- Email: [email protected]
Experimental study and predictions of an induced draft ceramic tile packing cooling tower
Energy Conversion and Management 47 (2006) 2034–2043 www.elsevier.com/locate/enconman
Experimental study and predictions of an induced draft ceramic tile packing cooling tower Esam Elsarrag
*
Department of Mechanical Engineering, Technical Studies Institute, P.O. Box 39219, Abu Dhabi, United Arab Emirates Received 9 January 2005; received in revised form 13 July 2005; accepted 24 December 2005 Available online 28 February 2006
Abstract Deterioration of the filling material in traditional cooling towers is of serious concern. In this study, long life burned clay is used as the filling material. It guards against common cooling tower problems resulting from chemical water treatment and deterioration. The size of the ceramic packing material and outlet conditions predictions by theoretical modeling require heat and mass transfer correlations. An experimental study to evaluate the heat and mass transfer coefficients is conducted. The previous correlations found in the literature could not predict the mass transfer coefficient for the tested tower. A mass transfer coefficient correlation is developed, and new variables are defined. This correlation can predict the mass transfer coefficient within an error of ±10%. The developed correlation is used along with theoretical modeling to predict the cooling tower outlet conditions within an error of ±5%. 2006 Elsevier Ltd. All rights reserved. Keywords: Cooling tower; Ceramic packing; Correlation
1. Introduction The cooling tower is a steady flow device that uses a combination of mass and energy transfer to cool water by exposing it as an extended surface to the atmosphere. The water surface is extended by filling, which presents a film surface or creates droplets. The air flow may be cross flow or counter flow and caused by mechanical means, convection currents or by natural wind. In mechanical draft towers, air is moved by one or more mechanically driven fans to provide a constant air flow. The function of the fill is to increase the available surface in the tower, either by spreading the liquid over a greater surface or by retarding the rate of fall of the droplet surface through the apparatus. The fill should be strong, light and deterioration resistant. In this study, long life burned clay bricks were used as the filling material. Its hardness, strength and composition guard against common cooling tower problems resulting from fire, chemical water treatment and deterioration.
*
Tel.: +971 507160317; fax: +971 84680127. E-mail addresses: [email protected], [email protected]
0196-8904/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2005.12.019
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2035
Nomenclature a Cp Dv deq E h hc K Kx Le m m0 M q t Z
area of heat and mass transfer (m2/m3) specific heat (kJ/kg K) diffusion coefficient (m2/s) equivalent diameter for structured packing (m) efficiency (%) enthalpy (kJ/kg) heat transfer coefficient (kW/m2 K) thermal conductivity (W/m K) mass transfer coefficient (kW/m2 K) Lewis number flow rate (kg/s) superficial flow rate (mass velocity) (kg/m2 s) molecular weight (kg/kmol) heat flux (kJ/kg) temperature (C) tower height (m)
Greeks l viscosity (Ns/m2) q density (kg/m3) x humidity ratio (kg water/kg dry air) Subscripts a air db dry bulb i inlet or interface m mean o outlet t total v vapor wb wet bulb w water
Several studies on cooling tower analysis were developed with different points of view. Webb and Villacres [1] described three computer algorithms that have been developed to perform rating calculations of three evaporatively cooled heat exchangers. The heat and mass transfer characteristic equation of one of the heat exchangers is derived from the manufacturer’s rating data at the design point. Jaber and Webb [2] produced the effectiveness-NTU (number of transfer unit) design method for counter flow towers using Merkel’s simplification theory [3]. Braun et al. [4] presented effectiveness models for cooling towers and cooling coils. The results of the models were compared with those of more detailed numerical solutions to the basic heat and mass transfer coefficients and experimental data. Osterle [5] pointed out that the Merkel assumptions underestimated the required NTU. Soylemez and Unsal [6] presented an interactive computer code for sizing forced draft, counter flow cooling towers using a closed formula offered by Unsal and Varol [7]. El-Dessouky et al. [8] modified the analysis done by Jaber and Webb. They presented a solution for the steady state counter flow wet cooling tower with new definitions of tower effectiveness and number of transfer units. Bernier [9] presented an analysis of the basic heat and mass transfer processes occurring around a droplet in transient cooling of a spray counter flow tower. The influence of fill height, water retention time and water–air flow ratio on the tower performance was represented.
2036
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
Nimr [10] presented a mathematical model to describe the thermal behavior of packed cooling towers. A closed form solution was obtained for both the transient and steady temperature distribution in a cooling tower. Jameel et al. [11] investigated the heat and mass transfer mechanism and performance characteristics using a detailed theoretical model in counter flow cooling towers. Fisenko et al. [12] developed a new mathematical model of a mechanical draft cooling tower performance. The model represented a boundary value problem for a system of ordinary differential equations describing a change in the droplets velocity, its radii and temperature, and also a change in the temperature and density of the water vapor in mist air in a cooling tower. So¨ylemez [13] presented a thermohydraulic performance optimization analysis yielding a simple algebraic formula for estimating the optimum performance point of counter current mechanical draft wet cooling towers. The effectiveness-NTU method was used, together with derivation of the psychrometric properties of moist air based on a numerical approximation method, for thermal performance analysis of counter flow type towers. Kloppers and Kro¨ger [14] investigated the effect of the Lewis factor on the performance prediction of natural draft and mechanical draft wet cooling towers. The design of a ceramic tile cooling tower requires heat and mass transfer correlations to estimate the packing height and to predict the water and air outlet conditions. Several workers have measured the heat and mass transfer coefficient in cooling towers. Thomas and Houston [15] developed heat and mass transfer correlations using a tower of 2 m height and 0.3 m2 cross section. They gave the following relations for the heat and mass 00:72 transfer coefficients: hc a ¼ 3:0m00:26 and k x a ¼ 2:95mw00:26 m00:72 . w ma a Lowe and Christie [16] measured the heat and mass transfer coefficients using 1.3 m2 experimental column 0n fitted with a number of different types of packing. They showed that in most cases hc aam01n w ma . This showed a close agreement with the results of Thomas and Houston, when n = 0.75. Jorge and Armando [17] tested a new closed wet cooling tower. They obtained experimental correlations for the heat and mass transfer coefficients. They concluded that the existing thermal models were found to predict 0:8099 reliably the thermal performance of cooling towers. They found that K x a ¼ 0:1703ðm=mmax Þsair and hc a ¼ 0:6584 700:3ðm=mmax Þwater . Lebrun and Silva [18] generated a correlation between the global heat transfer coefficient UA from experimental analysis as a function of water and air flow rates entering the tower. The best fit of the results gave the 01:03 following correlation: UA ¼ 745m00:43 . w ma Here, an induced draft counter flow ceramic tile packed cooling tower has been designed and tested for heat and mass transfer. The packing material used in the column was burned clay bricks. Some investigators have used theoretical models to predict the performance of cooling towers. However, the theoretical model requires that the heat and mass transfer coefficients be experimentally determined. In addition, these coefficients can be used to estimate the size of the packed tower. Other investigators developed correlations to predict the heat and mass transfer coefficients, but these correlations did not consider the effect of the packing type and the mass transfer driving force on the mass transfer coefficient. This paper presents the heat and mass transfer as calculated from the experimental measurements. The results from the experimental data were used to develop a new mass transfer coefficient including new parameters. The developed correlation is used along with Merkel’s theoretical model to predict the ceramic tower air and water outlet conditions. 2. Experimental setup The tested cooling tower is an induced draft counter flow type. The schematic diagram of the tower is shown in Fig. 1. The tower cross sectional area is 0.64 m2, the total height of the tower is 2 m and the filling portion is 0.8 m. Burned clay bricks were used as the packing material with a maximum number of 12 layers each consisting of 18 bricks. The brick dimensions are 235 · 120 · 64 mm, and its void fraction is 0.4. Water distributors were used to distribute the water uniformly over the packing. An axial fan was fixed on the top of the tower to extract the air from the bottom of the tower. Two pumps were used to circulate the hot water over the packing in a counter manner to the air flow. Before each experiment, the mains water was heated by solar collectors and stored in the tank. The water was allowed to re-circulate through the solar collectors to obtain the desired water temperature. The flow
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2037
Fig. 1. Schematic diagram for the tested ceramic cooling tower.
Table 1 Measuring devices specifications Device
Type
Accuracy
Operative range
Fluid
Sling psychrometer Thermometer Flowmeter Anemometer
Hand Ordinary Rotameter Vane
0.1 C 0.1 C 0.06 l/s 5% of measured air flow rate
0–60 C 0–100 C 0–0.4 l/s 0–5 m/s
Air (DB & WB) Water and air Water Air
regulating valve was adjusted and the water and air flow rates were measured. During the experiment, the hot water was distributed uniformly over the filling material. The axial fan extracts the air from the bottom of the tower in a counter manner to the water flow. The temperatures measurements were taken after allowing enough time for steady state readings. The inlet air and water temperatures were measured before and during the experiment. Three sets of experiments were performed for different heights of packing (0.77, 0.7 and 0.63 m). For each height, the experiments were performed for different water to air flow ratios, (1.13, 0.96, 0.8 and 0.7). The inlet water temperature was varied for each liquid to air flow rate ratio (42.5, 40, 38 and 35 C). The measurements during the experiment are shown in Fig. 1. The specifications of the different measuring devices are shown in Table 1. The rotameter was calibrated using the weighing cylinder method, ASME Standard [19]. The uncertainties of the experimental parameters are shown as error bars in the discussion figures. 3. Cooling tower theory When air flow passes a wetted surface there is a transfer of sensible and latent heat. If there is a difference in temperature between the air and the wetted surface, heat will be transferred. If there is a difference in the partial pressure of water vapor in the air and that of the water, there will be a mass transfer. This transfer of mass causes a thermal energy transfer because if some water evaporates from the water layer, the latent heat of this vaporized water will be supplied to the air. The concept of enthalpy potential is a very useful one in quantifying the transfer of heat (sensible and latent) in those processes and components where there is a direct contact between the air and water.
2038
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
The expression for transfer of the total heat dqt through a differential area dA is expressed by Stoecker [20]: dqt ¼
hc dA ðhi ha Þ Cp m
ð1Þ
The name of enthalpy potential originates from the above equation because the potential for the transfer of the sum of the sensible and latent heats is the difference between the enthalpy of the saturated air at the wetted surface temperature hi and the enthalpy of the air stream ha. The rate of heat removed from the water is equal to the rate gained by the air, so the following expression can be written: dqt ¼ ma dha ¼ 4:19mw dt
ð2Þ
4. Heat and mass transfer coefficients calculation The heat transfer coefficient can be calculated by equating Eqs. (1) and (2) and rearranging: Z out hc A dt ¼ 4:19 C p m mw hi h a in However, A = aV and V = SZ, so Eq. (3) can be written as: Z out hc aZ dt ¼ 4:19 C p m m0w h ha i in
ð3Þ
ð4Þ
The relation between the heat and mass transfer coefficients is expressed by Reynold’s analogy [21]: hc 2 ¼ Le3 K xCp m
ð5Þ
It is found that in most cases of air–water contact, the Lewis number Le can be considered to be unity as a good approximation [22]: hc ¼ Kx Cp m By substituting Eq. (6) in Eq. (4), the mass transfer coefficient can be expressed as: Z out K x aZ dt ¼ 4:19 0 mw hi ha in
ð6Þ
ð7Þ
The integration of Eq. (7) is solved numerically by dividing the packed height into small segments starting from the bottom to the top of the tower. 5. Results and discussion The mass transfer coefficient found from the experimental data and the existing correlations were depicted graphically, along with the design variables. The heat and mass transfer coefficients are related by Reynold’s analogy, so the factors that influence the mass transfer coefficient also affect the heat transfer coefficient. As shown in Fig. 2, the mass transfer coefficient increased with the increase of the water to air flow rate ratio. However, it can be observed that there is some degree of difficulty in the mass transfer when a high water to air flow rate was employed. The increase of the mass transfer coefficient with the water to air flow rate ratio gave good agreement with the previous correlations. It can be observed that the Thomas and Houston [15] values are closer than those of Leburn and Silva [18], but there is a big deviation between the experimental values and those obtained by their correlations. The mass transfer coefficient increased when the inlet water temperature increased from 35 to 38 C as shown in Fig. 3, but it decreased when the water temperature was raised above 38 C (from 38 to 42.5 C). This is mainly because the driving force increases with the increase of the inlet water temperature and a greater
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2039
Fig. 2. Influence of liquid to air flow rate on mass transfer.
Fig. 3. Influence of inlet water temperature on mass transfer.
heat and mass transfer occurs, but a higher outlet water temperature was obtained by continued increasing of the inlet water temperature. This is reflected as a decrease in the mass transfer coefficient. The mass transfer coefficient decreased with the increase of the inlet air enthalpy as shown in Fig. 4. This is due to the decrease in the driving force, which is reflected as a decrease in the mass transfer coefficient.
Fig. 4. Influence of inlet air enthalpy on mass transfer.
2040
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
In fact, the correlations developed by Thomas and Houston [15], Lowe and Christie [16] and Leburn and Silva [18] are functions of the air and water flow rate only. They did not consider the effect of the water temperature and the weather conditions on the mass transfer coefficient in addition to the packing type. The heat and mass transfer coefficients calculated from the previous correlations will remain constant with the variation in the air and water temperatures. Therefore, a big deviation was found between the calculated heat and mass transfer coefficient values and those obtained by these correlations. From the discussion, it can be found that the factors that have a greater effect on the heat and mass transfer coefficients are: the water to air flow rate ratio; the inlet water temperature and the inlet air enthalpy. 6. Correlation development Developing a correlation for the mass transfer coefficient is necessary to predict the packing height and the outlet conditions from the cooling tower. The factors found to have the greatest effect on the gas phase mass transfer coefficient are: the water and air flow rates; the inlet air and water conditions; the packing volume and equivalent diameter and the diffusion coefficient of water in air. K x a ¼ f ða; d eq ; qv ; Dv ; m0w ; m0a ; ha ; hi Þ
ð8Þ
The Buckingham Pi method was employed to obtain the pertinent dimensionless groups [23]: ! d 2eq p1 ¼ K x a Dv qv G
p2 ¼
m0w m0a
ð9Þ
ha p3 ¼ hi d 2eq Kxa Dv qv
!
ha m0w ; ¼f hi m0a
The mass transfer correlation obtained from the dimensional analysis is given by: ! a 0 b d 2eq ha mw K xa ¼c 1 Dv qv hi m0a
ð10Þ
The term ð1 hhai Þ represents the driving force (hi ha), which measures the degree of difficulty of the mass transfer. The experimental data of this study were employed along with a curve fitting computer program to obtain the constants of Eq. (10). ! 0:27 0 0:69 d 2eq ha mw K xa ð11Þ ¼ 4:62 1 Dv qv hi m0a The heat transfer coefficient can be predicted using Reynold’s analogy (Eq. (7)) hc a ¼ K xa Cp m The deviation between the predicted values and the experimental data is shown in Fig. 5. The mass transfer correlation can be predicted within an error of ±10%. This correlation can be used to estimate the height of the burned clay filling portion by rearranging Eq. (7).
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2041
Fig. 5. Relation between experimental and predicted mass transfer coefficient.
7. Modeling and predictions Fig. 6 shows a differential volume of a counter flow cooling tower. For the finite difference model, the tower fill height Z is divided into small segments, dZ, and the mass and energy balances are solved for each segment from the bottom to the top of the tower. The governing equations that describe the changes in air humidity, air temperature and water temperature across a segment are given below. A detailed derivation of these equations is given by Treybal [21]. 7.1. Change in air temperature across the segment The change in air temperature across the segment is obtained by applying an energy balance on the segment interface, control volume (I) in Fig. 6(b). hc adZðti ta Þ ¼ m0a C p m dta ð12Þ dta hc a ¼ 0 ðti ta Þ. ma dZ
mw tw
ma,o mw,i
ma + dma ta + dta ωa + dω a
n n-1 Water Air
Z 3 2 1
ti wi
II
dZ I
III INTERFACE
ma,i
mw,o ma ta
mw - dmw tw - dtw (a)
ωa
(b)
Fig. 6. Packed Tower: (a) tower Overview, (b) differential segment.
2042
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
7.2. Change in air humidity across the segment The change in air humidity is obtained from the mass balance on the segment, control volume (III) in Fig. 6(b) K x adZðxi xa Þ ¼ m0a dxa dxa K x a ¼ 0 ðxi xa Þ ma dZ
ð13Þ
Kxa and hca can be calculated by using the correlation (Eq. (11)) and Reynold’s analogy (Eq. (6)) ! 0:27 0 0:69 d 2eq ha mw ¼ 4:62 1 Kxa Dv qv hi m0a hc a ¼ K x a C p m 7.3. Change in water temperature across the segment By applying an energy balance across the segment, control volume (III) in Fig. 6(b) ma dha ¼ mw C p w dtw dtw ma dta dxa ¼ þ ðC p v ta þ kÞ ðC p a þ xa C p v Þ dZ mw C p w dZ dZ
Fig. 7. Relation between experimental and predicted tower outlet temperatures.
ð14Þ
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2043
A computer program was written to perform the finite difference analysis with the fill height Z divided into 1000 segments to solve Eqs. (12)–(14), and the mass and energy balances are solved for each segment. Fig. 7 shows the predicted outlet air temperature, air humidity and water temperature. The outlet air and water temperatures were predicted with a maximum error of ±5%. 8. Conclusions Several field tests using different variables were performed for an induced draft cooling tower using burned clay bricks as the fill material. It was found that the factors affecting the heat and mass transfer coefficients are: the water to air flow rate ratio; the inlet water temperature and the inlet air enthalpy. The previous correlations found in the literature could not predict the mass transfer coefficient for the tested tower. A mass transfer coefficient correlation was developed, and new variables were defined. This correlation can predict the mass transfer coefficient within a maximum error of ±10%. The developed correlation was used along with theoretical modeling to predict the cooling tower outlet conditions. The model with the correlation showed good predictions of the outlet water and air temperatures conditions within an error of ±5%. References [1] Webb RL, Villacres A. Algorithms for performance simulation of cooling towers, evaporative condensers, and fluid coolers. ASHRAE Trans 1984;90(2):416–58. [2] Jaber H, Webb RL. Design of cooling towers by the effectiveness-NTU method. ASME J Heat Transf 1989;111(4):837–43. [3] Merkel F. Verdunstungshuhlung. Zeitschrift des Vereines Deutscher Ingenieure (VDI) 1925;70:123–8. [4] Braun JE, Klein SA, Mitchell JW. Effectiveness models for cooling towers and cooling coils. ASHRAE Trans 1989;95(2):164–74. [5] Osterle F. On the analysis of counter-flow cooling towers. Int J Heat Mass Tran 1991;34(4/5):1313–6. ¨ nsal M. Computational analysis for sizing of cooling towers. In: Proceedings of the third national refrigeration and [6] So¨ylemez MS, U air conditioning congress, Adana, Turkey.1994. p.117–26. ¨ nsal M, Varol A. An analysis for sizing of cooling towers. In: Proceedings of the first national refrigeration and air conditioning [7] U congress, Adana, Turkey.1990. p. 52–6. [8] El-Dessouky HTA, Al-Haddad A, Al-Juwayhel F. A modified analysis of counter flow cooling towers. ASME J Heat Transf 1997; 119(3):617–26. [9] Bernier MA. Cooling tower performance: Theory and experiments. ASHRAE Trans 1999;100(2):114–21. [10] Nimr MA. Modeling the dynamic thermal behavior of cooling towers containing packing materials. Heat Transf Eng 1999;20(1): 91–6. [11] Jameel UK, Yaqub M, Zubair SM. Performance characteristics of counter flow wet cooling towers. Energ Convers Manage 2003; 44:2073–91. [12] Fisenko SP, Brin AA, Petruchik AI. Evaporative cooling of water in a mechanical draft cooling tower. Int J Heat Mass Tran 2004; 47:165–77. [13] So¨ylemez MS. On the optimum performance of forced draft counter flow cooling towers. Energ Convers Manage 2004;45:2335–41. [14] Kloppers JC, Kro¨ger DG. The Lewis factor and its influence on the performance prediction of wet-cooling towers. Int J Therm Sci 2005;44:879–84. [15] Thomas WJ, Houston P. Simultaneous heat and mass transfer in cooling towers. Brit Chem Eng 1959;160:217. [16] Lowe HJ, Christie DG. Heat transfer and pressure drop data on cooling tower packings, and model studies of the resistance of natural draft towers to air flow. Inst Mech Eng (Steam Group) Symposium on Heat Transfer 1962;113:933. [17] Jorge F, Armando CO. Thermal behavior of closed wet cooling towers for use with chilled ceilings. Appl Therm Eng 2000;20:1225–36. [18] Lebrun J, Silva CA. Cooling tower—model and experimental validation. ASHRAE Trans 2002:751–9. [19] ASME. Measurement of liquid flow in closed conduits by weighing method. American Society of Mechanical Engineers; 1988. [20] Stoecker WF, Jones JW. Refrigeration and air conditioning. Singapore: McGraw-Hill; 1985. [21] Treybal RE. Mass transfer operations. New York: McGraw-Hill; 1981. [22] Kern DQ. Process heat transfer. New York: McGraw-Hill; 1997. [23] Panton RL. Incompressible flow. New York: John Wiley & Sons; 1984.
Experimental study and predictions of an induced draft ceramic tile packing cooling tower Esam Elsarrag
*
Department of Mechanical Engineering, Technical Studies Institute, P.O. Box 39219, Abu Dhabi, United Arab Emirates Received 9 January 2005; received in revised form 13 July 2005; accepted 24 December 2005 Available online 28 February 2006
Abstract Deterioration of the filling material in traditional cooling towers is of serious concern. In this study, long life burned clay is used as the filling material. It guards against common cooling tower problems resulting from chemical water treatment and deterioration. The size of the ceramic packing material and outlet conditions predictions by theoretical modeling require heat and mass transfer correlations. An experimental study to evaluate the heat and mass transfer coefficients is conducted. The previous correlations found in the literature could not predict the mass transfer coefficient for the tested tower. A mass transfer coefficient correlation is developed, and new variables are defined. This correlation can predict the mass transfer coefficient within an error of ±10%. The developed correlation is used along with theoretical modeling to predict the cooling tower outlet conditions within an error of ±5%. 2006 Elsevier Ltd. All rights reserved. Keywords: Cooling tower; Ceramic packing; Correlation
1. Introduction The cooling tower is a steady flow device that uses a combination of mass and energy transfer to cool water by exposing it as an extended surface to the atmosphere. The water surface is extended by filling, which presents a film surface or creates droplets. The air flow may be cross flow or counter flow and caused by mechanical means, convection currents or by natural wind. In mechanical draft towers, air is moved by one or more mechanically driven fans to provide a constant air flow. The function of the fill is to increase the available surface in the tower, either by spreading the liquid over a greater surface or by retarding the rate of fall of the droplet surface through the apparatus. The fill should be strong, light and deterioration resistant. In this study, long life burned clay bricks were used as the filling material. Its hardness, strength and composition guard against common cooling tower problems resulting from fire, chemical water treatment and deterioration.
*
Tel.: +971 507160317; fax: +971 84680127. E-mail addresses: [email protected], [email protected]
0196-8904/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2005.12.019
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2035
Nomenclature a Cp Dv deq E h hc K Kx Le m m0 M q t Z
area of heat and mass transfer (m2/m3) specific heat (kJ/kg K) diffusion coefficient (m2/s) equivalent diameter for structured packing (m) efficiency (%) enthalpy (kJ/kg) heat transfer coefficient (kW/m2 K) thermal conductivity (W/m K) mass transfer coefficient (kW/m2 K) Lewis number flow rate (kg/s) superficial flow rate (mass velocity) (kg/m2 s) molecular weight (kg/kmol) heat flux (kJ/kg) temperature (C) tower height (m)
Greeks l viscosity (Ns/m2) q density (kg/m3) x humidity ratio (kg water/kg dry air) Subscripts a air db dry bulb i inlet or interface m mean o outlet t total v vapor wb wet bulb w water
Several studies on cooling tower analysis were developed with different points of view. Webb and Villacres [1] described three computer algorithms that have been developed to perform rating calculations of three evaporatively cooled heat exchangers. The heat and mass transfer characteristic equation of one of the heat exchangers is derived from the manufacturer’s rating data at the design point. Jaber and Webb [2] produced the effectiveness-NTU (number of transfer unit) design method for counter flow towers using Merkel’s simplification theory [3]. Braun et al. [4] presented effectiveness models for cooling towers and cooling coils. The results of the models were compared with those of more detailed numerical solutions to the basic heat and mass transfer coefficients and experimental data. Osterle [5] pointed out that the Merkel assumptions underestimated the required NTU. Soylemez and Unsal [6] presented an interactive computer code for sizing forced draft, counter flow cooling towers using a closed formula offered by Unsal and Varol [7]. El-Dessouky et al. [8] modified the analysis done by Jaber and Webb. They presented a solution for the steady state counter flow wet cooling tower with new definitions of tower effectiveness and number of transfer units. Bernier [9] presented an analysis of the basic heat and mass transfer processes occurring around a droplet in transient cooling of a spray counter flow tower. The influence of fill height, water retention time and water–air flow ratio on the tower performance was represented.
2036
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
Nimr [10] presented a mathematical model to describe the thermal behavior of packed cooling towers. A closed form solution was obtained for both the transient and steady temperature distribution in a cooling tower. Jameel et al. [11] investigated the heat and mass transfer mechanism and performance characteristics using a detailed theoretical model in counter flow cooling towers. Fisenko et al. [12] developed a new mathematical model of a mechanical draft cooling tower performance. The model represented a boundary value problem for a system of ordinary differential equations describing a change in the droplets velocity, its radii and temperature, and also a change in the temperature and density of the water vapor in mist air in a cooling tower. So¨ylemez [13] presented a thermohydraulic performance optimization analysis yielding a simple algebraic formula for estimating the optimum performance point of counter current mechanical draft wet cooling towers. The effectiveness-NTU method was used, together with derivation of the psychrometric properties of moist air based on a numerical approximation method, for thermal performance analysis of counter flow type towers. Kloppers and Kro¨ger [14] investigated the effect of the Lewis factor on the performance prediction of natural draft and mechanical draft wet cooling towers. The design of a ceramic tile cooling tower requires heat and mass transfer correlations to estimate the packing height and to predict the water and air outlet conditions. Several workers have measured the heat and mass transfer coefficient in cooling towers. Thomas and Houston [15] developed heat and mass transfer correlations using a tower of 2 m height and 0.3 m2 cross section. They gave the following relations for the heat and mass 00:72 transfer coefficients: hc a ¼ 3:0m00:26 and k x a ¼ 2:95mw00:26 m00:72 . w ma a Lowe and Christie [16] measured the heat and mass transfer coefficients using 1.3 m2 experimental column 0n fitted with a number of different types of packing. They showed that in most cases hc aam01n w ma . This showed a close agreement with the results of Thomas and Houston, when n = 0.75. Jorge and Armando [17] tested a new closed wet cooling tower. They obtained experimental correlations for the heat and mass transfer coefficients. They concluded that the existing thermal models were found to predict 0:8099 reliably the thermal performance of cooling towers. They found that K x a ¼ 0:1703ðm=mmax Þsair and hc a ¼ 0:6584 700:3ðm=mmax Þwater . Lebrun and Silva [18] generated a correlation between the global heat transfer coefficient UA from experimental analysis as a function of water and air flow rates entering the tower. The best fit of the results gave the 01:03 following correlation: UA ¼ 745m00:43 . w ma Here, an induced draft counter flow ceramic tile packed cooling tower has been designed and tested for heat and mass transfer. The packing material used in the column was burned clay bricks. Some investigators have used theoretical models to predict the performance of cooling towers. However, the theoretical model requires that the heat and mass transfer coefficients be experimentally determined. In addition, these coefficients can be used to estimate the size of the packed tower. Other investigators developed correlations to predict the heat and mass transfer coefficients, but these correlations did not consider the effect of the packing type and the mass transfer driving force on the mass transfer coefficient. This paper presents the heat and mass transfer as calculated from the experimental measurements. The results from the experimental data were used to develop a new mass transfer coefficient including new parameters. The developed correlation is used along with Merkel’s theoretical model to predict the ceramic tower air and water outlet conditions. 2. Experimental setup The tested cooling tower is an induced draft counter flow type. The schematic diagram of the tower is shown in Fig. 1. The tower cross sectional area is 0.64 m2, the total height of the tower is 2 m and the filling portion is 0.8 m. Burned clay bricks were used as the packing material with a maximum number of 12 layers each consisting of 18 bricks. The brick dimensions are 235 · 120 · 64 mm, and its void fraction is 0.4. Water distributors were used to distribute the water uniformly over the packing. An axial fan was fixed on the top of the tower to extract the air from the bottom of the tower. Two pumps were used to circulate the hot water over the packing in a counter manner to the air flow. Before each experiment, the mains water was heated by solar collectors and stored in the tank. The water was allowed to re-circulate through the solar collectors to obtain the desired water temperature. The flow
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2037
Fig. 1. Schematic diagram for the tested ceramic cooling tower.
Table 1 Measuring devices specifications Device
Type
Accuracy
Operative range
Fluid
Sling psychrometer Thermometer Flowmeter Anemometer
Hand Ordinary Rotameter Vane
0.1 C 0.1 C 0.06 l/s 5% of measured air flow rate
0–60 C 0–100 C 0–0.4 l/s 0–5 m/s
Air (DB & WB) Water and air Water Air
regulating valve was adjusted and the water and air flow rates were measured. During the experiment, the hot water was distributed uniformly over the filling material. The axial fan extracts the air from the bottom of the tower in a counter manner to the water flow. The temperatures measurements were taken after allowing enough time for steady state readings. The inlet air and water temperatures were measured before and during the experiment. Three sets of experiments were performed for different heights of packing (0.77, 0.7 and 0.63 m). For each height, the experiments were performed for different water to air flow ratios, (1.13, 0.96, 0.8 and 0.7). The inlet water temperature was varied for each liquid to air flow rate ratio (42.5, 40, 38 and 35 C). The measurements during the experiment are shown in Fig. 1. The specifications of the different measuring devices are shown in Table 1. The rotameter was calibrated using the weighing cylinder method, ASME Standard [19]. The uncertainties of the experimental parameters are shown as error bars in the discussion figures. 3. Cooling tower theory When air flow passes a wetted surface there is a transfer of sensible and latent heat. If there is a difference in temperature between the air and the wetted surface, heat will be transferred. If there is a difference in the partial pressure of water vapor in the air and that of the water, there will be a mass transfer. This transfer of mass causes a thermal energy transfer because if some water evaporates from the water layer, the latent heat of this vaporized water will be supplied to the air. The concept of enthalpy potential is a very useful one in quantifying the transfer of heat (sensible and latent) in those processes and components where there is a direct contact between the air and water.
2038
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
The expression for transfer of the total heat dqt through a differential area dA is expressed by Stoecker [20]: dqt ¼
hc dA ðhi ha Þ Cp m
ð1Þ
The name of enthalpy potential originates from the above equation because the potential for the transfer of the sum of the sensible and latent heats is the difference between the enthalpy of the saturated air at the wetted surface temperature hi and the enthalpy of the air stream ha. The rate of heat removed from the water is equal to the rate gained by the air, so the following expression can be written: dqt ¼ ma dha ¼ 4:19mw dt
ð2Þ
4. Heat and mass transfer coefficients calculation The heat transfer coefficient can be calculated by equating Eqs. (1) and (2) and rearranging: Z out hc A dt ¼ 4:19 C p m mw hi h a in However, A = aV and V = SZ, so Eq. (3) can be written as: Z out hc aZ dt ¼ 4:19 C p m m0w h ha i in
ð3Þ
ð4Þ
The relation between the heat and mass transfer coefficients is expressed by Reynold’s analogy [21]: hc 2 ¼ Le3 K xCp m
ð5Þ
It is found that in most cases of air–water contact, the Lewis number Le can be considered to be unity as a good approximation [22]: hc ¼ Kx Cp m By substituting Eq. (6) in Eq. (4), the mass transfer coefficient can be expressed as: Z out K x aZ dt ¼ 4:19 0 mw hi ha in
ð6Þ
ð7Þ
The integration of Eq. (7) is solved numerically by dividing the packed height into small segments starting from the bottom to the top of the tower. 5. Results and discussion The mass transfer coefficient found from the experimental data and the existing correlations were depicted graphically, along with the design variables. The heat and mass transfer coefficients are related by Reynold’s analogy, so the factors that influence the mass transfer coefficient also affect the heat transfer coefficient. As shown in Fig. 2, the mass transfer coefficient increased with the increase of the water to air flow rate ratio. However, it can be observed that there is some degree of difficulty in the mass transfer when a high water to air flow rate was employed. The increase of the mass transfer coefficient with the water to air flow rate ratio gave good agreement with the previous correlations. It can be observed that the Thomas and Houston [15] values are closer than those of Leburn and Silva [18], but there is a big deviation between the experimental values and those obtained by their correlations. The mass transfer coefficient increased when the inlet water temperature increased from 35 to 38 C as shown in Fig. 3, but it decreased when the water temperature was raised above 38 C (from 38 to 42.5 C). This is mainly because the driving force increases with the increase of the inlet water temperature and a greater
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2039
Fig. 2. Influence of liquid to air flow rate on mass transfer.
Fig. 3. Influence of inlet water temperature on mass transfer.
heat and mass transfer occurs, but a higher outlet water temperature was obtained by continued increasing of the inlet water temperature. This is reflected as a decrease in the mass transfer coefficient. The mass transfer coefficient decreased with the increase of the inlet air enthalpy as shown in Fig. 4. This is due to the decrease in the driving force, which is reflected as a decrease in the mass transfer coefficient.
Fig. 4. Influence of inlet air enthalpy on mass transfer.
2040
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
In fact, the correlations developed by Thomas and Houston [15], Lowe and Christie [16] and Leburn and Silva [18] are functions of the air and water flow rate only. They did not consider the effect of the water temperature and the weather conditions on the mass transfer coefficient in addition to the packing type. The heat and mass transfer coefficients calculated from the previous correlations will remain constant with the variation in the air and water temperatures. Therefore, a big deviation was found between the calculated heat and mass transfer coefficient values and those obtained by these correlations. From the discussion, it can be found that the factors that have a greater effect on the heat and mass transfer coefficients are: the water to air flow rate ratio; the inlet water temperature and the inlet air enthalpy. 6. Correlation development Developing a correlation for the mass transfer coefficient is necessary to predict the packing height and the outlet conditions from the cooling tower. The factors found to have the greatest effect on the gas phase mass transfer coefficient are: the water and air flow rates; the inlet air and water conditions; the packing volume and equivalent diameter and the diffusion coefficient of water in air. K x a ¼ f ða; d eq ; qv ; Dv ; m0w ; m0a ; ha ; hi Þ
ð8Þ
The Buckingham Pi method was employed to obtain the pertinent dimensionless groups [23]: ! d 2eq p1 ¼ K x a Dv qv G
p2 ¼
m0w m0a
ð9Þ
ha p3 ¼ hi d 2eq Kxa Dv qv
!
ha m0w ; ¼f hi m0a
The mass transfer correlation obtained from the dimensional analysis is given by: ! a 0 b d 2eq ha mw K xa ¼c 1 Dv qv hi m0a
ð10Þ
The term ð1 hhai Þ represents the driving force (hi ha), which measures the degree of difficulty of the mass transfer. The experimental data of this study were employed along with a curve fitting computer program to obtain the constants of Eq. (10). ! 0:27 0 0:69 d 2eq ha mw K xa ð11Þ ¼ 4:62 1 Dv qv hi m0a The heat transfer coefficient can be predicted using Reynold’s analogy (Eq. (7)) hc a ¼ K xa Cp m The deviation between the predicted values and the experimental data is shown in Fig. 5. The mass transfer correlation can be predicted within an error of ±10%. This correlation can be used to estimate the height of the burned clay filling portion by rearranging Eq. (7).
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2041
Fig. 5. Relation between experimental and predicted mass transfer coefficient.
7. Modeling and predictions Fig. 6 shows a differential volume of a counter flow cooling tower. For the finite difference model, the tower fill height Z is divided into small segments, dZ, and the mass and energy balances are solved for each segment from the bottom to the top of the tower. The governing equations that describe the changes in air humidity, air temperature and water temperature across a segment are given below. A detailed derivation of these equations is given by Treybal [21]. 7.1. Change in air temperature across the segment The change in air temperature across the segment is obtained by applying an energy balance on the segment interface, control volume (I) in Fig. 6(b). hc adZðti ta Þ ¼ m0a C p m dta ð12Þ dta hc a ¼ 0 ðti ta Þ. ma dZ
mw tw
ma,o mw,i
ma + dma ta + dta ωa + dω a
n n-1 Water Air
Z 3 2 1
ti wi
II
dZ I
III INTERFACE
ma,i
mw,o ma ta
mw - dmw tw - dtw (a)
ωa
(b)
Fig. 6. Packed Tower: (a) tower Overview, (b) differential segment.
2042
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
7.2. Change in air humidity across the segment The change in air humidity is obtained from the mass balance on the segment, control volume (III) in Fig. 6(b) K x adZðxi xa Þ ¼ m0a dxa dxa K x a ¼ 0 ðxi xa Þ ma dZ
ð13Þ
Kxa and hca can be calculated by using the correlation (Eq. (11)) and Reynold’s analogy (Eq. (6)) ! 0:27 0 0:69 d 2eq ha mw ¼ 4:62 1 Kxa Dv qv hi m0a hc a ¼ K x a C p m 7.3. Change in water temperature across the segment By applying an energy balance across the segment, control volume (III) in Fig. 6(b) ma dha ¼ mw C p w dtw dtw ma dta dxa ¼ þ ðC p v ta þ kÞ ðC p a þ xa C p v Þ dZ mw C p w dZ dZ
Fig. 7. Relation between experimental and predicted tower outlet temperatures.
ð14Þ
E. Elsarrag / Energy Conversion and Management 47 (2006) 2034–2043
2043
A computer program was written to perform the finite difference analysis with the fill height Z divided into 1000 segments to solve Eqs. (12)–(14), and the mass and energy balances are solved for each segment. Fig. 7 shows the predicted outlet air temperature, air humidity and water temperature. The outlet air and water temperatures were predicted with a maximum error of ±5%. 8. Conclusions Several field tests using different variables were performed for an induced draft cooling tower using burned clay bricks as the fill material. It was found that the factors affecting the heat and mass transfer coefficients are: the water to air flow rate ratio; the inlet water temperature and the inlet air enthalpy. The previous correlations found in the literature could not predict the mass transfer coefficient for the tested tower. A mass transfer coefficient correlation was developed, and new variables were defined. This correlation can predict the mass transfer coefficient within a maximum error of ±10%. The developed correlation was used along with theoretical modeling to predict the cooling tower outlet conditions. The model with the correlation showed good predictions of the outlet water and air temperatures conditions within an error of ±5%. References [1] Webb RL, Villacres A. Algorithms for performance simulation of cooling towers, evaporative condensers, and fluid coolers. ASHRAE Trans 1984;90(2):416–58. [2] Jaber H, Webb RL. Design of cooling towers by the effectiveness-NTU method. ASME J Heat Transf 1989;111(4):837–43. [3] Merkel F. Verdunstungshuhlung. Zeitschrift des Vereines Deutscher Ingenieure (VDI) 1925;70:123–8. [4] Braun JE, Klein SA, Mitchell JW. Effectiveness models for cooling towers and cooling coils. ASHRAE Trans 1989;95(2):164–74. [5] Osterle F. On the analysis of counter-flow cooling towers. Int J Heat Mass Tran 1991;34(4/5):1313–6. ¨ nsal M. Computational analysis for sizing of cooling towers. In: Proceedings of the third national refrigeration and [6] So¨ylemez MS, U air conditioning congress, Adana, Turkey.1994. p.117–26. ¨ nsal M, Varol A. An analysis for sizing of cooling towers. In: Proceedings of the first national refrigeration and air conditioning [7] U congress, Adana, Turkey.1990. p. 52–6. [8] El-Dessouky HTA, Al-Haddad A, Al-Juwayhel F. A modified analysis of counter flow cooling towers. ASME J Heat Transf 1997; 119(3):617–26. [9] Bernier MA. Cooling tower performance: Theory and experiments. ASHRAE Trans 1999;100(2):114–21. [10] Nimr MA. Modeling the dynamic thermal behavior of cooling towers containing packing materials. Heat Transf Eng 1999;20(1): 91–6. [11] Jameel UK, Yaqub M, Zubair SM. Performance characteristics of counter flow wet cooling towers. Energ Convers Manage 2003; 44:2073–91. [12] Fisenko SP, Brin AA, Petruchik AI. Evaporative cooling of water in a mechanical draft cooling tower. Int J Heat Mass Tran 2004; 47:165–77. [13] So¨ylemez MS. On the optimum performance of forced draft counter flow cooling towers. Energ Convers Manage 2004;45:2335–41. [14] Kloppers JC, Kro¨ger DG. The Lewis factor and its influence on the performance prediction of wet-cooling towers. Int J Therm Sci 2005;44:879–84. [15] Thomas WJ, Houston P. Simultaneous heat and mass transfer in cooling towers. Brit Chem Eng 1959;160:217. [16] Lowe HJ, Christie DG. Heat transfer and pressure drop data on cooling tower packings, and model studies of the resistance of natural draft towers to air flow. Inst Mech Eng (Steam Group) Symposium on Heat Transfer 1962;113:933. [17] Jorge F, Armando CO. Thermal behavior of closed wet cooling towers for use with chilled ceilings. Appl Therm Eng 2000;20:1225–36. [18] Lebrun J, Silva CA. Cooling tower—model and experimental validation. ASHRAE Trans 2002:751–9. [19] ASME. Measurement of liquid flow in closed conduits by weighing method. American Society of Mechanical Engineers; 1988. [20] Stoecker WF, Jones JW. Refrigeration and air conditioning. Singapore: McGraw-Hill; 1985. [21] Treybal RE. Mass transfer operations. New York: McGraw-Hill; 1981. [22] Kern DQ. Process heat transfer. New York: McGraw-Hill; 1997. [23] Panton RL. Incompressible flow. New York: John Wiley & Sons; 1984.