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Performance prediction of seawater shower cooling towers
Energy 97 (2016) 435e443
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Performance prediction of seawater shower cooling towers Xiaoni Qi a, Yongqi Liu a, *, Qianjian Guo b, Jie Yu b, Shanshan Yu b a b
College of Traffic and Vehicle Engineering, Shandong University of Technology, Zhangzhou Road 12, Zibo 255049, China College of Mechanical Engineering, Shandong University of Technology, Zhangzhou Road 12, Zibo 255049, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 April 2015 Received in revised form 6 November 2015 Accepted 28 December 2015 Available online xxx
The salt content in seawater results in many considerable engineering problems, including salt deposition, corrosion, and fill blockage. Seawater cooling towers are a promising potential remedy, but the lack of progress in cooling tower design technology calls for a more systematic investigation into this topic. In this study, a shower cooling tower without packing was used in seawater circulating cooling system, and a complete mathematical model of the shower cooling tower's performance was developed. The model describes the experimental data with an accuracy of about 5%. This study also conducted a comparative prediction of the outlet water temperature between freshwater and seawater in a shower cooling tower; results showed that cooling performance decreases as inlet water temperature increases. The results also show that cooling performance degrades as droplet diameter and salt concentration increase. When the air-to-water ratio increases, cooling efficiency improves, and when seawater concentration is reduced, air moisture increases at a higher rate. These results altogether provide a valuable theoretical basis for improving seawater cycling and cooling technologies in the future. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Shower cooling tower Seawater cooling Heat and mass transfer
1. Introduction Seawater cooling towers have been used in coastal facilities across the globe since the 1970s. During industrial activities at sea, it is necessary to reduce the emission of waste heat to the ocean and protect the marine environment. In order to ensure sustainability and prevent thermal pollution from damaging aquatic resources, effective measures must be adopted to sustain the water temperature in the vicinity of fishing waters in accordance with national water quality standards. Many governments have imposed regulations on high-temperature waste water that is discharged to the sea [1]. One effective way of meeting these regulations is the utilization of seawater-circulating cooling technology, including seawater cooling towers. The use of seawater cooling towers is an effective way not only to reduce marine pollution, but also to conserve the freshwater resources in coastal areas. Seawater salt content causes many engineering problems, including salt deposition, corrosion, fill blockage, and emission drift. In addition, salts change the thermal physical properties of seawater, which then changes the thermal properties of cooling towers. Conventional cooling towers are packed with fill that acts
* Corresponding author. E-mail address: [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.energy.2015.12.125 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
as the medium for heat and mass transfer, as shown in Fig. 1(a). Appropriate fill packing distributes the water current and increase the contact area between water and air [2]. The most common materials used for packing are wood and PVC (used separately) over which the water slowly drips. (More details about material selection for seawater cooling towers, which is beyond the scope of this paper, can be found in a previous study by Walston [3].) The use of these conventional cooling towers for seawater cooling is problematic, however; disadvantages of cooling towers with packing include corrosion, lower rates of temperature drop, higher power consumption, blocked packing, damage to the electric fan, unstable cooling effect, and difficulty in replacing and cleaning the fill. Though it is difficult to apply packing in a cooling tower, and special fill materials add to the overall cost of the tower, entirely removing the packing severely decreases draught drag, which significantly affects power consumption. Considering the above disadvantages of conventional PCTs (packed cooling towers), researchers have developed the SCT (shower cooling tower), in which packing is completely eliminated [4e6]. Unlike conventional cooling towers, which are subject to water quality, shower cooling towers are able to use contaminated water such as seawater or oil-water mixtures. This remarkable advantage lends SCTs enhanced reliability with fill-free maintenance. SCTs manage water spray distribution and cooling by separating the circulating water into tiny droplets in the spray
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X. Qi et al. / Energy 97 (2016) 435e443
List of symbols A c Cd g d hc hd iv m i Lef Nu Pr Re Sc Sh t T u
area [m2] specific heat [kJ/(kg C)] drag coefficient on droplet[dimensionless] gravitational acceleration [m/s2] equivalent diameter [m] heat transfer coefficient [W/m2 K] mass transfer coefficient [kg/m2s] specific vaporization heat of water [kJ/kg] mass or mass flow rate [kg] specific enthalpy [kJ/kg] Lewis factor Nusselt number Prantdl number Reynold number Schmidt number Sherwood number time [s] temperature [ C] velocity [m/s]
distributing drenching zone (in which adequate heat transfer is conducted without fill) and a circulating water zone, which cool the water to the desired temperature. The thermal performance of PCTs has already been thoroughly researched. Merkel proposed the first theory, which contained several assumptions, on conventional cooling towers: the Lewis factor is assumed to be 1, the water loss by evaporation is neglected, and air is assumed to be saturated at the outlet [7]. Sutherland concluded that the Merkel model underestimates tower sizes be€ gener developed a more actween 5% and 15% [8]. Poppe and Ro curate model without Merkel's approximations [9]; the cooling tower characteristics calculated by Poppe's model are about 10% higher than those calculated by the Merkel model [10]. In recent years, several researchers have also investigated shower cooling tower designs with notable results. For example, experimental comparisons of SCTs in different climates were described by Givoni and Yajima [11]. Previous research conducted in our laboratory investigated the relationship between water spray directions and tower performance in an SCT, and a set of equations were applied to predict cooling tower performance [12,13].
U w z
internal energy [J] humidity ratio of moist air evaluated at Ta [kg/kg] vertical coordinate [m]
Greek letters l thermal conductivity coefficient [W/mK] m dynamic viscosity coefficient [Pa/s] r density [kg/m3] Subscripts a air c convection d droplet e evaporation p constant pressure s saturated ss supersaturated v vapor w water 1 inlet 2 outlet
There have been relatively few studies regarding the thermal performance of seawater cooling towers, however. Some data is available in technical reports and design guidance [14,15]. Qualitative discussion on the effects of seawater thermophysical properties on the performance of cooling towers can be found in studies by Nelson [16] and Warner [17], though neither study provided quantitative performance information. Based on these studies, cooling tower companies have asserted that tower performance is degraded by about 1% for every 10,000 ppm of salts in the circulating water. Sharqawy provided a correction factor that relates the performance of seawater to that of freshwater in a cooling tower of the same size and under the same operating conditions [18]. The general lack of advances in seawater cooling tower design technologies calls for a more systematic investigation into the topic. The factor that differentiates seawater cooling towers from freshwater towers is the existence of dissolved minerals (salts) in the cooling water; therefore, establishing the impact of salt in the cooling water is the single most important technical feasibility concern. The purpose of this study is to apply a detailed model to determine the operating characteristics of an SCT. SCT performance
Fig. 1. (a) Schematic representation of conventional cooling tower (PCT) with fill pack. (b) Schematic representation of shower cooling tower (SCT) without fill pack.
X. Qi et al. / Energy 97 (2016) 435e443
is predicted by using heat and mass transfer between water and air, using the theory of heat and mass transfer exchange at the water droplet level, to drive the solution into steady-state conditions. Kloppers conducted a droplet analysis on conventional cooling towers, which can be used as a reference for SCT technology [19]; this model is used here to simulate the performance of a freshwater SCT and seawater SCT, respectively. Investigation of the calculated results can be used to further understand, and therefore more successfully design, seawater SCTs. The results of the present study provide a theoretical basis for improving seawater cycling and cooling technology, and also lay a foundation for the design of seawater cooling towers in future.
437
The heat rejected from water droplets includes convective heat and evaporative heat. The water droplet loses heat to the air at the expense of its internal energy e an energy balance on a control surface surrounding the water droplet yields:
dUd ¼ ðQdc þ Qde Þ dt
(1)
Where
Ud ¼ md cpw Tw ; Qdc ¼ hAd ðTw Ta Þ ; Qde ¼ hd Ad ðwsw wa Þiv (2) Combining the above equations gives
2. Seawater properties analysis As mentioned above, in conventional cooling towers, thermal performance degrades over time due to salt deposition on the packing and subsequent air flow blockage e this makes the application of PCTs altogether impractical. Eliminating the fill completely empties the tower, which benefits the process of circulating seawater with high temperature and turbidity [4]. Seawater characteristics that affect seawater cooling performance include temperature, salinity, density, and specific heat, among a few others. Seawater is a mixed liquid, in which are dissolved a variety of salts, organic substances, and gases, as well as suspended material; more than 80 types of elements have been detected in seawater. In the majority of the earth's seawater, the total content of dissolved inorganic salts accounts for about 35‰ (%), which causes the physical properties of seawater to differ from those of pure water. Relevant physical properties of different concentration seawater are shown in Table 1.
dTw ½hðTw Ta Þ þ hd ðwsw wÞiv Ad ¼ dt cpw rw md h i 6hd lef ðimasw ima Þ þ 1 lef ðwsw wÞiv ¼ cpw rw dd
The water evaporation rate, which is associated with mass transfer, is equal to:
dmd ¼ hd ðwsw wa ÞAd dt
(4)
where h ¼ Nud l=dd ，
Red ¼ ðud þ ua Þdd =n; Pr ¼ mcpa l Nu ¼ 2 þ 0:6Re1=2 Pr1=3
3. Shower cooling tower heat and mass transfer model
dwa ¼
3.1. Mathematical model at water droplet level It is helpful to first understand the heat and mass transfer process at the single water droplet level before investigating the thermal performance of the SCT shown in Fig. 2. A few assumptions are made concerning the water droplet to describe its motion in mathematical language. The droplet is assumed to be spherical, and its diameter small enough that its temperature is uniform. All water droplets are assumed to have uniform diameter, radiation exchange is ignored, collision or scattering of the water droplets are ignored, and circumgyration, libration, and the non-uniformity of internal flow and temperature distribution in the water droplets are also ignored [23].
(3)
dmw dmd ¼ ¼ Nd ma ma dt
(5) mw hd ðwsw wa ÞAd dz ma md ud
(6)
Please refer to Bosnjakovic's paper for a discussion on the derivation and development of the Lewis factor [24]. 3.2. Water droplet force analysis This study utilized information from previous study conducted in our laboratory that analyzed the force exerted on a single water droplet [25]. In the motion of water droplets sprayed from the nozzle, the forces exerted on a droplet moving with certain velocity include gravity, Gd , buoyancy from the air, Fd , and resistance from the air, Rd , which are expressed as follows:
Table 1 Calculating equations of revelant physical properties. Physical property Vapor pressure
Calculating equation pv;w =pv;sw ¼ 1 þ 0:57357
S 100S
[20]
S is seawater salinity in g/kg Specific heat
cp;sw ¼ A þ BT þ CT 2 þ DT 3 A ¼ 5:328 9:76 102 S þ 4:04 104 S2 B ¼ 6:913 103 þ 7:351 104 S 3:15 106 S2 C ¼ 9:6 106 1:927 106 S þ 8:23 109 S2 D ¼ 2:5 109 þ 1:666 109 S 7:125 1012 S2 [21]
Density
rsw ¼ rw þ Sðb1 þ b2 t þ b3 t 2 þ b4 t 3 þ b5 St 2 Þ
Viscosity
b1 ¼ 0:8020; b2 ¼ 2:001 103 ; b3 ¼ 1:677 105 ; b4 ¼ 3:060 108 ; b5 ¼ 1:613 1011 [18] msw ¼ mw ð1 þ AS þ BS2 ÞA ¼ 1:541 103 þ 1:988 105 t 9:52 108 t 2
Surface tension Thermal conductivity
B ¼ 7:974 106 7:561 108 t þ 4:724 1010 t 2 [18] ssw =sw ¼ 1 þ ð0:000226 t þ 0:00946Þlnð1 þ 0:0331 SÞ [18] log10 ðlsw Þ ¼ 3 þ log10 ð240 þ 0:0002SÞ þ 0:434 2:3 343:5þ0:037S 1 tþ273:15 [22] tþ273:15 647:096
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X. Qi et al. / Energy 97 (2016) 435e443
Fig. 2. Schematic representation of the energy exchange at the water droplet level. Fig. 3. Control volume of SCT.
gravity
. Gd ¼ md g ¼ pd3d rw g 6
(7)
buoyancy
. Fd ¼ pd3d ra g 6
(8)
resistance
. Rd ¼ pCd ra U 2 d2d 8
(9)
24 1 þ 0:15jRej0:687 jRej
Cd ¼ 0:44
jRej 1000
(10)
ad ¼
dud du ¼ ud d dt dz
(11)
The two equations given above can be combined to obtain the kinetic equation for water droplets in the SCT:
rw ud
. dud ¼ ðrw ra Þg 3Cd ra ðud þ ua Þ2 4dd dz
ma dima ¼ mw diw þ iw dmw
(12)
(14)
Eq. (13) is substituted into Eq. (14) to obtain:
dTw ¼
ma dima Tw dw mw cpw
(15)
Consider the interface between the water and the air in Fig. 3. An energy balance at the interface yields the following:
dQ ¼ dQc þ dQe
jRej > 1000
The physical definition and Newton's second law of motion are:
ud ¼ dz=dt;
(13)
The energy balance for the control volume of the SCT in Fig. 3 is:
According to the motion condition, the drag coefficient Cd , is expressed as [25]
Cd ¼
dmw ¼ ma dw
(16)
where dQc is a sensible amount of heat transfer due to the difference in temperature,
dQc ¼ hðTw Ta ÞdA
(17)
and dQe is the enthalpy transfer due to difference in vapor concentration between the saturated air at the interface and the mean stream air,
dQe ¼ iv hd ðwsw wa ÞdA
(18)
The enthalpy of the water vapor at the bulk water temperature, Tw , is given by the following: 3.3. SCT thermal balance equations [26e30]. Although it is informative and straightforward, the foregoing analysis represents only one single water droplet. In reality, there are millions of water droplets falling in an SCT, and air and water conditions change from the top to the bottom of the system e in order to predict the total amount of heat rejected, these factors must be accounted for. This section presents an extension of the energy exchange analysis at the water droplet level. The following analysis is based on a one-dimensional model that accounts for property variations in the vertical direction of a countercurrent SCT with height H, divided into N sections of finite thickness dz and finite volume dV. The water is assumed to be distributed evenly in the form of water droplets with average diameter dw. Analysis moves in a positive direction from the top to the bottom of the tower. A mass balance for the control volume in Fig. 3 yields the following:
iv ¼ ifgw0 þ cpv Tw
(19)
The enthalpy of saturated air evaluated at the local bulk water temperature Tw , is given by:
imasw ¼ cpa Tw þ wsw ifgw0 þ cpv Tw
(20)
Eq. (19) is substituted into Eq. (20) and rearranged to obtain:
imasw ¼ cpa Tw þ wiv þ ðwsw wÞiv
(21)
The enthalpy of the airewater vapor mixture per unit mass of dry air is expressed as follows:
ima ¼ cpa Ta þ w ifgw0 þ cpv Ta
(22)
Eq. (22) is then subtracted from Eq. (21). The resultant equation can be simplified if small differences in specific heats, which are evaluated at different temperatures, are ignored [19].
X. Qi et al. / Energy 97 (2016) 435e443
Tw Ta ¼
ðimasw ima Þ ðwsw wÞiv cpma
(23)
Eq. (23) is substituted into Eq. (17), then the resultant equation and Eq. (18) are substituted into Eq. (16) to obtain the following:
h iv ðwsw wÞ dA ðimasw ima Þ þ hd cpma cpma
dQ ¼
h
wsw þ 0:622 1 wa þ 0:622
wsw þ 0:622 ln wa þ 0:622
where Lef gives an indication of the relative rates of heat and mass transfer in an evaporative process. In the Merkel model, Lef is assumed to be 1 in order to simplify the simulation. According to other research, however, the water evaporation rate is a function of the actual value of the Lewis factor [28]. The enthalpy transfer to the air stream from Eq. (24) is:
i dQ h h ¼ ¼ d Lef ðimasw ima Þ þ 1 Lef iv ðwsw wÞ dA ma ma (26)
For a one-dimensional SCT model, the number of droplets per control volume with a section dz is:
Nd ¼
mw dz md ud
3.4. Governing equations of heat and mass transfer in SCT for supersaturated air The control volume in Fig. 3 is also applicable to supersaturated air. Because the excess water vapor condenses as a mist, the enthalpy of supersaturated air is expressed as follows:
iss ¼ cpa Ta þ wsa ifgw0 þ cpv Ta þ ðwa wsa Þcpw Ta (25)
dima
In this circumstance, however, the computed WBT (Wet Bulb Temperature) is higher than the DBT (Dry Bulb Temperature), which means the air is supersaturated. Thus, the excess water vapor transferred to the free stream air condenses as a mist, and the air is supersaturated before arriving at the outlet of the tower, so the assumption of the unsaturated air must be corrected.
(24)
where c h h ¼ Lef is an indication of the relative rates of heat and pma d mass transfer in an evaporative process. Bosnjakovic developed an empirical relation for the Lewis factor Lef for airewater vapor systems. The Lewis factor for unsaturated air, according to Bosnjakovic, is as follows [24] K:
Lef ¼ 0:8650:667
439
(32)
Assume that the heat and mass transfer coefficients for supersaturated and unsaturated air are the same, as proposed by Poppe €gener [29,30]. The potential for mass transfer is characterand Ro ized by the difference in humidity ratio between the saturated air at the airewater interface and the saturated free stream air, thus:
dmw ¼ hd ðwsw wsa ÞdA
(33)
Simulating the derivation process yields the following:
dQ ¼ hðTw Ta ÞdA þ iv hd ðwsw wsa ÞdA Tw Ta ¼
(34)
ðimasw iss Þ ðwsw wsa Þiv þ ðwa wsa Þcpw Tw cpa þ wsa cpv þ ðw wsa Þiv (35)
(27) Substituting Eq. (35) into Eq. (34) results in:
The transfer area for dz is usually expressed as follows:
dA ¼
mw dz 2 6mw dz pdd ¼ m d ud rw ud dd
(28)
dQ ¼ hc
ðimasw iss Þ ðwsw wsa Þiv þ ðwa wsa Þcpw Tw dA cpa þ wsa cpv þ ðw wsa Þiv
þ iv hd ðwsw wsa ÞdA
Eq. (28) is substituted into Eq. (27):
(36) dima
dQ ¼ ma mw 6hd h Lef ðimasw ima Þ ¼ ma rw ud dd i þ 1 Lef iv ðwsw wÞ dz
dima dQ ¼ ma dz mw 6hd h Lef ðimasw ima Þ ¼ ma rw ud dd i þ 1 Lef iv ðwsw wÞ
Proceeding along the same lines as in the case of unsaturated air,
dima ¼
(37)
(29)
Based on the equations above,
ma dwa ¼ hd ðwsw wa ÞdA
mw ma
6hd ðwsw wa Þdz rw ud dd
where cpmas is the specific heat of supersaturated air per unit mass, and cpmas ¼ cpa þ wsa cpv þ ðw wsa Þiv c h h ¼ Lef is defined as the pmas d Lewis factor for saturated air. The empirical relation used by Bosnjakovic can also be used to calculate the Lewis factor, which for supersaturated air is:
(30) Lef ¼ 0:8650:667
The above equation can be rearranged as follows:
dwa ¼
mw 6hd hc ðimasw iss Þ ðwsw wsa Þiv ma rw ud dd hd cpmas
þ ðwa wsa Þcpw Tw þ ½iv ðwsw wsa Þ dz
wsw þ 0:622 wsw þ 0:622 1 ln wsa þ 0:622 wsa þ 0:622 (38)
(31)
Proceeding along the same lines as in the case of unsaturated air, the governing equations for supersaturated air can be obtained as follows:
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dTw ¼
X. Qi et al. / Energy 97 (2016) 435e443
n 6hd Lef ðimasw iss Þ ðwsw wsa Þiv cpw rw ud dd þ ðwa wsa Þcpw Tw þ ½iv ðwsw wsa Þ ðwsw o wsa Þcpw Tw dz
dwa ¼
mw ma
6hd ðwsw wsa Þdz rw ud dd
(39)
(40)
At this point, the derivation of the system of governing equations for saturated air in SCTs is complete. 3.5. Calculation approach The fourth-order Runge-Kutta method can be applied to solve the differential equations for both unsaturated and supersaturated outlet air conditions [31,32]. The given parameters are: water to air flow rate ratio, air velocity, discharge droplet velocity, droplet diameter, tower spray zone height, inlet water temperature, and air inlet dry- and wet-bulb temperatures. The equations for unsaturated (or saturated) air are comprised of Eqs. (3), (12), (29) and (31). The equations for supersaturated air are comprised of Eqs. (3), (37), (39) and (40). ima should be replaced by iss for supersaturated air. Because the numerical equations for heat and mass transfer were derived under two respective cases, corresponding equations for the outlet air must be selected appropriately. The velocity of the water droplet though the tower changes with time and height. In order to calculate the heat transfer and temperature variations of a water droplet, the entire tower height was divided into n sections with thickness dz. Assume that section n is filled with water droplets entering the section at temperature Tw;n and exiting at Tw;nþ1 , and the air enters the section with enthalpy ima;nþ1 and exits with ima;n . Iterative calculation in each section is completed according to initial conditions and boundary conditions. The parameter conditions of water and air in each position are obtained after solving all iterations step-by-step; this method is dependable only if the step length is sufficiently brief.
Fig. 4. A schematic diagram of the test shower cooling tower.
times in all and their averages were considered the final results. When thermal balance error between air and water was less than 5 percent, the measured data were considered valid [33] and the original experimental data were recorded. The instruments used in the experiment are detailed in Table 2. A comparison of the outlet water temperature between the calculated and the experimental results is shown in Table 3 and Fig. 6. Note that the current model predicted the outlet water temperatures with an error of less than 6%, indicating that the theory is capable of estimating the performance of real freshwater and seawater SCTs accurately.
4. Experimental apparatus and procedure As discussed above, experimental studies on cooling towers reported in the literature depart from the type of tower examined here. For this reason, researching practical, full-scale towers is preferred. The experiment in this study was performed in a shower cooling tower at Jiangsu Seagull Cooling Tower Company, Ltd. A schematic diagram of the test rig is provided in Fig. 4, and a picture of the test SCT is shown in Fig. 5. For the seawater shower cooling tower, fill is removed. One side wall of the tower is made of polycarbonate material to allow direct test of the droplet diameter. The tower was 3.3 m 3.3 m across with a total height of 6.7 m. The nozzles were mounted to an adjustable frame. The test nozzle height H was adjusted from 4.0 m to 6.0 m. The water was pumped to a tank where its temperature was kept at a constant value during test. The experiment on droplet diameter was conducted by the DualPDA system, manufactured by Dantec Dynamics. This system includes Ar-Ion laser, transmitter, receiver, bandpass filter, signal processor, and so on. For all measurements, the droplet SMDs (Sauter mean diameters) are measured at three points randomly. By averaging the data acquired repeatedly, the local SMDs are finally obtained. The experiment was performed under steady state conditions, that is, the parameters described above were simultaneously measured when the system was stable, then re-measured after an appropriate period of time. Measurements were repeated five
Fig. 5. Photograph of the test shower cooling tower.
X. Qi et al. / Energy 97 (2016) 435e443
441
Table 2 Measuring device in the experiment. Measuring parameter
Device
Inlet air dry and wet bulb temperature Motor power Barometric pressure Inlet and outlet water temperature Cooling water flow rate and spray device flow rate Water pressure Inlet air capacity Air velocity Air capacity regulator Temperature acquisition
PHMZ ventilation psychrometer Three-phase power meter Aneroid barometer Thermometer Water flowmeter
Air temperature at the exit and in the tower
Pressure gage Standard pitot tube A4201 digital speed detector DV-707 variable-frequency Drive 34970A HP data acquisition instrument Copper-constantan thermocouple
5. Analysis and comparison between freshwater and seawater cooling tower The performance of a seawater SCT was investigated by means of the model described above, based on the characteristics of seawater parameters. For cooling tower service, any circulating water with chloride (NaCl) content above 750 parts per million (ppm) is generally considered to be “saltwater”. That said, the detrimental effects of chlorides are much less severe at 750 ppm than at higher concentrations. Saltwater may originate from the open ocean, brackish (estuarine) areas, or brine wells. Because an open recirculating system concentrates the dissolved solids in the makeup water, a cooling tower may be exposed to saltwater conditions even though the makeup contains less than 750 ppm NaCl. The parameters used in the calculations are shown in Table 4. The outlet water temperature of freshwater, seawater concentration “1”, seawater concentration “2”, and seawater concentration “3” were obtained respectively under varying conditions. Results show that the parameters that most strongly affect the thermal performance of SCT are specific heat capacity, density, and vapor pressure. Surface tension, viscosity, and thermal conductivity also affect the heat and mass transfer between air and droplets. Salt impacts water in several basic ways affecting thermal performance: salt lowers the vapor pressure, reduces the specific heat, reduces the thermal conductivity, and increases the density of the solution. The first three tend to decrease thermal performance, but the latter tends to increase it. The compensating effect of increased density is
Fig. 6. The calculated outlet water temperature vs. the measured outlet water temperature.
not sufficient to entirely offset the effects of reduced specific heat and vapor pressure, however, so some loss of thermal performance results. The amount of loss is greater at higher salt concentrations and during more difficult cooling processes. 5.1. Influence of droplet diameter on outlet water temperature As Fig. 7 shows, seawater cooling performance decreases with increasing diameter and saltwater concentration of water droplets. Seawater cooling performance decreased 2.17% at saltwater concentration 1, 5.59% at concentration 2, and 9.86% at concentration 3 compared to freshwater. Fig. 7 shows variations in predicted outlet water temperature with water droplet diameter for different concentrations. Results show that cooling performance reduces as droplet diameter and concentration increase. For clarity, the prediction in terms of convection and evaporation were also analyzed e about 97% of the heat load is dissipated by evaporation and the remaining 3% is dissipated through convection. The total heat transfer decreases as droplet diameter increases. Convective heat dissipation accounts for only 1.82% of the total heat transfer at droplet diameter of 1 mm. The heat dissipated by evaporation varies linearly based on the difference between air moisture at the inlet and that at the exit. For
Table 3 Comparison between the calculated and the experimental results. Parameters
Nozzle height (m) Water flow rate (m3/h) Air flow rate (m3/h) Droplet diameter (mm) Atmospheric pressure (kPa) Dry-bulb temperature of inlet air ( C) Wet-bulb temperature of inlet air ( C) Inlet water temperature ( C) Experimental outlet water temperature ( C)
Experimental average data ( C) Computed water temperature ( C) Relative error (%)
Test 1
2
3
4
5
6
7
4.4 48.45 86,206 1.6 102 25 20.6 43.6 31.5 31.6 31.3 31.7 31.4 31.5 31.1 3.4%
4.4 87.80 86206 1.6 101.6 28.6 21.6 43.8 33.5 33.7 33.2 33.1 33.5 33.4 33.1 2.9%
4.4 105.4 117,525 1.6 103.1 19 14.2 44.8 31.9 32.2 31.9 32.2 31.8 32 32.1 0.8%
4.9 97.72 101,987 1.6 102.1 28 21.7 42.8 33.0 32.7 32.8 32.5 32.5 32.7 32.2 4.76%
4.9 58.86 117,535 1.7 101.7 28.5 19 42.2 28.1 28.6 28.9 27.9 29.0 28.5 29.1 5.13%
5.4 103.4 86,206 1.8 102.3 26 21.3 45.5 35.5 34.7 35.0 34.9 35.9 35.2 34.9 2.91%
5.4 61.7 105,932 1.5 102.3 23.8 17.4 41.3 28.5 28.2 28.3 28.0 28.5 28.3 28.2 0.77%
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X. Qi et al. / Energy 97 (2016) 435e443
Table 4 Calculation parameters. Dry-bulb temperature of inlet air ( C)
Wet-bulb temperature of inlet air ( C)
Atmospheric pressure (kPa)
Water flow rate (m3/h)
Air flow rate (m3/h)
Inlet water temperature ( C)
33.5 10.5
26.7 3.7
102 102
55.21 55.21
86206 86206
48 48
related changes in the physical properties of seawater. The literature includes sufficient data for general seawater properties, but relevant thermophysical properties are available from relatively few sources. A recent assessment of seawater properties was provided by Sharqawy et al., who found that when water temperature is high, surface tension, specified heat capacity, and density decrease less drastically for seawater with higher salt concentration, and that the changing tendencies of other related properties are similar, as well [20]. Comprehensive results are shown in Fig. 8. 5.3. Influence of air flow rate on outlet water temperature
Fig. 7. Effects of droplet diameter and seawater concentration on the outlet water temperature.
larger droplet diameters, the amount of evaporative heat dissipation decreases with increasing seawater concentration due to changes in physical properties. In practice, smaller droplets are preferable for the sake of cooling performance. There remain some limitations, however, if the possibility of droplets escaping the tower is considered. Working conditions must be specified accordingly. 5.2. Influence of inlet water temperature on outlet water temperature Fig. 8 shows the predicted Tw,o with inlet water temperature for different seawater concentrations. Clearly, outlet water temperature decreases alongside inlet water temperature. Based on the predicted results, cooling performance decreases as seawater concentration increases and at higher inlet water temperatures. At higher temperatures of inlet water, the heat load decreases slightly less with increasing seawater concentration due to temperature-
Fig. 8. Effects of inlet water temperature and seawater concentration on the outlet water temperature.
Fig. 9 shows variations in the predicted Tw,o with varying droplet diameters for different seawater concentrations. Results show that the cooling efficiency of the SCT increases as RAW (airto-water ratio) increases. This observation most likely applies to all types of cooling towers, though larger RAW is possible in an SCT compared to a PCT because the tower resistance is relatively smaller. Additionally, when RAW increases, the cooling efficiency improves much more as droplet diameter shrinks. For larger droplet diameters, even if the RAW increases significantly, the cooling effect does not significantly change. At smaller RAW, the influence of droplet size on the cooling effect is also very small. In order to best detail the two groups of curves, only freshwater and seawater concentration 2 were drawn (Fig. 9). The droplet diameters of the two groups of curves are 1.5 mm and 3 mm, respectively. Fig. 7 shows where the cooling efficiency difference of the upper group of curves is much greater than that of the bottom group (see the explanation in Section 5.1). For larger droplet diameters, the amount of evaporative heat dissipation decreases much more with increasing seawater concentration due to changes in physical properties. 5.4. Influence of seawater concentration on relative humidity of air The relative humidity of air in an SCT varies as shown in Fig. 10. Relative humidity increases monotonically until reaching its the maximum at the SCT outlet. The higher the concentration of seawater, the weaker the heat and mass transfer process; therefore, when the seawater concentration is fairly uniform, the air moisture increases much faster (ceteris paribus).
Fig. 9. Outlet water temperature vs. ratio of air to water & droplet diameter.
X. Qi et al. / Energy 97 (2016) 435e443
443
Acknowledgments This study was supported by the Natural Science Foundation of China (51309147 and 51249001) and Project of Shandong Province Higher Educational Science and Technology Program (J11LD22). The authors also gratefully acknowledge the support of Dr. Qianjian Guo.
References
Fig. 10. Relative humidity of air in an SCT.
6. Conclusions It is very important for the health and future of the global environment to reduce the emission of waste heat to the sea due to marine industries. The use of seawater circulating cooling systems is an effective way not only to conserve freshwater resources but also to reduce marine pollution. The fill packing necessary in PCTs is subject to contamination during the seawater (which contains dissolved minerals, or salts, as opposed to freshwater) circulation cooling process, which gradually reduces the tower's cooling efficiency. In this study, an SCT was utilized as an alternative for the seawater cooling industry. Circulating seawater in an SCT is separated into thin droplets in the tower, in which normal heat transfer can be conducted without fill to cool the seawater to the desired temperature. This study was conducted in effort to provide a reference for future seawater shower cooling tower design technologies, as there has been a general lack of systematic investigation into the topic prior to now. This study numerically investigated an SCT model, and then validated the calculation results with experimental data. A comparative prediction of the outlet water temperature between freshwater and seawater at different salt concentrations was conducted and the results were carefully analyzed. Cooling performance was shown to reduce as droplet diameter and salt concentration increase. For clarity, the predictions were analyzed in terms of convection and evaporation, as well. For larger droplet diameters, the amount of evaporative heat dissipation decreases as seawater concentration increases due to changes in physical properties. The prediction results also showed that cooling performance decreases with increasing water concentration at higher inlet water temperatures. At higher temperatures of inlet water, the heat load decreases slightly less with increasing seawater concentration, because changes in the physical properties of seawater are related to temperature. Results also show that larger air-to-water ratio is possible in an SCT compared to a PCT, because the tower resistance is relatively smaller. When RAW increases, cooling efficiency improves as droplet diameter decreases. For larger droplet diameters, even if the RAW increases greatly, the cooling effect does not significantly change e this is because for larger droplet diameters, the amount of evaporative heat dissipation decreases with increasing seawater concentration due to changing physical properties. Relative humidity increases monotonically and reaches its maximum at the SCT outlet; when the seawater concentration is reduced, the air moisture increases (ceteris paribus). The above results altogether provide a valuable theoretical basis for advancing seawater cycling and cooling technologies, as well as lay the foundation for improving the design of seawater cooling towers in the future.
[1] Nester DM. Salt water cooling tower. Chem Eng Prog 1971;677:49e51. [2] KrVoger DG. Air-cooled heat exchangers and cooling towers. Begell House; 1998. p. 875. [3] Walston KR. Materials problems in salt water cooling towers. Mater Perform 1975;14(6):22e6. [4] Shiying Wei. WFL series cooling tower: vacuum and crynogerics, vol. 12; 1996. p. 187e93. [5] Yajima Satoshi. Experimental performance of the shower cooling tower. Renew Energy 1996;10(2/3):179e83. [6] Muangnoi Thirapong, Asvapoositkul Wanchai, Hungspreugs Pibool. Performance characteristics of a downward spray water-jet cooling tower. Appl Therm Eng 2014;69:165e76. [7] Verdunstungskuhlung MF. VDI-Zeitchrift 1995;70(1):123e8. [8] Sutherland JW. Thermal environmental engineering. 2nd ed. Prentice-Hall; 1983. [9] Poppe, M., Rogener. Berlin:VDI-Warmeatlas, Mi1-Mi 1991;1e15. [10] Kloppers JC, Kroger DG. Cooling tower performance evaluation: Merkel, Poppe, and e-NTU methods of analysis. J Eng Gas Turb Power 2005;127(1): 1e7. [11] Givoni B. Performance of the shower cooling tower in different climates. Renew Energy 1997;10(2e3):173e8. [12] Qi X, Liu Z, Li D. Performance characteristics of a shower cooling tower. Energy Conv Manag 2007;48(1):193e203. [13] Qi X, Liu Z, Li D. Prediction of the performance of a shower cooling tower based on projection pursuit regression. Appl Therm Eng 2008;28(8e9): 1031e8. [14] Ying BY, David S. The use of cooling towers for salt water heat rejection. KS: The Marley Cooling Tower; 1991. [15] Eftekharzadeh S, Baasiri. Feasibility of seawater cooling towers for large-scale petrochemical development. Cooling Tower Institute; 2003. Report No TP0317. [16] Nelson JA. Cooling tower and salt water. Marley Cool Tower; 1986. [17] Warner ME. Salt water natural-draft cooling tower design considerations. Proc Am Power Conf 1974;36:442e53. [18] Sharqawy MH, Lienhard. Thermophysical properties of seawater: a review of existing correlations and data. Desalination Water Treat 2010;16:354e80. [19] Kloppers JC, Kroger DG. A critical investigation into the heat and mass transfer analysis of counterflow wet-cooling towers. Int J Heat and Mass Trans 2005;48:765e77. [20] Millero FJ, Feistel. The composition of standard seawater and the definition of the reference-composition salinity scale. Deep-sea Res Part I 2008;55: 50e72. [21] Jamieson DT, Tudhope. Physical properties of sea water solutions: heat capacity. Desalination 1969;71:23e30. [22] Amieson DT, Tudhope. Physical properties of sea water Solutionsdthermal conductivity. Desalination 1970;8:393e401. [23] Baker D. Cooling tower performance. Chemical Publishing Co.; 1984. [24] Bosnjakovic F. The technology of thermodynamics. Theodor Steinkopf Press; 1965. [25] Narasimhamury GSR, Purushothaman A. Hydrodynamics of liquid drops in air. In: Cheremisinoff NP, editor. GaseLiquid flows, encyclopedia of fluid mechanics, vol. 3. Gulf Publishing; 1986. p. 250e79. [26] Kloppers JC. A critical evaluation and refinement of the performance prediction of wet-cooling towers [PhD thesis]. Stellenbosch, Western Cape: South Africa:University of Stellenbosch; 2003. €ger DG. Loss coefficient correlation for wet-cooling tower fills. [27] Kloppers JC, Kro Appl Therm Eng 2003;23(17):2201e11. € ger DG. The Lewis factor and its influence on the perfor[28] Kloppers JC, Kro mance prediction of wet-cooling towers. Int J Heat Mass Transf 2005a;44(9):879e84. €ger DG. Refinement of the transfer characteristic correlation [29] Kloppers JC, Kro of wet-cooling tower fills. Heat Transf Eng 2005c;26(4):35e41. € ger DG. Air-cooled heat exchangers and cooling towers. 1st ed. Tulsa, OK: [30] Kro Penn Well Corp; 2004. [31] Burden RL, Faires JD. Numerical analysis. 6th ed. Brooks/Cole Publishing Company; 1997. [32] Mathews JH. Numerical methods for mathematics, science, and engineering. 2nd ed. Rentice-Hall International, Inc; 1992. [33] Panwaree P. Experimental study in cooling Tower Spray nozzle characteristics [M.Eng. thesis]. Thailand: Mechanical Engineering, King Mongkut’s University of Technology Thonburi; 2010 [in Thai].
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Performance prediction of seawater shower cooling towers Xiaoni Qi a, Yongqi Liu a, *, Qianjian Guo b, Jie Yu b, Shanshan Yu b a b
College of Traffic and Vehicle Engineering, Shandong University of Technology, Zhangzhou Road 12, Zibo 255049, China College of Mechanical Engineering, Shandong University of Technology, Zhangzhou Road 12, Zibo 255049, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 April 2015 Received in revised form 6 November 2015 Accepted 28 December 2015 Available online xxx
The salt content in seawater results in many considerable engineering problems, including salt deposition, corrosion, and fill blockage. Seawater cooling towers are a promising potential remedy, but the lack of progress in cooling tower design technology calls for a more systematic investigation into this topic. In this study, a shower cooling tower without packing was used in seawater circulating cooling system, and a complete mathematical model of the shower cooling tower's performance was developed. The model describes the experimental data with an accuracy of about 5%. This study also conducted a comparative prediction of the outlet water temperature between freshwater and seawater in a shower cooling tower; results showed that cooling performance decreases as inlet water temperature increases. The results also show that cooling performance degrades as droplet diameter and salt concentration increase. When the air-to-water ratio increases, cooling efficiency improves, and when seawater concentration is reduced, air moisture increases at a higher rate. These results altogether provide a valuable theoretical basis for improving seawater cycling and cooling technologies in the future. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Shower cooling tower Seawater cooling Heat and mass transfer
1. Introduction Seawater cooling towers have been used in coastal facilities across the globe since the 1970s. During industrial activities at sea, it is necessary to reduce the emission of waste heat to the ocean and protect the marine environment. In order to ensure sustainability and prevent thermal pollution from damaging aquatic resources, effective measures must be adopted to sustain the water temperature in the vicinity of fishing waters in accordance with national water quality standards. Many governments have imposed regulations on high-temperature waste water that is discharged to the sea [1]. One effective way of meeting these regulations is the utilization of seawater-circulating cooling technology, including seawater cooling towers. The use of seawater cooling towers is an effective way not only to reduce marine pollution, but also to conserve the freshwater resources in coastal areas. Seawater salt content causes many engineering problems, including salt deposition, corrosion, fill blockage, and emission drift. In addition, salts change the thermal physical properties of seawater, which then changes the thermal properties of cooling towers. Conventional cooling towers are packed with fill that acts
* Corresponding author. E-mail address: [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.energy.2015.12.125 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
as the medium for heat and mass transfer, as shown in Fig. 1(a). Appropriate fill packing distributes the water current and increase the contact area between water and air [2]. The most common materials used for packing are wood and PVC (used separately) over which the water slowly drips. (More details about material selection for seawater cooling towers, which is beyond the scope of this paper, can be found in a previous study by Walston [3].) The use of these conventional cooling towers for seawater cooling is problematic, however; disadvantages of cooling towers with packing include corrosion, lower rates of temperature drop, higher power consumption, blocked packing, damage to the electric fan, unstable cooling effect, and difficulty in replacing and cleaning the fill. Though it is difficult to apply packing in a cooling tower, and special fill materials add to the overall cost of the tower, entirely removing the packing severely decreases draught drag, which significantly affects power consumption. Considering the above disadvantages of conventional PCTs (packed cooling towers), researchers have developed the SCT (shower cooling tower), in which packing is completely eliminated [4e6]. Unlike conventional cooling towers, which are subject to water quality, shower cooling towers are able to use contaminated water such as seawater or oil-water mixtures. This remarkable advantage lends SCTs enhanced reliability with fill-free maintenance. SCTs manage water spray distribution and cooling by separating the circulating water into tiny droplets in the spray
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X. Qi et al. / Energy 97 (2016) 435e443
List of symbols A c Cd g d hc hd iv m i Lef Nu Pr Re Sc Sh t T u
area [m2] specific heat [kJ/(kg C)] drag coefficient on droplet[dimensionless] gravitational acceleration [m/s2] equivalent diameter [m] heat transfer coefficient [W/m2 K] mass transfer coefficient [kg/m2s] specific vaporization heat of water [kJ/kg] mass or mass flow rate [kg] specific enthalpy [kJ/kg] Lewis factor Nusselt number Prantdl number Reynold number Schmidt number Sherwood number time [s] temperature [ C] velocity [m/s]
distributing drenching zone (in which adequate heat transfer is conducted without fill) and a circulating water zone, which cool the water to the desired temperature. The thermal performance of PCTs has already been thoroughly researched. Merkel proposed the first theory, which contained several assumptions, on conventional cooling towers: the Lewis factor is assumed to be 1, the water loss by evaporation is neglected, and air is assumed to be saturated at the outlet [7]. Sutherland concluded that the Merkel model underestimates tower sizes be€ gener developed a more actween 5% and 15% [8]. Poppe and Ro curate model without Merkel's approximations [9]; the cooling tower characteristics calculated by Poppe's model are about 10% higher than those calculated by the Merkel model [10]. In recent years, several researchers have also investigated shower cooling tower designs with notable results. For example, experimental comparisons of SCTs in different climates were described by Givoni and Yajima [11]. Previous research conducted in our laboratory investigated the relationship between water spray directions and tower performance in an SCT, and a set of equations were applied to predict cooling tower performance [12,13].
U w z
internal energy [J] humidity ratio of moist air evaluated at Ta [kg/kg] vertical coordinate [m]
Greek letters l thermal conductivity coefficient [W/mK] m dynamic viscosity coefficient [Pa/s] r density [kg/m3] Subscripts a air c convection d droplet e evaporation p constant pressure s saturated ss supersaturated v vapor w water 1 inlet 2 outlet
There have been relatively few studies regarding the thermal performance of seawater cooling towers, however. Some data is available in technical reports and design guidance [14,15]. Qualitative discussion on the effects of seawater thermophysical properties on the performance of cooling towers can be found in studies by Nelson [16] and Warner [17], though neither study provided quantitative performance information. Based on these studies, cooling tower companies have asserted that tower performance is degraded by about 1% for every 10,000 ppm of salts in the circulating water. Sharqawy provided a correction factor that relates the performance of seawater to that of freshwater in a cooling tower of the same size and under the same operating conditions [18]. The general lack of advances in seawater cooling tower design technologies calls for a more systematic investigation into the topic. The factor that differentiates seawater cooling towers from freshwater towers is the existence of dissolved minerals (salts) in the cooling water; therefore, establishing the impact of salt in the cooling water is the single most important technical feasibility concern. The purpose of this study is to apply a detailed model to determine the operating characteristics of an SCT. SCT performance
Fig. 1. (a) Schematic representation of conventional cooling tower (PCT) with fill pack. (b) Schematic representation of shower cooling tower (SCT) without fill pack.
X. Qi et al. / Energy 97 (2016) 435e443
is predicted by using heat and mass transfer between water and air, using the theory of heat and mass transfer exchange at the water droplet level, to drive the solution into steady-state conditions. Kloppers conducted a droplet analysis on conventional cooling towers, which can be used as a reference for SCT technology [19]; this model is used here to simulate the performance of a freshwater SCT and seawater SCT, respectively. Investigation of the calculated results can be used to further understand, and therefore more successfully design, seawater SCTs. The results of the present study provide a theoretical basis for improving seawater cycling and cooling technology, and also lay a foundation for the design of seawater cooling towers in future.
437
The heat rejected from water droplets includes convective heat and evaporative heat. The water droplet loses heat to the air at the expense of its internal energy e an energy balance on a control surface surrounding the water droplet yields:
dUd ¼ ðQdc þ Qde Þ dt
(1)
Where
Ud ¼ md cpw Tw ; Qdc ¼ hAd ðTw Ta Þ ; Qde ¼ hd Ad ðwsw wa Þiv (2) Combining the above equations gives
2. Seawater properties analysis As mentioned above, in conventional cooling towers, thermal performance degrades over time due to salt deposition on the packing and subsequent air flow blockage e this makes the application of PCTs altogether impractical. Eliminating the fill completely empties the tower, which benefits the process of circulating seawater with high temperature and turbidity [4]. Seawater characteristics that affect seawater cooling performance include temperature, salinity, density, and specific heat, among a few others. Seawater is a mixed liquid, in which are dissolved a variety of salts, organic substances, and gases, as well as suspended material; more than 80 types of elements have been detected in seawater. In the majority of the earth's seawater, the total content of dissolved inorganic salts accounts for about 35‰ (%), which causes the physical properties of seawater to differ from those of pure water. Relevant physical properties of different concentration seawater are shown in Table 1.
dTw ½hðTw Ta Þ þ hd ðwsw wÞiv Ad ¼ dt cpw rw md h i 6hd lef ðimasw ima Þ þ 1 lef ðwsw wÞiv ¼ cpw rw dd
The water evaporation rate, which is associated with mass transfer, is equal to:
dmd ¼ hd ðwsw wa ÞAd dt
(4)
where h ¼ Nud l=dd ，
Red ¼ ðud þ ua Þdd =n; Pr ¼ mcpa l Nu ¼ 2 þ 0:6Re1=2 Pr1=3
3. Shower cooling tower heat and mass transfer model
dwa ¼
3.1. Mathematical model at water droplet level It is helpful to first understand the heat and mass transfer process at the single water droplet level before investigating the thermal performance of the SCT shown in Fig. 2. A few assumptions are made concerning the water droplet to describe its motion in mathematical language. The droplet is assumed to be spherical, and its diameter small enough that its temperature is uniform. All water droplets are assumed to have uniform diameter, radiation exchange is ignored, collision or scattering of the water droplets are ignored, and circumgyration, libration, and the non-uniformity of internal flow and temperature distribution in the water droplets are also ignored [23].
(3)
dmw dmd ¼ ¼ Nd ma ma dt
(5) mw hd ðwsw wa ÞAd dz ma md ud
(6)
Please refer to Bosnjakovic's paper for a discussion on the derivation and development of the Lewis factor [24]. 3.2. Water droplet force analysis This study utilized information from previous study conducted in our laboratory that analyzed the force exerted on a single water droplet [25]. In the motion of water droplets sprayed from the nozzle, the forces exerted on a droplet moving with certain velocity include gravity, Gd , buoyancy from the air, Fd , and resistance from the air, Rd , which are expressed as follows:
Table 1 Calculating equations of revelant physical properties. Physical property Vapor pressure
Calculating equation pv;w =pv;sw ¼ 1 þ 0:57357
S 100S
[20]
S is seawater salinity in g/kg Specific heat
cp;sw ¼ A þ BT þ CT 2 þ DT 3 A ¼ 5:328 9:76 102 S þ 4:04 104 S2 B ¼ 6:913 103 þ 7:351 104 S 3:15 106 S2 C ¼ 9:6 106 1:927 106 S þ 8:23 109 S2 D ¼ 2:5 109 þ 1:666 109 S 7:125 1012 S2 [21]
Density
rsw ¼ rw þ Sðb1 þ b2 t þ b3 t 2 þ b4 t 3 þ b5 St 2 Þ
Viscosity
b1 ¼ 0:8020; b2 ¼ 2:001 103 ; b3 ¼ 1:677 105 ; b4 ¼ 3:060 108 ; b5 ¼ 1:613 1011 [18] msw ¼ mw ð1 þ AS þ BS2 ÞA ¼ 1:541 103 þ 1:988 105 t 9:52 108 t 2
Surface tension Thermal conductivity
B ¼ 7:974 106 7:561 108 t þ 4:724 1010 t 2 [18] ssw =sw ¼ 1 þ ð0:000226 t þ 0:00946Þlnð1 þ 0:0331 SÞ [18] log10 ðlsw Þ ¼ 3 þ log10 ð240 þ 0:0002SÞ þ 0:434 2:3 343:5þ0:037S 1 tþ273:15 [22] tþ273:15 647:096
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X. Qi et al. / Energy 97 (2016) 435e443
Fig. 2. Schematic representation of the energy exchange at the water droplet level. Fig. 3. Control volume of SCT.
gravity
. Gd ¼ md g ¼ pd3d rw g 6
(7)
buoyancy
. Fd ¼ pd3d ra g 6
(8)
resistance
. Rd ¼ pCd ra U 2 d2d 8
(9)
24 1 þ 0:15jRej0:687 jRej
Cd ¼ 0:44
jRej 1000
(10)
ad ¼
dud du ¼ ud d dt dz
(11)
The two equations given above can be combined to obtain the kinetic equation for water droplets in the SCT:
rw ud
. dud ¼ ðrw ra Þg 3Cd ra ðud þ ua Þ2 4dd dz
ma dima ¼ mw diw þ iw dmw
(12)
(14)
Eq. (13) is substituted into Eq. (14) to obtain:
dTw ¼
ma dima Tw dw mw cpw
(15)
Consider the interface between the water and the air in Fig. 3. An energy balance at the interface yields the following:
dQ ¼ dQc þ dQe
jRej > 1000
The physical definition and Newton's second law of motion are:
ud ¼ dz=dt;
(13)
The energy balance for the control volume of the SCT in Fig. 3 is:
According to the motion condition, the drag coefficient Cd , is expressed as [25]
Cd ¼
dmw ¼ ma dw
(16)
where dQc is a sensible amount of heat transfer due to the difference in temperature,
dQc ¼ hðTw Ta ÞdA
(17)
and dQe is the enthalpy transfer due to difference in vapor concentration between the saturated air at the interface and the mean stream air,
dQe ¼ iv hd ðwsw wa ÞdA
(18)
The enthalpy of the water vapor at the bulk water temperature, Tw , is given by the following: 3.3. SCT thermal balance equations [26e30]. Although it is informative and straightforward, the foregoing analysis represents only one single water droplet. In reality, there are millions of water droplets falling in an SCT, and air and water conditions change from the top to the bottom of the system e in order to predict the total amount of heat rejected, these factors must be accounted for. This section presents an extension of the energy exchange analysis at the water droplet level. The following analysis is based on a one-dimensional model that accounts for property variations in the vertical direction of a countercurrent SCT with height H, divided into N sections of finite thickness dz and finite volume dV. The water is assumed to be distributed evenly in the form of water droplets with average diameter dw. Analysis moves in a positive direction from the top to the bottom of the tower. A mass balance for the control volume in Fig. 3 yields the following:
iv ¼ ifgw0 þ cpv Tw
(19)
The enthalpy of saturated air evaluated at the local bulk water temperature Tw , is given by:
imasw ¼ cpa Tw þ wsw ifgw0 þ cpv Tw
(20)
Eq. (19) is substituted into Eq. (20) and rearranged to obtain:
imasw ¼ cpa Tw þ wiv þ ðwsw wÞiv
(21)
The enthalpy of the airewater vapor mixture per unit mass of dry air is expressed as follows:
ima ¼ cpa Ta þ w ifgw0 þ cpv Ta
(22)
Eq. (22) is then subtracted from Eq. (21). The resultant equation can be simplified if small differences in specific heats, which are evaluated at different temperatures, are ignored [19].
X. Qi et al. / Energy 97 (2016) 435e443
Tw Ta ¼
ðimasw ima Þ ðwsw wÞiv cpma
(23)
Eq. (23) is substituted into Eq. (17), then the resultant equation and Eq. (18) are substituted into Eq. (16) to obtain the following:
h iv ðwsw wÞ dA ðimasw ima Þ þ hd cpma cpma
dQ ¼
h
wsw þ 0:622 1 wa þ 0:622
wsw þ 0:622 ln wa þ 0:622
where Lef gives an indication of the relative rates of heat and mass transfer in an evaporative process. In the Merkel model, Lef is assumed to be 1 in order to simplify the simulation. According to other research, however, the water evaporation rate is a function of the actual value of the Lewis factor [28]. The enthalpy transfer to the air stream from Eq. (24) is:
i dQ h h ¼ ¼ d Lef ðimasw ima Þ þ 1 Lef iv ðwsw wÞ dA ma ma (26)
For a one-dimensional SCT model, the number of droplets per control volume with a section dz is:
Nd ¼
mw dz md ud
3.4. Governing equations of heat and mass transfer in SCT for supersaturated air The control volume in Fig. 3 is also applicable to supersaturated air. Because the excess water vapor condenses as a mist, the enthalpy of supersaturated air is expressed as follows:
iss ¼ cpa Ta þ wsa ifgw0 þ cpv Ta þ ðwa wsa Þcpw Ta (25)
dima
In this circumstance, however, the computed WBT (Wet Bulb Temperature) is higher than the DBT (Dry Bulb Temperature), which means the air is supersaturated. Thus, the excess water vapor transferred to the free stream air condenses as a mist, and the air is supersaturated before arriving at the outlet of the tower, so the assumption of the unsaturated air must be corrected.
(24)
where c h h ¼ Lef is an indication of the relative rates of heat and pma d mass transfer in an evaporative process. Bosnjakovic developed an empirical relation for the Lewis factor Lef for airewater vapor systems. The Lewis factor for unsaturated air, according to Bosnjakovic, is as follows [24] K:
Lef ¼ 0:8650:667
439
(32)
Assume that the heat and mass transfer coefficients for supersaturated and unsaturated air are the same, as proposed by Poppe €gener [29,30]. The potential for mass transfer is characterand Ro ized by the difference in humidity ratio between the saturated air at the airewater interface and the saturated free stream air, thus:
dmw ¼ hd ðwsw wsa ÞdA
(33)
Simulating the derivation process yields the following:
dQ ¼ hðTw Ta ÞdA þ iv hd ðwsw wsa ÞdA Tw Ta ¼
(34)
ðimasw iss Þ ðwsw wsa Þiv þ ðwa wsa Þcpw Tw cpa þ wsa cpv þ ðw wsa Þiv (35)
(27) Substituting Eq. (35) into Eq. (34) results in:
The transfer area for dz is usually expressed as follows:
dA ¼
mw dz 2 6mw dz pdd ¼ m d ud rw ud dd
(28)
dQ ¼ hc
ðimasw iss Þ ðwsw wsa Þiv þ ðwa wsa Þcpw Tw dA cpa þ wsa cpv þ ðw wsa Þiv
þ iv hd ðwsw wsa ÞdA
Eq. (28) is substituted into Eq. (27):
(36) dima
dQ ¼ ma mw 6hd h Lef ðimasw ima Þ ¼ ma rw ud dd i þ 1 Lef iv ðwsw wÞ dz
dima dQ ¼ ma dz mw 6hd h Lef ðimasw ima Þ ¼ ma rw ud dd i þ 1 Lef iv ðwsw wÞ
Proceeding along the same lines as in the case of unsaturated air,
dima ¼
(37)
(29)
Based on the equations above,
ma dwa ¼ hd ðwsw wa ÞdA
mw ma
6hd ðwsw wa Þdz rw ud dd
where cpmas is the specific heat of supersaturated air per unit mass, and cpmas ¼ cpa þ wsa cpv þ ðw wsa Þiv c h h ¼ Lef is defined as the pmas d Lewis factor for saturated air. The empirical relation used by Bosnjakovic can also be used to calculate the Lewis factor, which for supersaturated air is:
(30) Lef ¼ 0:8650:667
The above equation can be rearranged as follows:
dwa ¼
mw 6hd hc ðimasw iss Þ ðwsw wsa Þiv ma rw ud dd hd cpmas
þ ðwa wsa Þcpw Tw þ ½iv ðwsw wsa Þ dz
wsw þ 0:622 wsw þ 0:622 1 ln wsa þ 0:622 wsa þ 0:622 (38)
(31)
Proceeding along the same lines as in the case of unsaturated air, the governing equations for supersaturated air can be obtained as follows:
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dTw ¼
X. Qi et al. / Energy 97 (2016) 435e443
n 6hd Lef ðimasw iss Þ ðwsw wsa Þiv cpw rw ud dd þ ðwa wsa Þcpw Tw þ ½iv ðwsw wsa Þ ðwsw o wsa Þcpw Tw dz
dwa ¼
mw ma
6hd ðwsw wsa Þdz rw ud dd
(39)
(40)
At this point, the derivation of the system of governing equations for saturated air in SCTs is complete. 3.5. Calculation approach The fourth-order Runge-Kutta method can be applied to solve the differential equations for both unsaturated and supersaturated outlet air conditions [31,32]. The given parameters are: water to air flow rate ratio, air velocity, discharge droplet velocity, droplet diameter, tower spray zone height, inlet water temperature, and air inlet dry- and wet-bulb temperatures. The equations for unsaturated (or saturated) air are comprised of Eqs. (3), (12), (29) and (31). The equations for supersaturated air are comprised of Eqs. (3), (37), (39) and (40). ima should be replaced by iss for supersaturated air. Because the numerical equations for heat and mass transfer were derived under two respective cases, corresponding equations for the outlet air must be selected appropriately. The velocity of the water droplet though the tower changes with time and height. In order to calculate the heat transfer and temperature variations of a water droplet, the entire tower height was divided into n sections with thickness dz. Assume that section n is filled with water droplets entering the section at temperature Tw;n and exiting at Tw;nþ1 , and the air enters the section with enthalpy ima;nþ1 and exits with ima;n . Iterative calculation in each section is completed according to initial conditions and boundary conditions. The parameter conditions of water and air in each position are obtained after solving all iterations step-by-step; this method is dependable only if the step length is sufficiently brief.
Fig. 4. A schematic diagram of the test shower cooling tower.
times in all and their averages were considered the final results. When thermal balance error between air and water was less than 5 percent, the measured data were considered valid [33] and the original experimental data were recorded. The instruments used in the experiment are detailed in Table 2. A comparison of the outlet water temperature between the calculated and the experimental results is shown in Table 3 and Fig. 6. Note that the current model predicted the outlet water temperatures with an error of less than 6%, indicating that the theory is capable of estimating the performance of real freshwater and seawater SCTs accurately.
4. Experimental apparatus and procedure As discussed above, experimental studies on cooling towers reported in the literature depart from the type of tower examined here. For this reason, researching practical, full-scale towers is preferred. The experiment in this study was performed in a shower cooling tower at Jiangsu Seagull Cooling Tower Company, Ltd. A schematic diagram of the test rig is provided in Fig. 4, and a picture of the test SCT is shown in Fig. 5. For the seawater shower cooling tower, fill is removed. One side wall of the tower is made of polycarbonate material to allow direct test of the droplet diameter. The tower was 3.3 m 3.3 m across with a total height of 6.7 m. The nozzles were mounted to an adjustable frame. The test nozzle height H was adjusted from 4.0 m to 6.0 m. The water was pumped to a tank where its temperature was kept at a constant value during test. The experiment on droplet diameter was conducted by the DualPDA system, manufactured by Dantec Dynamics. This system includes Ar-Ion laser, transmitter, receiver, bandpass filter, signal processor, and so on. For all measurements, the droplet SMDs (Sauter mean diameters) are measured at three points randomly. By averaging the data acquired repeatedly, the local SMDs are finally obtained. The experiment was performed under steady state conditions, that is, the parameters described above were simultaneously measured when the system was stable, then re-measured after an appropriate period of time. Measurements were repeated five
Fig. 5. Photograph of the test shower cooling tower.
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Table 2 Measuring device in the experiment. Measuring parameter
Device
Inlet air dry and wet bulb temperature Motor power Barometric pressure Inlet and outlet water temperature Cooling water flow rate and spray device flow rate Water pressure Inlet air capacity Air velocity Air capacity regulator Temperature acquisition
PHMZ ventilation psychrometer Three-phase power meter Aneroid barometer Thermometer Water flowmeter
Air temperature at the exit and in the tower
Pressure gage Standard pitot tube A4201 digital speed detector DV-707 variable-frequency Drive 34970A HP data acquisition instrument Copper-constantan thermocouple
5. Analysis and comparison between freshwater and seawater cooling tower The performance of a seawater SCT was investigated by means of the model described above, based on the characteristics of seawater parameters. For cooling tower service, any circulating water with chloride (NaCl) content above 750 parts per million (ppm) is generally considered to be “saltwater”. That said, the detrimental effects of chlorides are much less severe at 750 ppm than at higher concentrations. Saltwater may originate from the open ocean, brackish (estuarine) areas, or brine wells. Because an open recirculating system concentrates the dissolved solids in the makeup water, a cooling tower may be exposed to saltwater conditions even though the makeup contains less than 750 ppm NaCl. The parameters used in the calculations are shown in Table 4. The outlet water temperature of freshwater, seawater concentration “1”, seawater concentration “2”, and seawater concentration “3” were obtained respectively under varying conditions. Results show that the parameters that most strongly affect the thermal performance of SCT are specific heat capacity, density, and vapor pressure. Surface tension, viscosity, and thermal conductivity also affect the heat and mass transfer between air and droplets. Salt impacts water in several basic ways affecting thermal performance: salt lowers the vapor pressure, reduces the specific heat, reduces the thermal conductivity, and increases the density of the solution. The first three tend to decrease thermal performance, but the latter tends to increase it. The compensating effect of increased density is
Fig. 6. The calculated outlet water temperature vs. the measured outlet water temperature.
not sufficient to entirely offset the effects of reduced specific heat and vapor pressure, however, so some loss of thermal performance results. The amount of loss is greater at higher salt concentrations and during more difficult cooling processes. 5.1. Influence of droplet diameter on outlet water temperature As Fig. 7 shows, seawater cooling performance decreases with increasing diameter and saltwater concentration of water droplets. Seawater cooling performance decreased 2.17% at saltwater concentration 1, 5.59% at concentration 2, and 9.86% at concentration 3 compared to freshwater. Fig. 7 shows variations in predicted outlet water temperature with water droplet diameter for different concentrations. Results show that cooling performance reduces as droplet diameter and concentration increase. For clarity, the prediction in terms of convection and evaporation were also analyzed e about 97% of the heat load is dissipated by evaporation and the remaining 3% is dissipated through convection. The total heat transfer decreases as droplet diameter increases. Convective heat dissipation accounts for only 1.82% of the total heat transfer at droplet diameter of 1 mm. The heat dissipated by evaporation varies linearly based on the difference between air moisture at the inlet and that at the exit. For
Table 3 Comparison between the calculated and the experimental results. Parameters
Nozzle height (m) Water flow rate (m3/h) Air flow rate (m3/h) Droplet diameter (mm) Atmospheric pressure (kPa) Dry-bulb temperature of inlet air ( C) Wet-bulb temperature of inlet air ( C) Inlet water temperature ( C) Experimental outlet water temperature ( C)
Experimental average data ( C) Computed water temperature ( C) Relative error (%)
Test 1
2
3
4
5
6
7
4.4 48.45 86,206 1.6 102 25 20.6 43.6 31.5 31.6 31.3 31.7 31.4 31.5 31.1 3.4%
4.4 87.80 86206 1.6 101.6 28.6 21.6 43.8 33.5 33.7 33.2 33.1 33.5 33.4 33.1 2.9%
4.4 105.4 117,525 1.6 103.1 19 14.2 44.8 31.9 32.2 31.9 32.2 31.8 32 32.1 0.8%
4.9 97.72 101,987 1.6 102.1 28 21.7 42.8 33.0 32.7 32.8 32.5 32.5 32.7 32.2 4.76%
4.9 58.86 117,535 1.7 101.7 28.5 19 42.2 28.1 28.6 28.9 27.9 29.0 28.5 29.1 5.13%
5.4 103.4 86,206 1.8 102.3 26 21.3 45.5 35.5 34.7 35.0 34.9 35.9 35.2 34.9 2.91%
5.4 61.7 105,932 1.5 102.3 23.8 17.4 41.3 28.5 28.2 28.3 28.0 28.5 28.3 28.2 0.77%
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Table 4 Calculation parameters. Dry-bulb temperature of inlet air ( C)
Wet-bulb temperature of inlet air ( C)
Atmospheric pressure (kPa)
Water flow rate (m3/h)
Air flow rate (m3/h)
Inlet water temperature ( C)
33.5 10.5
26.7 3.7
102 102
55.21 55.21
86206 86206
48 48
related changes in the physical properties of seawater. The literature includes sufficient data for general seawater properties, but relevant thermophysical properties are available from relatively few sources. A recent assessment of seawater properties was provided by Sharqawy et al., who found that when water temperature is high, surface tension, specified heat capacity, and density decrease less drastically for seawater with higher salt concentration, and that the changing tendencies of other related properties are similar, as well [20]. Comprehensive results are shown in Fig. 8. 5.3. Influence of air flow rate on outlet water temperature
Fig. 7. Effects of droplet diameter and seawater concentration on the outlet water temperature.
larger droplet diameters, the amount of evaporative heat dissipation decreases with increasing seawater concentration due to changes in physical properties. In practice, smaller droplets are preferable for the sake of cooling performance. There remain some limitations, however, if the possibility of droplets escaping the tower is considered. Working conditions must be specified accordingly. 5.2. Influence of inlet water temperature on outlet water temperature Fig. 8 shows the predicted Tw,o with inlet water temperature for different seawater concentrations. Clearly, outlet water temperature decreases alongside inlet water temperature. Based on the predicted results, cooling performance decreases as seawater concentration increases and at higher inlet water temperatures. At higher temperatures of inlet water, the heat load decreases slightly less with increasing seawater concentration due to temperature-
Fig. 8. Effects of inlet water temperature and seawater concentration on the outlet water temperature.
Fig. 9 shows variations in the predicted Tw,o with varying droplet diameters for different seawater concentrations. Results show that the cooling efficiency of the SCT increases as RAW (airto-water ratio) increases. This observation most likely applies to all types of cooling towers, though larger RAW is possible in an SCT compared to a PCT because the tower resistance is relatively smaller. Additionally, when RAW increases, the cooling efficiency improves much more as droplet diameter shrinks. For larger droplet diameters, even if the RAW increases significantly, the cooling effect does not significantly change. At smaller RAW, the influence of droplet size on the cooling effect is also very small. In order to best detail the two groups of curves, only freshwater and seawater concentration 2 were drawn (Fig. 9). The droplet diameters of the two groups of curves are 1.5 mm and 3 mm, respectively. Fig. 7 shows where the cooling efficiency difference of the upper group of curves is much greater than that of the bottom group (see the explanation in Section 5.1). For larger droplet diameters, the amount of evaporative heat dissipation decreases much more with increasing seawater concentration due to changes in physical properties. 5.4. Influence of seawater concentration on relative humidity of air The relative humidity of air in an SCT varies as shown in Fig. 10. Relative humidity increases monotonically until reaching its the maximum at the SCT outlet. The higher the concentration of seawater, the weaker the heat and mass transfer process; therefore, when the seawater concentration is fairly uniform, the air moisture increases much faster (ceteris paribus).
Fig. 9. Outlet water temperature vs. ratio of air to water & droplet diameter.
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Acknowledgments This study was supported by the Natural Science Foundation of China (51309147 and 51249001) and Project of Shandong Province Higher Educational Science and Technology Program (J11LD22). The authors also gratefully acknowledge the support of Dr. Qianjian Guo.
References
Fig. 10. Relative humidity of air in an SCT.
6. Conclusions It is very important for the health and future of the global environment to reduce the emission of waste heat to the sea due to marine industries. The use of seawater circulating cooling systems is an effective way not only to conserve freshwater resources but also to reduce marine pollution. The fill packing necessary in PCTs is subject to contamination during the seawater (which contains dissolved minerals, or salts, as opposed to freshwater) circulation cooling process, which gradually reduces the tower's cooling efficiency. In this study, an SCT was utilized as an alternative for the seawater cooling industry. Circulating seawater in an SCT is separated into thin droplets in the tower, in which normal heat transfer can be conducted without fill to cool the seawater to the desired temperature. This study was conducted in effort to provide a reference for future seawater shower cooling tower design technologies, as there has been a general lack of systematic investigation into the topic prior to now. This study numerically investigated an SCT model, and then validated the calculation results with experimental data. A comparative prediction of the outlet water temperature between freshwater and seawater at different salt concentrations was conducted and the results were carefully analyzed. Cooling performance was shown to reduce as droplet diameter and salt concentration increase. For clarity, the predictions were analyzed in terms of convection and evaporation, as well. For larger droplet diameters, the amount of evaporative heat dissipation decreases as seawater concentration increases due to changes in physical properties. The prediction results also showed that cooling performance decreases with increasing water concentration at higher inlet water temperatures. At higher temperatures of inlet water, the heat load decreases slightly less with increasing seawater concentration, because changes in the physical properties of seawater are related to temperature. Results also show that larger air-to-water ratio is possible in an SCT compared to a PCT, because the tower resistance is relatively smaller. When RAW increases, cooling efficiency improves as droplet diameter decreases. For larger droplet diameters, even if the RAW increases greatly, the cooling effect does not significantly change e this is because for larger droplet diameters, the amount of evaporative heat dissipation decreases with increasing seawater concentration due to changing physical properties. Relative humidity increases monotonically and reaches its maximum at the SCT outlet; when the seawater concentration is reduced, the air moisture increases (ceteris paribus). The above results altogether provide a valuable theoretical basis for advancing seawater cycling and cooling technologies, as well as lay the foundation for improving the design of seawater cooling towers in the future.
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