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Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts
Applied Thermal Engineering 30 (2010) 1531e1537
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts Erling Næss* Norwegian University of Science and Technology, Dept. of Energy and Process Engineering, Kolbjorn Hejes vei 1A, 7491 Trondheim, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 October 2006 Accepted 23 February 2010 Available online 11 March 2010
An experimental investigation of the heat transfer and pressure drop performance of ten finned tube bundles using serrated fins is presented. All tube bundles had staggered layouts, and the influence on varying tube bundle layout, tube and fin parameters are presented. The heat transfer coefficient experienced a maximum when the flow areas in the transversal and diagonal planes were equal. An increase in the fin pitch increased the heat transfer coefficient; the same was observed with an increase in fin height. The pressure drop coefficient showed no influence of the tube bundle layout for small pitch ratios, but dropped significantly for higher ratios. Increasing fin pitch reduced the pressure drop, whereas varying fin height had insignificant effect. None of the literature correlations were able to reproduce the experiments for the entire range of tested conditions. A set of correlations were developed, reproducing the experimental data to within 5% at a confidence interval of 95%. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Pressure drop Finned tubes Serrated fins
1. Introduction In heat recovery from high temperature flue gases, externally finned heat transfer surfaces are frequently used in order to compensate for the low gas-side heat transfer coefficient. Among the large variety of fin types, the most commonly used for high temperature heat recovery applications are the annular or helically wound solid fins and the serrated (or pin) fins, shown in Fig. 1. For equal tube and fin dimensions, solid-fin tubes possess a larger heat transfer surface than serrated fins per unit tube length. On the other hand, the cut geometry of the serrated fins leads to frequent boundary layer breakup and potentially better flow penetration to the fin root, yielding higher heat transfer coefficients. In view of this, serrated fin tubes are attractive for heat recovery applications. However, the published experimental data on heat transfer and pressure drop with such tubes are limited, and the available predictive correlations seem to indicate conflicting effects of geometry variations on the performance of serrated-fin tubes. Hence, a set of experiments were performed with the objective of providing guidelines to the optimum choice of parameters for compact heat recovery units, as well as to extend the data range for the evaluation of existing predictive correlations. The present study is limited to heat transfer and pressure drop in tube bundles with staggered layouts, as in-line layouts have shown a significantly
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lower heat transfer performance Weierman [1], PFR [2], Rabas and Eckels [3], Weierman et al. [4], and are also generally less compact than staggered layouts. Serrated fins may be in the form of L-foot fins (Figure 1a), where the serrations penetrate all the way to the fin root, or as I-foot fins (Figure 1b), where the innermost region close to the tube wall consists of a solid-fin geometry. Another alternative is stud-fins, which consist of individual studs of various shapes welded to the tube surface in a regular pattern, yielding geometries similar to the L-foot fin type. For high temperature applications, the tubes and fins are normally made from carbon steel, and the fin assembly is welded to the tube surface. The available body of experimental data on heat transfer and pressure drop in tube bundles in staggered arrangements using serrated fins is, however, limited. For L-foot fins, Rabas and Eckels [3] reported pressure drop and heat transfer data from 2 different tube geometries (3 tube bundle layouts), and Schryber [5] presented heat transfer data from one geometry. Heat transfer and pressure drop for I-foot fins were reported by Hashizume [6] (1 geometry), Weierman et al. [7] (1 geometry) and recently by Kawaguchi et al. [8,9] (12 tube bundles, 2 different tube geometries). Weierman [4] presented pressure drop data from one staggered geometry. Cox [10] performed heat transfer and pressure drop measurements on one tube geometry with two different tube layouts using aluminum tubes with integral serrated fins, i.e. fins carved from the tube surface, resembling L-foot fins. Results on stud-fin tubes were reported by Ackerman and Brunsvold [11] (one tube geometry, 5
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E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537
2. Experimental setup and data reduction 2.1. Experimental setup
Fig. 1. L-foot and I-foot serrated fins (from GEA Spiro-Gills Ltd).
tube layouts), Vampola [12] (1 geometry) and Worley and Ross [13], who performed an extensive experimental program using a variety of stud shapes, tube dimensions and tube bundle layouts. Worley and Ross concluded from their work that the stud geometry had little, if any influence on the heat transfer performance. From this it may be argued that results from both L-foot, I-foot and stud-fins may be representative for serrated-fin tubes. Predictive correlations for heat transfer were presented by Worley and Ross [13], Weierman [1], PFR [2], Mieth [14] and Nir [15]. The correlations of Worley and Ross and Mieth do not distinguish between solid-fin tubes and serrated-fin tubes, and the Weierman, PFR and Nir correlations were derived assuming similarity in behavior for serrated fin and annular (or helically) finned tubes. Pressure drop correlations were presented by Gunther and Shaw [16], Weierman [1], PFR [2], ConRad (see Weierman [17]), and Nir [15].
The experimental setup is shown in Fig. 2. Hot air was used on the fin side, and city water or a water/glycol mixture was used as coolant. Upstream the test section (pos. 12), the air passed through a calming section equipped with flow straighteners and several fine wire meshes (pos. 3e10) in order to reduce the large-scale turbulence and provide a uniform velocity profile at the test section entrance. The turbulence pffiffiffiffiffiffiffi level at the test section entrance, defined as Tu ¼ u0 2=u$100, where u’ was the turbulent velocity fluctuation component in the mean flow direction, and u was the mean (time averaged) fluid velocity was measured to approximately 5%. Downstream the test section the air was rejected to the atmosphere. The air inlet temperature was maintained at approximately 100 C for all experiments by means of an electric heater. In the initial experiments city water was used as coolant, but due to the low coolant inlet temperature, some indications of moisture condensation from the air was detected. The cooling circuit was therefore modified to consist of a closed circuit system using water/glycol as coolant and rejecting the heat through a separate heat exchanger. In this manner the coolant inlet temperature could be maintained above the air dew-point temperature. Flow rates were measured using orifice plates on both the air (pos. 2) and coolant (pos. 15) sides, and thermocouples at the air and coolant inlet and outlet ends were used to register the fluid temperatures. The air side temperatures (pos. 7 and 14) were measured by sucking off a small flow rate from several grid points in the flow crosssectional area, and measuring the mixing-cup temperature. In this manner a representative air mixing-cup temperature was obtained. The coolant flow was mixed in a mixing chamber at the exit from the test section, providing a representative mixing-cup temperature measurement. The heat balance deviations for the air and coolant sides had a 95% confidence level of approximately 2%. The air side pressure drop across the tube bundle was measured using measurement stations upstream and downstream the tube
Fig. 2. Test rig for heat transfer and pressure drop measurements.
E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537
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Fig. 3. Test section dimensions.
bundle, each consisting of four parallel connected pressure tappings around the test section circumference. A sketch of the test section is shown in Fig. 3. The test section consisted of 32 active tubes for heat transfer (4 transversal and 8 longitudinal tube rows) with dummy half-tubes at the section walls in order to obtain hydraulic similitude. Based on the results of Weierman [1], fully developed conditions for pressure drop is reached within 2e3 longitudinal tube rows, and for heat transfer within ca. 4 tube rows for staggered arrangements. Hence, eight longitudinal tube rows were considered sufficient to obtain representative heat transfer and pressure drop data. The coolant was passing in parallel in each of the transversal tube rows. The transversal rows were connected in series, providing an overall cross-countercurrent arrangement for the air/coolant flow. The test section width (i.e. the active tube length) was 500 mm, and the section height was 4,5 times the transversal pitch. 2.2. Data reduction The heat duty was calculated from the measured mass flow rates and overall temperature changes, and the overall heat transfer coefficient was then calculated from equation (1), using the arithmetic average of the air and coolant heat duties.
U ¼
Q_ Atot $LMTD
(1)
where Q_ is the heat duty, Atot is the total external heat transfer surface including the fin surface and LMTD is the logarithmic mean temperature difference for countercurrent flow. The LMTD was shown by analysis to be accurate to within 0,1% of the actual crosscountercurrent arrangement mean temperature difference for all experiments and was therefore considered representative. From this, the gas-side heat transfer coefficient was extracted using equation (2)
ho ¼
1 U
Atot Atot $lnðde =di Þ þ Ai $hi 2$Nl $Nt $p$Lt $kw
1
$
Atot
jf $Af þ At;net
(2)
Here, ho is the external side heat transfer coefficient, hi is the internal (tube side) heat transfer coefficient, Ai is the tube side surface area, Af is the surface area of the fins, At,net is the net exposed interfin tube surface area and Atot ¼ Af þ At,net. de is the tube effective outer diameter (tube outside diameter (do) plus twice the fin thickness (tf), see Fig. 4), di is the tube inside diameter, Nt and Nl are the number of tubes in the transversal and longitudinal directions respectively, Lt is the exposed tube length and kw is the tube wall thermal conductivity. j is the fin efficiency, given by equation (4) and discussed below. Fully turbulent flow with Reynolds numbers in excess of 104 was assured on the tube side, and the tube side heat transfer coefficient (hi) was calculated using the simplified Petukhov et al. correlation (valid for 5$103 < Re < 5 106 and 0,5 < Pr < 2 103), see e.g. Bhatti and Shah [18]. The uncertainty
Fig. 4. Tube geometry and tube bundle layouts.
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in hi was estimated to 10%, which is twice the reported uncertainty in [18]. The appropriate fin efficiency, which compensates for the finite conductance in the fins can according to Gardner [19], under the assumption of a uniform gas-side heat transfer coefficient, be expressed as:
jth
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i u u2$ho $ t þ w tanh M$ le þ tf =2 f f t ¼ ; where M ¼ kf $tf $wf M$ le þ tf =2
(3)
Here, tf is the fin thickness, le is the net fin height (le ¼ hfetf), wf is the fin segment width and kf is the fin material thermal conductivity. However, as pointed out by Weierman [1], PFR [2] and Hashizume [20], the heat transfer coefficient distribution is not uniform, yielding lower actual fin efficiencies than predicted by equation (3). In the present analysis, the empirical correction factor to the theoretical fin efficiency proposed by Weierman [1] was used, shown in equation (4). The magnitude of the correction introduced by using equation (4) instead of equation (3) is relatively small (less than 7%) for all experiments.
jf ¼ jth $ð0; 9 þ 0; 1$jth Þ
(4)
The pressure drop tests were performed at adiabatic conditions, and the pressure loss coefficient per tube row passed (Eu) was calculated from equation (5):
Eu ¼
2$Dp$r _ 002 Nl $m
(5)
Here, Δp is the measured pressure loss, r is the average gas _ 00 is the gas mass flux in the narrowest cross-flow density and m area. The tube bundle entry and exit losses are ignored in the calculation of Eu. The exact magnitude of these losses could not be determined from the measurements, but were estimated to be small (less than 5%). Hence, the calculated Eu-numbers may be slightly conservative. All data were recorded at 10 s intervals for at least 10 min per experiment after stable operating conditions were assured. This assured a sufficient number of data points in each experiment for statistical analysis. Furthermore, the first experiment in each series was repeated at the end of a run in order to assure repeatability. The experimental uncertainties were estimated using the procedures presented by Moffat [21], and were calculated to approximately 4e8% for the heat transfer coefficients and 10e2% for Euler numbers at low and high flow rates, respectively. 2.3. Test geometries The test tubes used were commercially available tubes having L-foot fins, as shown in Fig. 1a. Tubes and fins were made from carbon steel. The fin foot was resistance-welded to the tubes, providing negligible thermal contact resistance between the fin and tube outer surface. The fin thickness and segment width were kept constant for all test geometries, with tf ¼ 0.91 mm and wf ¼ 3,97 mm. The main features of the test geometries are shown in Table 1 with the geometric variables explained in Fig. 4. The fin-tip clearance between neighboring tubes was kept as small as practically possible. A certain minimum clearance is normally required in order to accommodate production tolerances, tube vibrations, servicing requirements etc., and a common minimum fin-tip clearance of 8,0 mm was used for all of the test geometries, with the exception of geometry 10, which had identical tube layout as geometries 6 and 9, but with higher fins. A total of 10 tube bundles were tested. Tube bundles 1e8 basically consisted of tubes with different tube outside diameters, but with
Table 1 Main geometry data for test bundles. Geometry no.
de ¼ d0þ2tf [mm]
Pt [mm]
P1 [mm]
le ¼ lfetf [mm]
sf [mm]
tf [mm]
wf [mm]
1 2 3 4 5 6 7 8 9 10
20,89 20,89 20,89 20,89 27,24 27,24 27,24 33,59 27,24 27,24
46,1 65,2 70,6 79,8 52,5 79,8 90,8 58,8 79,8 79,8
39,9 32,6 29,6 23,1 45,4 34,0 26,2 50,9 34,0 34,0
8,61 8,61 8,61 8,61 8,61 8,61 8,61 8,61 11,38 8,61
5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 3,63 3,63
0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91
3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97
identical fin geometries. The main geometric parameter varied for these bundles (aside from the tube diameter) was the tube bundle layout, i.e. Pt/Pl. Tube bundles 9 and 10 explored the effect of fin pitch and fin height for a tube bundle layout where the flow areas in the transversal and diagonal planes were approximately equal. 3. Results and discussion 3.1. On the choice of length scale The most frequently adopted length scale in the Reynolds (Re) and Nusselt (Nu) numbers is the (effective) tube outside diameter, de. However, several other length scales are possible, such as the equivalent tube diameter (Kawaguchi [9]), the fin diameter (Nir [15]) and various definitions of the hydraulic diameter (e.g. Gunther and Shaw [16], PFR [2] and Nir [15]). All of the suggested length scales were used in the data reduction, but no clear preference was found. There are, however, some indications that the use of the fin diameter as length scale gives a slightly better collection of the heat transfer data than other choices. In lack of a clear preference, the common convention of using the base tube effective outside diameter (de) as length scale in Re for both heat transfer and pressure drop data analysis, as well as in Nu was applied. Further, the mass flux in the narrowest free-flow area (i.e. transversal area, St, for geometries 1, 2, 5 and 8, and diagonal flow area, Sd, for the other geometries) was applied. 3.2. Heat transfer 3.2.1. Influence of Reynolds number The Nusselt number dependency on the Reynolds number can generally be expressed as Nu ¼ C$Rem$Pr1/3, where C is a geometryspecific constant. The experimentally obtained exponent m varied
Fig. 5. Constants in equation (6) for the different tube bundles tested.
E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537
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Fig. 6. Tube bundle layout effect on Nu relative to NuEq.
Fig. 8. Constants in equation (10) for the different tube bundles tested.
between 0,63 and 0,68, with an arithmetic average value of 0,65. This dependency was in good agreement with the published correlations discussed above, where m varied in the range 0,59e0,7. The geometry-specific constants C1 were established by regression analysis, fitting the experimental data to equation (6), and are shown in Fig. 5.
Brunsvold and Rabas and Eckels as well as Geometry 1 and 2 of the present study, the group ðPt =de Þ0:35 was found to reproduce the tube bundle layout dependency adequately. When the transversal flow area was larger than the diagonal flow area (i.e. St/Sd > 1), the heat transfer coefficient dropped markedly. None of the published correlations were able to reproduce this behavior. This was not unexpected, however, since none of the correlations were claimed valid in this region. Several investigators (e.g. Weierman (1976), PFR (1976), Ackerman and Brunsvold [11], Rabas and Eckels [3], Weierman et al. [7] have pointed out that in-line layouts experience significantly lower heat transfer coefficients than staggered layouts, ranging from 25% (Ackerman and Brunsvold) to approximately 75% (Weierman et al) reduction relative to equilateral tube layouts. From this it is expected that the heat transfer at some point should start decreasing with increasing Pt/Pl-ratios, in this study found to be the interception point where St and Sd are equal. Based on the limited data shown in Fig. 6, the presently suggested representation of the tube bundle layout effect on heat transfer in the region where St/Sd > 1:
Nude ¼ C1 $Re0;65 $Pr1=3 d
(6)
e
3.2.2. Influence of tube bundle layout The tube bundle layout effect on the heat transfer performance is demonstrated in Fig. 6, showing the Nusselt number for the geometries with identical fin geometries relative to the geometries with equilateral tube layouts (geometries 1 and 5) as function of the ratio of transversal to diagonal free-flow areas, St/Sd. Also shown are the data of Ackerman and Brunsvold [11], and the predicted dependency from the published correlations. As the figure shows, the Nusselt number increases with increasing St/Sd up to maximum of ca. 1,15 at St/Sd ¼ 1,0, from where it decreases monotonically. When the flow area in the transversal plane was smaller than the flow area in the diagonal plane, the heat transfer dependency followed the predictions from Weierman, except for one of the Ackerman/Brunsvold data sets. Inspection of the data of Ackerman and Brunsvold indicate that Nu was independent of Pl, which was also confirmed by data of Rabas and Eckels [3] (tube banks 3 and 4) and Worley and Ross [13]. The best representation of the bundle layout influence using these data was found to be the ratio (Pt/de) rather than (St/S0), (St/Sd) or (Pt/Pl), where S0 is the gross frontal cross-sectional flow area. From the data of Ackerman and
Nu ¼ 0; 6 þ 14; 3$e3;23$St =Sd NuEq
where NuEq is the Nusselt number for an equilateral layout. The expression has an asymptotic value of 0,6 as St/Sd approaches infinity, which may be taken as a representative value for in-line layouts according to PFR [2]. Further experiments are required in order to evaluate other variables (such as Pt and Pl) influence on the heat transfer coefficient in this region.
1,1
Changing lf
Changing sf
Nu/NuGeo 6 [-]
(Geo 6)
(Geo 9)
Worley/Ross [4]
1
Weierman PFR Nir
(Geo 10) 0,9
Mieth 0,8 1,5
2
2,5
lf/sf [-]
3
Fig. 7. Effect of fin height and fin pitch on the Nusselt number.
(7)
3,5
Fig. 9. Tube bundle layout effect on the Euler number.
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E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537 1,5
2,5
Experimental Gunther/Shaw Nir Weierman ConRad PFR
1,4 1,3
Experimental PFR Weierman ConRad Gunther/Shaw Nir
Gunther/Shaw , Nir
2,0
1,2
Eu/Eu6 [-]
Eu/Eu10 [-]
ConRad 1,1 1,0
Geometry 9
Geometry 10
0,9
1,5
Geometry 10
Weierman
Geometry 6 1,0
PFR
0,8
0,5
0,7 0,6
0,0 0,5
8,0
8,5
9,0
9,5
10,0
10,5
11,0
11,5
12,0
0
1
2
3
4
5
6
7
8
Sf [mm]
le [mm]
Fig. 10. Effect on Euler number by fin height (le)and fin pitch (sf).
The increase in Nu for St/Sd < 1 is similar to observations for plain tube bundles. The behavior may be explained from the definition of Re, where the maximum fluid velocity in the narrowest free-flow area is used, rather than an average velocity, which may be more representative. As St/Sd increases, so does the ratio of the geometric average fluid velocity between the open and narrow free-flow area to the maximum fluid velocity [22]. Hence, on the basis of constant Re, the average fluid velocity approaches the maximum velocity as St/Sd increases, increasing the average heat transfer coefficient. The decline in heat transfer for St/Sd > 1 is believed to be caused by a reduction in fluid mixing in the downstream zone of the tubes, leading to a reduction in the effective temperature driving force. Such behavior have frequently been reported for in-line arrangements, see e.g. Brauer [23] and Hashizume [20]. 3.2.3. Influence of fin spacing (sf) and fin height (le) The effective fin height is defined as the distance between the fin tip and the effective tube outside diameter, de, i.e. le ¼ hfetf, where tf is the fin thickness (see Fig. 4). Geometries 6, 9 and 10 had various fin pitches and fin heights, but were arranged in identical tube bundle layouts. For these geometries, the effect of fin parameters could be investigated with comparable bundle arrangements. It should be noted that (St/Sd) > 1 in these tests, hence the available correlations were strictly not valid. However, (St/Sd) was only slightly higher than unity (in the range 1,12e1,20), and it was assumed that the observed influence would also be representative for St/Sd < 1.
Fig. 7 shows the dependency of the normalized Nusselt number (Nu/NuGeo6) on the fin variables. Also shown are predictions from the published correlations. The measured effect of changing sf was reasonably well reproduced by most correlations, and accurately reproduced by the correlation of Weierman. On the other hand, the observed Nusselt number increased with increased fin height, whereas the predictions showed constant or decreasing Nusselt numbers. It may be speculated that the difference in this behavior was attributed to the fact that most of the correlations were based on the assumption of similar behavior with annular fins, where fluid may not penetrate as efficiently to the fin root as in serratedfin tubes, and possibly also more efficient fluid mixing between the serrated fins. The observed discrepancy between measurements and predictions was however moderate (less than 7%) for the correlations showing no le-dependency. 3.2.4. Correlation of the results Taking into consideration the observations described above, the experimental data were correlated using a linear regression analysis on the basis of equation (8).
C1 ¼
Nu Re0;65 $Pr1=3
¼ C$f2 ðLayoutÞ$f3 ðFin parametersÞ
(8)
Several possibilities were investigated for the term f3(Fin parameters), the best overall fit was obtained using the parameters (le/de), (sf/de) and (le/sf). The resulting correlation for Nu is shown in
Fig. 11. Measured vs. predicted NuPr1/3 and Eu for all tested geometries. Predicted values calculated from equations (9) and (12).
E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537
equation (9), correlating 95% of the data to within 4,2%. The overall prediction accuracy is shown in Fig. 11.
0;35 0;13 Nu ¼ 0; 107$Re0;65 $Pr1=3 $ dPt $ dle e e 0;14 0;2 sf le St $ sf Sd < 1; 0 de Nu ¼ 0; 141$Re0;65 $Pr1=3 $ 0; 43 þ 9; 75,e3:23,St =Sd $
0;13 0;14 0;2 sf le St $ slef Sd > 1; 0 d d e
ð9Þ
e
3.3. Pressure drop The Euler number did not follow a simple power-law dependency on the Reynolds number, and a regression analysis suggested a dependency in the form of equation (10). This dependency was reasonable in that it contains an apparent form drag term and a skin-friction term, the latter becoming dominant at low Reynolds numbers. The individual constants C2 in equation (10) are shown in Fig. 8.
" Eu ¼ C2 $ 0; 86 þ
29; 5
# (10)
Re0;5 de
The tube bundle layout effect is shown using the geometries with identical fin dimensions in Fig. 9, showing the Euler numbers relative to an equilateral layout as function of the pitch ratio (Pt/Pl). As observed, only the correlation of Weierman [1] reproduced the data at St/Sd < 1 (corresponding to Pt/Pl < 2,2), whereas none of the correlations captured the behavior at St/Sd > 1. The observed behavior was empirically fitted as shown in equation (11), using a typical asymptotic value of about 0,5 as an in-line layout is approached (Pt/Pl approaches infinity).
Eu ¼ min 1; 0 ; Eueq
0; 52 þ 964; 5$e3;24$Pt =Pl
(11)
The individual fin parameters influence on the pressure loss coefficient is seen in Fig. 10. The behavior is similar to that observed for heat transfer, however, the effect of varying the fin height had negligible effect on the Euler number. The published correlations were only moderately successful in reproducing the observed trends. A linear regression analysis of the experimentally obtained C2’s from all geometries resulted in the correlation shown in equation (12), having a 95% confidence interval of 3,7%.
8; 2 Eu ¼ 0; 24 þ 0;5 $min 1; 0; 0; 52 þ 964; 5$e3;24,Pt =Pl Re 0;18 0;74 sf le $ ð12Þ $ de de The overall prediction accuracy is shown in Fig. 11. 4. Conclusions A set of experiments were performed in order to evaluate the influence of tube layout and fin geometry on heat transfer and pressure drop performance in serrated-fin tubes for high temperature heat recovery applications. Based on the experimental results, the following conclusions were drawn: Heat transfer undergoes a maximum when the flow areas in the transversal and diagonal planes are equal. The maximum value is
1537
approximately 15% higher than for equilateral tube layouts at equal Re-numbers. Fin parameters had moderate effects on heat transfer; increasing the fin pitch reduced the heat transfer coefficient, increasing fin height increased the heat transfer coefficient. Pressure drop was little influenced by the tube bundle layout for St < Sd. At St > Sd, the Euler number decreased monotonically. Increased fin pitch reduced the Euler number, whereas increasing fin height had negligible effect on Eu. None of the available heat transfer and pressure drop correlations were able to reproduce the effect of tube bundle layout. Predictive correlations for Nu and Eu were developed from the data presented. The heat transfer data were correlated as shown in equation (9) with a 95% confidence interval of 4,2%. Eu was correlated as shown in equation (12), with a 95% confidence interval of 3,7%. Further data covering a wider range of geometric parameters are however needed in order to establish generalized predictive correlations. References [1] C. Weierman, Correlations ease the selection of finned tubes. Oil Gas J. (1976) 94e100. [2] PFR Engineering Systems, Heat Transfer and Pressure Drop Characteristics of Dry Tower Extended Surfaces PFR Report BNWL-PFR-7 100. PFR Engineering Systems Inc., 1976. [3] T.J. Rabas, P.W. Eckels, Heat Transfer and Pressure Drop Performance of Segmented Extended Surface Tube Bundles, ASME Paper 75-HT-45, 1975. [4] C. Weierman, Pressure drop data for heavy-duty finned tubes. Chem. Eng. Prog. 73 (No. 2) (1978) 69e72. [5] E.A. Schryber, Heat transfer coefficients and other data of individual serratedfin surfaces. Trans. ASME 67 (No. 8) (1945) 683e686. [6] K. Hashizume, Heat transfer and pressure drop characteristics of finned tubes in crossflow. Heat Transfer Eng. 3 (No. 2) (1981) 15e20. [7] C. Weierman, J. Taborek, W.J. Marner, Comparison of the performance of inline and staggered banks of tubes with segmented fins. AIChE Symp. Ser. 74 (1978) 39e46. [8] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (Comparison of pressure drop characteristics between spiral fin and serrated fin). Heat Transfer Asian Res. 33 (No. 72) (2004) 120e133. [9] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (Comparison of heat transfer characteristics between spiral fin and serrated fin). Heat Transf. Asian Res. 34 (No. 2) (2005) 120e133. [10] B. Cox, Heat transfer and pumping power performance in tube banks e finned and bare, ASME Paper 73-HT-27, 1973. [11] J.W. Ackerman, A.R. Brunsvold, Heat transfer and draft loss performance of extended surface tube banks. J. Heat Transfer 92 (May 1970) 215e220. [12] J. Vampola, Heat and Pressure Losses for Gases Flowing through Bundles of Finned Tubes, (in Russian). Strojirenstvi 16 (1966) 501e507 Results also available in [2]. [13] N.G. Worley, W. Ross, Heat transfer and pressure loss characteristics of crossflow tubular arrangements with studded surfaces. Inst. Mech. Engrs. (Nov 1960) 15e26. [14] H.C. Mieth, Method for Heat Transfer Calculation of Helical-Wound Fin Tubes, ASME-70, Pet 4, 1970. [15] A. Nir, Heat transfer and friction factor correlations for crossflow over staggered finned tube banks. Heat Transf. Eng. 12 (No. 1) (1991) 43e58. [16] A.Y. Gunter, W.A. Shaw, A general correlation of friction factors for various types of surfaces in crossflow. Trans. ASME 67 (Nov 1945). [17] C. Weierman, Pressure Drop Tests on Welded Plain and Segmented Fins, 16th Nat. Heat Transfer Conf., USA, paper AIChE-27, 1976. [18] M.S. Bhatti, R.K. Shah, Turbulent and transition flow convective heat transfer in ducts. in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single Phase Convective Heat Transfer. John Wiley & Sons, 1987. [19] K.A. Gardner, Efficiency of extended surfaces. Trans. ASME 67 (1945) 621e631. [20] K. Hashizume, R. Morikawa, T. Koyama, T. Matsue, Fin efficiency of serrated fins. Heat Transf. Eng. 23 (No. 2) (2002) 7e14. [21] R.J. Moffat, Describing the uncertainties in experimental results. Exp. Therm. Fluid Sci. 1 (1988) 3e17. [22] J. Stasiulevicius, A. Skrinska, Heat Transfer of Finned Tube Bundles in Crossflow. Hemisphere Publishing Company, 1988. [23] H. Brauer, Compact heat exchangers. Chem. Prog. Eng. 45 (No. 8) (1964) 315e321.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts Erling Næss* Norwegian University of Science and Technology, Dept. of Energy and Process Engineering, Kolbjorn Hejes vei 1A, 7491 Trondheim, Norway
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 October 2006 Accepted 23 February 2010 Available online 11 March 2010
An experimental investigation of the heat transfer and pressure drop performance of ten finned tube bundles using serrated fins is presented. All tube bundles had staggered layouts, and the influence on varying tube bundle layout, tube and fin parameters are presented. The heat transfer coefficient experienced a maximum when the flow areas in the transversal and diagonal planes were equal. An increase in the fin pitch increased the heat transfer coefficient; the same was observed with an increase in fin height. The pressure drop coefficient showed no influence of the tube bundle layout for small pitch ratios, but dropped significantly for higher ratios. Increasing fin pitch reduced the pressure drop, whereas varying fin height had insignificant effect. None of the literature correlations were able to reproduce the experiments for the entire range of tested conditions. A set of correlations were developed, reproducing the experimental data to within 5% at a confidence interval of 95%. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Pressure drop Finned tubes Serrated fins
1. Introduction In heat recovery from high temperature flue gases, externally finned heat transfer surfaces are frequently used in order to compensate for the low gas-side heat transfer coefficient. Among the large variety of fin types, the most commonly used for high temperature heat recovery applications are the annular or helically wound solid fins and the serrated (or pin) fins, shown in Fig. 1. For equal tube and fin dimensions, solid-fin tubes possess a larger heat transfer surface than serrated fins per unit tube length. On the other hand, the cut geometry of the serrated fins leads to frequent boundary layer breakup and potentially better flow penetration to the fin root, yielding higher heat transfer coefficients. In view of this, serrated fin tubes are attractive for heat recovery applications. However, the published experimental data on heat transfer and pressure drop with such tubes are limited, and the available predictive correlations seem to indicate conflicting effects of geometry variations on the performance of serrated-fin tubes. Hence, a set of experiments were performed with the objective of providing guidelines to the optimum choice of parameters for compact heat recovery units, as well as to extend the data range for the evaluation of existing predictive correlations. The present study is limited to heat transfer and pressure drop in tube bundles with staggered layouts, as in-line layouts have shown a significantly
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lower heat transfer performance Weierman [1], PFR [2], Rabas and Eckels [3], Weierman et al. [4], and are also generally less compact than staggered layouts. Serrated fins may be in the form of L-foot fins (Figure 1a), where the serrations penetrate all the way to the fin root, or as I-foot fins (Figure 1b), where the innermost region close to the tube wall consists of a solid-fin geometry. Another alternative is stud-fins, which consist of individual studs of various shapes welded to the tube surface in a regular pattern, yielding geometries similar to the L-foot fin type. For high temperature applications, the tubes and fins are normally made from carbon steel, and the fin assembly is welded to the tube surface. The available body of experimental data on heat transfer and pressure drop in tube bundles in staggered arrangements using serrated fins is, however, limited. For L-foot fins, Rabas and Eckels [3] reported pressure drop and heat transfer data from 2 different tube geometries (3 tube bundle layouts), and Schryber [5] presented heat transfer data from one geometry. Heat transfer and pressure drop for I-foot fins were reported by Hashizume [6] (1 geometry), Weierman et al. [7] (1 geometry) and recently by Kawaguchi et al. [8,9] (12 tube bundles, 2 different tube geometries). Weierman [4] presented pressure drop data from one staggered geometry. Cox [10] performed heat transfer and pressure drop measurements on one tube geometry with two different tube layouts using aluminum tubes with integral serrated fins, i.e. fins carved from the tube surface, resembling L-foot fins. Results on stud-fin tubes were reported by Ackerman and Brunsvold [11] (one tube geometry, 5
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2. Experimental setup and data reduction 2.1. Experimental setup
Fig. 1. L-foot and I-foot serrated fins (from GEA Spiro-Gills Ltd).
tube layouts), Vampola [12] (1 geometry) and Worley and Ross [13], who performed an extensive experimental program using a variety of stud shapes, tube dimensions and tube bundle layouts. Worley and Ross concluded from their work that the stud geometry had little, if any influence on the heat transfer performance. From this it may be argued that results from both L-foot, I-foot and stud-fins may be representative for serrated-fin tubes. Predictive correlations for heat transfer were presented by Worley and Ross [13], Weierman [1], PFR [2], Mieth [14] and Nir [15]. The correlations of Worley and Ross and Mieth do not distinguish between solid-fin tubes and serrated-fin tubes, and the Weierman, PFR and Nir correlations were derived assuming similarity in behavior for serrated fin and annular (or helically) finned tubes. Pressure drop correlations were presented by Gunther and Shaw [16], Weierman [1], PFR [2], ConRad (see Weierman [17]), and Nir [15].
The experimental setup is shown in Fig. 2. Hot air was used on the fin side, and city water or a water/glycol mixture was used as coolant. Upstream the test section (pos. 12), the air passed through a calming section equipped with flow straighteners and several fine wire meshes (pos. 3e10) in order to reduce the large-scale turbulence and provide a uniform velocity profile at the test section entrance. The turbulence pffiffiffiffiffiffiffi level at the test section entrance, defined as Tu ¼ u0 2=u$100, where u’ was the turbulent velocity fluctuation component in the mean flow direction, and u was the mean (time averaged) fluid velocity was measured to approximately 5%. Downstream the test section the air was rejected to the atmosphere. The air inlet temperature was maintained at approximately 100 C for all experiments by means of an electric heater. In the initial experiments city water was used as coolant, but due to the low coolant inlet temperature, some indications of moisture condensation from the air was detected. The cooling circuit was therefore modified to consist of a closed circuit system using water/glycol as coolant and rejecting the heat through a separate heat exchanger. In this manner the coolant inlet temperature could be maintained above the air dew-point temperature. Flow rates were measured using orifice plates on both the air (pos. 2) and coolant (pos. 15) sides, and thermocouples at the air and coolant inlet and outlet ends were used to register the fluid temperatures. The air side temperatures (pos. 7 and 14) were measured by sucking off a small flow rate from several grid points in the flow crosssectional area, and measuring the mixing-cup temperature. In this manner a representative air mixing-cup temperature was obtained. The coolant flow was mixed in a mixing chamber at the exit from the test section, providing a representative mixing-cup temperature measurement. The heat balance deviations for the air and coolant sides had a 95% confidence level of approximately 2%. The air side pressure drop across the tube bundle was measured using measurement stations upstream and downstream the tube
Fig. 2. Test rig for heat transfer and pressure drop measurements.
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Fig. 3. Test section dimensions.
bundle, each consisting of four parallel connected pressure tappings around the test section circumference. A sketch of the test section is shown in Fig. 3. The test section consisted of 32 active tubes for heat transfer (4 transversal and 8 longitudinal tube rows) with dummy half-tubes at the section walls in order to obtain hydraulic similitude. Based on the results of Weierman [1], fully developed conditions for pressure drop is reached within 2e3 longitudinal tube rows, and for heat transfer within ca. 4 tube rows for staggered arrangements. Hence, eight longitudinal tube rows were considered sufficient to obtain representative heat transfer and pressure drop data. The coolant was passing in parallel in each of the transversal tube rows. The transversal rows were connected in series, providing an overall cross-countercurrent arrangement for the air/coolant flow. The test section width (i.e. the active tube length) was 500 mm, and the section height was 4,5 times the transversal pitch. 2.2. Data reduction The heat duty was calculated from the measured mass flow rates and overall temperature changes, and the overall heat transfer coefficient was then calculated from equation (1), using the arithmetic average of the air and coolant heat duties.
U ¼
Q_ Atot $LMTD
(1)
where Q_ is the heat duty, Atot is the total external heat transfer surface including the fin surface and LMTD is the logarithmic mean temperature difference for countercurrent flow. The LMTD was shown by analysis to be accurate to within 0,1% of the actual crosscountercurrent arrangement mean temperature difference for all experiments and was therefore considered representative. From this, the gas-side heat transfer coefficient was extracted using equation (2)
ho ¼
1 U
Atot Atot $lnðde =di Þ þ Ai $hi 2$Nl $Nt $p$Lt $kw
1
$
Atot
jf $Af þ At;net
(2)
Here, ho is the external side heat transfer coefficient, hi is the internal (tube side) heat transfer coefficient, Ai is the tube side surface area, Af is the surface area of the fins, At,net is the net exposed interfin tube surface area and Atot ¼ Af þ At,net. de is the tube effective outer diameter (tube outside diameter (do) plus twice the fin thickness (tf), see Fig. 4), di is the tube inside diameter, Nt and Nl are the number of tubes in the transversal and longitudinal directions respectively, Lt is the exposed tube length and kw is the tube wall thermal conductivity. j is the fin efficiency, given by equation (4) and discussed below. Fully turbulent flow with Reynolds numbers in excess of 104 was assured on the tube side, and the tube side heat transfer coefficient (hi) was calculated using the simplified Petukhov et al. correlation (valid for 5$103 < Re < 5 106 and 0,5 < Pr < 2 103), see e.g. Bhatti and Shah [18]. The uncertainty
Fig. 4. Tube geometry and tube bundle layouts.
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in hi was estimated to 10%, which is twice the reported uncertainty in [18]. The appropriate fin efficiency, which compensates for the finite conductance in the fins can according to Gardner [19], under the assumption of a uniform gas-side heat transfer coefficient, be expressed as:
jth
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i u u2$ho $ t þ w tanh M$ le þ tf =2 f f t ¼ ; where M ¼ kf $tf $wf M$ le þ tf =2
(3)
Here, tf is the fin thickness, le is the net fin height (le ¼ hfetf), wf is the fin segment width and kf is the fin material thermal conductivity. However, as pointed out by Weierman [1], PFR [2] and Hashizume [20], the heat transfer coefficient distribution is not uniform, yielding lower actual fin efficiencies than predicted by equation (3). In the present analysis, the empirical correction factor to the theoretical fin efficiency proposed by Weierman [1] was used, shown in equation (4). The magnitude of the correction introduced by using equation (4) instead of equation (3) is relatively small (less than 7%) for all experiments.
jf ¼ jth $ð0; 9 þ 0; 1$jth Þ
(4)
The pressure drop tests were performed at adiabatic conditions, and the pressure loss coefficient per tube row passed (Eu) was calculated from equation (5):
Eu ¼
2$Dp$r _ 002 Nl $m
(5)
Here, Δp is the measured pressure loss, r is the average gas _ 00 is the gas mass flux in the narrowest cross-flow density and m area. The tube bundle entry and exit losses are ignored in the calculation of Eu. The exact magnitude of these losses could not be determined from the measurements, but were estimated to be small (less than 5%). Hence, the calculated Eu-numbers may be slightly conservative. All data were recorded at 10 s intervals for at least 10 min per experiment after stable operating conditions were assured. This assured a sufficient number of data points in each experiment for statistical analysis. Furthermore, the first experiment in each series was repeated at the end of a run in order to assure repeatability. The experimental uncertainties were estimated using the procedures presented by Moffat [21], and were calculated to approximately 4e8% for the heat transfer coefficients and 10e2% for Euler numbers at low and high flow rates, respectively. 2.3. Test geometries The test tubes used were commercially available tubes having L-foot fins, as shown in Fig. 1a. Tubes and fins were made from carbon steel. The fin foot was resistance-welded to the tubes, providing negligible thermal contact resistance between the fin and tube outer surface. The fin thickness and segment width were kept constant for all test geometries, with tf ¼ 0.91 mm and wf ¼ 3,97 mm. The main features of the test geometries are shown in Table 1 with the geometric variables explained in Fig. 4. The fin-tip clearance between neighboring tubes was kept as small as practically possible. A certain minimum clearance is normally required in order to accommodate production tolerances, tube vibrations, servicing requirements etc., and a common minimum fin-tip clearance of 8,0 mm was used for all of the test geometries, with the exception of geometry 10, which had identical tube layout as geometries 6 and 9, but with higher fins. A total of 10 tube bundles were tested. Tube bundles 1e8 basically consisted of tubes with different tube outside diameters, but with
Table 1 Main geometry data for test bundles. Geometry no.
de ¼ d0þ2tf [mm]
Pt [mm]
P1 [mm]
le ¼ lfetf [mm]
sf [mm]
tf [mm]
wf [mm]
1 2 3 4 5 6 7 8 9 10
20,89 20,89 20,89 20,89 27,24 27,24 27,24 33,59 27,24 27,24
46,1 65,2 70,6 79,8 52,5 79,8 90,8 58,8 79,8 79,8
39,9 32,6 29,6 23,1 45,4 34,0 26,2 50,9 34,0 34,0
8,61 8,61 8,61 8,61 8,61 8,61 8,61 8,61 11,38 8,61
5,08 5,08 5,08 5,08 5,08 5,08 5,08 5,08 3,63 3,63
0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91 0,91
3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97 3,97
identical fin geometries. The main geometric parameter varied for these bundles (aside from the tube diameter) was the tube bundle layout, i.e. Pt/Pl. Tube bundles 9 and 10 explored the effect of fin pitch and fin height for a tube bundle layout where the flow areas in the transversal and diagonal planes were approximately equal. 3. Results and discussion 3.1. On the choice of length scale The most frequently adopted length scale in the Reynolds (Re) and Nusselt (Nu) numbers is the (effective) tube outside diameter, de. However, several other length scales are possible, such as the equivalent tube diameter (Kawaguchi [9]), the fin diameter (Nir [15]) and various definitions of the hydraulic diameter (e.g. Gunther and Shaw [16], PFR [2] and Nir [15]). All of the suggested length scales were used in the data reduction, but no clear preference was found. There are, however, some indications that the use of the fin diameter as length scale gives a slightly better collection of the heat transfer data than other choices. In lack of a clear preference, the common convention of using the base tube effective outside diameter (de) as length scale in Re for both heat transfer and pressure drop data analysis, as well as in Nu was applied. Further, the mass flux in the narrowest free-flow area (i.e. transversal area, St, for geometries 1, 2, 5 and 8, and diagonal flow area, Sd, for the other geometries) was applied. 3.2. Heat transfer 3.2.1. Influence of Reynolds number The Nusselt number dependency on the Reynolds number can generally be expressed as Nu ¼ C$Rem$Pr1/3, where C is a geometryspecific constant. The experimentally obtained exponent m varied
Fig. 5. Constants in equation (6) for the different tube bundles tested.
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Fig. 6. Tube bundle layout effect on Nu relative to NuEq.
Fig. 8. Constants in equation (10) for the different tube bundles tested.
between 0,63 and 0,68, with an arithmetic average value of 0,65. This dependency was in good agreement with the published correlations discussed above, where m varied in the range 0,59e0,7. The geometry-specific constants C1 were established by regression analysis, fitting the experimental data to equation (6), and are shown in Fig. 5.
Brunsvold and Rabas and Eckels as well as Geometry 1 and 2 of the present study, the group ðPt =de Þ0:35 was found to reproduce the tube bundle layout dependency adequately. When the transversal flow area was larger than the diagonal flow area (i.e. St/Sd > 1), the heat transfer coefficient dropped markedly. None of the published correlations were able to reproduce this behavior. This was not unexpected, however, since none of the correlations were claimed valid in this region. Several investigators (e.g. Weierman (1976), PFR (1976), Ackerman and Brunsvold [11], Rabas and Eckels [3], Weierman et al. [7] have pointed out that in-line layouts experience significantly lower heat transfer coefficients than staggered layouts, ranging from 25% (Ackerman and Brunsvold) to approximately 75% (Weierman et al) reduction relative to equilateral tube layouts. From this it is expected that the heat transfer at some point should start decreasing with increasing Pt/Pl-ratios, in this study found to be the interception point where St and Sd are equal. Based on the limited data shown in Fig. 6, the presently suggested representation of the tube bundle layout effect on heat transfer in the region where St/Sd > 1:
Nude ¼ C1 $Re0;65 $Pr1=3 d
(6)
e
3.2.2. Influence of tube bundle layout The tube bundle layout effect on the heat transfer performance is demonstrated in Fig. 6, showing the Nusselt number for the geometries with identical fin geometries relative to the geometries with equilateral tube layouts (geometries 1 and 5) as function of the ratio of transversal to diagonal free-flow areas, St/Sd. Also shown are the data of Ackerman and Brunsvold [11], and the predicted dependency from the published correlations. As the figure shows, the Nusselt number increases with increasing St/Sd up to maximum of ca. 1,15 at St/Sd ¼ 1,0, from where it decreases monotonically. When the flow area in the transversal plane was smaller than the flow area in the diagonal plane, the heat transfer dependency followed the predictions from Weierman, except for one of the Ackerman/Brunsvold data sets. Inspection of the data of Ackerman and Brunsvold indicate that Nu was independent of Pl, which was also confirmed by data of Rabas and Eckels [3] (tube banks 3 and 4) and Worley and Ross [13]. The best representation of the bundle layout influence using these data was found to be the ratio (Pt/de) rather than (St/S0), (St/Sd) or (Pt/Pl), where S0 is the gross frontal cross-sectional flow area. From the data of Ackerman and
Nu ¼ 0; 6 þ 14; 3$e3;23$St =Sd NuEq
where NuEq is the Nusselt number for an equilateral layout. The expression has an asymptotic value of 0,6 as St/Sd approaches infinity, which may be taken as a representative value for in-line layouts according to PFR [2]. Further experiments are required in order to evaluate other variables (such as Pt and Pl) influence on the heat transfer coefficient in this region.
1,1
Changing lf
Changing sf
Nu/NuGeo 6 [-]
(Geo 6)
(Geo 9)
Worley/Ross [4]
1
Weierman PFR Nir
(Geo 10) 0,9
Mieth 0,8 1,5
2
2,5
lf/sf [-]
3
Fig. 7. Effect of fin height and fin pitch on the Nusselt number.
(7)
3,5
Fig. 9. Tube bundle layout effect on the Euler number.
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2,5
Experimental Gunther/Shaw Nir Weierman ConRad PFR
1,4 1,3
Experimental PFR Weierman ConRad Gunther/Shaw Nir
Gunther/Shaw , Nir
2,0
1,2
Eu/Eu6 [-]
Eu/Eu10 [-]
ConRad 1,1 1,0
Geometry 9
Geometry 10
0,9
1,5
Geometry 10
Weierman
Geometry 6 1,0
PFR
0,8
0,5
0,7 0,6
0,0 0,5
8,0
8,5
9,0
9,5
10,0
10,5
11,0
11,5
12,0
0
1
2
3
4
5
6
7
8
Sf [mm]
le [mm]
Fig. 10. Effect on Euler number by fin height (le)and fin pitch (sf).
The increase in Nu for St/Sd < 1 is similar to observations for plain tube bundles. The behavior may be explained from the definition of Re, where the maximum fluid velocity in the narrowest free-flow area is used, rather than an average velocity, which may be more representative. As St/Sd increases, so does the ratio of the geometric average fluid velocity between the open and narrow free-flow area to the maximum fluid velocity [22]. Hence, on the basis of constant Re, the average fluid velocity approaches the maximum velocity as St/Sd increases, increasing the average heat transfer coefficient. The decline in heat transfer for St/Sd > 1 is believed to be caused by a reduction in fluid mixing in the downstream zone of the tubes, leading to a reduction in the effective temperature driving force. Such behavior have frequently been reported for in-line arrangements, see e.g. Brauer [23] and Hashizume [20]. 3.2.3. Influence of fin spacing (sf) and fin height (le) The effective fin height is defined as the distance between the fin tip and the effective tube outside diameter, de, i.e. le ¼ hfetf, where tf is the fin thickness (see Fig. 4). Geometries 6, 9 and 10 had various fin pitches and fin heights, but were arranged in identical tube bundle layouts. For these geometries, the effect of fin parameters could be investigated with comparable bundle arrangements. It should be noted that (St/Sd) > 1 in these tests, hence the available correlations were strictly not valid. However, (St/Sd) was only slightly higher than unity (in the range 1,12e1,20), and it was assumed that the observed influence would also be representative for St/Sd < 1.
Fig. 7 shows the dependency of the normalized Nusselt number (Nu/NuGeo6) on the fin variables. Also shown are predictions from the published correlations. The measured effect of changing sf was reasonably well reproduced by most correlations, and accurately reproduced by the correlation of Weierman. On the other hand, the observed Nusselt number increased with increased fin height, whereas the predictions showed constant or decreasing Nusselt numbers. It may be speculated that the difference in this behavior was attributed to the fact that most of the correlations were based on the assumption of similar behavior with annular fins, where fluid may not penetrate as efficiently to the fin root as in serratedfin tubes, and possibly also more efficient fluid mixing between the serrated fins. The observed discrepancy between measurements and predictions was however moderate (less than 7%) for the correlations showing no le-dependency. 3.2.4. Correlation of the results Taking into consideration the observations described above, the experimental data were correlated using a linear regression analysis on the basis of equation (8).
C1 ¼
Nu Re0;65 $Pr1=3
¼ C$f2 ðLayoutÞ$f3 ðFin parametersÞ
(8)
Several possibilities were investigated for the term f3(Fin parameters), the best overall fit was obtained using the parameters (le/de), (sf/de) and (le/sf). The resulting correlation for Nu is shown in
Fig. 11. Measured vs. predicted NuPr1/3 and Eu for all tested geometries. Predicted values calculated from equations (9) and (12).
E. Næss / Applied Thermal Engineering 30 (2010) 1531e1537
equation (9), correlating 95% of the data to within 4,2%. The overall prediction accuracy is shown in Fig. 11.
0;35 0;13 Nu ¼ 0; 107$Re0;65 $Pr1=3 $ dPt $ dle e e 0;14 0;2 sf le St $ sf Sd < 1; 0 de Nu ¼ 0; 141$Re0;65 $Pr1=3 $ 0; 43 þ 9; 75,e3:23,St =Sd $
0;13 0;14 0;2 sf le St $ slef Sd > 1; 0 d d e
ð9Þ
e
3.3. Pressure drop The Euler number did not follow a simple power-law dependency on the Reynolds number, and a regression analysis suggested a dependency in the form of equation (10). This dependency was reasonable in that it contains an apparent form drag term and a skin-friction term, the latter becoming dominant at low Reynolds numbers. The individual constants C2 in equation (10) are shown in Fig. 8.
" Eu ¼ C2 $ 0; 86 þ
29; 5
# (10)
Re0;5 de
The tube bundle layout effect is shown using the geometries with identical fin dimensions in Fig. 9, showing the Euler numbers relative to an equilateral layout as function of the pitch ratio (Pt/Pl). As observed, only the correlation of Weierman [1] reproduced the data at St/Sd < 1 (corresponding to Pt/Pl < 2,2), whereas none of the correlations captured the behavior at St/Sd > 1. The observed behavior was empirically fitted as shown in equation (11), using a typical asymptotic value of about 0,5 as an in-line layout is approached (Pt/Pl approaches infinity).
Eu ¼ min 1; 0 ; Eueq
0; 52 þ 964; 5$e3;24$Pt =Pl
(11)
The individual fin parameters influence on the pressure loss coefficient is seen in Fig. 10. The behavior is similar to that observed for heat transfer, however, the effect of varying the fin height had negligible effect on the Euler number. The published correlations were only moderately successful in reproducing the observed trends. A linear regression analysis of the experimentally obtained C2’s from all geometries resulted in the correlation shown in equation (12), having a 95% confidence interval of 3,7%.
8; 2 Eu ¼ 0; 24 þ 0;5 $min 1; 0; 0; 52 þ 964; 5$e3;24,Pt =Pl Re 0;18 0;74 sf le $ ð12Þ $ de de The overall prediction accuracy is shown in Fig. 11. 4. Conclusions A set of experiments were performed in order to evaluate the influence of tube layout and fin geometry on heat transfer and pressure drop performance in serrated-fin tubes for high temperature heat recovery applications. Based on the experimental results, the following conclusions were drawn: Heat transfer undergoes a maximum when the flow areas in the transversal and diagonal planes are equal. The maximum value is
1537
approximately 15% higher than for equilateral tube layouts at equal Re-numbers. Fin parameters had moderate effects on heat transfer; increasing the fin pitch reduced the heat transfer coefficient, increasing fin height increased the heat transfer coefficient. Pressure drop was little influenced by the tube bundle layout for St < Sd. At St > Sd, the Euler number decreased monotonically. Increased fin pitch reduced the Euler number, whereas increasing fin height had negligible effect on Eu. None of the available heat transfer and pressure drop correlations were able to reproduce the effect of tube bundle layout. Predictive correlations for Nu and Eu were developed from the data presented. The heat transfer data were correlated as shown in equation (9) with a 95% confidence interval of 4,2%. Eu was correlated as shown in equation (12), with a 95% confidence interval of 3,7%. Further data covering a wider range of geometric parameters are however needed in order to establish generalized predictive correlations. References [1] C. Weierman, Correlations ease the selection of finned tubes. Oil Gas J. (1976) 94e100. [2] PFR Engineering Systems, Heat Transfer and Pressure Drop Characteristics of Dry Tower Extended Surfaces PFR Report BNWL-PFR-7 100. PFR Engineering Systems Inc., 1976. [3] T.J. Rabas, P.W. Eckels, Heat Transfer and Pressure Drop Performance of Segmented Extended Surface Tube Bundles, ASME Paper 75-HT-45, 1975. [4] C. Weierman, Pressure drop data for heavy-duty finned tubes. Chem. Eng. Prog. 73 (No. 2) (1978) 69e72. [5] E.A. Schryber, Heat transfer coefficients and other data of individual serratedfin surfaces. Trans. ASME 67 (No. 8) (1945) 683e686. [6] K. Hashizume, Heat transfer and pressure drop characteristics of finned tubes in crossflow. Heat Transfer Eng. 3 (No. 2) (1981) 15e20. [7] C. Weierman, J. Taborek, W.J. Marner, Comparison of the performance of inline and staggered banks of tubes with segmented fins. AIChE Symp. Ser. 74 (1978) 39e46. [8] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (Comparison of pressure drop characteristics between spiral fin and serrated fin). Heat Transfer Asian Res. 33 (No. 72) (2004) 120e133. [9] K. Kawaguchi, K. Okui, T. Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection (Comparison of heat transfer characteristics between spiral fin and serrated fin). Heat Transf. Asian Res. 34 (No. 2) (2005) 120e133. [10] B. Cox, Heat transfer and pumping power performance in tube banks e finned and bare, ASME Paper 73-HT-27, 1973. [11] J.W. Ackerman, A.R. Brunsvold, Heat transfer and draft loss performance of extended surface tube banks. J. Heat Transfer 92 (May 1970) 215e220. [12] J. Vampola, Heat and Pressure Losses for Gases Flowing through Bundles of Finned Tubes, (in Russian). Strojirenstvi 16 (1966) 501e507 Results also available in [2]. [13] N.G. Worley, W. Ross, Heat transfer and pressure loss characteristics of crossflow tubular arrangements with studded surfaces. Inst. Mech. Engrs. (Nov 1960) 15e26. [14] H.C. Mieth, Method for Heat Transfer Calculation of Helical-Wound Fin Tubes, ASME-70, Pet 4, 1970. [15] A. Nir, Heat transfer and friction factor correlations for crossflow over staggered finned tube banks. Heat Transf. Eng. 12 (No. 1) (1991) 43e58. [16] A.Y. Gunter, W.A. Shaw, A general correlation of friction factors for various types of surfaces in crossflow. Trans. ASME 67 (Nov 1945). [17] C. Weierman, Pressure Drop Tests on Welded Plain and Segmented Fins, 16th Nat. Heat Transfer Conf., USA, paper AIChE-27, 1976. [18] M.S. Bhatti, R.K. Shah, Turbulent and transition flow convective heat transfer in ducts. in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single Phase Convective Heat Transfer. John Wiley & Sons, 1987. [19] K.A. Gardner, Efficiency of extended surfaces. Trans. ASME 67 (1945) 621e631. [20] K. Hashizume, R. Morikawa, T. Koyama, T. Matsue, Fin efficiency of serrated fins. Heat Transf. Eng. 23 (No. 2) (2002) 7e14. [21] R.J. Moffat, Describing the uncertainties in experimental results. Exp. Therm. Fluid Sci. 1 (1988) 3e17. [22] J. Stasiulevicius, A. Skrinska, Heat Transfer of Finned Tube Bundles in Crossflow. Hemisphere Publishing Company, 1988. [23] H. Brauer, Compact heat exchangers. Chem. Prog. Eng. 45 (No. 8) (1964) 315e321.