Thermal performance analysis of a closed wet cooling tower

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Thermal performance analysis of a closed wet cooling tower V D Papaefthimiou∗ , T C Zannis, and E D Rogdakis Laboratory of Applied Thermodynamics, National Technical University of Athens (NTUA), Athens, Greece The manuscript was received on 27 December 2006 and was accepted after revision for publication on 23 May 2007. DOI: 10.1243/09544089JPME119

Abstract: A detailed model was developed and employed to examine the thermal performance of a closed wet cooling tower. The model is capable of predicting the variation of air thermodynamic properties, sprayed and serpentine water temperature as well as heat transfer rates exchanged between air and falling water stream inside the indirect wet cooling tower. The reliability of simulations was tested against experimental data obtained from the literature. A parametric study was conducted to evaluate the thermal behaviour of the indirect cooling tower under various air mass flowrates, serpentine water mass flowrates and inlet temperatures. The results of the theoretical investigation revealed an increase in cooling capacity and percentage loss of sprayed water due to evaporation, with increasing air mass flowrate. On the other hand, the increase of serpentine water mass flowrate resulted in slight increase in the overall temperature reduction of serpentine water. The effect of variable serpentine water inlet temperature on thermal performance of the indirect wet cooling tower was insignificant compared to other cases. Keywords: closed wet cooling tower, serpentine water, sprayed water, thermal performance

1

INTRODUCTION

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same heat transfer increasing thus, the cost of the installation. Theoretical modelling of closed wet cooling tower is complicated because cooling water, process fluid, and air stream, which are flowing in different directions, interact with each other through heat and mass transfer processes.Various attempts with different degree of accuracy have been made since the late 1930s for modelling the combined heat and mass transfer phenomena taking place inside an evaporative cooler [1–3]. A constant temperature approximation for injected cooling water was often assumed. However, Parker and Treybal [4] discovered that this approximation lead to mathematical inconsistencies, which gave erroneous results. In fact, Finlay and Grant [5] showed that constant temperature assumption may lead to 30 per cent error in large tube banks. Leidenfrost and Korenic [6] developed a methodology similar to the one of Parker and Treybal [4] with which they found that accurate prediction of performance characteristics of an evaporative cooler can be attained through iterative procedures. In addition, various researchers suggested different methods for dimensioning evaporative coolers [7, 8]. Finlay and Grant [9] suggested

JPME119 © IMechE 2007

Proc. IMechE Vol. 221 Part E: J. Process Mechanical Engineering

In a closed wet cooling tower, heat is transferred from hot water or other fluid, circulating inside a serpentine to a water film, which is formed on the tube surface and then, to a rising air stream. Indirect cooling towers can substitute cooling systems comprised of tube heat exchanger and cooling tower. This is one of the reasons why evaporative coolers are used in industrial processes and in air-conditioning systems to reject heat to the surrounding environment. Furthermore, in closed cooling towers the water flowing into the tube is protected from various contaminations limiting thus, the vulnerability of inner tube surface to corrosion. However, a higher exchange area is needed compared to direct-contact wet cooling towers for the

∗ Corresponding

author: Laboratory of Applied Thermodynamics,

Thermal Engineering Section, School of Mechanical Engineering, National Technical University of Athens, Heroon Polytechniou Street 9, Zografou Campus, Athens 15780, Greece. email:

140

V D Papaefthimiou, T C Zannis, and E D Rogdakis

a simplified model for describing the mass transfer process inside an evaporative cooler, which was based on the expression of vapour pressure of saturated moist air as linear function of temperature. Dreyer [10] presented different mathematical models for the thermal evaluation of evaporative coolers and condensers [4, 7, 11–14]. Analytical models [10–13, 15, 16] are based on the implementation of energy and mass conservation laws making various assumptions concerning the spayed water temperature distribution and the sprayed water loss due to evaporation. Aiming to a more realistic description of the transport phenomena taking place inside an evaporative cooler, sophisticated mathematical models [17, 18] have been developed and CFD packages have been used [19–21], which provide predictions of the temperature and flow field inside the cooling tower. Though that these models are more detailed and informative compared with analytical models, they are time-consuming and thus, cannot provide performance predictions for large periods of time. However, such simulations are necessary when designing large power installations or cogeneration systems, since it is of utmost importance to have a quick and reliable estimation of the annual amount of water lost due to evaporation in order to calculate the annual operational cost of the installation. Recently, the present research group has developed a detailed thermodynamic model and used it to assess the thermal performance of a wet cooling tower [22]. The success of this application has resulted in the utilization of the principles of thermodynamics for developing a computational model. The newly-developed model is used to evaluate the thermal behaviour of an indirect wet cooling tower. Energy and mass conservation laws are employed in conjunction with semiempirical correlations to describe the combined heat and mass transfer phenomena taking place inside the closed wet cooling tower. Specifically, the model is used to examine the effect of air mass flowrate, serpentine water mass flowrate, and inlet temperature on the variation of the thermodynamic state of moist air inside the cooler and on its cooling capacity and thermal efficiency. Comparison of the simulations with experimental results obtained from the literature was made to secure the predictive ability of the model. The analysis of the theoretical results revealed that the increase of the air mass flowrate results in increase of the cooling capacity and thermal efficiency of the indirect wet cooling tower. However, in this case the penalty in sprayed water loss due to evaporation is increased. On the other hand, the increase of serpentine water mass flowrate results in decrease of its overall temperature reduction and decrease of the thermal efficiency of the process. The thermal performance of the closed wet cooling tower is not


seriously affected by the change of serpentine water inlet temperature. 2 2.1

MODEL DESCRIPTION General outline

A comprehensive mathematical model based on the conservation laws for energy and mass is used to describe the coupled heat and mass transfer processes taking place inside an indirect wet cooling tower. A representative description of the closed wet cooling tower considered in the present analysis is illustrated in Fig. 1. The model was implemented for an indirect wet cooling tower having a bank of 16 × 31 plain tubes. The length of tube bundle is 0.888 m. The tube length is 0.913 m and the outer and the inner tube diameter are 0.0191 and 0.0150 m, respectively. The ratio of pitch to outside tube diameter is 1.5. The aforementioned geometrical specifications of the closed wet cooling tower used herein were taken from reference [23]. Model development was based on the following assumptions. 1. The heat and mass transfer processes occur under steady-state conditions, in a direction perpendicular to the tower walls. 2. The specific heat capacity of sprayed water, serpentine water, and dry air are constant in the temperature range considered. 3. The specific enthalpy of dry air, water, and serpentine water is equal to zero at 0 ◦ C. 4. Owing to the small temperature differences at which the process occurs heat transferred by radiation is not taken into account.

Fig. 1

Schematic view of the closed wet cooling tower


Thermal performance analysis of a closed wet cooling tower

5. At the interfacial surface air reaches the temperature of water and its humidity corresponds to the state of equilibrium. 6. The thermal resistance between the bulk and the interface of falling water film is negligible. 7. Water and air are in counter-flow. 2.2

The development of the analytical model is based on the implementation of energy balance for each one of the working fluids taking part in the process. The implementation of the energy balance for the gaseous phase (refer to Fig. 2) implies that sensible and latent heat is exchanged between the falling water film and the air stream resulting in the change of moist air enthalpy as follows ˙ S + dQ ˙L ˙ a dha = dQ m

(1)

Above relation can be rewritten in the following form ˙ S + dQ ˙ L = (ha + dha )m ˙ a ha + d Q ˙a m

(2)

The sensible load exchanged between moist air and sprayed water film is ˙ S = aLA (Tw − Ta )dA dQ

(3)

The latent load carried to the air stream due to water evaporation is ˙ L = dm ˙ w his dQ

sat ha = cpa Ta + W (cps Ta + hw )

(5)

(6)

Differentiation of above relationship with respect to air temperature Ta provides (7)

Hence, the rate of change of dry bulb air temperature along wetted tube surface is sat dW (Tw − Ta ) cps aLA dTa = + (8) ˙a dA dA cpm m where cpm is the specific heat capacity of moist air, which is defined as cpm = cpa + Wcsat ps

(9)

The term (dW /dA) in equation (8) corresponds to the evaporated water mass per unit heat exchange area at the water–vapour interface and it is given by the following expression dW β (W sat (Tw ) − Wa ) = ˙a dA m

(10)

The saturation humidity ratio of air W sat is calculated using the following mathematical formula W sat (Tw ) = 0.622

(4)

where his is the specific enthalpy of saturated moist air evaluated at air–water interface temperature defined as sat his = cps Tw + hw

The specific enthalpy of moist air is

sat sat Ta + hw ) + Wcps dTa dha = cpa dTa + dW (cps

Mathematical treatment

141

sat (Tw ) pws sat (T ) pa − pws w

(11)

The definition of air humidity ratio is employed to derive the rate of change of evaporated sprayed water mass per unit of heat exchange area as follows ˙w ˙ aW ) ˙w ˙w dm d(m dm m =⇒ = =⇒ ˙a dA dA dA m dW ˙a =m dA

W =

(12)

The temperature difference between the recirculating water and the sprayed water results in transfer of sensible heat load to the falling film. Furthermore, the sprayed water mass is progressively decreased because of the evaporation process and the vaporized mass fraction is transferred to the rising air stream. Hence, the application of the energy balance between serpentine water and falling water film provides ˙S ˙ w hw = (m ˙ w + dm ˙ w )(hw + dhw ) + dQ m ˙ L − dQ ˙f + dQ Fig. 2

Representative schematic description of the energy contribution of sprayed water and air stream in a counter-flow closed wet cooling tower


(13)

˙ w dhw is The second-order differential term dm significantly lower compared with the other terms Proc. IMechE Vol. 221 Part E: J. Process Mechanical Engineering

142


and thus, it can be neglected from the previous relationship. Hence, equation (13) can be written as follows ˙ S + dQ ˙ L − dQ ˙ f) ˙ w dhw = −(dm ˙ w hw + d Q m

(14)

Above relation can be rewritten by taking into account equation (12) dTw 1 dW ˙a aLA (Tw − Ta ) + m =− ˙ w c pw m dA dA sat Ta + cpw Tw + hw ) + U (Tw − Tf ) × (cps

2.3

Heat and mass transfer coefficients

The heat transfer coefficient between falling water film and air stream (Le = 1) is given by the following relation [7, 11, 25, 26] αLA = βcpm

(20)

where β is the mass transfer coefficient, which is calculated as follows β = 6.0 × 10−8 (Rea )0.9 (Rew )0.15 (Do )−1.6

(21)

(15) The rejection of sensible heat from the circulating water to the falling water film results in its temperature fall as shown in the following relations ˙f = m ˙ f cpf dTf dQ

and

˙ f = U dA(Tf − Tw ) dQ

(16)

Combining above relations the rate of change of cooled water temperature along wetted tube area is derived dTf U (Tw − Tf ) = ˙ f cpf dA m

(17)

Finally, a system of four ordinary differential equations is constituted sat dW (Tw − Ta ) cps dTa aLA = + ˙a dA m dA cpm dTw 1 dW ˙a aLA (Tw − Ta ) + m =− ˙ dA dA mw c pw sat × cps Ta + cpw Tw + hw + U (Tw − Tf ) U (Tw − Tf ) ˙ f cpf m

β sat dW = W (Tw ) − Wa ˙a dA m ˙w dm dW ˙a =m dA dA

dTf dA =

and Rea , Rew are the Reynolds numbers of the air and the sprayed water stream, respectively Ga D o Gw Do , Rew = , μa μw ˙w ˙a m m Gw = , and Ga = Ac Ac

Rea =

The minimum cross-sectional area for flow Ac in equation (22) is calculated as follows Ac =

L − Do Ml M

(23)

where L is the length of tube bundle, M is the number of row tubes, and l is the tube length. The overall heat transfer coefficient U between circulating water, tube wall, and water film is calculated by the following formula U=

Ro 1 Ro 1 Ro + + ln Ri h f k Ri αTL

−1 (24)

where the convection heat transfer coefficient of circulating water hf is given by the Dittus–Boelter relation (18)

hf =

with the following boundary conditions

0.3 0.023 Re0.8 f Prf λ Di

(25)

According to the literature [4, 11], the heat transfer coefficient between the tube and the water film aTL is calculated by the following expression

(Ta )Z =0 = Ta0 (Tw )Z =L = Tw0 (Tf )Z =L = Tf0

(W )Z =0 = W0 ˙ w )Z =L = m ˙ w0 (m

(22)

αTL (19)

A variable-step non-stiff method (Runge–Kutta 5(4)) was used to numerically solve the boundary-value problem [24]. Proc. IMechE Vol. 221 Part E: J. Process Mechanical Engineering

= 704(1.39 + 0.022Tw ) Do

1/3 (26)

where is a parameter defined as =

˙w m 4Ml

(27) JPME119 © IMechE 2007


3

OVERVIEW OF THE PARAMETRIC STUDY

the objective here is to investigate thoroughly this case by examining the changes in the thermal behaviour and process efficiency from the variation of chilled water inlet temperature and then, from the corresponding change of the circulating water mass flowrate. This will contribute on the better understanding regarding suitability of such cooling devices in space air-conditioning systems.

An extensive theoretical investigation was conducted to examine the effect of various operating parameters on the thermal performance of the evaporative cooling tower. Hence, the following cases were considered. ˙ a,i : The efficiency 1. Variable inlet air mass flowrate m of the evaporation process depends on the relative velocity of the water/air stream. Specifically, the residence time of the falling water film on the tubes is insufficient for high air velocities and as a result the evaporation process is uncompleted. Furthermore, it has been implied that for velocities higher than a critical value, the water droplets are entrained by the air stream with detrimental effects on the operation of the cooling device. Hence, two different air mass flowrates were considered namely 1.0 and 4.0 kg/s beyond the ‘reference case’ (2.0 kg/s). The following inlet conditions constitute the ‘reference case’ of the closed wet cooling tower operation: (a) sprayed water temperature: Tw,i = 20 ◦ C; ˙ w,i = 1.85 kg/s; (b) sprayed water mass flowrate: m ˙ a,i = 2.0 kg/s; (c) air massflow rate: m (d) serpentine water temperature: Tf ,i = 35 ◦ C; ˙ f ,i = 2.67 kg/s. (e) serpentine water mass flowrate: m The purpose is to scrutinize the effect on the variation of the thermodynamic parameters of the moist air inside the evaporative cooler, on the thermal performance and the effectiveness of the process. 2. Variable inlet temperature Tf ,i of circulating water ˙ f ,i : water evaporation and its water mass flowrate m may be an efficient way to cool warm water coming from the heat exchangers of an air-conditioning system after exchanging heat with hot air. Hence,

Fig. 3

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4 4.1

RESULTS AND DISCUSSION Experimental validation

Before proceeding to the examination of the effect of various operating parameters on the thermal performance of the closed wet cooling tower, it is of utmost importance to validate the predictive ability of the proposed model. For this reason, in Fig. 3 a comparison is made between predicted and experimental results obtained from reference [23] for dry bulb air temperature, falling water film temperature and cooled water temperature for two different ‘temperature approaches’. The ‘temperature approach’ is defined as the difference between the outlet wet bulb air temperature Twb,o and the inlet dry bulb temperature Ta,i and thus, simulations were conducted in order the ‘temperature approach’ to be constant at two different cases. The inlet conditions considered to make these simulations are given in Table 1. In the case of dry bulb temperature, measured data for the variation of this value inside the cooling tower were unavailable and for this reason, the comparison is limited to the inlet and outlet conditions. A very good coincidence between calculated and measured results at the entrance and the exit of the cooler is evidenced

Effect of ‘temperature approach’ (Twb,o − Tdb,i ) on the variation of dry bulb air temperature, sprayed water and cooled water inside the closed wet cooling tower. Theoretical results are given as function of the wetted tube surface and are contrasted with corresponding experimental data obtained from reference [23]



144


Table 1

Inlet conditions considered for conducting the experimental validation

The sensitivity of the variation of air temperature and humidity ratio to the change of air stream mass flowrate is displayed in Figs 4(a) and (b), respectively. An increase of dry bulb air temperature with increasing wetted tube surface is observed for low (1 kg/s) and moderate (2 kg/s) values of air mass flowrate. In the ˙ a,i = 4 kg/s, the dry bulb temperature is inicase of m tially curtailed for values of tube surface up to 7.5 m2 and then, increases progressively. The increase at all cases is curtailed near the air outlet from the cooling tower. The highest overall increase of dry bulb temperature is observed for the higher air mass flowrate

(4 kg/s). The air humidity ratio increases with increasing wetted tube surface at all cases of air mass flowrate. The increase of air mass flowrate results in decrease of the values of humidity ratio inside the cooling tower. Lower outlet values of dry bulb temperature and humidity ratio are observed with increasing air mass flowrate. Examination of the effect of air mass flowrate on the evolution of serpentine water temperature, sprayed water temperature and relative change of sprayed water mass is facilitated through Figs 4(c) to (e). The increase of the air inlet mass intensifies the reduction rate of serpentine water temperature. Hence, the lowest outlet serpentine water temperature is witnessed ˙ a,i = 4 kg/s). in the case of high air stream flowrate (m An abrupt increase of sprayed water temperature is observed for tube surface up to 7.5 m2 while for higher values of tube surface, the falling water temperature is curtailed. This limits the overall temperature increase of sprayed water. The highest overall increase of sprayed water temperature is observed in the case of low air inlet mass (1 kg/s). It must be noted that the difference of the sprayed water temperature between the entrance and the exit of the cooling tower depends on the amount of the sprayed water lost because of evaporation. The last depends strongly on the relative velocity of falling water film with respect to the air stream. Hence, there is an ‘optimum’ ratio of sprayed water to air mass flowrate, which provides a certain degree of falling water evaporation and compels water to enter and leave cooling tower with almost the same temperature. Deviations in air or water mass flowrate from the optimum values results in differences of water temperature between the entrance and the exit of the cooling tower. The variation of the percentage loss of sprayed water mass inside the closed wet cooling tower with air mass flowrate is shown in Fig. 4(e). As evidenced, the increase of air mass flowrate intensifies the reduction of sprayed water mass because of evaporation. Hence, the highest overall percentage loss of sprayed water is observed in the case of high air mass flowrate (4 kg/s). The curtailment of dry bulb temperature and humidity ratio, which is evidenced close to the exit of the tower, can be explained as follows: The air temperature becomes higher than the falling water film temperature and the air humidity ratio higher than the saturation humidity ratio at the sprayed water temperature. Hence, heat is rejected from the air to the falling water stream both as sensible and latent load. The high gradients of sprayed water temperature increase and serpentine water temperature reduction, which are observed up to 7.5 m2 of wetted tube surface, are attributed to the amplification of the evaporation process because of the high temperature difference between air and sprayed water



Parameter (◦ C)

Twb,o − Tdb,i = 5.1 ◦ C

Twb,o − Tdb,i = 8.3 ◦ C

Tdb,i Twb,i Tw,i Tf ,i

10 8.45 12.8 15.6

8.5 7.0 13.6 18

for all the parameters shown in Fig. 3 in both cases of ‘temperature approach’. Furthermore, a close examination of the corresponding curves for sprayed water and cooled water temperature reveals that the model predicts successfully not only the boundary values for these two parameters but also their variation during the process. The overall relative error between calculated and experimental results was less than 5 per cent for all cases considered. This enhances our confidence on the reliability of the simulations, which will be presented herein. As observed, the temperature of the serpentine water is decreased and the rate of decrease is more intense during the initial stages of the evaporation process (up to 7.5 m2 ) whereas, for higher values of wetted tube surface the slope of reduction is constant. In addition, a slight increase of sprayed water temperature is evidenced for values of heat exchange area up to 7.5 m2 being in accordance with the corresponding decrease of serpentine water temperature in the same surface range. For values of tube surface higher than 7.5 m2 the temperature of the sprayed water is decreased because of the evaporation of a fraction of the falling water film mass, which is transferred as latent load to the surrounding air. As a consequence the temperature of sprayed water at the tower exit is almost the same with the one at the entrance. Finally, an increase of dry bulb air temperature is observed because of the absorption of sensible and latent heat loads from the falling water film during the evaporation process.

4.2

Effect of air mass flowrate


Fig. 4

145

Effect of air mass flowrate on the variation of (a) dry bulb temperature, (b) humidity ratio, (c) sprayed water temperature, (d) serpentine water temperature, and (e) relative change of sprayed water mass inside the indirect wet cooling tower

stream and the high affinity of air for water vapour absorption. The increase of air mass results in the increase of the overall temperature reduction of serpentine

water and subsequently, to the cooling capacity of the closed wet cooling tower. Increase of the thermal efficiency is observed also with increasing air mass flowrate.



146


Fig. 5

4.3

Effect of serpentine water inlet temperature on the variation of (a) dry bulb temperature, (b) humidity ratio, (c) sprayed water temperature, (d) serpentine water temperature, and (e) relative change of sprayed water mass inside the closed wet cooling tower

Effect of inlet temperature of serpentine water

The influence of cooled water inlet temperature on the variation of dry bulb air temperature and humidity

ratio is shown in Figs 5(a) and (b). The increase of serpentine water inlet temperature results in increase of in-tower and outlet values dry bulb temperature and humidity ratio. For moderate values of chilled water




Fig. 6

147

Effect of serpentine water mass flowrate on the variation of (a) dry bulb temperature, (b) humidity ratio, (c) sprayed water temperature, (d) serpentine water temperature, and (e) relative change of sprayed water mass inside the closed wet cooling tower

inlet temperature (30 ◦ C), the overall change of dry bulb temperature is almost insignificant whereas for pertinent low values (25 ◦ C), the air stream is cooled up to almost 10 per cent. As observed in Fig. 5(c), the rate

of decrease of cooled water temperature is amplified with increasing inlet temperature. However, the higher outlet temperatures of chilled water are witnessed in the case of high inlet temperature (35 ◦ C).



148


According to Fig. 5(d), the rate of increase of sprayed water temperature is enhanced with increasing circulating water inlet temperature for values of wetted surface up to 7.5 m2 whereas for higher tube surfaces, the sprayed water temperature is curtailed at all cases of cooled water inlet temperature. Hence, the highest peak and outlet temperature of falling water stream is observed for highest inlet temperature of circulating water (35 ◦ C). In the latter case, the highest overall increase of falling water film is evidenced. As observed from Fig. 5(e), the rate of change of sprayed water mass flowrate is similar for the three cooled water inlet temperatures for values of wetted tube surface up to 12.5 m2 . However, for higher values of tube surface the reduction rate of sprayed water mass is amplified with increasing cooled water temperature. Thus, the highest overall percentage loss of sprayed water mass is observed for the highest inlet temperature of circulating water. The variations of sprayed water temperature, circulating water temperature and percentage reduction of falling water mass, which were observed in the case of Tf ,i = 25 ◦ C, may provide an explanation to the aforementioned cooling of the air stream. Specifically, the phenomenon of ‘evaporative cooling’ can be attributed to the relatively low temperature difference between air stream and circulating water at the beginning of the process. In this case, a considerable limitation of the sensible heat load, which is partially transferred from the serpentine water to the sprayed water and then, to the air stream, is conducted. When the inlet temperature of circulating water is high (35 ◦ C), the sensible fraction of heat load carried to the air stream overwhelms its heat rejection, which is necessary for the evaporation of cooling water. However, in the specific case, the sensible portion is negligible and thus, the air stream is cooled and humidified because of the water–vapour absorption. Furthermore, the increase of cooled water inlet temperature results in the slight increase of cooled water temperature fall. Overall, the variation of thermal efficiency and cooling capacity with increasing circulating water inlet temperature is inconsiderable.

resulting thus, to an overall cooling of the air stream. According to Figs 6(c) and (d), the increase of circulating water mass results in higher sprayed water and cooled water temperatures either inside the tower or at its exit. As shown in Fig. 6(e), the highest overall percentage reduction of sprayed water mass is observed for the highest value of processed water mass flowrate. In addition, decrease of the total temperature reduction of cooled water temperature and the thermal efficiency of the evaporative cooling tower is observed with increasing chilled water mass flowrate.

5

CONCLUSIONS

A detailed model was developed and used to simulate the processes taking place inside a closed wet cooling tower and mainly, to investigate the effect of various operating parameters on its thermal behaviour. The reliability of model predictions was tested against experimental results obtained from the literature and the suggested model was found capable of predicting the thermal performance of a closed wet cooling tower with sufficient accuracy. This facilitated the examination of the effect of air mass flowrate, serpentine water temperature, and mass flowrate on the evolution of the thermodynamic characteristics of the air stream, sprayed water, and serpentine water as well as on the overall performance and efficiency characteristics of the closed wet cooling tower. The evaluation of the theoretical results resulted in the derivation of the following conclusions.

The influence of variable recirculating water mass on the variation of dry bulb air temperature and humidity ratio is presented in Figs 6(a) and (b). As observed, the increase of chilled water mass results in the increase of dry bulb temperatures and humidity ratio inside the closed wet cooling tower and at the tower outlet. The dry bulb temperature and humidity ratio are curtailed close to exit of the cooler. For low values of chilled water mass (1.34 kg/s), the dry bulb temperature is initially curtailed and then, increases slightly

1. The increase of air mass flowrate results in: (a) reduction of dry bulb temperature and humidity ratio; (b) decrease of the overall temperature fall of sprayed water; (c) increase of percentage losses of sprayed water mass because of evaporation; (d) increase of the overall temperature reduction of serpentine water (cooling capacity). 2. The increase of inlet temperature of serpentine water results in: (a) increase of dry bulb temperature and humidity ratio; (b) increase of overall sprayed water temperature; (c) increase of the total amount of vaporized sprayed water mass; (d) small increase of the cooling capacity of indirect wet cooling tower. 3. The increase of serpentine water mass flowrate results in: (a) increase of dry bulb temperature and humidity ratio;



4.4

Effect of serpentine water mass flowrate


(b) increase of the overall sprayed water temperature and percentage losses because of evaporation; (c) decrease of the overall temperature reduction of serpentine water. In general, the highest temperature fall of serpentine water (i.e. increase of cooling capacity) can be attained with increasing air mass flowrate. In other words, less heat exchange area and thus, a lower constructional cost is required for achieving a certain temperature fall of serpentine water. However, this cannot be done without exacerbating the penalty in sprayed water losses. Promising results concerning simultaneous cooling of the air stream and the serpentine water can be obtained when the inlet temperature of the process fluid is close to the inlet temperature of air and falling water film. However, these effects would be preserved if the cooling water sink was supplied with additional water mass to ensure constant inlet temperature of sprayed water. REFERENCES 1 Goodman, W. The evaporative condenser. Heat Pip. Air Cond., 1938, 10, 165–328. 2 Thomsen, E. G. Heat transfer in an evaporative condenser. Refrig. Eng., 1946, 51(5), 425–431. 3 Wile, D. D. Evaporative condenser performance factors. Refrig. Eng., 1950, 58(1), 55–63. 4 Parker, R. O and Treybal, R. E. The heat mass transfer characteristics of evaporative coolers. Chem. Eng. Prog. Symp. Ser., 1961, 57(32), 138–149. 5 Finlay, C. I. and Grant, W. D. The accuracy of some simple methods of rating evaporative coolers. Report no. 584, National Engineering Laboratory, East Kilbride, Glasgow, 1974. 6 Leidenfrost, W. and Korenic, B. Evaporative cooling and heat transfer augmentation related to reduce condenser temperatures. Heat Transf. Eng., 1982, 3(3–4), 38–59. 7 Mizushina, T., Ito, R., and Miyashita, H. Characteristics and methods of thermal design of evaporative coolers. Int. Chem. Eng., 1968, 8(3), 532–538. 8 Tezuka, S., Takada, T., and Kasai, S. Performance of an evaporative cooler. Heat Transf. – Jpn. Res., 1976, 6(1), 1–18. 9 Finlay, C. I. and Grant, W. D. Air coolers, cooling towers and evaporative coolers. Report no. 534, National Engineering Laboratory, East Kilbride, Glasgow 1972, pp. 165–328. 10 Dreyer, A. A. Analysis of evaporative cooler and condenser. MSc Thesis, University of Stellenbosch, Republic of South Africa, 1988. 11 Webb, R. L. and Villacres, A. Algorithms for performance simulation of cooling towers, evaporative condensers and fluid coolers. ASHRAE Trans., 1984, 90(2B), 416–458. 12 Webb, R. L. A unified theoretical treatment for thermal analysis of cooling towers, evaporative condensers and fluid coolers. ASHRAE Trans., 1984, 90(2B), 398–415. JPME119 © IMechE 2007

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APPENDIX Notation aLA aTL A Ac

water to air heat transfer coefficient (W/m2 /◦ C) tube to water film heat transfer coefficient (W/m2 /◦ C) wetted tube surface (m2 ) minimum cross-sectional area for flow on the air side (m2 )


150

cpa cpm sat cps cpw cpf D G ha hf his

hw k l L Le ˙a m ˙f m ˙w m M n pa sat pws Pr ˙f Q ˙L Q ˙S Q R Re RH Ta Tf


specific heat at constant pressure of dry air (J/kg/K) specific heat of moist air (J/kg/K) specific heat of saturated steam (J/kg/K) specific heat of water (J/kg/K) specific heat of process fluid (J/kg/K) tube diameter (m) air mass velocity (m/s) specific enthalpy of moist air (J/kg) convection heat transfer coefficient of process fluid (W/m2 /◦ C) specific enthalpy of saturated moist air evaluated at air–water interface temperature (J/kg) specific enthalpy of water (J/kg) tube thermal conductivity (W/m/◦ C) tube length (m) length of tube bundle (m) Lewis number air mass flowrate (kg/s) process fluid mass flowrate (kg/s) sprayed water mass flowrate (kg/s) number of tubes in a row thermal efficiency moist air pressure (Pa) saturation pressure of moist air (Pa) Prandtl number process fluid heat flowrate (W) latent heat flowrate (W) sensible heat flowrate (W) tube radius (m) Reynolds number relative humidity air temperature (◦ C) process fluid temperature (◦ C)


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Tw U W W sat Z β hw λ μ

sprayed water temperature (◦ C) overall heat transfer coefficient of falling water film (W/m2 /◦ C) air humidity ratio (kg/kgda ) saturation humidity ratio of moist air (kgw /kg da ) tower height (m) mass transfer coefficient (kg/m2 /s) ˙ w /4Ml parameter defined as m (kg/m/s) latent heat of vaporization for water (J kg−1 ) thermal conductivity of water (W/m/◦ C) dynamic viscosity (kg/m/s)

Subscripts a c db f i is L LA m o s sat S TL w ws wb w, s

air coolant dry bulb process fluid inner steam at the interface latent liquid to air air–steam (mixture) outer steam saturated sensible tube to liquid water water–vapour wet bulb saturated steam


Thermal performance analysis of a closed wet cooling tower

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