Dissertation Cover Page

Thermal Performance Analysis of Counterflow

Cooling Tower by Merkel’s Method

DE ZG628T: Dissertation

By

Name: Alomoy Banerjee

Student ID: 2018HT30501

Dissertation work carried out at

Paharpur Cooling Towers Ltd, Kolkata

Submitted in partial fulfillment of M-Tech Design Engineering

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE

PILANI (RAJASTHAN)

December 2020
Dissertation Title Page

Thermal Performance Analysis of Counterflow

Cooling Tower by Merkel’s Method

DE ZG628T: Dissertation

By

Name: Alomoy Banerjee

Student ID: 2018HT30501

Dissertation work carried out at

Paharpur Cooling Towers Ltd, Kolkata

Submitted in partial fulfillment of M-Tech Design Engineering

Under the Supervision of

Anindya Sundar Giri
Assistant Manager- Paharpur Cooling towers Ltd Kolkata

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE

PILANI (RAJASTHAN)

December 2020
Certificate from the Supervisor

CERTIFICATE

This is to certify that the Dissertation entitled Thermal Performance

Analysis of Counterflow Cooling Tower by Merkel’s Method and

submitted by Alomoy Banerjee having ID-No. 2018HT30501 for the partial

fulfillment of the requirements of MTech in Design Engineering degree of

BITS embodies the bonafide work done by him/her under my supervision.

Signature of the Supervisor

Place: Kolkata

Date: 01/12/2020
Anindya Sundar Giri
Assistant Manager- Paharpur Cooling towers Ltd Kolkata
 Birla Institute of Technology & Science, Pilani
Work-Integrated Learning Programmes Division
First Semester 2020-2021

DEZG628T: Dissertation Final Report

ID No. : 2018HT30501

NAME OF THE STUDENT : Alomoy Banerjee

EMAIL ADDRESS : alomoybanerjee@gmail.com

STUDENT’S EMPLOYING : Paharpur Cooling Towers Ltd. Kolkata

ORGANIZATION & LOCATION

SUPERVISOR’S NAME : Aninda Sundar Giri

SUPERVISOR’S EMPLOYING : Paharpur Cooling Towers Ltd. Kolkata

ORGANIZATION & LOCATION

SUPERVISOR’S EMAIL ADDRESS: anindasundar.giri@paharpur.com

DISSERTATION TITLE : Thermal Performance Analysis of Counterflow

Cooling Tower by Merkel’s method

______________________________________________________________________
Abstract

The thermal parameters that directly affect the performance of a cooling tower are water flow rate,
cooling range and wet bulb temperature. Since, evaporative cooling or latent heat transfer is the
primary mode of heat transfer in a cooling tower, the cold water outlet temperature of the system is
limited by the Wet Bulb Temperature (WBT) of the location. WBT of a cooling tower erection site is not
at the control of the manufacturer; hence it is highly likely to be different than the design WBT. Because
of some other technical reasons, cooling range and water flow rate may also be off from design
conditions.

In order to test the cooling tower at varying operational conditions and predict whether, the tower is
giving adequate performance as per requirement, manufacturer-provided performance curves are
referred. These performance curves need to be submitted to the customer during order finalization
process and they follow a standard format as per CTI ATC 105.

In Paharpur Cooling Towers Ltd. performance curves of cooling towers are drawn by extrapolation of
experimental on-site data. However, due to the unavailability of testing all cooling tower models
experimentally, performance data extrapolation has given erroneous results for a few cooling towers in
the past. Non-compliance to performance curves after tower installation, leads to loss of customer
confidence and even attracts penalty at certain instances.

The project, at hand, deals with formulating an analytical model that can accurately predict the
performance of a counterflow cooling tower. The project will be using Merkel’s method of heat transfer
inside the cooling tower to generate the tower demand curves, by Chebychev’s method of integration.
The results obtained from tower demand curves can be used to predict approach at different wet bulb
temperatures. The activity will be repeated for some pre-designated cooling ranges, to predict thermal
performance.

An iterative method needs to be designed to predict the variation of L/G with varying water flow rate.
Literature survey illustrates that with drop in water flow rate air flow will increase, but a strict
mathematical model is yet to be developed that can quantify the variation of L/G.

With the rectified L/G, cooling tower demand curves are to be regenerated to find out the operational
approach. Finally, collating all the data, performance curves are drawn as per CTI-ATC 105.

Signature of the Student

Signature of the Supervisor
Name: Alomoy Banerjee
Name: Aninda Sundar Giri
Date: 30.08.2020
Date: 30.08.2020
Place: Kolkata
Place: Kolkata
 ACKNOWLEDGEMENT

This research was supported by Paharpur Cooling Towers Ltd. I thank my colleagues from
Paharpur Cooling Towers Ltd. who provided insight and expertise that greatly assisted the
research and accelerated the outcome of the project.

I thank Mr. Anindya Sundar Giri, Assistant Manger Paharpur Cooling Towers Ltd. for assistance
with respect to general supervision of the project and thermal site testing of the cooling tower.
I also thank Mr. Varun Swarup Senior VP Paharpur Cooling Towers Ltd for his valuable insights
about the mathematical modeling of the cooling tower performance. He also played a vital role
in convincing the customer to carry out thermal testing at site.

We would also like to show our gratitude to Dr. Kiran D Mali, BITS Pilani for sharing his pearls of
wisdom with us during the course of this research, through his precious comments at several
stages of progress in the report.
 Table of Contents

Chapte Topic Description Page

r No. No.
Introduction 1
1.1 Cooling Tower Classification 1
1 1.2 Cooling Tower Operation 2
1.3 Background of Research 3
1.4 Objective of Research 3
Heat & Mass Transfer in Counterflow Cooling Tower 4
2.1 Scope of Work 4
2 2.2 Merkel Theory of Heat & Mass Transfer 4
2.3 NTU & Tower Characteristic Derivation for Heat & Mass Transfer 5
2.4 Heat & Mass Balance Conservation for Cooling Tower 7
Cooling Tower Demand Curve & Superimposition of Fill Characteristic Curve 9
3.1 Tower Demand & Characteristic-Advent of Black, Brown & Bluebook 9
3 3.2 Basis of Calculation 9
3.3 Limitations 9
3.4 Tower Characteristic Curve 10
Mathematical Modeling of Project-Specific Induced Draft Counterflow Cooling 12
Tower
4.1 Project Specific Inputs 12
4.2 Mathematical Model Description-Chebychev Discretization 12
4.3 Mathematical Modeling of Cooling Tower Performance at design WBT ±8.5 14
4
°C 14
4.4 Mathematical Modeling of Cooling Tower Performance at Cooling Range 15
±20%
4.5 Mathematical Modeling of Cooling Tower Performance at Design Flow rate
±10%
Experimental Data Recording at Site Conditions 19
5.1 Site Testing Types of Cooling Tower 19
5 5.2 The Typical Test Procedure 19
5.3 Project Specific Test Parameters 20
5.4 Data Recorded at Site 20
Conclusion 21
6 6.1 Relevance to Company Work 21
6.2 Future Scope of Work 21
Literature References 22
List of Figures

Fig Fig Description Page No.

No.
1 Schematic of Steam Power plant with cooling tower 1
2 Induced Draft Counterflow Cooling Tower 2
3 Enthalpy Balance Diagram of Cooling Tower 5
4 Heat Balance Diagram 7
5 Plot of enthalpy vs. exit air temperature 8
6 Plot of NTU vs. L/G 10
7 Plot of NTU vs. L/G superimposed with Fill Characteristic 11
8 VBA Code to generate data for Cooling Tower Demand Curve 13
9 Data for Cooling Tower Demand Curve at Design Conditions 13
10 Cooling Tower Demand Curve at Design Conditions 13
11 VBA Code to generate data for Cooling Tower performance curve 14
12 Iterative Computation of L/G at 90% flow rate 16
13 Iterative Computation of L/G at 110% flow rate 17

List of Tables

Table Table Description Page No.

No.
1 Project-Specific Cooling Tower Design Parameters 12
2 Chebychev Method of Discretization 12
3 Cold Water Temperature at 100% flow and WBT ±8.5 °C and Cooling Range 15
±20%
4 Cold Water Temperature at 90% flow and WBT ±8.5 °C and Cooling Range 17
±20%
5 Cold Water Temperature at 110% flow and WBT ±8.5 °C and Cooling Range 18
±20%
6 Cooling Tower Test Specific Conditions 20
7 Experimental vs. Predicted CWT dataset 1 20
8 Experimental vs. Predicted CWT dataset 2 21
9 Experimental vs. Predicted CWT dataset 3 21
 Chapter 1 – Introduction

1.1 Cooling Tower Classification

Heat is discharged in power generation, refrigeration, petrochemical, steel, processing and many other
industrial plants. In many cases, this heat is discharged into the atmosphere with the aid of a cooling
tower. Figure 1 shows an example of the application of a cooling tower in a simple steam power plant.
Heat is discharged into the atmosphere by the cooling tower via a secondary cycle with water as the
process fluid.

Fig 1- Sample Steam Power plant with cooling tower

Wet-cooling towers are considered in this study. Wet-cooling takes place when the water is in direct
contact with the air. Cooling is the result of sensible and latent heat transfer where the latent heat
transfer component generally dominates. Cooling towers can be classified according to the type of draft
through the tower. The draft in natural draft towers is established by the buoyancy of the hotter air
inside the tower shell compared to the cooler ambient air on the outside of the tower shell. Draft in
mechanical draft towers is established by fans that force or draw air through the towers, usually
referred to as forced draft and induced draft respectively.
A further distinction between cooling towers is whether they are counterflow or cross flow towers. In a
cross flow tower the fill is usually installed at some angle to the vertical to make provision for the inward
motion of the droplets due to drag forces caused by the entering cooling air. Less pumping power is
needed for modern counterflow towers, as the towers are generally not as high as cross flow cooling
towers. Icing and wind effects are more prevalent in cross flow towers than in counterflow towers.

When a single cooling tower incorporates a wet and a dry section, this is also sometimes referred to as a
hybrid system. Hybrid cooling towers are generally used for plume abatement and in regions where
water is relatively scarce.

1.2 Cooling Tower Operation

Hot water is sprayed over the fill material. The spray zone can account for as much as 25% of the total
heat transfer in a tower. It is very important that the water is distributed uniformly over the fill.
Maldistribution of liquid flow is often cited as a cause of reduced performance in packed towers.

A poor water flow distribution over the fill is commonly experienced at water flow rates in excess of
around 4.2 kg/m2s. If the flow rate is increased beyond this value, the water cascades in thick streams
instead of falling as a spray, so that the effective area is reduced. This condition is called flooding. On the
other hand, if the water flow rate drops to about 0.8 kg/m 2s or less, surface tension causes the water
flow to channel. This gives a poor water distribution, and hence a marked drop in performance.

Fig 2- Induced Draft Counterflow Cooling Tower

The fill increases the transfer area by breaking the water up into smaller droplets or by forming a thin
film depending on the type of fill. The fill also increases the contact time between the water and the air.
The factors influencing the choice of fill are its heat transfer performance, quality of water, pressure
drop, cost and durability. Over the last 30 years, there has been a gradual change in the types of fill used
in process cooling towers. The most dramatic change has been the introduction of film fills that provide
significantly higher thermal performance through the increase of water-to-air contact area and a
reduction in pressure drop. This results in a reduction in capital expenditures, lower operating costs and
smaller tower footprint. However, in many applications, due to poor water quality or potential process
contamination, these benefits are forfeited and the older splash fill technology is still used.

From the fill the water falls unobstructed through the rain zone into the water basin. A significant
amount of heat and mass transfer takes place in the rain zone. The drift eliminator is situated on the air
downstream side of the fill as shown in figure 2. Drift refers to the small droplets of circulating water
that are carried out of the cooling tower by the exhaust air. Inertial impaction separators, known as drift
eliminators, are used to strip the water droplets from the warm exhaust air. In this type of separator,
the two-phase exhaust flow is forced to abruptly change direction. This causes the dense drift droplets
to hit the eliminator walls and become trapped inside the cooling tower. Drift eliminators have evolved
from early single-pass wood lath to multiple-pass wood and then to sinusoidal-wave shapes. These were
followed by combinations of sinusoidal and honeycomb shapes. Currently, various styles of cellular drift
eliminator packs are constructed from thermoformed sheets of polyvinylchloride (PVC). The
performance of these drift eliminator packs is measured by two criteria: droplet collection efficiency and
system pressure loss caused by the eliminator pack. To achieve peak operating efficiency of the overall
cooling tower system, it is desirable that the system pressure loss from the eliminators be minimized.

1.3 Background of Research

Discharge of process heat is an important technical challenge in power plants, oil refinery, refrigeration,
steel, sugar mills, processing, HVAC and many other industrial plants. In almost all these cases, this heat
is discharged into the atmosphere with the help of a cooling tower. In a few of these cases, heat
discharge takes place via a secondary cycle with water as the process fluid. The present scope of study
involves wet cooling towers. Wet-cooling takes place by direct contact of air and water. The resultant
cooling is the summation of sensible and latent heat transfer where the latent heat transfer takes the
dominant role.
Cooling towers can be classified according to the type of draft through the tower. The draft in Natural
Draft Cooling Towers (NDCT) is established by the chimney effect of the hotter air inside the tower shell
compared to the cooler ambient air on the outside of the tower shell. Draft in mechanical draft towers is
established by motor driven fans that force or draw air through the towers, usually referred to as forced
draft and induced draft respectively. Cooling Towers can also be classified according to the direction of
flow. In a cross flow tower the water and air flow direction is perpendicular to each other and the fill is
usually installed at some angle to the vertical to make provision for the inward motion of the droplets
because of drag forces caused by the entering cooling air. Counterflow cooling towers on the other hand
have water and airflow direction directly opposite to each other. Less pumping power is needed for
modern counterflow towers, as the towers are generally not as high as cross flow cooling towers. Icing
and wind effects are more prevalent in cross flow towers than in counterflow towers.

The thermal parameters that directly affect the performance of a cooling tower are water flow rate,
cooling range and wet bulb temperature. Since, evaporative cooling or latent heat transfer is the
primary mode of heat transfer in a cooling tower, the cold water outlet temperature of the system is
limited by the Wet Bulb Temperature (WBT) of the location. The project, to be undertaken deals with
thermal performance of Induced Draft Counterflow cooling tower. In order to capture all three thermal
performance parameters of a cooling tower, into a standard plot, cooling tower performance curve is
published by the product manufacturer. The purpose of having thermal performance curves of cooling
towers is to gauge the expected product performance at varying WBT, water flow rate and cooling
range.
1.4 Objective

 The objective of the present research project is to develop an analytical model to predict the
thermal performance of an induced draft counterflow cooling tower as per CTI ATC 105.
 Evaluation of cooling tower performance by using Merkel’s analysis and e-NTU analysis.
 The analytical model can solve a long-standing issue of the company to predict cooling tower
performance accurately, before experimentally testing the tower’s performance on-site.
 After development of the model, the output data will be tested against experimental data to predict
the accuracy of the model.

Chapter 2- Heat and Mass Transfer in Counterflow Cooling Tower

2.1 Scope of Work

The scope of the present work involves developing a mathematical model to evaluate heat transfer
inside the cooling tower, using the Merkel and e-NTU method by Chebychev’s method of integration.
The cooling tower demand curves thus obtained, from the Kav/L and L/G values serve as an input to the
evaluation of cooling tower performance curves. Another important factor that needs to be considered
in the present scope of work is to evaluate the L/G ratio at changing operational water flow rate. The
ideal model will incorporate all these factors and give predicted cold water performance as output as
per CTI-ATC 105.
Thus the present scope of study deals with developing an analytical thermal model that can accurately
predict cooling tower performance curves. The broader scope of the project is to make the model
universal for all counterflow cooling towers, such that on giving certain tower specific inputs, the same
model can give the necessary output irrespective of cooling tower capacity.

2.2 Merkel Theory of Heat & Mass Transfer

Quite a number of theories have been developed since the early 20th century in an effort to formulate
the heat and mass transfer in cooling towers. The cooling tower may be considered as a heat exchanger
in which water and air are in direct contact with each another. However, the issue with cooling tower is
that there is no acceptable method to accurately estimate the total contact surface between water and
air. Hence, a heat transfer coefficient cannot be determined directly from experimental data or by
known heat transfer theories. The factor of mass transfer further complicates the process. Experimental
tests conducted on the specified equipment designs can be evaluated using accepted theories which
have been developed using dimensional analysis techniques. Similar methods and theories can be used
for thermal design and to predict performance at the operating conditions other than the design point.

The Merkel theory overcame the issue of dual heat & mass transfer by combining the two into a single
process based on enthalpy potential. Dr. Frederick Merkel, the faculty of the Technical College of
Dresden in Germany developed a cooling tower theory for the mass (evaporation of a small portion of
water) and sensible heat transfer between the air and water in a counter flow cooling tower. The theory
considered the mass and energy flows from the bulk water to an intermediate interface, and then from
the interface to the surrounding air mass. The flow crosses both these boundaries, each offering its
 respective resistance resulting in temperature, enthalpy, and humidity ratio gradient. Merkel
demonstrated that the total heat transfer is proportional to the difference between the enthalpy of
saturated air at the water temperature and the enthalpy of air at the point of contact with process
water.
Basic assumptions for the Merkel design of cooling tower are as follows:

 the rate of evaporation of water is 1% of the rate of water flow to the tower
 evaporative cooling of water occurs in the tower

2.3 NTU & Tower Characteristic Derivation for Heat & Mass Transfer

Fig 3- Enthalpy Balance Diagram of Cooling Tower

Let,
L be the design water flow rate (kg/m2s)
Gs be the air rate (kg dry air/m 2s).
Across a differential thickness dz of the bed ,
Temperature of water is decreased by dTL
The enthalpy of air is increased by dH’.
Hence,
Change in enthalpy of water=L.cWL.dTL
Change in enthalpy of air =Gs.dH’
Differential enthalpy balance over dz is

L.cWL.dTL=Gs.dH’…………………………………………. (i)

Enthalpy balance over envelope I,

LcWL (TL-TL1) = Gs (H’-H’1)…………………………………(ii)

This is the operating line for air-water contact.

Enthalpy balance over entire tower (envelope II)
 LcWL (TL2-TL1) = Gs (H2’-H’1)…………………………………(iii)

The equilibrium curve for air-water system on TL-H plane is the plot of enthalpy of saturated air
versus liquid temperature at equilibrium.
Rate of transfer of water vapor to air in the differential volume is

Gz dY '=k Y a(Y i '−Y ' ) ……………………………………………..(iv)

The decrease in temperature of air for sensible heat transfer to water is

−Gz c H dT G=hG adz(T g −T i ) ……………………………………..(v)

Gz dH'=G z cH dT G +G z dY 'λ 0
Gz dH'=−hG adz(T G −T i )+kY 'adz(Y i '−Y ')λ 0 ¿
Gz dH'=k' y adz¿
¿
The height (z) of the packing in the cooling tower is obtained by

dH ' k 'Y a
∫ ( H '−H ' ) G z................................................................(vii )
=
i z Number of gas-enthalpy
transfer units

H' 2
dH '
N tG= ∫ . .. .. . .. .. . .. .. .. . .. .. . .. .. . ..... .. .. . .. .. . .. .. .. . .. .. . .. .. . .. .. . .. ..( viii)
H '1 ( H i '−H ' )

Height of gas-enthalpy transfer units

Gz
H tG= .............................................................................(ix )
k 'Y a
The height of cooling tower packing section (z) is thus expressed as

z=H tG N tG ..........................................................................( x)
Volumetric mass or enthalpy transfer coefficient ( Y k' a
) should be known. Then HtG can be estimated
from given mass flow rate. There is no direct relation available between enthalpy of bulk gas H’ and that
of H’i . So, integral cannot be evaluated analytically. For numerical or graphical evaluation of the integral,
it is important to know the values of interfacial enthalpy (H’ i) for a set of values of H’.
Let, hLa is volumetric heat transfer coefficient on the water side.

Gz dH '=Lc WL dT L=hL a(T L−T Li )

Gz dH '=k Y ' adz( H 'i −H ' )=−h L a(T Li−T L )
H ' i−H ' h L
=− ....................................................( xi)
T Li −T L k ' Y

A point (TL, H’) on the operating line meets the equilibrium line at the point (T Li, H’i)
Substituting
Gz dH '=Lc WL dT L in equation (vi),
LcWL dT L =k Y ' adz(H 'i −H ' ).....................................( xii)
T L0
L dT k' a
∫ ( H ' −H = Y z .. .. . ..... .. .. . .. .. . .. .. . .. .. . .. .. .. ... .. . .. .. .( xiii)
T Li ' ) Lc
i WL
The equation (xiii) is known as the Merkel Equation.
If overall enthalpy transfer coefficient K’ Y is used, differential mass balance equation becomes
Gs dH '=K ' y adz(H *'−H ' )
H*’ is the enthalpy of saturated air at T L(bulk liquid temperature)

H2'
dH ' k'Y a
∫ ( H *'−H = z .. . .. .. . .. .. . .. .. . .. .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. .. . .. .. . .. .. .( xiv )
H '1 ') Gs

This is defined as the overall enthalpy transfer units (N tg).

q=K Y '( H ' i −H ' )=hL (T L−T Li )=K ' Y ( H *'−H ' )
( H *'−H ' )=( H *'−H ' i )+( H ' i−H ' )
q ( H *'−H ' i ) q
=q +
K 'Y h L (T L−T Li ) k Y '
1 ( H *'−H ' i ) 1
= +
K ' Y (T L−T Li ) kY '

Hence the simplified Merkel Equation is given as,

T L0
K 'Y a V dT L
=∫ .. ... ... .... ... ... .... ... .. . .... .. ... ... .... ... ... .... ... .. . .. .. .. . .. ... .... .( xv)
L T L 1 ( H ' i−H ' )
The left hand side of the equation is called “tower characteristic” where, V is active cooling volume/plan
area.
2.4 Heat & Mass Balance Conservation for Cooling Tower

Fig 4- Heat Balance Diagram

Heat in =Heat out

( Heat Waster +Heat air )in =( Heat Waster +Heat air )out
C w L2 t w 2 +Gha1 =C w L1 t w 1+Gha 2 ...........................................( xvi)

The difference in discharge of water at the inlet and outlet may be related by the following equation
where wi represents the specific humidity of the air at inlet and outlet conditions.

L2−L1 =G(w 2 −w1 )

Substituting this in equation (xvi), the expression converts to,

C w L2 t w 2 +Gh a1 =C w {L2−G( w2 −w 1 )}t w 1 +Gha 2

C w L2 (t w 2−tw 1 )=G(h a2 −h a1 )−C w t w 1 G(w 2−w1 )

The 2nd term on the right hand side G (w 2-w1) is ignored to simplify the calculation under the
assumption that the specific humidity at the inlet and outlet of the cooling tower are equal.
Thus the above equation reduces to,

C w L2 (t w 2−tw 1 )=G(h a2 −h a1 )

Thus the enthalpy of exit air is finally expressed as,

L
ha 2 =ha 1 + (t w 2 −t w1 )......................................................................(xvii).
G
Consequently, the enthalpy of exit air is a summation of the enthalpy of entering air
and the addition of enthalpy from water to air (this is a value of L/G x Range).
 Fig 5- Plot of enthalpy vs. exit air temperature

Chapter 3 – Cooling Tower Demand Curve & Superimposition of Fill Characteristic Curve

3.1 Tower Demand & Characteristic-Advent of Black, Brown & Bluebook

Liechtenstein introduced the Cooling Tower equation in 1943 and he used Merkel heat transfer theory
along with differential and fundamental equations to define cooling tower boundary conditions. The
resulting dimensionless variables and series of equations related the variables for heat and mass
transfer on the counter flow type tower. Liechtenstein determined that his equation did not fully
account for the air mass rate or velocity from experimental results. Several investigators have
substantiated the effect of hot water temperature and air velocity on the counter flow tower. The
Merkel equation calculates the thermal demand based on the design temperature and selected mass
flow of liquid-to-gas ratios (L/G). The value of KaV/L indicates the difficulty of water cooling. The design
temperature and L/G relate the thermal demand to the MTD (Mean Temperature Difference) used in
any heat transfer problem. During Liechtenstein’s employment with the Foster-Wheeler Corporation, he
published a limited edition of "Cooling Tower Black Book" in 1943. The tower demand calculations were
incorporated into a volume of curves eliminating the need for for rigorous calculations. The so-called
"Brown Book" presented a change in format to a multi-cycle log plot. This format allows the cooling
tower characteristic curves to be plotted as straight lines. The publication includes cooling tower design
data for various types of counter flow fill. Design procedures affecting cooling tower selection and
performance have been discussed. With the advent of the computer age the Cooling Tower Institute
published the "Blue Book" entitled "Cooling Tower Performance Curves" in 1967. The CTI curves were
calculated and plotted by computer over a large span of temperature and operating conditions. The
curves are plotted with the thermal demand, KaV/L as a function of the liquid-to-gas ratio, L/G. The
approach lines (tw1 - WBT) are shown as parameters. The curves contain a set of 821 curves, giving the
values of KaV/L for 40 wet bulb temperature, 21 cooling ranges and 35 approaches.

3.2 Basis of Calculation

 Effect of heat of evaporated liquids on the results is negligible.
 The set of equations is based on counter-current flow of air & water. Vertical towers having upward
air flow & downward water flow predominantly are counterflow. Towers with inclined structural
columns, along with horizontal air flow and downward water flow are predominantly cross flow.
Most towers in reality are a combination of counter & cross flow. Although the calculation is based
on pure countercurrent flow, the curves are applicable within the limits, set forth in CTI Bulletin
ATC-105 to both cross flow & counterflow towers.

3.3 Limitations

 The accuracy decreases as the calculations and tests are run at conditions further from design.
However within the temperature limits of ±8.5°C as listed in ATC-105, these deviations will be less
than the test measurement inaccuracies. Under conditions beyond the aforementioned limit, the
deviations may become larger than test inaccuracies. However the curves will still have sufficient
accuracy to be successful to the tower operator.
 Actual tower performance may deviate from predicted performance at water loading considerably
different from design, because of uneven water distribution and possible channeling of air & water.
Also it is necessary to correct or control airflow at water loadings considerably different from design,
since water loading affects air pressure drop.

Fig 6- Plot of NTU vs. L/G

3.4 Tower Characteristic Curve

Currently, the following equation is widely accepted predict the thermal performance of a specified
cooling tower and is very useful to be able to superimpose on each demand curve, since KaV/L vs.
L/G relationship is a linear function on log-log demand curve.

Kav L
=C( )−m
L G

Where,
KaV/L=Tower Characteristic, as determined by Merkel equation
C=Constant related to the cooling tower design, or the intercept of the characteristic
m=Exponent related to the cooling tower design (called slope), determined from the test data

The characteristic curve may be determined in one of the following three ways;

 The vendor supplied characteristic curve may be used. In all cases the slope of this curve can be
taken as the slope of the operating curve.
 By field testing, one characteristic point can be determined and the characteristic curve is drawn
through this point parallel to the original characteristic curve.
 By field testing 2 characteristic points are determined at different L/G ratios. The line through
these two points is the characteristic curve. The slope of this line falls within the expected range,
and serves as a check on the accuracy.

A characteristic point is experimentally determined by first measuring the wet bulb temperature, air
discharge temperature, and cooling water inlet and outlet temperature. The L/G ratio is then
calculated as follows:
 The air discharge is assumed to be saturated. Therefore, the air discharge is at its wet bulb
temperature. Knowing wet bulb temperature at the inlet of tower, the enthalpy increase of the
air stream can be obtained from a psychometric chart. Air and water flow rates have to be in
the proper range as per CTI ATC 105 for uniform flow distribution. In case of recirculation of the
air discharge, the inlet wet bulb may be 1 or 2 oF above the atmospheric design wet bulb
temperature.

 From a heat and mass balance the dry air rate and the prevailing L/G ratio in the tower can be
calculated as
L Dh a
=
G C w (t w 2 −t w1 )

Next, the corresponding KaV/L value has to be established. This is simply done by plotting the
calculated L/G and approach on the demand curve for the proper wet bulb and range as in Fig 7.

Fig 7- Plot of NTU vs. L/G superimposed with Fill Characteristic

 Chapter 4- Mathematical Modeling of Project-Specific Induced Draft Counterflow Cooling Tower

4.1 Project Specific Inputs

The developed mathematical model will be tested against an induced draft counterflow cooling tower
installed at Chhattisgarh. In order to maintain the confidentiality of the data, the site of installation and
the cooling tower model no. is not being disclosed. However, some confidential information is being
shared in the below table, to render relevance to the context of the thesis.

Parameters Value
Design Flow rate 400 CMH
Hot Water Temperature 42 °C
(HWT)
Cold Water Temperature 32 °C
(CWT)
Wet Bulb Temperature 28 °C
(WBT)
Air Inlet Height 15.3 ft
Fill Film Type with 0.67 inches Pitch
Fan Diameter 10 m
Fan Blades 6
Fan RPM 114
Gearbox Ratio 12.93:1
End Wall Open
Table 1- Project-Specific Cooling Tower Design Parameters

4.2 Mathematical Model Description-Chebychev Discretization

Using the above inputs Equation (xv) will be solved by Chebychev’s method of integration for different
L/G values in order to compute the characteristic demand curve of Kav/L vs. L/G. Enthalpy on the air side
is computed by using equation (xvii) to act as an input to the Chebychev discretization method. Each plot
on the demand curve corresponds to a specific approach and thus the NTU is computed for a set of
approach and L/G values. Combination of VBA coding and Excel Macros has been used to create the
mathematical model to predict the thermal performance of the cooling tower.

Water Side Air Side

hw1 = CWT+0.1 X Range ha1= hwbt +0.1X L/G X Range
hw2 = CWT+0.4 X Range ha2= hwbt +0.4X L/G X Range
hw3 = CWT+0.6 X Range ha3= hwbt +0.6X L/G X Range
hw4 = CWT+0.9 X Range ha4= hwbt +0.9X L/G X Range
Table 2- Chebychev Method of Discretization

Range 1 1 1 1
Kav /L= X( + + + )
4 hw 1 −ha 1 hw 2−ha 2 h w 3−ha 3 h w 4−h a4

NTU or Kav/L is calculated for every value of L/G from 0.1 to 5 at an interval of 0.1 and for
every value of approach from 2°F to 26°F at an interval of 1 °F. The below VBA code is used to populate
the data set in order to generate the cooling tower demand curves at design conditions. The code runs
the Chebychev discretization in loop considering every possible combination of L/G and approach in the
aforementioned range.

Fig 8- VBA Code to generate data for Cooling Tower Demand Curve
Fig 9- Data for Cooling Tower Demand Curve at Design Conditions

After the generation of the cooling tower demand curves at design condition, the fill characteristic curve
is superimposed on the same to compute the characteristic point as per CTI ATC 105. The NTU and L/G
design data are noted to be 1.73 and 1.43 respectively

Fig 10- Cooling Tower Demand Curve at Design Conditions

4.3 Mathematical Modeling of Cooling Tower Performance at design WBT ±8.5 °C

In order to compute the cold water temperatures for various WBT, NTU is computed for a series of WBT
combinations. In the previous section, cooling tower demand curves were generated only for the design
wet bulb temperature. Now for each wet bulb temperature data, as per CTI-ATC 105, the demand
curves are generated.

The design Kav/L and L/G values are noted from the characteristic point in the previous section. Now,
for each wet bulb temperature, the characteristic point is marked on the newly generated demand
curve. The line of approach, with which the characteristic point coincides, is the new approach for the
specific wet bulb temperature.

To put the same in terms of mathematical modeling, another demand curve data table is created
identical to Fig 9. However, this table is dynamic and changes with every new wet bulb temperature that
is incorporated as input to the system. Thus, the VBA module in Fig 8 is repeated with a dynamic set of
wet bulb temperature as input, in the form of a loop.

Each wet bulb temperature generates its corresponding approach from this mathematical model.
Hence, the performance of the cooling tower (i.e. Cold Water Temperature) can be predicted at 100%
design flow rate and 100% cooling range for a set of WBT, as per CTI ATC 105. The output dataset
generates a plot between cold water temperature and wet bulb temperature.

4.4 Mathematical Modeling of Cooling Tower Performance at Cooling Range ±20%

As per CTI ATC 105, performance prediction needs to be done for 80%, 100% and 120% of cooling range.
The algorithm followed is identical to the mathematical modeling done for wet bulb temperature. For
cooling range, another loop is run outside the loop for wet bulb temperature. In the last section, cold
water temperature was predicted for each wet bulb temperature at 100% range. Now, the same
calculations are repeated for 80% range and 120% range.

The mathematical model illustrated in the last two sections has been executed in the VBA code shown in
Fig 11. The “design Kavl table” function referred in the code has already been shown in Fig 8. The “kavl
table” referred in the code is an identical table to the design Kav/L table with a dynamic set of WBT and
range as input.

Fig 11- VBA Code to generate data for Cooling Tower performance curve

The output generated by the VBA code shown in Fig 11 is tabulated below:

100% Flow
80% Range 100% Range 120% Range
WBT
Approach CWT Approach CWT Approach CWT
(°C)
(°C) (°C) (°C) (°C) (°C) (°C)
18.50 6.66 25.16 7.61 26.11 8.38 26.88
19.50 6.29 25.79 7.18 26.68 7.92 27.42
20.50 5.93 26.43 6.76 27.27 7.47 27.97
21.50 5.55 27.05 6.37 27.87 7.02 28.53
22.50 5.22 27.72 5.97 28.47 6.59 29.09
23.50 4.88 28.38 5.58 29.08 6.17 29.67
24.50 4.55 29.05 5.22 29.72 5.77 30.27
25.50 4.25 29.75 4.86 30.36 5.38 30.88
26.50 3.92 30.43 4.51 31.01 4.98 31.48
27.50 3.65 31.15 4.19 31.69 4.63 32.13
28.50 3.35 31.85 3.85 32.35 4.28 32.78
29.50 3.10 32.60 3.56 33.06 3.92 33.43
30.50 2.82 33.33 3.25 33.76 3.62 34.12
31.50 2.60 34.10 2.98 34.48 3.29 34.79
32.50 2.35 34.86 2.70 35.21 3.01 35.51
33.50 2.13 35.64 2.46 35.96 2.72 36.22
34.50 1.94 36.44 2.20 36.70 2.47 36.97
35.50 1.71 37.22 2.00 37.50 2.20 37.70
36.50 1.55 38.05 1.77 38.27 1.98 38.49
 37.50 1.39 38.89 1.58 39.08 1.75 39.25

Table 3- Cold Water Temperature at 100% flow and WBT ±8.5 °C and Cooling Range ±20%

4.5 Mathematical Modeling of Cooling Tower Performance at Design Flow rate ±10%

Prediction of cooling tower performance at 90%, 100% and 110% flow rate presents a mathematical
challenge. This is because the algorithm followed till now is based on a primary assumption that the
design NTU and L/G remained fixed irrespective of the operating conditions. The constant NTU and L/G
were used to compute the approach at various combinations of range and WBT. However, with the flow
changing in this case, L/G will change. To complicate matters further, the airflow increases by a certain
percentage, when the water flow reduces. There is no dedicated formula to calculate the increase in
airflow, when water flow reduces, as the same depends on the nature of the fill and the design thermal
duty conditions.

An iterative process is formulated to calculate the precise increase in air mass flow rate on reduction in
water flow rate to 90%. To begin with, the iteration process starts with the design L/G value. The mass
flow rate of liquid is already fixed at 100% of the design flow. So the design L/G gives an output of mass
flow rate of air at design conditions. Thermal parameters like enthalpy, specific volume and density are
computed at the inlet design wet bulb temperature. The exit wet bulb temperature is determined from
heat balance equation, as per equation (i), (ii) and (iii).

Thermal parameters are determined at the exit WBT, that in turn leads to computation of inlet and exit
volumetric airflow. In the next step, the total static pressure drop across the cooling tower is calculated
by analytically determining the pressure drop at each static component. The pressure drop points
considered in the airflow path are the following:

i. Inlet Pressure Drop

ii. Rain zone Pressure Drop
iii. Fill Pressure Drop
iv. Eliminator Pressure Drop
v. Plenum Pressure Drop

The volumetric flow of air at design conditions and the corresponding static pressure drop have now
been computed. From the concerned fan performance curve, the fan motor power consumed by the
cooling tower can be obtained. (In order to maintain confidentiality of the project, fan performance
curves are not enclosed here). The fan power is hence calculated at the design thermal duty conditions.

When the flow drops to 90% of the design flow rate, the fan power consumption remains constant. The
fan power obtained in the design condition is fixed to back calculate the L/G at 90% water flow rate. The
iteration begins with an assumed value of L/G, where L is taken as 90% of the design mass flow rate.
Much like computing the fan power at design conditions, the air volume flow rate and the static
pressure drop of air is calculated at 90% of the design flow rate. But, in this case, the fan motor power is
already fixed from the design calculations. Hence, the motor power and the static pressure drop give a
unique airflow value from the fan performance curves.
Thus, we end up with 2 unique values of airflow rate- one from the assumed value of L/G and the other
from the fan performance curve. Iterations are carried out unless the 2 airflow rates become equivalent
and the assumed L/G for which, the airflow rates match is the L/G at 90% water flow rate.

Fig 12- Iterative computation of L/G at 90% flow rate

In fig 12, the iterative mathematical formulation to determine L/G at 90% flow rate is shown. The
“Design L/G” in the fig is the assumed L/G, which is considered as an input to the iteration loop. G is the
mass flow rate of air from the assumed L/G and G-Itr is the mass flow rate of air obtained from the fan
performance curves. At the end of the iteration, both G and G-Itr numerically match each other that
indicate that the design L/G value is correct at 90% water flow rate. The L/G computed at 90% water
flow rate is 1.27.

Fig 13- Iterative computation of L/G at 110% flow rate

Like fig 12, in fig 13, the iterative mathematical formulation to determine L/G at 110% flow rate is
shown. In this case as well, both G and G-Itr numerically match each other that indicate that the design
L/G value is correct at 110% water flow rate. The L/G computed at 110% water flow rate is 1.61.

The VBA code that runs in the background to carry out the iteration to compute L/G for 90% and 110%
flow rate is shown in Fig 14. The code runs a series of L/G values in the relevant range, to serve as an
input to the algorithm. The code moves towards convergence, as the difference between G & G-Itr is
gradually lead to 0 in order to compute the correct value of L/G.

90% Flow
WBT 80% Range 100% Range 120% Range
 Approach CWT Approach CWT Approach CWT
(°C)
(°C) (°C) (°C) (°C) (°C) (°C)
18.50 5.73 24.23 6.56 25.06 7.25 25.75
19.50 5.39 24.89 6.17 25.67 6.83 26.33
20.50 5.04 25.54 5.80 26.30 6.41 26.91
21.50 4.73 26.23 5.42 26.93 6.00 27.50
22.50 4.40 26.91 5.06 27.56 5.60 28.10
23.50 4.11 27.61 4.72 28.23 5.23 28.73
24.50 3.81 28.31 4.38 28.88 4.86 29.36
25.50 3.54 29.04 4.06 29.57 4.50 30.00
26.50 3.26 29.76 3.75 30.26 4.17 30.67
27.50 3.01 30.51 3.45 30.95 3.83 31.33
28.50 2.74 31.24 3.17 31.67 3.52 32.02
29.50 2.52 32.03 2.89 32.40 3.22 32.72
30.50 2.28 32.78 2.64 33.14 2.93 33.43
31.50 2.08 33.58 2.39 33.90 2.66 34.16
32.50 1.88 34.38 2.15 34.66 2.40 34.91
33.50 1.66 35.16 1.95 35.45 2.15 35.66
34.50 1.52 36.02 1.72 36.23 1.94 36.44
35.50 1.35 36.85 1.55 37.05 1.70 37.20
36.50 1.17 37.67 1.38 37.88 1.53 38.03
37.50 1.04 38.54 1.19 38.69 1.34 38.85
Table 4- Cold Water Temperature at 90% flow and WBT ±8.5 °C and Cooling Range ±20%

Fig 14- VBA Code for Iterative computation of L/G at flowrate±10%

The L/G value for 90% flow rate and 110% flow rate comes out to be 1.27 and 1.61 respectively. With
these new design parameters, the algorithm shown in Fig 8 & Fig 11 is implemented to fill the
performance curve tables for both 90% and 110% design flow rate in Table 4 and Table 5.

110% Flow
80% Range 100% Range 120% Range
WBT
(°C) Approach CWT Approac CWT Approach CWT
(°C) (°C) h (°C) (°C) (°C) (°C)
 18.5
0 7.57 26.07 8.61 27.11 9.44 27.94
19.5
0 7.15 26.65 8.15 27.65 8.95 28.45
20.5
0 6.76 27.26 7.70 28.20 8.47 28.97
21.5
0 6.38 27.88 7.26 28.76 8.00 29.50
22.5
0 6.00 28.50 6.84 29.34 7.54 30.04
23.5
0 5.62 29.13 6.43 29.93 7.08 30.58
24.5
0 5.28 29.78 6.02 30.53 6.64 31.14
25.5
0 4.93 30.43 5.63 31.13 6.21 31.72
26.5
0 4.60 31.10 5.26 31.77 5.81 32.31
27.5
0 4.28 31.78 4.89 32.40 5.41 32.91
28.5
0 3.96 32.46 4.54 33.04 5.01 33.51
29.5
0 3.68 33.18 4.21 33.71 4.65 34.15
30.5
0 3.37 33.87 3.87 34.37 4.29 34.79
31.5
0 3.12 34.62 3.57 35.07 3.93 35.44
32.5
0 2.83 35.34 3.26 35.76 3.62 36.12
33.5
0 2.60 36.10 2.98 36.49 3.29 36.79
34.5
0 2.36 36.86 2.70 37.21 3.00 37.51
35.5
0 2.13 37.63 2.46 37.96 2.71 38.21
36.5
0 1.93 38.43 2.19 38.70 2.45 38.95
37.5
0 1.70 39.21 1.99 39.49 2.18 39.69
Table 5- Cold Water Temperature at 110% flow and WBT ±8.5 °C and Cooling Range ±20%

Chapter 5 - Experimental Data Recording at Site Conditions

In order to test the accuracy of the mathematical model, onsite performance data of the specific cooling
tower was recorded at Chhattisgarh. Since, the site- testing was done over a limited period of time, wide
variations in wet bulb temperature could not be captured. However, flow and range were varied to find
out a set of cold water temperature data that can be used to test the correctness of this mathematical
model.

5.1 Site Testing Types of Cooling Tower

The CTI site testing code followed is CTI-ATC 105. Currently, it is common to refer to cooling tower tests
as either Class A or B. A ‘Class A’ test is one that is conducted with mercury-in-glass thermometers and
grade level psychrometers. A Class B test on the other hand, uses a data acquisition system and usually
finds the psychrometers hung in an array over the air inlet face of the tower. Of course data acquisition
system can also be used in conjunction with grade level psychrometers. The cooling tower
psychrometers are typically used to measure the wet bulb temperature.

It is extremely important to recognize the difference between an ambient and entering wet bulb test,
because of the effect of recirculation. Both ASME and CTI recommend that towers be thermally sized
and tested based on entering wet bulb temperatures. This consideration can affect the selected tower
size and thermal test results .The entering WBT measures the average temperature of the air entering
the tower regardless of its source. While it is easier to separate the influence of several air masses, it still
requires careful analysis by the test staff to ensure that the number of instruments and their locations
are sufficient.

5.2 The Typical Test Procedure

In this project, a mercury-in-glass thermometer is utilized to determine the cold water temperature at
site. The first order of business to conduct a test is to inspect the tower for test readiness and identify
measurement points for various parameters. The customer maintained the condition of the tower and
prepared it for the test on the date prenotified by the manufacturer. The manufacturer also needs to
produce the calibration certificates for the instruments used to measure the cold water temperature.
Once this is complete and both customer and manufacturer are satisfied, instruments are deployed and
the testing begins. This process duration can range from a couple of hours to one or more days usually
depending on the size of the tower.
To begin the testing process, the test engineers begin taking data. Usually, the thermal data is
monitored for a brief period to check the site feasibility for the test. Once the feasibility check is done
and this process is underway, the test staff monitors the system, and measures the water flow rate and
fan power. The codes offer recommendations on deviation from design conditions for the test
parameters of 25-30% from the design conditions as per CTI-ATC 105.
A Pitot tube traverse of the piping carrying water to the cooling tower is used to measure the testing
flow rate. A wattmeter is used to measure fan input power consumption on mechanical draft tower
systems up to 600 volts. The following parameters must always be measured:
 Water flow rate
 Hot water temperature
 Cold water temperature
 Wet bulb temperature
 Fan power.
The hot water temperature is normally taken in the hot water distribution basin for cross-flow towers
and through a pitot tap in the piping for counterflow cooling towers. The cold water temperature is
normally taken at taps on the pump discharge side. The codes have explicitly defined the
instrumentation and procedures very clearly, leaving no room for confusion.

5.3 Project Specific Test Parameters

Parameters Specifications
Cooling Tower Test Site Chhattisgarh
Test Date 17th-19th March 2020
 Test Engineers 1. Mr. Alomoy Banerjee
2. Mr. Anindya Sundar Giri
Test Code CTI ATC 105 Class A
Thermometer Mercury-in-Glass (Technisys Make)
Flow Measuring Device Pitot Tube (Nanda Manufacturing Make)
Wet Bulb Temperature Measurement Device Cooling Tower Psychrometer ( Kaizen Imperial
Make)
Fan Power Measurement Device Wattmeter (Lutron Make with LSI circuit)
Table 6 – Cooling Tower Test Specific Conditions

The allowable error limit for the mathematical model was set to be ±2% by Paharpur Cooling towers Ltd.
The cooling tower performance test was carried out at site between 17 th-19th March 2020 under the
supervision of two Paharpur engineers and two engineers from customer side. The test data recorded
was agreed upon by both parties and signed off by both cooling tower manufacturer and the customer.

5.4 Data Recorded at Site

The dataset in Table 7 was recorded at 110% of design flow rate and 100% cooling range. The dataset in
Table 8 was recorded at 90% of design flow rate and 80% cooling range. The dataset in Table 9 was
recorded at 100% of design flow rate and 100% cooling range. Both the flow rate and cooling range for
all the conditions were within the limits as mentioned under CTI ATC 105.

110% Flow
100% Range
WBT Predicted Site Error
(°C) CWT CWT Percentage
(°C) (°C) (%)
26.50 31.77 32.15 1.2%
27.50 32.40 31.95 1.4%
28.50 33.04 32.91 0.4%
Table 7- Experimental vs. Predicted CWT dataset 1

90% Flow
80% Range
WBT Predicted Site Error
(°C) CWT CWT Percentage
(°C) (°C) (%)
28.50 31.24 31.49 0.8%
29.50 32.03 31.87 0.5%
27.50 30.51 31.12 1.9%
Table 8- Experimental vs. Predicted CWT dataset 2
 100% Flow
100% Range
WBT Predicted Site Error
(°C) CWT CWT Percentage
(°C) (°C) (%)
26.50 30.43 30.89 1.5%
27.50 31.15 30.98 0.5%
28.50 31.85 31.98 0.4%
Table 9- Experimental vs. Predicted CWT dataset 3

Chapter 6 - Conclusion

As observed from the 9 data points recorded in the test, it is concluded that the error in cold water
temperature prediction does not exceed 2%, which validates the mathematical model proposed in the
thesis. The validation of the model indicates that the algorithm can be applied to all counterflow
induced draft cooling towers for performance prediction. This will benefit Paharpur Cooling Towers Ltd
during CTI testing process and also in projects where there is a high penalty on performance test failure.
The best part about this mathematical model is it does not use extrapolation of experimentally recorded
data to predict the cold water temperature. This model uses analytical method to accurately predict the
thermal performance of each cooling tower and hence, the same algorithm can be applied to any
induced draft counterflow cooling tower irrespective of thermal duty parameters and cooling tower
specifications.

6.1 Relevance to Company Work

Inaccurate performance curves have been causing issues with thermal performance testing at site for
quite some time now. An analytical thermal model, which can be uniformly applied to all counterflow
induced draft cooling towers, was the need of the hour for the organization. The project has ventured
into very high prospects in terms of original research as well. A suitable mathematical method to
calculate corrected L/G for varying flow rate was developed and tested. Thus, the scope of the present
project was not only beneficial to the company, but also opened new avenues of research in the field of
cooling tower analytical thermal modeling approach.

6.2 Future Scope of Work

The mathematical model developed in this project has been tested against an induced draft counterflow
cooling tower at site. Similar tests at varied wet bulb condition for different cooling tower model will
give a better idea about the accuracy of this method. Paharpur Cooling Towers Ltd, is looking to carry
out further tests on its broad cooling tower installation base all around the country, in order to
universally validate this model.

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Supervisor & Additional Examiner Details

Supervisor Additional Examiner

Name Mr. Aninda Sundar Giri Mr. Varun Swarup

Qualification B-Tech Mechanical Engineering MS Design Methodology with

with 16 years Work Experience 10 years Work Experience

Designation Assistant Manager Senior VP

Employing Orgn Paharpur Cooling Towers Ltd. Paharpur Cooling Towers Ltd.
and Location Kolkata Kolkata
Phone No.
(with STD Code) +918075301152 +913340133215

Email Address anindasundar.giri@paharpur.com varunswarup@paharpur.com

Signature

Date 29-08-2020 29-08-2020

Remarks of Supervisor

The project is ambitious and bears a very high significance on behalf of the organization.

_________________ ___________________ __________________________

Signature of Student Signature of Supervisor Signature of Additional Examiner

Name: Alomoy Banerjee Name Aninda Sundar Giri Name: Varun Swarup