Study on the heat transfer characteristics of an evaporative cooling tower B

Study on the heat transfer characteristics of an evaporative cooling tower B Paisarn Naphon Department of Mechanical Engineering, Faculty of Engineering, Srinakharinwirot University, 63 Rangsit-Nakhonnayok, Ongkharak, Nakhon-Nayok, 261, Thailand Abstract In the present study, both experimental and theoretical results of the heat transfer characteristics of the cooling tower are investigated. A column packing unit is fabricated from the laminated plastic plates consists of eight layers. Air and water are used as working fluids and the test runs are done at the air and water mass flow rates ranging between 0.01 and 0.07 kg/s, and between 0.04 and 0.08 kg/s, respectively. The inlet air and inlet water temperatures are 23 8C, and between and 8C, respectively. A mathematical model based on the conservation equations of mass and energy is developed and solved by an iterative method to determine the heat transfer characteristics of the cooling tower. There is reasonable agreement from the comparison between the measured data and predicted results. D 05 Elsevier Ltd. All rights reserved. Keywords: Heat transfer characteristics; Evaporative cooling tower 1. Introduction Cooling towers have been introduced as one of the direct contact heat exchangers and the most used widely in several heat transfer applications, for example, power generation units, chemical, petrochemical, refrigeration and air conditioning processes, industrial processes. A few theoretical and experimental works have been reported on the heat transfer and flow characteristics. Kachhwaha et

al. [1] experimentally and theoretically studied a vertical evaporative cooler. The measured data were compared with the predicted results. Facao and Oliveira [2] tested a new closed wet cooling tower. Correlations for mass and heat transfer coefficients were proposed. Khan and Zubair [3] presented a detail model of counter flow wet cooling towers. Fisenko et al. [4] developed a mathematical model for predicting the performance of a cooling tower. The calculated results were validated by the measured data. In their second paper, Fisenko et al. [5] developed the mathematical model of a mechanical draft cooling tower performance. The model represents a boundary-value problem for a system of ordinary differential equations. Hawlader and Lui [6] considered the effect of non-spherical shape of water drops on the flow, heat and mass transfer in an evaporative natural draft cooling tower. Stabat and Marchio [7] presented a model for predicting the behavior of the indirect cooling towers. The model introduces airside and water-side heat transfer coefficients. Prasad [8] applied the novel numerical and experimental techniques to determine the performance of the multi-cell crossflow evaporative cooling tower. As described above, heat and mass transfer characteristics, and pressure drop of the cooling towers are still limited. The objective of this paper is to experimentally and theoretically study the heat transfer characteristics and pressure drop of the cooling tower. Experiments are conducted to obtain the heat transfer characteristics for verifying the mathematical model. 2. Experimental apparatus and procedure A schematic diagram of the experimental apparatus is shown in Fig. 1. The test loop consists of the cooling tower unit, hot water loop, and data acquisition system. Water and air are used as working fluids. The cooling tower columns and the connections of the piping system are designed such that parts can be changed or repaired easily. Air flow entering the cooling tower is discharged by a centrifugal blower and is passed through a column packing, rectifier, orifice, and then discharged to the atmosphere. Air velocity is measured by an orifice and inclined manometer, and controlled through the use of a damper on the blower case. Four type-k thermocouples T wb T db Air Outlet Orifice Temp. Controller T Water Inlet P Rectifier By Pass Flowmeter P Packing Hot Water Heater Pump Valve T wb T db Blower T Water Outlet Air Inlet Fig. 1. Schematic diagram of experimental apparatus.

Table 1 Dimensions of the cooling tower Parameters Dimensions Height of column packing, m 0.48 Width of cooling tower, m 0.15 Length of cooling tower, m 0.15 Number of packing layers 8 Number of plates in each layer 10 Total surface area of packing, m 2 1.19 Packing density, m 1 110 with the uncertainty of F0.5 8C are employed to measure the inlet- and outlet-air temperatures (wet bulb, dry bulb). Pressure drop across the cooling tower is measured by the inclined manometer with the uncertainty of F0.5 Pa. The close-loop of hot water consists of a 0.2 m 3 storage tank, an electric heater controlled by adjusting the voltage. After the temperature of the water is adjusted to achieve the desired level, the hot water is pumped out of the storage tank, and is passed through a filter, flow meter, cooling tower, and returned to the storage tank. The flow rate of the water is controlled by adjusting the valve and measured by a flow meter with a range of 0 4 LPM. The uncertainty of the water flow meter is F0.1 LPM. The cooling tower consists of an acrylic shell and a packing unit with the column packing height of 48 cm. The packing unit is fabricated from the laminated plastic plates consists of eight layers of packing. The dimensions of the cooling tower are listed in Table 1. The thermocouples are installed to measure the water temperature at the inlet and outlet sections. Experiments were conducted with various inlet temperatures of water and flow rates of chilled air and hot water entering the cooling tower. In the experiments, the hot water flow rate was increased in small increments while the air flow rate, inlet hot water and inlet chilled air temperatures were kept constant. Before any data were recorded, the systeas allowed to approach the steady state. 3. Mathematical modelling The heat and mass transfer characteristics of the evaporative cooling tower can be determined by the conservation equations of energy and mass. The mathematical model is based on that of Khan and Zubir [3] and Kuehn et al. [9] with the main following assumptions: Temperature distribution of the water stream at any cross section is uniform. No heat and mass transfer between the system and the surrounding. Lewis number is constant along the column. Specific heats of water and dry air are constant along the column. Heat and mass transfer coefficients are constant along the column. By considering the control volume of each segment as shown in Fig. 2, the energy balance can be written as follows: m a d di ¼ d di f;w þ m a d i f;w d dx ð1þ where m a is the air mass flow rate, is the water mass flow rate, i is the enthalpy of moist air, i f,w is the enthalpy of water, x is the humidity ratio of the moist air.

m a, T a,out,ω out, i a,out Water,,i f,w m a,ω +dω, i+di -m a (ω 2 -ω )+m a dω, i f,w dv m a,ω, i -m a (ω 2 -ω ) i f,w +di f,w m a,,ω in, i a,in Air [ -m a (ω 2 -ω 1 )],T a,out, i f,w,out Fig. 2. Schematic diagram of simulation approach and control volume of each segment. The water-side energy balance can be written in terms of convective heat and mass transfer coefficients as follows: d di f;w ¼ h a d A v d dv d ðt w TÞþh D d A v d dv d i fg;w d x sat;w x ð2þ where h a is the convective heat transfer coefficient, A v is the surface area of the droplets per unit volume of the tower, V is the volume of the tower, T w is the water temperature, T is the dry-bulb temperature of the moist air, h D is the convective mass transfer coefficient, i fg,w is the phase change enthalpy, x sat,w is the saturated humidity ratio at the water temperature. The mass balance of the water and water vapor over the control volume for each segment can be given as: m a d dx ¼ h D d A v d dv d x sat;w x ð3þ Substituting Lewis number, Le =(h a /(h D C p,a )), into Eq. (2) gives d di f;w ¼ h D d A v d dv hled C p;a ðt w TÞþi fg;w d x sat;w x i ð4þ Substituting Eq. (1) into Eq. (4), we get m a d di m a d i f;w d dx ¼ h D d A v d dvhled C p;a ðt w TÞþi fg;w d x sat;w x i ð5þ Combining Eqs. (5) and (3), we get di dx ¼ i f;w þ hled C p;aðt w TÞþi fg;w d x sat;w x i ð6þ x sat;w x

On rearranging, we get or di dx ¼ i f;w þ hled C p;aðt w TÞi þ i fg;w ð7þ x sat;w x di dx ¼ Led C p;a ðt w TÞ þ i g;w ð8þ x sat;w x The specific heat of air, C p,a, is approximately constant, we get i sat;w i ¼ C p;a ðt w TÞþi o g x sat;w x ð9þ Substituting Eq. (9) into Eq. (8) then gives di dx ¼ Led C i sat;w i p;a þ i g;w ig o x sat;w x d Le The water temperature distribution can be calculated from DT w ¼ m a hdh xd i f;w i: ð10þ ð11þ 4. Solution method The cooling tower is divided into various segments along the flow direction as shown in Fig. 2. Eqs. (10) and (11) are solved simultaneously by the iterative technique to determine the temperature distributions of air and water, and humidity distribution along the cooling tower. In order to solve the model, the cooling tower configurations and properties of working fluids, as well as the operating conditions, are needed. 5. Results and discussion Fig. 3 shows the variation of outlet air and water temperatures with air mass flow rate. It can be seen from Fig. 3a that the outlet air temperature tends to decrease with increasing air mass flow rate. However, for high air mass flow rate region, decreasing rate of outlet air temperature decreases. At a specific air and water mass flow rates, and inlet air temperature, effect of inlet water temperature on the outlet air temperature is very small. The reasonable agreement is obtained from the comparison between the predicted results and the present experimental data. Considering Fig. 3b also shows the variation of outlet water temperature with air mass flow rate. As seen, outlet water temperature decreases as air mass flow rate increases. The decrease of the outlet water temperature caused by the increase of air mass flow rate results in an increase of the heat transfer rate. In order to maintain the heat transfer rate equal the air side heat transfer rate, the outlet water temperature must be decreased as air mass flow rate increases. In the present experiment, the outlet water temperature slightly increases as the inlet water temperature increases. The results obtained from the model are reasonable agreement with the measured data. Fig. 4 shows the variation of the pressure drop across the cooling tower with air mass flow rate. It can be seen that the pressure drop tends to increase as the air mass flow rate increases. The pressure drop increases rapidly in

(a) Outlet air temperature, o C 35 25 15 ( o C) Exp. data Math. model 39.0 34.0 = 23.0 o C = 0.04 kg/s 10.01.02.03.04.05.06.07 the high air mass flow rate and moderately increases as air mass flow rate decreases. Effect of inlet water temperature on the pressure drop is quite low. Fig. 5 shows the comparison between the total data points of the outlet air and outlet water temperatures obtained from the experiment and those obtained from the model. It can be seen that the majority of the data fall within F10% of the model. A number of graphs can be drawn from the output simulation but, due to the space limitation, only typical results are shown. Fig. 6 shows the variation of temperature ratio with air mass flow rate. The temperature ratio can be calculated from (b) Outlet water temperature, o C 35 25 Fig. 3. Variation of T a,out and T w,out with m a. = 23.0 o C = 0.04 kg/s ( o C) Exp. data Math. model 15 39.0 34.0 10.01.02.03.04.05.06.07 R ¼ T w;in T w;out T w;in T a;wb;in : ð12þ As given inlet air and inlet water temperatures, and water mass flow rate, the temperature ratio increases with increasing air mass flow rate. This phenomenon can be clearly explained by Eq. (12) in which the outlet water temperature decreases as air mass flow rate increases. But the inlet water and inlet air wet bulb temperatures are maintained constant. Therefore the temperature ratio also increases with increasing air mass flow rate. For a given 80 Pressure drop, Pa 70 60 50 10 ( o C) 39.0 34.0 = 23.0 o C = 0.04 kg/s 0.01.02.03.04.05.06.07 Fig. 4. Variation of DP with m a.

(a) Predicted outlet air temperature, o C 35 25 +10% -10% 15 15 25 35 Experimental outlet air temperature, o C (b) Predicted outlet water temperature, o C 35 25 15 +10% -10% 10 10 15 25 35 Experimental outlet water temperature, o C air mass flow rate, the inlet water temperature has significant effect on the decrease of the temperature ratio as shown in Fig. 6a. The reason for this is similar to the one as described above. Effect of water mass flow rate on the temperature ratio is shown in Fig. 6b. It can be seen that increase of temperature ratio becomes relative less as water mass flow rate increases. This is because the outlet water temperature increases with increasing water mass flow rate. Fig. 7 shows the variation of the number of transfer unit with temperature ratio for different mass flow rate ratios. These conditions can be performed by varying inlet air wet bulb temperature. The number of transfer unit representing the size of the cooling towers can be calculated from NTU ¼ h Dd A V d V m a ¼ Z xo x i Fig. 5. Comparison of T a,out and T w,out. dx x sat;w x : For a given mass flow rate ratio, /m a, inlet water and inlet air dry bulb temperatures, the temperature ratio can be increased by the decrease of outlet water temperature and/or the increase of inlet air wet bulb temperature. ð13þ (a) Temperature ratio.8.7.6.5.4.3.2.1 ( o C) 45 50 = 25 o C = 0.04 kg/s 0.0 0.00.02.04.06.08.10 (b) Temperature ratio.8.7.6.5.4.3.2.1 Fig. 6. Variation of R with m a. (kg/s) 0.04 0.06 0.08 = 25 o C = o C 0.0 0.00.02.04.06.08.10

(a) NTU 3.0 2.5 2.0 1.5 1.0.5 =.0 o C = 25.0 o C /m a 4 3 2 0.0.10.12.14.16.18..22 (b) Tower effectiveness 1.0.8.6 =.0 o C = 25.0 o C.4 /m a.2 4 3 2 0.0.10.12.14.16.18..22 Temperature ratio Temperature ratio Fig. 7. Variation of NTU, e with R. This means that the size of the cooling tower must be increased. It can be seen from Fig. 7a that at /m a =4, the number of transfer unit increases moderately as the temperature ratio increases and rapidly increases as the temperature ratio reach over 0.18. However, trends of curves become flatter as /m a decreases. Fig. 7b also shows the variation of the tower effectiveness with temperature ratio. The tower effectiveness can be determined from e ¼ h o h i h sat;wi h i : ð14þ Due to higher temperature ratio as inlet air wet bulb temperature increases, the tower effectiveness also increases. This phenomenon can be clearly explained by Eq. (14). This means that given inlet air dry bulb temperature, the humidity ratio increases as inlet air wet bulb temperature increases. Outlet and inlet air enthalpy (h o, h i ) also increase. But the saturated enthalpy (h sat,wi ) at inlet water temperature is kept constant. Therefore the tower effectiveness increases as temperature ratio increases. In general, the outlet water temperature increases as water mass flow rate increases. However, in order to keep the outlet water temperature constant (R = constant) as water mass flow rate increases, the heat transfer rate must be increased. Therefore the tower effectiveness also increases with increasing water mass flow rate as shown in Fig. 7b. 6. Conclusions This paper presents new heat transfer data of cooling tower. The cooling tower consists of eight layers of packing. Water and air are used as working fluids. The effects of relevant parameters are investigated. Experiments are conducted to obtain the heat transfer characteristics for verifying the mathematical model. The mathematical model is solved by the iterative method. Reasonable agreement is obtained from the comparison between the results obtained from the experiment and those obtained from the model. Nomenclature A v surface area of the droplets per unit volume of the tower, m 2 /m 3 C p specific heat, kj/kg 8C

h D i f,w o i g i sat,w m a mass transfer coefficient, kg/m 2 s enthalpy of water, kj/kg enthalpy of saturated water vapor at 0 8C, kj/kg saturated enthalpy of moist air at T w, kj/kg air mass flow rate, kg/s NTU number of transfer unit T air temperature, 8C V volume of the tower, m 3 x sat,w saturated humidity ratio at T w,kg wv /kg da h a heat transfer coefficient, kw/m 2 8C i enthalpy of moist air, kj/kg i fg,w phase change enthalpy, kj/kg i g,w enthalpy of water, kj/kg Le Lewis number water mass flow rate, kg/s R Temperature ratio T w water temperature, 8C x humidity ratio of the air, kg wv /kg da e Effectiveness Subscripts a moist air in inlet sat saturated wv water vapor da dry air out outlet w water References [1] S.S. Kachhwaha, P.L. Dhar, S.R. Kale, Proceedings of the 3rd ISHMT-ASME Heat and Mass Transfer Conference, and 14th National Heat and Mass Transfer Conference, India, 1997 (Dec.), p. 29. [2] J. Facao, A. Oliveira, Appl. Therm. Eng. (00) 1225. [3] J.R. Khan, S.M. Zubir, Trans. ASME 123 (01) 770. [4] S.P. Fisenko, A.I. Petruchik, A.D. Solodukhim, Int. J. Heat Mass Transfer 45 (02) 4683. [5] S.P. Fisenko, A.A. Brin, A.I. Petruchik, Int. J. Heat Mass Transfer 47 (04) 165. [6] M.N.A. Hawlader, B.M. Lui, Appl. Therm. Eng. 22 (02) 41. [7] P. Stabat, D. Marchio, Appl. Energy 78 (04) 433. [8] M. Prasad, Appl. Therm. Eng. 24 (04) 579. [9] T.H. Kuehn, J.W. Ramsey, J.L. Threlkeld, Thermal Environmental Engineering, 3rd ed., Prentice-Hall Inc., New York, 1998.