Evaporative Condensers

Heat Transfer Engineering, 22:41–55, 2001 C 2001 Taylor & Francis Copyright ° 0145–7632/01 $12.00 + .00

Performance of Evaporative Condensers HISHAM M. ETTOUNEY, HISHAM T. EL-DESSOUKY, WALID BOUHAMRA, and BADER AL-AZMI Department 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 coefŽ cient and the system efŽ ciency. The evaporative condenser includes two Ž 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 efŽ ciency increases at lower L/G ratios and higher steam temperatures. The system efŽ ciency for various conŽ gurations for the evaporative condenser varies between 97% and 99%. Lower efŽ ciencies are obtained for the air-cooled condenser, with values between 88% and 92%. The highest efŽ ciency is found for the two condensers in series, followed by two condensers in parallel and then the single condenser. The parallel condenser conŽ guration can handle a larger amount of inlet steam and can provide the required system efŽ ciency and degree of subcooling. The correlation for the system efŽ ciency gives a simple tool for preliminary system design. The correlation developed for the external heat transfer coefŽ cient is found to be consistent with the available literature data.

Condensers are found in a wide range of applications, such as petroleum reŽ 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,

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 it

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]

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possible to use a lower air  ow rate and consequently the fan capacity and its power consumption are reduced. Further, the heat transfer coefŽ 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 coefŽ 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 energyefŽ 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 uniŽ ed theory for modeling of cooling towers, evaporative condensers, and evaporative coolers. Various correlations are adopted to deŽ ne the water Ž lm heat transfer coefŽ cient and the mass transfer coefŽ cient for water transport from the water Ž lm to the air stream. In modeling the condenser and cooler units, additional 42

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correlations are used to deŽ ne the heat transfer coefŽ cient for the  uid inside the tubes of the heat exchanger. The heat transfer coefŽ cient for the water Ž lm used by Webb [2] corresponds to a water Ž 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 manufacturer’s 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 deŽ ned as the ratio between the drop in the primary air temperature and the wet-bulb depression (deŽ 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 ofŽ ce building in Dallas, Texas. Analysis of the data shows a system efŽ 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 one vol. 22 no. 4 2001

element. The Ž rst and second models are differential, where the Ž 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 Ž lm. Results show that the simpliŽ ed 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 Ž 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 Ž 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 modiŽ ed model for analysis and rating of cooling towers. The model presents new deŽ 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 model heat 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 modiŽ 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 coefŽ 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 proŽ 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 efŽ ciency at different operating conditions. Development of correlations for the heat transfer coefŽ cient 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 efŽ ciency and the heat transfer coefŽ 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 efŽ 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 temperature vol. 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 Ž ne mist, with an average drop diameter of 5 £ 10¡4 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 power 44

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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 efŽ ciency than Sheathy leaf or natural Ž 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 efŽ ciency. Each layer has a thickness of 0.1 m, which gives sufŽ cient internal surface area for air and water contact. Use of the three packing layers maintains proper water distribution and sufŽ cient contact area between the air and water streams. The two condenser units have proper piping that allow operation of a single condenser or the vol. 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 Ž ns hold the tube bundle together, and each Ž n has dimensions of 0.02 £ 0.6 £ 0.0015 m in height, length, and thickness. The number of Ž 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 Ž 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 Ž 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 conŽ 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 proŽ 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  ow heat transfer engineering

rate, steam pressures, and condenser conŽ gurations, are identical to those of the evaporative conŽ 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 proŽ les for the water stream and calculations of the efŽ ciency, e , which is deŽ 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 00 ( ) M s Hs ¡Hw 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 speciŽ c heat at constant pressure, H is the condensate enthalpy, and the subscripts s; u, and w deŽ nes 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 proŽ 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 proŽ le of the water stream in the evaporative condenser tower are very important in modeling the system characteristics. This proŽ le can be used to deŽ ne the driving force for heat transfer, which is necessary for heat transfer calculations. In literature studies, it is common to vol. 22 no. 4 2001

45

Figure 2 in series.

Variation in the water axial temperature proŽ 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 efŽ 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 efŽ ciency from values of below 92% to values above 99%. Inspection of the efŽ ciency variations shows the decrease in the efŽ ciency of all systems during the daytime. The lowest efŽ ciency is found at noontime, and the highest efŽ 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 efŽ ciency of the evaporative condenser are shown in Figures 4 – 6. As is shown, the efŽ 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 efŽ ciency of the two condensers in series is caused by the larger heat transfer area, which allows 46

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for additional subcooling of the condensate. Increase in L/G results in decrease of the efŽ 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 efŽ ciency as a function condenser conŽ guration and measuring time.

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Figure 5 Variation in the efŽ 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 efŽ 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 efŽ ciency decreases. Effects of the steam temperature are not discernable; however, at higher steam temperatures, a higher efŽ 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, and heat 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 transfer vol. 22 no. 4 2001

47

Figure 7 Variation in condensate temperature as a function condenser conŽ 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 coefŽ cient, which include the speciŽ c heat at constant pressure, the density, the viscosity, and the thermal conductivity, are obtained at the mean temperature of the stream.

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

coefŽ cient. The opposite is true for the condensation process, where the overall heat transfer coefŽ 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 coefŽ 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

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Operation of the coil heat exchangers in series allows for simple calculations of the heat transfer coefŽ cient for the two cases of condensation with two-phase  ow and subcooling with a single phase. In this case the Ž 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 proŽ les in the two heat exchangers and in the air/water system outside the heat exchanger tubes. Heat Transfer CoefŽ 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 deŽ ned by q D qc C qu

vol. 22 no. 4 2001

(2 )

Figure 8

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

where

LMTDu D (3 )

qc D Ms k and qu D Ms C p (Tc ¡ Tu )

(4 )

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 deŽ ne the corresponding overall heat transfer coefŽ cients: qc D Ms k D Uc A c LMTDc

(5 )

qu D Ms C p (Tc ¡ Tu ) D Uu A u LMTDu

(6 )

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 (7 )

At D Ac C Au

(T3 ¡ T2 ) lnfR=[R C ln(1 ¡ RP )]g

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

Tc ¡ Tu T3 ¡ T2

PD

T3 ¡ T2 Tc ¡ T2

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 coefŽ cients, Uc and Uu , are deŽ ned by Ao d p 1 1 Ao 1 D C C Uc h c A p;i A p;m k ho

(T2 ¡ T1 ) ( ln[ Tc ¡ T1 )=(Tc ¡ T2 )]

(8 )

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³ 1C

1¡u A p;o = A F C Á

´

(10 )

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

In Eqs. (5 ) and (6 ) the values of LMTD are deŽ ned by LMTDc D

(9 )

³ 1C

1¡u A p;o = A F C u

´ (11 )

where h o is the external heat transfer coefŽ cient, u is the Ž n efŽ ciency, and k is the thermal conductivity of vol. 22 no. 4 2001

49

the tube wall. The surface areas in Eqs. (10 ) and (11 ) are given by The tube inner surface area,

0:01 · v · 0:99 158 · q¯ · 1:6 £ 106 W=m2 11 · G¯ · 4;000 kg=m2 s

A p;i D np Di Z p

7 · P · 18;000 kPa

The tube outer surface area,

0:0019 · Pr · 0:82

A p;o D n (p Do Z p ¡ mp Do d )

350 · Re · 100;000

The Ž n surface area, ³

np Di2 AF D m BW ¡ 4

´

The Ž 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 Ž ns, Do and Di are the tube outer and inner diameters, Z p is the tube length, B is the Ž n height, and W is the Ž n width. In Eq. (10 ) the internal heat transfer coefŽ cient for condensation, h c , is deŽ ned by the correlation of Shah [25]. This relation is given by ³ ´ hc 3:8 (12 ) D1C h lo z 0:95 The parameter z is deŽ ned by z D

³

´0:8 1 ¡1 P¯ 0:4 v

(13 )

where P¯ is the reduced pressure, and v is the vapor mass fraction. The local superŽ cial heat transfer coefŽ 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 coefŽ cient, assuming all  owing mass as liquid, and is calculated by the wellknown Dittus-Bolter equation: ³ ´ k` 0:8 0:4 (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 mm ±

50

21 · Ts · 355 C

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The average heat transfer coefŽ 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 coefŽ cient, h o . This coefŽ cient is obtained from the analysis of heat transfer in the second heat exchanger, which is described in the next section. Heat Transfer CoefŽ cient with Single Phase As is shown in Figure 8, the subccoled condensate leaves the Ž 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 )

In Eq. (16 ), q; M , and C p deŽ ne the thermal load, the  ow rate, and the speciŽ c heat at constant pressure of the  uid  owing inside the heat exchanger tubes. Also, Tu and Tv deŽ 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

(T4 ¡ T3 ) lnfR=[R C ln(1 ¡ RP )]g

where RD

Tu ¡ Tv T4 ¡ T3

PD

T4 ¡ T3 Tu ¡ T3

vol. 22 no. 4 2001

(17 )

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 coefŽ cient. This correlation relates the wet and dry heat transfer coefŽ 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 coefŽ cient, with an average of 157.5 W/m2 ± C, and the void space air velocity gives a wet heat transfer coefŽ cient of 206.9 W/m2 ± C, which is consistent with the data shown in Figure 9. Figure 9 Variation in outside heat transfer coefŽ cient as a function of water-to-air  ow-rate ratio and steam temperature.

where (T4 ¡ T3 ) is the difference in the water Ž lm temperature. The overall heat transfer coefŽ 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 coefŽ cient, h u . Therefore, Eqs. (11 ), (16 ), and (17 ) are used to determine the external heat transfer coefŽ cient, h o . The outside heat transfer coefŽ 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 coefŽ 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 coefŽ 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 Ž 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 coefŽ cient is calculated using the same procedure as for the evaporative condenser. The results give a dry heat transfer coefŽ cient that varies over a range of 150 – 165 W/m2 ± C. Comparison of the measured values of the wet heat transfer coefŽ cient is made against literature data. This required measurements of the air velocity inside the heat transfer engineering

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 coefŽ 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.

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

e

The efŽ 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 efŽ ciency correlation for the evaporative condenser is given by e

D 98:57 ¡ 1:76( L/G ) ¡ 2:09 £ 10¡2 ( Ts ) C 0:27 A C 4:83 £ 10¡2 (Tw )

(19 )

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

e

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 efŽ ciency correlation for the air condenser is given by a

D 223:03 C 1:81 £ 10¡2 ( Ts ) ¡ 0:31 A ¡ 5:29(Tw ) (20 )

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 coefŽ 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 deŽ ned as the root sum square of the

Figure 11 efŽ ciency.

52

Variation in measured and calculated system

heat transfer engineering

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

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Ž 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 coefŽ cient and system efŽ ciency are 5.3% and 6.59%, respectively, from the true value. CONCLUSIONS

Cp d D G G¯ h H H 00 k L m M n P P¯

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 efŽ 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 conŽ 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 efŽ 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 efŽ 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 coefŽ cient is expressed as a function of the steam temperature and L/G. The correlation predictions are consistent with literature studies. NOMENCLATURE A B

heat transfer area, m2 Ž n height, m

Pr q q¯ Re T U V W Z d e k l

u q v

Subscripts a c d e F i ` lo m o p s t u v w

heat transfer engineering

speciŽ c heat at constant pressure, J/kg ± C Ž n thickness, m tube diameter, m air  ow rate, kg/s steam mass  ux, kg/m 2 s heat transfer coefŽ cient, W/m2 ± C liquid enthalpy, J/kg vapor enthalpy, J/kg thermal conductivity, W/m ± C liquid  ow rate, kg/s number of Ž 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 coefŽ cient, W/m2 ± C velocity, m/s Ž n width, m length, m thickness of tube wall, m system efŽ ciency [D (Ts ¡ Te )=( Ts ¡ Tw )] latent heat, J/kg dynamic viscosity, kg/m s Ž n efŽ ciency density, kg/m 3 vapor mass fraction

air stream or air condenser condensate or condensation area dry-bulb or dry heat transfer coefŽ cient evaporative condenser Žn inner tube liquid water local heat transfer coefŽ cient of liquid water mean outer tube tube heating steam total heat transfer area subcooled condensate leaving Ž rst heat exchanger subcooled condensate leaving second heat exchanger wet-bulb or wet heat transfer coefŽ cient vol. 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 UniŽ 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 ModiŽ 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.

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[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 ModiŽ 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 DehumidiŽ cation on the Air Side Heat Transfer CoefŽ 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 ScientiŽ 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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