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Experimental and numerical analysis of a cross-flow closed wet cooling tower
Applied Thermal Engineering 61 (2013) 678e689
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental and numerical analysis of a cross-flow closed wet cooling tower Jing-Jing Jiang, Xiao-Hua Liu*, Yi Jiang Department of Building Science, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A cross-flow closed wet cooling tower (CWCT) is experimentally analyzed. Empirical correlations of the heat and mass transfer coefficients are obtained. Numerical model of the CWCT is established and validated by experimental data. Heat and mass transfer driving forces inside a cross-flow CWCT are more uniform. Performance of a cross-flow CWCT is better than parallel/counter-flow patterns.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 January 2013 Accepted 31 August 2013 Available online 10 September 2013
Closed wet cooling tower (CWCT) is an indirect-contact evaporative cooler, in which ambient air, spray water and process water function together. In this study, a cross-flow CWCT unit based on the plateefin heat exchanger was designed and tested under various conditions in an environmental chamber. The test results suggest that the heat and mass transfer coefficients and the cooling efficiency are remarkably affected by the temperature of the process water and the flow rates of the air, the spray water and the process water. Heat and mass transfer coefficients were correlated based on the sensitive parameters. Two-dimensional steady-state numerical model of the cross-flow CWCT was established and validated by the experimental data. The numerical analyses revealed that the cross-flow CWCT could breakthrough the structure limitation of the commonly parallel/counter-flow configuration and obtain more uniform driving forces, which is beneficial for the cooling performance. The flow pattern optimization of the CWCT shows that air and process water in the opposite direction, spray water and the other fluids in the cross direction is the best flow pattern, which is distinct from the general knowledge of the researches. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Closed wet cooling tower Experiment Numerical model Flow pattern Cross flow
1. Introduction Closed wet cooling tower (CWCT) has been adopted in a wide range of application fields [1], such as refrigeration, airconditioning, manufacturing, power generation, etc. CWCT is an indirect-contact evaporative cooler mostly based on tubular heat exchanger structure. Three fluids function together in the CWCT, which are ambient air and spray water flowing outside the tubes and process water running inside the serpentine tubes. The principle of CWCT can be split into evaporative heat and mass transfer process between the ambient air and the spray water, and heat transfer process between the spray water and the process water. As the fluid inside the tubes never contact the ambient air, the CWCT
* Corresponding author. Tel.: þ86 10 6277 3772; fax: þ86 10 6277 0544. E-mail address: [email protected] (X.-H. Liu). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.08.043
can be used to cool fluids other than water and prevent contamination of the airborne dirt and impurities. Furthermore, CWCT could operate as an air cooling tower by stopping spray water in severe cold days which makes it possible to run continuously yearround in hospitals, schools, data centers, etc. However, the cost of CWCT is often higher since tubular heat exchanger needs quantity of metallic materials [2]. Series of experiments have been conducted for the fundamental researches of the heat and mass transfer processes in CWCTs. Niitsu et al. [3] tested the performance of the plain and finned tubes, including the film heat transfer coefficient and airewater mass transfer coefficient. Experimental tests by Heyns and Kröger [4] showed the water-film heat transfer coefficient was a function of spray water temperature, spray water and air flow rates, while the airewater mass transfer coefficient was a function of air and spray water flow rates. Sarker et al. [5] assessed CWCTs with staggered arranged bare-type or finned tubes, from the perspectives of
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Fig. 1. The cross-flow CWCT unit: (a) the schematic diagram of the three fluids; and (b) the photo from the front view.
Fig. 2. The louver structure of the fin.
cooling capacity, wet-bulb efficiency and pressure drop. Experimental tests showed that the fin-tube CWCT had better thermal performance although the pressure drop was higher than that of the bare-tube one. Zheng et al. [6] investigated the thermal behavior of an oval tube CWCT under different operating conditions. The results showed that the oval tube had a better combined thermal-hydraulic performance. Some novel CWCTs consisting of indirect evaporative cooling stage and direct evaporative cooling
stage (or heat transfer stage) were proposed, constructed and tested by Xia et al. [2] and Heidarinejad et al. [7]. Besides the experimental researches, a number of theoretical and computational analyses have been conducted aiming to a more realistic description of the transport phenomena taking place inside a CWCT. Hasan and Sirén [8] presented a computational model to simulate the performance of the CWCT. The variation of the spray water temperature was taken into consideration and the saturation enthalpy was calculated from psychometric relations for moist air. The coefficients of mass transfer were derived from experimental data and then implemented in the computational model. Koschenz [9] presented an analytical model for a CWCT for use with chilled ceilings, assuming that the spray water temperature kept constant along the way and the constant temperature was equal to the outlet process water temperature. However, the accuracy levels of these assumptions were not quantified with respect to other approaches or relevant experimental works. Hasan and Gan [10] compared the cooling performances calculated by the computational model established by Hasan and the analytical models utilizing the assumptions raised by Koschenz. Gan and Riffat [11] conducted a CFD
Fig. 3. The schematic diagram of the testing configuration.
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Table 1 Accuracies of the measuring instruments. Parameter
Sensor
Accuracy
Air dry/wet bulb temperatures Air flow rate Spray water/process water temperatures Spray water flow rate Process water flow rate
T-type thermocouple Standard nozzle (GB14294) T-type thermocouple
0.2 [ C] 1 [%] 0.2 [ C]
Rotameter Water meter
1.5 [%] 3 [L/h]
method to predict the performance of CWCT according to the cooling capacity and the pressure drop. Plenty of works have been done by the researchers concerning experimental tests and theoretical analyses, which give a good description of the performance of the CWCT. Moreover, many novel designs of structures or components have been put forward and have already reformed the CWCT to a great extent. However, the flow pattern analysis of the CWCT has barely been involved in available literature. The majority of the flow pattern of the CWCT [3e6,8e16] is air flowing from the bottom to the top, while the process water inside the serpentine tubes and the spray water outside the tubes flowing in the opposite direction, which has been proved the best one-dimensional flow pattern of CWCT by Ren and Yang [17]. Little work [18,19] has been carried out on the cross-flow CWCT. The performance of a cross-flow CWCT, with a counter flow between the air and the process water and two cross flows between the air and the other two fluids, will be analyzed in present study. Experimental tests will be carried out to investigate the behavior and influencing factors of the CWCT. Numerical models of parallel/ counter-flow and cross-flow CWCTs will be established and validated to optimize the flow pattern of the CWCT. 2. Experimental test of the CWCT unit
Fig. 2, to strengthen the heat and mass transfer performance and the wettability of the fins by disturbing the boundary layer of the spray water. The size of the unit is 570 mm (H, the spray water flow direction) 310 mm (W, width) 180 mm (L, the air flow direction). Its fin thickness is 0.127 mm, and the distance between the fins is 2.2 mm. The inner and external diameters of the tubes are 9.42 mm and 10.02 mm, respectively. The tube bundle consists of 8 rows of steel tubes. The tubes are 0.31 m long and are arranged in a triangular pattern at a transversal pitch of 25.4 mm. There are 20 tubes per tube row. The external surface of the whole unit is 24.336 m2 (Fm), 0.784 m2 of which is the external surface of the tubes and 23.552 m2 of which is the surface of the fins. The specific surface area of the CWCT unit is 790 m2/m3. 2.2. The CWCT testing configuration The tests for assessing the performance of the CWCT unit were performed in an environmental chamber. The system configuration can realize wide range of air, spray water and process water states, as displayed in Fig. 3. The cooling coil, heater A and humidifier can regulate the air inlet temperature and humidity independently. The variable frequency fan can control the volume flow rate of the inlet air. Also, the temperature and flow rate of the process water can be controlled by Heater B and the water valves. The environmental chamber provided the measuring instruments for the flow rates and inlet/outlet temperatures of the air, the spray water and the process water. As listed in Table 1, the flow rate of the air ṁa was measured by standard nozzles (GB14294) with the accuracy of 1%. The flow rate of the spray water ṁs was measured by a rotameter with the range from 60 to 600 L/h and the accuracy of 1.5%. The flow rate of the process water ṁw was measured by water meter with the accuracy of 3 L/h. The temperatures of the three fluids were measured by T-type thermocouples with the accuracy of 0.2 C.
2.1. Description of the cross-flow CWCT unit 2.3. Verification of the experimental data Fig. 1(a) indicates the flow directions of the three fluids in the cross-flow CWCT unit, which are spray water flowing from top to bottom, ambient air flowing from front to back through the fins and process water flowing in the serpentine tubes from back to the front. In other words, the ambient air and process water are in counter flow and spray water is in cross flow with the other two fluids. As shown in Fig. 1(b), the CWCT unit employs fin-tube structure to expand the heat and mass transfer area. The tubes and fins of the unit are made of stainless steel to ensure perfect heat transfer between the spray water and the process water. Furthermore, there are discontinuous louvers on the fins, presented in
In order to study the CWCT unit, a series of experiments were conducted which intended for finding out the effects of the inlet parameters on cooling performance. The main parameters are the flow rate of the three fluids and the inlet temperature of the process water etc. Variable condition analyses were conducted with 11 operating conditions and 46 sets of data. Each set of data was recorded under approximately steady states, which required all the temperature points fluctuated within 0.2 C for longer than 20 min. The typical experiment data is listed in Table 2. To verify the reliability of the experiment data, energy balance of the air, spray
Table 2 The experimental data of the CWCT test. No.
Inlet parameters
1 2 3 4 5 6 7 8 9 10 11
Outlet parameters
ε
Qc kW
0.36 0.35 0.37 0.28 0.32 0.36 0.40 0.45 0.34 0.38 0.40
4.94 5.65 7.26 3.31 4.31 3.49 4.10 3.39 3.22 3.58 3.77
ta,in C
twb,in C
ts,in C
tw,in C
ṁa kg/s
ṁs kg/s
ṁw kg/s
ta,out C
twb,out C
ts,out C
tw,out C
24.8 25.3 27.0 27.2 26.7 27.3 25.1 25.1 26.8 26.9 27.0
20.1 20.9 22.0 21.1 20.6 22.9 20.8 21.1 22.6 22.8 22.6
24.7 25.8 27.9 26.2 25.6 26.1 24.8 24.6 26.2 25.9 25.8
30.3 32.9 36.6 30.2 30.8 30.2 30.4 30.2 30.2 30.2 29.9
0.35 0.35 0.35 0.19 0.27 0.35 0.35 0.35 0.35 0.35 0.35
0.13 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.06 0.09 0.13
0.32 0.32 0.32 0.32 0.32 0.31 0.26 0.20 0.29 0.30 0.30
24.2 25.3 27.3 26.0 25.2 25.6 24.4 24.2 25.1 25.3 25.3
23.9 25.0 27.0 25.7 24.8 25.2 24.0 23.8 24.6 25.0 25.0
24.4 25.8 27.8 26.0 25.3 25.8 24.5 24.3 25.6 25.5 25.4
26.7 28.8 31.2 27.7 27.6 27.5 26.6 26.1 27.6 27.4 27.0
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Gained heat of the air (kW)
8
3. Experimental results and influencing factors
7
3.1. Effect of the air flow rate
+ 20
6 5 4
-20 %
3 2 1 0
681
0
1 2 3 4 5 6 7 Heat loss of process/spray water (kW)
8
Fig. 4. Energy balance of the CWCT test.
water and process water was adopted. As shown in Fig. 4, the unbalance ratios of the heat gained by the ambient air and the heat lost by the process water and the spray water are within 20%. The average absolute unbalance ratio is 7.4%, which means the data are reliable. To better describe the cooling processes, some indexes are introduced, seen in Eqs. (1) and (2). The wet-bulb cooling efficiency ε [5,13,16] illustrates the distance between the outlet process water temperature (tw,out) and the ambient wet bulb temperature (twb,in), which is the limit of the outlet process water temperature. The cooling capacity Qc [5,12,15] presents the cooling capacity of the CWCT unit.
In the environmental chamber shown in Fig. 3, the flow rate of the ambient air is easily conditioned and controlled by regulating the rotate speed of the fan. The flow rate of the air was at the lowest rate of 0.19 kg/s and up to the maximum of 0.35 kg/s Fig. 5 displays that mass transfer coefficient between the spray water and the air (Km) increased greatly by increasing the air flow rate. While the heat transfer coefficient between the spray water and the process water (Kh) was generally constant since the increase of the air flow rate had little relationship with the heat transfer between the spray water and the process water. As a result of the strengthening of the heat and mass transfer performance between the spray water and the air, ε and Qc increased with the increase of ṁa. Thus, increasing air flow rate is a good way to improve the performance of the CWCT. However, the air flow rate is not the bigger the better if taking the fan power consumption into consideration. There is an optimal value of air flow rate depending on the balance of the CWCT performance and the fan power consumption. Uncertainty analyses for the experimental results, based on the accuracies of the measuring instruments introduced in Section 2.2, were conducted in this study using the method proposed by Kline and McClintock [20] according to the following expression (Eq. (3)):
Dy ¼
vf vx1
2
ðDx1 Þ2 þ
vf vx2
2
ðDx2 Þ2 / þ
vf vxn
2
ðDxn Þ2
1=2 (3)
ε ¼
tw;in tw;out tw;in ta;wb
(1)
_ w tw;in tw;out Qc ¼ cp;w m
(2)
The uncertainties of ε, Qc, Km, and Kh were calculated and expressed in Fig. 5 in the way of error bars. Results show that the Ttype thermocouples are the main sources of errors. Taking Km as an example, the uncertainties of the air wet-bulb temperature and spray water temperature account for 81.3% and 16.6% of the total uncertainty, respectively, while that of the air mass flow rate only
Fig. 5. Effects of the air flow rate (ṁa) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
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Fig. 6. Effects of the spray water flow rate (ṁs) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
accounts for 0.8%. Thus improving the temperature measurement accuracy is the key point of improving the accuracy of the test. 3.2. Effect of the spray water flow rate The flow rate of the spray water was regulated by changing the valves in the pipelines. The flow rate of the spray water was from
0.06 kg/s to 0.13 kg/s. When the flow rate of the spray water increased, wetting degree of the CWCT was improved and heat and mass transfer area was expanded to a certain extent. Also, the increase of the spray water flow rate would strengthen the heat transfer process between the spray water and the process water, so as to take away more heat from the process water. As a result, ε, Qc, and Kh increased, as shown in Fig. 6. On the other hand, the
Fig. 7. Effects of the process water flow rate (ṁw) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
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Fig. 8. Effects of the process water temperature (tw,in) on the CWCT: (a) cooling capacity; (b) spray water inlet temperature; (c) Km; and (d) Kh.
(b)
(a)
Fig. 9. Calculated results of Eqs. (4) and (5): (a) Kh; and (b) Km.
Table 3 Comparison of the experimental parameters in literature [4,6,15,16]. Source
Flow pattern
Ga (kg/m2s)
Gs (kg/m2s)
Gw (kg/m2s)
Kma (kg/m3s)
Kha (kW/m3 K)
a (m2/m3)
ε
Correlations
Heyns [4]
Parallel/counter
0.7e3.6
1.7e4.5
-
0.5e3.2
42.0e67.2
24
e
Zheng [6]
Parallel/counter
2.5e5.0
1.2e3.2
2.8e5.3
2.7e5.0
23.9e60.4
31
0.11e0.19
Shim [15] Facão [16]
Parallel/counter Parallel/counter
1.2e4.2 0.7e2.4
1.1e3.3 0.3e1.9
0.9e4.8 0.6e1.1
6.6e21.5 1.6e4.3
18.2 31.4 5.5e17.5
33 25
e 0.2e0.65
Present study
Cross
1.3e2.4
1.1e2.3
1.1e1.8
10.3e19.0
30.8e45.0
790
0.28e0.46
0.35 0.3 ts Kh ¼ 470G0.1 a Gs Km ¼ 0.038G0.73 G0.2 a s Kh ¼ 350.3(1 þ 0.0169ts)G0.59 G1/3 a s 0.977 Km ¼ 0.034Ga e Kh ¼ 700.3(ṁs/1.39)0.6584 Km ¼ 0.1703(ṁa/1.7)0.8099 0.547 Kh ¼ 31.79Gs0.238Gw Km ¼ 0.00154t0.471 G0.694 G0.512 w a s
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(b)
(a)
Fig. 10. Comparison with literature [4,6]: (a) Kha; and (b) Kma.
improvement of the spray water flow rate enhanced heat and mass transfer between the ambient air and the spray water, which resulted in the growth of Km.
by the air and process water states, it rose with the growth of the process water temperature, as shown in Fig. 8(b). 3.5. Comparison with experimental results from previous studies
3.3. Effect of the process water flow rate The flow rate of the process water is also a key parameter influencing the CWCT performance. It was from 0.20 kg/s to 0.32 kg/s in this set of experiments. Apparently, the rise of the process water flow rate promoted the heat and mass transfer between the spray water and the process water, therefore Kh increased. Thus process water could release more heat to the spray water, which led to the increase of Qc, as shown in Fig. 7(b). Since the influence of ṁw to the outlet temperature of the process water was more remarkable than that of Kh, the cooling effect of the process water per unit mass was definitely worsened, though the total cooling capacity was improved. In this way, the outlet temperature of the process water increased and ε dropped. Since the process water barely touched the ambient air, Km between the air and the spray water scarcely changed. 3.4. Effect of the process water temperature This set of experiment was meant to study the performance of the CWCT at different process water temperatures. The inlet temperature of the process water was from 30.1 C to 36.6 C. The results showed that Qc and Km increased with the growth of the process water temperature, seen in Fig. 8(a) and (c), due to the increase of the heat and mass transfer driving forces between the three fluids. Since the temperature of the spray water was decided
Fig. 11. Control volume schematic of the cross-flow CWCT.
From the sensitivity analyses we could see that Kh is mainly influenced by the flow rates of the spray water and the process water, while Km is dominated by the flow rates of the air and spray water and the inlet temperature of the process water. Therefore, for the specific geometry of the tower, the correlation equations for Kh and Km could be presented as follows:
Kh ¼ 31:79G0:238 G0:547 s w
(4)
0:471 0:694 0:512 Km ¼ 0:00154tw;in Ga Gs
(5)
where Ga is the air velocity in the minimum flow area, Gs ¼ G/do, Gw ¼ ṁw/(H$L) is the process water flow rate per flow area (1.3 < Ga < 2.4 kg/m2 s; 1.1 < Gs < 2.3 kg/m2 s; 1.1 < Gw < 1.8 kg/ m2 s; 30.1 < Tw,in<36.6 C). Fig. 9 compares the calculated results based on the correlation equations and the experimental data. Since good agreement is obtained, the correlation equations can be used to predict the coefficients. Table 3 compares the experimental parameters of previous studies in literature and present study. The flow pattern of parallel/ counter can refer to Fig. 15(a) and the flow pattern of cross can refer to Fig. 11. As listed in Table 3, the most popular flow pattern is parallel/counter-flow, while the most common structure is planetube bundles with specific surface area of around 25e35 m2/m3. In present study, the CWCT is cross-flow with a considerable specific surface area of 790 m2/m3. The correlations of Heyns et al. [4] shows that Kh has positive correlations with the air and the spray water flow rates and the spray water temperature, while Km has positive correlations with the air and the spray water flow rates. Km is only influenced by the air flow rate in the studies of Zheng et al. [6] and Facão et al. [16]. In present study, similar correlations of Kh and Km were obtained. There are some modifications about the selection of the influencing factors. Firstly, tw,in, instead of ts, is seen an influencing factor because it’s the source of the heat and mass transfer process while ts is only an equilibrium parameter of the air and process water states. Secondly, the process flow rate Gw is adopted to describe the correlation of Kh since the heat transfer process actually happens between the spray water and the process water. In Fig. 10, Eqs. (4) and (5) are compared to the correlations given by Heyns et al. [4] and Zheng et al. [6]. Compared to the bare-tube parallel/counter-flow CWCT, the cross-flow CWCT with plateefin tube structure studied in this paper has much larger volume mass
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Fig. 12. Comparison of the calculated values and the experimental results of the cross-flow CWCT: (a) the variance of the air humidity ratio; and (b) the variance of the temperature of the process water.
transfer coefficient Kma, due to that the fin-tube structure tremendously extends the contact area, which is exactly the restriction point of the heat and mass transfer between the air and the spray water. In contract, the performance improvement of the fin-tube structure for waterewater heat transfer process is insignificant. That’s why the volume heat transfer coefficient Kha is no bigger than the others. 4. Numerical model of the cross-flow CWCT 4.1. Theoretical model Two-dimensional steady-state model of the cross-flow CWCT, in which air and process water flowing in the opposite direction, spray water flowing in the cross direction with the other two fluids, seen in Fig. 11, will be illustrated in this section. In the CWCT, process water releases heat to the metal finned tubes while the tubes are cooled by the spray water. At the same time, heat and mass transfer takes place between the spray water and the air. The main assumptions for the numerical model are presented as follows [8,13,17]: 1) Heat and mass transfer processes are at steady state; 2) The heat and mass exchange between the CWCT unit and the surroundings is negligible; 3) The specific heat of the fluids are assumed to be constant; 4) The spray water film uniformly covers all the wall of the tubes and fins, so that Fh equals to Fm and the heat exchange between the air and process water is negligible; and 5) The flow of the process water and the air is approximately counter flow. Define the air flow direction as z axis and the spray water flow direction as x axis. The energy balance equation for the three fluids is:
_ s hs Þ _ a vha 1 vðm _ w vtw m m cp;w þ ¼ 0 L vx H vz H vz
(6)
Mass conversion equation of the spray water and the air is given
_s _ a vda 1 vm m þ ¼ 0 L vx H vz
(7)
Heat transfer between the spray water and the process water driven by the temperature difference between them is shown as:
Table 4 Simulated condition of the cross-flow CWCT. ta,in C da,in kg/kg tw,in C ṁa kg/s ṁs kg/s ṁw kg/s KmFm kg/s KhFh kW/K 0.0136
30.3
(8)
As well known, there is a thin film of saturated air at the interface between the spray water and the air. The temperature of the saturated air is close to that of the spray water. The humidity ratio of the saturated air is also called the equivalent humidity ratio of the spray water, which is de. Heat transfer driven by the temperature difference of the saturated air film and the air flow and mass transfer driven by the water vapor partial pressure difference between the two streams take place simultaneously. Thus the mass transfer equation and the energy balance equation for the air flow can be expressed by the following equations separately:
vda Km Fm ¼ ðde da Þ _ aL vz m
(9)
vha K 0 Fm vda ¼ h ðt ta Þ þ r _ aL s vz vz m
(10)
The Lewis factor or Lewis relation Lef could be defined to indicate the relation between the heat and mass transfer in an evaporative process [21e23]. The definition of Lef is as follows:
Lef ¼
K 0h Km cp;m
(11)
Substitute Eq. (11) into Eq. (10):
i vha Km Fm h ¼ Lef $cp;a ðts ta Þ þ rðde da Þ _ aL vz m As the enthalpy of the air can be expressed ha ¼ cp;m ta þ r$da ; Eq. (12) can be transformed into:
vha Km Fm 1 ¼ $Lef ðhe ha Þ þ r 1 ðde da Þ _ aL Lef vz m
(12) as
(13)
Thus we get all the governing equations of the cross-flow CWCT. The boundary conditions are shown as follows:
by:
27.2
vtw Kh Fh ðt ts Þ ¼ _ wL w vz cp;w m
0.19
0.12
0.32
0.365
1.17
ta ¼ ta;in ;
da ¼ da;in ;
ha ¼ ha;in ;
z ¼ 0
(14)
ts jx¼0 ¼ ts jx¼H
(15)
tw ¼ tw;in ;
(16)
z ¼ L
By discretizing the governing equations, the heat and mass transfer process could be numerically solved. When solving the model, Lef could be equal to 1 [6,8,14]. The model of the cross-flow CWCT was validated by the experimental results described in
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Fig. 13. Simulated field distribution of the cross-flow CWCT: (a) the air wet-bulb temperature; (b) the spray water temperature; (c) the process water temperature; (d) the temperature difference between the spray water and the process water; and (e) the temperature difference between the spray water and the air (wet-bulb).
Section 3. As shown in Fig. 12, the maximal differences between the calculated results and the experimental values are within 8.0%, and the average absolute differences are 3.0% and 4.0% for the variance of the air humidity ratio and the process water temperature respectively. On the whole, the calculated parameters by the numerical model agree well with the experimental results, the model could be used to analyze the heat and mass transfer performance of the CWCT unit in the following content. 4.2. Typical simulation result of cross-flow CWCT Since the distribution parameters of the cross-flow CWCT are two-dimensional, it is difficult to describe it through experimental
results of limited measurement points. Therefore, numerical modeling results were introduced to investigate the performance of the CWCT. The boundary conditions from the experimental results are displayed in Table 4. As seen in Fig. 13, the wet-bulb temperature of the air increases in the air flow direction, while the temperature of the process water decreases in the opposite direction. Heat is transferred from the process water to the air. Without the circulation of the spray water, the temperature distributions of the air and the process water should be one-dimensional and the temperature gradients of the two fluids along z should be consistent. Once the spray water is brought in, the consistency will be disturbed. To better explain the heat and mass transfer process of crossflow CWCT, we could divide it into enough control volumes along
Fig. 14. Simulated temperatures of the x sections: (a) x ¼ 0.05H; (b) x ¼ 0.5H; and (c) x ¼ 0.95H.
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Fig. 15. (a) Parallel/counter-flow CWCT configuration; and (b) simulated temperatures.
z axis and assume that the heat and mass transfer between each two control volumes could be ignored, which means the performance of the spray water is only affected by the air and the process water inside the volume. If the inlet temperature of the spray water is lower than those of the process water and the air (wet-bulb), spray water will absorb heat from both the fluids when falling along the x axis. As a result, the spray water temperature will go up until it gains the same heat from the process water as the heat released to the air. Vice versa, when the inlet temperature of the spray water is higher than those of the other fluids, spray water will discharge heat to the air and the process water until it transfers the same quantity of heat from the process water to the air. In this way, there is an equilibrium temperature of spray water in each control volume, which is somewhere between the temperatures of the air and the process water, determined by the heat and mass transfer ability of the CWCT. As shown in Fig. 13(b), on the bottom of the CWCT, the spray water temperature barely changes along the way, which means it already reaches the equilibrium temperature. Fig. 14 shows the temperatures of the three fluids at the sections of x ¼ 0.05H, x ¼ 0.5H and x ¼ 0.95H, which represent the states of the spray water from the inlet to the outlet. It can be observed from Fig. 14(c) that the equilibrium temperature rises from the air inlet to the process water inlet. Since there is only one sink at the outlet, spray water of different control volumes with different
Fig. 16. Flow pattern optimization of the CWCT.
temperatures must be mixed to the medium temperature before going to the inlet. Because of the mixture, the heat and mass transfer driving forces at the inlet are not uniform, shown in Fig. 14(a). Fortunately, the spray water of the cross-flow CWCT has the self-adjust ability to achieve proper equilibrium temperature. As the simulated mass flow rate of spray water is relatively small in this article, according to Table 4, its state is easy to be influenced by the other two fluids and it reaches the equilibrium temperature very quickly (at about x ¼ 0.2H). When x ¼ 0.5H, shown in Fig. 14(b), the three fluids have already reached the equilibrium states and had rather uniform heat and mass transfer driving forces. On the whole, the heat and mass transfer driving forces are relatively uniform in the cross-flow CWCT, especially in the lower part. 5. Effect of flow pattern on the performance of the CWCT For two-flow heat and mass transfer system, scholars have agreed that counter flow achieves the best performance, followed by the cross flow and the parallel flow. By analogy, the recommended flow pattern in the CWCT is two counter flows and one parallel flow between the three fluids, achieving as many counter flows as possible and abandoning the mediocre cross flow. Ren and Yang [17] studied all the parallel/counter-flow patterns of the CWCT, finding that the flow pattern shown in Fig. 15(a) achieves the best cooling performance. Following this conclusion, we simulated the performance of the model to test the analogy. The boundary conditions are listed in Table 4. For the parallel/counter-flow CWCT, the distribution parameters are one-dimensional. As shown in Fig. 15(b), the process water is cooled along the way while the air is continuously heated. Since the inlet and outlet temperatures of the spray water should be the same, the one-dimensional spray water temperature could not keep pace with the temperature gradient along x. As a result, the heat transfer driving force between the process water and the spray water is not uniform. Neither is the heat and mass transfer driving force between the air and the spray water. This phenomenon is also stated by many other researchers [4,10]. Unfortunately, the uneven driving forces could not be avoided by improving the heat and mass transfer area or regulating the flow ratios of the three fluids. In other words, the one-dimensional parallel/counter-flow CWCT has the structural limitation. As mentioned in Section 4.2, the crossflow CWCT could achieve uniform heat and mass transfer driving forces in the most part of the module. In this way, the cross-flow CWCT turns up the ideal flow pattern, although the two-flow cross-flow heat and mass transfer performance is not the best.
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The cooling capacity comparison of the parallel/counter-flow and cross-flow CWCTs under different KmFm are shown in Fig. 16. The flow rates of the air, the spray water and the process water are all 0.5 kg/s, while the other boundary conditions are presented in Fig. 16. As shown in Fig. 16, the cross-flow CWCT would always have a larger cooling capacity Qc, and the superiority will be amplified when the heat and mass transfer coefficient is increased, which means the cross-flow CWCT has better cooling performance than the commonly used parallel/counter-flow CWCT. 6. Conclusion A cross-flow CWCT based on the fin-tube structure was designed and tested in present study. The flow arrangement of the air and the process water was counter flow, while that of the air and the spray water was cross flow. Experimental tests were conducted to investigate the cooling performance and the influencing factors on the basis of a good energy balance discrepancy. The main conclusions are: 1) Effect of the process water temperature and flow rates of the air, spray water and process water on the cooling capacity, wetbulb efficiency, heat and mass transfer coefficients were studied. Empirical correlations of the heat and mass transfer coefficients based on the influencing factors were obtained. 2) Compared to the bare-tube structure in literature, the fin-tube structure tremendously extends the contacting area between the air and the spray water, thus improves the heat and mass transfer coefficient. While for the heat transfer coefficient between the spray water and the process water, the fin-tube structure has little impact. 3) Two-dimensional steady-state numerical model of the crossflow CWCT was built and validated by the experimental data. The deviation between the model and the experimental data was less than 8%, which ensures the accuracy of the model. 4) The numerical results show that the spray water temperature of the cross-flow CWCT would automatically form a gradient in the air/process water flow direction to match the temperature variances of the air and the process water. As a result, the heat and mass transfer driving forces of the cross-flow CWCT are fairly uniform, which is beneficial for the behavior of the CWCT. 5) The flow pattern optimization of the CWCT shows that the cooling performance of the cross-flow CWCT is better than that of the commonly studied parallel/counter-flow CWCT due to more uniform driving forces. The superiority will be amplified when heat and mass transfer coefficients are increased. Acknowledgements The research described in this paper was supported by National Natural Science Foundation of China (No. 51138005) and the foundation for the author of National Excellent Doctoral Dissertation of China (No. 201049). Nomenclature a cp d do Fh Fm G H h
specific surface area (m2/m3) specific heat capacity (kJ/kg C) humidity ratio (g/kg) external diameter of the tube (m) heat transfer area (m2) mass transfer area (m2) mass flow rate per flow area (kg/m2s) height of the CWCT unit (m) enthalpy (kJ/kg)
Kh Kh0 Km L Lef _ m Qc r t W
heat transfer coefficient between spray water and process water (kW/m2 K) heat transfer coefficient between spray water and air (kW/m2 K) mass transfer coefficient between air and spray water (kg/ m2 s) thickness of the CWCT unit (m) Lewis factor (dimensionless) mass flow rate (kg/s) cooling capacity (kW) vaporization latent heat (kJ/kg) temperature ( C) width of the CWCT unit (m)
Greek symbols G spray water flow per unit breadth (kg/m s) D change of or difference between parameters ε wet-bulb cooling efficiency Subscripts a air e air in equilibrium with spray water in inlet m moist air out outlet s spray water w process water wb wet-bulb References [1] M. Lemouari, M. Boumaza, A. Kaabi, Experimental analysis of heat and mass transfer phenomena in a direct contact evaporative cooling tower, Energy Convers. Manage. 50 (2009) 1610e1617. [2] Z.Z. Xia, C.J. Chen, R.Z. Wang, Numerical simulation of a closed wet cooling tower with novel design, Int. J. Heat Mass Transf. 54 (2011) 2367e2374. [3] Y. Niitsu, K. Naito, T. Anazai, Studies on characteristics and design procedure of evaporative coolers, J. SHASE. Jpn. 43 (7) (1969) 581e590. [4] J.A. Heyns, D.G. Kröger, Experimental investigation into the thermal-flow performance characteristics of an evaporative cooler, Appl. Therm. Eng. 30 (2010) 492e498. [5] M.M.A. Sarker, G.J. Shim, H.S. Lee, C.G. Moon, J.I. Yoon, Enhancement of cooling capacity in a hybrid closed circuit cooling tower, Appl. Therm. Eng. 29 (2009) 3328e3333. [6] W.Y. Zheng, D.S. Zhu, J. Song, L.D. Zeng, H.J. Zhou, Experimental and computational analysis of thermal performance of the oval tube closed wet cooling tower, Appl. Therm. Eng. 35 (2012) 233e239. [7] G. Heidarinejad, M. Bozorgmehr, S. Dlfani, J. Esmaeelian, Experimental investigation of two-stage indirect/direct evaporative cooling system in various climatic conditions, Build. Environ. 44 (2009) 2073e2079. [8] A. Hasan, K. Sirén, Theoretical and computational analysis of closed wet cooling tower and its applications in cooling of buildings, Energy Build. 34 (5) (2002) 477e486. [9] M. Koschenz, Model for closed circuit evaporative cooling tower, in: Proceedings of the 4th International Conference, International Building Performance Simulation Association, Madison, Wisconsin, USA, 1995. [10] A. Hasan, G. Gan, Simplification of analytical models and incorporation with CFD for the performance predication of closed-wet cooling towers, Int. J. Energy Res. 26 (2002) 1161e1174. [11] G. Gan, S.B. Riffat, Numerical simulation of closed wet cooling towers for chilled ceiling systems, Appl. Therm. Eng. 19 (1999) 1279e1296. [12] S.Y. Yoo, J.H. Kim, K.H. Han, Thermal performance analysis of heat exchanger for closed wet cooling tower using heat and mass transfer analogy, J. Mech. Sci. Technol. 24 (4) (2010) 893e898. [13] P. Stabat, D. Marchio, Simplified model for indirect-contact evaporative cooling-tower behavior, Appl. Energy 78 (2004) 433e451. [14] V.D. Papaefthimiou, E.D. Rogdakis, I.P. Koronaki, T.C. Zannis, Thermodynamic study of the effects of ambient conditions on the thermal performance characteristics of a closed wet cooling tower, Appl. Therm. Eng. 33e34 (2012) 199e207. [15] G.J. Shim, M.M.A. Sarker, C.G. Moon, H.S. Lee, J.I. Yoon, Performance characteristics of a closed-circuit cooling tower with multiple paths, Heat Transfer Eng. 31 (12) (2010) 992e997. [16] J. Facão, A.C. Oliveira, Thermal behavior of closed wet cooling towers for use with chilled ceilings, Appl. Therm. Eng. 20 (2000) 1225e1236.
J.-J. Jiang et al. / Applied Thermal Engineering 61 (2013) 678e689 [17] C.Q. Ren, H.X. Yang, An analytical model for the heat and mass transfer processes in indirect evaporative cooling with parallel/counter flow configurations, Int. J. Heat Mass Transf. 49 (2006) 617e627. [18] J. Yan, N. Liu, X.P. Ouyang, L.X. Zhang, H. Li, Experimental research on crossclosed cooling tower, Fluid Machinery 37 (6) (2009) 53e56 (in Chinese). [19] C.H. Zhan, X.D. Zhao, Z.Y. Duan, S.B. Riffat, Numerical study on indirect evaporative cooling performance comparison between counterflow and crossflow heat exchangers, Int. J. Low-Carbon Technol. 6 (2011) 100e106. [20] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 78 (1953) 3e8.
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[21] P.F. Li, Y.Y. Li, J.E. Seem, Modelica-based dynamic modeling of a chilled-water cooling coil, HVAC&R Res. 16 (1) (2010) 35e38. [22] T. Kusuda, Humidity and Moisture: Measurement and Control in Science and Industry, Calculation of the Temperature of a Flat-plate Wet Surface under Adiabatic Conditions with Respect to the Lewis Relation, Reinhold Publishing, New York, 1965. [23] J.C. Kloppers, D.G. Kröger, The Lewis factor and its influence on the performance prediction of wet-cooling towers, Int. J. Therm. Sci. 44 (2005) 879e884.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental and numerical analysis of a cross-flow closed wet cooling tower Jing-Jing Jiang, Xiao-Hua Liu*, Yi Jiang Department of Building Science, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A cross-flow closed wet cooling tower (CWCT) is experimentally analyzed. Empirical correlations of the heat and mass transfer coefficients are obtained. Numerical model of the CWCT is established and validated by experimental data. Heat and mass transfer driving forces inside a cross-flow CWCT are more uniform. Performance of a cross-flow CWCT is better than parallel/counter-flow patterns.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 January 2013 Accepted 31 August 2013 Available online 10 September 2013
Closed wet cooling tower (CWCT) is an indirect-contact evaporative cooler, in which ambient air, spray water and process water function together. In this study, a cross-flow CWCT unit based on the plateefin heat exchanger was designed and tested under various conditions in an environmental chamber. The test results suggest that the heat and mass transfer coefficients and the cooling efficiency are remarkably affected by the temperature of the process water and the flow rates of the air, the spray water and the process water. Heat and mass transfer coefficients were correlated based on the sensitive parameters. Two-dimensional steady-state numerical model of the cross-flow CWCT was established and validated by the experimental data. The numerical analyses revealed that the cross-flow CWCT could breakthrough the structure limitation of the commonly parallel/counter-flow configuration and obtain more uniform driving forces, which is beneficial for the cooling performance. The flow pattern optimization of the CWCT shows that air and process water in the opposite direction, spray water and the other fluids in the cross direction is the best flow pattern, which is distinct from the general knowledge of the researches. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Closed wet cooling tower Experiment Numerical model Flow pattern Cross flow
1. Introduction Closed wet cooling tower (CWCT) has been adopted in a wide range of application fields [1], such as refrigeration, airconditioning, manufacturing, power generation, etc. CWCT is an indirect-contact evaporative cooler mostly based on tubular heat exchanger structure. Three fluids function together in the CWCT, which are ambient air and spray water flowing outside the tubes and process water running inside the serpentine tubes. The principle of CWCT can be split into evaporative heat and mass transfer process between the ambient air and the spray water, and heat transfer process between the spray water and the process water. As the fluid inside the tubes never contact the ambient air, the CWCT
* Corresponding author. Tel.: þ86 10 6277 3772; fax: þ86 10 6277 0544. E-mail address: [email protected] (X.-H. Liu). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.08.043
can be used to cool fluids other than water and prevent contamination of the airborne dirt and impurities. Furthermore, CWCT could operate as an air cooling tower by stopping spray water in severe cold days which makes it possible to run continuously yearround in hospitals, schools, data centers, etc. However, the cost of CWCT is often higher since tubular heat exchanger needs quantity of metallic materials [2]. Series of experiments have been conducted for the fundamental researches of the heat and mass transfer processes in CWCTs. Niitsu et al. [3] tested the performance of the plain and finned tubes, including the film heat transfer coefficient and airewater mass transfer coefficient. Experimental tests by Heyns and Kröger [4] showed the water-film heat transfer coefficient was a function of spray water temperature, spray water and air flow rates, while the airewater mass transfer coefficient was a function of air and spray water flow rates. Sarker et al. [5] assessed CWCTs with staggered arranged bare-type or finned tubes, from the perspectives of
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679
Fig. 1. The cross-flow CWCT unit: (a) the schematic diagram of the three fluids; and (b) the photo from the front view.
Fig. 2. The louver structure of the fin.
cooling capacity, wet-bulb efficiency and pressure drop. Experimental tests showed that the fin-tube CWCT had better thermal performance although the pressure drop was higher than that of the bare-tube one. Zheng et al. [6] investigated the thermal behavior of an oval tube CWCT under different operating conditions. The results showed that the oval tube had a better combined thermal-hydraulic performance. Some novel CWCTs consisting of indirect evaporative cooling stage and direct evaporative cooling
stage (or heat transfer stage) were proposed, constructed and tested by Xia et al. [2] and Heidarinejad et al. [7]. Besides the experimental researches, a number of theoretical and computational analyses have been conducted aiming to a more realistic description of the transport phenomena taking place inside a CWCT. Hasan and Sirén [8] presented a computational model to simulate the performance of the CWCT. The variation of the spray water temperature was taken into consideration and the saturation enthalpy was calculated from psychometric relations for moist air. The coefficients of mass transfer were derived from experimental data and then implemented in the computational model. Koschenz [9] presented an analytical model for a CWCT for use with chilled ceilings, assuming that the spray water temperature kept constant along the way and the constant temperature was equal to the outlet process water temperature. However, the accuracy levels of these assumptions were not quantified with respect to other approaches or relevant experimental works. Hasan and Gan [10] compared the cooling performances calculated by the computational model established by Hasan and the analytical models utilizing the assumptions raised by Koschenz. Gan and Riffat [11] conducted a CFD
Fig. 3. The schematic diagram of the testing configuration.
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Table 1 Accuracies of the measuring instruments. Parameter
Sensor
Accuracy
Air dry/wet bulb temperatures Air flow rate Spray water/process water temperatures Spray water flow rate Process water flow rate
T-type thermocouple Standard nozzle (GB14294) T-type thermocouple
0.2 [ C] 1 [%] 0.2 [ C]
Rotameter Water meter
1.5 [%] 3 [L/h]
method to predict the performance of CWCT according to the cooling capacity and the pressure drop. Plenty of works have been done by the researchers concerning experimental tests and theoretical analyses, which give a good description of the performance of the CWCT. Moreover, many novel designs of structures or components have been put forward and have already reformed the CWCT to a great extent. However, the flow pattern analysis of the CWCT has barely been involved in available literature. The majority of the flow pattern of the CWCT [3e6,8e16] is air flowing from the bottom to the top, while the process water inside the serpentine tubes and the spray water outside the tubes flowing in the opposite direction, which has been proved the best one-dimensional flow pattern of CWCT by Ren and Yang [17]. Little work [18,19] has been carried out on the cross-flow CWCT. The performance of a cross-flow CWCT, with a counter flow between the air and the process water and two cross flows between the air and the other two fluids, will be analyzed in present study. Experimental tests will be carried out to investigate the behavior and influencing factors of the CWCT. Numerical models of parallel/ counter-flow and cross-flow CWCTs will be established and validated to optimize the flow pattern of the CWCT. 2. Experimental test of the CWCT unit
Fig. 2, to strengthen the heat and mass transfer performance and the wettability of the fins by disturbing the boundary layer of the spray water. The size of the unit is 570 mm (H, the spray water flow direction) 310 mm (W, width) 180 mm (L, the air flow direction). Its fin thickness is 0.127 mm, and the distance between the fins is 2.2 mm. The inner and external diameters of the tubes are 9.42 mm and 10.02 mm, respectively. The tube bundle consists of 8 rows of steel tubes. The tubes are 0.31 m long and are arranged in a triangular pattern at a transversal pitch of 25.4 mm. There are 20 tubes per tube row. The external surface of the whole unit is 24.336 m2 (Fm), 0.784 m2 of which is the external surface of the tubes and 23.552 m2 of which is the surface of the fins. The specific surface area of the CWCT unit is 790 m2/m3. 2.2. The CWCT testing configuration The tests for assessing the performance of the CWCT unit were performed in an environmental chamber. The system configuration can realize wide range of air, spray water and process water states, as displayed in Fig. 3. The cooling coil, heater A and humidifier can regulate the air inlet temperature and humidity independently. The variable frequency fan can control the volume flow rate of the inlet air. Also, the temperature and flow rate of the process water can be controlled by Heater B and the water valves. The environmental chamber provided the measuring instruments for the flow rates and inlet/outlet temperatures of the air, the spray water and the process water. As listed in Table 1, the flow rate of the air ṁa was measured by standard nozzles (GB14294) with the accuracy of 1%. The flow rate of the spray water ṁs was measured by a rotameter with the range from 60 to 600 L/h and the accuracy of 1.5%. The flow rate of the process water ṁw was measured by water meter with the accuracy of 3 L/h. The temperatures of the three fluids were measured by T-type thermocouples with the accuracy of 0.2 C.
2.1. Description of the cross-flow CWCT unit 2.3. Verification of the experimental data Fig. 1(a) indicates the flow directions of the three fluids in the cross-flow CWCT unit, which are spray water flowing from top to bottom, ambient air flowing from front to back through the fins and process water flowing in the serpentine tubes from back to the front. In other words, the ambient air and process water are in counter flow and spray water is in cross flow with the other two fluids. As shown in Fig. 1(b), the CWCT unit employs fin-tube structure to expand the heat and mass transfer area. The tubes and fins of the unit are made of stainless steel to ensure perfect heat transfer between the spray water and the process water. Furthermore, there are discontinuous louvers on the fins, presented in
In order to study the CWCT unit, a series of experiments were conducted which intended for finding out the effects of the inlet parameters on cooling performance. The main parameters are the flow rate of the three fluids and the inlet temperature of the process water etc. Variable condition analyses were conducted with 11 operating conditions and 46 sets of data. Each set of data was recorded under approximately steady states, which required all the temperature points fluctuated within 0.2 C for longer than 20 min. The typical experiment data is listed in Table 2. To verify the reliability of the experiment data, energy balance of the air, spray
Table 2 The experimental data of the CWCT test. No.
Inlet parameters
1 2 3 4 5 6 7 8 9 10 11
Outlet parameters
ε
Qc kW
0.36 0.35 0.37 0.28 0.32 0.36 0.40 0.45 0.34 0.38 0.40
4.94 5.65 7.26 3.31 4.31 3.49 4.10 3.39 3.22 3.58 3.77
ta,in C
twb,in C
ts,in C
tw,in C
ṁa kg/s
ṁs kg/s
ṁw kg/s
ta,out C
twb,out C
ts,out C
tw,out C
24.8 25.3 27.0 27.2 26.7 27.3 25.1 25.1 26.8 26.9 27.0
20.1 20.9 22.0 21.1 20.6 22.9 20.8 21.1 22.6 22.8 22.6
24.7 25.8 27.9 26.2 25.6 26.1 24.8 24.6 26.2 25.9 25.8
30.3 32.9 36.6 30.2 30.8 30.2 30.4 30.2 30.2 30.2 29.9
0.35 0.35 0.35 0.19 0.27 0.35 0.35 0.35 0.35 0.35 0.35
0.13 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.06 0.09 0.13
0.32 0.32 0.32 0.32 0.32 0.31 0.26 0.20 0.29 0.30 0.30
24.2 25.3 27.3 26.0 25.2 25.6 24.4 24.2 25.1 25.3 25.3
23.9 25.0 27.0 25.7 24.8 25.2 24.0 23.8 24.6 25.0 25.0
24.4 25.8 27.8 26.0 25.3 25.8 24.5 24.3 25.6 25.5 25.4
26.7 28.8 31.2 27.7 27.6 27.5 26.6 26.1 27.6 27.4 27.0
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Gained heat of the air (kW)
8
3. Experimental results and influencing factors
7
3.1. Effect of the air flow rate
+ 20
6 5 4
-20 %
3 2 1 0
681
0
1 2 3 4 5 6 7 Heat loss of process/spray water (kW)
8
Fig. 4. Energy balance of the CWCT test.
water and process water was adopted. As shown in Fig. 4, the unbalance ratios of the heat gained by the ambient air and the heat lost by the process water and the spray water are within 20%. The average absolute unbalance ratio is 7.4%, which means the data are reliable. To better describe the cooling processes, some indexes are introduced, seen in Eqs. (1) and (2). The wet-bulb cooling efficiency ε [5,13,16] illustrates the distance between the outlet process water temperature (tw,out) and the ambient wet bulb temperature (twb,in), which is the limit of the outlet process water temperature. The cooling capacity Qc [5,12,15] presents the cooling capacity of the CWCT unit.
In the environmental chamber shown in Fig. 3, the flow rate of the ambient air is easily conditioned and controlled by regulating the rotate speed of the fan. The flow rate of the air was at the lowest rate of 0.19 kg/s and up to the maximum of 0.35 kg/s Fig. 5 displays that mass transfer coefficient between the spray water and the air (Km) increased greatly by increasing the air flow rate. While the heat transfer coefficient between the spray water and the process water (Kh) was generally constant since the increase of the air flow rate had little relationship with the heat transfer between the spray water and the process water. As a result of the strengthening of the heat and mass transfer performance between the spray water and the air, ε and Qc increased with the increase of ṁa. Thus, increasing air flow rate is a good way to improve the performance of the CWCT. However, the air flow rate is not the bigger the better if taking the fan power consumption into consideration. There is an optimal value of air flow rate depending on the balance of the CWCT performance and the fan power consumption. Uncertainty analyses for the experimental results, based on the accuracies of the measuring instruments introduced in Section 2.2, were conducted in this study using the method proposed by Kline and McClintock [20] according to the following expression (Eq. (3)):
Dy ¼
vf vx1
2
ðDx1 Þ2 þ
vf vx2
2
ðDx2 Þ2 / þ
vf vxn
2
ðDxn Þ2
1=2 (3)
ε ¼
tw;in tw;out tw;in ta;wb
(1)
_ w tw;in tw;out Qc ¼ cp;w m
(2)
The uncertainties of ε, Qc, Km, and Kh were calculated and expressed in Fig. 5 in the way of error bars. Results show that the Ttype thermocouples are the main sources of errors. Taking Km as an example, the uncertainties of the air wet-bulb temperature and spray water temperature account for 81.3% and 16.6% of the total uncertainty, respectively, while that of the air mass flow rate only
Fig. 5. Effects of the air flow rate (ṁa) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
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Fig. 6. Effects of the spray water flow rate (ṁs) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
accounts for 0.8%. Thus improving the temperature measurement accuracy is the key point of improving the accuracy of the test. 3.2. Effect of the spray water flow rate The flow rate of the spray water was regulated by changing the valves in the pipelines. The flow rate of the spray water was from
0.06 kg/s to 0.13 kg/s. When the flow rate of the spray water increased, wetting degree of the CWCT was improved and heat and mass transfer area was expanded to a certain extent. Also, the increase of the spray water flow rate would strengthen the heat transfer process between the spray water and the process water, so as to take away more heat from the process water. As a result, ε, Qc, and Kh increased, as shown in Fig. 6. On the other hand, the
Fig. 7. Effects of the process water flow rate (ṁw) on the CWCT: (a) wet-bulb efficiency; (b) cooling capacity; (c) Km; and (d) Kh.
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683
Fig. 8. Effects of the process water temperature (tw,in) on the CWCT: (a) cooling capacity; (b) spray water inlet temperature; (c) Km; and (d) Kh.
(b)
(a)
Fig. 9. Calculated results of Eqs. (4) and (5): (a) Kh; and (b) Km.
Table 3 Comparison of the experimental parameters in literature [4,6,15,16]. Source
Flow pattern
Ga (kg/m2s)
Gs (kg/m2s)
Gw (kg/m2s)
Kma (kg/m3s)
Kha (kW/m3 K)
a (m2/m3)
ε
Correlations
Heyns [4]
Parallel/counter
0.7e3.6
1.7e4.5
-
0.5e3.2
42.0e67.2
24
e
Zheng [6]
Parallel/counter
2.5e5.0
1.2e3.2
2.8e5.3
2.7e5.0
23.9e60.4
31
0.11e0.19
Shim [15] Facão [16]
Parallel/counter Parallel/counter
1.2e4.2 0.7e2.4
1.1e3.3 0.3e1.9
0.9e4.8 0.6e1.1
6.6e21.5 1.6e4.3
18.2 31.4 5.5e17.5
33 25
e 0.2e0.65
Present study
Cross
1.3e2.4
1.1e2.3
1.1e1.8
10.3e19.0
30.8e45.0
790
0.28e0.46
0.35 0.3 ts Kh ¼ 470G0.1 a Gs Km ¼ 0.038G0.73 G0.2 a s Kh ¼ 350.3(1 þ 0.0169ts)G0.59 G1/3 a s 0.977 Km ¼ 0.034Ga e Kh ¼ 700.3(ṁs/1.39)0.6584 Km ¼ 0.1703(ṁa/1.7)0.8099 0.547 Kh ¼ 31.79Gs0.238Gw Km ¼ 0.00154t0.471 G0.694 G0.512 w a s
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(b)
(a)
Fig. 10. Comparison with literature [4,6]: (a) Kha; and (b) Kma.
improvement of the spray water flow rate enhanced heat and mass transfer between the ambient air and the spray water, which resulted in the growth of Km.
by the air and process water states, it rose with the growth of the process water temperature, as shown in Fig. 8(b). 3.5. Comparison with experimental results from previous studies
3.3. Effect of the process water flow rate The flow rate of the process water is also a key parameter influencing the CWCT performance. It was from 0.20 kg/s to 0.32 kg/s in this set of experiments. Apparently, the rise of the process water flow rate promoted the heat and mass transfer between the spray water and the process water, therefore Kh increased. Thus process water could release more heat to the spray water, which led to the increase of Qc, as shown in Fig. 7(b). Since the influence of ṁw to the outlet temperature of the process water was more remarkable than that of Kh, the cooling effect of the process water per unit mass was definitely worsened, though the total cooling capacity was improved. In this way, the outlet temperature of the process water increased and ε dropped. Since the process water barely touched the ambient air, Km between the air and the spray water scarcely changed. 3.4. Effect of the process water temperature This set of experiment was meant to study the performance of the CWCT at different process water temperatures. The inlet temperature of the process water was from 30.1 C to 36.6 C. The results showed that Qc and Km increased with the growth of the process water temperature, seen in Fig. 8(a) and (c), due to the increase of the heat and mass transfer driving forces between the three fluids. Since the temperature of the spray water was decided
Fig. 11. Control volume schematic of the cross-flow CWCT.
From the sensitivity analyses we could see that Kh is mainly influenced by the flow rates of the spray water and the process water, while Km is dominated by the flow rates of the air and spray water and the inlet temperature of the process water. Therefore, for the specific geometry of the tower, the correlation equations for Kh and Km could be presented as follows:
Kh ¼ 31:79G0:238 G0:547 s w
(4)
0:471 0:694 0:512 Km ¼ 0:00154tw;in Ga Gs
(5)
where Ga is the air velocity in the minimum flow area, Gs ¼ G/do, Gw ¼ ṁw/(H$L) is the process water flow rate per flow area (1.3 < Ga < 2.4 kg/m2 s; 1.1 < Gs < 2.3 kg/m2 s; 1.1 < Gw < 1.8 kg/ m2 s; 30.1 < Tw,in<36.6 C). Fig. 9 compares the calculated results based on the correlation equations and the experimental data. Since good agreement is obtained, the correlation equations can be used to predict the coefficients. Table 3 compares the experimental parameters of previous studies in literature and present study. The flow pattern of parallel/ counter can refer to Fig. 15(a) and the flow pattern of cross can refer to Fig. 11. As listed in Table 3, the most popular flow pattern is parallel/counter-flow, while the most common structure is planetube bundles with specific surface area of around 25e35 m2/m3. In present study, the CWCT is cross-flow with a considerable specific surface area of 790 m2/m3. The correlations of Heyns et al. [4] shows that Kh has positive correlations with the air and the spray water flow rates and the spray water temperature, while Km has positive correlations with the air and the spray water flow rates. Km is only influenced by the air flow rate in the studies of Zheng et al. [6] and Facão et al. [16]. In present study, similar correlations of Kh and Km were obtained. There are some modifications about the selection of the influencing factors. Firstly, tw,in, instead of ts, is seen an influencing factor because it’s the source of the heat and mass transfer process while ts is only an equilibrium parameter of the air and process water states. Secondly, the process flow rate Gw is adopted to describe the correlation of Kh since the heat transfer process actually happens between the spray water and the process water. In Fig. 10, Eqs. (4) and (5) are compared to the correlations given by Heyns et al. [4] and Zheng et al. [6]. Compared to the bare-tube parallel/counter-flow CWCT, the cross-flow CWCT with plateefin tube structure studied in this paper has much larger volume mass
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Fig. 12. Comparison of the calculated values and the experimental results of the cross-flow CWCT: (a) the variance of the air humidity ratio; and (b) the variance of the temperature of the process water.
transfer coefficient Kma, due to that the fin-tube structure tremendously extends the contact area, which is exactly the restriction point of the heat and mass transfer between the air and the spray water. In contract, the performance improvement of the fin-tube structure for waterewater heat transfer process is insignificant. That’s why the volume heat transfer coefficient Kha is no bigger than the others. 4. Numerical model of the cross-flow CWCT 4.1. Theoretical model Two-dimensional steady-state model of the cross-flow CWCT, in which air and process water flowing in the opposite direction, spray water flowing in the cross direction with the other two fluids, seen in Fig. 11, will be illustrated in this section. In the CWCT, process water releases heat to the metal finned tubes while the tubes are cooled by the spray water. At the same time, heat and mass transfer takes place between the spray water and the air. The main assumptions for the numerical model are presented as follows [8,13,17]: 1) Heat and mass transfer processes are at steady state; 2) The heat and mass exchange between the CWCT unit and the surroundings is negligible; 3) The specific heat of the fluids are assumed to be constant; 4) The spray water film uniformly covers all the wall of the tubes and fins, so that Fh equals to Fm and the heat exchange between the air and process water is negligible; and 5) The flow of the process water and the air is approximately counter flow. Define the air flow direction as z axis and the spray water flow direction as x axis. The energy balance equation for the three fluids is:
_ s hs Þ _ a vha 1 vðm _ w vtw m m cp;w þ ¼ 0 L vx H vz H vz
(6)
Mass conversion equation of the spray water and the air is given
_s _ a vda 1 vm m þ ¼ 0 L vx H vz
(7)
Heat transfer between the spray water and the process water driven by the temperature difference between them is shown as:
Table 4 Simulated condition of the cross-flow CWCT. ta,in C da,in kg/kg tw,in C ṁa kg/s ṁs kg/s ṁw kg/s KmFm kg/s KhFh kW/K 0.0136
30.3
(8)
As well known, there is a thin film of saturated air at the interface between the spray water and the air. The temperature of the saturated air is close to that of the spray water. The humidity ratio of the saturated air is also called the equivalent humidity ratio of the spray water, which is de. Heat transfer driven by the temperature difference of the saturated air film and the air flow and mass transfer driven by the water vapor partial pressure difference between the two streams take place simultaneously. Thus the mass transfer equation and the energy balance equation for the air flow can be expressed by the following equations separately:
vda Km Fm ¼ ðde da Þ _ aL vz m
(9)
vha K 0 Fm vda ¼ h ðt ta Þ þ r _ aL s vz vz m
(10)
The Lewis factor or Lewis relation Lef could be defined to indicate the relation between the heat and mass transfer in an evaporative process [21e23]. The definition of Lef is as follows:
Lef ¼
K 0h Km cp;m
(11)
Substitute Eq. (11) into Eq. (10):
i vha Km Fm h ¼ Lef $cp;a ðts ta Þ þ rðde da Þ _ aL vz m As the enthalpy of the air can be expressed ha ¼ cp;m ta þ r$da ; Eq. (12) can be transformed into:
vha Km Fm 1 ¼ $Lef ðhe ha Þ þ r 1 ðde da Þ _ aL Lef vz m
(12) as
(13)
Thus we get all the governing equations of the cross-flow CWCT. The boundary conditions are shown as follows:
by:
27.2
vtw Kh Fh ðt ts Þ ¼ _ wL w vz cp;w m
0.19
0.12
0.32
0.365
1.17
ta ¼ ta;in ;
da ¼ da;in ;
ha ¼ ha;in ;
z ¼ 0
(14)
ts jx¼0 ¼ ts jx¼H
(15)
tw ¼ tw;in ;
(16)
z ¼ L
By discretizing the governing equations, the heat and mass transfer process could be numerically solved. When solving the model, Lef could be equal to 1 [6,8,14]. The model of the cross-flow CWCT was validated by the experimental results described in
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Fig. 13. Simulated field distribution of the cross-flow CWCT: (a) the air wet-bulb temperature; (b) the spray water temperature; (c) the process water temperature; (d) the temperature difference between the spray water and the process water; and (e) the temperature difference between the spray water and the air (wet-bulb).
Section 3. As shown in Fig. 12, the maximal differences between the calculated results and the experimental values are within 8.0%, and the average absolute differences are 3.0% and 4.0% for the variance of the air humidity ratio and the process water temperature respectively. On the whole, the calculated parameters by the numerical model agree well with the experimental results, the model could be used to analyze the heat and mass transfer performance of the CWCT unit in the following content. 4.2. Typical simulation result of cross-flow CWCT Since the distribution parameters of the cross-flow CWCT are two-dimensional, it is difficult to describe it through experimental
results of limited measurement points. Therefore, numerical modeling results were introduced to investigate the performance of the CWCT. The boundary conditions from the experimental results are displayed in Table 4. As seen in Fig. 13, the wet-bulb temperature of the air increases in the air flow direction, while the temperature of the process water decreases in the opposite direction. Heat is transferred from the process water to the air. Without the circulation of the spray water, the temperature distributions of the air and the process water should be one-dimensional and the temperature gradients of the two fluids along z should be consistent. Once the spray water is brought in, the consistency will be disturbed. To better explain the heat and mass transfer process of crossflow CWCT, we could divide it into enough control volumes along
Fig. 14. Simulated temperatures of the x sections: (a) x ¼ 0.05H; (b) x ¼ 0.5H; and (c) x ¼ 0.95H.
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Fig. 15. (a) Parallel/counter-flow CWCT configuration; and (b) simulated temperatures.
z axis and assume that the heat and mass transfer between each two control volumes could be ignored, which means the performance of the spray water is only affected by the air and the process water inside the volume. If the inlet temperature of the spray water is lower than those of the process water and the air (wet-bulb), spray water will absorb heat from both the fluids when falling along the x axis. As a result, the spray water temperature will go up until it gains the same heat from the process water as the heat released to the air. Vice versa, when the inlet temperature of the spray water is higher than those of the other fluids, spray water will discharge heat to the air and the process water until it transfers the same quantity of heat from the process water to the air. In this way, there is an equilibrium temperature of spray water in each control volume, which is somewhere between the temperatures of the air and the process water, determined by the heat and mass transfer ability of the CWCT. As shown in Fig. 13(b), on the bottom of the CWCT, the spray water temperature barely changes along the way, which means it already reaches the equilibrium temperature. Fig. 14 shows the temperatures of the three fluids at the sections of x ¼ 0.05H, x ¼ 0.5H and x ¼ 0.95H, which represent the states of the spray water from the inlet to the outlet. It can be observed from Fig. 14(c) that the equilibrium temperature rises from the air inlet to the process water inlet. Since there is only one sink at the outlet, spray water of different control volumes with different
Fig. 16. Flow pattern optimization of the CWCT.
temperatures must be mixed to the medium temperature before going to the inlet. Because of the mixture, the heat and mass transfer driving forces at the inlet are not uniform, shown in Fig. 14(a). Fortunately, the spray water of the cross-flow CWCT has the self-adjust ability to achieve proper equilibrium temperature. As the simulated mass flow rate of spray water is relatively small in this article, according to Table 4, its state is easy to be influenced by the other two fluids and it reaches the equilibrium temperature very quickly (at about x ¼ 0.2H). When x ¼ 0.5H, shown in Fig. 14(b), the three fluids have already reached the equilibrium states and had rather uniform heat and mass transfer driving forces. On the whole, the heat and mass transfer driving forces are relatively uniform in the cross-flow CWCT, especially in the lower part. 5. Effect of flow pattern on the performance of the CWCT For two-flow heat and mass transfer system, scholars have agreed that counter flow achieves the best performance, followed by the cross flow and the parallel flow. By analogy, the recommended flow pattern in the CWCT is two counter flows and one parallel flow between the three fluids, achieving as many counter flows as possible and abandoning the mediocre cross flow. Ren and Yang [17] studied all the parallel/counter-flow patterns of the CWCT, finding that the flow pattern shown in Fig. 15(a) achieves the best cooling performance. Following this conclusion, we simulated the performance of the model to test the analogy. The boundary conditions are listed in Table 4. For the parallel/counter-flow CWCT, the distribution parameters are one-dimensional. As shown in Fig. 15(b), the process water is cooled along the way while the air is continuously heated. Since the inlet and outlet temperatures of the spray water should be the same, the one-dimensional spray water temperature could not keep pace with the temperature gradient along x. As a result, the heat transfer driving force between the process water and the spray water is not uniform. Neither is the heat and mass transfer driving force between the air and the spray water. This phenomenon is also stated by many other researchers [4,10]. Unfortunately, the uneven driving forces could not be avoided by improving the heat and mass transfer area or regulating the flow ratios of the three fluids. In other words, the one-dimensional parallel/counter-flow CWCT has the structural limitation. As mentioned in Section 4.2, the crossflow CWCT could achieve uniform heat and mass transfer driving forces in the most part of the module. In this way, the cross-flow CWCT turns up the ideal flow pattern, although the two-flow cross-flow heat and mass transfer performance is not the best.
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The cooling capacity comparison of the parallel/counter-flow and cross-flow CWCTs under different KmFm are shown in Fig. 16. The flow rates of the air, the spray water and the process water are all 0.5 kg/s, while the other boundary conditions are presented in Fig. 16. As shown in Fig. 16, the cross-flow CWCT would always have a larger cooling capacity Qc, and the superiority will be amplified when the heat and mass transfer coefficient is increased, which means the cross-flow CWCT has better cooling performance than the commonly used parallel/counter-flow CWCT. 6. Conclusion A cross-flow CWCT based on the fin-tube structure was designed and tested in present study. The flow arrangement of the air and the process water was counter flow, while that of the air and the spray water was cross flow. Experimental tests were conducted to investigate the cooling performance and the influencing factors on the basis of a good energy balance discrepancy. The main conclusions are: 1) Effect of the process water temperature and flow rates of the air, spray water and process water on the cooling capacity, wetbulb efficiency, heat and mass transfer coefficients were studied. Empirical correlations of the heat and mass transfer coefficients based on the influencing factors were obtained. 2) Compared to the bare-tube structure in literature, the fin-tube structure tremendously extends the contacting area between the air and the spray water, thus improves the heat and mass transfer coefficient. While for the heat transfer coefficient between the spray water and the process water, the fin-tube structure has little impact. 3) Two-dimensional steady-state numerical model of the crossflow CWCT was built and validated by the experimental data. The deviation between the model and the experimental data was less than 8%, which ensures the accuracy of the model. 4) The numerical results show that the spray water temperature of the cross-flow CWCT would automatically form a gradient in the air/process water flow direction to match the temperature variances of the air and the process water. As a result, the heat and mass transfer driving forces of the cross-flow CWCT are fairly uniform, which is beneficial for the behavior of the CWCT. 5) The flow pattern optimization of the CWCT shows that the cooling performance of the cross-flow CWCT is better than that of the commonly studied parallel/counter-flow CWCT due to more uniform driving forces. The superiority will be amplified when heat and mass transfer coefficients are increased. Acknowledgements The research described in this paper was supported by National Natural Science Foundation of China (No. 51138005) and the foundation for the author of National Excellent Doctoral Dissertation of China (No. 201049). Nomenclature a cp d do Fh Fm G H h
specific surface area (m2/m3) specific heat capacity (kJ/kg C) humidity ratio (g/kg) external diameter of the tube (m) heat transfer area (m2) mass transfer area (m2) mass flow rate per flow area (kg/m2s) height of the CWCT unit (m) enthalpy (kJ/kg)
Kh Kh0 Km L Lef _ m Qc r t W
heat transfer coefficient between spray water and process water (kW/m2 K) heat transfer coefficient between spray water and air (kW/m2 K) mass transfer coefficient between air and spray water (kg/ m2 s) thickness of the CWCT unit (m) Lewis factor (dimensionless) mass flow rate (kg/s) cooling capacity (kW) vaporization latent heat (kJ/kg) temperature ( C) width of the CWCT unit (m)
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