MERKEL S METHOD FOR DESIGNING INDUCED DRAFT COOLING TOWER

INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 6480(Print), ISSN 0976 6499(Online), AND TECHNOLOGY Volume 6, Issue 2, February (IJARET) (2015), pp. 63-70 IAEME ISSN 0976-6480 (Print) ISSN 0976-6499 (Online) Volume 6, Issue 2, February (2015), pp. 63-70 IAEME: www.iaeme.com/ IJARET.asp Journal Impact Factor (2015): 8.5041 (Calculated by GISI) www.jifactor.com IJARET I A E M E MERKEL S METHOD FOR DESIGNING INDUCED DRAFT COOLING TOWER Parin Shah 1 Nishant Tailor 2 1,2, Department of Chemical Engineering, Institute of Technology, Nirma University, Ahmedabad, Gujarat, INDIA ABSTRACT In general, cooling towers are used to dissipate process waste heat into the atmosphere. In this paper, induced draft cooling tower has been designed by simplified merkel s method. The design of cooling tower is based on Merkel s method. The tower characteristic is determined by the ratio of range and log-mean-enthalpy difference. Optimization of the operating conditions for cooling tower applications in cooling water is extremely significant in order to get the most energy efficient operating point for these systems. A simple algebraic formula is used to calculate the optimum water-to-air flow rate. Merkel s method is the most widely accepted theory for cooling tower calculations. It combines equations for heat and water vapor transfer. The objective of this paper is to present the design procedure of counter flow cooling towers in a simplified manner Keywords: Cooling Tower; Merkel s Method; Optimization; Tower Characteristic 1. INTRODUCTION Cooling towers are widely used to dissipate process waste heat into the atmosphere. The interaction of water and air in cooling tower may be counter or cross current. In counter flow cooling towers, heat and mass transfer takes place between a falling liquid film and the air stream moving counter currently. Film type fills are used in counter flow cooling towers. Drift eliminators are provided at the top of the tower to avoid drift losses. Supply of fresh water is required to compensate blow-down losses, evaporation losses and drift losses. The transfer of heat from water to air takes place by convection and through evaporation of water. Merkel s method is the most widely accepted theory for cooling tower calculations. It combines equations for heat and water vapor transfer. The objective of this paper is to present the design procedure of counter flow cooling towers in a simplified manner. 63

NOMENCLATURE a surface area per unit volume (m -1 ) C p,a specific heat of saturated air, (kj/kg) C w specific heat of water, (kj/kg K) D distance between cooling tower packing, (mm) e height of roughness element, (mm) G air flow rate (kg/sec) h fg latent heat of evaporation of water vapor, (kj/kg) H s enthalpy of saturated air at local water temperature, (kj/kg) H s1 enthalpy of saturated air at outlet, (kj/kg) H s2 enthalpy of saturated air at inlet, (kj/kg) H a enthalpy of local air stream, (kj/kg) H a1 enthalpy of inlet air, (kj/kg) H a2 enthalpy of outlet air, (kj/kg) H 1 inlet enthalpy difference, (kj/kg) H 2 outlet enthalpy difference, (kj/kg) δh Enthalpy correction factor, (kj/kg) K mass transfer coefficient, (kg/m 2 sec) L water flow rate, (kg/sec) P ambient pressure, (kpa) P distance between repeated ribs, (mm) p pitch of packing, (mm) T w mean water temperature, (K) [= (T w,i + T w,o ) / 2) T w,i inlet water temperature, (K) T w,o outlet water temperature, (K) V volume of packing, (m 3 ) θ angle of inclination of cross ribbing with the horizontal, ( ) 2. PROCEDURE FOR ESTIMATING THE SIZE OF COOLING TOWER Before designing a cooling tower, it is very important to determine the range and approach. Approach varies with the entering air wet bulb temperature, flow rate of water and the heat load. The first step in design a cooling tower is to choose the design conditions like inlet water temperature, outlet water temperature, water flow rate and inlet air wet bulb temperature. 2.1 Calculation of Merkel integral The Merkel s method is the most widely used method for cooling tower design. The equation for Merkel s method is: (1) 64

Where K is the mass transfer coefficient, a is the surface area per unit volume of the packing, V is the volume of the packing. H s is the enthalpy of saturated air at local water temperature and H a is the enthalpy of local air stream.the conventional method to calculate the Merkel integral (KaV/L) makes use of an enthalpy-temperature diagram (Fig. 1). The values of H s at different temperatures are obtained from Perry s Chemical Engineers Handbook. The enthalpy of inlet air H a1 is taken at prevailing air wet bulb temperature. The amount of heat lost by water is equal to the enthalpy rise in air. The heat balance equation is written as: C w t w L = H a G (2) Where C w is the specific heat of water, t w is the temperature of water stream, L is the flow rate of water and G is the flow rate of air. H a is written as: Therefore, the enthalpy of outlet air H a2 is calculated as: H a = C w t w (L / G) (3) H a2 =H a1 + (L / G)C w (T w,i - T w,o ) (4) It is observed in Fig.1 that the curve of H a against the water temperature is a linear line making an angle of α with the horizontal. The value of tan α is equal to the ratio of flow rate of water to the flow rate of air [1]. Fig.1. Enthalpy-Temperature diagram [1] The curve for 1 / (H s H a ) is plotted as a function of the local water temperature (Fig.2). The value of tower characteristic (KaV/L) is obtained by determining the area under the curve in Fig.2. 65

Fig.2. 1/(H s H a ) plotted against local water temperature [1] This method of calculating the tower characteristic (KaV/L) is tedious and time consuming. In place of this method, following simplified may be useful. The curve for H s in Fig. 1 was modified using a straight line drawn in the manner shown in Fig. 3 Fig.3. Approximating the curve for H s with a straight line [1] 66

The position of this line was defined by introducing the correction factor δh, where δh= (5) H s1 and H s2 are the values of H s at the outlet and inlet respectively, and H sm is the value of H s at the mean water temperature. The tower characteristic was calculated from the following equation: where H m is the log-mean-enthalpy difference, defined as (6) (7) where H 1 and H 2 are inlet and outlet enthalpy differences between H s and H a [1]. 3.1.1 Case Study A cooling tower is used to cool 50 C water to yield an approach temperature of 5 C when the entering air wet bulb temperature is 25 C. The L/G ratio was considered as 1.25. The Merkel integral was calculated by conventional method as well as by equation (6). For an approach temperature of 5 C and a wet bulb temperature of 25 C, the temperature of the water at the cooling tower outlet is 30 C. Hence the temperature range is 50 30 = 20 C. The enthalpy of air stream H a increases linearly with the water temperature, and the total increase of enthalpy H is evaluated using Eqn as: H = (L/G) C w T w = 1.25 4.186 20 = 104.65 kj/kg. Since the air enters the tower at a wet bulb temperature of 25 C, the air enthalpy at the air inlet is 94.38 kj/kg, while that at the air outlet is 94.38 + 104.65 = 199.03 kj/kg. For numerical integration for the tower characteristic, refer table 1. Water temperature, T w, ( C) Table 1: Numerical integration for tower characteristic Enthalpy at Enthalpy of H T w, air, H s - H a a kj/kg 1 /(H H s (kj/kg) (kj/kg) s - H a ) Average 1 /(H s - H a ) 30 117.84 94.38 23.46 0.0426 35 147.34 120.54 26.80 0.0373 0.0399 40 184.48 146.71 37.77 0.0265 0.0319 45 232.01 172.87 59.14 0.0169 0.0217 50 293.03 199.03 94.00 0.0106 0.0137 0.1072 KaV/L = 4.186 5 0.1072 = 2.24 As a check, the tower characteristic is calculated by the log-mean-enthalpy method. The inlet and outlet enthalpy differences between the H s and H a curves are H 2 = 293.03 199.03 = 94.00 kj/kg; H 1 = 117.84 94.38 = 23.46 kj/kg. The enthalpy correction factorδhis found to be equal to 10.47 kj/kg. H m is calculated using equation (7), H m = 37.94 and the corrected tower characteristic from equation (6) is 2.20 which is within 2% of the value obtained by numerical integration [1]. 67

3.2 Determination of optimum (L/G). Optimization of the operating conditions for cooling tower applications in cooling water is extremely significant in order to get the most energy efficient operating point for these systems. The optimum ratio of flow rate of water to flow rate of dry air can be determined by using the following equation. (8) For a typical cooling tower problem, it is assumed that = 4.181 kj/(kg K), = 1.0035 kj/(kg K), = 2500 kj/kg and = 101.325 kpa. The value of (L/G) opt can also be obtained from the plot of (L/G) opt for different T w (Fig.4) [2]. Fig.4. Variation of optimum L/G values for P = 101.325 kpa [2] 3.3 Determination of packing size The value of V (volume of packing) was obtained from the calculated KaV/L. For this the values of K (mass transfer coefficient) and a (surface area per unit volume) were needed. Different types of fills have different values of K and a. Now-a-days cooling tower manufacturers are using PVC packing with smooth and cross ribbing. Manufacturers treat such data as proprietary. Experiments conducted by Goshayshi H.R. and Missenden J.F. [3] were helpful to obtain the values of K and a for different types of PVC packings. The values of a was obtained from Table 2. 68

Fig.5. PVC packing used in cooling tower [3]. Table 2: Characteristics of different type of packings [3] Type of a p D Type of θ Packing corrugation (m -1 p / D P / e ) (mm) (mm) surface ( ) C1 Sinusoidal 200 70 50 1.40 Rough 1 45 C2 Sinusoidal 250 65 40 1.65 Rough 3 0 C3 Triangular 300 45 40 1.13 Smooth - - C4 Triangular 350 50 35 1.43 Rough 4 0 C5 Hexagonal 470 40 25 1.32 Rough 5 0 C6 Sinusoidal 500 30 20 1.50 Rough 4 45 C7 Triangular 500 30 20 1.50 Rough 5 0 The correlations for K were also determined experimentally. The values of K for different (L/G) were obtained for Fig. 7. Having determined the values of K and a, the value of V was determined. By fixing the cross-sectional area, the height of packing was calculated. Fig.6. Heat transfer characteristic of packing with different spacing and surface roughness [3] 69

3.4 Experimental work and conclusion Based on the above integrated method, a lab scale induced draft cooling tower was designed and fabricated. The optimum value of L/G = 1.75 was determined from the experimental results of M. S. Soylemez. The values of K and a for the PVC fills used came out to be 0.06 kg/(m 2 sec) and 200 m -1 respectively. The average dry and wet bulb temperatures of ambient air were 33 C and 23 C respectively. It was measured using a digital thermo-hygrometer. The inlet water temperature was 50 C and the approach was 5 C hence giving a temperature range of 22 C. Later the tower was operated at different (L/G) ratios and the performance was evaluated. When the temperature of the entering and leaving cooling water is constant, the thermal efficiency of the cooling tower was controlled by the mass rate ratio of water and air. The larger the mass rate ratio of water and air is, the lower the thermal efficiency is, that is, the evaporation rate of the moisture is small. When the thermal load increases, it is needed to increase the air mass rate to maintain the thermal efficiency constant. This is demonstrated in Table 3. The air flow rate was varied by installing a fan regulator. The temperature of water was measured using a thermocouple attached to a digital temperature indicator. A vane anemometer was used to measure the air velocity which was multiplied with the cross sectional area and air density to obtain the mass flow rate of air. REFERENCES Table 3: Performance evaluation of cooling tower L/G Range Approach Efficiency 1.25 23 4 85.18 % 1.75 21 6 77.78 % 2.25 18 9 66.67% 1. Frass AP. Heat Exchanger Design. Wiley Interscience [chapter 19 p. 383-400] 2. Soylemez MS. On the optimum performance of forced draft counter flow cooling towers. Energy Conservation and Management 2004; 45: 2335-41. 3. Goshayshi HR, Missenden JF. Investigation of cooling tower packings in various arrangements. Applied Thermal Engineering 2000; 20: 69-80. 4. Li KW, Priddy AP. Power Plant System Design. Wiley; 1985 [chapter 8 p.326] 5. Sowmya G, S.Nagendra Prasad and N.Kumar, Optimal Placement Of Custom Power Devices In Power System Network For Load And Voltage Balancing International Journal of Electrical Engineering & Technology (IJEET), Volume 5, Issue 8, 2014, pp. 148-160, ISSN Print : 0976-6545, ISSN Online: 0976-6553. 6. Sachin Kulkarni and Prof A. V. Kulkarni, Static and Dynamic Analysis of Hyperbolic Cooling Tower International Journal of Civil Engineering & Technology (IJCIET), Volume 5, Issue 9, 2014, pp. 9-26, ISSN Print: 0976 6308, ISSN Online: 0976 6316. 7. Esmaeil Asadzadeh, PROF. Mrs. A. RAJAN, Mrudula S. Kulkarni and SahebaliAsadzadeh, Finite Element Analysis For Structural Response of RCC Cooling Tower Shell Considering Alternative Supporting Systems International Journal of Civil Engineering & Technology (IJCIET), Volume 3, Issue 1, 2014, pp. 82-98, ISSN Print: 0976 6308, ISSN Online: 0976 6316. 70