Design of Cooling Tower Although the world’s total fresh water supply is abundant, some areas have water usage demands that are heavily out of balance with neutral replenishment. Conservation and efficient reuse of this precious and versatile resource are mandatory if such areas are to achieve proper development. Cooling Tower used to reuse of water in Industry.
A Project Report on
Submitted by
Mr. Avinash M. Nirwan Mr. Dayanand Dayanand T. Mehar Mr. Vedant V. Khadkekar
Guided By Prof. P. G. Jadhav Submitted in partial fulfillment of the requirement for the award of the degree of
BACHELOR OF TECHNOLOGY TECHNOLOGY (Chemical Engineering) at
SHRI GURU GOBIND SINGHJI INSTITUT INSTITUTE E OF ENGINEERING ENGINEERING AND TECHNOLOGY TECHNOLOGY VISHNUPURI, NANDED. (MAHARASHTRA STATE) PIN 431606 INDIA 2012-2013
DECLARATION I Mr./ Ms. Vedant Vasantrao Khadkekar, hereby declare that this project report is the record of authentic work carried out by me during the period from July 2012 to May 2013 and has not been submitted to any other University or Institute for the award of any degree / diploma etc.
Signature Name of the student : Mr. Vedant Vasantrao Khadkekar Date : 01/05/2013
I
Vishnupuri, Nanded , (M.S.) India – 431 606 (An Autonomous Institute)
This is to certify that the Project report entitled
Being submitted by Mr. Vedant Vasantrao Khadkekar, for the award of the degree of Bachelor of Technology in Chemical Engineering is a record of benefice work carried out by
them under my supervision and guidance satisfactorily in the year 2012-13.
Date: 20 / 05 / 2013.
Prof. P.G.Jadhav
Prof. P.G. Jadhav
Head of Department
(Project Guide)
Chemical Engineering Department
Chemical Engineering Department
SGGS IE&T, Nanded.
SGGS IE&T, Nanded.
Acknowledgment The satisfaction that accompanies the successful completion of any task would be incomplete without mentioning the people who made it possible. We are grateful to a number of individuals whose professional guidance along with encouragement have made it very pleasant endeavor to present this project. We have a great pleasure in presenting the project report on “Design of Cooling Tower ” with the kind permission from respected Dr. L. M. Waghmare, Director and Prof. P. G. Jadhav , Head, Department of Chemical Engineering of S.G.G.S.I.E. &T., Nanded.
We are truly grateful to our Project guide Prof. P. G. Jadhav for his valuable guidance and encouragement. Her encouraging words went a long way in providing the patience and perseverance which were needed to present this project successfully. Also her true criticism towards technical issues provided me to concentrate o n transparency of our project. We take an opportunity to thank all the staff members of our department. Finally we express our sincere thanks to all those who helped us directly or indirectly in many ways in completion of this work.
Projectees…
III
INDEX Particulars
Page No.
I.
Declaration
I
II.
Certificate
II
III.
Acknowledgment
III
IV.
Index
IV
V.
List of Tables
VI
VI.
List of Symbols/Abbreviations
VII
VII.
List of figures
VIII
VIII.
Abstract
IX
1. Introduction
1
1.1. Classification
2
1.2. Categorization by air-to-water flow
4
1.3. Parameters
8
1.4. Components of Cooling Tower
10
1.5. Cooling Tower Internals and the Role of Fill
11
1.6. Experimental Objective
14
2. Literature Review
16
2.1. Research in cooling tower
17
3. Analysis of Cooling Tower
21
3.1 Analysis of Cooling Tower
22
3.2 Temperature and Concentration Profile at Interface 3.3 Characteristics of cooling tower
23 24
4. Cooling Tower Technical Specifications
27
4.1. Cooling Tower Technical Specifications 4.2. Data from Psychometric Chart and Steam Table 4.3. Design Calculation
28 28 29
5. Experimental Procedure
33
IV
6. Observations & Discussion
35
6.1 Observations
36
6.2 Design Calculation
36
6.3 The influence of process conditions upon design
37
7. Cost Estimation of Cooling Tower
41
8. Energy Saving Opportunities
44
9. Typical Problems and Trouble shootings for CT
46
10. Conclusion
49
11. Bibliography
51
IX.
Appendix
53
V
LIST OF TABLES
Table no.
Particulars
Page no.
1.
Cooling Tower Technical Specifications
29
2.
Data from Psychometric Chart and Steam Table
29
3.
Observation table
37
4.
Observation Table -2
37
5.
Typical Problems & Trouble Shooting
48
6.
Steam Table
53
VI
LIST OF SYMBOLS / ABBREVIATION Symbol
Meaning
CTA
Cooling Tower Approach
CTR
Cooling Tower Range
N ∆Hlom
Efficiency Log mean temperature difference
DL
Drift losses
WL
Windage Losses
EL
Evaporation losses
BL
Bow down losses
XC
Concentration of solids in circulating water
XM
Concentration of solids in Make-up water
CWT
Cold Water Temperature
DBT
Dry Bulb Temperature
G1
Flow rate of inlet Air
G2
Floe rate of Outlet Air
H1
Enthalpy of water at outlet temperature
H2
Enthalpy of water at inlet temperature
Ha1
Humidity of Inlet Air
Ha2
Humidity of Outlet Air
HOG
Height of Heat Transfer Unit
HWT
Hot water Temperature
KaV/L
Cooling Tower Characteristics
K Ga
Mass Transfer Coefficient
L1
Outlet water Flow rate
L2
Inlet water Flow rate
MB
Average Molecular Weight of Air
Mw
Mass flow rate of water
VII
NOG
Number of Heat Transfer Unit
P
Pressure
Q
Quantity of heat loss
T1
Outlet water Temperature
T2
Inlet water Temperature
Ta1
Inlet Tempretute of air
Ta2
outlet Tempretute of air
WBT Z
Wet bulb temperature Height of Cooling Tower
VIII
LIST OF FIGURES
Fig. No.
Name of Figure
1.1
Cooling Water System
1.2
Typical Cross Flow Cooling Tower
1.3
Typical Counter flow Cooling Tower
1.4
Different types of Cooling Towers
1.5
Range and Approch
1.6
Free and Interrupted Fall.
1.7 (a)
Rectangular Fills
1.7(b)
Triangular Fills
3.1
Schematic Diagram of a cooling tower
3.2
Water Drop Balance
3.3
Temperature and concentration profile in upper part of cooling tower
3.4
Characteristics of Cooling Tower
5.1
Arrangement of cooling tower
6.1
Effects of design Variables on the size of potential
IX
Abstract Although the world’s total fresh water supply is abundant, some areas have water usage demands that are heavily out of balance with neutral replenishment. Conservation and efficient reuse of this precious and versatile resource are mandatory if such areas are to achieve proper development. And, the need for water conservation does not limit its self only to arid regions. Recognition of the detrimental environmental impact of high temp. water discharge into an estuary, whose inhabitants are accustomed to more moderate temperature levels, make one realize that the re-cooling and reuse of water, however abundant ,conserves not just that natural resource-It conserves nature as well one helpful means to that end is the water cooling tower. Cooling towers are one of the biggest heat and mass transfer devices that are in widespread use. In this paper, we use a detailed model of cooling towers in investigating the performance characteristics. The validity of the model is checked by experimental data reported in the literature. The thermal performance of the cooling towers is clearly explained in terms of varying air and water temperatures, as well as the driving potential for convection and evaporation heat transfer, along the height of the tower. The relative contribution of each mode of heat transfer rate to the total heat transfer rate in the cooling tower is established. The variation of air and water temperatures along the height of the tower (process line) is explained on psychometric charts. In Project, we use a detailed model of cooling towers in investigating the performance characteristics.
X
Design of Cooling Tower
Design of Cooling Tower
Chapter 1 INTRODUCTION A hyperboloid cooling tower was patented by Frederik van Iterson and Gerard Kuypers in 1918 [1]. The first hyperboloid cooling towers were built prior to 1930 in Liverpool, England to cool water used at a electrical power station that used coal [2]. A cooling tower is a unit where water is cooled with air. Warm water enters the top of the tower, runs down the column and chills because it partially vaporizes to air, which flows upward. Also, the air flow is usually colder than the water flow, so water is chilled because of the heat exchange. Since both mass and heat transfer phenomena are present, the theory of cooling towers is a bit complicated. Certain simplifications can be made because the liquid phase is pure water, and therefore there is no driving force for mass transfer in that phase. As many other vapor-liquid mass transfer units, the cooling tower is packed with packing materials, which increases the surface area, in order to enhance the mass and heat transfer [3]. Cooling towers are a very important part of many chemical plants. The primary task of a cooling tower is to reject heat into the atmosphere. They represent a relatively inexpensive and dependable means of removing low-grade heat from cooling water. The make-up water source is used to replenish water lost to evaporation. Hot water from heat exchangers is sent to the cooling tower. The water exits the cooling tower and is sent back to the exchangers or to other units for further cooling. Typical closed loop cooling tower system is shown in Figure 1.1.
Fig.1.1, Cooling Water System
Design of Cooling Tower
1.1. Classification 1.1.1. Air flow generation methods With respect to drawing air through the tower, there ar e three types of cooling towers:
Natural draft — Utilizes buoyancy via a tall chimney. Warm, moist air naturally
rises due to the density differential compared to the dry, cooler outside air. Warm moist air is less dense than drier air at the same pressure. This moist air buoyancy produces an upwards current of air through the tower.
Mechanical draft — Uses power-driven fan motors to force or draw air through the
tower. o
Induced draft — A mechanical draft tower with a fan at the discharge (at
the top) which pulls air up through the tower. The fan induces hot moist air out the discharge. This produces low entering and high exiting air velocities, reducing the possibility of recirculation in which discharged air flows back into the air intake. This fan/fin arrangement is also known as draw-through. o
Forced draft — A mechanical draft tower with a blower type fan at the
intake. The fan forces air into the tower, creating high entering and low exiting air velocities. The low exiting velocity is much more susceptible to recirculation. With the fan on the air intake, the fan is more susceptible to complications due to freezing conditions. Another disadvantage is that a forced draft design typically requires more motor horsepower than an equivalent induced draft design. The benefit of the forced draft design is its ability to work with high static pressure. Such setups can be installed in more-confined spaces and even in some indoor situations. This fan/fill geometry is also known as blow-through.
Fan assisted natural draft — A hybrid type that appears like a natural draft setup,
though airflow is assisted by a fan. Hyperboloid (sometimes incorrectly known as hyperbolic) cooling towers have become the design standard for all natural-draft cooling towers because of their structural strength and minimum usage of material. The hyperboloid shape also aids in accelerating the upward convective air flow, improving cooling efficiency. These designs are popularly associated with nuclear power plants. However, this association is misleading, as the same
Design of Cooling Tower kind of cooling towers are often used at large coal-fired power plants as well. Conversely, not all nuclear power plants have cooling towers, and some instead cool their heat exchangers with lake, river or ocean water.
1.2. Categorization by air-to-water flow 1.2.1. Cross flow Cross flow is a design in which the air flow is directed perpendicular to the water flow (see diagram below). Air flow enters one or more vertical faces of the cooling tower to meet the fill material. Water flows (perpendicular to the air) through the fill by gravity. The air continues through the fill and thus past the water flow into an open plenum volume. Lastly, a fan forces the air out into the atmosphere. A distribution or hot water basin consisting of a deep pan with holes or nozzles in its bottom is located near the top of a cross flow tower. Gravity distributes the water through the nozzles uniformly across the fill material. Mechanical draft cross flow cooling tower used in an HVAC application. Advantages of the cross flow design:
Gravity water distribution allows smaller pumps and maintenance while in use. Non-pressurized spray simplifies variable flow. Typically lower initial and long-term cost, mostly due to pump requirements.
Disadvantages of the cross flow design:
More prone to freezing than counter flow designs.
Variable flow is useless in some conditions.
Design of Cooling Tower
Fig. 1.2, Typical Cross Flow Cooling Tower
1.2.2. Counter flow In a counter flow design, the air flow is directly opposite of the water flow (see diagram below). Air flow first enters an open area beneath the fill media, and is then drawn up vertically. The water is sprayed through pressurized nozzles near the top of the tower, and then
flows
downward
through
the
fill,
opposite
to
the
air
flow.
Advantages of the counter flow design:
Spray water distribution makes the tower more freeze-resistant.
Breakup of water in spray makes heat transfer more efficient.
Disadvantages of the counter flow design:
Typically higher initial and long-term cost, primarily due to pump requirements.
Difficult to use variable water flow, as spray characteristics may be negatively affected.
Design of Cooling Tower
Fig.1.3, Typical Counter flow Cooling Tower
Common aspects of both designs:
The interactions of the air and water flow allow a partial equalization of temperature, and evaporation of water.
The air, now saturated with water vapor, is discharged from the top of the cooling tower.
A collection or cold water basin is used to collect and contain the cooled water after its interaction with the air flow.
Both cross flow and counter flow designs can be used in natural draft and in mechanical draft cooling towers.
Design of Cooling Tower
Fig. 1.4, Different types of Cooling Towers
Design of Cooling Tower
1.3. Parameters
Range: It is the difference between the cooling tower water inlet and outlet
temperature.
Approach: It is the difference between the cooling tower outlet cold water
temperature and ambient wet bulb temperature. Although, both range and approach should be monitored, the `Approach’ is a better indicator of cooling towe r performance.
Effectiveness: Cooling tower effectiveness (in percentage) is the ratio of range, to
the ideal range, i.e., difference between cooling water inlet temperature and ambient wet bulb temperature, or in other words it is = Range / (Range + Approach).
Fig. 1.5, Range and Approch
Capacity: Cooling capacity is the heat rejected in kCal/hr or TR, given as product
of mass flow rate of water, specific heat and temperature difference.
Design of Cooling Tower
Evaporation loss: It is the water quantity evaporated for cooling duty and,
theoretically, for every 10,00,000 kCal heat rejected, evaporation quantit y works out 3
to 1.8 m . An empirical relation used often is: 3
3
Evaporation Loss (m /hr) = 0.00085 x 1.8 x circulation rate (m /hr) x (T -T ) 1
2
T -T = Temperature difference between inlet and outlet water. 1
2
Cycles of concentration (C.O.C): is the ratio of dissolved solids in circulating
water to the dissolved solids in makeup water.
Blow down losses depend upon cycles of concentration and the evaporation losses and is given by relation:
Blow Down = Evaporation Loss / (C.O.C. – 1)
Wet bulb temperature:
It is the temperature measure in the saturated air. Wet bulb temperature is an important factor in performance of evaporative water cooling equipment. It is a controlling factor from the aspect of minimum cold water temperature to which water can be cooled by the evaporative method. Thus, the wet bulb temperature of the air entering the cooling tower determines operating temperature levels throughout the plant, process, or system. Theoretically, a cooling tower will cool water to the entering wet bulb temperature, when operating without a heat load. However, a thermal potential is required to reject heat, so it is not possible to cool water to the entering air wet bulb temperature, when a heat load is applied. The approach obtained is a function of thermal conditions and tower capability.
Design of Cooling Tower
1.4. Components of Cooling Tower The basic components of an evaporative tower are: Frame and casing, fill, cold water basin, drift eliminators, air inlet, louvers, nozzles and fans.
Frame and casing: Most towers have structural frames that support the exterior
enclosures (casings), motors, fans, and other components. With some smaller designs, such as some glass fiber units, the casing may essentially be the frame.
Fill: Most towers employ fills (made of plastic or wood) to facilitate heat transfer
by maximizing water and air contact. Fill can either be splash or film type. With splash fill, water falls over successive layers of horizontal splash bars, continuously breaking into smaller droplets, while also wetting the fill surface. Plastic splash fill promotes better heat transfer than the wood splash fill. Film fill consists of thin, closely spaced plastic surfaces over which the water spreads, forming a thin film in contact with the air. These surfaces may be flat, corrugated, honeycombed, or other patterns. The film type of fill is the more efficient and provides same heat transfer in a smaller volume than the splash fill.
Cold water basin: The cold water basin, located at or near the bottom of the tower,
receives the cooled water that flows down through the tower and fill. The basin usually has a sump or low point for the cold water discharge connection. In many tower designs, the cold water basin is beneath the entire fill. In some forced draft counter flow design, however, the water at the bottom of the fill is channeled to a perimeter trough that functions as the cold water basin. Propeller fans are mounted beneath the fill to blow the air up through the tower. With this design, the tower is mounted on legs, providing easy access to the fans and their motors.
Drift eliminators: These capture water droplets entrapped in the air stream that
otherwise would be lost to the atmosphere.
Design of Cooling Tower
Air inlet: This is the point of entry for the air entering a tower. The inlet may take
up an entire side of a tower — cross flow design — or be located low on the side or the bottom of counter flow designs.
Louvers: Generally, cross-flow towers have inlet louvers. The purpose of louvers is
to equalize air flow into the fill and retain the water within the tower. Many counter flow tower designs do not require louvers.
Nozzles: These provide the water sprays to wet the fill. Uniform water distribution
at the top of the fill is essential to achieve proper wetting of the entire fill surface. Nozzles can either be fixed in place and have either round or square spray patterns or can be part of a rotating assembly as found in some circular cross-section towers.
Fans: Both axial (propeller type) and centrifugal fans are used in towers. Generally,
propeller fans are used in induced draft towers and both propeller and centrifugal fans are found in forced draft towers. Depending upon their size, propeller fans can either be fixed or variable pitch. A fan having non-automatic adjustable pitch blades permits the same fan to be used over a wide range of kW with the fan adjusted to deliver the desired air flow at the lowest power consumption. Automatic variable pitch blades can vary air flow in response to changing load conditions.
Design of Cooling Tower
1.5. Cooling Tower Internals and the Role of Fill If the water passes through a nozzle capable of producing small droplets, a large surface becomes available for air-water contact .Since the water – air interface is also the heat transfer surface, the use of the nozzle permits the attainable of considerable performance per cubic foot of contact appratus. This is the principal of spray pond and the spray tower. Consider a hypothetical spray tower as shown in fig.1.6.
Fig.1.6, Free and Interrupted Fall.
Liquid fed to it falls through by gravity. if tower is 16 ft. high and no initial velocity imparted to the droplet ,it falls in approximate according with the free fall low, Z=1/2gθ2, Where, Z is the height, g the acceleration of gravity, and θ the time. A droplet of water will fall through height of the tower in 1 sec. if liquid is fed at the rate of one droplet per second and there is no obstruction, one droplet be always present in the tower and one droplet will continuously remove from the tower per second [4]. Now suppose that by introducing some geometrical forms on which the droplet may impinge or be deflected it is possible to make a droplet take 4 sec to fall through the height of the tower. Then as shown in fig.1.6 ,one droplet is fed per sec at the top and one droplet
Design of Cooling Tower the later is that of four droplets remain in the tower. The function of fill is to increase the available surface in the tower is either by spreading the liquid over a great surface or by retarding the rate fall of the droplet surface through the apparatus. In ordinary diffusion towers such as chemical absorbers the packing is introduced in the form of Rasching Rings, Berl Saddles, or other objects which are very compact and provide a surface on which the liquid spreads and exposes a large film. This is Film Surface. In the cooling tower, because of the requirement of the large air volume and the allowable pressure drop , It is customary to use spaced wooden slats of triangular or rectangular cross sections, leaving the tower substantially unobstructed. The packing, or fill, in the cooling tower is almost entirely fabricated in either of the forms of fig.1.7, and its purpose is to interrupt the descent liquid.
Fig. 1.7 (a), Rectangular Fills
Design of Cooling Tower
Fig. 1.7(b), Triangular Fills Fig. 1.7, Common Types of Cooling Tower Fills
Design of Cooling Tower
1.6. Experimental Objective Our lab-scale cooling tower is designed to mimic an industrial operation, except it recycles and re-heats the water as it is cooled. The goals of the experiment are: 1). To perform mass and energy balances on the system. 2). To determine average heat & mass transfer coefficient. 3). To observe the effects of process variables on the exit temperature of the water.
- Air flow rate - Water flow rate (cooling load) - Inlet water temperature - packing density
Design of Cooling Tower
Design of Cooling Tower
Chapter 2 Literature Review This chapter has the research from other people regarding the performance of cooling tower. The explanation on types, parts and theory involving cooling tower are describe thoroughly as the cooling tower used in the industry. Without cooling tower, a big facility or building tower might not stable at it will increased the heat to the people in the building. There are also some explanation about the system and the transfer between air and the cooling tower.
2.1. Research in cooling tower: 1. Rafat Al-Waked and Behnin made research about computational fluid dynamics
(CFD) simulation of wet cooling tower. Heat and mass transfer inside a natural draft wet cooling tower (NDWCT) have been investigated numerically under different operating and crosswind conditions. The three-dimensional CFD model has utilized the standard k-ἐ turbulence model as the turbulence closure. The current simulation has adopted both the Eulerian approach for the air phase and the Langrangian approach for the water phase. The film nature of the water flow in the fill zone has been approximated by droplets flow within a given velocity. At that specific droplet velocity, effects of the following operating parameters on the thermal performance of the NDWCT have been investigated: droplet diameter, inlet water temperature, number nozzles, water flow rate and number of tracks per nozzle. As a result, the effect of crosswind velocity on the thermal performance has been found to be significant. Crosswind with velocity magnitude higher than 7.5 m/s have enhanced the thermal performance of the NDWCT. 2. S. V. Bedekar, P. Nithiarasu and K. N. Seetharamu have studied the performance of
fluidized bed cooling towers; ignoring the higher pressure drop compared to other film and splash type towers, their performance was excellent. Sisupalan and Seetharamu examined the performance variation of a fluidized-bed cooling tower for different statics bed heights. Recently, Dreyer and Evens studied the modeling of a cooling tower splash pack. The performance of a falling-film type cooling tower has been studied by Ibrahim. There are many studies available on mathematical modeling of cooling tower heat and mass transport, including a
Design of Cooling Tower number of recent publications. The available literature shows a lack of experimental data on film type, packed-bed cooling towers. 3. To relief hot climate in summer season, direct evaporative cooling system (shower
Cooling Tower System) was examined. Satoshi Yajima has studied the performance of the shower cooling in Japan. This system was developed by B. Givoni. In general, evapotive cooling system is recognized that it is suit for hot and dry climate. But this system can supply cooled water and generate cooled air flow. This characteristics means the ability of utilize this system also in humid climate. They tested this system with objective to plan and apply this in Japan, and examined its cooling effectiveness and air flow generation. 4. J. C. Kloppers and D. G. Kroger have made a critical investigation into the heat and
mass transfer analysis of counter flow wet-cooling towers. This study gives a detailed derivation of the mass transfer equations of evaporative cooling in wetcooling towers. The governing equations of the rigorous Poppe method of analysis are derived from first principle. The method of Poppe is well suited for the analysis of hybrid cooling towers as the state of the outlet air is accurately predicted the governing equations of the Merkel method of analysis are subsequently derived after some simplifying assumptions are made. The equations of the effectiveness NTU method applied to wet cooling tower also presented. The governing equations of the Merkel method of analysis are subsequently derived after some simplifying assumption are made. The equations of effectiveness -NTU method applied to wetcooling towers also presented. The governing equations of Poppe method are extended to give more detailed presentation of Merkel number. The differences in the heat and mass transfer analysis and solution techniques of the Merkel and Poppe methods are described with the aid of enthalpy diagrams and psychometric charts. The psychometric chart is extended to accommodate air in the supersaturated state. 5. J. Smrekar, J. Oman and B. Sirok have made a research to improve the efficiency of
natural draft cooling towers. This study shows how the efficiency of natural draft cooling tower cab be improved by optimizing the heat transfer along the cooling tower (CT) packing using a suitable water distribution across the plane area of cooling tower. On the basis of cooling air measurements, it is possible to distribute the water in such a way that it approaches the optimal local water/air mass flow ratio and ensures the homogeneity of the heat transfer and a reduction of entropy generation, thus minimizing the amount of energy lost. The velocity and
Design of Cooling Tower temperature fields of the airflow were measured with the aid of remote control mobile robot unit that has developed to enable measurements at an arbitrary point above the spray zone over entire plane area of the cooling tower. The topological structures of the moist air velocity profiles and the temperature profiles above the spray zone were used as input data for calculation of the entropy generation in the cooling tower. On the basis of measured boundary conditions, a numerical analysis of the influence of the water distri bution across the cooling tower’s plane area on entropy generation and energy destruction in the cooling tower was conducted. 6. J. C. Kloppers and D. G. Kroger have studied the influence of temperature
inversions on wet-cooling tower performance. Nocturnal temperature inversions have detrimental effect on the performance of natural draft wet cooling towers. The effects of the temperature inversion profile, the height of inversion and height from which air is drawn into the cooling tower, on the performance of cooling towers are investigated. Relatively simple and accurate equations are employed in the analysis to determine the temperature inversion profiles and inversion heights, which only have ground based measurements as input. The detrimental effect in tower performance, during nocturnal temperature inversions, is due to the reduced potential in draft and the increase of the effective air inlet temperature. 7. Jameel-Ur-Rehman Khan and M. Yaqub, Syed M. Zubair studied the performance
characteristics of counter flow wet cooling towers. Cooling towers are one of the biggest heat and mass transfer devices that are in widespread use. Here, we use a detailed model of counter flow wet cooling towers in investigating the performance characteristics. The validity of the model is checked by experimental data reported in the literature. The thermal performance of cooling towers is clearly explained in terms of varying air and water temperatures, as well as the driving for convection and evaporation heat transfer, along the height of the cooling tower. The relative contribution of each mode of heat transfer rate to the total heat transfer in cooling tower established. It is demonstrated with an example that the predominant mode of heat transfer is evaporation. For example, evaporation contributes about62.5% of the total rate of heat transfer at the bottom of the tower and almost 90% at the top of the tower. The variation of air and water temperatures along the height of the tower (process line) is explained on psychometric charts. 8. Paisarn Naphon studied on the heat transfer characteristics of an evaporative cooling
tower. In the present study, both experimental and theoretical results of the heat
Design of Cooling Tower transfer characteristics of the cooling tower are investigated. A column packing unit is fabricated from the laminated plastic plates consist of eight layers. Air and water are used as working fluids and the test runs are done at the air and water mass flow rates ranging between 0.01 and 0.07 kg/s, and between 0.04 and 0.08 kg/s, respectively. The inlet air and inlet water temperatures are 23 0C, and between 30 and 400C, respectively. A mathematical model based on the conservation equations of mass and energy is developed and solved by an iterative method to determine the heat transfer characteristics of the cooling tower. There is reasonable agreement from the comparison between the measured data and predicted results .
Design of Cooling Tower
Design of Cooling Tower
Chapter 3 Analysis of Cooling Tower 3.1. Analysis of Cooling Tower A schematic of a counter flow cooling tower, the major assumptions that are used to derive the basic modeling equations are: • Heat and mass transfer is in a direction normal to the flows only; • Negligible heat and mass transfer through the tower walls to the environment; • Negligible heat transfer from the tower fans to the air or water streams; • Constant water and dry air specific heats; • Constant heat and mass transfer coefficients throughout the tower; • Constant value of Lewis number throughout the tower; • Water lost by drift is negligible; • Uniform temperature throughout the water stream at each cross section; and • Uniform crosses sectional area of the tower.
Ta1
Fig 3.1, Schematic Diagram of a cooling tower
3.1.1. Overall Mass Balance Input = Output L2-L1 = G2-G1 Where, L2-Flow rate of inlet water, L1- Flow rate of outlet water, G1-Air Inlet, G2-Air Outlet.
Design of Cooling Tower
Fig. 3.2, Water Drop Balance
3.1.2. Water Mass Balance L2-L1 = G2 * Ha2 - G1 * Ha1 G2 = G1 = G L2-L1 = G *(Ha2- Ha1) Where, Ha1 – Humidity of Inlet Air, Ha2 – Humidity of Outlet Air
3.1.3 Energy Balance Q = H2 – H1 Where, H2 = Enthalpy of Inlet Air H1 = Enthalpy of Outlet Air
3.1.4. Determination of Number of Transfer Units
Where, NOG – Number of transfer units (Dimensionless)
3.1.5. To Calculate Mean Driving Force
⁄
3.1.6. To Calculate Over all Mass Transfer Coefficient
Design of Cooling Tower
Where, HOG – Height of Transfer Unit, MB – Molecular Weight P - Pressure, and K Ga - Mass Transfer Coefficient.
3.2. Temperature and Concentration Profile at Interface
Fig. 3.3, Temperature and concentration profile in upper part of cooling tower
3.3. Characteristics of cooling tower The basic function of a cooling tower is to cool water by intimately mixing it with air. This cooling is accomplished by a combination of sensible heat transfer between the air and the water and the evaporation of a small portion of the water. This type of transfer is represented by the following equation:
This equation is commonly referred to as the Merkel equation. The left-hand side of this equation is called the "tower characteristic," which basically indicates the 'degree of difficulty to cool' the water or the 'performance demand' of the tower.
Design of Cooling Tower The tower characteristic and the cooling process can best be explained on a Psychometric Chart. The process is shown in the figure on the right -known as the Driving Force Diagram. The upper curve shows the relation between the temperature and enthalpy of the saturated air . This curve applies to the air film surrounding the water. Merkel assumed that the drops of water falling through the tower are surrounded by a film of saturated air and the heat and mass transfer basically takes place between this film [which has the same temperature as of the water] and the upstream air. The condition of the air film is represented by the Water Operating Line and is limited by the hot and cold water temperatures, points A and B.
Fig.3.4, Characteristics of Cooling Tower
The lower curve known as the Air Operating Line, represents the condition of air flowing through the cooling tower. The origin of this line, point C, is vertically below B and is positioned to have an enthalpy corresponding to that of the entering wet bulb temperature. As the water is cooled one degree, the enthalpy of the air is increased 1 Btu multiplied by L/G [water circulation -lbs.per unit time/ air circulation -lbs. per unit time]. Thus, the L/G ratio is the slope of the air operating line C-D. Point D, representing the air leaving the cooling tower, is the point on the air operating line vertically below point A. The projected length C-D is the cooling range. The Merkel Equation primarily says that at any point in the tower, heat and water
Design of Cooling Tower air at the surface of the water [represented by the Water Operating Line A-B] and the main stream of the air [represented by the Air Operating Line C-D]. Thus, the driving force at any point is the vertical distance between the two operating lines. And therefore, the performance demanded from the tower is the inverse of this difference. The integrand of the Merkel equation can be represented by the Demand Curve -shown on fig.3.4.
Design of Cooling Tower
Design of Cooling Tower
Chapter 4 Cooling Tower Technical Specifications
4.1. Cooling Tower Technical Specifications Water Flow Rate, (L2)
0.116 m /hr
Inlet Tempretute of Water (T2)
45 C
outlet Tempretute of Water (T 1)
35 C
Wet Bulb Tempreture (WBT)
29 C
Height of Cooling Tower (Z)
0.762 m
Inlet Tempretute of air (T a1)
30 C
outlet Tempretute of air (Ta2)
39 C
Air Flow Rate, (G)
150 m /hr
Table 4.1, Cooling Tower Technical Specifications
4.2. Data from Psychometric Chart and Steam Table:
Enthalpy of water at inlet temperature(H 2)
188.4 kJ/kg
Enthalpy of water at outlet temperature(H 1)
146.6kJ/kg
Humidity of Inlet Air (Ha1)
0.025 Kg Water / Kg dry air
Humidity of Outlet Air (H a2)
0.03 Kg Water / Kg dry air
Table 4.2, Data from psychometric chart & Steam table
Design of Cooling Tower
4.3. Design Calculation 4.3.1. Water Mass Balance L2-L1 = G2 * Ha2 - G1 * Ha1 G2 = G1 = G L2-L1 = G *(H a2- Ha1) L1 =0.116 – 150 * (0.003-0.0025) L1 = 0.041 m 3/hr
4.3.2. Energy Balance Q = H2 – H1 =188.4 kJ/kg – 146.6 kJ/kg = 41.8 kJ/kg
4.3.3. Calculate number of transfer unite (NTU) :
= (H2 – H1) / ∆Hlm Mean driving force,
⁄ = (188.4 - 146.6) / ln (188.4/146.6) = 166.62 kJ/kg
NOG = (188.4 - 146.6) / 166.62 = 0.25 Now, Height of Cooling tower, z = 2.5 ft = 0.762 m Z = HOG*NOG Hence, HOG= z / NOG = 0.762/0.25 = 3.048 m
3.048 m= (1.236 kg / m 2sec) / (1 atm * 29 kg / kgmol*K Ga)
Design of Cooling Tower Overall mass transfer coefficient, K Ga = 0.01398 kgmol / atm *m 2*s. Cooling Tower Characteristics are given as,
= 0.149 kg0K / kJ
4.3.4. Characteristics of Cooling Tower 1. Cooling Tower Approach (CTA) CTA = T1 – WBT = 35 – 29 = 6 0C
2. Cooling Tower Range (CTR) CTR = T2 – T1 = 45 – 35 = 10 0C Now, Mass of water circulated in cooling tower Mw = Flow Rate of Water x Mass density of water Mw = 0.116 x 1000 Mw = 116 Kg / hr
3. Heat Loss By Water (HL) HL = M w1 x C pw x (T2 – T1) HL = 116 x 4.186 x (45 - 35) HL = 4855.76 KJ / hr
4. Effectiveness in % Effectiveness = Range / (Range + Approach) = 100* (cooling water Inlet Temperature- cooling water Inlet Temperature) / (Cooling water Inlet Temperature-Wet Bulb Temperature)
Design of Cooling Tower = 100* (45-35) / (45-29) = 62.5 %
5. Cooling Capacity Cooling Capacity = mass flow rate of water *Specific heat *Temperature difference = 116 * 4.185 * (45-35) = 4854.6 kJ/hr
6. Evaporation Losses Evaporation Losses = 0.00085 * 1.8 * circulation rate (m3/hr) * (T1-T2) = 0.00085 *1.8 *0.116 * 10 = 1.7748 *10-3 m3/hr
7. Efficiency of Cooling Tower Efficiency of Cooling Tower = N = (T1 – T2) / (T1 – WBT)
N = (45 - 35) / (45 - 29) N = 62.5 %
4.3.5. Different Types of Losses 1. Drift Losses (DL) Drift losses are generally taken as 0.10 to 0.20% of circulating water. DL = 0.20 x mw1 / 100 DL = 0.20 x 116 / 100 DL = 2320 Kg / hr
2. Windage Losses (WL) Windage losses are generally taken as 0.005 of circulating water. WL = 0.005 x mw1 WL = 0.005 x 116 WL = 0.58 Kg / hr
3. Evaporation Losses (EL )
Design of Cooling Tower Evaporation losses are generally taken as 0.00085 of circulating water. EL = 0.00085 x mw1 x (T1 – T2) EL = 0.00085 x 116 x (45 - 35) EL = 0.986 Kg / hr
4. Blow Down Losses (BL) Number of cycles required for cooling tower is given by Cycles = XC / XM Where, XC = Concentration of solids in circulating water XM = Concentration of solids in Make-up water Water balance equation for cooling tower is M = WL + EL + DL M = 2320 + 0.986 + 0.58 M = 2321.566 Kg / hr XC / XM = M / (M - EL) XC / XM = 2321.566 / (2321.566 - 0.986) XC / XM = Cycles = 1.0004 So, Blow down loss BL = EL / (Cycles - 1) BL = 0.986 / (1.0004 - 1) BL = 2465 Kg / hr
Design of Cooling Tower
Design of Cooling Tower
Chapter 5 Experimental Procedure 1- Introduce water and record its flow rate. 2- Put the heaters on so that water is heated to the required temperature. 3- Introduce air and record its flow rate. 4- Wait for steady state then record steady state dry and wet bulb temperature of air at the entrance and exit. 5- Record the inlet and outlet temperature and flow rate of water also record temperature at different stages. 6- Change the air flow rate & Water flow rate and repeat step 3.
Fig. 5.1, Arrangement of cooling tower
Design of Cooling Tower
Design of Cooling Tower
Chapter 6 Observations & Discussion 6.1. Observations 0
1. Inlet water Temperature= 45 C 0
2. Wet Bulb Tempreture =29 C 3
3. Air flow rate =2.5 m /min
Sr. No.
Flow rate of water 3
0
Water Temperature, C
m /hr
Inlet
outlet
1.
0.0847
45 C
32 C
2.
0.1101
45 C
35 C
3.
0.213
45 C
36 C
Table 6.1, Observation Table
Design and Operation Conditions
Water Distribution System and Material of Construction
Tower Type
Mechanical Forced draft
Stand Pipe
PVC
Flow Type
Counter Flow
Flexible Pipe
PVC
Water Flow Rate
0.116 m3/hr
Distributer
Steel Sheet
Hot Water Temp.
45 0C
Mechanical Equipment
Cold Water Temp.
35 0C
Blower
Centrifugal
Wet Bulb Temp.
29 0C
Manufacturer
Black & Deckars
Flow Rate
2.5 m /min
Structural Details
Height of CT
2.5 ft
Water Motor
Area of Cross Sect. 0.44 ft
Manufacturer
YANG Pumps
Basic Tower Construction Material
Flow rate
6 lit/min
Tower Frame
Acrylic Sheet
Power Consumption
18W
Casing
Aluminium
Piping Connections & Distributers
Cold Water Basin
Plastic Material
Inlet Pipe Dia.
½ inch
Filling
PVC
Distributer Area
0.34 ft
Bolt Nuts
Cast Iron
Area of Holes (10)
70.68 mm
Table 6.2, Observation Table
Design of Cooling Tower
6.2. Design Calculation 6.2.1. Water Mass Balance L2-L1 = G2 * Ha2 - G1 * Ha1 G2 = G1 = G L2-L1 = G *(H a2- Ha1) L1 =0.116 – 150 * (0.003-0.0025) L1 = 0.041 m 3/hr
6.2.2. Energy Balance Q = H2 – H1 =188.4 kJ/kg – 146.6 kJ/kg = 41.8 kJ/kg
6.2.3. Calculate number of transfer unite (NTU):
∫
= (H2 – H1) / ∆Hlm
Mean driving force,
⁄ = (188.4 - 146.6) / ln (188.4/146.6) = 166.62 kJ/kg
NOG= (188.4 - 146.6)/ 166.62 = 0.25 Now, Height of Cooling tower, z= 2.5 ft = 0.762 m z= HOG*NOG Hence, HOG= z/NOG = 0.762/0.25 = 3.048 m
3.048 m=(1.236 kg/m 2sec)/(1 atm * 29 kg/kgmol*K Ga) K Ga = 0.01398 kgmol/atm *m 2*s Overall mass transfer coefficient, K Ga = 0.01398 kgmol/atm *m 2*s.
Design of Cooling Tower
6.3. The influence of process conditions upon design It is rewarding to study the effects of various process changes upon the height and cross section of the apparatus or the cost of its operation. Six of the considerations which affects the size of the tower are indicated in fig.6.1. They are analyzed best by means of the enthalpy- temperature diagram, since the area between the saturation and operating lines is a measure of the total potential. The smaller the area the greater the height of tower required for fulfillment of the process conditions [4]. a. Unsaturation of the inlet air. Heretofore reference has been made only to the wet bulb temperature of the inlet air ant not to its dry bulb. In each case it is assumed identical with wet bulb, i.e., adiabatically saturated. Suppose the air is at a dry bulb of 850F when the wet bulb is 75 0 F. the air will be unsaturated, and its enthalpy will be41.7Btu/lb instead of 39.1.In fig.6.1(a) this will drop the operating line insignificantly from H1-H2 to (H1)- (H2), the cross hatch area representing the increase in potential. Failure to correct the enthalpy for dry bulb gives results which are slightly on the safe side, and for this reason it is customary to specify only the wet bulb. b. Close Approach. Both operating lines in fig.6.1(b) have the same L/G ratio and equal ranges of 35 0 F for the removal of the same process heat load. The operating line (H1)-(H2) attempts to do the same cooling as H 1-H2 and with the same inlet air but between the temperatures of 115 and 800F instead of 120 and 85 0F. The area between the saturation curve and the operating line is greatly decreased by (H1)(H2). Similarly it might be desired to obtain water from 120 to 85 0F with 800 wet bulb instead of 75 0F wet bulb air. This will raise the operating line H 1- H2 vertically and also decrease the potential. c. Changing the L/G ratio. If the ground area is too limited, such as when a cooling tower is erected atop a building, it may necessary to employ a relatively high liquid loading without increasing the air quantity, since 400fpm is about the maximum economical air velocity. This will decrease the cross section of the tower but increase the slope of the tower line H1 – H 2 to H1 – (H2) as in fig.6.1(c), resulting in decreased potential and higher tower. This is simple observation that the less air circulated per pound of water the less the extent of cooling[6]. d.
Location of the operation range. The saturation line has a varying curvature. In fig.6.1(d) an operating line H 1- H2 is shown with a range from 105 to 70 0F. Suppose
Design of Cooling Tower 600F. This would be impossible with the same L/G ratio, since the operating line (H1)-(H2) would intersect the saturation line. Obviously heat transfer would stop at the intersection (H’2), since the potential would be required, which in turn means more air must be circulated for the removal of the same number of Btu.
Fig. 6.1, Effects of design Variables on the size of potential
Design of Cooling Tower
e. Staying. One of the means of overcoming the small L/G ratio in the preceding paragraph can be accomplished by the use of two towers. This is staying. The water at the top of the first tower is hot and contacts air of enthalpy H 2 along the operating line H1-H2 as shown in fig. 6.1(e). the water is removed from the basin at temperature T2 and is pumped over the second tower, which also uses atmospheric air of enthalpy H1. The second tower operates between H 1 and H3. In this way both operating line may have large slopes without intersecting the saturation line. The fixed charges and operating cost of two towers increases the cost of water considerably, but water produced in this manner should be regarded as chilled water, and its cost and range compared with that of refrigerator water. f. Elevation. Some plants are located at high elevations. Should this be mentioned in the process conditions? At reduced atmospheric pressure, as seen in fig. 6.1(f), the saturation line is higher, which in turn increases the potential and reduces the required size of tower if all other conditions are the same. This occurs because the partial pressure of the water is fixed whereas the total pressure has been decreased. The humidity of saturated air at higher elevation is also greater.
Design of Cooling Tower
Design of Cooling Tower
Chapter 7 Cost Estimation Total Cost = Fixed Cost + Operating Cost
7.1. Fixed / Construction Cost 1. Cooling Tower frame (Acrylic Sheet)= Rs. 1000/2. Fill Material =Rs.300/3. Water Pump = Rs.200/4. Air Blower = Rs.4000/5. Pipes = Rs.200/6. Valves and Couplings = Rs. 250/7. Basin = Rs. 300/8. Distributer = Rs. 300/Total Fixed Cost = Rs. 6550/-
7.2. Operating Cost Energy required for water Pump= 18 W Energy required for Air Blower = 250W Total Energy Consumed = 268W = 0.268kW Now, 1 Unit of electricity = 1kW * 1 hr Hence, for 1 hr Number of units consumed = 0.268 Units For 1 day, it will be = 0.268 * 24 = 6.432 units. At the rate of Rs. 7 per unit, Total Working Cost of 1 Day =7 * 6.432 = Rs. 45.024
7.3. Total Cost Total Cost = Fixed cost + Operating Cost = 6550 + 45.024 = Rs.6595.024
Rs. 6600
Design of Cooling Tower
Design of Cooling Tower
Chapter 8 Energy Saving Opportunities From the above data of the design of cooling tower and observations & discussions we are able to conclude some energy saving opportunities for the cooling tower is as given below:
Optimize cooling tower fan blade angle on a seasonal and/or load basis.
Correct excessive and/or uneven fan blade tip clearance and poor fan balance.
On old counter-flow cooling towers, replace old spray type nozzles with new square spray ABS practically non-clogging nozzles.
Replace splash bars with self-extinguishing PVC cellular film fill.
Install new nozzles to obtain a more uniform water pattern
Periodically clean plugged cooling tower distribution nozzles.
Balance flow to cooling tower hot water basins.
Cover hot water basins to minimise algae growth that contributes to fouling.
Optimise blow down flow rate, as per COC limit.
Replace slat type drift eliminators with low pressure drop, selfextinguishing, PVC cellular units.
Restrict flows through large loads to design values.
Monitor L/G ratio, CW flow rates w.r.t. design as well as seasonal variations. It would help to increase water load during summer and times when approach is high and increase air flow during monsoon times and when approach is narrow.
Monitor approach, effectiveness and cooling capacity for continuous optimisation efforts, as per seasonal variations as well as load side variations.
Consider COC improvement measures for water savings.
Design of Cooling Tower
Consider energy efficient FRP blade adoption for fan energy savings.
Consider
possible
improvements
on
CW
pumps
w.r.t.
efficiency
improvement.
Control cooling tower fans based on leaving water temperatures especially in case of small units.
Optimize process CW flow requirements, to save on pumping energy, cooling load, evaporation losses (directly proportional to circulation rate) and blow down losses.
Design of Cooling Tower
Design of Cooling Tower
Chapter 9 Typical Problems and Trouble Shootings for Cooling Tower Problem /
Possible Causes
Remedies/Rectifying
Difficulty
1.
Action
Excessive Voltage Reduction
Check the voltage
absorbed current /
2a. Incorrect angle of axial fan
electrical load
blades 2b. Loose belts on centrifugal
Adjust the blade angle
Check belt tightness
fans (or speed reducers) 3.
Overloading
excessive
air
owing flow-fill
to
Regulate the water flow by
has means of the valve
minimum water loading per m
2
of tower section 4. Low ambient air temperature
The
motor
is
cooled
proportionately and hence delivers more than name plate power 2. Drift/carry-over Uneven
operation
of
spray
Adjust the nozzle orientation
of water outside the
nozzles
and eliminate any dirt
unit
2. Blockage of the fill pack
Eliminate any dirt in the top of the fill
3. Defective or displaced droplet
Replace
or
eliminators
eliminators
realign
the
4. Excessive circulating water Adjust the water flow-rate flow (possibly owing to too high by means of the regulating pumping head)
valves. Check for absence of damage to the fill
3.Loss
of
water 1. Float-valve not at correct
from basins/pans
level
Adjust the make-up valve
Design of Cooling Tower 2.
4.Lack of cooling
Lack
of
equalizing
Equalize
the
basins
connections
towers operating in parallel
1. Water flow below the design
Regulated
the
flow
and hence increase valve
means of the valves
in
Check
temperatures 2. Irregular airflow or lack of air
Flowing
of
to
the
by
direction
of
rotation of the fans and/or
increased
belt tension (broken belt
temperature range
possible) 3a.
Recycling
of
humid
Check
the
air
discharge air
velocity
3b. Intake of hot air from other
Install deflectors
descent
sources 4a. Blocked spray nozzles (or
Clean the nozzles and/or the
even blocked spray tubes)
tubes
4b. Scaling of joints
Wash or replace the item
5. Scaling of the fill pack
Clean material
or
replace (washing
the with
inhibited aqueous sulphuric acid is possible but long, complex and expensive)
Table 9.1, Typical Problem and Trouble Shooting for CT
Design of Cooling Tower
Design of Cooling Tower
Chapter 10 Conclusion
It is deduced that the condition of the surface area and the distribution of water on the sheets such as the distance between the repeated ribs and their angle to air flow and water flow play an important part in the efficiency of each pack, resulting from the influence of the different water distribution on the two sides of the sheets. It has been found that a packing with high air turbulence in combination with relatively low fluid velocity is more economic than a fairly smooth and straight packing in combination with high liquid velocity.
The mass transfer and heat transfer is decreased with increase inlet air humidity and, the objective of use packing is to increase area of contact between water and air. The cooling tower does not use in the place which the air have high humidity.
The theoretical calculations are approximately matches with the experimental observations and observations shows that cooling tower range is decreases with the increase in inlet Water flow rate.
Design of Cooling Tower
Design of Cooling Tower
Chapter 11 Bibliography [1] Improved Construction of Cooling Towers of Reinforced Concrete. UK Patent No. 108,863 [2] ―Power Plant Cooling Towers Like Big Milk Bottle" Popular Mechanics , February 1930 bottom-left of pg 201 [3] Richardson & Coulson, Chemical Engineering, Fifth Edition 2002, University of Wales Swansea. [4]D. Q. kern, Process Heat Transfer, Tata McGraw-Hill Edition 1997. [5]McCabe Smith, Harriott, Unit operation of Chemical Engineering, Fifth Edition 1993, Tata McGraw Hill. [6] Perry R. H. and Chilton, C. H., eds., Chemical Engineering handbook,5 th Edition, Tata McGraw Hill,1973. [7] London. A. L., W.E. Mason and L.M. K. Bolter, Trans. ASME, 62, Page no. 41-50 (1940) [8] Robert E. Treybal, Mass transfer Operations, Third Edition, Tata McGraw Hill, 1981. [9] R. Burger, Wiley, Maintenance, Upgrading and Rebuilding Cooling Tower Technology, Wiley, 1995. [10] S. Johnson, A. Barz, Comparative performance characteristic of cooling tower packings, in: LAR 7th Cooling Tower and Spring Pond Composium, Leningrad, Russia, 1990. [11] F. McQuiston, Heat, mass and momentum transfer data for ®ve plate ®n tube heat transfer surfaces, ASHRAETrans. Part 1 84 (1978) 226±308. [12] Narendra Gosain, Ph.D., P.E. and Farouk Mahama, Ph.D., Walter P. Moore And Associates, Inc., Complex Structural Analysis Simplifies Repair Phasing In Restoration Of Hyperbolic Cooling Towers 2010.
Design of Cooling Tower
Appendix
Design of Cooling Tower
1. Steam Table
Design of Cooling Tower
Design of Cooling Tower
2. Psychometric Chart