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Comparative analysis of heat transfer and pressure drop in helically segmented finned tube heat exchangers
Applied Thermal Engineering 30 (2010) 1470e1476
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Comparative analysis of heat transfer and pressure drop in helically segmented finned tube heat exchangers E. Martinez a, W. Vicente b, *, G. Soto a, M. Salinas b a b
Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Azcapotzalco, 02200 Mexico City, Mexico Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 Mexico City, Mexico
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 May 2009 Accepted 3 March 2010 Available online 10 March 2010
Four different semi-empirical models of heat transfer and pressure drop for helically segmented finned tubes in staggered layout were analyzed. The performance of a Helically Segmented Finned Tubes Heat Exchanger on an industrial scale was obtained and the predictions were compared with experimental data. The method used for thermal analysis is the Logarithmic Mean Temperature Difference (LMTD). Comparisons between predictions and experimental data show a precision greater than 95% in heat transfer for a combination between the Kawaguchi and Gnielinski models at a flue gas Reynolds number, based on the outside bare tube, of about 10,000. In the case of pressure drop, there is a precision of approximately 90% for the Weierman model at a Reynolds number, based on the outside bare tube, of about 10,000. And so, the results show that the best flow regime in which heat transfer and pressure drop are optimum, is for a Reynolds number (based on the outside bare tube) of about 10,000. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Experiment Compact heat exchangers Segmented fins Pressure drop Heat transfer coefficient
1. Introduction The design of compact heat recovery systems requires appropriate knowledge of heat transfer and fluid dynamics phenomena. Nowadays, there are two main design methods; the first uses Computational Fluid Dynamics (CFD) techniques, and the second uses semi-empirical models. The CFD method provides complete and detailed information on thermo-physical phenomena. However, it requires good computational support and long calculation times, which are not always available in industrial applications. Semi-empirical models allow a quick evaluation of thermo-physical phenomena with minimum computational infrastructure. Therefore, the technique chosen for industrial applications in the design of heat recovery is the semi-empirical method, which is analyzed in the present paper. Segmented helically finned tubes are used in industrial applications for obtaining compact heat recoveries because gas-phase turbulence and heat transfer surface are increased. However, pressure drop in the gas phase increases and, consequently, operational problems can emerge. Therefore, the use of appropriate predictive models for heat transfer and pressure drop is necessary.
* Corresponding author. E-mail addresses: [email protected] (E. Martinez), [email protected] (W. Vicente). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.03.007
In the open literature, there are many studies on compact heat exchangers and some of them are focused on helically finned tubes. The majority of the papers have studied solid fins, like Genic et al. [1]. Only a few papers focus on segmented fins, and so, there are few correlations for heat transfer and pressure drop. One of the most commonly used models was developed by Weierman [2,3], who developed heat transfer and friction factor correlations for different tube bundles (inline and staggered) with solid and serrated fins. These correlations were modified by ESCOA (Extended Surface Corporation of America) in order to obtain better predictive models (Ganapathy [4]). Later, Nir [5] analyzed heat transfer and pressure drop in helically finned tube bundles and the results were validated with experimental data; he found a maximum deviation of 10% in the predictions. Finally, Kawaguchi et al. [6] analyzed heat transfer and pressure drop in helically segmented finned tubes for Reynolds numbers of 7000e50,000 and 2000e30,000. On the other hand, there are some authors, like Martin [7,8], who tried to use Lévêque’s [9] generalized equation in complex finned tubes with the model of Gaddis and Gnielinski [10]. However, the model of Gaddis and Gnielinski [10] has to be modified for helically segmented finned tubes and, therefore, the results are not conclusive yet. Some models from previous studies for helically segmented finned tubes were analyzed and only the correlations of Weierman [2,3], Nir [5], ESCOA [4], and Lévêque [9] were validated with experimental data. For example, Hoffmann et al. [11] carried out
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
a comparative analysis with academic equipment for heat transfer and pressure drop correlations of Weierman [2,3] and Lévêque [9]. Other authors, such as Naess [12,13], analyzed the models of Weierman [2,3] and Nir [5] with academic equipment. Finally, Martinez et al. [14] analyzed the models of Weierman [2,3] and ESCOA [4] and the predictions were validated with experimental data in heat recovery on an industrial scale. The objective of the present paper is the comparative analysis of heat transfer and pressure drop models with experimental data for Helically Segmented Finned Tube Heat Exchanger (HSFHE) on an industrial scale. The heat transfer and pressure drop models will be obtained from the studies of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6] on staggered tube bundles. The configuration of equipment, the operating conditions, and the experimental data were taken from Martinez et al. [14] in order to validate the predictions. The results can be used to find the relevant phenomena that affect HSFHE performance, for detailed studies such as numerical simulations. Moreover, models with better predictions will be proposed for the design of industrial HSFHE.
2. Methodology The present paper shows a comparative analysis of heat transfer and pressure drop models for helically segmented finned tubes with staggered tube bundles in an industrial HSFHE. Heat transfer and pressure drop were evaluated with the models of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6]. The models were applied to predict HSFHE performance according to the geometry, configuration, and operating conditions of the industrial equipment tested by Martinez et al. [14]. The predictions of four models were compared with experimental data from the equipment installed in a paper factory. In the HSFHE, the liquid phase (treated feedwater) flows inside the tubes and the gas-phase (flue gases) flows on the outside of the finned tubes. The diagram of finned tubes and the values of equipment geometry and configuration are shown in Fig. 1 and Table 1. The thermal performance of equipment was evaluated with the Logarithmic Mean Temperature Difference (LMTD) method and the gas-phase pressure drop was calculated using semi-empirical correlations. The equipment’s evaluation was performed in two steps: 1) thermal analysis of liquid and gas phases, and 2) analysis of gas-phase pressure drop. The thermal analysis was conducted using the LMTD method with fouling factors, fluid properties, tube and fin materials, finned tube geometry, tube bundle layout, and operating conditions of equipment used by Martinez et al. [14]. The overall heat transfer
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Table 1 Characteristics of helically segmented finned tubes. Tubes
Fins
do (mm) ew (mm) di (mm) Ltf (m) Ltb (m) Ltube (m)
50.8 3.4 44.0 3.4 0.05 3.5
lf (mm) ls (mm) ef (mm) sf (mm) fs (mm) fd (fins/m) df (mm)
Tube layout 25.4 19.05 1.24 3.0 3.94 236 101.6
St (mm) Sl (mm) Nr Nt Tube bundles
114.3 99.06 8 12 Staggered
coefficient (Uo) was based on the outside surface as shown in the following equation:
Uo ¼
1 Ao þ Ao Rfo ðho þ hr Þ e A 1 Ao þ w oþ þ Rfi hi kw Ai Ai ðho þ hr Þ hf Af þ At
(1)
where ho, hi, and hr are outside convective coefficient, inside convective coefficient, and radiation heat transfer coefficient, respectively. In the case of flue gas temperatures lower than 300 C, the value of hr could be negligible [4], and so this value is considered zero. Rfo and Rfi, are the outside and inside fouling factors, respectively. hf, Af, At, Ao, and Ai are fin efficiency, fin surface area, bare tube surface area, total surface area, and inside surface area, respectively. Finally, ew and kw are tube wall thickness and tube material thermal conductivity, respectively. Convective coefficients were calculated for the inside and outside of finned tubes. The inside convective coefficient (hi) used in the evaluation was Gnielinski’s correlation [15], which, according to Bejan [16], is the best available in the open literature. The model of Gnielinski [15] has been validated with satisfactory results by Rane and Tandale [17]. And so, the inside heat transfer coefficient was evaluated as a function of the Nusselt number, according to the following equation:
Nu ¼
hi di ðfi =8ÞðRe 1000ÞPr ¼ k 1 þ 12:7ðf =8Þ1=2 Pr2=3 1
(2)
where di and k are inside diameter of tube and thermal conductivity of fluid. Re and Pr are the Reynolds Number and Prandtl Number. Finally, fi is the friction factor, which is defined in the following equation:
fi ¼
1
(3)
ð1:82 log10 Re 1:64Þ2
In the case of outside convective coefficients (ho), four different models were used for staggered tube bundles and segmented fins. The models that were used were the correlations of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi [6]. The Weierman’s model [2,3] was calculated in terms of the Colburn heat transfer factor, as shown in the following equation:
j ¼ ¼
ho Pr2=3 c p Go h
0:25Re0:35 o
i
"
0:55 þ 0:45e
0:35*lf sf
#
1=2 Sl df Tb 1=4 0:15Nr2 Þ ð 0:7 þ 0:7 0:8e e St do Ts (4) Fig. 1. Geometry of helically segmented finned tubes.
where Reo, Go, and cp are Reynolds number based on outside bare tube, gas mass flux and specific heat capacity at constant pressure,
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respectively. Tb and Ts are average outside fluid temperature and average fin temperature, respectively. df and do are outside diameter of finned tube and outside diameter of bare tube, respectively. The terms lf and sf, Sl, St, and Nr are fin height, clear space between fins, longitudinal pitch, transversal pitch, and number of tube rows, respectively. The model of ESCOA [4] for outside convective coefficient was calculated in terms of the Colburn heat transfer factor. This equation is very similar to Weierman’s model [2,3], since some terms were corrected. Therefore, this correlation was calculated in terms of the Colburn heat transfer factor as shown in the following equation: 2=3
j ¼ ¼
ho Pr cp Go h
1=4 0:091Reo
i
"
0:35 þ 0:65e
0:17*lf sf
#
(5)
In the case of the model recommended by Nir [5] for tube banks with plain and segmented fins, the outside convective coefficient was defined in terms of the Stanton number as shown in the following equation:
ho Pr Go cp
¼ 1:745Re0:4 D
Ao;f Ao;t
0:4
2=3
At Xt ð1 ðD=Xt Þð1 Rt ÞÞ
Kz;h
0:062 Nu ¼ A2 Re0:784 Pr1=3 sf =dv v
A ¼
1 þ B2 rgp
(7)
(10)
4Nr
where B is defined as the square relation between free gas area and total area. In the case of Weierman’s model [2,3], the gas-phase friction factor (fo) was evaluated with the following equation:
"
0:23 # 0:05St 0:7ðlf =sf Þ 0:11 fo ¼ 0:07 þ do h 2 1:1 þ 1:8 2:1e0:15Nr e2ðSl =St Þ
8Re0:45 o
i
i d 1=2 2 f 0:7 0:8e0:15Nr e0:6ðSl =St Þ do
(11)
On the other hand, the gas-phase friction factor in ESCOA’s model [4] was evaluated with the following equation:
" 0:2 # i h 0:05St 0:7ðlf =sf Þ 0:11 fo ¼ 0:075 þ 1:85Re0:3 o do h 2 1:1 þ 1:8 2:1e0:15Nr e2ðSl =St Þ
(6)
where ReD, Go, and cp are the Reynolds number at fin diameter, flow mass velocity at frontal free cross section, and specific heat at constant pressure, respectively. The terms At, Ao,t, Ao,f, D, Xt, Rt, and Kz,h are the heat transfer area of unit length finned tube, fin-side free cross section of one tube unit length, frontal free cross section of unit length per tube, fin diameter, tube transverse pitch, ratio of frontal free flow area of tube to tube face area, and heat transfer correction factor, respectively. Finally, Kawaguchi’s model [6] for staggered tube banks and segmented fins is presented in terms of the Nusselt number, according to the following equation:
(9)
where fo and rgp are the friction factor and density of gas phase at average outside temperature, respectively. A is defined in the following equation:
h
1=2 Sl df Tb 1=4 0:15Nr2 Þ ð e St 0:7 þ 0:7 0:8e do Ts
2=3
ðfo þ AÞG2o Nr 1:083 109 rgp
DPg ¼
i d 1=2 2 f 0:7 0:8e0:15Nr e0:6ðSl =St Þ do
(12)
In the case of Nir’s model [5], the isothermal pressure drop in the heat exchanger was calculated according to the following equation:
DP ¼
fo
At Xt ð1ðD=Xt Þð1Rt ÞÞ
Nz G2o
2rgp
(13)
where Nz is the number of rows. The friction factor is defined in the following equation:
fo ¼ 1:75Re0:25 h
0:57 At Kzp Xt ð1 ðD=Xt Þð1 Rt ÞÞ
(14)
where Rev is the Reynolds number based on equivalent diameter in volume. The terms A2, sf, and dv are the experimental coefficient for tube rows, fin gap, and equivalent diameter in volume, respectively. The equivalent diameter in volume is defined by following equation:
where Reh and Kzp are Reynolds number based on the hydraulic diameter and the pressure drop’s correction factor, respectively. Nir [5] defines the Reynolds number based on the hydraulic diameter, with the following equation:
2 i1=2 h to þ 2hf d2o þ d2o dv ¼ tf nf
Reh ¼
(8)
where tf, nf, and hf are fin thickness, fin number per unit length, and fin height, respectively. Gas-phase pressure drop was calculated with the models of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6]. In the analysis, a maximum pressure drop of 248.9 Pa [18] (1 inch (in) of water column (wc)) was considered in order to avoid technical problems such as backpressure. In the case of the models of Weierman [2,3] and ESCOA [4], pressure drop was calculated with the following empirical equation:
4DðXt ð1 ðD=Xt Þð1 Rt ÞÞÞ At
(15)
Finally, pressure drop in the Kawaguchi’s model [6] is calculated with the following equation:
DP ¼
fo Nz G2o 2rgp
(16)
where the gas-phase friction factor is defined according to following equation:
0:354 sf =tf fo ¼ 6:46Re0:179 h
(17)
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
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In the equation (17), Reh is the Reynolds number based on the hydraulic diameter, as shown in the following correlation:
dh ¼
4 St Sl pd2v =4
(18)
Ao
where Ao is the total heat transfer area per unit tube length. 3. Experimental setup A helically serrated finned tube heat exchanger was designed for industrial applications and installed in a paper factory. The HSFHE heats feedwater using residual energy of flue gases from a Steam Generator (SG). The heat exchanger consists of carbon steel tubes (fluxing10) and carbon steel serrated fins which are welded to achieve a good contact between them. The HSFHE has bimetallic thermometers, Bourdon manometers, and test ports, and it was setup next to the SG chimney, as shown in Fig. 2. The flue gas measurement ports (points C and D, Fig. 2) are located on the interconnect ducts of the chimney equipment and the feedwater test ports (points A and B, Fig. 2) are located in the inlet and exit headers. The size of the rectangular ducts is 1.4 1.0 m for chimney-HSFHE and 1.4 0.8 m for HSFHE-chimney. These rectangular ducts cannot be too long due to financial and technical (assembly) aspects, and so the flue gas measurement ports are located as far as possible from the equipment outlet or chimney (approximately 1.5 times the hydraulic diameter, 1.75 m). The length of 1.5 times the hydraulic diameter could be acceptable, because only static pressure and bulk temperature were measured. Moreover, the lowest flue gas Reynolds number in the ducts is 1.97 105, which is much higher than the value required for the gas-phase flow pattern to easily become stabilized (Reynolds number above 10,000 [19]). Measurements taken for feedwater were bulk temperature at the inlet and outlet of finned tubes (A and B), with bimetallic thermometers. Measurements taken for flue gases were bulk temperature and static pressure at the inlet and outlet of the equipment (ports C and D) with bimetallic thermometers, portable mercury thermometer, and differential manometer. Tests were conducted every 15 min in samples of 5 readings per operating condition for three weeks. However, the flow of combustion gases was varied with each chimney-damper position in order to have more information on the equipment performance because the industrial process could not be affected. Thus, the chimney-damper position was varied so as to obtain 78%, 68%, and 61% of flue gases
Fig. 2. HSFHE Configuration.
mass flow. Only flue gases flow was manipulated and the samples were taken at the different chimney-damper positions mentioned before. The samples were analyzed and the most reliable (stable conditions) were chosen. Two samples at different stable operating conditions (samples 1 and 2) and three samples with different chimney-damper positions (samples 3e5) were used for the analysis. Samples 1 and 2 were taken at 100% flue gases and samples 3e5 were taken at 78%, 68% and 61% flue gases, respectively. The summary of mean values measured with their respective standard deviations are shown in Table 2, according to the following nomenclature: Twi,o (water temperature at inlet or outlet), Tgi,o (flue gases temperature at inlet or outlet), DPg (pressure drop gas side), :mv (steam water mass flow), :mg (flue gases mass flow), SD (standard deviation), and SE (standard error). Among the values reported experimentally, there are some mean values with zero
Table 2 Experimental tests. Values
Twi ( C)
Two ( C)
Tgi ( C)
Tgo ( C)
DPg (Pa)
:mv (kg/h)
:mg (kg/h)
Sample 1 SD SE
105.0 0.354 0.158
128.0 0.791 0.354
184.0 0.548 0.245
120.0 0.224 0.100
199.14 0.071 0.032
24,400 0.019 0.008
34,003
Sample 2 SD SE
108.0 0.707 0.316
128.0 0.707 0.316
180.0 0.791 0.354
122.0 0.894 0.400
174.24 0.061 0.027
22,700 0.025 0.011
32,330
Sample 3 SD SE
108.0 0.224 0.100
126.0 0 0
180.0 0.447 0.200
122.0 0.274 0.122
74.68 0 0
22,600 0.021 0.009
25,098
Sample 4 SD SE
108.0 0 0
124.0 0.224 0.100
178.0 0.224 0.100
114.0 0.224 0.100
49.78 0.035 0.016
22,600 0.015 0.007
21,972
Sample 5 SD SE
108.0 0.224 0.100
122.0 0 0
179.0 0.224 0.100
114.0 0 0
24.89 0.041 0.018
22,600 0.028 0.012
19,522
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Fig. 3. Relationship between flue gas pressure drop and Reynolds number based on the outside bare tube.
standard deviation and standard error by coincidence. However, all the measurements showed different values.
4. Results The results of pressure drop and Reynolds number for gas phase are shown in Fig. 3. The graph shows that the best predictions are obtained by Weierman’s [2,3] correlation, because its values are always higher than the experimental data, and it has the best precision (over 89%) for Reynolds numbers (based on the outside bare tube, Reo) over 10,000. These characteristics are essential because technical problems, like backpressure, will be avoided, guaranteeing equipment performance. Nir’s correlation [5] is a good option for a quick calculation, because its results are higher than the experimental data. However, its predictions have a precision of 65% for Reynolds numbers (Reo) over to 10,000, which decreases at lower Reynolds numbers. In the case of the ESCOA [4] and Kawaguchi [6] models, there is a special situation, because their results are the same in spite of their correlations being different. Both models have the worst predictions (precisions of 40e75%) for low Reo (6348e8131), but the best precisions (85.71e90.73%) for Reynolds numbers (Reo) higher than 10,000. Moreover, their predictions are lower than the experimental data for Reynolds numbers (Reo) over 10,000. This situation is critical, because backpressure could appear. On the other hand, the experimental data show an exponential tendency. Therefore, the predictions could be lower than the experimental data for Reynolds numbers (Reo) higher than 11,000.
Fig. 4. Relationship between theoretical and experimental Overall Heat Transfer Coefficient.
The relationship between theoretical and experimental overall heat transfer coefficients are shown in Fig. 4. The results show that the best predictions are obtained with the KawaguchieGnielinski model, because their precision is 93.75e99.59% for Reynolds numbers (Reo) between 6348 and 10 951. However, at a Reynolds number (Reo) of 8131, there is a precision of 77.74%. In spite of this deviation, the results are reliable, as will be shown in the predictions of fluid temperatures. The WeiermaneGnielinski model has a precision of 83.8e97.66% for Reynolds numbers (Reo) between 6348 and 10,951. The values are less precise than those obtained with the KawaguchieGnielinski models, but are adequate in spite of some cooling-gas temperature predictions are lower than the experimental data. The ESCOAeGnielinski model has a precision of 81.15e94.41% for Reynolds numbers (Reo) between 8131 and 10,951. The precision did not seem adequate but the predictions of working fluid temperatures are lower than the experimental data. Therefore, the equipment performance is guaranteed and these models are a good option to design. Finally, the NireGnielinski model shows poor precision in the predictions, between 66.77 and 73.87%, at Reynolds numbers (Reo) over 10,000. However, these models could be a good choice because their predictions of working fluid temperatures are higher than the experimental values and the final flue gas temperatures are lower than the experimental data. Flue gas cooling temperatures and their Reynolds number base on the outside bare tube are shown in Fig. 5. The graph shows that all performance curves have the same tendency and there is an inflection point (Reo ¼ 10,438) in which flue gases are cooling more efficiently. The reason for this behavior is that the HSFHE was designed to operate at a Reynolds number (Reo) around 10,000. On the other hand, gas flow is more turbulent at higher Reynolds numbers and, therefore, heat transfer is better. The results show that the best combination of models is the KawaguchieGnielinski, because they have the best precision (higher than 99%) for most of the predictions. The worst precision is obtained at a Reynolds number (Reo) of 8131, with 95.55%, representing a deviation of 4.45% that could be compensated with a low security factor. The WeiermaneGnielinski model has a precision higher than 96.61% for Reynolds numbers (Reo) over 6348 and most of the predictions of flue gas temperatures are lower than the experimental data. Only at a Reynolds number (Reo) of 8131 is the final temperature of flue gases higher than the experimental value. This situation is not serious, because the deviation is 3.39%, which could be compensated with a low security factor. Another good combination of models is the ESCOAeGnielinski, because their minimum precision is 96.61% (Reo ¼ 6348) and most of the predictions of flue gas cooling temperatures are lower than the experimental data. There
Fig. 5. Relationship between flue gas temperature and Reynolds number based on the outside bare tube.
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
Fig. 6. Relationship between feedwater temperature and Reynolds number based on the outside bare tube.
is a value, at a Reynolds number (Reo) of 8131, at which final temperature is higher than the experimental data. The NireGnielinski model has the worst precision (94.79e99.67%) for the range of Reynolds numbers (Reo) from 6348 to 10,951. This precision is acceptable because the maximum deviation is 5.21% and all predictions are higher than the experimental values. Therefore, the NireGnielinski model could be used for the design of equipments without the use of a security factor. Finally, the comparative analysis of results and the experimental data show that the best predictions are obtained at a Reynolds number (Reo) of about 10,000, because at this flow regime pressure drop is close to 248.9 Pa. The final water temperature and its Reynolds number are shown in Fig. 6. The theoretical curves for all models have the same tendency and there is an inflection point (Reo ¼ 69,447) at which final temperature decreases due to the increase in mass flow. The inflection point of water corresponds to the gas point at a Reynolds number (Reo) of 10,438 and both are located under the same conditions. Therefore, the best equipment performance is at a Reynolds number (Reo) e in gas phase e of about 10,000. The results show that the best models are the KawaguchieGnielinski, because they have a precision of 99.3e100% for a Reynolds number (Reo) of 67,698e73,373. Thus, the maximum deviation of 0.7% could be compensated by a minimum-security factor. The WeiermaneGnielinski model has a precision of 98.89e99.84% with a Reynolds number (Reo) of 67,698e73,373. Most results are lower than the experimental values, but at a Reynolds number (Reo) of 68,443, the prediction is higher than the measurements. Therefore, the critical deviation is 0.72%, which could be solved by a low security factor. In the ESCOAeGnielinski model, all predictions are lower than the experimental data and the minimum precision is 98.41%, which represents a maximum deviation of 1.59% that could be considered a security factor. Thus, the equipment performance is guaranteed. The NireGnielinski model is appropriate because all the predictions are lower than the experimental data, which is the best situation. The apparent weakness of this combination of models is precision, which ranges between 97.6 and 99.17%, but the maximum deviation of the predictions is 2.4%, which is acceptable for industrial equipments.
5. Conclusions A comparative analysis of performance and experimental data of heat transfer and pressure drop for industrial HSFHE was conducted. Flue gas pressure drop shows the ESCOA [4] and Kawaguchi [6] models to have predictions lower than the experimental data for Reynolds numbers (Reo) over 10,000. This situation is not
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recommendable, because backpressure could appear, resulting in operational problems. Therefore, these models are not recommended for the design of heat recoveries. On the other hand, the Nir model [5] shows that all predictions are higher than the experimental data, which is the best situation since backpressure will be avoided. However, the curve has an exponential tendency for Reynolds numbers over 8000, and consequently the predictions have more deviations. Hence, this model is appropriated for a quick calculus. The best correlation for pressure drop is the Weierman model [2,3], because all predictions are higher than the experimental data and precision is over 89% for Reynolds numbers (Reo) upper to 10,000. Therefore, this model is recommended for the design of heat recoveries on an industrial scale. On the other hand, the results show that the best flow regime is at a Reynolds number (Reo) of about 10,000 with a length-width ratio (cross section area) around 2.5, because at this zone, pressure drop is lower than 249 Pa (1 in water column) [18] and, consequently, the heat recoveries do not affect the process. The heat transfer was analyzed for Overall Heat Transfer Coefficient and final temperatures of fluids (feedwater and flue gases). The Overall Heat Transfer Coefficient results show that the NireGnielinski model has the worst predictions, since precision ranges between 57.42 and 73.87%, and there is only one value of 95.71%. In spite of this situation, the results are reliable because temperature predictions are around 96%. The ESCOAeGnielinski model has a precision in U of 69.94e94.41%, but its temperature predictions are acceptable because precision is around 97%. In the case of the WeiermaneGnielinski model, it has better predictions than the previous models; with precisions between 83.8% and 97.66% in U. Fluid temperature predictions are better because their precision is around 98%. Finally, the KawaguchieGnielinski model has the best results, with precisions of 93.75e99.59% for Overall Heat Transfer Coefficient and there is only a single precision of 77.74%. In spite of that, these predictions are the best because the evaluation of temperatures has a precision of approximately 99%. So, the best model combination is the KawaguchieGnielinski, which is recommended for the heat transfer design of compact heat recoveries. However, the model of Weierman [2,3] should be considered if finned tube geometry and fluid conditions are outside the range of application of Kawaguchi model [6]. On the other hand, the results of all the models show an apparent discrepancy between Overall Heat Transfer Coefficient and fluid temperatures, because their precision is too different. However, there is a strong dependence of U with T, because a deviation of 1 C in predictions represents approximately 5% (WeiermaneGnielinski, ESCOAeGnielinski, and NireGnielinski) to 1% (KawaguchieGnielinski) deviation in Overall Heat Transfer Coefficient. Therefore, a detailed study focused on the outer finned tube is recommended, since flue gas heat transfer dominates the liquid phase. Acknowledgements We appreciate the support given to the research presented here by Consejo Nacional de Ciencia y Tecnologia (CONACYT), Universidad Nacional Autonoma de Mexico (Direccion General de Asuntos del Personal Academico, PAPIIT-IN111709-3), and Universidad Autonoma Metropolitana Azcapotzalco. On the other hand, we appreciate the information provided by Professor Holger Martin and Professor Erling Naess. References [1] Srbislav B. Genic, Branislav M. Jacimovic, Boris R. Latinovic, Research on air pressure drop in helically-finned tube heat exchangers. Applied Thermal Engineering 26 (2006) 478e485.
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[2] C. Weierman, Correlations ease the selection of finned tubes. Oil and Gas Journal 74 (36) (1976) 94e100. [3] C. Weierman, J. Taborek, W.J. Marner, Comparison of the performance of in-line and staggered banks of tubes with segmented fins. The American Institute of Chemical Engineers Symposium 74 (174) (1978) 39e46. [4] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators: Design, Applications and Calculations. Marcel Dekker, 2003. [5] A. Nir, Heat transfer and friction factor correlations for crossflow over staggered finned tube banks. Heat Transfer Engineering 12 (1) (1991) 43e58. [6] Kiyoshi Kawaguchi, Kenichi Okui, Takaharu Kashi, Heat transfer and pressure drop characteristics of finned tube banks in forced convection. Journal of Enhanced Heat Transfer 12 (1) (2005) 1e20. [7] Holger Martin, The generalized Lévêque equation and its practical use for the prediction of heat and mass transfer rates from pressure drop. Chemical Engineering Science 57 (2002) 3217e3223. [8] Holger Martin. How to predict heat and mass transfer from fluid friction, in: 4th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics HEFAT, Cairo, Egypt, 2005. [9] A. Lévêque, Les lois de la transmission de chaleur par convection. Annales des Mines 13 (1928) 201e299 305e362, 381e415. [10] E.S. Gaddis, V. Gnielinski, Pressure drop in cross row across tube bundles. International Journal of Chemical Engineering 25 (1985) 1e15.
[11] R. Hofmann, F. Frasz, K. Ponweiser, Performance evaluation of solid and serrated finned-tube bundles with different fin geometries in forced convection, in: Fifth European Thermal-sciences Conference, 2008. [12] Erling Naess, Heat Transfer in Serrated-Fin Tube Bundles with Staggered Tube Layouts, in: 9th UK, National Heat Transfer Conference, Manchester, UK, 2005. [13] Erling Naess. Heat transfer and pressure drop in serrated-fin tube bundles for waste heat recovery applications, in: 6th World Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, Miyagi, Japan, 2005. [14] E. Martínez, W. Vicente, M. Salinas, G. Soto, Single-phase experimental analysis of heat transfer in helically finned heat exchangers. Applied Thermal Engineering 29 (2009) 2205e2210. [15] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering 16 (1976) 359e367. [16] A. Bejan, Convection Heat Transfer, second ed. Wiley, 1995. [17] M.V. Rane, S. Tandale, Water-to-water heat transfer in tube-tube heat exchanger: experimental and analytical study. Applied Thermal Engineering 25 (2005) 2715e2729. [18] Jonh Weale, Peter H. Rumsey, Dale Sartor, Lee Eng Lock, Laboratory lowpressure drop design. ASHRAE Journal (2002) 38e42 August. [19] E.L. Upp, Paul J. Lanasa, Fluid Flow Measurement: a Practical Guide to Accurate Flow Measurement, second ed. Butterworth-Heineman, 2002.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Comparative analysis of heat transfer and pressure drop in helically segmented finned tube heat exchangers E. Martinez a, W. Vicente b, *, G. Soto a, M. Salinas b a b
Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Azcapotzalco, 02200 Mexico City, Mexico Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 Mexico City, Mexico
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 May 2009 Accepted 3 March 2010 Available online 10 March 2010
Four different semi-empirical models of heat transfer and pressure drop for helically segmented finned tubes in staggered layout were analyzed. The performance of a Helically Segmented Finned Tubes Heat Exchanger on an industrial scale was obtained and the predictions were compared with experimental data. The method used for thermal analysis is the Logarithmic Mean Temperature Difference (LMTD). Comparisons between predictions and experimental data show a precision greater than 95% in heat transfer for a combination between the Kawaguchi and Gnielinski models at a flue gas Reynolds number, based on the outside bare tube, of about 10,000. In the case of pressure drop, there is a precision of approximately 90% for the Weierman model at a Reynolds number, based on the outside bare tube, of about 10,000. And so, the results show that the best flow regime in which heat transfer and pressure drop are optimum, is for a Reynolds number (based on the outside bare tube) of about 10,000. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Experiment Compact heat exchangers Segmented fins Pressure drop Heat transfer coefficient
1. Introduction The design of compact heat recovery systems requires appropriate knowledge of heat transfer and fluid dynamics phenomena. Nowadays, there are two main design methods; the first uses Computational Fluid Dynamics (CFD) techniques, and the second uses semi-empirical models. The CFD method provides complete and detailed information on thermo-physical phenomena. However, it requires good computational support and long calculation times, which are not always available in industrial applications. Semi-empirical models allow a quick evaluation of thermo-physical phenomena with minimum computational infrastructure. Therefore, the technique chosen for industrial applications in the design of heat recovery is the semi-empirical method, which is analyzed in the present paper. Segmented helically finned tubes are used in industrial applications for obtaining compact heat recoveries because gas-phase turbulence and heat transfer surface are increased. However, pressure drop in the gas phase increases and, consequently, operational problems can emerge. Therefore, the use of appropriate predictive models for heat transfer and pressure drop is necessary.
* Corresponding author. E-mail addresses: [email protected] (E. Martinez), [email protected] (W. Vicente). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.03.007
In the open literature, there are many studies on compact heat exchangers and some of them are focused on helically finned tubes. The majority of the papers have studied solid fins, like Genic et al. [1]. Only a few papers focus on segmented fins, and so, there are few correlations for heat transfer and pressure drop. One of the most commonly used models was developed by Weierman [2,3], who developed heat transfer and friction factor correlations for different tube bundles (inline and staggered) with solid and serrated fins. These correlations were modified by ESCOA (Extended Surface Corporation of America) in order to obtain better predictive models (Ganapathy [4]). Later, Nir [5] analyzed heat transfer and pressure drop in helically finned tube bundles and the results were validated with experimental data; he found a maximum deviation of 10% in the predictions. Finally, Kawaguchi et al. [6] analyzed heat transfer and pressure drop in helically segmented finned tubes for Reynolds numbers of 7000e50,000 and 2000e30,000. On the other hand, there are some authors, like Martin [7,8], who tried to use Lévêque’s [9] generalized equation in complex finned tubes with the model of Gaddis and Gnielinski [10]. However, the model of Gaddis and Gnielinski [10] has to be modified for helically segmented finned tubes and, therefore, the results are not conclusive yet. Some models from previous studies for helically segmented finned tubes were analyzed and only the correlations of Weierman [2,3], Nir [5], ESCOA [4], and Lévêque [9] were validated with experimental data. For example, Hoffmann et al. [11] carried out
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
a comparative analysis with academic equipment for heat transfer and pressure drop correlations of Weierman [2,3] and Lévêque [9]. Other authors, such as Naess [12,13], analyzed the models of Weierman [2,3] and Nir [5] with academic equipment. Finally, Martinez et al. [14] analyzed the models of Weierman [2,3] and ESCOA [4] and the predictions were validated with experimental data in heat recovery on an industrial scale. The objective of the present paper is the comparative analysis of heat transfer and pressure drop models with experimental data for Helically Segmented Finned Tube Heat Exchanger (HSFHE) on an industrial scale. The heat transfer and pressure drop models will be obtained from the studies of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6] on staggered tube bundles. The configuration of equipment, the operating conditions, and the experimental data were taken from Martinez et al. [14] in order to validate the predictions. The results can be used to find the relevant phenomena that affect HSFHE performance, for detailed studies such as numerical simulations. Moreover, models with better predictions will be proposed for the design of industrial HSFHE.
2. Methodology The present paper shows a comparative analysis of heat transfer and pressure drop models for helically segmented finned tubes with staggered tube bundles in an industrial HSFHE. Heat transfer and pressure drop were evaluated with the models of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6]. The models were applied to predict HSFHE performance according to the geometry, configuration, and operating conditions of the industrial equipment tested by Martinez et al. [14]. The predictions of four models were compared with experimental data from the equipment installed in a paper factory. In the HSFHE, the liquid phase (treated feedwater) flows inside the tubes and the gas-phase (flue gases) flows on the outside of the finned tubes. The diagram of finned tubes and the values of equipment geometry and configuration are shown in Fig. 1 and Table 1. The thermal performance of equipment was evaluated with the Logarithmic Mean Temperature Difference (LMTD) method and the gas-phase pressure drop was calculated using semi-empirical correlations. The equipment’s evaluation was performed in two steps: 1) thermal analysis of liquid and gas phases, and 2) analysis of gas-phase pressure drop. The thermal analysis was conducted using the LMTD method with fouling factors, fluid properties, tube and fin materials, finned tube geometry, tube bundle layout, and operating conditions of equipment used by Martinez et al. [14]. The overall heat transfer
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Table 1 Characteristics of helically segmented finned tubes. Tubes
Fins
do (mm) ew (mm) di (mm) Ltf (m) Ltb (m) Ltube (m)
50.8 3.4 44.0 3.4 0.05 3.5
lf (mm) ls (mm) ef (mm) sf (mm) fs (mm) fd (fins/m) df (mm)
Tube layout 25.4 19.05 1.24 3.0 3.94 236 101.6
St (mm) Sl (mm) Nr Nt Tube bundles
114.3 99.06 8 12 Staggered
coefficient (Uo) was based on the outside surface as shown in the following equation:
Uo ¼
1 Ao þ Ao Rfo ðho þ hr Þ e A 1 Ao þ w oþ þ Rfi hi kw Ai Ai ðho þ hr Þ hf Af þ At
(1)
where ho, hi, and hr are outside convective coefficient, inside convective coefficient, and radiation heat transfer coefficient, respectively. In the case of flue gas temperatures lower than 300 C, the value of hr could be negligible [4], and so this value is considered zero. Rfo and Rfi, are the outside and inside fouling factors, respectively. hf, Af, At, Ao, and Ai are fin efficiency, fin surface area, bare tube surface area, total surface area, and inside surface area, respectively. Finally, ew and kw are tube wall thickness and tube material thermal conductivity, respectively. Convective coefficients were calculated for the inside and outside of finned tubes. The inside convective coefficient (hi) used in the evaluation was Gnielinski’s correlation [15], which, according to Bejan [16], is the best available in the open literature. The model of Gnielinski [15] has been validated with satisfactory results by Rane and Tandale [17]. And so, the inside heat transfer coefficient was evaluated as a function of the Nusselt number, according to the following equation:
Nu ¼
hi di ðfi =8ÞðRe 1000ÞPr ¼ k 1 þ 12:7ðf =8Þ1=2 Pr2=3 1
(2)
where di and k are inside diameter of tube and thermal conductivity of fluid. Re and Pr are the Reynolds Number and Prandtl Number. Finally, fi is the friction factor, which is defined in the following equation:
fi ¼
1
(3)
ð1:82 log10 Re 1:64Þ2
In the case of outside convective coefficients (ho), four different models were used for staggered tube bundles and segmented fins. The models that were used were the correlations of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi [6]. The Weierman’s model [2,3] was calculated in terms of the Colburn heat transfer factor, as shown in the following equation:
j ¼ ¼
ho Pr2=3 c p Go h
0:25Re0:35 o
i
"
0:55 þ 0:45e
0:35*lf sf
#
1=2 Sl df Tb 1=4 0:15Nr2 Þ ð 0:7 þ 0:7 0:8e e St do Ts (4) Fig. 1. Geometry of helically segmented finned tubes.
where Reo, Go, and cp are Reynolds number based on outside bare tube, gas mass flux and specific heat capacity at constant pressure,
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respectively. Tb and Ts are average outside fluid temperature and average fin temperature, respectively. df and do are outside diameter of finned tube and outside diameter of bare tube, respectively. The terms lf and sf, Sl, St, and Nr are fin height, clear space between fins, longitudinal pitch, transversal pitch, and number of tube rows, respectively. The model of ESCOA [4] for outside convective coefficient was calculated in terms of the Colburn heat transfer factor. This equation is very similar to Weierman’s model [2,3], since some terms were corrected. Therefore, this correlation was calculated in terms of the Colburn heat transfer factor as shown in the following equation: 2=3
j ¼ ¼
ho Pr cp Go h
1=4 0:091Reo
i
"
0:35 þ 0:65e
0:17*lf sf
#
(5)
In the case of the model recommended by Nir [5] for tube banks with plain and segmented fins, the outside convective coefficient was defined in terms of the Stanton number as shown in the following equation:
ho Pr Go cp
¼ 1:745Re0:4 D
Ao;f Ao;t
0:4
2=3
At Xt ð1 ðD=Xt Þð1 Rt ÞÞ
Kz;h
0:062 Nu ¼ A2 Re0:784 Pr1=3 sf =dv v
A ¼
1 þ B2 rgp
(7)
(10)
4Nr
where B is defined as the square relation between free gas area and total area. In the case of Weierman’s model [2,3], the gas-phase friction factor (fo) was evaluated with the following equation:
"
0:23 # 0:05St 0:7ðlf =sf Þ 0:11 fo ¼ 0:07 þ do h 2 1:1 þ 1:8 2:1e0:15Nr e2ðSl =St Þ
8Re0:45 o
i
i d 1=2 2 f 0:7 0:8e0:15Nr e0:6ðSl =St Þ do
(11)
On the other hand, the gas-phase friction factor in ESCOA’s model [4] was evaluated with the following equation:
" 0:2 # i h 0:05St 0:7ðlf =sf Þ 0:11 fo ¼ 0:075 þ 1:85Re0:3 o do h 2 1:1 þ 1:8 2:1e0:15Nr e2ðSl =St Þ
(6)
where ReD, Go, and cp are the Reynolds number at fin diameter, flow mass velocity at frontal free cross section, and specific heat at constant pressure, respectively. The terms At, Ao,t, Ao,f, D, Xt, Rt, and Kz,h are the heat transfer area of unit length finned tube, fin-side free cross section of one tube unit length, frontal free cross section of unit length per tube, fin diameter, tube transverse pitch, ratio of frontal free flow area of tube to tube face area, and heat transfer correction factor, respectively. Finally, Kawaguchi’s model [6] for staggered tube banks and segmented fins is presented in terms of the Nusselt number, according to the following equation:
(9)
where fo and rgp are the friction factor and density of gas phase at average outside temperature, respectively. A is defined in the following equation:
h
1=2 Sl df Tb 1=4 0:15Nr2 Þ ð e St 0:7 þ 0:7 0:8e do Ts
2=3
ðfo þ AÞG2o Nr 1:083 109 rgp
DPg ¼
i d 1=2 2 f 0:7 0:8e0:15Nr e0:6ðSl =St Þ do
(12)
In the case of Nir’s model [5], the isothermal pressure drop in the heat exchanger was calculated according to the following equation:
DP ¼
fo
At Xt ð1ðD=Xt Þð1Rt ÞÞ
Nz G2o
2rgp
(13)
where Nz is the number of rows. The friction factor is defined in the following equation:
fo ¼ 1:75Re0:25 h
0:57 At Kzp Xt ð1 ðD=Xt Þð1 Rt ÞÞ
(14)
where Rev is the Reynolds number based on equivalent diameter in volume. The terms A2, sf, and dv are the experimental coefficient for tube rows, fin gap, and equivalent diameter in volume, respectively. The equivalent diameter in volume is defined by following equation:
where Reh and Kzp are Reynolds number based on the hydraulic diameter and the pressure drop’s correction factor, respectively. Nir [5] defines the Reynolds number based on the hydraulic diameter, with the following equation:
2 i1=2 h to þ 2hf d2o þ d2o dv ¼ tf nf
Reh ¼
(8)
where tf, nf, and hf are fin thickness, fin number per unit length, and fin height, respectively. Gas-phase pressure drop was calculated with the models of Weierman [2,3], ESCOA [4], Nir [5], and Kawaguchi et al. [6]. In the analysis, a maximum pressure drop of 248.9 Pa [18] (1 inch (in) of water column (wc)) was considered in order to avoid technical problems such as backpressure. In the case of the models of Weierman [2,3] and ESCOA [4], pressure drop was calculated with the following empirical equation:
4DðXt ð1 ðD=Xt Þð1 Rt ÞÞÞ At
(15)
Finally, pressure drop in the Kawaguchi’s model [6] is calculated with the following equation:
DP ¼
fo Nz G2o 2rgp
(16)
where the gas-phase friction factor is defined according to following equation:
0:354 sf =tf fo ¼ 6:46Re0:179 h
(17)
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
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In the equation (17), Reh is the Reynolds number based on the hydraulic diameter, as shown in the following correlation:
dh ¼
4 St Sl pd2v =4
(18)
Ao
where Ao is the total heat transfer area per unit tube length. 3. Experimental setup A helically serrated finned tube heat exchanger was designed for industrial applications and installed in a paper factory. The HSFHE heats feedwater using residual energy of flue gases from a Steam Generator (SG). The heat exchanger consists of carbon steel tubes (fluxing10) and carbon steel serrated fins which are welded to achieve a good contact between them. The HSFHE has bimetallic thermometers, Bourdon manometers, and test ports, and it was setup next to the SG chimney, as shown in Fig. 2. The flue gas measurement ports (points C and D, Fig. 2) are located on the interconnect ducts of the chimney equipment and the feedwater test ports (points A and B, Fig. 2) are located in the inlet and exit headers. The size of the rectangular ducts is 1.4 1.0 m for chimney-HSFHE and 1.4 0.8 m for HSFHE-chimney. These rectangular ducts cannot be too long due to financial and technical (assembly) aspects, and so the flue gas measurement ports are located as far as possible from the equipment outlet or chimney (approximately 1.5 times the hydraulic diameter, 1.75 m). The length of 1.5 times the hydraulic diameter could be acceptable, because only static pressure and bulk temperature were measured. Moreover, the lowest flue gas Reynolds number in the ducts is 1.97 105, which is much higher than the value required for the gas-phase flow pattern to easily become stabilized (Reynolds number above 10,000 [19]). Measurements taken for feedwater were bulk temperature at the inlet and outlet of finned tubes (A and B), with bimetallic thermometers. Measurements taken for flue gases were bulk temperature and static pressure at the inlet and outlet of the equipment (ports C and D) with bimetallic thermometers, portable mercury thermometer, and differential manometer. Tests were conducted every 15 min in samples of 5 readings per operating condition for three weeks. However, the flow of combustion gases was varied with each chimney-damper position in order to have more information on the equipment performance because the industrial process could not be affected. Thus, the chimney-damper position was varied so as to obtain 78%, 68%, and 61% of flue gases
Fig. 2. HSFHE Configuration.
mass flow. Only flue gases flow was manipulated and the samples were taken at the different chimney-damper positions mentioned before. The samples were analyzed and the most reliable (stable conditions) were chosen. Two samples at different stable operating conditions (samples 1 and 2) and three samples with different chimney-damper positions (samples 3e5) were used for the analysis. Samples 1 and 2 were taken at 100% flue gases and samples 3e5 were taken at 78%, 68% and 61% flue gases, respectively. The summary of mean values measured with their respective standard deviations are shown in Table 2, according to the following nomenclature: Twi,o (water temperature at inlet or outlet), Tgi,o (flue gases temperature at inlet or outlet), DPg (pressure drop gas side), :mv (steam water mass flow), :mg (flue gases mass flow), SD (standard deviation), and SE (standard error). Among the values reported experimentally, there are some mean values with zero
Table 2 Experimental tests. Values
Twi ( C)
Two ( C)
Tgi ( C)
Tgo ( C)
DPg (Pa)
:mv (kg/h)
:mg (kg/h)
Sample 1 SD SE
105.0 0.354 0.158
128.0 0.791 0.354
184.0 0.548 0.245
120.0 0.224 0.100
199.14 0.071 0.032
24,400 0.019 0.008
34,003
Sample 2 SD SE
108.0 0.707 0.316
128.0 0.707 0.316
180.0 0.791 0.354
122.0 0.894 0.400
174.24 0.061 0.027
22,700 0.025 0.011
32,330
Sample 3 SD SE
108.0 0.224 0.100
126.0 0 0
180.0 0.447 0.200
122.0 0.274 0.122
74.68 0 0
22,600 0.021 0.009
25,098
Sample 4 SD SE
108.0 0 0
124.0 0.224 0.100
178.0 0.224 0.100
114.0 0.224 0.100
49.78 0.035 0.016
22,600 0.015 0.007
21,972
Sample 5 SD SE
108.0 0.224 0.100
122.0 0 0
179.0 0.224 0.100
114.0 0 0
24.89 0.041 0.018
22,600 0.028 0.012
19,522
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E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
Fig. 3. Relationship between flue gas pressure drop and Reynolds number based on the outside bare tube.
standard deviation and standard error by coincidence. However, all the measurements showed different values.
4. Results The results of pressure drop and Reynolds number for gas phase are shown in Fig. 3. The graph shows that the best predictions are obtained by Weierman’s [2,3] correlation, because its values are always higher than the experimental data, and it has the best precision (over 89%) for Reynolds numbers (based on the outside bare tube, Reo) over 10,000. These characteristics are essential because technical problems, like backpressure, will be avoided, guaranteeing equipment performance. Nir’s correlation [5] is a good option for a quick calculation, because its results are higher than the experimental data. However, its predictions have a precision of 65% for Reynolds numbers (Reo) over to 10,000, which decreases at lower Reynolds numbers. In the case of the ESCOA [4] and Kawaguchi [6] models, there is a special situation, because their results are the same in spite of their correlations being different. Both models have the worst predictions (precisions of 40e75%) for low Reo (6348e8131), but the best precisions (85.71e90.73%) for Reynolds numbers (Reo) higher than 10,000. Moreover, their predictions are lower than the experimental data for Reynolds numbers (Reo) over 10,000. This situation is critical, because backpressure could appear. On the other hand, the experimental data show an exponential tendency. Therefore, the predictions could be lower than the experimental data for Reynolds numbers (Reo) higher than 11,000.
Fig. 4. Relationship between theoretical and experimental Overall Heat Transfer Coefficient.
The relationship between theoretical and experimental overall heat transfer coefficients are shown in Fig. 4. The results show that the best predictions are obtained with the KawaguchieGnielinski model, because their precision is 93.75e99.59% for Reynolds numbers (Reo) between 6348 and 10 951. However, at a Reynolds number (Reo) of 8131, there is a precision of 77.74%. In spite of this deviation, the results are reliable, as will be shown in the predictions of fluid temperatures. The WeiermaneGnielinski model has a precision of 83.8e97.66% for Reynolds numbers (Reo) between 6348 and 10,951. The values are less precise than those obtained with the KawaguchieGnielinski models, but are adequate in spite of some cooling-gas temperature predictions are lower than the experimental data. The ESCOAeGnielinski model has a precision of 81.15e94.41% for Reynolds numbers (Reo) between 8131 and 10,951. The precision did not seem adequate but the predictions of working fluid temperatures are lower than the experimental data. Therefore, the equipment performance is guaranteed and these models are a good option to design. Finally, the NireGnielinski model shows poor precision in the predictions, between 66.77 and 73.87%, at Reynolds numbers (Reo) over 10,000. However, these models could be a good choice because their predictions of working fluid temperatures are higher than the experimental values and the final flue gas temperatures are lower than the experimental data. Flue gas cooling temperatures and their Reynolds number base on the outside bare tube are shown in Fig. 5. The graph shows that all performance curves have the same tendency and there is an inflection point (Reo ¼ 10,438) in which flue gases are cooling more efficiently. The reason for this behavior is that the HSFHE was designed to operate at a Reynolds number (Reo) around 10,000. On the other hand, gas flow is more turbulent at higher Reynolds numbers and, therefore, heat transfer is better. The results show that the best combination of models is the KawaguchieGnielinski, because they have the best precision (higher than 99%) for most of the predictions. The worst precision is obtained at a Reynolds number (Reo) of 8131, with 95.55%, representing a deviation of 4.45% that could be compensated with a low security factor. The WeiermaneGnielinski model has a precision higher than 96.61% for Reynolds numbers (Reo) over 6348 and most of the predictions of flue gas temperatures are lower than the experimental data. Only at a Reynolds number (Reo) of 8131 is the final temperature of flue gases higher than the experimental value. This situation is not serious, because the deviation is 3.39%, which could be compensated with a low security factor. Another good combination of models is the ESCOAeGnielinski, because their minimum precision is 96.61% (Reo ¼ 6348) and most of the predictions of flue gas cooling temperatures are lower than the experimental data. There
Fig. 5. Relationship between flue gas temperature and Reynolds number based on the outside bare tube.
E. Martinez et al. / Applied Thermal Engineering 30 (2010) 1470e1476
Fig. 6. Relationship between feedwater temperature and Reynolds number based on the outside bare tube.
is a value, at a Reynolds number (Reo) of 8131, at which final temperature is higher than the experimental data. The NireGnielinski model has the worst precision (94.79e99.67%) for the range of Reynolds numbers (Reo) from 6348 to 10,951. This precision is acceptable because the maximum deviation is 5.21% and all predictions are higher than the experimental values. Therefore, the NireGnielinski model could be used for the design of equipments without the use of a security factor. Finally, the comparative analysis of results and the experimental data show that the best predictions are obtained at a Reynolds number (Reo) of about 10,000, because at this flow regime pressure drop is close to 248.9 Pa. The final water temperature and its Reynolds number are shown in Fig. 6. The theoretical curves for all models have the same tendency and there is an inflection point (Reo ¼ 69,447) at which final temperature decreases due to the increase in mass flow. The inflection point of water corresponds to the gas point at a Reynolds number (Reo) of 10,438 and both are located under the same conditions. Therefore, the best equipment performance is at a Reynolds number (Reo) e in gas phase e of about 10,000. The results show that the best models are the KawaguchieGnielinski, because they have a precision of 99.3e100% for a Reynolds number (Reo) of 67,698e73,373. Thus, the maximum deviation of 0.7% could be compensated by a minimum-security factor. The WeiermaneGnielinski model has a precision of 98.89e99.84% with a Reynolds number (Reo) of 67,698e73,373. Most results are lower than the experimental values, but at a Reynolds number (Reo) of 68,443, the prediction is higher than the measurements. Therefore, the critical deviation is 0.72%, which could be solved by a low security factor. In the ESCOAeGnielinski model, all predictions are lower than the experimental data and the minimum precision is 98.41%, which represents a maximum deviation of 1.59% that could be considered a security factor. Thus, the equipment performance is guaranteed. The NireGnielinski model is appropriate because all the predictions are lower than the experimental data, which is the best situation. The apparent weakness of this combination of models is precision, which ranges between 97.6 and 99.17%, but the maximum deviation of the predictions is 2.4%, which is acceptable for industrial equipments.
5. Conclusions A comparative analysis of performance and experimental data of heat transfer and pressure drop for industrial HSFHE was conducted. Flue gas pressure drop shows the ESCOA [4] and Kawaguchi [6] models to have predictions lower than the experimental data for Reynolds numbers (Reo) over 10,000. This situation is not
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recommendable, because backpressure could appear, resulting in operational problems. Therefore, these models are not recommended for the design of heat recoveries. On the other hand, the Nir model [5] shows that all predictions are higher than the experimental data, which is the best situation since backpressure will be avoided. However, the curve has an exponential tendency for Reynolds numbers over 8000, and consequently the predictions have more deviations. Hence, this model is appropriated for a quick calculus. The best correlation for pressure drop is the Weierman model [2,3], because all predictions are higher than the experimental data and precision is over 89% for Reynolds numbers (Reo) upper to 10,000. Therefore, this model is recommended for the design of heat recoveries on an industrial scale. On the other hand, the results show that the best flow regime is at a Reynolds number (Reo) of about 10,000 with a length-width ratio (cross section area) around 2.5, because at this zone, pressure drop is lower than 249 Pa (1 in water column) [18] and, consequently, the heat recoveries do not affect the process. The heat transfer was analyzed for Overall Heat Transfer Coefficient and final temperatures of fluids (feedwater and flue gases). The Overall Heat Transfer Coefficient results show that the NireGnielinski model has the worst predictions, since precision ranges between 57.42 and 73.87%, and there is only one value of 95.71%. In spite of this situation, the results are reliable because temperature predictions are around 96%. The ESCOAeGnielinski model has a precision in U of 69.94e94.41%, but its temperature predictions are acceptable because precision is around 97%. In the case of the WeiermaneGnielinski model, it has better predictions than the previous models; with precisions between 83.8% and 97.66% in U. Fluid temperature predictions are better because their precision is around 98%. Finally, the KawaguchieGnielinski model has the best results, with precisions of 93.75e99.59% for Overall Heat Transfer Coefficient and there is only a single precision of 77.74%. In spite of that, these predictions are the best because the evaluation of temperatures has a precision of approximately 99%. So, the best model combination is the KawaguchieGnielinski, which is recommended for the heat transfer design of compact heat recoveries. However, the model of Weierman [2,3] should be considered if finned tube geometry and fluid conditions are outside the range of application of Kawaguchi model [6]. On the other hand, the results of all the models show an apparent discrepancy between Overall Heat Transfer Coefficient and fluid temperatures, because their precision is too different. However, there is a strong dependence of U with T, because a deviation of 1 C in predictions represents approximately 5% (WeiermaneGnielinski, ESCOAeGnielinski, and NireGnielinski) to 1% (KawaguchieGnielinski) deviation in Overall Heat Transfer Coefficient. Therefore, a detailed study focused on the outer finned tube is recommended, since flue gas heat transfer dominates the liquid phase. Acknowledgements We appreciate the support given to the research presented here by Consejo Nacional de Ciencia y Tecnologia (CONACYT), Universidad Nacional Autonoma de Mexico (Direccion General de Asuntos del Personal Academico, PAPIIT-IN111709-3), and Universidad Autonoma Metropolitana Azcapotzalco. On the other hand, we appreciate the information provided by Professor Holger Martin and Professor Erling Naess. References [1] Srbislav B. Genic, Branislav M. Jacimovic, Boris R. Latinovic, Research on air pressure drop in helically-finned tube heat exchangers. Applied Thermal Engineering 26 (2006) 478e485.
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