Comparison and evaluation of air cooling and water cooling in resource consumption and economic performance

Comparison and evaluation of air cooling and water cooling in resource consumption and economic performance

Energy 154 (2018) 157e167 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Comparison and evaluati...

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Energy 154 (2018) 157e167

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Comparison and evaluation of air cooling and water cooling in resource consumption and economic performance Haitian Zhang a, Xiao Feng a, *, Yufei Wang b a b

School of Chemical Engineering & Technology (XJTU), Xi'an Jiaotong University, Xi'an, Shaanxi, PR China School of Chemical Engineering, China University of Petroleum (CUP), Beijing, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 18 April 2018

Cooling systems have been widely applied in the process industry, which generally falls into two categories: air cooling and water cooling. Despite that both of these cooling types has their own specific advantages, resource consumption, especially energy and water, is inevitable to maintain system operation. Facing with overwhelming challenges in the industry field such as energy and water conservation, given selection of cooling type, it is imperative to take resource consumption and economy effect into account. In this paper, comparison among four different cooling types is carried out, including dry air coolers, spray type air coolers, evaporative air coolers, and circulating cooling water systems, for energy and water consumption and economy performance. Considering the cooling range from 95  C to 40  C, under circumstance of different dry bulb temperature and relative humidity, energy and water consumption can be calculated, while annual total cost, as a measure index of economic indication, is compared in the condition of different price ratio of fresh water and industrial electricity likewise. This work contributes to the determination of optimal cooling method, which has instructive significance in actual industrial processes. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Cooling type Comparison Price ratio Economic analysis

1. Introduction

1.1. Different types of air coolers

Heat recovery systems play an important role in energy conservation of the whole industrial process. Subsequently, its remaining heat needs cooling treatment by coolers. In accordance with the cooling medium, the cooling method can usually be categorized into two sections: water cooling and air cooling. During the last several decades, in literature, a considerable number of available studies have concerned with performance of air cooling and water cooling, since a series of global concerns such as impending climate changes, reliance on fossil fuels, acute water scarcity, highlight the importance of the excessive energy and water consumption [1]. Furthermore, stringent environment regulations, soaring resource demand and other elements oblige industrial agglomeration to enhance resource utilization efficiency as much as possible [2]. Therefore, it is of vital significance to make contrastive studies on air cooling and water cooling on energy and water consumption, as well as economic performance.

Air coolers, as the name indicates, have process streams cooled when ambient air is regarded as cooling medium instead of water, which in general, has a higher capital cost but a lower operating cost in comparison with water-cooled heat exchanger [3]. There are diverse taxonomic approaches with regard to the classification of air coolers. For instance, air coolers can be divided into dry type air coolers and wet type air coolers, while the latter comes in quite a few varieties such as spray type air coolers and evaporative air coolers, according to jetting modes. For wet style air coolers, there are numerous means contributing to the intensification of heat transfer, counting humidification and mist spray. The following three types of air coolers are discussed in this paper.

* Corresponding author. E-mail address: [email protected] (X. Feng). https://doi.org/10.1016/j.energy.2018.04.095 0360-5442/© 2018 Elsevier Ltd. All rights reserved.

a) Dry type air cooler (DAC). In a dry type air cooler, air flows blow over the smooth or finned tubes while hot streams through the tubes. Heat transfer between hot streams and ambient air leads to temperature rise of air flows and temperature fall of hot streams [4].

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b) Spray type air cooler (SAC). The primary characteristic of a spray type air cooler is that the spray water is sprinkled onto the surface of heat transfer tubes, which results in sufficient surface wettability of tubes and evaporative heat dissipation, inducing the enhancement of heat transfer efficiency. The heat transfer mechanism of spray type cooling can be associated with kinds of phenomena including direct evaporation from the interface of liquid membrane [5], and convection heat transfer [6]. c) Evaporative air cooler (EAC). For an evaporative air cooler (EAC), the evaporation of water in the surface of heat transfer tubes is able to exert an influence on cooling effects, causing the decrease of inlet air temperature [7]. By dint of the latent heat of evaporative water, the water evaporation can not only cool down the air flows but also improve its humidity [8]. The previous researches were performed for the sake of further exploration of issues on air coolers in various ways. As far back as late 1960s, Schulenberg [9] discussed the theory of the finned elliptical tube and its application, comparing with the circumstance of finned circular tube on the part of air-cooled heat exchangers. In the last few years, given thermal economic optimization, Kashani et al. [10] developed a thermodynamic model as well as its optimal design of an air-cooled heat exchanger plant, with the evaluation of pressure drops and outlet temperatures of streams both in air and tube sides. Du et al. [11] studied two types of finned tube heat exchangers in an indirect air-cooling tower experimentally, providing a contrast in comprehensive heat transfer performance. Manassaldi et al. [12] introduced a disjunctive mathematical model of air coolers targeting the optimal design pertaining to optimization criteria including the minimization of the total annual total cost and operating cost. Shirazi et al. [13] focused on a mathematical model for a gas turbine cycle with inlet air cooling by thermal, economic and environmental analysis, taking the thermodynamic and economic objectives into account. Lu et al. [14] performed an investigation into cooling issues on a practical operating cooler in a coal seam gas industry, showing cooling performance under different operating conditions. 1.2. Cooling water systems The cooling water system (CWS) could fairly claim to be one of the major portions of industrial energy systems in the field of chemical processes, which can be classified into the once-through cooling water system and the circulating water cooling system [15]. Relatively speaking, heat recovery for energy synthesis and conservation of fresh water contributes to the preference of circulating water cooling systems, in contrast to once-through cooling water systems [16]. In consequence, among assorted kinds of water cooling systems, the open type circulating cooling water system is selected to evaluate in this work. In recent years, none the less, most of studies in this field have obtained certain achievements to some extent. Panjeshahi and Ataei [17] extended the integrated ozone treatment cooling system design, intending to minimize cost and to maximize resource conservation. Souza et al. [18] studied the optimization of the hydraulic debottlenecking of cooling water systems through a MINLP problem, with comparison showing economic performance. Muller and Craig [19] explored the control of hybrid non-linear model predictive control (HNMPC) and economic HNMPC with the regard to the reduction of energy consumption and total cost for a dual circuit induced draft cooling water system. 1.3. Comparison among different kinds of cooling methods Since different cooling methods have their own merits

respectively, for the reasonable lectotype, comparison and evaluation deserve great attention. Alhazmy et al. [20] compared water spray cooling process with direct mechanical air-cooling systems in terms of energy analysis, with presentation of performance between two kinds of coolers, drawing a conclusion that the former is able to gain the maximum power and the latter is more appropriate for drier air conditions. Bolotin et al. [21] showed a comparative study of two types of evaporative air coolers: typical cross-flow evaporative air cooler and regenerative cross-flow evaporative air cooler, with the key target of analysis on the basis of numerical methods, coming to a decision that the typical cross-flow evaporative air cooler is more favourable with higher air flowrates, and the regenerative cross-flow evaporative air cooler is supposed to be operated under the condition of lower air flowrates. Jeng et al. [22] conducted a comparative study experimentally on the heat transfer characteristics and pressure drops of cross-runner heat exchangers with different configurations using air cooling and water cooling respectively, arriving at a conclusion that, the heat exchanger with rectangular punched holes forming cross-runners has the greatest commercial potential in both air cooling and water cooling. 1.4. The work in this paper Although there have been a considerable number of researches on different cooling methods, rare studies have made a general analysis among these different cooling types, in the way of resource consumption and economic performance. In this work, different types of cooling methods including DAC, SAC, EAC, and CWS are taken as candidates for cooler selection. When selecting a suitable cooling method, it is extremely necessary to consider not only environmental conditions corresponding to different seasons, such as dry bulb temperature and relative humidity, but also price factors consistent with different regions, which have large influence on economic performance of coolers. In this paper, the price ratio of fresh water to industrial electricity is regarded as the price factor of economic analysis, in order to choose the cost-optimal cooling type. Such work is not reported before. It can contribute to the reduction of both resource consumption and overall cost implementation, which is of vital importance to resource conservation and sustainable development of the process industry. 2. Mathematical model In this section, the mathematical model for cooling methods will be introduced. The design of DAC and CWS can be built up by Aspen EDR, while the determination of parameters related to the calculation is based upon measures of heat transfer enhancement on referring to series of formulas. 2.1. Energy and water consumption of DAC The module of air cooler is chosen in Aspen Exchanger Design and Rating (EDR), with the set of parameters including the flowrates of streams, physical property data concerned and so on, while air is selected as cooling medium under different relative humidity, bringing about data through simulation process, such as number of tube rows. The film heat transfer coefficient outside surface (ho) of the DAC is calculated as follows [23]:

la s A ho ¼ 0:1378$ $Re0:718 $Pr0:333 $ i$ i a a dr h Ao

(1)

where la refers to the thermal conductivity of air; Rea and Pra are

H. Zhang et al. / Energy 154 (2018) 157e167

the Reynolds number and the Prandtl number of air respectively, and dr is finned tube root diameter (i.e. outside diameter of bare tube). Moreover, si means transverse tube pitch, and h is defined as fin height; Ai and Ao are total outside surface area of tube bank and bare bank, respectively. When 2100
"  23 #  0:14  1 di mD hi ¼ 0:116$ $ Re  125 $ 1 þ $Pr3 $ di Li mW

li 

2 3

(2)

(3)

where li mD the thermal conductivity of media at qualitative temperature, and di is the internal diameter of heat transfer tube; Li is the length of heat transfer tube. Besides, mD and mw are the viscosity of hot streams at qualitative temperature and wall temperature respectively. The static pressure drop (Dpst) of DAC can be formulated as follows [24]:

Dpst ¼ 37:86$

    dr $Gm 0:316 si 0:927 $ ma dr

(4)

where Gm is mass velocity of moist air in minimum cross-section, while ma means air viscosity at qualitative temperature. The dynamic pressure drop (Dpd) of DAC is calculated as follows [23]:

Dpd ¼

ra 2

$

V

!2 (5)

900,p,D2f

where ra refers to the air density, and V is the actual air flowrate. Considering influence from standard derivation and swirl characteristic of airflow, in the computational formula of full air pressure drop, the static pressure drop needs to be multiplied by a safety factor. Here the value of safety factor is taken as 1.16 [23]. So the full air pressure drop (HF) can be calculated as follows:

HF ¼ 1:16$Dpst þ Dpd

(6)

For the most part, the fan power (N) results in energy consumption (Ec) of DAC, which can be computed as follows [25]:

Ec ¼ N ¼

2.2. Energy and water consumption of SAC The energy consumption of the SAC comes mainly from both fan and spray water pump. Other parameters come from the module of air cooler in Aspen EDR. For SAC, the film heat transfer coefficient of tube side (hi) is computed as Eqs. (2) and (3). The film heat transfer coefficient of the shell side (ho) can be calculated as follows [26]: 0:05þ0:08,Np

When Rea is greater than 10000, the film heat transfer coefficient of tube side (hi) is computed as eq. (3) [23].

 0:14 1 l mD hi ¼ 0:027$ i $Re0:8 $Pr3 $ di mW

159

ho ¼ 90:7$4q $GF

0:770:35,Np

$BS

$q0:35 with q ¼

tb  tgl tgl  tpl (9)

where 4q is fin height influence coefficient, and q means temperature coefficient; Bs means spraying intensity. As a footnote, if the high finned tube is applied, the value of 4q is 1; if the low finned tube is used, the value of 4q is 0.91. The calculation of the SAC can be carried out in subsequent process after the inlet air is humidified. The outlet air temperature (tg2) can be formulated as Eq.(10) [23].

tg2 ¼ tg1 þ

 3600Q  q0:35 2:55 þ 0:51Np fq B0:54 S Wa Cpa

(10)

where tg1 and tg2 are the inlet and outlet air temperature of the SAC respectively, Wa is the air flowrate of the SAC, and Cpa is the specific heat of air. Under the circumstance that 2
Dpst ¼ 2:16$j$Np $B0:12 $G1:54 s F

(11)

where j is influence coefficient of fin height. For high finned tubes, j ¼ 1; for low finned tubes, j ¼ 0.91. High finned tubes are adopted by SAC, while low finned tubes are used in EAC. The dynamic pressure drop (Dpd) of SAC is computed as Eq. (5). So the full air pressure drop (HF) of SAC is formulated as follows:

HF ¼ 1:16$Dpst þ Dpd

(12)

For the SAC, the calculating formula of the fan power is the same as Eq. (7) mentioned above, while the motor power of the spray water pump (PN) is calculated as follows [27]:

PN ¼

1:25$WA $g$H 3600$h

(13)

where PN refers to the motor power of the spray water pump, while

  2:778  107 $H$V$ 0:98604 þ 0:01435  102 $HL þ 2:495  109 $HL2

h1 $h2 $h3

(7)

where h1 is fan efficiency; h2 is transmission efficiency; h3 is motor efficiency. As is well known, dry air cooler has no water consumption (Wc), which means:

h is pump efficiency. The reflection of safety factor is 1.25 in the formula. For SAC, the energy consumption comes from a fan power and spray water pump, which can be computed as follows:

W c¼ 0

Ec ¼ N þ PN

(8)

(14)

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For wet style air coolers, moreover, water consumption consists of water evaporation and blowdown. The water evaporation (We) of SAC is computed as Eq. (15) [28].

We ¼

W A $ðX 2 ­X s Þ

rs

(15)

where WA refers to flowrate of spray water, rs is density of spray water, and X2 and Xs are the absolute humidity of outlet air and inlet air after sprayed, respectively. Besides, the blowdown is taken as 30% percent of the water evaporation [28,29]. Therefore, the water consumption of SAC can be formulated as follows:

W c ¼ 1:3$W e

(16)

We ¼

W A $ðX 2 ­X 1 Þ

rs

(21)

where X1 is the absolute humidity of inlet air. Considering blowdown, the water consumption of EAC can also be formulated as Eq. (16). 2.4. Energy and water consumption of CWS As mentioned earlier, the open type CWS is chosen to analyse because of its wide application in the practical process industry. The circulating water pump of the CWS occupies the majority of energy consumption, which can be calculated with Eq (8). According to conservation of energy, the circulating water volume (Wrc) is computed as follows:

C$m$ðT2  T1 Þ Crc $DT

2.3. Energy and water consumption of EAC

Wrc ¼

In term of energy and water consumption, the computational process of EAC seems to be similar to that of SAC, except that latent heat of vaporization plays a larger role in heat transfer enhancement. The heat transfer coefficient between outside surface of heat transfer tube and spray water (hL) can be computed as Eq. (17) under the condition that 5000
where Crc is specific heat of the circulating water. The water consumption of the CWS (Wm) is chiefly composed of evaporation loss, windage loss and blowdown loss, which can be formulated as follows [25]:

  1  Ts þ Tm G 3 $ hL ¼ 55$ 1 þ 0:016$ 2 d0

(18)

In addition, for the EAC, the enthalpy of the outlet air (H2) is computed as Eq. (19), according to the heat conservation.

C$m$ðT2  T1 Þ H2 ¼ H1 þ WA

(23) where n is design cycles of concentration, Tw is wet bulb temperature of ambient air, and DT means temperature difference of cooling water between inlet and outlet. 2.5. Cost model of cooling methods The total annual cost (TAC) is considered as the objective function, which can be computed as follows:

TAC ¼

ECC þ OAC y

(24)

(19)

where H1 and H2 are the enthalpy of inlet and outlet air, while T1 and T2 are the inlet and outlet temperatures of the hot stream, respectively, C is the specific heat of the hot stream, and m means the flowrate of the hot stream. The static pressure drop (Dpst) and dynamic pressure drop (Dpd) of EAC can be formulated as Eqs. (5) and (11). The full pressure drop (HF) is calculated as follows:

HF ¼ 1:16$Dpst þ 1:15$Dpd

n  3 2 $  2:7778  109 $Tw  3:5714  108 $Tw n1  þ 2:0635  105 $Tw þ 0:0012 $DT$Wrc

(17)

where G refers to a unit width of stream flowrate, while Ts and Tm are respectively the temperature of spray water and the mean temperature of hot stream. The heat loss of hot stream meets the following condition [28]:

C$m$ðT2  T1 Þ ¼ hL $ðTm  Ts Þ$Ao

W c¼ W m ¼

(22)

(20)

The safety factor of static pressure drop is also regarded as 1.16, while the dynamic pressure drop of EAC needs increasing coefficient because of water spray, which is taken as 1.15. Supposing the spray water volume of EAC is equivalent to that of SAC, according to calculation of quantities including heat transfer coefficient and so on, the energy consumption of EAC can also be formulated as Eq. (14). Since the absolute humidity of air can be derived from its enthalpy, the water evaporation (We) of EAC is calculated as Eq. (21) [28].

where ECC and OAC refers to the capital cost of equipment and annual operating cost, respectively, and y means period of depreciation.

AOC ¼ Ec $pe þ Wc $pw

(25)

where pe and pw are, respectively, the price of electricity and fresh water. 2.6. Contrast test of mathematical model Here contrast test is provided to prove the effectiveness of the mathematical model above. The case from Literature [29] is used to validate the model. In Literature [29], the cost of cold utility ranges around 15 $/(kW$y). Under the circumstance that the dry bulb temperature of ambient air is 15  C and its relative humidity is 0.4, the cooling costs calculated by the mathematical model in this paper are shown in Table 1. As is demonstrated in Table 1, the calculation results show that the cooling costs are accordant with the literature values.

H. Zhang et al. / Energy 154 (2018) 157e167

161

Table 1 Cooling costs calculated by the mathematical model. Cooling types

Energy consumption (kW)

Water consumption (m3/h)

Total annual cost ($/y)

Cooling cost ($$kW1$y1)

DAC SAC EAC CWS

18.87 13.79 4.58 13.55

0 0.44 1.43 2.06

30705 29221 27302 23563

16.01 15.23 14.23 12.28

Table 2 Sensitivity analysis of some fixed variables. Variable

Relative sensitivity

Judgement

HDAC HSAC HEAC HCWS Ts,DAC Ts,SAC Ts,EAC Tcwi,CWS

0 4.479  103 3.832  103 4.558  103 0 6.449  106 2.510  105 4.682  103

No influence Little influence Little influence Little influence No influence Little influence Little influence Little influence

Sensitivity Analysis of some fixed variables on cooling method choice. Sensitivity analysis is of vital importance to the validation of mathematical models. In order to judge whether those fixed variables have a major impact on the calculation results of TAC which is related to the lectotype of cooling types, in this paper, sensitivity analysis of some fixed variables, including head of delivery, temperature of spray water for wet style air coolers or circulating cooling water for the CWS, is presented in Table 2. From Table 2 it can be seen that those fixed variables have little influence on the results of TAC, so that they will not affect the selection of cooling method. 3. Analysis of resource consumption of cooling processes 3.1. Conditions in this comparison study Some conditions of this comparative study among these types of cooling in this work might be listed as follows. The hot stream is chosen as water with cooling range from 95  C to 40  C, chilled off by these methods mentioned above, comparing energy and water consumption along with the annual total cost as economic criteria. In terms of air cooler, the DAC and SAC need to use high finned tubes, while the EAC requires low finned tubes. These two finned tubes adopt steel tubes and aluminum fins. The value of fan efficiency is considered as 0.65; the transmission efficiency amounts to 0.95; the motor efficiency is chosen as 0.9. For SAC and EAC, the selection of the spray water flowrate is related to tube rows, which can refer to literature [23]. Additionally, on the basis of characteristic curve of pump and that of pipe line, for the circulating water pump of the CWS, its head of delivery is taken as 20 m, while its pump efficiency is taken as 79.3%; the design cycles of concentration is taken as 3. For the SAC and EAC, the head of delivery of spray water pump is regarded as 20 m, while its pump efficiency is taken as 45.3%.

Fig. 1. Relationship between Tw and energy consumption when relative humidity is 0.4.

As Figs. 1 and 2 shows, when the dry bulb temperature of ambient air (Tw) is below 32  C, Ec of the EAC is the lowest one among these four types; when Tw is above 32  C, that of the CWS is the lowest one, perhaps because under the condition of higher air temperature, the air cooler requires a great deal of air to chill down the hot stream, causing lots of energy consumption. In this situation, the DAC has the highest energy consumption when Tw is higher than 11  C. Since the specific heat of air is much smaller than that of water, a dry air cooler requires more air to meet

3.2. Analysis of energy consumption Figs. 1 and 2 present the energy consumption of cooling types under different conditions of the relative humidity in ambient air, 0.4 and 0.6 respectively.

Fig. 2. Relationship between Tw and energy consumption when relative humidity is 0.6.

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4. 4Economic analysis of cooling processes 4.1. Conditions of economic analysis To a great extent, the economic analysis of cooling processes is related to the price ratio between fresh water and industrial electricity. In this work, k is defined as the price ratio of fresh water to industrial electricity, and the relationship between k and TAC is analysed as indicated below. Aspen EDR and the Economics module in Aspen Plus are conductive to determine the cost of those cooling methods. In view of Aspen EDR, the price of industrial electricity (pe) is taken as 0.06 $/kWh. The ambient air temperature of 5  C, 15  C, 25  C, and 35  C can correspond to temperatures in all seasons [30]. The amortization and depreciation for equipment adopts the double-decliningbalance method [31]. In accordance with “Regulations for the Implementation of the PRC Enterprise Income Tax Law” under the provisions of Article 60, the minimum depreciation period of chemical equipment can be determined as 10 years. Fig. 3. Relationship between Tw and water consumption when relative humidity is 0.4.

4.2. Economic analysis at ambient temperature of 5  C

Fig. 4. Relationship between Tw and water consumption when relative humidity is 0.6.

the demand for cooling process, under the condition of the same cooling duty, giving rise to higher energy consumption caused by the fan. Meanwhile, Ec of the CWS is the highest one when Tw is lower than 11  C. For air coolers, air with lower temperature has higher cooling ability, leading to less air volume and lower energy consumption compared with the CWS, under the same condition of cooling duty.

Figs. 5 and 6 demonstrate the relationship between the price ratio of water and electricity (k) and the TAC at ambient temperature of 5  C, under the circumstance that the value of relative humidity is 0.4 and 0.6 respectively. In the situation of lower relative humidity (0.4), as Fig. 5 shows, the DAC has the lowest total annual cost among these cooling methods when the price ratio is higher than 7.4, while the CWS has the lowest total annual cost when the price ratio is lower than 7.4. The total annual cost of CWS is the highest one with the situation that k is greater than 8.1, since the heavy use of cooling water results in high economic cost when the price of fresh water is higher; the EAC has the highest total annual cost when 5 < k < 8.1; under the condition that 1.5 < k < 5, the SAC has the highest total annual cost, while the DAC has the highest one when k is less than 1.5, since the TAC of cooling methods using water drops considerably due to low water price with the extreme condition. Under the condition of higher relative humidity (0.6), Fig. 6 demonstrates that, the lowest total annual cost gives the DAC an edge in economic performance when k is higher than 7.2, which is similar to that as the relative humidity is 0.4; when k is lower than 7.2, the CWS has the lowest total annual cost. At the same time, the

3.3. Analysis of water consumption Under different relative humidity, the water consumption of these cooling methods can be demonstrated in Figs. 3 and 4. Figs. 3 and 4 illustrate that the highest water consumption belongs to the CWS; besides, the EAC has higher water consumption than the SAC. That is because a great quantity of water is needed for the CWS to cool down the hot stream, owing to mainly evaporation loss, windage loss and blowdown loss; meanwhile, in comparison with the SAC, more spray water is required for the EAC, leading to higher water consumption, since for the EAC, heat will be taken away by the evaporation of water film over the surface of heat transfer tubes. In addition, the DAC has no water consumption.

Fig. 5. Relationship between k and TAC at 5  C when relative humidity is 0.4.

H. Zhang et al. / Energy 154 (2018) 157e167

163

TAC of CWS is the highest among these cooling methods on condition that k > 7.8, while that of EAC is the highest one when 6.4 < k < 7.8; the SAC has the highest total annual cost in the situation that 3 < k < 6.4, while the DAC has highest one under the condition that k < 3. Comparatively speaking, with the situation that ambient temperature is 5  C, which can be regarded as conditions in winter, when k is higher than about 7, the DAC has an edge on economic performance, in virtue of the favourable cooling effect of cooling air. If k is lower than about 7, the CWS has the lowest total annual cost, which might be given rise to its lower equipment cost. And compared to the DAC, the specific heat capacity of water is roughly four times as large as that of air so that water has better cooling efficiency than air. 4.3. Economic analysis at ambient temperature of 15  C

Fig. 6. Relationship between k and TAC at

5 C

when relative humidity is 0.6.

Fig. 7. Relationship between k and TAC at 15  C when relative humidity is 0.4.

Fig. 8. Relationship between k and TAC at 15  C when relative humidity is 0.6.

The relationship between the price ratio and the TAC at ambient air temperature of 15  C is illustrated in Figs. 7 and 8, when the relative humidity has a value of 0.4 and 0.6. Under the circumstance that the relative humidity of ambient air is 0.4, as is shown in Fig. 7, the CWS is supposed to be the optimum selection with the lowest total annual cost when k < 7.6, while the EAC has the lowest total annual cost in the situation that 9.2 < k < 9.6; the SAC is the most advantageous one when 9.6 < k < 11, and under the condition that k is greater than 11, the DAC seems to be the best choice. When k is below 7.6, the DAC has the highest total annual cost, while the TAC of CWS is the highest one when the price ratio is above 7.6, owing to the usage of cooling water and its relatively high price. Just as Fig. 8 shows, under the circumstance of higher relative humidity, the CWS has the lowest total annual cost when k is less than 7.2, while the TAC of SAC is the lowest one when 7.2 < k < 8.6; the SAC can be considered as the best choice on condition that 8.6 < k < 11.4; the DAC has the lowest total annual cost when k is greater than 11.4. In the situation that k is lower than 7.8, the TAC of DAC is the highest; the CWS has the highest total annual cost when k is higher than 7.8. This case seems to be similar to the situation of lower relative humidity. Under the condition that ambient temperature is 15  C, which seems the temperature in spring or autumn, when the value of k is small, the CWS is supposed to be selected; when the value of k is moderate, the choice between SAC and EAC depends on the specific

Fig. 9. Relationship between k and TAC at 25  C when relative humidity is 0.4.

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H. Zhang et al. / Energy 154 (2018) 157e167

Fig. 10. Relationship between k and TAC at 25  C when relative humidity is 0.6.

Fig. 11. Relationship between price ratio and TAC at 35  C when relative humidity is 0.4.

value of k; when the value of k is fairly large, the DAC is considered to be selected. 4.4. Economic analysis at ambient temperature of 25  C When the value of relative humidity is 0.4 and 0.6, Figs. 9 and 10 demonstrate the relationship between the price ratio and the TAC at ambient air temperature of 25  C. According to Fig. 9, in the situation that the relative humidity of ambient air has a value of 0.4, when k is lower than 7.5, the TAC of CWS is the lowest among these cooling types; on condition that 7.5 < k < 19, it is the most favourable to select the EAC because of lowest total annual cost; the SAC is taken as the option in extremity when k is higher than 19. In addition, the DAC has the highest total annual cost due to the decline in cooling ability of air with the situation that k < 11.6, and the TAC of CWS is the highest when k > 11.6. As is shown in Fig. 10, under the circumstance of higher relative humidity, The CWS will be the optimal choice since it has the lowest total annual cost on condition that k < 7, while the EAC has the lowest total annual cost when 7 < k < 15.6. If k is greater than 15.6, with this extreme condition, the SAC has the most advantages on economic performance. Moreover, the TAC of DAC is the highest among these cooling types when k < 11, while the CWS has the highest total annual cost when k is greater than 11. In the situation that ambient temperature is 25  C, the DAC does not need to be concerned about, since cooling capacity of air is poor in such temperature, causing much more total annual cost. In general, on condition that k is less than around 7, the CWS seems to be the optimum considering the economic factor; when k is greater than around 7, if k has a moderate value, the EAC will be the best choice owing to the lowest total annual cost, while if k has an extremely large value, the SAC is supposed to be selected.

Fig. 12. Relationship between price ratio and TAC at 35  C when relative humidity is 0.6.

the optimum when k is greater than 9. Fig. 12 demonstrates that the CWS has the lowest total annual cost when k < 8.5, while the EAC is taken as the best choice when k is greater than 8.5. In this situation, the DAC has the highest annual total cost, since it is difficult for the ambient air at high temperature to cool down the hot stream into lower specified temperature, unless substantial industrial electricity is consumed. Thus it can be seen that in summer, the DAC is excluded when choosing suitable cooling method. On condition that the value of k is relatively small, which means the price of fresh water is quite inexpensive, the CWS has the lowest total annual cost, while when the value of k is relatively large, the EAC is supposed to be the optimum.

4.5. Economic analysis at ambient temperature of 35  C The relationship between the price ratio and the TAC at ambient air temperature of 35  C can be presented in Figs. 11 and 12, under the condition that the relative humidity has a value of 0.4 and 0.6. Under the circumstance that ambient air temperature is 35  C, as Fig. 11 shows, the CWS has an advantage over the other cooling types on condition that k is less than 9, while the EAC is regarded as

4.6. Comprehensive analysis on economic performance under different conditions According to the results of analysis above, ambient air temperature and price ratio of fresh water to industrial electricity have strong influences on the total annual cost of cooling types. As discussed above, relative humidity of ambient air has less influence on

H. Zhang et al. / Energy 154 (2018) 157e167

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the selection results of cooling methods. Therefore, in this section, the relative humidity is taken as 0.4. By MATLAB software, figures representing total annual cost (z axis) under different air temperature (x axis) and price ratios of fresh water to industrial electricity (y axis) are shown in Figs. 13 and 14. To visualize and delimitate the conditions for choosing a suitable cooling method, the results in this paper are summarized in Fig. 15. Thus it can be seen intuitively that, on condition of low price ratio, the CWS is supposed to be the optimum selection. When the price ratio is at medium level, if Tw is relatively high, the EAC is generally the preferred method, while the DAC has the minimum total annual cost if Tw is low. In most areas where price ratio is fairly high, the DAC should be a top priority on condition of low Tw, and the first option is SAC when Tw is moderate, while the EAC is at the top of list in the situation of high Tw.

Fig. 15. Suitable cooling types with Tw and k.

5. Conclusions

Fig. 13. TAC of different cooling types varying with Tw and k.

13000

10 4

12000

1.4

1.3 11000

Total annual cost ($/y)

1.2

1.1 10000

1

0.9

9000

0.8

0.7

0.6

8000

20 35

15 30 10

25

7000

20

Price ratio of water to

5

15

electricity (kWh/m 3 )

10 0

5

In this paper, the dry air cooler, spray type air cooler, evaporative air cooler and the open style circulating water cooling system are calculated and compared under different circumstance, in order to evaluate and assess the resource consumption and economic performance, picking up the best candidates. Among these cooling methods, the DAC has the highest energy consumption in most cases, except that air temperature is fairly low, while the energy consumption of CWS is the highest among these cooling methods at low temperature. The EAC has the lowest energy consumption when air temperature is relatively low, while the CWS has advantages on energy conservation on condition of high air temperature. In terms of water consumption, the DAC has no water consumption as common sense, while the CWS has the highest water consumption, followed by EAC and SAC. The price ratio of fresh water to industrial electricity exerts tremendous influences on economic performance of cooling methods. In all cases, the CWS is the optimal selection when price ratio is comparatively small. The CWS seems to be the best choice at all seasons at low price ratio. Under the circumstance of moderate price ratio, the DAC has an edge in economic performance in cold weather, during warm weather the EAC is the preferred cooling method. For areas with high price ratio, the DAC makes the most sense when Tw is relatively low, especially in winter, while the SAC is considered as the optimum in spring or autumn, and the EAC is supposed to be selected in summer when Tw is comparatively high. In this paper, however, combination of different cooling methods like in Ref. [32] is not considered. For example, restricted to the cooling medium, the DAC might not cool hot fluid into lower temperature, which can be solved in the way of following by water cooling. Optimization of a cooler network considering different cooling methods including their combinations will be our future work. Acknowledgments

Ambient air temperature (°C)

Fig. 14. The minimum TAC among different cooling types varying with Tw and k.

Financial supports from the National Key Research and Development Program of China (2017YFF0206700) and the National

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H. Zhang et al. / Energy 154 (2018) 157e167

Natural Science Foundation of China (21736008) are gratefully acknowledged.

X1 X2 Xs

Nomenclature Y Ai Ao Bs C Crc Cpa Df di dr Ec ECC GF Gm g H HF HL H1 H2 h hi hL ho k Li m N Np N OAC pe pw PN Pr Pra Re Rea si TAC Tcwi Tm Ts Tw T1 T2 tb tgl tg1 tg2 tpl V WA Wa Wc We Wrc

total outside surface area of tube bank, m2 total outside surface area of bare tube, m2 spraying intensity, kg$m2$h1 specific heat of hot stream, kJ$kg1$oC1 specific heat of circulating water, kJ$kg1$oC1 specific heat of air, kJ$kg1$oC1 fan impeller diameter, m inside tube diameter, m finned tube root diameter, m energy consumption, kW capital cost of equipment, $ mass flowrate of air on the windward side, kg$m2$s1 mass velocity of moist air in minimum cross-section, kg$m2$s1 acceleration of gravity, m$s2 head of delivery, m full air pressure drop, Pa altitude, m enthalpy of inlet air, kJ$kg (dry air)1 enthalpy of outlet air, kJ$kg (dry air)1 fin height, m film heat transfer coefficient of tube side, W$m2$oC 1 heat transfer coefficient between outside surface of heat transfer tube and spray water film heat transfer coefficient outside surface, W$m2$oC 1 price ratio of fresh water to industrial electricity, kWh$m3 length of heat transfer tube, m flowrate of hot stream, kg$s 1 fan power, kW number of tube rows design cycles of concentration operating annual cost,$$y1 price of industrial electricity, $$(kWh) 1 price of fresh water, $$(m3$h) 1 motor power of spray water pump, kW Prandtl number of hot stream Prandtl number of air Reynolds number of hot stream Reynolds number of air transverse tube pitch, m total annual cost, $$y1 inlet temperature of circulating cooling water, oC mean temperature of hot stream, oC temperature of spray water, oC wet bulb temperature of ambient air, oC temperature of inlet hot stream, oC temperature of outlet hot stream, oC mean temperature outside tube, oC dry bulb temperature of sprayed inlet air, oC inlet air temperature of wet style air cooler, oC outlet air temperature of air cooler, oC dew point temperature of inlet air, oC actual air flowrate, m3$h1 flowrate of spray water, m3$h1 air flowrate of the SAC, kg$s1 water consumption, m3$h1 water evaporation quantity, kg$h1 circulating water volume, m3$h1

Greek

G Dpst DT h h1 h2 h3 q la li ma mD mw ra rs

4q

j

absolute humidity of inlet air, kg (steam)$kg (dry air)1 absolute humidity of outlet air, kg (steam)$kg (dry air)1 absolute humidity of outlet air after sprayed, kg (steam)$kg (dry air)1 period of depreciation, y

a unit width of stream flowrate, kg$m1$h 1 static pressure drop in air side, Pa temperature difference of cooling water between inlet and outlet, oC pump efficiency fan efficiency transmission efficiency motor efficiency temperature coefficient thermal conductivity of air, W$m1$oC 1 thermal conductivity of media at qualitative temperature, W$m1$oC 1 air viscosity at qualitative temperature, Pa$s viscosity of hot streams at qualitative temperature, Pa$s viscosity of hot streams at qualitative wall temperature, Pa$s air density, kg$m3 density of spray water, kg$m3 fin height influence coefficient influence coefficient of fin height

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