. [12] K. Kawaguchi, K. Okui, T. Asai, et al., The heat transfer and pressure drop characteristics of the finned tube banks in forced convection (effects of fin height on pressure drop characteristics), Heat Transfer Asian Research 35 (No.3) (2006) 179e193. [13] E. Næss, Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts, Applied Thermal Engineering 30 (2010) 1531e1537. [14] T.J. Rabas, G.A. Myers, P.W. Eckels, Comparison of the thermal performance of serrated high-finned tubes used in heat-recovery systems. ASME, heat transfer division, Anaheim, Heat Transfer in Waste Heat Recovery and Heat Rejection Systems 59 (1986) 33e40. [15] E. Martinez, W. Vicente, M. Salinas, et al., Single-phase experimental analysis of heat transfer in helically finned heat exchanger, Applied Thermal Engineering 29 (2009) 2205e2210. [16] E. Martinez, W. Vicente, G. Soto, et al., Comparative analysis of heat transfer and pressure drop in helically segmented finned tube heat exchangers, Applied Thermal Engineering 30 (2010) 1470e1476. [17] C. Weierman, Correlations ease the selection of fin tubes, The Oil and Gas Journal 74 (6) (1976) 94e100.
Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323 [18] ESCOA Corp., ESCOA Fintube Manual, ESCOA, Tulsa, OK, 1979. [19] A. Nir, Heat transfer and friction factor correlations for cross-flow over staggered finned tube banks, Heat Transfer Engineering 12 (No.1) (1991) 43e58. [20] D.E. Briggs, E.H. Young, Convective heat transfer and pressure drop of air flowing across triangular pitch banks of finned tubes, Chemical Engineering Progress Symposium Series 59 (No.41) (1963) 1e10. [21] K.K. Robinson, D.E. Briggs, Pressure drop of air flowing across triangular pitch banks of finned tubes, Chemical Engineering Progress Symposium Series 62 (No.64) (1966) 177e184.
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[22] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (1976) 359e368. [23] K.A. Gardner, Efficiency of extended surface, Transactions of the ASME 67 (1945) 621e631. [24] K. Hashizume, R. Morikawa, T. Koyama, et al., Fin efficiency of serrated fins, Heat Transfer Engineering 23 (No.2) (2002) 6e14. [25] A.A. Zukauskas, Convective Heat Transfer in Heat Exchangers, China Science Press, Beijing, 1986, 296e323.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation of heat transfer and pressure drop in serrated finned tube banks with staggered layouts Youfu Ma*, Yichao Yuan, Yuzheng Liu, Xiaohong Hu, Yan Huang College of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2011 Accepted 20 November 2011 Available online 28 November 2011
An experimental study was performed to investigate the heat transfer and pressure drop characteristics of serrated finned tube banks with staggered layouts. The influences of varied fin densities, transversal tube spacing and longitudinal tube spacing were presented. For a constant fin height, an increase in the fin density resulted in an increase in the Euler number, and a gradual decrease in the Nusselt number was observed as the Reynolds number increased. An increase in the transversal tube spacing corresponded to a significant reduction in the Euler number, whereas the Nusselt number essentially remained unchanged. The longitudinal tube spacing had an insignificant effect on the Nusselt and Euler numbers, and the optimum ratio of the transversal tube spacing to longitudinal tube spacing increased with an increase in the transversal tube spacing. Scaling of the tube spacing had little effect on the Nusselt number but had a significant influence on the Euler number. Finally, predictive correlations for Nusselt and Euler numbers were developed based on the data presented here, and comparisons between the test data from this paper and the predictive values from previously published correlations were performed. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Pressure drop Heat recovery steam generator Finned tube Serrated fin
1. Introduction Helical finned tubes are widely used in large-scale heat transfer equipment with flue gas emissions, such as combined cycle heat recovery steam generators (HRSGs) in power plants and waste heat boilers in chemical industries. For high-temperature applications, tubes and fins are normally made from carbon steel, and the fin assembly is welded to the tube surface. Due to restrictions in the required technical level of welding, early helical steel-finned tubes had an L-shaped fin-root (known as an L-foot fin) that was used to increase the welding area. With recent technical developments in high-frequency electric resistance welding techniques, stripshaped fins (called I-foot fins) can now be directly welded to a tube surface. Due to the poor ductility of steel, the manufacturing of solid steel fins consumes a large amount of energy in the winding process, and the fin height must be within the limits of radial deformation and fin-end rips. Hence, serrated helical steel-finned tubes emerged in industrial applications in the 1960s to overcome these defects related to solid fins. Compared to solid fins, serrated fins are easier to manufacture and have a larger finned ratio. Serrated fins can also exhibit a higher fin efficiency and heat
* Corresponding author. Tel.: þ86 021 55272320. E-mail addresses: [email protected], [email protected] (Y. Ma). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.11.037
transfer coefficient as a result of the better penetrativity and turbulent condition of the fin-side gas. However, the number of published experimental studies on the heat transfer and pressure drop characteristics of serrated helical finned tube banks is very limited. Among the available studies on serrated helical finned tube banks, many experiments have focused on comparisons between solid fins and serrated fins tube banks, such as Sparrow and Myrum [1], Zhuo et al. [2], Chen et al. [3] and Kawaguchi et al. [4,5]. In general, these studies found that serrated fins could increase the fin-side heat transfer coefficient by approximately 10e25% relative to solid fins, whereas the pressure drop is enhanced by approximately 10e15%. Moreover, Reid [6] compared two types of finned tubes while also considering the cost of finned tubes, and recommended to choose serrated finned tube when fin heights are greater than 12 mm. Early in the 1940s, Schryber and Brooklyn [7] presented heat transfer data for 3 L-foot serrated copper-finned tube banks. Subsequently, I-foot serrated steel-finned tube received widespread attention. For example, Weierman (1977) [8] reported pressure drop data for 6 tube banks and later compared the effects of square and equivalent triangle tube layouts on heat transfer and pressure drop through 2 tube banks [9]. Later, Hashizume [10], Zhuo et al. [2], Chen et al. [3] and Kawaguchi et al. [4,5,11,12] reported heat transfer and pressure drop data for I-foot serrated
Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323
finned tube banks with staggered layouts. In addition, Næss [13] also recently investigated L-foot serrated steel-finned tube. In contrast to the aforementioned experiments conducted in laboratory wind tunnels, Rabas et al. [14] and Martinez et al. [15,16] obtained measurements from an operating combined cycle HRSG and an economizer with a serrated finned tube bank, respectively. Heat transfer and pressure drop correlations are generally applicable and remain important topics in the study of serrated finned tube banks. In this regard, correlations developed by Weierman [17], who served at the Extended Surface Corporation Of America (ESCOA) Fin-tube Corporation, have been widely referenced, and ESCOA revised several correlation coefficients in 1979 [18]; however, the experimental data on which the ESCOA correlations were based have not been published. Nir [19] presented a set of correlations based on the collection of published experimental data available in 1991. Chen et al. [3], Kawaguchi et al. [11,12] and Næss [13] also presented correlations based on their experiments. For solid finned tube banks with staggered layouts, the heat transfer correlations presented by Briggs and Young [20] and the pressure drop correlations presented by Robinson and Briggs [21] have been widely recommended. These correlations are compared with the experimental data of this paper in a later section. When considering the multiform geometric factors of helical finned tubes, the fin height-spacing ratio (hf/sf) is essential for the formation of flow between fins and tubes [22]. For instance, the experimental results presented by Chen et al. [3] showed that the fin height-spacing ratio, within the range of 1.1e3.8, influenced the heat transfer and pressure drop by approximately 27% and 45%, respectively; within this same range, the heat transfer and pressure drop values predicted according to the ESCOA correlations [18] showed an alteration of 20% and 28%, respectively. In the above studies, the fin height-spacing ratio ranges of Chen et al. [3], Kawaguchi et al. [4,5,11,12] and Næss [13] were 1.1e3.8, 2.2e3.8 and 2.1e4.2, respectively. To our knowledge, the heat transfer and pressure drop data for serrated finned tube bank with higher fin height-spacing ratios were not reported. However, a higher fin height-spacing ratio is often preferred in combined cycle HRSGs due to the small quantity of fly ash in working flue gas. Therefore, four types of I-foot serrated finned tubes with different fin densities and fin height-spacing ratios ranging from 5.0 to 5.5 were investigated in this paper. Moreover, because serrated finned tube banks are typically arranged in staggered layouts [9], and non-equilateral triangular tube layouts are very common in practical applications, the effects of transversal and longitudinal tube spacing on the heat transfer and pressure drop of tube banks with staggered layouts were also investigated. 2. Experimental setup and data processing 2.1. Experimental setup Experiments were carried out in a circulating wind tunnel consisting of air circulation and cooling water systems, as shown in Fig. 1. Air was pulled using a draft fan, and the air flow rate was adjusted using an analog input on the fan. The air then passed through an electric heater that maintained the test section inlet temperature at approximately 180 C for all experiments. In the upstream wind tunnel of the test section, the hot air was passed through a calming section equipped with flow straighteners and several fine wire meshes to reduce the large-scale turbulence and to provide a uniform velocity profile at the test section entrance. The hot air then passed across the tube banks, and heat was transferred to the cooling water in the test section. Subsequently, the low-temperature air was directed to a wind box for measuring
315
Fig. 1. Schematic diagram of the experimental system.
the air flux and was then passed back to the draft fan to complete the air circulation cycle. To minimize the heat loss, all surfaces of the wind tunnel and test section were covered with thermal insulators. The inlet and outlet air temperatures were measured by placing fine wire meshes in the wind tunnel; sixteen thermocouples were attached to the meshes and spaced equally over the cross-sectional area. The air flow was determined using four nozzles, which were placed in the wind box and had various combinations of different diameters for varying the air flow. The air-side pressure drop across the tube banks was determined using measurements of the static pressure difference between the upstream and downstream sides of the tube banks, and each side consisted of four parallel connected pressure taps located around the test section circumference. A sketch of the test section is shown in Fig. 2. The test section width (i.e., the active tube length) was 400 mm, and the section height was 4.5 times the transversal tube spacing. The test section consisted of forty active tubes for heat transfer (four transversal and ten longitudinal tube rows), and ten dummy half-tubes were located at the section walls to obtain hydraulic similitude. As confirmed by most previous experiments on finned tube banks with cross flow, fully developed conditions for heat transfer and pressure drop were reached within four tube rows for staggered layouts. Hence, ten longitudinal tube rows were considered sufficient to obtain representative heat transfer and pressure drop data. City water was used as coolant in the tubes. A water tank was used to maintain a steady water level and thus sustain a steady water flux during the course of the experiments. In addition, an electric heater was placed inside the water tank to raise the temperature of the water to prevent moisture condensation on the fin side. The cooling water was pumped using a water pump, and the water flow was adjusted using a valve placed at the outlet pipe of the tube bank. In the test section, the cooling water was passed through a single tube, and the forty active tubes were connected in series to provide an overall cross-countercurrent arrangement for
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Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323
Fig. 2. Dimensions of the test section.
the air/water flow. The inlet and outlet water temperatures were measured using platinum resistance thermometers, and the water flow rate was measured using a turbine flowmeter. All of the meters, including the thermocouples, platinum resistance thermometers, differential pressure transmitters, turbine flowmeter and nozzles, were calibrated before use. During the experiments, all measured data were recorded at 5-s intervals for at least 15 min per experiment after stable operating conditions were ensured. Furthermore, the first experiment in each series was repeated at the end of a run to substantiate the repeatability. The air-side and water-side heat balance deviations were within 3% in all experiments.
2.3. Data processing The heat duty was calculated based on the measured mass flow rates and overall temperature changes, and the overall heat transfer coefficient was then calculated from Eq. (1) using the arithmetic average of the air-side and water-side heat duties.
K ¼
The testing tubes were commercially available tubes with I-foot fins, as shown in Fig. 3. The tubes and fins were made from carbon steel. The fin root was resistance-welded to the tubes, providing negligible thermal contact resistance between the fin and the outer surface of the tube. The outer diameter of the tube, fin thickness, fin height, segment width and segment height of do ¼ 38.1 mm, df ¼ 1 mm, hf ¼ 16 mm, ws ¼ 4 mm and hs ¼ 10 mm, respectively, remained constant for all testing tube banks. The main features of the testing tube banks are shown in Table 1, and the geometric variables are explained in Fig. 3. All finned tubes and tube spacing geometries were selected from several operating combined cycle HRSGs. A total of 12 tube banks were tested. Banks 1e4 consisted of tubes with different fin densities (i.e., varied fin pitch or spacing), but the tube spacing and other finned tube geometries were identical. Banks 4e12 consisted of tubes with different transversal or longitudinal tube spacing, but with identical finned tube geometries. Therefore, banks 1e4 were used to explore the effect of the fin height-spacing ratio (hf/sf) in the range of 5.0e5.5, and banks 4e12 were used to explore the effects of the relative transversal tube spacing (ST/do) in the range of 2.3e3.2, the relative longitudinal tube spacing (SL/do) in the range of 2.4e3.1 and the effects of the transversalelongitudinal tube spacing ratio (ST/SL) in the range of 0.75e1.30.
(1)
The fin-side heat transfer coefficient was determined using Eq. (2)
ao ¼
2.2. Testing tube banks
Q Ao $Dtm
1 dt Ao 1 Ao $ $ K kt Aav ai Ai
1
Ao At þ Ef Af
(2)
In Eq. (2), the tube-side heat transfer coefficient was calculated using the Gnielinski correlation [22] (valid for 2300 < Re<106, 0.6 < Pr<105 and l/d 1), and the fin efficiency was given by Eq. (3) as discussed below. To ensure the validity of using the Gnielinski correlation, fully turbulent flow was maintained on the tube side during the experiments in this paper, in which the corresponding flow conditions for water were 2 104 < Re<4 104, 4.0 < Pr<7.0 and l/d ¼ 12.5. Thus, the conditions for the use of the Gnielinski correlation were satisfied. In addition, the uncertainty in the tubeside heat transfer coefficient was estimated to be 10% according to the reported accuracy of the Gnielinski correlation, and therefore, the sensitivity of the fin-side heat transfer coefficient was approximately 5% for this paper. The appropriate fin efficiency, which compensates for the finite conductance of the fins according to Gardner [23], under the assumption of a uniform fin-side heat transfer coefficient, is expressed as:
Eth
h i tanh m hf þ df =2 ¼ where m ¼ m hf þ df =2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u u2ao d þ ws f t kf df ws
(3)
However, as pointed out by Hashizume [24], the heat transfer coefficient distribution is not uniform, yielding actual fin
Fig. 3. Geometric schematic of the serrated finned tube and tube bank with staggered layouts.
Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323 Table 1 Main geometry data for testing tube banks. Tube banks no.
ST [mm]
SL [mm]
do [mm]
Nf [fins/m]
hf [mm]
df [mm]
hs [mm]
ws [mm]
1 2 3 4 5 6 7 8 9 10 11 12
88 88 88 88 88 88 104 104 104 120 120 120
92 92 92 92 105 117 92 105 117 92 105 117
438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1 438.1
257 252 245 241 241 241 241 241 241 241 241 241
16 16 16 16 16 16 16 16 16 16 16 16
1 1 1 1 1 1 1 1 1 1 1 1
10 10 10 10 10 10 10 10 10 10 10 10
4 4 4 4 4 4 4 4 4 4 4 4
efficiencies that are lower than predicted by Eq. (3). In the analysis presented here, the empirical correction factor proposed by Weierman [17] was applied to the theoretical fin efficiency, as shown in Eq. (4). The magnitude of the correction introduced using Eq. (4) relative to the uncorrected value obtained using Eq. (3) was relatively small (less than approximately 1e5%) for all experiments.
Ef ¼ Eth ð0:9 þ 0:1Eth Þ
(4)
To represent the correlativity between the heat transfer or pressure drop and the fin-side flow conditions, the dimensionless norms, such as the Nusselt number, Prandtl number, Euler number and Reynolds number, were used in this paper. In the calculations of the above norms, the arithmetic mean temperature was used for the calculations of gas physical properties. The outer diameter of the tube was adopted as the characteristic length for the Reynolds and Nusselt numbers, and the gas mass flux in the narrowest crossflow area was adopted to calculate the characteristic velocity for the Reynolds and Euler numbers. Because the pressure drop of the gas across the tube banks was determined using measurements of the static pressure difference and the pressure drop data were recorded with simultaneously the heat transfer data, the dynamic pressure differences of the gas between the upstream and downstream sides of the tube banks should be considered in the determination of the real pressure drop of the tube banks. Because the gas was cooled in the tube banks, the measured static pressure drops were smaller relative to the real pressure drops of the gas. Therefore, the dynamic pressure differences between the upstream and downstream sides of the tube banks were added to the measured pressure drop in this paper to provide the resistance coefficients of the tube banks in the cold tests. Specifically, the rectified Euler number of each tube bank was 0.8e2.0% greater than that of the actual measurements. For the comparison of the overall thermalehydraulic performance of the tube banks, the Colburn-Fanning factor ratio (j/f), representing the heat transfer efficiency of a surface with a given resistance coefficient, was used for the tested tube banks. The definitions of the Colburn heat transfer factor and the Fanning friction factor are shown in the nomenclature. Based on the error analyses of the experiments in this paper, the maximum experimental uncertainties for the Nusselt and Euler numbers were 4.5% and 2.7%, respectively.
geometries but differed in their fin density (Fig. 4). The Nusselt numbers of banks 2, 3 and 4 were larger than that of bank 1 by approximately 3%, 4% and 5%, respectively, demonstrating a quantitative increase in the Nusselt numbers with decreasing fin density under the same Reynolds number. This result is qualitatively consistent with the corresponding results obtained for solid finned tube banks with staggered layouts and can be attributed to the enhanced action of gases penetrating into fin gaps due to a decrease in the fin heightespacing ratio or a decrease in the fin density with a constant fin height. In previous experiments on serrated finned tube banks, Chen [3] demonstrated an approximately 27% decrease in the Nusselt number with an increase in the fin heightespacing ratio from 1.1 to 3.8, which is consistent with the results obtained here using a fin height-spacing ratio range of 5.0e5.5. However, Kawaguchi [11] reported that an increase in the Nusselt number of approximately 7% corresponded to an increase in the fin height-spacing ratio from 2.2 to 3.8; Næss [13] presented a similar result when using two tube banks. These contradictory findings likely resulted from differences in the fin heights: a lower fin height (8.6 mme13 mm) was used by Kawaguchi [11] and Næss [13], and a higher fin height (15 mme16 mm) was used by Chen [3] and in the present study. Specifically, an increase in the fin height can enhance the gas turbulence due to the shape of the serrated fins, whereas there is no obvious effect on the gas penetrability when the fin height is relatively low; however, this effect is reversed when the fin height is relatively high. Banks 1e4 had identical fin heights, and therefore, this mechanism needed to be confirmed using additional experimental data for tube banks with various fin heights. As shown in Fig. 4, a smaller decrease in the Nusselt number due to differences in the fin density occurred as the Reynolds number increased; similar results were also observed for the solid finned tube banks [25]. This trend is mainly attributed to the thinning of the gas boundary layer such that the influence of the fin spacing on heat transfer tends to weaken with an increase in the Reynolds number. The Nusselt number for bank 1 was lower than that of bank 4 by 11e0% with Reynolds numbers increasing from 4000 to 30,000; at the same time, the total external surface area (Ao) of bank 1 was larger than that of bank 4 by approximately 8%. Thus, there is a minimum critical Reynolds number (Remc) for bank 1 below which the fin-side heat transfer quantity per meter (aoAoEo) is less than that of bank 4 under the same Reynolds number. This minimum critical Reynolds number was approximately 15,000
3. Results and discussion 3.1. Heat transfer 3.1.1. Effect of the fin density The effect of the fin density on the heat transfer performance is demonstrated using testing banks 1e4, which had identical
317
Fig. 4. Fin-side Nu vs. Re in terms of the various fin densities.
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when comparing banks 1 and 4, as shown in Fig. 5. According to the analysis, the minimum critical Reynolds number must decrease with an increase in the fin density difference of the compared tube banks; therefore, the minimum critical Reynolds number may be worthy of further attention in the case of a small fin density difference. 3.1.2. Effects of tube spacing The effects of tube spacing on heat transfer were demonstrated using testing banks 4e12, which had identical geometries but differed in their transversal and longitudinal tube spacing (Fig. 6). Changes in the transversal tube spacing resulted in a heat transfer difference of less than 3%, and therefore, the effects were negligible. In contrast, the longitudinal tube spacing had a greater effect on the heat transfer: the Nusselt numbers for the tube banks with SL ¼ 105 mm were always approximately 6% higher than those of the tube banks with SL ¼ 92 mm and SL ¼ 117 mm. Thus, for typical tube arrangements, the longitudinal tube spacing had a more distinct effect on the heat transfer, which was mainly due to the influence of the longitudinal tube spacing on the reflow region on the leeward side of the tube. Although the effect of the transversal tube spacing on heat transfer can be neglected in typical tube arrangements, as indicated by Kawaguchi [4,11] (ST/df ¼ 1.3e1.5) and corroborated in this paper (ST/df ¼ 1.3e1.7), the heat transfer would evidently decrease when the ratio of transversal tube spacing to fin tip diameter (ST/df) is greater than 2, as shown by Næss [13] (ST/df ¼ 2.04 and 2.09). This influence of the transversal tube spacing may mainly result from the clear increase in the free longitudinal flow (i.e., the bypass flow) in staggered tube banks, which would induce a marked increase in the stagnation flow regions on the windward side and the reflow regions on the leeward side of the tube. In the heat transfer correlation analysis for the finned tube banks in a cross flow configuration, the transversal-longitudinal tube spacing ratio (ST/SL) was usually used as a geometric factor for determining the influences of tube spacing. The comparison of banks 4e12 indicated that the optimum transversalelongitudinal tube spacing ratio for achieving the maximum heat transfer increased with an increase in the relative transversal tube spacing. These findings are distinct from prevailing views: the Nusselt number is expected to increase with an increase in the transversalelongitudinal tube spacing ratio, which is generally attributed to an increase in the average gas velocity or level of turbulence
Fig. 5. Fin-side heat transfer quantities per meter of finned tube vs. Re for banks 1 and 4.
Fig. 6. Fin-side Nu vs. Re in terms of the various tube spacing.
at the same Reynolds number (i.e., the Reynolds number is usually defined by the gas velocity in the narrowest flow area, and in most cases, the area is dependent on the transversal tube spacing). On the other hand, an increase in the transversal-longitudinal tube spacing ratio shortens the travel distance of the gas and also increases the proportion of free longitudinal flow; these effects tend to cause a decrease in the Nusselt number with an increase in the transversalelongitudinal tube spacing ratio. Therefore, the overall effect is that there must be an optimum transversallongitudinal tube spacing ratio for a certain relative transversal tube spacing to maximize heat transfer. However, there was only an approximately 6% variation in the Nusselt number with varied transversalelongitudinal tube spacing ratios in this paper, and thus, this type of active mechanism for the tube spacing needs to be confirmed by further experimental data. Testing bank 4 (ST/do ¼ 2.3, SD/do ¼ 2.7) could be considered an approximate scaled-down version of bank 12 (ST/do ¼ 3.1, SD/ do ¼ 3.5) with respect to the tube spacing with the shortest fin-tip clearance increasing from 18 mm to 50 mm. The comparison of banks 4 and 12 indicated that their heat transfer performances were almost identical. This result was corroborated by the work of Chen [3] in which the tube banks were arranged in an equilateral triangle configuration and the relative transversal tube spacing ranged from 2.0 to 3.1. Thus, the scaled tube spacing had a negligible effect on the heat transfer performance for serrated finned tube banks with approximate equilateral triangular layouts with the exception, based on reasonable deduction, of cases where the ratio of the transversal tube spacing to fin tip diameter is greater than 2. 3.1.3. Heat transfer correlations For the heat transfer correlation of this paper, the geometric factors of the fin heightespacing ratio and transversalelongitudinal tube spacing ratio, which have been adopted in most existing studies on solid or serrated finned tube banks, such as Briggs and Young [20], Weierman [17], Chen [3], Næss [13], were used to present the influences of the finned tube and tube layouts geometries. In contrast to the fin height-spacing ratio, the transversalelongitudinal tube spacing ratio often has a marginal effect on the heat transfer performance in common tube layouts, thus, its influence was presented in the heat transfer correlation using a constant exponent derived from the linear regression of heat transfer data, like the traditional processing method for the
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Reynolds number. However, in this study, the heat transfer value does not deviate in direct correlation with varied fin heightespacing ratios; in addition, the influences on the heat transfer tend to be weak when the fin height-spacing ratio is decreased, as confirmed in solid finned tube banks where the Nusselt number is independent of the fin spacing when the fin spacing is larger than 4.5 mm [25]. To present the composite effects of the fin heightspacing ratio, a special corrective factor (see Eq. (5)) was used in the heat transfer correlation based on the experimental data in this paper. In contrast with the typical approach for imposing a constant exponent on fin heightespacing ratio, this fin height-spacing ratio correction factor also took into account the decreased effect on the heat transfer as the Reynolds number increased. To address the influences of the gas physical properties, an analytic solution of 0.33 was used as a constant exponent on the Prandtl number. Thus, the heat transfer correlation for the serrated finned tube banks was presented as follows using a multiple linear regression analysis of the experimental data:
0 Nu ¼ 0:117Re
0:717
Pr
0:33 B
@0:6 þ 0:4e
1 250h =s Ref f
0:06 C ST A SL
Fig. 8. Fin-side Eu vs. Re in terms of the various fin densities.
(5)
The validated ranges for Eq. (5) are Re ¼ 4000e30,000, hf/ sf ¼ 5.0e5.5 and ST/SL ¼ 0.75e1.30. Eq. (5) has a 95% confidence interval of the standard deviation of 4.4%. The overall prediction accuracy is shown in Fig. 7. 3.2. Pressure drop 3.2.1. Effect of the fin density The effect of the fin density on the pressure drop characteristics was demonstrated using testing banks 1e4, which had identical geometries but differed in their fin density (Fig. 8). An increase in the fin density resulted in an increase in the Euler number under constant Reynolds number conditions. Specifically, the Euler numbers of bank 1, 2 and 3 were greater than that of bank 4 by approximately 8%, 6% and 2%, respectively. This observation is qualitatively consistent with the corresponding results for the solid finned tube banks with staggered layouts and is likely the result of additional frictional surface and stronger gas disturbance caused by the serrated fins as the fin density increases.
Fig. 7. Measured Nuexp vs. predicted Nucalc values calculated using Eq. (5).
In previous experiments on serrated finned tube banks, Chen [3] concluded that the Euler number increased by approximately 45% as the fin heightespacing ratio increased from 1.1 to 3.8; this finding is qualitatively consistent with the results of this paper for a fin heightespacing ratio range of 5.0e5.5, representing a proportional change in the Euler number of approximately 16% for each unit interval change in the fin height-spacing ratio. However, the results of Kawaguchi [12] appear to be conservative, showing an increase in the Euler number of only 4% as the fin heightespacing ratio was increased from 2.2 to 3.8. 3.2.2. Effects of tube spacing The effects of the tube spacing on the pressure drop characteristics were demonstrated using testing banks 4e12, which had identical geometries but differed in their transversal and longitudinal tube spacing (Fig. 9). As shown in Fig. 9, the transversal tube spacing had a significant influence on the pressure drop; specifically, the Euler numbers of the tube banks with ST ¼ 104 mm and ST ¼ 120 mm decreased by approximately 8% and 20%, respectively, relative to the tube banks with ST ¼ 88 mm. In addition, the longitudinal tube spacing had a modest influence on the pressure drop; specifically, the Euler numbers of the tube banks with
Fig. 9. Fin-side Eu vs. Re in terms of the various tube spacing.
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SL ¼ 105 mm and SL ¼ 117 mm decreased by approximately 1% and 5%, respectively, relative to the tube banks with SL ¼ 92 mm. Hence, the transversal tube spacing had a more distinct effect on the pressure drop than the longitudinal tube spacing in these reasonable tube arrangements. It is generally acknowledged that the pressure loss of the cross flow in tube banks with staggered layouts is the result of three main components: the flow around loss, the frictional loss and the loss due to gas volume expansion and contraction. Therefore, with an increase in the transversal tube spacing, the flow around loss may decrease due to the additional flow of gas across the tube bank in a similar manner as bypass flow. In addition, the loss due to gas volume expansion and contraction tends to decrease because the transversal free cross sectional area is less than the diagonal free cross sectional in typical tube arrangements. Moreover, an increase in the ratio of the free longitudinal flow also tends to reduce the frictional loss. Hence, the Euler number evidently decreases with an increase in the transversal tube spacing. With respect to the longitudinal tube spacing, an increase in the longitudinal tube spacing can increase the leeward reflow region, thus decreasing the flow around and frictional losses; however, the loss due to gas volume expansion and contraction may increase slightly because the Euler number generally decreases with an increase in the longitudinal tube spacing. As mentioned above, the tube spacing of banks 4 and 12 were approximately proportional in scale. The comparison of these two banks indicated that the Euler number of bank 12 (ST/do ¼ 3.1) was approximately 23% less than that of bank 4 (ST/do ¼ 2.3). Chen [3] presented a similar decrease of approximately 18% in equilateral triangular tube banks as the relative transversal tube spacing increased from 2.0 to 3.1. Thus, in contrast to its small effect on the heat transfer, the scaled tube spacing has a noticeable influence on the pressure drop. In addition, it is noteworthy that the tube spacing is also related to the compactness of the tube bank. 3.2.3. Pressure drop correlations The geometric factor of the fin height-spacing ratio was used to represent the influences of the finned tube geometries in the pressure drop correlation analysis in this paper. With respect to the tube spacing effects, the dimensionless geometric factors of the relative transversal tube spacing and relative longitudinal tube spacing were used because these factors influence the pressure drop to a varied extent. The pressure drop correlation for the serrated finned tube banks was presented using a multiple linear regression analysis of the experimental data as follows:
Eu ¼ 1:773Re
0:184
hf sf
!0:556
S1 do
0:673
S2 do
Fig. 10. Measured Euexp vs. predicted Eucalc values calculated using Eq. (6).
and only bank 7 showed a monotonically decreasing trend (Fig. 11). In general, the Reynolds number range corresponding to the higher Colburn-Fanning factor ratios was approximately 7000e10,000. Regarding the influences of the geometries, as shown in Fig. 11, an increase in the fin pitch and transversal tube spacing resulted in clear improvements in the Colburn-Fanning factor ratios of tube banks. However, the longitudinal tube spacing had a relatively small influence on the Colburn-Fanning factor ratios. More specifically, the Colburn-Fanning factor ratio for bank 4 was greater than that of bank 1 by approximately 28% due to an decrease in the fin density from 257 fins/m to 241 fins/m; the Colburn-Fanning factor ratio increased by approximately 25% as the transversal tube spacing increased from 88 mm to 120 mm with a constant longitudinal tube spacing. Although a larger fin pitch and transversal tube spacing may be helpful in improving the overall thermalehydraulic performance of the tube banks, these geometries also had a detrimental effect on the compactness of the tube banks. As far as the longitudinal tube spacing was concerned, the tube banks with SL ¼ 105 mm always had the highest Colburn-Fanning factor ratios with the same transversal tube spacing, the tube banks with SL ¼ 117 mm were the second highest and the tube banks with SL ¼ 92 mm showed the lowest ratio. This result
0:133 (6)
The validated ranges for Eq. (6) are Re ¼ 4000e30,000, hf/sf ¼ 5.0e5.5, ST/do ¼ 2.3e3.2 and SL/do ¼ 2.4e3.1. Eq. (6) has a 95% confidence interval of the standard deviation of 2.7%. The overall prediction accuracy is shown in Fig. 10.
3.3. Overall thermalehydraulic performances Various assessment criteria have been used previously to evaluate the overall performance of tube banks depending on the different desired goals, including the Colburn-Fanning factor ratio (j/f) that is mainly used for the assessment of the overall thermale hydraulic performance of finned tube banks. Fig. 11 shows the Colburn-Fanning factor ratios for the twelve tested tube banks. The Colburn-Fanning factor ratio of eleven tube banks increased initially and then gradually decreased as the Reynolds number increased,
Fig. 11. The overall thermalehydraulic performances of the tested tube banks.
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indicated that the Colburn-Fanning factor ratio increased initially and then showed a modest decrease as the longitudinal tube spacing increased, i.e., there were an optimum longitudinal tube spacing that resulted in a maximum Colburn-Fanning factor ratio for a given transversal tube spacing. However, the extent of effect of the longitudinal tube spacing was relatively small, as the greatest difference in Colburn-Fanning factor ratio at the same transversal tube spacing was approximately 7%. 3.4. Comparisons of the correlations 3.4.1. Comparison of the heat transfer correlations Fig. 12 shows a comparison between the heat transfer test data of banks 1e12 and the predicted values calculated using previously published correlations (identified here as Weierman1976 [17], ESCOA1979 [18], Nir1991 [19], Chen1998 [3], Kawaguchi2006 [11], Næss2010 [13] and Briggs1963 [20]). As shown in Fig. 12, the predicted Nusselt values from Weierman1976, ESCOA1979 and Næss2010 correlations deviated from the test data of banks 1e12 within the range of 10%, among which the ESCOA1979 heat transfer correlation showed the greatest degree of consistency with the test data as the standard deviations for each tube bank being less than 5%. The deviations of the predicted Nusselt values from the Chen1998 and Kawaguchi2006 correlations were in the range of 20%, whereas the predicted Nusselt values from Nir1991 correlation was approximately 45% less than the test data. The predicted Nusselt values from Briggs1963 correlation was approximately 35% less than the test data, which indicates that serrated finned tube banks have a superior heat transfer performance relative to solid finned tube banks, as confirmed by Zhuo [2] and Chen [3]. 3.4.2. Comparison of the pressure drop correlations Fig. 13 shows a comparison between the pressure drop test data of banks 1e12 and the predicted values calculated using previously published correlations (identified here as Weierman1976 [17], ESCOA1979 [18], Nir1991 [19], Chen1998 [3], Kawaguchi2006 [12], Næss2010 [13] and Robinson1966 [21]). As shown in Fig. 13, the predicted Euler values from ESCOA1979 correlation also had the greatest consistency with the test data, as the standard deviations for each tube bank were less than 10%. The predicted Euler values from Weierman1976 and Chen1998
Fig. 12. Comparison between the heat transfer test data and the predicted values calculated from previously published correlations.
Fig. 13. Comparison between the pressure drop test data and the predicted values calculated from previously published correlations.
correlations were greater than the test data by approximately 10e20% and Kawaguchi2006 correlation were also greater by approximately 50%. However, the predicted Euler values from Nir1991 and Næss2010 correlations were 2.5 times higher than the test data, and therefore, these predicted values are not displayed in Fig. 13. The predicted Euler values from Robinson1966 correlation lower initially and then was greater than the tested data as the Euler number increased (or the Reynolds number decreased), which indicates that the additional pressure drop induced by the serrated fins tends to increase as the Reynolds number increases; however, the Euler number differences between the test data from this paper and the predicted values from Robinson1966 correlation remain within 15% as the Reynolds number increases from 4000 to 30,000. 4. Conclusions A set of experiments was performed to evaluate the influence of the tube layout and fin density on the heat transfer, pressure drop and overall thermalehydraulic performance of serrated finned tube banks with staggered layouts. Based on the experimental results, the following conclusions were drawn. The Nusselt number ranged from showing no difference to decreasing up to 11% and the Euler number increased by approximately 8% as the fin heightespacing ratio increased from 5.0 to 5.5 while the Reynolds number was held constant. Because the extent of the effect of the fin density on heat transfer decreased as the Reynolds number increased, there must be a minimum critical Reynolds number for the tube bank with higher fin density that will avoid fin-side heat transfer per meter tube that is less than the tube bank with the lower fin density under the same Reynolds number. The transversal tube spacing had a negligible effect on the heat transfer over the spacing range used in the tested tube banks, whereas the pressure drop decreased by approximately 20% as the relative transversal tube spacing increased from 2.3 to 3.2. Variations in the longitudinal tube spacing had insignificant effects on the heat transfer and pressure drop (less than 6%) over the relative longitudinal tube spacing range of 2.4e3.1, and the optimum transversalelongitudinal tube spacing ratio that results in the maximum heat transfer increased as the relative transversal tube spacing increased. Moreover, scaling of the tube spacing had little
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effect on the heat transfer but had a significant influence on the pressure drop. With respect to the overall thermal-hydraulic performances of the tube banks, increases in the fin pitch and transversal tube spacing corresponded to an approximately 28% and 25% increase, respectively, in the Colburn-Fanning factor. As the longitudinal tube spacing increased, the Colburn-Fanning factor increased initially and then showed a modest decrease; thus, there must be an optimum longitudinal tube spacing for maximizing the Colburn-Fanning factor ratio for a given transversal tube spacing. However, the influence of the longitudinal tube spacing on the Colburn-Fanning factor ratio was relatively small (approximately 7%). Predictive correlations for the Nusselt and Euler numbers were developed based on the data presented here. In addition, comparisons between the tested data from this paper and the predicted values from previously published correlations were performed. The ESCOA1979 correlations showed the greatest degree of consistency with the experimental data. Nomenclature
Re sf SD
fin spacing, pfedf [m] diagonal tube spacing [m]
Ai Af At Ao cp,g df do Ef Eo Eth Eu f G hf hf/sf hs j j/f kf kg kt K l/d Nf Nr Nu pf Pr Q
relative diagonal tube spacing longitudinal tube spacing [m] relative longitudinal tube spacing transversal tube spacing [m] ratio of transversal tube spacing to fin tip diameter relative transversal tube spacing transversal-longitudinal tube spacing ratio
Greek symbols ai tube-side (internal side) heat transfer coefficient [W m2 K1] ao fin-side (external side) heat transfer coefficient [W m2 K1] rg density of gas [kg m3] df fin thickness [m] dt tube wall thickness [m] Dp pressure drop of gas [Pa] Dtm logarithmic mean temperature difference for countercurrent flow [ C] mg dynamic viscosity of gas [kg m1 s1] References
arithmetic average area of bare tube inside and outside surface [m2] tube inside surface area [m2] surface area of the fins, including the fin-ends surface [m2] net exposed inter-fins tube surface area [m2] total external heat transfer surface (including the fins surface), Af þ At [m2] gas specific heat at constant pressure [J kg1 K1] fin tip diameter [m] outer diameter of the tube [m] fin efficiency overall surface efficiency, (At þ Ef$Af)/Ao theoretical fin efficiency rg Dp Euler number, 2 > G Nr rg Dp Fanning fraction factor, 2 2 G Nr gas mass flux in the narrowest cross-flow area [kg m2 s1] fin height [m] fin height-spacing ratio segment height [m] Nu Colburn heat transfer factor, Re$Pr 1=3 Colburn-Fanning factor ratio thermal conductivity of fin material [W m1 K1] thermal conductivity of gas [W m1 K1] thermal conductivity of tube wall [W m1 K1] overall heat transfer coefficient [W m2 K1] ratio of tube length to tube inside diameter fin density [fins/m] number of longitudinal tube rows ao do Nusselt number, kg fin pitch [m] cp;g mg Prandtl number, kg heat duty [W] do G Reynolds number,
Aav
SD/do SL SL/do ST ST/df ST/do ST/SL
mg
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Y. Ma et al. / Applied Thermal Engineering 37 (2012) 314e323 [18] ESCOA Corp., ESCOA Fintube Manual, ESCOA, Tulsa, OK, 1979. [19] A. Nir, Heat transfer and friction factor correlations for cross-flow over staggered finned tube banks, Heat Transfer Engineering 12 (No.1) (1991) 43e58. [20] D.E. Briggs, E.H. Young, Convective heat transfer and pressure drop of air flowing across triangular pitch banks of finned tubes, Chemical Engineering Progress Symposium Series 59 (No.41) (1963) 1e10. [21] K.K. Robinson, D.E. Briggs, Pressure drop of air flowing across triangular pitch banks of finned tubes, Chemical Engineering Progress Symposium Series 62 (No.64) (1966) 177e184.
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[22] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (1976) 359e368. [23] K.A. Gardner, Efficiency of extended surface, Transactions of the ASME 67 (1945) 621e631. [24] K. Hashizume, R. Morikawa, T. Koyama, et al., Fin efficiency of serrated fins, Heat Transfer Engineering 23 (No.2) (2002) 6e14. [25] A.A. Zukauskas, Convective Heat Transfer in Heat Exchangers, China Science Press, Beijing, 1986, 296e323.