MERKELS METHOD FOR DESIGNING INDUCED DRAFT COOLING TOWER

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online), Volume 6, Issue 2, February (2015), pp. 63-70 © IAEME
63
MERKEL’S METHOD FOR DESIGNING INDUCED
DRAFT COOLING TOWER
Parin Shah1
Nishant Tailor2
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.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
AND TECHNOLOGY (IJARET)
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

64
NOMENCLATURE
a surface area per unit volume (m-1
)
Cp,a specific heat of saturated air, (kJ/kg)
Cw 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)
hfg latent heat of evaporation of water vapor, (kJ/kg)
Hs enthalpy of saturated air at local water temperature, (kJ/kg)
Hs1 enthalpy of saturated air at outlet, (kJ/kg)
Hs2 enthalpy of saturated air at inlet, (kJ/kg)
Ha enthalpy of local air stream, (kJ/kg)
Ha1 enthalpy of inlet air, (kJ/kg)
Ha2 enthalpy of outlet air, (kJ/kg)
∆H1 inlet enthalpy difference, (kJ/kg)
∆H2 outlet enthalpy difference , (kJ/kg)
δh Enthalpy correction factor, (kJ/kg)
K mass transfer coefficient, (kg/m2
sec)
L water flow rate, (kg/sec)
P ambient pressure, (kPa)
P distance between repeated ribs, (mm)
p pitch of packing, (mm)
Tw mean water temperature, (K) [= (Tw,i+ Tw,o) / 2)
Tw,i inlet water temperature, (K)
Tw,o outlet water temperature, (K)
V volume of packing, (m3
)
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)

65
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. Hs is the enthalpy of saturated air at local water temperature and Ha 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 Hs at different temperatures are
obtained from Perry’s Chemical Engineers’ Handbook. The enthalpy of inlet air Ha1 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:
Cw∆twL = ∆HaG (2)
Where Cwis the specific heat of water, tw is the temperature of water stream, L is the flow rate of
water and G is the flow rate of air. ∆Hais written as:
∆Ha= Cw∆tw(L / G) (3)
Therefore, the enthalpy of outlet air Ha2 is calculated as:
Ha2 =Ha1 + (L / G)Cw (Tw,i - Tw,o) (4)
It is observed in Fig.1 that the curve of Ha 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 / (Hs – Ha) 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.

66
Fig.2. 1/(Hs – Ha) 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 Hs in Fig. 1 was modified
using a straight line drawn in the manner shown in Fig. 3
Fig.3. Approximating the curve for Hs with a straight line [1]

67
The position of this line was defined by introducing the correction factor δh, where
δh=
(5)
Hs1 and Hs2 are the values of Hsat the outlet and inlet respectively, and Hsmis the value of Hs at the
mean water temperature. The tower characteristic was calculated from the following equation:
(6)
where∆Hm is the log-mean-enthalpy difference, defined as
(7)
where ∆H1and ∆H2 are inlet and outlet enthalpy differences between Hsand Ha [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 Ha increases linearly with the water temperature, and the total increase of
enthalpy ∆H is evaluated using Eqn as: ∆H = (L/G) Cw∆Tw = 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.
Table 1: Numerical integration for tower characteristic
Water
temperature,
Tw, (°C)
Enthalpy at
Tw,
Hs(kJ/kg)
Enthalpy of
air, Ha
(kJ/kg)
Hs - Ha
kJ/kg 1 /(Hs - Ha)
Average
1 /(Hs - Ha)
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 Hs and Ha curves are ∆H2 = 293.03 – 199.03 = 94.00
kJ/kg; ∆H1 = 117.84 – 94.38 = 23.46 kJ/kg. The enthalpy correction factorδhis found to be equal to
10.47 kJ/kg. ∆Hm is calculated using equation (7), ∆Hm = 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].

68
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 Tw (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.

69
Fig.5. PVC packing used in cooling tower [3].
Table 2: Characteristics of different type of packings [3]
Packing
Type of
corrugation
a
(m-1
)
p
(mm)
D
(mm)
p / D
Type of
surface
P / e
θ
(°)
C1 Sinusoidal 200 70 50 1.40 Rough 1 45
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
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]

70
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/(m2
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.
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%
REFERENCES
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.

MERKELS METHOD FOR DESIGNING INDUCED DRAFT COOLING TOWER

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