Energy Conversion and Management

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1 Energy Conversion and Management 51 (2010) Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: Thermal performance of cross flow cooling towers in variable wet bulb temperature Ebrahim Hajidavalloo a, *, Reza Shakeri b, Mozaffar A. Mehrabian b a Mechanical Engineering Department, Shahid Chamran University, Ahvaz, Iran b Mechanical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran article info abstract Article history: Received 3 October 2008 Received in revised form 11 June 2009 Accepted 9 January 2010 Available online 4 February 2010 Keywords: Variable wet bulb Cooling tower Mathematical model Thermal performance Impact separator Cooling towers are widely used in most industrial units to reject waste heat to the atmosphere. Wet towers are usually designed to operate in hot and dry weather conditions with narrow range of wet bulb temperature, but many cooling towers are required to operate in weather condition with large variation of wet bulb temperature which strongly affects the thermal performance of the towers. In this paper a conventional mathematical model is used to predict the thermal behavior of an existing cross flow tower under variable wet bulb temperature and the results are compared with experimental data in various operating conditions. Available fill characteristic curve of the tower is obtained to estimate its departure from the design conditions. It is found that when the wet bulb temperature increases, the approach, range and evaporation loss would increase considerably. Variation of evaporation loss versus wet bulb temperature was estimated. Finally the effect of placing an impact separator in front of air louvers on thermal performance of the tower is investigated. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Cooling towers are the heat and mass transfer devices being in widespread use. Due to their important role, different kinds of cooling towers have been introduced to address the various demands of industries. Different mathematical models have been developed to predict the thermal behavior of wet cooling towers. The first practical model to describe the heat and mass transfer mechanisms in wet cooling towers was proposed by Merkel [1]. Using Merkel s theory, most of the studies have paid more attention to analyze the counter flow towers compared to the cross flow towers. The reasons for the lack of studies on the cross flow towers are the widespread use of counter flow towers and also the difficulty in the analysis of cross flow towers as compared to the counter flow towers. Snyder [2] applied the theory of heat exchanger design to calculate the driving force of a cross flow tower in the same way as was used to calculate the mean temperature difference in a cross flow heat exchanger and obtained the overall enthalpy transfer coefficient. He assumed a linear relationship between the water temperature and enthalpy of saturated air. Zivi and Brand [3] solved the differential equations numerically using a non-linear relationship between the water temperature and enthalpy of saturated air. Schechter and Kang [4] applied the Zivi and Brand s method to more general operating conditions by representing an exponential function to express the equilibrium relation between the water temperature and enthalpy of saturated air * Corresponding author. Tel.: ; fax: address: hajidae_1999@yahoo.com (E. Hajidavalloo). at a limited range. Baker and Shryock [5] proposed an integral solution based on Merkel s theory. Poppe and Rogener [6] developed a new model for cooling towers which did not use the simplifying assumptions made by Merkel. The critical differences between Merkel, Poppe and e-ntu models were investigated by Kloppers and Kroger [7]. They concluded that when the water outlet temperature is the only important parameter to the tower designer, the less accurate Merkel and e-ntu approaches can be used but when the heat transfer rates are concerned; they give lower values than that predicted by Poppe approach. Hayashi and Hirai [8] approximated the enthalpy of saturated air by a first-order equation with respect to the water temperature, and applied the cross flow heat exchanger calculations to obtain the overall enthalpy transfer coefficient by using a chart. Inazumi and Kageyama [9] proposed a graphical method for calculation of the enthalpy driving force in a cross flow cooling tower. Khan and Zubair [10,11] considered the effect of Lewis number and heat transfer resistance in the air water interface and developed a detailed model for counter flow wet cooling towers. Halasz [12,13] developed a general mathematical model to describe the thermal characteristics of all types of evaporative cooling devices. The main feature of this model is its non-dimensionality which efficiently reduces the required parameters to analyze an evaporative device. He then applied his model to predict the thermal behavior of wet cooling towers and compared the model results with an accurate model. Kairouni et al. [14] applied the Halasz s model to predict the thermal performance of cooling towers in south Tunisia. Prasad [15] developed a numerical model for cross flow wet cooling towers and applied the model to estimate the /$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi: /j.enconman

2 E. Hajidavalloo et al. / Energy Conversion and Management 51 (2010) Nomenclature A v surface area of water droplets per unit volume of tower, m 2 m 3 c w specific heat of water at constant pressure, J kg 1 C 1 h m mass transfer coefficient, kg m 2 h 1 H enthalpy, J kg 1 L length of the tower, m _m mass flow rate per square meter of the tower, kg m 2 h 1 t temperature, C x,y coordinates shown in Fig. 1 V volume of the selected tower, m 3 FC fill characteristic = hmav V _mw FR flow ratio, water to air = _mw _ma Subscripts a air av available db dry bulb i inlet o outlet s refers to saturated air wb wet bulb temperature w water departure of available fill characteristics (FC av ) of the packing of a multi-cell cross flow cooling tower from their values at design state. In spite of vast application of cross flow cooling towers in industries, there are limited investigations to address the effect of large variation of wet bulb temperature on the performance of this type of cooling towers and most researches are devoted to the counter flow cooling towers. Moreover, since cross flow cooling towers have large inlet area for air as compared to counter flow cooling towers, therefore, more pollution, and the way of cleaning the air before tower is very important in this type of towers. This matter has not been discussed yet. In this study, the conventional Merkel s model is used to analyze the thermal behavior of the tower at different wet bulb temperatures for an existing cooling tower working in south of Iran and located in steel company in Ahvaz city. Ahvaz city has variable wet bulb temperature due to its closeness to the Persian Gulf in the Middle East. When the weather gets humid, the performance of cooling towers deteriorates considerably. Experimental test was carried out to validate the predicted results. Moreover, impact type separator is introduced as an effective way to prevent polluted and dusty air from entering the tower. 2. Mathematical modeling Merkel s model is used to investigate the behavior of the tower. The basic assumptions of this model are: 1. The heat transfer resistance of the liquid film is negligible. 2. The mass flow rate of water per unit cross sectional area of the tower is constant (neglecting the mass of evaporated water). 3. The specific heat of moist air at constant pressure is the same as that of dry air. 4. Lewis number for moist air is unity. According to the Merkel s theory, all the heat and mass transfer occurring at each point of the cooling tower can be treated as a y Air x dx dy Water Fig. 1. A differential element of a cross flow cooling tower. single transfer process with enthalpy difference as the driving force. Unlike the analysis of counter flow tower which is one dimensional, the cross flow tower must be treated as a two dimensional system because there are variation of temperature and humidity both in vertical and horizontal directions. Considering a differential element of a cross flow cooling tower (Fig. 1), the energy balance equation inside the tower is: _m w c w dt w dx ¼ _m a dh a dy ¼ h m A v dxdy½h s H a Š where, dxdy is the volume of the element, with its width assumed unity. Rearranging Eq. (1) results in the following set of PDEs for the variations of water temperature and air enthalpy throughout the w _m w c w ¼ h m A v ðh s H a Þ _m ¼ h m A v ðh s H a Þ The boundary conditions are: t w ðx; 0Þ ¼t wi H a ð0; yþ ¼H ai The relation between water temperature and enthalpy of saturated air [16] is: H s ¼ 4:7926 þ 2:568t w 0:029834t 2 w þ 0: t3 w ð6þ The governing equations (Eqs. (2) and (3)) in conjunction with Eq. (6) are coupled and non-linear, which should be solved simultaneously. Finite difference technique is used to solve the set of governing equations to find air and water properties in each point of the tower. 3. Tower specifications and required characteristic curve Fig. 2 shows a schematic diagram of the cooling tower, it is a cross flow cooling tower with three cells (six cell halves). The fills are splash type with rectangular cross section and made from redwood. The design conditions of the tower are listed in Table 1. The required characteristic curve (FC r ) of the tower for specified conditions is shown in Fig. 3. In this figure two characteristic curves are drawn, one, which is used frequently, is based on the assumption that the inlet air is saturated at its wet bulb temperature (RH = 100%). The other one is based on real relative humidity of inlet air (RH = 22%). As the two curves almost coincide, assuming saturated inlet air is reasonable. ð1þ ð3þ ð4þ ð5þ

3 10 E. Hajidavalloo et al. / Energy Conversion and Management 51 (2010) Water inlet Air inlet Fill Drift eliminators Fill Water inlet Fig. 2. Schematic diagram of the selected tower. Table 1 Design conditions of the selected tower. Air inlet Mass flow rate of water kg/h Mass flow rate of air per fan kg/h Inlet water temperature 58.0 C Outlet water temperature.0 C Wet bulb temperature of inlet air 24.0 C Expected evaporation loss 5.0 % Cell half dimensions Length 5.5 m Height 9.6 m Width 12.0 m 2.5 RH=100% RH=22% material doesn t follow its design curve and it is required to be obtained experimentally. Obtaining this curve has two main advantages: 1. Predicting the thermal behavior of the tower with varying _m w and _m a, which helps the user to find the optimum operating point of the tower at present conditions. 2. Estimating the departure of FC av from design conditions, this feature helps the user to find the percentage of degradation of packing material, which can be used in maintenance program of the tower. Available fill characteristic curve for one cell-half of the tower has been obtained using a numerical experimental method described by Prasad [15]. He used measured values of t wo,min and t wo,max in order to predict FC av of the tower, since these values are unique functions of FC av for a given set of wet bulb and inlet water temperatures. For this purpose a set of experimental data at four various operating conditions of the selected tower has been obtained which is shown in Table 2. In order to determine FC av after a period of service, Eqs. (2) and (3) are used together with measured values of t wo,min and t wo,max.a two-way iteration is performed, one for adjusting unknown FR and the other for modifying unknown FC av, until the computed results for t wo,min and t wo,max match with their respective measured values. Each of the temperatures t wo,min and t wo,max represent the average of a number of measurements recorded at equidistant points on outer and inner ends of the fill bottom. Measurement at different values of FR, which itself is an unknown, and computing the corresponding values using the developed computer program establishes current relationship between FR and FC. Available fill FCr 2 Table 2 Measured data at four operating conditions of the tower. t wi t wo,min t wo,max t wb t db FR FC mw FR =. ma Fig. 3. Required characteristic curves of the tower at two different conditions of inlet air Available fill characteristic curve (FC av ) FCav In order to simulate the existing cooling tower, it is required to obtain the current fill characteristic curve of the tower. Fill characteristic is a non-dimensional parameter in each wet cooling tower, which represents the overall potential of the fill to cool water and is written as: FC av ¼ h ma v V _m w FC av curves for different packing shapes and materials are obtained by fill suppliers using appropriate tests. After a length of service, the FC av value of packing may diminish due to several reasons, like fill damage and water misdistribution. Therefore, the fill ð7þ mw FR =. m Fig. 4. Available fill characteristic curve for cell-half. a

4 E. Hajidavalloo et al. / Energy Conversion and Management 51 (2010) characteristic values obtained from the illustrated numericalexperimental method are plotted against the respective FR for the tower in Fig. 4. To estimate the percentage of degradation of packing characteristic from the design condition, the current value should be compared with the design value obtained from Fig. 3. The design values are: FR r = 0.587, FC r = From Fig. 4, the available fill characteristic at design flow ratio (FR r = 0.587) is FC av = So the degradation of the tower is about 33%. 5. Results and discussion After finding the existing fill characteristic of the tower, the performance of the tower can be predicted at different conditions using the mathematical model. Variations of air enthalpy and water temperature through the packing are shown in Fig. 5, which is in agreement with results reported in [5]. Hot water at temperature of 58 C enters from the top and is cooled as it falls downward. The solid lines represent constant water temperatures. Air with 24 C wet bulb temperature enters from the left, across the OY axis, and is heated as it moves to the right. The dotted lines show constant air enthalpies in the tower. This figure shows that air and water properties vary in X and Y directions, contrary to the counter flow tower where the properties only depend on Y direction. Table 3 presents the model predictions and experimental data from cooling tower at eight various operating conditions. The relative error of the model predictions when compared with experimental results is less than 8%. Fig. 6 shows the model predictions and experimental data for water outlet temperatures. Having confirmed the accuracy of the model and cooling tower characteristics, we can use the model to study the effect of other parameters on the performance of the existing cooling tower. Table 3 Comparing the model predictions of outlet water temperature with experimental data at different wet bulb temperatures. t wb t db t wi t wo,min t wo,max t wo,ave,exp t wo,ave,merkel Error (%) Water outlet temperature Experiment Merkel Water inlet temperature Fig. 6. Comparing the model predictions of outlet water temperature with experimental data at different wet bulb temperatures. Z Y X O X Water outlet temperature FR=0.6 FR=0.5 FR= Wet bulb temperature Fig. 7. Effect of ambient air wet bulb temperature on the water outlet temperature of tower. 8 Y Fig. 5. Variations of air enthalpy and water temperature through the packing. One of the most important parameters that should be considered in the design and operating of wet cooling towers in mixed weather conditions, like Ahvaz climate, is the effect of wet bulb temperature on tower performance. In Ahvaz climate, the maximum dry bulb temperature in summer approaches 52 C, while the wet bulb temperature is moderately low, around 24 C. But sometimes this situation is changed and weather becomes humid

5 12 E. Hajidavalloo et al. / Energy Conversion and Management 51 (2010) with 100% relative humidity and wet bulb temperature reaches around C. This large change in the wet bulb temperature has an important effect on the tower performance and the tower does not work efficiently. Fig. 7 shows the effect of wet bulb temperature on water outlet temperature at different FRs. The figure shows that increasing the wet bulb temperature will increase the water outlet temperature. The rate of increase is higher as the wet bulb temperature increases. This means that the tower approach decreases as the Evaporation loss (% of circulating water) Wet bulb temperature t50 db =50 C t46 db =46 C t42 db =42 C Fig. 8. Effect of ambient air wet bulb temperature on the evaporation loss of the tower. Table 4 Effect of wet bulb on outlet water temperature at four hot summer days in Ahvaz. Date Time t db t wb t wo,ave 2007/6/ 5: /7/31 6: /7/26 7: /8/28 6: wet bulb temperature increases. This is in agreement with the same result reported for counter flow cooling tower in [11]. Fig. 8 shows the effect of wet bulb variations on the evaporation loss of water at different dry bulb temperatures. This figure shows that increasing the wet bulb temperature, decreases the evaporation rate of water considerably. It also shows that increasing the dry bulb temperature at constant wet bulbs, increases the evaporation rate. The rate of increase in the evaporation rate at different dry bulb temperatures is almost constant as the wet bulb temperature increases. Comparing these results with the evaporation loss data at design conditions (Table 1), shows that the evaporation loss at design conditions is only consistent at dry bulb temperature of 42 C, which is not a good estimate for the tower, since the ambient air temperature reaches to a maximum of 52 C with summer average temperature of 46 C. The effect of wet bulb temperature on water temperature distribution along the tower has been investigated at four hot summer days in Ahvaz and shown in Table 4 and Fig. 9. The figure shows Air enthalpy (kj/kg) FR=0.9 FR=0.7 FR= X (m) Fig. 10. Effect of FR on air enthalpy variations across the cell-half. Water outlet temperature t wb = t wb = t wb = t wb =18.6 Water outlet temperature FR=0.6 FR=0.5 FR= Y (m) Y (m) Fig. 9. Effect of wet bulb on water temperature distribution along the tower. Fig. 11. Effect of FR on temperature distribution along the cell-half.

6 E. Hajidavalloo et al. / Energy Conversion and Management 51 (2010) suspended in its immediate surrounding. Dust deposit on the inlet louvers and packings of cooling tower creates a thick layer of scale around these parts after a while as shown in Fig. 12. In order to reduce entering dust and suspended solids in the tower, an impact separator was proposed to place in front of air louvers of the tower. High collection efficiency [17], simple construction and low cost, stable operation, low pressure drop, and easy scale up are the major attractions of impact separators for applications in cooling towers. The effect of putting a U-shaped impact separator with 5% reduction in air flow rate, on the outlet water temperature of the tower has been shown in Fig. 13. This figure shows that the impact separator has no important effect on increasing the outlet water temperature and may be used easily in front of the towers to filter dusty air. Water outlet temperature Fig. 12. Layer of dust scale on the body and packing of the tower without impact separator with impact separator Water inlet temperature Fig. 13. Effect of impact separator on water outlet temperature of cooling tower. that increasing the wet bulb temperature is more effective in the bottom section of the tower. Fig. 10 shows the effect of various FR on the air enthalpy across the tower, at design conditions. The figure shows that increasing FR will increase the air enthalpy at any position in the cooling tower. The effect of FR on water temperature along the tower has been shown in Fig. 11. The figure shows that the temperature of water is increased when FR is increased. This can be explained from the fact that an increase in FR, means that more water should be cooled for a given tower volume. Therefore, one would expect that the surface area required both for convection and evaporation will be reduced, resulting in higher water outlet temperatures. 6. Effect of impact separator on tower performance Many cooling towers working at polluted areas, suffer from scale forming as a result of entering considerable amount of dust 7. Conclusions A mathematical model is used to simulate the effect of any change in operating conditions of cooling tower, especially the wet bulb temperature, on the thermal performance of a cross flow tower. Available characteristic curve for packing material has been obtained using a numerical experimental method which provides an insight on the current performance of the tower. It is found that increasing the wet bulb temperature, at constant dry bulb, will decrease the approach, range and evaporation loss in the tower considerably. The evaporation rate is increased as the dry bulb temperature increases and the rate of increase is almost constant at different wet bulb temperatures. An impact separator could be used as a reasonable solution to reduce the amount of suspended solids in the air without any considerable loss in the tower performance. References [1] Merkel F. Evporative cooling. Z Verein Deutsch Ingen (VDI) 19;70: [2] Snyder NW. CEP Sympos Ser 1956: [3] Zivi SM, Brand BB. An analysis of the cross flow cooling tower. Refrig Eng 1956;64:31 4. [4] Schecheter RS, Kang TL. Ind Eng Chem 1959;51: [5] Baker DR, Shryock HA. A comprehensive approach to the analysis of cooling tower performance. J Heat Transf 1961;83: [6] Popp M, Rogener H. Calculation of cooling process. VDI-Warmeatlas; p. Mi 1 Mi 15. [7] Kloppers JC, Kroger DG. Cooling tower performance evaluation: Merkel, Poppe, and e-ntu methods of analysis. J Eng Gas Turbines Power 2005;127:1 7. [8] Hayashi Y, Hirai E. Analysis of a multi-unit co current cross flow cooling tower. J Heat Transf 1974;3: [9] Inazumi H, Kageyama S. A successive graphical method of design of a cross flow cooling tower. Chem Eng Sci 1974;: [10] Khan JR, Zubair SM. Performance characteristics of counter flow wet cooling towers. Energy Convers Manage 2002;44: [11] Khan JR, Zubair SM. An improved design and rating analyses of counter flow wet cooling towers. J Heat Transf Trans ASME 2001;123: [12] Halasz B. A general mathematical model of evaporative cooling devices. Int J Therm Sci 1998;37: [13] Halasz B. Application of a general non-dimensional mathematical model to cooling towers. Int J Therm Sci 1999;38: [14] Kairouani L, Hassairi M, Tarek Z. Performance of cooling tower in south of Tunisia. Build Environ 2003;39:1 5. [15] Prasad M. Economic upgradation and optimal use of multi-cell cross flow evaporative water cooling tower through modular performance appraisal. Appl Therm Eng 2003;24: [16] Stoecker WP, Jones JW. Refrigeration and air conditioning. New York: McGraw Hill; [17] De S, Lal AK, Nag PK. An experimental investigation on pressure drop and collection efficiency of simple plate-type impact separator. Powder Technol 1999;106:192 8.