- Email: [email protected]
Thermodynamic study of the effects of ambient air conditions on the thermal performance characteristics of a closed wet cooling tower
Applied Thermal Engineering 33-34 (2012) 199e207
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermodynamic study of the effects of ambient air conditions on the thermal performance characteristics of a closed wet cooling tower V.D. Papaefthimiou a, *, E.D. Rogdakis a, I.P. Koronaki a, T.C. Zannis b a
Laboratory of Applied Thermodynamics, School of Mechanical Engineering, Thermal Engineering Section, National Technical University of Athens, Heroon Polytechniou 9, Zografou Campus, 15780 Athens, Greece b Laboratory of Naval Propulsion Systems, Naval Architecture & Marine Engineering Sector, Hellenic Naval Academy, Hatzikyriakou Ave, 18539 Piraeus, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 December 2010 Accepted 26 September 2011 Available online 2 October 2011
A thermodynamic model was developed and used to assess the sensitivity of thermal performance characteristics of a closed wet cooling tower to inlet air conditions. In the present study, three cases of different ambient conditions are considered: In the first case, the average mid-winter and mid-summer conditions as well as the extreme case of high temperature and relative humidity, in Athens (Greece) during summer are considered according to the Greek Regulation for Buildings Energy Performance. In the second case, the varied inlet air relative humidity while the inlet air dry bulb temperature remains constant were taken into account. In the last case, the effects on cooling tower thermal behaviour when the inlet air wet bulb temperature remains constant were examined. The proposed model is capable of predicting the variation of air thermodynamic properties, sprayed water and serpentine water temperature inside the closed wet cooling tower along its height. The reliability of simulations was tested against experimental data, which were obtained from literature. Thus, the proposed model could be used for the design of industrial and domestic applications of conventional air-conditioning systems as well as for sorption cooling systems with solid and liquid desiccants where closed wet cooling towers are used for precooling the liquid solutions. The most important result of this theoretical investigation is that the highest fall of serpentine water temperature and losses of sprayed water are observed for the lowest value of inlet wet bulb temperature. Hence, the thermal effectiveness, which is associated with the temperature reduction of serpentine water as well as the operational cost, which is related to the sprayed water loss due to evaporation, of a closed wet cooling tower depend predominantly on the degree of saturation of inlet air. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Closed wet cooling tower Ambient conditions Serpentine water Sprayed water Thermal performance
1. Introduction In a closed wet cooling tower, heat is transferred from serpentine water to a water film, which is formed on the tube surface and then, to a rising air stream. For this reason, closed wet cooling towers are used in industrial and domestic applications so as to reject heat to the surrounding environment. They are divided into natural or mechanical (forced or induced) draught towers with counter or cross flow. The most commonly used type of cooling tower for air conditioning is the induced-draught counter-flow cooling tower. The induced-draught tower has a major advantage over the forced-draught. The basic components of an induceddraught cooling tower are the casing, the fan, the mist eliminators, the water distribution system (pumps), the packing, the
* Corresponding author. Tel.: þ30 210 7721014. E-mail address: [email protected] (V.D. Papaefthimiou). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.09.035
intakes and louvres and the water collection sump. An evaporative cooler (closed-circuit wet cooling tower) is an indirect-contact cooling tower in which the packing is the outer surface of a heat exchanger comprising of a bank of tubes [1e3]. The design theories of a conventional cooling tower and a closed wet cooling tower (evaporative cooler) have many characteristics in common. The primary difference between them is that the packing temperature is constant in the conventional cooling tower whereas the temperature of the fluid in the tubes and therefore the tube surface temperature vary in the evaporative cooler [1e3]. Thus, the design models for the closed wet cooling tower are more complicated than those for the conventional cooling tower. Various attempts with different degree of accuracy have been made since the late 1930s for modelling the combined heat and mass transfer phenomena taking place inside a closed wet cooling tower [1e3]. A constant temperature approximation for injected cooling water was often assumed. However, Parker and Treybal [4] discovered that this approximation lead to mathematical
200
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Nomenclature A aLA aTL cpa cpm csat ps cpw cpf D hf k L Le _a m _w m _f m pa psat ws Pr R Re RH Ta Tf
wetted tube surface (m2) water to air heat transfer coefficient (Wm2 C1) tube to water film heat transfer coefficient (Wm2 C1) specific heat at constant pressure of dry air (J kg1 K1) specific heat of moist air (J kg1 K1) specific heat of saturated steam (J kg1 K1) specific heat of water (J kg1 K1) specific heat of serpentine water (J kg1 K1) tube diameter (m) convection heat transfer coefficient of serpentine water (Wm2 C1) tube thermal conductivity (Wm2 C1) length of tube bundle (m) Lewis number air mass flow rate (kg s1) sprayed water mass flow rate (kg s1) serpentine water mass flow rate (kg s1) moist air pressure (Pa) saturation pressure of moist air (Pa) Prandtl number tube radius (m) Reynolds number relative humidity dry bulb air temperature ( C) serpentine water temperature ( C)
inconsistencies, which gave erroneous results. In fact, Finlay and Grant [5] showed that constant temperature assumption may lead to 30% error in large tube banks. Leidenfrost and Korenic [6] developed a methodology similar to the one of Parker and Treybal [4] with which they found that accurate prediction of performance characteristics of closed wet cooling tower can be attained through iterative procedures. In addition, various researchers suggested different methods for dimensioning closed wet cooling towers [7,8]. Finlay and Grant [9] suggested a simplified model for describing the mass transfer process inside a closed wet cooling tower, which was based on the expression of vapour pressure of saturated moist air as linear function of temperature. Dreyer [10] presented different mathematical models for the thermal evaluation of evaporative coolers and closed wet cooling towers [4,7,11e14]. Analytical models [10e13,15,16] are based on the implementation of energy and mass conservation laws making various assumptions concerning the spayed water temperature distribution and the sprayed water loss due to evaporation. Aiming to a more realistic description of the transport phenomena taking place inside a closed wet cooling tower, sophisticated mathematical models [17,18] have been developed and CFD packages have been used [19e21] which provide predictions of the temperature and flow field inside cooling tower. Though that these models are more detailed and informative compared to analytical models, they are time-consuming and thus, cannot provide performance predictions for large periods of time. The current literature shows that no generally accepted method exists for predicting the performance of closed wet cooling towers. Recently, the present research group has developed a detailed thermodynamic model and used it to assess the thermal performance of a closed wet cooling tower [22]. The success of this application has motivated us to utilise it to examine the effect of inlet air conditions on the thermal behaviour of an indirect wet cooling tower operating in the area of Athens, Greece. The model is used to examine the effect of variable dry bulb air temperature and
Tw U W Wsat Z
sprayed water temperature ( C) overall heat transfer coefficient of falling water film (Wm2 C1) air humidity ratio (kgw kg1 da ) saturation humidity ratio of moist air (kgw kg1 da ) tower height (m)
Greek symbols b mass transfer coefficient (kg m2 s1) Dhw latent heat of vapourisation for water (J kg1) l thermal conductivity of water (W m1 C1) Subscripts a air db dry bulb i inner f serpentine water L latent LA liquid to air o outer s steam sat saturated TL tube to liquid w water ws waterevapour wb wet bulb w,s saturated steam
humidity ratio, according to the design as well as extreme conditions given by the Greek Regulation for Buildings Energy Performance [23], on the variation of the thermodynamic state of moist air inside the cooling tower and on its cooling capacity and thermal efficiency. Comparison of the simulations with experimental results obtained from the literature was made to assess the predictive ability of the model. The main outcome, which revealed from the analysis of the theoretical results, was that the highest temperature fall of serpentine water and the highest losses of sprayed water mass are observed for the lowest value of inlet wet bulb temperature. The presented outcomes could be very useful not only for industrial applications but also for domestic applications with liquid desiccant air-conditioning systems providing heatingecooling and dehumidification of the process air without using conventional energy consuming components and environmentally harmful refrigerants [24e27]. The liquid desiccant systems are designed to serve as open-cycle absorption systems that operate with low-grade heat in combination with closed wet cooling tower for precooling of liquid desiccant solution in the absorber, where the dehumidification takes place, and for regeneration of liquid solution in the regenerator [26,27]. 2. Model description 2.1. General outline A comprehensive thermodynamic model based on the conservation laws for energy and mass is used to describe the coupled heat and mass transfer processes taking place inside an indirect wet cooling tower. The model was implemented for a closed wet cooling tower having a bank of 16 31 plain tubes. The length of tube bundle is 0.888 m. The tube length is 0.913 m and the outer and the inner tube diameter are 0.0191 m and 0.0150 m respectively. The ratio of pitch to outside tube diameter is 1.5. The aforementioned schematic view of the closed wet cooling tower
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
used herein is shown in Fig. 1. Model development was based on the following assumptions: The heat and mass transfer processes occur under steady state conditions, in a direction perpendicular to the tower walls. The specific heat capacity of sprayed water, serpentine water and dry air is constant in the temperature range considered. The specific enthalpy of dry air, water and serpentine water is equal to zero at 0 C. Owing to the small temperature differences at which the process occurs heat transferred by radiation is not taken into account. At the interface air reaches the temperature of water and its humidity corresponds to the state of equilibrium. The thermal resistance between the bulk and the interface of falling water film is negligible. Water and air are in counter-flow.
Model development is based on the implementation of energy balance for each one of the working fluids taking part in the process. The implementation of the energy balance for the gaseous phase implies that sensible and latent heat is exchanged between the falling water film and the air stream resulting in the change of dry bulb air temperature along wetted tube surface as follows [22]:
dTa ¼ dA
aLA dW ðTw Ta Þ þ csat ps _a m dA cpm
where cpa is the specific heat at constant pressure of dry air and W is the humidity ratio. The term dW/dA in Equation (1) corresponds to the evaporated water mass per unit heat exchange area at the waterevapour interface and it is given by the following expression:
b sat dW W ðTw Þ Wa ¼ _a m dA
(1)
(3)
where b is the mass transfer coefficient. The saturation humidity ratio of air Wsat is calculated using the following relation:
W sat ðTw Þ ¼ 0:622
psat ws ðTw Þ pa psat ws ðTw Þ
(4)
where psat ws is the saturation pressure of moist air. The definition of air humidity ratio is employed to derive the rate of change of _ w per unit of heat exchange area evaporated cooling water mass m as follows:
_ dm dW _w ¼ m _ a W0 w ¼ m _a m dA dA
2.2. Mathematical formulation
201
(5)
The application of the energy balance between serpentine water and falling water film provides
dTw 1 dW sat _a ½aLA ðTw Ta Þ þ m ¼ cps Ta þ cpw Tw þ Dhw _ dA mw cpw dA i (6) þU Tw Tf where Dhw is the latent heat of vapourisation for water and U is the overall heat transfer coefficient of falling water film. The rejection of sensible heat from the circulating water to the falling water film results in its temperature fall as shown in the following relation:
_ a is the air where aLA is the water to air heat transfer coefficient, m mass flow rate, csat ps is the specific heat of saturated steam, Tw is the cooling water temperature, Ta is dry bulb air temperature and cpm is the specific heat capacity of moist air, which is defined as
U Tw Tf dTf ¼ _ f cpf m dA
cpm ¼ cpa þ Wcsat ps
Finally, a system of four (4) ordinary differential equations is constituted [22]
(2)
sat dTa aLA cps dW þ ¼ _a m dA dA
(7)
!
ðTw Ta Þ cpm
dTw 1 dW sat _a ½a ðT Ta Þþ m ¼ c Ta þcpw Tw þ Dhw _ w cpw LA w dA m dA ps i þU Tw Tf dTf U Tw Tf ¼ _ f cpf m dA b sat dW W ðTw ÞWa ¼ _a dA m _w dm dW _a ¼m dA dA
9 > > > > > > > > = ð8Þ > > > > > > > > ;
with the following boundary conditions:
ðTa ÞZ¼0 ¼ Ta0 ðT w ÞZ¼L ¼ Tw0 Tf ¼ Tf 0
9 > > > > =
Z¼L > > > ; ðWÞZ¼0 ¼ W0 > _ w0 _ w Z¼L ¼ m m
Fig. 1. Schematic view of the closed wet cooling tower.
(9)
A variable-step non-stiff method (RungeeKutta 5(4)) was used to numerically solve the boundary-value problem [29]. The model was developed using the Mathcad software where all the thermodynamic characteristics of the tower are calculated from the
202
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
point where the water is sprinkled till the end of the tubes bundle. The energy and mass balance of the sprayed water contribution as well as the stream in a counter-flow closed wet cooling tower is shown in Fig. 2. The heat transfer coefficient between falling water film and air stream (Le ¼ 1) is given by the following relation [7,11,29,30]:
aLA ¼ bcpm
(10)
where b is the mass transfer coefficient, which is calculated as follows:
b ¼ 6:0 108 ðRea Þ0:9 ðRew Þ0:15 ðDo Þ1:6
(11)
and Rea, Rew are the Reynolds numbers of the air and the sprayed water stream respectively [22]. The overall heat transfer coefficient U between serpentine water, tube wall and water film is calculated by the following formula:
U ¼
Ro 1 Ro Ro 1 þ ln þ Ri hf k Ri aTL
!1 (12)
where the convection heat transfer coefficient of serpentine water hf is given by the “DittuseBoelter” relation [31]
hf ¼
! 0:3 0:023Re0:8 f Prf l Di
(13)
where Ref and Prf are the Reynolds and Prandtl numbers respectively of the process water and l is the thermal conductivity of the process water.
given as design conditions for winter and summer and extreme conditions for summer according to the Greek Regulation for Buildings Energy Performance for the climate of Athens in Greece. For this reason, three cases of different ambient conditions are considered. In the first case, the mean monthly values for January [23] (Tdb,i ¼ 10.3 C e RH ¼ 74.4%) and the mean monthly values for June [23] (Tdb,i ¼ 27.1 C e RH ¼ 45.8%) occurring in Athens, Greece as well as the extreme summer conditions of high temperature and average relative humidity (Tdb,i ¼ 45 C e RH ¼ 35.0%) according to the Greek Regulation for Buildings Energy Performance, were assumed. The objective of this case was the assessment of the thermal performance characteristics of the closed wet cooling tower under diverse ambient conditions occurring in Athens, Greece. The second case was considered in order to solely examine the influence of inlet air relative humidity on the thermal behaviour of closed wet cooling tower. For this reason, inlet air relative humidity was varied while inlet air dry bulb temperature remained constant. In the third case, an attempt was made to assess the effects on the thermal behaviour of the closed wet cooling tower when the inlet air wet bulb temperature remains constant. All calculations were made herein adopting the parameter values for inlet conditions given in Table 1. The thermodynamic properties of air and water are calculated from top to bottom of the tube bundles while the mass and heat transfer coefficients were calculated according to Equations (10) and (11). Taking into account the inlet conditions, the Reynolds number of water is 130.12 while the Reynolds number of air is 8.407 103.
4. Results and discussion 3. Overview of the parametric study 4.1. Experimental validation A theoretical assessment is conducted to evaluate the sensitivity of thermal performance characteristics of a closed wet cooling tower under variable surrounding air conditions, which are
A comparison between predicted and experimental results for sprayed water temperature, serpentine water temperature and dry bulb air temperature at various positions along the closed wet cooling tower’s height is given in Tables 2 and 3. The total wetted area of the tubes bundle was calculated as 27 m2, and the numerical solution is given from 0 to 27 m2. The exact position along the height and the wetted area is given from the first column of Tables 2 and 3. Due to the fact that experimental data for the variation of dry bulb temperature inside the cooling tower were unavailable, the comparison was limited to the inlet and outlet conditions. The tabulated theoretical data were produced for two different “temperature approaches” (Twb,oeTdb,i), which are equal to 5.1 C and 8.3 C. The experimental data in both tables were obtained from Finlay and Harris [28]. As it can be observed, the calculated results are in acceptable agreement with the corresponding measured data throughout the wet cooling tower. This can be verified by the low values of the relative error (not exceed 5.5%) between theoretical and experimental results enhancing our confidence on the reliability of the simulations, which will be presented in Tables 2 and 3.
Table 1 Parameter values of the inlet conditions.
Fig. 2. Schematic description of the energy contribution of sprayed water and air stream in a counter flow closed wet cooling tower.
Twi, Sprayed water temperature ( C) mwi, Sprayed water mass flow rate (kg/s) ma,i, Air mass flow rate (kg/s) Tfi, Serpentine water temperature ( C) mfi, Serpentine water mass flow rate (kg/s)
20 1.85 2.07 35 2.67
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
203
Table 2 Comparison between predicted and experimental values for sprayed water Tw, serpentine water temperature Tf and dry bulb air temperature Ta. Predictions were made for Tw,o Twb,i ¼ 5.1 C and the corresponding experimental data were obtained from Ref. [28]. Wetted tube Surface (m2)
Tc_exp ( C)
Tc_calc ( C)
Error (%)
Tf_exp ( C)
Tf_calc ( C)
Error (%)
Ta_exp ( C)
Ta_calc ( C)
Error (%)
0.0 1.8 3.6 7.2 10.8 14.4 18.0 21.6 25.2 27.0
12.80 13.60 14.10 14.00 14.00 13.77 13.51 13.09 12.70 12.30
12.80 13.44 13.78 13.99 13.93 13.73 13.45 13.08 12.62 12.34
0.00 1.21 2.30 0.04 0.50 0.27 0.45 0.07 0.66 0.32
15.60 15.00 14.70 14.70 14.40 14.30 14.07 13.60 13.50 13.30
15.60 15.16 14.89 14.58 14.38 14.20 14.05 13.76 13.46 13.29
0.00 1.10 1.30 0.83 0.13 0.68 0.47 1.19 0.28 0.10
13.60 e e e e e e e e 15.45
13.60 e e e e e e e e 14.60
0.00 e e e e e e e e 5.39
4.2. Effect of the variation of ambient conditions on the thermodynamic properties of air along tower’s height In Fig. 3(a) the variation of dry bulb air temperature and humidity ratio with the wetted tube surface (along the height of the wetted cooling tower, where Z ¼ 0 at the position where the water is sprinkled) for the three cases of ambient conditions is shown. Increase of the outlet dry bulb temperature is observed in the low wet bulb temperature case (Twb ¼ 8.1 C e mean monthly values for January), which is up to 60%. This trend is reversed in the high wet bulb temperature case (Twb ¼ 25.2 C e extreme conditions for July) where the dry bulb temperature decreases with increasing tube banks surface along the height of tower. For a mid-range value of inlet wet bulb temperature (design conditions for June) the variation of dry bulb temperature is insignificant compared to the other cases. In Fig. 3(b) the outdoor dry bulb air temperature for extreme conditions in Athens during summer remains constant while the relative humidity is changed from 20 to 35% resulting in increase of wet bulb temperature. At all cases of wet bulb temperature, the dry
bulb temperature along the height of wet cooling tower is noticeably reduced. The increase of the relative humidity results in small increase of outlet air dry bulb temperature. In Fig. 3(c) the variation of the outlet dry bulb air temperature is considerable when extreme and design climatic conditions are considered. For similar values of inlet wet bulb temperature of air the outlet dry bulb air temperature is reduced more than 15 C when the wetted tube surface takes its highest value. According to Fig. 4(a), an increase of humidity ratio is witnessed in the case of low (Twb ¼ 8.1 C), mid-range (Twb ¼ 18.9 C) and high inlet wet bulb temperature (Twb ¼ 25.2 C). However, the humidity ratio during the last stages is decreased, although it is increased for the higher percentage of wetted tube surface. This means that the outlet air of the cooling tower has less temperature and less absolute humidity than inlet air which could be used for space air condition and dehumidification when it is combined with liquid desiccant systems. In Fig. 4(b) for high values of relative humidity the humidity ratio is increased and at the last stages of the process, a significant reduction is observed.
Fig. 3. Effect of ambient conditions of Athens (Greece) on the variation of dry bulb temperature inside the closed wet cooling tower.
204
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Table 3 Comparison between predicted and experimental values for sprayed water Tw, serpentine water temperature Tf and dry bulb air temperature Tdb. Predictions were made for Tw,o Twb,i ¼ 8.3 C and the corresponding experimental data were obtained from Ref. [28]. Wetted tube Surface (m2)
Tc_exp ( C)
Tc_calc ( C)
Error (%)
Tf_exp ( C)
Tf_calc ( C)
Error (%)
Ta_exp ( C)
Ta_calc ( C)
Error (%)
0.0 1.8 3.6 7.2 10.8 14.4 18.0 21.6 25.2 27.0
13.60 15.45 15.76 15.80 15.70 15.50 15.30 14.80 14.20 13.80
13.60 14.60 15.20 15.60 15.50 15.30 15.00 14.60 14.10 13.80
0.00 5.39 3.71 1.43 1.03 1.16 1.99 1.48 0.94 0.23
18.00 17.40 16.90 16.40 16.00 15.80 15.75 15.52 15.16 14.60
18.00 17.30 16.90 16.40 16.10 15.90 15.70 15.40 15.00 14.80
0.00 0.48 0.05 0.13 0.92 0.73 0.52 0.90 0.83 1.61
18.00 e e e e e e e e 17.40
18.00 e e e e e e e e 17.30
0.00 e e e e e e e e 0.48
In Fig. 4(c) a similar increase of humidity ratio occurs in combination with high wetted tube surface.
4.3. Effect of ambient conditions on sprayed water temperature, serpentine water temperature and sprayed water mass losses along the wet cooling tower’s height The effect of ambient air conditions on the variation of cooling water temperature inside the closed wet cooling tower is given in Fig. 5(a). As evidenced, in the low wet bulb temperature case (Twb ¼ 8.1 C), the cooling water temperature rises for values of the wetted tube surface up to 7.5 m2 and then, decreases progressively receiving finally, a value close to its initial one. For the same ambient conditions, the process water is cooled and the falling water film mass is evaporated with increasing rate. Similar observations can be made for the case of Twb ¼ 18.9 C. In the case of ambient conditions of high temperature and relative humidity, a steep increase of cooling water temperature is observed during the initial stages of the evaporation process whereas, for values higher than 7.5 m2 a smooth decrease of cooling water temperature is observed.
According to Fig. 5(b), along the way of sprayed water, higher values of relative humidity result in constant values of sprayed water temperature till the outlet of the tower. As observed in Fig. 5(c) the variation of sprayed water temperature through the closed wet cooling tower remains the same when the inlet wet bulb air temperature is similar. As evidenced from Fig. 6(a), for values of wetted tube surface up to 7.5 m2, the rate of cooling of the serpentine water is steep and similar for different values of outdoor dry bulb temperature. For values of tube banks surface higher than 7.5 m2, the temperature of serpentine water and the rate of evaporated water mass drops significantly especially during January. The effects of inlet air conditions on serpentine water temperature are the same but the reduction of the temperature is less steep comparing to the aforementioned case when the relative humidity is varied from 20 to 35%. Finally, according to Fig. 6(c) when the inlet air wet bulb temperature remains constant the effect on serpentine water temperature is limited. The influence of ambient conditions on the percentage losses of cooling water mass is shown in Fig. 7(a)e(c). According to Fig. 7(a), the increase of humidity ratio for the case of mid-winter conditions results in a significant reduction of the cooling water mass
Fig. 4. Effect of ambient conditions of Athens (Greece) on the variation of humidity ratio inside the closed wet cooling tower.
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
205
Fig. 5. Effect of ambient conditions of Athens (Greece) on the variation of sprayed water temperature inside the closed wet cooling tower.
evaporated during the process that could be up to 72% at the outlet (comparing with the inlet). During summer there is a significant decrease of sprayed water mass flow rate which is observed even when the relative humidity is increased (Fig. 7(b)). This decrease could become 42% for extreme summer conditions. According to Fig. 7(c) similar values of inlet air wet bulb temperature provide approximately the same decreased sprayed water mass flow rate.
Fig. 8 presents the variation of the dry bulb air temperature, the sprayed water temperature as well as the serpentine water temperature along tower’s height (from top to bottom) for summer design conditions. From the figure above, it can be derived that the serpentine water temperature falls significantly taking similar values with the sprayed water temperature at the outlet of the tower while the air exits the tower warmer and more humid. The
Fig. 6. Effect of ambient conditions of Athens (Greece) on the variation of serpentine water temperature inside the closed wet cooling tower.
206
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Fig. 7. Effect of ambient conditions of Athens (Greece) on the variation of the percentage change of sprayed water mass flow rate inside the closed wet cooling tower.
The variation from mid-summer to mid-winter conditions (i.e., increase of humidity ratio) results in: a) Heating and humidification of the outlet air, b) Decrease of the cooling water mass that is evaporated during the process and needs to be replaced from the network, c) Significant temperature fall of the cooled water and, d) Increase of the effectiveness of the cooling tower due to the reduction of the temperature deviation of outlet cooled water from the ideal case (i.e., Tw,o ¼ Ta,i).
Fig. 8. Distribution of dry bulb air temperature, of sprayed water temperature and serpentine water temperature inside the closed wet cooling tower along its height.
outlet serpentine water temperature can be used for precooling purposes in industrial applications and for sorption air-conditioning systems with liquid desiccant where the absorber, the component where the dehumidification takes place, should be internally or externally cooled by a cooling tower. 5. Conclusions A newly developed model was used to simulate the processes taking place inside a closed wet cooling tower and mainly, to investigate the effect of ambient air conditions on its thermal behaviour. The reliability of the simulations was well tested against experimental results obtained from literature. The analysis of the theoretical results leads to the derivation of the following conclusions.
Consequently, the optimum thermal performance of the closed wet cooling tower can be attained in the case where the air stream enters into the cooling tower with low humidity ratio (relatively hot and humid ambient conditions). Reduction of the operating cost of the cooling tower is achieved in this case due to the decrease of overall evaporated water mass. Increase also of the efficiency of the evaporation process is accomplished as revealed by the increase of heat exchange effectiveness. The only minor obstacle in this case is the disability of achieving considerable temperature falls for the cooling water. The beneficial effect of the serpentine water temperature fall of the examined closed wet cooling tower can be observed when it is combined with liquid desiccant air-condition systems, providing heatingecooling and dehumidification for buildings without using energy consuming equipments and common environmentally harmful refrigerants.
References [1] W. Goodman, The evaporative condenser, Heating Piping Air Conditioning 10 (1938) 165e328. [2] E.G. Thomsen, Heat transfer in an evaporative condenser, Refrigeration Engineering 51 (1946) 425e431. [3] D.D. Wile, Evaporative condenser performance factors, Refrigeration Engineering 58 (1950) 55e63. [4] R.O. Parker, R.E. Treybal, The heat mass transfer characteristics of evaporative coolers, Chemical Engineering Progress Symposium Series 57 (32) (1961) 138e149.
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207 [5] C.I. Finlay, W.D. Grant, The Accuracy of Some Simple Methods of Rating Evaporative Coolers Report No. 584. National Engineering Laboratory, East Kilbride, Glasgow, 1974. [6] W. Leidenfrost, B. Korenic, Evaporative cooling and heat transfer augmentation related to reduce condenser temperatures, Heat Transfer Engineering 3 (1982) 38e59. [7] T. Mizushina, R. Ito, H. Miyashita, Characteristics and methods of thermal design of evaporative coolers, International Chemical Engineering 8 (1968) 532e538. [8] S. Tezuka, T. Takada, S. Kasai, Performance of an evaporative cooler, Heat Transfer e Japanese Research 6 (1976) 1e18. [9] C.I. Finlay, W.D. Grant, Air Coolers, Cooling Towers and Evaporative Coolers Report No. 534. Nat. Engng Lab., East Kilbride, Glasgow, 1972, pp. 165e328. [10] A.A. Dreyer, Analysis of evaporative cooler and condenser, MSc Thesis, University of Stellenbosch, Rep. of South Africa, 1988. [11] R.L. Webb, A. Villacres, Algorithms for performance simulation of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions 90 (2B) (1984) 416e458. [12] R.L. Webb, A unified theoretical treatment for thermal analysis of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions 90 (2B) (1984) 398e415. [13] J. Erens, A.A. Dreyer, An improved procedure for calculating the performance of evaporative closed circuit coolers, in: The 25th National Heat Transfer Conference, Houston, AIChE Symp. Ser. 84, 1988, pp. 140e145. [14] M. Poppe, H. Rögener, Evaporative Cooling Systems. VDI- Warmeatlas: Section Mh, 1984. [15] B.A. Qureshi, S.M. Zubair, A comprehensive design and rating study of evaporative coolers and condensers. Part I. Performance evaluation, International Journal of Refrigeration 29 (2006) 645e658. [16] B.A. Qureshi, S.M. Zubair, A comprehensive design and rating study of evaporative coolers and condensers. Part II. Sensitivity analysis, International Journal of Refrigeration 29 (2006) 659e668. [17] W. Zalewski, P.A. Gryglaszewski, Mathematical model of heat and mass transfer process in evaporative fluid coolers, Journal of Chemical Engineering and Processing 36 (1997) 271e280.
207
[18] W. Zalewski, B. Niezgoda-Zelasko, M. Litwin, Optimization of evaporative fluid coolers, International Journal of Refrigeration 7 (2000) 342e347. [19] G. Gan, S.B. Riffat, L. Shao, P. Doherty, Application of CFD to closed-wet cooling towers, Applied Thermal Engineering 21 (2001) 79e92. [20] G. Gan, S.B. Riffat, Numerical simulation of closed wet cooling towers for cooled ceiling systems, Applied Thermal Engineering 19 (1999) 1279e1296. [21] A. Hasan, G. Gan, Simplification of analytical models and incorporation with CFD for the performance of prediction of closed-wet cooling towers, International Journal of Energy Research 26 (1938) 1161e1174. [22] V.D. Papaefthimiou, T.C. Zannis, E.D. Rogdakis, Thermodynamic study of wet cooling tower performance, International Journal of Energy Research 30 (2006) 411e426. [23] Greek Regulation for Buildings Energy Performance, Technical Notes 20701e3/2010. [24] X.H. Liu, X.M. Chang, J.J. Xia, Y. Jiang, Performance analysis on the internally cooled dehumidifier using liquid desiccant, Building and Environment 44 (2009) 299e308. [25] Ch.-Q. Ren, Corrections to the simple effectiveness-NTU method for counterflow cooling towers and packed bed liquid desiccanteair contact systems, International Journal of Heat and Mass Transfer 51 (2008) 237e245. [26] Ch.Q. Ren, M. Tu, H.H. Wang, An analytical model for heat and mass transfer processes in internally cooled or heated liquid desiccant-air contact units, International Journal of Heat and Mass Transfer 50 (2007) 3545e3555. [27] L. Mei, Y.J. Dai, A technical review on use of liquid-desiccant dehumidification for air-conditioning application, Renewable and Sustainable Energy Reviews 12 (2008) 662e689. [28] C.I. Finlay, D. Harris, Evaporative cooling of tube banks, International Journal of Refrigeration 7 (1984) 214e224. [29] T. Mizushina, R. Ito, H. Miyashita, Experimental study of an evaporative cooler, International Chemical Engineering 7 (1967) 727e732. [30] J. Facao, A. Oliveira, Heat and mass transfer correlations for the design of small indirect contact cooling towers, Applied Thermal Engineering 24 (2004) 1969e1978. [31] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, fifth ed. John Wiley and Sons, New York, 2002.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermodynamic study of the effects of ambient air conditions on the thermal performance characteristics of a closed wet cooling tower V.D. Papaefthimiou a, *, E.D. Rogdakis a, I.P. Koronaki a, T.C. Zannis b a
Laboratory of Applied Thermodynamics, School of Mechanical Engineering, Thermal Engineering Section, National Technical University of Athens, Heroon Polytechniou 9, Zografou Campus, 15780 Athens, Greece b Laboratory of Naval Propulsion Systems, Naval Architecture & Marine Engineering Sector, Hellenic Naval Academy, Hatzikyriakou Ave, 18539 Piraeus, Greece
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 December 2010 Accepted 26 September 2011 Available online 2 October 2011
A thermodynamic model was developed and used to assess the sensitivity of thermal performance characteristics of a closed wet cooling tower to inlet air conditions. In the present study, three cases of different ambient conditions are considered: In the first case, the average mid-winter and mid-summer conditions as well as the extreme case of high temperature and relative humidity, in Athens (Greece) during summer are considered according to the Greek Regulation for Buildings Energy Performance. In the second case, the varied inlet air relative humidity while the inlet air dry bulb temperature remains constant were taken into account. In the last case, the effects on cooling tower thermal behaviour when the inlet air wet bulb temperature remains constant were examined. The proposed model is capable of predicting the variation of air thermodynamic properties, sprayed water and serpentine water temperature inside the closed wet cooling tower along its height. The reliability of simulations was tested against experimental data, which were obtained from literature. Thus, the proposed model could be used for the design of industrial and domestic applications of conventional air-conditioning systems as well as for sorption cooling systems with solid and liquid desiccants where closed wet cooling towers are used for precooling the liquid solutions. The most important result of this theoretical investigation is that the highest fall of serpentine water temperature and losses of sprayed water are observed for the lowest value of inlet wet bulb temperature. Hence, the thermal effectiveness, which is associated with the temperature reduction of serpentine water as well as the operational cost, which is related to the sprayed water loss due to evaporation, of a closed wet cooling tower depend predominantly on the degree of saturation of inlet air. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Closed wet cooling tower Ambient conditions Serpentine water Sprayed water Thermal performance
1. Introduction In a closed wet cooling tower, heat is transferred from serpentine water to a water film, which is formed on the tube surface and then, to a rising air stream. For this reason, closed wet cooling towers are used in industrial and domestic applications so as to reject heat to the surrounding environment. They are divided into natural or mechanical (forced or induced) draught towers with counter or cross flow. The most commonly used type of cooling tower for air conditioning is the induced-draught counter-flow cooling tower. The induced-draught tower has a major advantage over the forced-draught. The basic components of an induceddraught cooling tower are the casing, the fan, the mist eliminators, the water distribution system (pumps), the packing, the
* Corresponding author. Tel.: þ30 210 7721014. E-mail address: [email protected] (V.D. Papaefthimiou). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.09.035
intakes and louvres and the water collection sump. An evaporative cooler (closed-circuit wet cooling tower) is an indirect-contact cooling tower in which the packing is the outer surface of a heat exchanger comprising of a bank of tubes [1e3]. The design theories of a conventional cooling tower and a closed wet cooling tower (evaporative cooler) have many characteristics in common. The primary difference between them is that the packing temperature is constant in the conventional cooling tower whereas the temperature of the fluid in the tubes and therefore the tube surface temperature vary in the evaporative cooler [1e3]. Thus, the design models for the closed wet cooling tower are more complicated than those for the conventional cooling tower. Various attempts with different degree of accuracy have been made since the late 1930s for modelling the combined heat and mass transfer phenomena taking place inside a closed wet cooling tower [1e3]. A constant temperature approximation for injected cooling water was often assumed. However, Parker and Treybal [4] discovered that this approximation lead to mathematical
200
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Nomenclature A aLA aTL cpa cpm csat ps cpw cpf D hf k L Le _a m _w m _f m pa psat ws Pr R Re RH Ta Tf
wetted tube surface (m2) water to air heat transfer coefficient (Wm2 C1) tube to water film heat transfer coefficient (Wm2 C1) specific heat at constant pressure of dry air (J kg1 K1) specific heat of moist air (J kg1 K1) specific heat of saturated steam (J kg1 K1) specific heat of water (J kg1 K1) specific heat of serpentine water (J kg1 K1) tube diameter (m) convection heat transfer coefficient of serpentine water (Wm2 C1) tube thermal conductivity (Wm2 C1) length of tube bundle (m) Lewis number air mass flow rate (kg s1) sprayed water mass flow rate (kg s1) serpentine water mass flow rate (kg s1) moist air pressure (Pa) saturation pressure of moist air (Pa) Prandtl number tube radius (m) Reynolds number relative humidity dry bulb air temperature ( C) serpentine water temperature ( C)
inconsistencies, which gave erroneous results. In fact, Finlay and Grant [5] showed that constant temperature assumption may lead to 30% error in large tube banks. Leidenfrost and Korenic [6] developed a methodology similar to the one of Parker and Treybal [4] with which they found that accurate prediction of performance characteristics of closed wet cooling tower can be attained through iterative procedures. In addition, various researchers suggested different methods for dimensioning closed wet cooling towers [7,8]. Finlay and Grant [9] suggested a simplified model for describing the mass transfer process inside a closed wet cooling tower, which was based on the expression of vapour pressure of saturated moist air as linear function of temperature. Dreyer [10] presented different mathematical models for the thermal evaluation of evaporative coolers and closed wet cooling towers [4,7,11e14]. Analytical models [10e13,15,16] are based on the implementation of energy and mass conservation laws making various assumptions concerning the spayed water temperature distribution and the sprayed water loss due to evaporation. Aiming to a more realistic description of the transport phenomena taking place inside a closed wet cooling tower, sophisticated mathematical models [17,18] have been developed and CFD packages have been used [19e21] which provide predictions of the temperature and flow field inside cooling tower. Though that these models are more detailed and informative compared to analytical models, they are time-consuming and thus, cannot provide performance predictions for large periods of time. The current literature shows that no generally accepted method exists for predicting the performance of closed wet cooling towers. Recently, the present research group has developed a detailed thermodynamic model and used it to assess the thermal performance of a closed wet cooling tower [22]. The success of this application has motivated us to utilise it to examine the effect of inlet air conditions on the thermal behaviour of an indirect wet cooling tower operating in the area of Athens, Greece. The model is used to examine the effect of variable dry bulb air temperature and
Tw U W Wsat Z
sprayed water temperature ( C) overall heat transfer coefficient of falling water film (Wm2 C1) air humidity ratio (kgw kg1 da ) saturation humidity ratio of moist air (kgw kg1 da ) tower height (m)
Greek symbols b mass transfer coefficient (kg m2 s1) Dhw latent heat of vapourisation for water (J kg1) l thermal conductivity of water (W m1 C1) Subscripts a air db dry bulb i inner f serpentine water L latent LA liquid to air o outer s steam sat saturated TL tube to liquid w water ws waterevapour wb wet bulb w,s saturated steam
humidity ratio, according to the design as well as extreme conditions given by the Greek Regulation for Buildings Energy Performance [23], on the variation of the thermodynamic state of moist air inside the cooling tower and on its cooling capacity and thermal efficiency. Comparison of the simulations with experimental results obtained from the literature was made to assess the predictive ability of the model. The main outcome, which revealed from the analysis of the theoretical results, was that the highest temperature fall of serpentine water and the highest losses of sprayed water mass are observed for the lowest value of inlet wet bulb temperature. The presented outcomes could be very useful not only for industrial applications but also for domestic applications with liquid desiccant air-conditioning systems providing heatingecooling and dehumidification of the process air without using conventional energy consuming components and environmentally harmful refrigerants [24e27]. The liquid desiccant systems are designed to serve as open-cycle absorption systems that operate with low-grade heat in combination with closed wet cooling tower for precooling of liquid desiccant solution in the absorber, where the dehumidification takes place, and for regeneration of liquid solution in the regenerator [26,27]. 2. Model description 2.1. General outline A comprehensive thermodynamic model based on the conservation laws for energy and mass is used to describe the coupled heat and mass transfer processes taking place inside an indirect wet cooling tower. The model was implemented for a closed wet cooling tower having a bank of 16 31 plain tubes. The length of tube bundle is 0.888 m. The tube length is 0.913 m and the outer and the inner tube diameter are 0.0191 m and 0.0150 m respectively. The ratio of pitch to outside tube diameter is 1.5. The aforementioned schematic view of the closed wet cooling tower
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
used herein is shown in Fig. 1. Model development was based on the following assumptions: The heat and mass transfer processes occur under steady state conditions, in a direction perpendicular to the tower walls. The specific heat capacity of sprayed water, serpentine water and dry air is constant in the temperature range considered. The specific enthalpy of dry air, water and serpentine water is equal to zero at 0 C. Owing to the small temperature differences at which the process occurs heat transferred by radiation is not taken into account. At the interface air reaches the temperature of water and its humidity corresponds to the state of equilibrium. The thermal resistance between the bulk and the interface of falling water film is negligible. Water and air are in counter-flow.
Model development is based on the implementation of energy balance for each one of the working fluids taking part in the process. The implementation of the energy balance for the gaseous phase implies that sensible and latent heat is exchanged between the falling water film and the air stream resulting in the change of dry bulb air temperature along wetted tube surface as follows [22]:
dTa ¼ dA
aLA dW ðTw Ta Þ þ csat ps _a m dA cpm
where cpa is the specific heat at constant pressure of dry air and W is the humidity ratio. The term dW/dA in Equation (1) corresponds to the evaporated water mass per unit heat exchange area at the waterevapour interface and it is given by the following expression:
b sat dW W ðTw Þ Wa ¼ _a m dA
(1)
(3)
where b is the mass transfer coefficient. The saturation humidity ratio of air Wsat is calculated using the following relation:
W sat ðTw Þ ¼ 0:622
psat ws ðTw Þ pa psat ws ðTw Þ
(4)
where psat ws is the saturation pressure of moist air. The definition of air humidity ratio is employed to derive the rate of change of _ w per unit of heat exchange area evaporated cooling water mass m as follows:
_ dm dW _w ¼ m _ a W0 w ¼ m _a m dA dA
2.2. Mathematical formulation
201
(5)
The application of the energy balance between serpentine water and falling water film provides
dTw 1 dW sat _a ½aLA ðTw Ta Þ þ m ¼ cps Ta þ cpw Tw þ Dhw _ dA mw cpw dA i (6) þU Tw Tf where Dhw is the latent heat of vapourisation for water and U is the overall heat transfer coefficient of falling water film. The rejection of sensible heat from the circulating water to the falling water film results in its temperature fall as shown in the following relation:
_ a is the air where aLA is the water to air heat transfer coefficient, m mass flow rate, csat ps is the specific heat of saturated steam, Tw is the cooling water temperature, Ta is dry bulb air temperature and cpm is the specific heat capacity of moist air, which is defined as
U Tw Tf dTf ¼ _ f cpf m dA
cpm ¼ cpa þ Wcsat ps
Finally, a system of four (4) ordinary differential equations is constituted [22]
(2)
sat dTa aLA cps dW þ ¼ _a m dA dA
(7)
!
ðTw Ta Þ cpm
dTw 1 dW sat _a ½a ðT Ta Þþ m ¼ c Ta þcpw Tw þ Dhw _ w cpw LA w dA m dA ps i þU Tw Tf dTf U Tw Tf ¼ _ f cpf m dA b sat dW W ðTw ÞWa ¼ _a dA m _w dm dW _a ¼m dA dA
9 > > > > > > > > = ð8Þ > > > > > > > > ;
with the following boundary conditions:
ðTa ÞZ¼0 ¼ Ta0 ðT w ÞZ¼L ¼ Tw0 Tf ¼ Tf 0
9 > > > > =
Z¼L > > > ; ðWÞZ¼0 ¼ W0 > _ w0 _ w Z¼L ¼ m m
Fig. 1. Schematic view of the closed wet cooling tower.
(9)
A variable-step non-stiff method (RungeeKutta 5(4)) was used to numerically solve the boundary-value problem [29]. The model was developed using the Mathcad software where all the thermodynamic characteristics of the tower are calculated from the
202
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
point where the water is sprinkled till the end of the tubes bundle. The energy and mass balance of the sprayed water contribution as well as the stream in a counter-flow closed wet cooling tower is shown in Fig. 2. The heat transfer coefficient between falling water film and air stream (Le ¼ 1) is given by the following relation [7,11,29,30]:
aLA ¼ bcpm
(10)
where b is the mass transfer coefficient, which is calculated as follows:
b ¼ 6:0 108 ðRea Þ0:9 ðRew Þ0:15 ðDo Þ1:6
(11)
and Rea, Rew are the Reynolds numbers of the air and the sprayed water stream respectively [22]. The overall heat transfer coefficient U between serpentine water, tube wall and water film is calculated by the following formula:
U ¼
Ro 1 Ro Ro 1 þ ln þ Ri hf k Ri aTL
!1 (12)
where the convection heat transfer coefficient of serpentine water hf is given by the “DittuseBoelter” relation [31]
hf ¼
! 0:3 0:023Re0:8 f Prf l Di
(13)
where Ref and Prf are the Reynolds and Prandtl numbers respectively of the process water and l is the thermal conductivity of the process water.
given as design conditions for winter and summer and extreme conditions for summer according to the Greek Regulation for Buildings Energy Performance for the climate of Athens in Greece. For this reason, three cases of different ambient conditions are considered. In the first case, the mean monthly values for January [23] (Tdb,i ¼ 10.3 C e RH ¼ 74.4%) and the mean monthly values for June [23] (Tdb,i ¼ 27.1 C e RH ¼ 45.8%) occurring in Athens, Greece as well as the extreme summer conditions of high temperature and average relative humidity (Tdb,i ¼ 45 C e RH ¼ 35.0%) according to the Greek Regulation for Buildings Energy Performance, were assumed. The objective of this case was the assessment of the thermal performance characteristics of the closed wet cooling tower under diverse ambient conditions occurring in Athens, Greece. The second case was considered in order to solely examine the influence of inlet air relative humidity on the thermal behaviour of closed wet cooling tower. For this reason, inlet air relative humidity was varied while inlet air dry bulb temperature remained constant. In the third case, an attempt was made to assess the effects on the thermal behaviour of the closed wet cooling tower when the inlet air wet bulb temperature remains constant. All calculations were made herein adopting the parameter values for inlet conditions given in Table 1. The thermodynamic properties of air and water are calculated from top to bottom of the tube bundles while the mass and heat transfer coefficients were calculated according to Equations (10) and (11). Taking into account the inlet conditions, the Reynolds number of water is 130.12 while the Reynolds number of air is 8.407 103.
4. Results and discussion 3. Overview of the parametric study 4.1. Experimental validation A theoretical assessment is conducted to evaluate the sensitivity of thermal performance characteristics of a closed wet cooling tower under variable surrounding air conditions, which are
A comparison between predicted and experimental results for sprayed water temperature, serpentine water temperature and dry bulb air temperature at various positions along the closed wet cooling tower’s height is given in Tables 2 and 3. The total wetted area of the tubes bundle was calculated as 27 m2, and the numerical solution is given from 0 to 27 m2. The exact position along the height and the wetted area is given from the first column of Tables 2 and 3. Due to the fact that experimental data for the variation of dry bulb temperature inside the cooling tower were unavailable, the comparison was limited to the inlet and outlet conditions. The tabulated theoretical data were produced for two different “temperature approaches” (Twb,oeTdb,i), which are equal to 5.1 C and 8.3 C. The experimental data in both tables were obtained from Finlay and Harris [28]. As it can be observed, the calculated results are in acceptable agreement with the corresponding measured data throughout the wet cooling tower. This can be verified by the low values of the relative error (not exceed 5.5%) between theoretical and experimental results enhancing our confidence on the reliability of the simulations, which will be presented in Tables 2 and 3.
Table 1 Parameter values of the inlet conditions.
Fig. 2. Schematic description of the energy contribution of sprayed water and air stream in a counter flow closed wet cooling tower.
Twi, Sprayed water temperature ( C) mwi, Sprayed water mass flow rate (kg/s) ma,i, Air mass flow rate (kg/s) Tfi, Serpentine water temperature ( C) mfi, Serpentine water mass flow rate (kg/s)
20 1.85 2.07 35 2.67
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
203
Table 2 Comparison between predicted and experimental values for sprayed water Tw, serpentine water temperature Tf and dry bulb air temperature Ta. Predictions were made for Tw,o Twb,i ¼ 5.1 C and the corresponding experimental data were obtained from Ref. [28]. Wetted tube Surface (m2)
Tc_exp ( C)
Tc_calc ( C)
Error (%)
Tf_exp ( C)
Tf_calc ( C)
Error (%)
Ta_exp ( C)
Ta_calc ( C)
Error (%)
0.0 1.8 3.6 7.2 10.8 14.4 18.0 21.6 25.2 27.0
12.80 13.60 14.10 14.00 14.00 13.77 13.51 13.09 12.70 12.30
12.80 13.44 13.78 13.99 13.93 13.73 13.45 13.08 12.62 12.34
0.00 1.21 2.30 0.04 0.50 0.27 0.45 0.07 0.66 0.32
15.60 15.00 14.70 14.70 14.40 14.30 14.07 13.60 13.50 13.30
15.60 15.16 14.89 14.58 14.38 14.20 14.05 13.76 13.46 13.29
0.00 1.10 1.30 0.83 0.13 0.68 0.47 1.19 0.28 0.10
13.60 e e e e e e e e 15.45
13.60 e e e e e e e e 14.60
0.00 e e e e e e e e 5.39
4.2. Effect of the variation of ambient conditions on the thermodynamic properties of air along tower’s height In Fig. 3(a) the variation of dry bulb air temperature and humidity ratio with the wetted tube surface (along the height of the wetted cooling tower, where Z ¼ 0 at the position where the water is sprinkled) for the three cases of ambient conditions is shown. Increase of the outlet dry bulb temperature is observed in the low wet bulb temperature case (Twb ¼ 8.1 C e mean monthly values for January), which is up to 60%. This trend is reversed in the high wet bulb temperature case (Twb ¼ 25.2 C e extreme conditions for July) where the dry bulb temperature decreases with increasing tube banks surface along the height of tower. For a mid-range value of inlet wet bulb temperature (design conditions for June) the variation of dry bulb temperature is insignificant compared to the other cases. In Fig. 3(b) the outdoor dry bulb air temperature for extreme conditions in Athens during summer remains constant while the relative humidity is changed from 20 to 35% resulting in increase of wet bulb temperature. At all cases of wet bulb temperature, the dry
bulb temperature along the height of wet cooling tower is noticeably reduced. The increase of the relative humidity results in small increase of outlet air dry bulb temperature. In Fig. 3(c) the variation of the outlet dry bulb air temperature is considerable when extreme and design climatic conditions are considered. For similar values of inlet wet bulb temperature of air the outlet dry bulb air temperature is reduced more than 15 C when the wetted tube surface takes its highest value. According to Fig. 4(a), an increase of humidity ratio is witnessed in the case of low (Twb ¼ 8.1 C), mid-range (Twb ¼ 18.9 C) and high inlet wet bulb temperature (Twb ¼ 25.2 C). However, the humidity ratio during the last stages is decreased, although it is increased for the higher percentage of wetted tube surface. This means that the outlet air of the cooling tower has less temperature and less absolute humidity than inlet air which could be used for space air condition and dehumidification when it is combined with liquid desiccant systems. In Fig. 4(b) for high values of relative humidity the humidity ratio is increased and at the last stages of the process, a significant reduction is observed.
Fig. 3. Effect of ambient conditions of Athens (Greece) on the variation of dry bulb temperature inside the closed wet cooling tower.
204
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Table 3 Comparison between predicted and experimental values for sprayed water Tw, serpentine water temperature Tf and dry bulb air temperature Tdb. Predictions were made for Tw,o Twb,i ¼ 8.3 C and the corresponding experimental data were obtained from Ref. [28]. Wetted tube Surface (m2)
Tc_exp ( C)
Tc_calc ( C)
Error (%)
Tf_exp ( C)
Tf_calc ( C)
Error (%)
Ta_exp ( C)
Ta_calc ( C)
Error (%)
0.0 1.8 3.6 7.2 10.8 14.4 18.0 21.6 25.2 27.0
13.60 15.45 15.76 15.80 15.70 15.50 15.30 14.80 14.20 13.80
13.60 14.60 15.20 15.60 15.50 15.30 15.00 14.60 14.10 13.80
0.00 5.39 3.71 1.43 1.03 1.16 1.99 1.48 0.94 0.23
18.00 17.40 16.90 16.40 16.00 15.80 15.75 15.52 15.16 14.60
18.00 17.30 16.90 16.40 16.10 15.90 15.70 15.40 15.00 14.80
0.00 0.48 0.05 0.13 0.92 0.73 0.52 0.90 0.83 1.61
18.00 e e e e e e e e 17.40
18.00 e e e e e e e e 17.30
0.00 e e e e e e e e 0.48
In Fig. 4(c) a similar increase of humidity ratio occurs in combination with high wetted tube surface.
4.3. Effect of ambient conditions on sprayed water temperature, serpentine water temperature and sprayed water mass losses along the wet cooling tower’s height The effect of ambient air conditions on the variation of cooling water temperature inside the closed wet cooling tower is given in Fig. 5(a). As evidenced, in the low wet bulb temperature case (Twb ¼ 8.1 C), the cooling water temperature rises for values of the wetted tube surface up to 7.5 m2 and then, decreases progressively receiving finally, a value close to its initial one. For the same ambient conditions, the process water is cooled and the falling water film mass is evaporated with increasing rate. Similar observations can be made for the case of Twb ¼ 18.9 C. In the case of ambient conditions of high temperature and relative humidity, a steep increase of cooling water temperature is observed during the initial stages of the evaporation process whereas, for values higher than 7.5 m2 a smooth decrease of cooling water temperature is observed.
According to Fig. 5(b), along the way of sprayed water, higher values of relative humidity result in constant values of sprayed water temperature till the outlet of the tower. As observed in Fig. 5(c) the variation of sprayed water temperature through the closed wet cooling tower remains the same when the inlet wet bulb air temperature is similar. As evidenced from Fig. 6(a), for values of wetted tube surface up to 7.5 m2, the rate of cooling of the serpentine water is steep and similar for different values of outdoor dry bulb temperature. For values of tube banks surface higher than 7.5 m2, the temperature of serpentine water and the rate of evaporated water mass drops significantly especially during January. The effects of inlet air conditions on serpentine water temperature are the same but the reduction of the temperature is less steep comparing to the aforementioned case when the relative humidity is varied from 20 to 35%. Finally, according to Fig. 6(c) when the inlet air wet bulb temperature remains constant the effect on serpentine water temperature is limited. The influence of ambient conditions on the percentage losses of cooling water mass is shown in Fig. 7(a)e(c). According to Fig. 7(a), the increase of humidity ratio for the case of mid-winter conditions results in a significant reduction of the cooling water mass
Fig. 4. Effect of ambient conditions of Athens (Greece) on the variation of humidity ratio inside the closed wet cooling tower.
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
205
Fig. 5. Effect of ambient conditions of Athens (Greece) on the variation of sprayed water temperature inside the closed wet cooling tower.
evaporated during the process that could be up to 72% at the outlet (comparing with the inlet). During summer there is a significant decrease of sprayed water mass flow rate which is observed even when the relative humidity is increased (Fig. 7(b)). This decrease could become 42% for extreme summer conditions. According to Fig. 7(c) similar values of inlet air wet bulb temperature provide approximately the same decreased sprayed water mass flow rate.
Fig. 8 presents the variation of the dry bulb air temperature, the sprayed water temperature as well as the serpentine water temperature along tower’s height (from top to bottom) for summer design conditions. From the figure above, it can be derived that the serpentine water temperature falls significantly taking similar values with the sprayed water temperature at the outlet of the tower while the air exits the tower warmer and more humid. The
Fig. 6. Effect of ambient conditions of Athens (Greece) on the variation of serpentine water temperature inside the closed wet cooling tower.
206
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207
Fig. 7. Effect of ambient conditions of Athens (Greece) on the variation of the percentage change of sprayed water mass flow rate inside the closed wet cooling tower.
The variation from mid-summer to mid-winter conditions (i.e., increase of humidity ratio) results in: a) Heating and humidification of the outlet air, b) Decrease of the cooling water mass that is evaporated during the process and needs to be replaced from the network, c) Significant temperature fall of the cooled water and, d) Increase of the effectiveness of the cooling tower due to the reduction of the temperature deviation of outlet cooled water from the ideal case (i.e., Tw,o ¼ Ta,i).
Fig. 8. Distribution of dry bulb air temperature, of sprayed water temperature and serpentine water temperature inside the closed wet cooling tower along its height.
outlet serpentine water temperature can be used for precooling purposes in industrial applications and for sorption air-conditioning systems with liquid desiccant where the absorber, the component where the dehumidification takes place, should be internally or externally cooled by a cooling tower. 5. Conclusions A newly developed model was used to simulate the processes taking place inside a closed wet cooling tower and mainly, to investigate the effect of ambient air conditions on its thermal behaviour. The reliability of the simulations was well tested against experimental results obtained from literature. The analysis of the theoretical results leads to the derivation of the following conclusions.
Consequently, the optimum thermal performance of the closed wet cooling tower can be attained in the case where the air stream enters into the cooling tower with low humidity ratio (relatively hot and humid ambient conditions). Reduction of the operating cost of the cooling tower is achieved in this case due to the decrease of overall evaporated water mass. Increase also of the efficiency of the evaporation process is accomplished as revealed by the increase of heat exchange effectiveness. The only minor obstacle in this case is the disability of achieving considerable temperature falls for the cooling water. The beneficial effect of the serpentine water temperature fall of the examined closed wet cooling tower can be observed when it is combined with liquid desiccant air-condition systems, providing heatingecooling and dehumidification for buildings without using energy consuming equipments and common environmentally harmful refrigerants.
References [1] W. Goodman, The evaporative condenser, Heating Piping Air Conditioning 10 (1938) 165e328. [2] E.G. Thomsen, Heat transfer in an evaporative condenser, Refrigeration Engineering 51 (1946) 425e431. [3] D.D. Wile, Evaporative condenser performance factors, Refrigeration Engineering 58 (1950) 55e63. [4] R.O. Parker, R.E. Treybal, The heat mass transfer characteristics of evaporative coolers, Chemical Engineering Progress Symposium Series 57 (32) (1961) 138e149.
V.D. Papaefthimiou et al. / Applied Thermal Engineering 33-34 (2012) 199e207 [5] C.I. Finlay, W.D. Grant, The Accuracy of Some Simple Methods of Rating Evaporative Coolers Report No. 584. National Engineering Laboratory, East Kilbride, Glasgow, 1974. [6] W. Leidenfrost, B. Korenic, Evaporative cooling and heat transfer augmentation related to reduce condenser temperatures, Heat Transfer Engineering 3 (1982) 38e59. [7] T. Mizushina, R. Ito, H. Miyashita, Characteristics and methods of thermal design of evaporative coolers, International Chemical Engineering 8 (1968) 532e538. [8] S. Tezuka, T. Takada, S. Kasai, Performance of an evaporative cooler, Heat Transfer e Japanese Research 6 (1976) 1e18. [9] C.I. Finlay, W.D. Grant, Air Coolers, Cooling Towers and Evaporative Coolers Report No. 534. Nat. Engng Lab., East Kilbride, Glasgow, 1972, pp. 165e328. [10] A.A. Dreyer, Analysis of evaporative cooler and condenser, MSc Thesis, University of Stellenbosch, Rep. of South Africa, 1988. [11] R.L. Webb, A. Villacres, Algorithms for performance simulation of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions 90 (2B) (1984) 416e458. [12] R.L. Webb, A unified theoretical treatment for thermal analysis of cooling towers, evaporative condensers and fluid coolers, ASHRAE Transactions 90 (2B) (1984) 398e415. [13] J. Erens, A.A. Dreyer, An improved procedure for calculating the performance of evaporative closed circuit coolers, in: The 25th National Heat Transfer Conference, Houston, AIChE Symp. Ser. 84, 1988, pp. 140e145. [14] M. Poppe, H. Rögener, Evaporative Cooling Systems. VDI- Warmeatlas: Section Mh, 1984. [15] B.A. Qureshi, S.M. Zubair, A comprehensive design and rating study of evaporative coolers and condensers. Part I. Performance evaluation, International Journal of Refrigeration 29 (2006) 645e658. [16] B.A. Qureshi, S.M. Zubair, A comprehensive design and rating study of evaporative coolers and condensers. Part II. Sensitivity analysis, International Journal of Refrigeration 29 (2006) 659e668. [17] W. Zalewski, P.A. Gryglaszewski, Mathematical model of heat and mass transfer process in evaporative fluid coolers, Journal of Chemical Engineering and Processing 36 (1997) 271e280.
207
[18] W. Zalewski, B. Niezgoda-Zelasko, M. Litwin, Optimization of evaporative fluid coolers, International Journal of Refrigeration 7 (2000) 342e347. [19] G. Gan, S.B. Riffat, L. Shao, P. Doherty, Application of CFD to closed-wet cooling towers, Applied Thermal Engineering 21 (2001) 79e92. [20] G. Gan, S.B. Riffat, Numerical simulation of closed wet cooling towers for cooled ceiling systems, Applied Thermal Engineering 19 (1999) 1279e1296. [21] A. Hasan, G. Gan, Simplification of analytical models and incorporation with CFD for the performance of prediction of closed-wet cooling towers, International Journal of Energy Research 26 (1938) 1161e1174. [22] V.D. Papaefthimiou, T.C. Zannis, E.D. Rogdakis, Thermodynamic study of wet cooling tower performance, International Journal of Energy Research 30 (2006) 411e426. [23] Greek Regulation for Buildings Energy Performance, Technical Notes 20701e3/2010. [24] X.H. Liu, X.M. Chang, J.J. Xia, Y. Jiang, Performance analysis on the internally cooled dehumidifier using liquid desiccant, Building and Environment 44 (2009) 299e308. [25] Ch.-Q. Ren, Corrections to the simple effectiveness-NTU method for counterflow cooling towers and packed bed liquid desiccanteair contact systems, International Journal of Heat and Mass Transfer 51 (2008) 237e245. [26] Ch.Q. Ren, M. Tu, H.H. Wang, An analytical model for heat and mass transfer processes in internally cooled or heated liquid desiccant-air contact units, International Journal of Heat and Mass Transfer 50 (2007) 3545e3555. [27] L. Mei, Y.J. Dai, A technical review on use of liquid-desiccant dehumidification for air-conditioning application, Renewable and Sustainable Energy Reviews 12 (2008) 662e689. [28] C.I. Finlay, D. Harris, Evaporative cooling of tube banks, International Journal of Refrigeration 7 (1984) 214e224. [29] T. Mizushina, R. Ito, H. Miyashita, Experimental study of an evaporative cooler, International Chemical Engineering 7 (1967) 727e732. [30] J. Facao, A. Oliveira, Heat and mass transfer correlations for the design of small indirect contact cooling towers, Applied Thermal Engineering 24 (2004) 1969e1978. [31] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, fifth ed. John Wiley and Sons, New York, 2002.