The document details a study on cooling towers, focusing on the creation of a mathematical model implemented in the Engineering Equation Solver (EES) for thermodynamic analysis. It includes various types of cooling towers, governing equations, and results from experimental and modeled comparisons. Key findings emphasize the accuracy of simulations, with suggestions for further investigation into errors and additional theories.

1. COOLING TOWER
MODELLING IN EES
Theses Presentation
DT 022/4
SHIYAS BASHEER Supervisor: ANTHONY REYNOLDS

2. Objectives
Study on Cooling Towers
Recent developments
Create a mathematical model
Implement it on EES (Engineering
Equation Solver)
Verify the results
Create a user interface
Sensitivity analysis

3. Implementation
Mathematical modelling
(governing equations)
Input
· variables
· fixed
parameters
Results
Database of
thermodynamic
properties
Write the
code
Run the
program

4. Engineering Equation Solver
Equation solving program
Useful in thermodynamic and heat
transfer problems
Equations entered in any order
High accuracy
Graphical Input/output
No real programming

5. Cooling Tower
Extract heat
Reduce temperature
Emit to atmosphere
Schematic diagram of a cooling tower(Energy, 2011)

6. Types of Cooling Towers
Wet Cooling tower
Once through cooling tower
Direct dry cooling
Indirect dry cooling
Wet dry cooling tower

7. Hilton H892

8. Theory

9. Assumptions
Steady state
Relative Humidity – 100%
Negligible Kinetic and potential energy
Fully saturated
Ambient temperature of air going in

10. Control
Volume

11. Control
Volume

12. Mathematical Model
Mass Balance
𝒊𝒏
𝒎 =
𝒐𝒖𝒕
𝒎
Conservation of mass for water:
𝑚 𝑎 𝜔1 + 𝑚 𝑤1 = 𝑚 𝑎 𝜔2 + 𝑚 𝑤2
Conservation of mass for air:
𝑚 𝑎,𝑖𝑛 = 𝑚 𝑎,𝑜𝑢𝑡 = 𝑚 𝑎𝑖𝑟

13. Mathematical Model
Energy Balance
𝑬𝒊𝒏 = 𝑬 𝒐𝒖𝒕
At the water side:
𝑄 = 𝑚 𝑤1ℎ3 − 𝑚 𝑤2ℎ4
On the moist air side :
𝑄 = 𝑚 𝑎(ℎ2 − ℎ2)

14. Mathematical Model
Mass Balance
𝒊𝒏
𝒎 =
𝒐𝒖𝒕
𝒎
Conservation of mass principle
𝑚 𝑚𝑎𝑘𝑒−𝑢𝑝 + 𝑚 𝑐𝑜𝑙𝑑 𝑤𝑎𝑡𝑒𝑟,𝑖𝑛 = 𝑚ℎ𝑜𝑡𝑒 𝑤𝑎𝑡𝑒𝑟.𝑜𝑢𝑡

15. Mathematical Model
At the mixing point:
𝑄ℎ𝑒𝑎𝑡𝑒𝑟 − 𝑊𝑝𝑢𝑚𝑝 = 𝑚 𝑤1ℎ3 − 𝑚 𝑤2ℎ4
Energy Balance
𝑬𝒊𝒏 = 𝑬 𝒐𝒖𝒕

16. Implementation in EES
35 Equations

17. Results
Experimental Modelled
TEST No. Units 1 2 3 4 1 2 3 4
Air inlet Dry Bulb (t1) oC 19 19 19.4 19.7 19 19 19.4 19.7
Air inlet Wet Bulb (t2) oC 15.6 15.4 15.8 16.5 15.34 15.34 15.7 15.97
Air Outlet Dry Bulb (t3) oC 16.8 18.4 20.5 23 16.02 18.72 21.44 23.81
Air Outlet Wet Bulb (t4) oC 16 18 20.4 23 15.85 18.54 21.24 23.6
Water Inlet Temperature (t5) oC 17 21.6 27.2 32.7 16.84 21.47 27.09 33.34
Water Outlet Temperature (t6) oC 16.4 18.6 21.3 23.9 16.28 18.7 21.5 24.0
Cooling Load (Q) kW 0 0.5 1 1.5 0 0.5 1 1.5
Make-up Quantity (me) kg 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Time Interval (y) s 600 600 600 600 600 600 600 600
Water Flow Rate (Mw) g/s 40 40 40 40 40 40 40 40
CALCULATIONS
Air Flow Rate (ma) kg/s 0.05728 0.05728 0.05728 0.05728 0.05728 0.05728 0.05728 0.05728
Evaporation Rate kg/s 0.00049 0.00049 0.00049 0.00049 0.00049 0.00049 0.00049 0.00049
Make-up Rate kg/s 9.6E-07 9.6E-07 9.6E-07 9.6E-07 9.6E-07 9.6E-07 9.6E-07 9.6E-07
Rate of Make-up Quantity (mE) kg/s 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042 0.00042
Approach to Wet Bulb oC 0.8 3.2 5.5 7.4 0.88 3.36 5.8 7.7
Cooling Range oC 0.6 3 5.9 8.8 0.56 2.77 5.59 9.34

18. Verification of Results
y = 1.0292x - 0.5149
R² = 0.9992
15
16
17
18
19
20
21
22
23
24
25
15 16 17 18 19 20 21 22 23 24 25
Modelled
Experimental
Comparison of Water outlet temperature 0C

19. Verification of Results
y = 1.0631x - 0.2988
R² = 0.9933
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
Modelled
Experimental
Comparison of Cooling Range 0C

20. Overall Difference
-0.74%
0.53% 0.93% 0.42%
9.09%
4.76% 5.17%
3.90%
-7.14%
-8.30%
-5.55%
5.78%
-0.95% -0.61% -0.41%
1.92%
-0.95%
2.91% 3.95%
2.54%
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
1 2 3 4
DifferenceBetweenExperimentalandModelledData
Difference Plot
Water Outlet Temperature Approach to Wet bulb Temperature Cooling Range
Water Inlet Temperature Air Outlet Wet-bulb Temperature

21. Overall Difference
-5%
-6%
-4% -4% -4%
20%
7%
32%
-2% -2%-2%
7%
-5%
-3%
36%
-14%
-7%
-23% -23%
4%
-4%
-1%
-4% -3%
1%
-30%
-20%
-10%
0%
10%
20%
30%
40%
1 2 3 4 5
Differencebetweenexperimentalandmodelleddata
Difference Plot
Water outlet temperature Approach to wet bulb Cooling Range Air outlet wet bulb Water inlet temperature

22. Sensitivity Analysis
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Outletwatertemperature0C
Cooling Load kW
Relationship between cooling load and water inlet temperature
EES Results Actual Results

23. Sensitivity Analysis
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Temperature0C
Cooling Load kW
Relationship between cooling load and range
EES Water outlet temperature EES Water inlet temperature EES Wet bulb temperature
Actual water outlet temp Actual water inlet temperature Actual wet bulb temperature
Cooling Range

24. Sensitivity Analysis
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2 2.5 3
Approachtowetbulbtemperature0C
Air Velocity m/s
Relationship between Air velocity and approach
EES Results
Actual Results

25. User Interface

26. Conclusion and Future Work
All objectives met
Low simulation time
High accuracy
Investigate more into the errors
Investigate the equations
Add Merkel’s Theory of evaporation

27. Thank you

28. Reference
 2013a. ACHE [Online]. Available: http://www.thermopedia.com/content/663/.
 2013b. EES: Engineering Equation Solver | F-Chart Software : Engineering Software [Online].
Available: http://www.fchart.com/ees/.
 2013c. Natural Draft Cooling Towers | Hamon Group [Online]. Available:
http://www.hamon.com/en/cooling-systems/wet-cooling-systems/natural-draft-cooling-
towers/natural-draft/.
 BURGER, R. 1994. Cooling Tower Technology. Maintenance, Upgrading and Rebuilding.
United States of America: The Fairmont Press, Inc. .
 ENERGY, U. S. D. O. 2011. Cooling Towers: Understanding Key Components of Cooling
Towers and How to Improve Water Efficiency. In: ENERGY (ed.).
 HEATING, A. I. O. A. C. R. A. 2009. Types of Cooling Towers In: Selecting a Cooling Tower
Level 1 – Participant Guide Version 1.0.
 TAWNEY, R., KHAN, Z. & ZACHARY, J. 2005. Economic and performance evauation of heat
sink Options in combined cycle applications. Journal of engineering for Gas Turbine and Power,
127, 397-403.
Cooling Tower Technical Site of Daeil Aqua Co., L. (n.d.). Cooling Tower Thermal Design Manual. Retrieved
from http://myhome.hanafos.com/~criok/english/publication/thermal/thermal12eng.html
Ltd, P. H. (2003, February). Experimental operating and maintanence manual.