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Evaporative Condensers

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Evaporative Condensers
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Heat Transfer Engineering, 22:4155, 2001 C Copyright 2001 Taylor & Francis 01457632/01 $12.00 + .00

Performance of Evaporative CondensersHISHAM M. ETTOUNEY, HISHAM T. EL-DESSOUKY, WALID BOUHAMRA, and BADER AL-AZMIDepartment of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, Safat, Kuwait

Experimental investigation is conducted to study the performance of evaporative condensers/coolers. The analysis includes development of correlations for the external heat transfer coef cient and the system ef ciency. The evaporative condenser includes two nned-tube heat exchangers. The system is designed to allow for operation of a single condenser, two condensers in parallel, and two condensers in series. The analysis is performed as a function of the water-to-air mass ow rate ratio (L/G) and the steam temperature. Also, comparison is made between the performance of the evaporative condenser and same device as an air-cooled condenser. Analysis of the collected data shows that the system ef ciency increases at lower L/G ratios and higher steam temperatures. The system ef ciency for various con gurations for the evaporative condenser varies between 97% and 99%. Lower ef ciencies are obtained for the air-cooled condenser, with values between 88% and 92%. The highest ef ciency is found for the two condensers in series, followed by two condensers in parallel and then the single condenser. The parallel condenser con guration can handle a larger amount of inlet steam and can provide the required system ef ciency and degree of subcooling. The correlation for the system ef ciency gives a simple tool for preliminary system design. The correlation developed for the external heat transfer coef cient is found to be consistent with the available literature data.

Condensers are found in a wide range of applications, such as petroleum re neries, petrochemical plants, power-generation stations, chemical process industries, and air-conditioning units. The cooling uid in conventional condensers is commonly fresh water, which can be costly or not readily accessible. However, demands for conservation of the limited fresh-water resources on a global scale necessitates the use of abundant cooling media, which includes seawater or ambient air. Use of seawater as the cooling medium is limited to low condensation temperatures to avoid scale and fouling by the seawater at temperatures above 60 C. Moreover,Address correspondence to Hisham Ettouney, Chemical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait. E-mail: [email protected]

the feed seawater must be treated to remove particulate matter and chemically treated to control scale formation, fouling, and corrosion. The rejected seawater has an adverse effect on the environment, due to the thermal pollution caused in the locality of the discharge area. Applications of air-cooled condensers are found in conventional air-conditioning units, where ambient air is used as a heat sink to condense the refrigerant vapor. On an industrial scale, air condensers are also used in power plants, where fresh water may be inaccessible and expensive. Use of evaporative cooling improves the performance of air-cooled condensers. The evaporative effect cools the condensate to a temperature lower than the air ambient temperature. This increases the thermal capacity of the air stream and as a result makes it41

possible to use a lower air ow rate and consequently the fan capacity and its power consumption are reduced. Further, the heat transfer coef cient for the evaporative system is higher than for air-cooled condensers. This enhances the heat transfer rate and increases the value of the overall heat transfer coef cient. As a result, a smaller heat transfer area is used to remove the same thermal load in air-cooled condensers. Use of evaporative condensers eliminates the shell cover for the heat exchange tubes, which is an expensive element in conventional condenser units that combines a cooling tower and an external heat exchanger. Also, placement of the evaporative unit inside the cooling tower reduces the space requirements for piping connections and valves used in conventional units. LITERATURE REVIEW Literature studies for modeling and analysis of evaporative condensers are limited in number. On the other hand, the major fraction of the literature studies on air water evaporative systems focuses on performance and analysis of cooling towers and the indirect evaporative cooling systems. The latter have a number of similarities with the evaporative condenser, especially when considering heat and mass transfer in the air water system outside the heat exchanger tubes. Therefore, analysis of literature studies for indirect evaporative coolers as well as evaporative condensers is considered in the following discussion. Differences in modeling these systems are caused primarily by variations in the driving force between the uid inside the tubes of the heat exchanger and the water/air streams owing outside the heat exchanger tubes, and the heat transfer mechanisms inside the tubes. The driving force in evaporative condensers is primarily equal to the difference of the condensing vapor temperature and the external temperature between the surface and the air water mixture. The condensation process also includes vapor desuperheating and condensate subcooling. Either process is similar to uid cooling inside the heat exchanger tubes in indirect evaporative coolers. The main focus of the literature studies on indirect evaporative coolers is the development of more energyef cient air-conditioning systems. This is achieved by various combinations of cooling towers, indirect and direct evaporative coolers, and conventional mechanical vapor compression units [1]. Webb [2] presented a uni ed theory for modeling of cooling towers, evaporative condensers, and evaporative coolers. Various correlations are adopted to de ne the water lm heat transfer coef cient and the mass transfer coef cient for water transport from the water lm to the air stream. In modeling the condenser and cooler units, additional42 heat transfer engineering

correlations are used to de ne the heat transfer coef cient for the uid inside the tubes of the heat exchanger. The heat transfer coef cient for the water lm used by Webb [2] corresponds to a water lm owing under gravity conditions and in the absence of the air stream. Subsequently, three algorithms and computer models are presented by Webb and Villacres [3] for analysis of cooling towers, uid coolers, and evaporative condensers. The algorithms are found to predict accurately the duty of the three systems, within 3% of the manufacturers rating data. Models of indirect evaporative cooling towers are developed by Maclaine-Cross and Banks [4], Kettleborough and Hsieh [5], Chen et al. [6]. These models are found to give reasonable agreement for outdoor air applications. However, the models overpredict the cooling effectiveness of the system during certain operations, which include mixed or exhaust-air applications. This motivated Peterson [7] to develop a mathematical model for analysis of indirect evaporative coolers. Predictions of the mathematical model are validated against experimental data. This comparison shows the limitations of the model in accurate predictions of energy savings or performance at some operating conditions. At such conditions, Peterson [7] recommends the use of correlations generated from experimental data to obtain necessary design or performance data. Kettleborough [8] presented a numerical model for evaluation of the effectiveness of indirect evaporative coolers. The numerical model evaluates the temperatures of the plate, secondary air, and primary air. Also, the model calculates the humidity of the outlet secondary air stream. Since the model equations are coupled and nonlinear, an iterative and numerical solution is found necessary to determine the system effectiveness, which is de ned as the ratio between the drop in the primary air temperature and the wet-bulb depression (de ned as the difference of the dry- and wet-bulb temperatures ) of the inlet primary air with respect to the secondary air stream. Experimental evaluation of indirect evaporative coolers, when combined with conventional airconditioning systems, are presented by Peterson and Hunn [9] for a small of ce building in Dallas, Texas. Analysis of the data shows a system ef ciency higher by 70% than conventional air-conditioning units. This allows for a 12% reduction in the capacity of the airconditioning system. Further evaluation of the evaporative air precooling system shows that the water pump is the largest energy-using component, rather than the air fan. Erens and Dreyer [10] tested the performance of three mathematical models for simulation of evaporative coolers. The mathematical development of the models is based on either dividing the cooler into differential elements or by considering the cooler as onevol. 22 no. 4 2001

element. The rst and second models are differential, where the rst model evaluates the Lewis number and the second model assumes the Lewis number is equal to one. The third model assumes unit Lewis number, constant water temperature, and negligible thermal resistance in the water lm. Results show that the simplied model gives accurate results for evaluation of small units, and it is useful to obtain preliminary design and rating data. On the other hand, the detailed models are suitable for more accurate performance predictions. Effect of tube arrangement in indirect evaporative cooling is analyzed by Erens [11]. Results show that the performance of bare tubes is enhanced through the use of plastic ll, which can be integrated with the tubes or placed below the tubes. The improved performance is caused by the increase of the water residence time in the ll material, which generates higher rates of heat and mass transfer between the air and water streams. A similar effect on enhancement of the performance of cooling towers is reported by El-Dessouky [12] on the use of rough surface packing material. Goswami et al. [13] studied performance enhancement of small to medium-size air-conditioning units by evaporative cooling of the ambient air used to condense the refrigerant uid. The study follows a similar approach adopted in air-conditioning units for large facilities and buildings. Evaporative cooling of the air is found to increase the temperature driving force for the condensation process. In turn, energy savings up to 20% are reported for the evaporatively cooled air against system operation without the evaporative cooler. Simulation of cooling towers includes analytical models, i.e., the model by Merkel [14], and numerical models, i.e., the models by Nahavandi et al. [15] and Sutherland [16]. Comparison of both models shows small differences of 5 12% in their predictions. El-Dessouky et al. [17] developed a modi ed model for analysis and rating of cooling towers. The model presents new de nitions for the number of transfer units and the effectiveness of the cooling tower. The number of transfer units is expressed in terms of the air and water heat capacity, and the effectiveness is expressed as a function of the tower cooling range and the approach to equilibrium. The model also considers the nonlinear dependence of the air/water vapor enthalpy on the temperature. Early models of evaporative condensers by Goodman [18] and Thomsen [19] assumed constant temperature for the water stream. This assumption is found to generate poor predictive results for the system and was eliminated in the study by Parker and Treybal [20]. In their model, they assumed a Lewis number of unity, linear dependence of the air enthalpy on temperature, and negligible change in the water ow rate. The modelheat transfer engineering

by Parker and Treybal [20] does not require numerical solution and can be solved using a simple analytical procedure. A more detailed numerical model is developed by Leidenfrost and Korenic [21], in which the three assumptions in the Parker and Treybal model are eliminated. However, a number of inconsistencies in the model were later cited by Peterson et al. [22], who modi ed the Parker and Treybal model and validated their results against experimental data. Their analysis shows that the value for the water-side heat transfer coef cient of the water tube interface proposed by Parker and Treybal is low, since the model underpredicts the condenser load by 30%. From the above survey it can be concluded that a limited number of studies are found on performance of evaporative condensers. The survey shows the need for execution of the following. Experimental measurements of the temperature pro le in the evaporative condenser are necessary for better understanding of the system performance and in development of accurate models for the system. Evaluation of the evaporative condenser ef ciency at different operating conditions. Development of correlations for the heat transfer coefcient of the air/water side. Development of accurate mathematical models for the evaporative condenser and validation against experimental data. This will be executed in a subsequent study. Accordingly, the main objective of this study is to determine experimentally the performance of evaporative condensers as a function of the ow rate ratio of water to air and the thermal load. This involves measurements of the axial temperature distribution and calculating the system ef ciency and the heat transfer coef cient. The study also compares the performance of evaporative condensers versus air condensers. Results and analysis gives better understanding in the performance of evaporative condensers, which is necessary to develop and design more ef cient systems. EXPERIMENTAL APPARATUS AND PROCEDURE Figure 1 shows a schematic for the evaporative condenser system. As is shown, the system is made of a metal frame and includes a water basin, a water circulation pump, an air fan, packing material, two evaporative condenser units, water spray nozzles, siding sheets of Plexiglas, connection tubes, and valves. The measuring devices include water ow meters and temperaturevol. 22 no. 4 2001 43

Figure 1

Schematic of the evaporative condenser.

thermocouples. The sides of the apparatus are tightly sealed with the Plexiglas sheets, which is necessary to prevent air leakage to or from the system. The system dimensions are 0.83 0.6 2 m in width, length, and height, respectively. The water basin has dimensions of 0.83 0.6 0.32 m in width, length, and height. The oat control in the water basin is adjusted to a height of 0.3 m, which allows for accumulation of 0.1494 m3 of water in the basin. This volume is necessary to maintain a nearly constant water temperature in the system. The water circulates from the water basin to the spray nozzles via the water circulation pump and the ow meter. The circulation pump has a maximum power of 0.278 kW and provides a maximum ow rate of 2 kg/s. The spray nozzle system breaks the water stream into a ne mist, with an average drop diameter of 5 104 m, which is evenly distributed over the packing material. Therefore, the water ows from the top of the column toward the basin in a countercurrent direction to the air stream. The suction fan has an input/output power44 heat transfer engineering

rating of 440/350 W. The fan moves the air stream from the side openings near the water basin to the top of the column. The suction fan has a constant speed and moves the air at an average ow rate of 2.767 m3 (STP )/s or 2.68 kg/s. As is shown in Figure 1, structured packing material is used and is divided into three layers. As reported by El-Dessouky et al. [23], this type of packing gives higher system ef ciency than Sheathy leaf or natural ber. Each layer has the same cross-sectional area as the metal frame (0.83 0.6 m ). This prevents bypass of the air or water streams, which would result in reduction of the contact area between the two streams and consequently decrease in the cooling ef ciency. Each layer has a thickness of 0.1 m, which gives suf cient internal surface area for air and water contact. Use of the three packing layers maintains proper water distribution and suf cient contact area between the air and water streams. The two condenser units have proper piping that allow operation of a single condenser or thevol. 22 no. 4 2001

two condensers in series or parallel. The two condensers are identical, and each has a single path and dimensions of 0.83 0.6 0.02 m in length, width, and thickness, respectively. Each condenser contains a single row of 18 tubes with an outer diameter of 0.011 m and an inner diameter of 0.008 m. Thin at sheet ns hold the tube bundle together, and each n has dimensions of 0.02 0.6 0.0015 m in height, length, and thickness. The number of ns in a 1-m length is 394. This arrangement gives a total heat transfer area of 3.672 m2 , which includes a heat transfer area of 0.312 m2 for the tubes and 3.36 m2 for the ns. The measuring devices are used to determine the ow rates of circulating water and condensing steam as well as the dry- and wet-bulb temperatures of the ambient air, the water temperature inside the column, and the steam inlet and condensate temperatures. Locations for the thermocouple measurements are shown in Figure 1. Accuracy of the temperature-measuring device is 0.1 C and for water ow is 1% of the full scale. Experimental Procedure Operation of the evaporative condenser requires lling the water basin prior to operating the water pump and opening the steam valve. The system operating conditions are determined by adjusting the water ow rate, setting the steam pressure, and selecting the condenser con guration (single, two in series, or two in parallel ). At the start of operation, the system is monitored for a period of 1 h before commencing data collection. All temperature measurements are stored in a data logger at an interval of 5 min. Other data, which includes the ow rate of the steam condensate and the circulating water, are measured repeatedly on hourly basis over a period of 12 h. Temperature measurements include the water temperature pro le inside the column as well as the temperatures of the ambient air, inlet steam, and condensate. In all experiments, the air ow rate is kept constant at 9,660 m3 (STP)/h or 2.68 kg/s, and the water ow rate is varied and maintained at values of 0.44, 0.63, 0.82, and 0.95 kg/s. These values give water-toair ow rate ratios ( L/G ) of 0.164, 0.235, 0.306, and 0.354. The steam inlet temperatures used in the experiments are 111.9 and 120.8 C, which correspond to saturation pressures of 1.5 and 2 bar. In all experiments, which include the evaporative and air condensers, complete condensation of the inlet steam is achieved. The condensate ow rate varies over a range of 0.014 to 0.012 kg/s. Operation of the system as an air condenser is done simply by keeping the packing and the water basin dry and turning off the water pump. Other operating procedures and conditions, which include the air owheat transfer engineering

rate, steam pressures, and condenser con gurations, are identical to those of the evaporative con guration. EXPERIMENTAL RESULTS AND DISCUSSION The collected data are used to analyze the performance of the evaporative condenser and the air condenser. This includes analysis of the axial temperature pro les for the water stream and calculations of the ef ciency, e , which is de ned as the ratio of the actual to the maximum possible amounts of heat that can be removed from the condenser. The maximum amount of heat removed from the condenser occurs as the condensate steam temperature cools to the wet-bulb temperature of the air owing to the column. That is, e D Ms [k C C p (Ts Tu )] Ms ( Hs00 Hu ) D ( Hs00 Hw ) Ms Ms [k C C p ( Ts Tw )] (1 )

where Hs00 is the saturated steam enthalpy, k is the latent heat, Ms is the steam mass ow rate, T is the temperature, C p is the speci c heat at constant pressure, H is the condensate enthalpy, and the subscripts s; u, and w denes the saturated steam or condensate, the subcooled condensate, and the wet-bulb condition of the ambient air. It should be emphasized that the steam condensed in the evaporator is in the saturation state. The axial temperature pro les for the water stream in the evaporative condensers are shown in Figure 2 for the two condensers in series. Results are obtained for steam temperatures of 111.9 and 120.8 C and L/G values of 0.235 and 0.353. As is shown, the lowest water temperature is found in the water basin, and its value is above the wet-bulb temperature of the ambient air. The water temperature increases as it ows from the spray nozzles through the tower. The maximum water temperature occurs below the second heat exchanger. The water temperature and the condensate temperature increases at higher steam temperatures and as L/G increases. It should be noted that the effect of the wet-bulb temperature is consistent with the measured results. With regard to this, an increase in the wet-bulb temperature results in an increase of the condensate and water temperature in the system. This is caused by the small difference of the humidity for the dry and wet air. Therefore, at high wet-bulb temperatures the amount of water evaporated per unit ow rate of the water stream is reduced. The measured data for the temperature pro le of the water stream in the evaporative condenser tower are very important in modeling the system characteristics. This pro le can be used to de ne the driving force for heat transfer, which is necessary for heat transfer calculations. In literature studies, it is common tovol. 22 no. 4 2001 45

Figure 2 in series.

Variation in the water axial temperature pro le as a function of measuring hour, steam temperature, and L/G for two condensers

assume constant water temperature throughout the column, which is equal to the wet-bulb temperature [2]. This assumption is not consistent with the above measurements, and its adoption may lead to inaccuracies in the model predictions. Hourly variations in the ef ciency of the evaporative condenser and the air condenser are shown in Figure 3 for the single condenser, two condensers in parallel, and two condensers in series. The evaporative effect increases the system ef ciency from values of below 92% to values above 99%. Inspection of the ef ciency variations shows the decrease in the ef ciency of all systems during the daytime. The lowest ef ciency is found at noontime, and the highest ef ciency is measured during the early morning and the evening hours. This increase is associated with the decrease in the wet-bulb temperature of the ambient air owing to the column. Effects of the steam temperature and L/G on the ef ciency of the evaporative condenser are shown in Figures 4 6. As is shown, the ef ciency averages are 97.7%, 98.1%, and 98.9% for the single condenser, two condensers in parallel, and two condensers in series. The higher ef ciency of the two condensers in series is caused by the larger heat transfer area, which allows46 heat transfer engineering

for additional subcooling of the condensate. Increase in L/G results in decrease of the ef ciency for all systems. This is because the wet-bulb temperature of the ambient air sets the amount of water evaporated inside the tower. Therefore, increase in the ow rate of

Figure 3 Variation in the system ef ciency as a function condenser con guration and measuring time.

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Figure 5 Variation in the ef ciency of two condensers in parallel as a function of the water-to-air ow-rate ratio and the steam temperature. Figure 4 Variation in the ef ciency of the single condenser as a function of the water-to-air ow-rate ratio and the steam temperature.

the cooling water results in reduction of the amount of water evaporated per unit mass ow rate of cooling water. Therefore, at higher L/G ratios an increase occurs in the cooling-water temperature and consequently the condensate temperature increases and the system ef ciency decreases. Effects of the steam temperature are not discernable; however, at higher steam temperatures, a higher ef ciency is expected because of the increase in the heat transfer driving force. Comparison of the condensate temperature for the evaporative condenser (wet ) and the air condenser (wet) is shown in Figure 7 for the single condenser, two condensers in parallel, and two condensers in series. As is shown, the averages for the condensate temperature for the air system are 76.9, 86.5, and 97.2 C for the two condensers in series, two condensers in parallel, andheat transfer engineering

the single condenser, respectively. Lower condensate temperatures are obtained for the evaporative system, with values of 30.3, 35.6, and 37.8 C for the two condensers in series, two condensers in parallel, and the single condenser, respectively. Comparison of these results shows that the evaporative system is capable of removing larger amounts of heat than the air system, which results in a higher degree of subcooling. The above results show that the degree of condensate subcooling is large, with values between 73.3 and 90 C. As is shown, the largest subcooling is obtained for the two condensers in series. Comparison of the energy release accompanied with the subcooling process and the latent heat for the same amount of condensate show that the subcooling energy is less than 15% of the condensation energy. However, the subcooling heat transfer area is comparable to the heat transfer area required for condensation. This is because the low thermal energy of subcooling is also associated with a low overall heat transfervol. 22 no. 4 2001 47

Figure 7 Variation in condensate temperature as a function condenser con guration and measuring time.

The steam stream entering the condenser unit is saturated. Condensate subcooling follows steam condensation. The thermophysical properties of air and water in the heat transfer coef cient, which include the speci c heat at constant pressure, the density, the viscosity, and the thermal conductivity, are obtained at the mean temperature of the stream. Operation of the coil heat exchangers in series allows for simple calculations of the heat transfer coef cient for the two cases of condensation with two-phase ow and subcooling with a single phase. In this case the rst heat exchanger performs the condensation step, and it includes steam and its condensate; the second heat exchanger includes only the condensate. The following two sections give the analysis for each heat exchanger. Figure 8 shows a schematic for the temperature pro les in the two heat exchangers and in the air/water system outside the heat exchanger tubes. Heat Transfer Coef cient with Two Phases As is shown in Figure 8, the steam condenses inside the heat exchanger tubes at the saturation temperature, Tc , and then is subcooled to a lower temperature, Tu . On the outside of the heat exchanger tubes, the water temperature increases from T1 to T2 during steam condensation and then from T2 to T3 during subcooling. The thermal load for condensation is then de ned by q D qc C qu (2 )

Figure 6 Variation in the ef ciency of two condensers in series as a function of the water-to-air ow-rate ratio and the steam temperature.

coef cient. The opposite is true for the condensation process, where the overall heat transfer coef cient is high, as well as the thermal energy for condensation. CALCULATIONS OF THE HEAT TRANSFER COEFFICIENTS The following assumptions are made to calculate the heat transfer coef cients: Steady-state operation. The surfaces are clean or fouling resistant is zero. The condenser surface is clean or the fouling resistance is zero. Uniform distribution of the air and water stream in the column and on the outside surface of the condenser. Water losses in the column are negligible.48 heat transfer engineering

vol. 22 no. 4 2001

Figure 8

Schematic of the temperature pro les inside the heat exchangers in the air/water stream on the outside.

where qc D Ms k and qu D Ms C p (Tc Tu ) (4 ) (3 )

LMTDu D

(T3 T2 ) lnfR=[R C ln(1 RP )]g

(9 )

where ( T2 T1 ) is the difference of the water lm temperature due to steam condensation and ( T3 T2 ) is difference of the water lm temperature during condensate steam. The two terms R and P in Eq. (9 ) are given by RD PD Tc Tu T3 T2 T3 T2 Tc T2

In the above equations, qc and qu are the thermal loads due to condensation and subcooling, respectively, M s is the steam ow rate, and Tc and Tu are the condensation and subcooling temperatures. The two thermal loads are then used to de ne the corresponding overall heat transfer coef cients: qc D Ms k D Uc A c LMTDc qu D Ms C p (Tc Tu ) D Uu A u LMTDu (5 ) (6 )

The expression for LMTDu given in Eq. (9 ) is obtained from the work by Threlkeld [24]. In Eqs. (5 ) and (6 ) the overall heat transfer coef cients, Uc and Uu , are de ned by Ao d p 1 1 Ao 1 D C C Uc h c A p;i A p;m k ho 1u 1C A p;o = A F C

where A c and Au are the heat transfer areas required for condensation and subcooling, respectively. The sum of the two areas is equal to the total heat transfer area, A t , or At D Ac C Au (7 )

(10 ) (11 ) where h o is the external heat transfer coef cient, u is the n ef ciency, and k is the thermal conductivity ofvol. 22 no. 4 2001 49

1 1 Ao Ao d p 1 D C C Uu h u A p;i A p;m k ho

1C

1u A p;o = A F C u

In Eqs. (5 ) and (6 ) the values of LMTD are de ned by LMTDc D (T2 T1 ) (Tc T1 )=(Tc T2 )] ln[ (8 )

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the tube wall. The surface areas in Eqs. (10 ) and (11 ) are given by The tube inner surface area, A p;i D np Di Z p The tube outer surface area, A p;o D n (p Do Z p mp Do d ) The n surface area, np Di2 AF D m BW 4

0:01 v 0:99 158 q 1:6 106 W=m2 11 G 4;000 kg=m2 s 7 P 18;000 kPa 0:0019 Pr 0:82 350 Re 100;000 The average heat transfer coef cient is obtained by considering an average value of 0.5 for complete condensation of steam. The correlation for heat transfer during subcooling, h u , is given by the Dittus and Bolter relation [Eq. (15 )]. The above system of equations (2 ) (15 ) is used to calculate qc ; qu ; h u ; h c ; Uc ; Uu ; T2 ; A c ; and A u . However, determination of these requires calculations of the outside heat transfer coef cient, h o . This coef cient is obtained from the analysis of heat transfer in the second heat exchanger, which is described in the next section. Heat Transfer Coef cient with Single Phase As is shown in Figure 8, the subccoled condensate leaves the rst heat exchanger at temperature Tu and is cooled further in the second heat exchanger to a lower temperature, Tv . On the outside of the heat exchanger tubes, the water temperature increases from T3 to T4 . The thermal load for the second heat exchanger is given by q D M C p (Tu Tv ) D Uu A LMTD (16 )

The n and tube outer surface area, A o D A F C A p;o In the above relations, n is the number of tubes, m is the number ns, Do and Di are the tube outer and inner diameters, Z p is the tube length, B is the n height, and W is the n width. In Eq. (10 ) the internal heat transfer coef cient for condensation, h c , is de ned by the correlation of Shah [25]. This relation is given by hc 3:8 (12 ) D1C h lo z 0:95 The parameter z is de ned by z D 0:8 1 1 P 0:4 v (13 )

where P is the reduced pressure, and v is the vapor mass fraction. The local super cial heat transfer coef cient h lo is calculated using the relation h lo D h u (1 v )0:8 (14 )

where h u is the heat transfer coef cient, assuming all owing mass as liquid, and is calculated by the wellknown Dittus-Bolter equation: 0:8 ( )0:4 k ` (15 ) h u D 0:023 (Re ) Pr Di The ranges of data over which the equation by Shah can be used are 2:8 Di 40 mm50

In Eq. (16 ), q; M , and C p de ne the thermal load, the ow rate, and the speci c heat at constant pressure of the uid owing inside the heat exchanger tubes. Also, Tu and Tv de ne the inlet and outlet temperatures of the uid inside the heat exchanger tubes. The LMTD value in Eq. (16 ) is given by LMTD D where RD PD Tu Tv T4 T3 T4 T3 Tu T3 (T4 T3 ) lnfR=[R C ln(1 RP )]g (17 )

21 Ts 355 C

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column and in the void space of the heat exchanger. The measured averages are 5.39 and 7.85 m/s for the air velocity in the column and the heat exchanger void space, respectively. The former value gives a free ow area of 68.6% of the face area of the heat exchanger. The correlation by Myers [26] is used to calculate the wet heat transfer coef cient. This correlation relates the wet and dry heat transfer coef cients, or h w D h d (1:07 )Va0:101 (18 )

where Va is the air velocity in m/s. Substituting the values for the dry heat transfer coef cient, with an average of 157.5 W/m2 C, and the void space air velocity gives a wet heat transfer coef cient of 206.9 W/m2 C, which is consistent with the data shown in Figure 9.Figure 9 Variation in outside heat transfer coef cient as a function of water-to-air ow-rate ratio and steam temperature.

HEAT TRANSFER AREA FOR CONDENSATION AND SUBCOOLING Variations in the heat transfer area for condensation and subcooling are shown in Figure 10 as a function of the water-to-air ow ratio. The data are shown for inlet steam temperature of 120.8 C. The higher condensation area is a result of higher thermal load for condensation than subcooling. Also, the decrease in the condensation area at higher values for L/G is caused by the increase in the heat transfer coef cient as shown in Figure 9. On the other hand, the increase in the subcooling area upon the increase in the L/G ratio is caused by the constraint imposed on the total heat transfer area. Since the total area of the condenser is constant, it is equal to the summation of the condensation and subcooling heat transfer areas.

where (T4 T3 ) is the difference in the water lm temperature. The overall heat transfer coef cient in Eq. (16 ) is given by Eq. (11 ). As discussed before, the Dittus and Bolter relation given by Eq. (15 ) is used to calculate the internal heat transfer coef cient, h u . Therefore, Eqs. (11 ), (16 ), and (17 ) are used to determine the external heat transfer coef cient, h o . The outside heat transfer coef cient is determined as a function of the air-to-water ow rate ratio and the temperature of the inlet steam. As is shown in Figure 9, the heat transfer coef cient varies over a range of 150 to 230 W/m2 C. The two sets of data given in Figure 9 show that the outside heat transfer coef cient increases at higher inlet steam temperatures. This is caused by the increase in the driving force for heat transfer rate across the surface area of the heat exchanger at higher temperatures. This enhancement is caused by reduction in the water viscosity and increase in the thermal conductivity of the air and water at higher temperatures. Regardless of this, the thermal resistance on the water/air side increases at higher L/G values. This is because of the increase in the water lm thickness. Evidently, this effect is masked by the enhancement caused by the high steam temperature and the increase in the water temperature at higher L/G values. For a zero ow rate of the water stream, the system is reduced to an air condenser. At this condition the heat transfer coef cient is calculated using the same procedure as for the evaporative condenser. The results give a dry heat transfer coef cient that varies over a range of 150 165 W/m2 C. Comparison of the measured values of the wet heat transfer coef cient is made against literature data. This required measurements of the air velocity inside theheat transfer engineering

Figure 10 Variation in the condensation and subcooling heat transfer area as a function of water-to-air ow-rate ratio.

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CORRELATIONS OF EXPERIMENTAL RESULTS The ef ciency data for the evaporative condenser and air condenser are correlated as a function of the steam temperature (Ts ), the wet-bulb temperature ( Tw ), the heat transfer area ( A ), and the water-to-air ow rate ratio ( L/G ). The heat transfer area for the two condensers in parallel is set equal to the area of the single condenser. The resulting ef ciency correlation for the evaporative condenser is given by e ee

correlations are limited to the ranges 0:164 L/G 0:352; 23:1 Tw 26; 111:9 Ts 120:8, and 3:68 A 7:36, where the temperatures are in C and the area is in m2 . Similarly, the ef ciency correlation for the air condenser is given bya

D 223:03 C 1:81 102 ( Ts ) 0:31 A 5:29(Tw ) (20 )

D 98:57 1:76( L/G ) 2:09 102 ( Ts ) C 0:27 A C 4:83 102 (Tw ) (19 )

with an R 2 value of 0.89, average deviation of 0.15%, and maximum deviation of 0.39%. The above

with an R 2 value of 0.97, average deviation of 0.28%, and maximum deviation of 1.18%. The results for the two correlations are shown in Figure 11. The above correlations are limited to the ranges 24:52 Tw 26; 111:9 Ts 120:7, and 3:68 A 7:36, where the temperatures are in C and the area is in m2 . The wet heat transfer coef cient data are correlated as a function of the water-to-air ow rate ratio and the steam temperature. The resulting correlation is given by h o D 0:16( L/G )0:23 (Ts )2:13 (21 )

The above correlations are limited to the ranges 0:164 L/G 0:352 and 111:9 Ts 120:8, where the temperature is in C. The R 2 value for the above correlation is 0.94, with an average deviation of 1.7%, and maximum deviation of 5.8%. The correlation results are shown in Figure 12. ERROR ANALYSIS Error analysis in calculating the dimensionless groups presented in this article is performed by the KlineMcClintock procedure [27]. The uncertainty in measurements is de ned as the root sum square of the

Figure 11 ef ciency.

Variation in measured and calculated system

Figure 12 Variation in measured and calculated heat transfer coef cient.

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xed error by the instrumentation and the random error observed during different measurements. The error analysis includes measured temperature and ow rate. The calculated errors are 3.1% of the full scale for the temperature measurement and 2.45% of the full scale for the ow-rate measurements. Accordingly, deviations in the calculated heat transfer coef cient and system ef ciency are 5.3% and 6.59%, respectively, from the true value. CONCLUSIONS An experimental investigation is conducted to study the performance of evaporative condensers. In the light of results and analysis, the following conclusions are made. The evaporative condenser ef ciency increases at lower L/G ratios and higher inlet steam temperatures. The system performance shows that the parallel condenser arrangement allows for processing the maximum amount of inlet steam. On the other hand, the series con guration provides the maximum degree of subcooling. Performance of the single condenser unit is similar to that of the two condensers in parallel. However, for the same amount of steam load, the single condenser results in a higher water temperature inside the column and a lower degree of subcooling. Proper design of the evaporative condenser and ef cient use of the heat transfer area for condensation rather than subcooling, would allow the evaporative condenser to handle a thermal load 60% higher than that of the air condenser. In other words, for the same amount of inlet steam, the higher thermal capacity of the evaporative condenser allows for use of a smaller heat transfer surface area and fan power than the air condenser. The ef ciency correlation is expressed in terms of the steam temperature, the heat transfer area, L/G, and the ambient air wet-bulb temperature. The correlation is simple and can provide preliminary design data. The correlation for the water/air heat transfer coef cient is expressed as a function of the steam temperature and L/G. The correlation predictions are consistent with literature studies. d e k u q NOMENCLATURE A B heat transfer area, m2 n height, mheat transfer engineering

Cp d D G G h H H 00 k L m M n P P Pr q q Re T U V W Z

l

v

speci c heat at constant pressure, J/kg C n thickness, m tube diameter, m air ow rate, kg/s steam mass ux, kg/m 2 s heat transfer coef cient, W/m2 C liquid enthalpy, J/kg vapor enthalpy, J/kg thermal conductivity, W/m C liquid ow rate, kg/s number of ns mass ow rate of condensate vapor, kg/s number of tubes pressure, kPa reduced pressure, uid pressure/critical pressure, dimensionless Prandtl number (D C p l = k ) thermal load, W heat ux, W/m2 Reynolds number (D q V D =l ) temperature, C overall heat transfer coef cient, W/m2 C velocity, m/s n width, m length, m thickness of tube wall, m system ef ciency [D (Ts Te )=( Ts Tw )] latent heat, J/kg dynamic viscosity, kg/m s n ef ciency density, kg/m 3 vapor mass fraction

Subscripts a c d e F i ` lo m o p s t u v w air stream or air condenser condensate or condensation area dry-bulb or dry heat transfer coef cient evaporative condenser n inner tube liquid water local heat transfer coef cient of liquid water mean outer tube tube heating steam total heat transfer area subcooled condensate leaving rst heat exchanger subcooled condensate leaving second heat exchanger wet-bulb or wet heat transfer coef cientvol. 22 no. 4 2001 53

REFERENCES[1] Al-Juwayhel, F. I., Al-Haddad, A. A., Shaban, H. I., and El-Dessouky, H. T. A., Experimental Investigation of the Performance of Two-Stage Evaporative Cooler, Heat Transfer Eng., vol. 18, no. 2, pp. 21 33, 1997. [2] Webb, R. L., A Uni ed Theoretical Treatment of Thermal Analysis of Cooling Towers, Evaporative Condensers, and Fluid Coolers, ASHRAE Trans., vol. 90, pp. 398 415, 1984. [3] Webb, R. L., and Villacres, A., Algorithms for Performance Simulation of Cooling Towers, Evaporative Condensers, and Fluid Coolers, ASHRAE Trans., vol. 90, pp. 416 458, 1984. [4] Maclain-Cross,I. L., and Banks, P. J., A General Theory of Wet Surface Heat Exchangers and Its Application to Regenerative Evaporative Cooling, J. Heat Transfer, vol. 103, pp. 579 584, 1981. [5] Kettleborough, C. F., and Hsieh, C. S., The Thermal Performance of the Wet Surface Plastic Plate Heat Exchanger Used as an Indirect Evaporative Cooler, ASME J. Heat Transfer, vol. 105, pp. 366 373, 1983. [6] Chen, P., Qin, H., Huang, Y. J., and Wu, H., A Heat and Mass Transfer Model for Thermal and Hydraulic Calculations of Indirect Evaporative Cooler Performance, ASHRAE Trans., vol. 97, Part 2, pp. 852 865, 1991. [7] Peterson, J. L., An Effectiveness Model for Indirect Evaporative Coolers, ASHRAE Trans., vol. 99, pp. 392 399, 1993. [8] Kettleborough, C. F., The Thermal Performance of Cross-Flow Indirect Evaporative Cooler, Proc. ASME-JSME Thermal Engineering Joint Conf., vol. 3, pp. 195 201, 1987. [9] Peterson, J. L., and Hunn, B. D., Experimental Performance of an Indirect Evaporative Cooler, ASHRAE Trans., vol. 98, pp. 15 23, 1992. [10] Erens, P. J., and Dreyer, A. A., Modelling of Indirect Evaporative Air Coolers, Int. J. Heat Mass Transfer, vol. 36, pp. 17 26, 1993. [11] Erens, P. J., Comparison of Some Design Choices for Evaporative Cooler Cores, Heat Transfer Eng., vol. 9, no. 2, pp. 29 35, 1988. [12] El-Dessouky, H., Enhancement of the Thermal Performance of a Wet Cooling Tower, Can. J. Chem. Eng., vol. 71, no. 3, pp. 1 8, 1996. [13] Goswami, D. Y., Mathur, G. D., and Kulkarni, S. M., Experimental Investigation of Performance of a Residential Air Conditioning System with an Evaporatively Cooled Condenser, J. Solar Energy Eng., vol. 115, no. 4, pp. 206 211, 1993. [14] Merkel, F., Verdunstungshuhlung, Z. Ver. Deutsch. Ing. (V.D.I.), vol. 70, pp. 123 128, 1925. [15] Nahavandi, A. N., Kershah, R. M., and Serico, B. J., The Effect of Evaporation Losses in the Analysis of Counter Flow Cooling Towers, J. Nuclear Eng. Design, vol. 32, pp. 29 36, 1975. [16] Sutherland, J. W., Analysis of Mechanical-Draught Counter Flow Air/Water Cooling Towers, J. Heat Transfer, vol. 105, pp. 576 583, 1983. [17] El-Dessouky, H. T. A., Al-Haddad, A., and Al-Juwayhel, F., A Modi ed Analysis of Counter Flow Wet Cooling Towers, ASME J. Heat Transfer, vol. 119, no. 3, pp. 617 626, 1997. [18] Goodman, W., The Evaporative Condenser, Heating, Piping, and Air Conditioning, vol. 10, pp. 165 328, 1938. [19] Thomsen, E. G., Heat Transfer in an Evaporative Condenser, Refrig. Eng., vol. 51, pp. 425 431, 1946. [20] Parker, R. O., and Treybal, R. E., The Heat, Mass Transfer Characteristics of Evaporative Coolers, Chem. Eng. Prog. Symp. Ser., vol. 57, pp. 138 149, 1961.

[21] Leidenfrost, W., and Korenic, B., Evaporative Cooling and Heat Transfer Augmentation Related to Reduced Condenser Temperature, Heat Transfer Eng., vol. 3, no. 3 4, pp. 38 59, 1982. [22] Peterson, D., Glasser, D., and Williams, D., Predicting the Performance of an Evaporative Condenser, ASME Trans., J. Heat Transfer, vol. 110, no. 3, pp. 748 753, 1988. [23] El-Dessouky, H. T., Al-Haddad, A. A., and Al-Juwayhel, F. I., Thermal and Hydraulic Performance of a Modi ed TwoStage Evaporative Cooler, J. Renewable Energy, vol. 7, no. 2, pp. 165 176, 1996. [24] Threlkeld, J., Thermal Environmental Engineering, 2d ed., pp. 235 275, Prentice-Hall, Englewood Cliff, NJ, 1970. [25] Shah, M. M., General Correlation for Heat Transfer during Film Condensation inside Pipes, Int. J. Heat Mass Transfer, vol. 22, no. 4, pp. 547 556, 1979. [26] Myers, R. J., The Effect of Dehumidi cation on the Air Side Heat Transfer Coef cient for a Finned-Tube Coil, M.Sc. thesis, University of Minnesota, 1967. [27] Kline, S. J., and McClintock, F. A., Describing Uncertainities in Single Sample Experiments, in Mech. Eng. ASME, New York, 1953.

Hisham Ettouney has been Professor of Chemical Engineering at Kuwait University since 1988. Previously, he was a faculty member at the King Saud University, Saudi Arabi, and University of New Hampshire, USA. He received his Ph.D. in Chemical Engineering from MIT, USA, in 1983. Also, he received his B.Sc. in Chemical Engineering from Cairo University, Egypt, in 1975. He has more than 100 research publications and conference presentations in desalination, evaporative cooling, energy storage, and membrane separation.

Hisham El-Dessouky has been Professor of Chemical Engineering at Kuwait University since 1991. Previously, he was a faculty member at Qatar University, Qatar, and Zagazzig University, Egypt. He received his Ph.D. in Chemical Engineering from the University of Hannover, West Germany, in 1981. Also, he received his M.Sc. and B.Sc. in Chemical Engineering from Cairo University, Egypt, in 1976 and 1971, respectively. He is an Associate Editor of Heat Transfer Engineering and Desalination. He has more than 100 research publications and conference presentations in desalination, evaporative cooling, energy storage, and membrane separation.

Waleed S. Bouhamra is Professor of Chemical Engineering at Kuwait University since 1999. He received his Ph.D. and M.Sc. in Chemical Engineering from Oklahoma State University in 1988 and 1985. His B.Sc. in Chemical Engineering was received from Kuwait University in 1981. He has held a number of academic positions at Kuwait University, which includes Assistant Vice Rector for Scienti c Affairs, Director for the Center of Evaluation and Measurement, Vice Dean for Research and Academic Affairs at the College of Engineering and Petroleum, and currently he is the Vice Rector for Academic Support and Services. His research interests include environmental and indoor air pollution, reactor design, and energy. He has published and presented more than 50 research articles in refereed journals and international conferences.

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Bader Al-Azmi has been an Instructor of Chemical Engineering at Kuwait University since 1994. He received his M.Sc. and B.Sc. in Chemical Engineering from Kuwait University in 1998 and 1994, respectively. Currently, he is pursuing his Ph.D. studies in heat transfer.

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