MEE 491, Spring 2023
Experimental Design Project – Part 1 of 3
Submit via Gradescope by 11:59pm on Friday, 4/7/2023
Part 1 of Experimental Design Project
Prepare a proposal for your experimental design by answering the questions in Sections
A, B, and C contained in this document (i.e., “Analysis of System Scope,” “Measurement
Requirements,” and “Impact Factors”). Your answers for part 1 should NOT be written in the report
format used for your main laboratory reports. Please submit your assignment as a numbered list
with responses to the questions in Sections A, B, and C. This assignment should be typed and
be a maximum of 6 pages long. It is due by Friday April 7 at 11:59 PM.
Part 2 of Experimental Design Project
You will attend a brief (1 hour) in-person lab session to conduct experiments on a labscale cooling tower. Please review the course syllabus for the exact date of your lab session,
which will occur sometime between Tuesday 3/28/23 and Thursday 4/6/23. While this is an
individual assignment, students will attend lab with their normal lab groups at designated times.
Groups with an A or B in their group number will attend the week of 3/27 - 3/30/23 while students
with a C or D in their group number will attend the week of 4/3 - 4/6/23. Prior to coming to lab, you
must submit answers for problems 1-3 from the Experimental Design Project Part 2 to
Gradescope (i.e., the pre-lab assignment). You will consult the Part 2 document of the
experimental design project in preparation for this portion of the lab. After collecting data, you will
analyze the data and submit your responses in the Part 3 document. Parts 2 and 3 of the
experimental design project will culminate in a final submission that will consist of experimental
data (from Part 2) and data from the cooling tower simulator discussed in Part 3.
Part 3 of Experimental Design Project
You will receive additional information for Part 3 later this semester. This information will
include the description of a specific system, factors (i.e., variables), and levels (i.e., specific values
for the variables). You will collect “experimental data” that corresponds to the testing of these
factors and levels using a cooling tower simulator. Part 3 will consist of the analysis and
interpretation of the experimental data from Part 2 and from the simulator data of Part 3 and will
culminate in a final assignment.
Grading breakdown for experimental design project. In order to get a C or better in this course,
you must receive a score of 70 or higher on Part #1 assignment or Part #2 assignment.
Weighting
Points in Course
Grade
#1 Part 2 pre-lab 1-3 due night before lab session at 11:59pm
15
14%
Part 1 due by 4/7/23 at 11:59pm
85
#2 Part 2 answers submitted with Part 3 by 4/28 at 11:59pm
100
14%
Part 3 answers submitted by 4/28 at 11:59pm
Understanding the Cooling Tower Design Problem
The second law of thermodynamics requires that power plants (i.e. heat engines) reject
waste heat to the environment while producing work. In practice, this heat is removed via a
condenser that transfers the heat to a cooling water circuit. The design of this cooling water circuit
is of critical importance to the overall functionality of power generation plants. In this lab, you will
design and carry out a set of experiments on a cooling circuit that rejects heat to the environment
via a cooling tower. Your goal is to deduce the most important factors that affect the performance
of the cooling tower, as though you were a thermal design engineer working for a power
production company.
Motivation and Background
Where there is a heat engine, there is waste heat. Traditional power generation plants
driven by fossil fuels, nuclear power plants, solar farms, etc., all generate heat as a byproduct of
power generation. This waste heat can be released into the environment in many ways. Some
power generation plants are built near rivers, lakes, or oceans and leverage the large thermal
masses of these bodies of water to dissipate thermal energy, while some solar farms may be able
to rely entirely on passive free convection to dissipate their comparatively small thermal loads.
One of the most common infrastructures for handling waste heat is the wet cooling tower, which
leverages the latent heat of vaporization to reject thermal energy to the air surrounding the power
generation plant.
The Cooling Tower
Figure 1 shows a schematic of a concentrating solar vapor power plant, in which solar
energy is used to generate steam for turbine-based power generation (Rankine cycle). Here, we
are interested in the cooling water circuit (red box). Cold water enters from one side of the
condenser and then leaves the condenser as warm water (the process condenses the lowpressure steam on the heat engine side of the condenser). This warm water is then cooled in a
cooling tower and recycled back to the power plant. In the cooling tower, heat is transferred from
the warm water to the atmospheric air, which serves as a large heat sink. Some of the cooling
water escapes by evaporation, which is considered a waste of a precious natural resource, but
we get evaporative cooling and cold water at the end for the cost of losing the evaporated water.
Engineers strive to transfer heat from the cooling tower to the atmospheric air while considering
other metrics such as water retention and cost.
Figure 1. Concentrating Solar Vapor Power Plant based on [1].
Cooling towers can be either wet or dry. In a dry cooling tower, a closed-circuit coolant
(which can be water) is cooled by the environmental air and the coolant does not come in contact
with the air. The dry cooling tower is used where water is scarce. A dry cooling tower is more
expensive than a wet cooling tower of the same capacity, but the cost of a cooling tower is a small
fraction of the total cost of the power plant. In a wet cooling tower, such as the one under study
here, the water heated by the power plants condenser comes in direct contact with the
atmospheric air and both energy and mass transfer (evaporation) occur during this process inside
the tower. A fraction of the water stream evaporates into the air stream. The evaporation process
requires heat of vaporization energy, and this energy transfer results in a cooling of the remaining
water stream. Since a portion of the cooling water is evaporated into the air stream, an equivalent
amount of water must be added as make-up somewhere in the flow cycle.
Cooling Tower Jargon
Like with all technical fields, there are certain terms that people use when discussing cooling
tower performance. Some common cooling tower jargon is listed below.
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

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Cooling Range – The difference between the liquid water temperature at the entry and exit
of the tower (𝑇𝑤,in − 𝑇𝑤,out ).
Approach – The difference between the temperature of the liquid water exiting the tower
and the wet bulb temperature of the air entering (𝑇𝑤,out − 𝑇wb,in ).
Cooling Load – The rate at which energy is transferred to the liquid water before it is
pumped to the top of the packing.
Make-up – The quantity of liquid water that must be supplied to the water circuit to
compensate for the water removed from the water circuit because of evaporation, drift,
and other causes.
Drift or Carry Over – Droplets of liquid water that are entrained by the air stream leaving
the tower and carried out to the atmosphere.
Packing or Fill – The media over which the liquid water flows as it falls through the tower,
so that a large surface area is presented to the air stream flowing up through the tower.
Blow Down – Water deliberately removed from the water circuit to prevent the excessive
concentration of dissolved solids as a result of evaporation and the build-up of sludge from
impurities in the atmosphere.
Design of Experiment
For this overall project, you will play the role of a thermal design engineer tasked with providing
recommendations for the design and operating conditions of a wet cooling tower. There are nearcountless parameters that will affect the performance of a cooling tower, but you will only focus
on a few for this design experiment. Your goal is to find a combination of system parameters that
strikes a reasonable balance between cooling tower efficiency and operating cost. To do this, you
will utilize the tools of experimental design, keeping in mind that you only need a good solution,
not the best solution.
Cooling Tower Design Considerations
There are several performance metrics associated with the design of a cooling tower. In
this laboratory exercise, you will focus on cooling efficiency and cost. You will also have to
consider what we will call the cooling tower effectiveness, which is a nominal metric of whether
or not the wet cooling tower is the ‘right’ cooling technology for the given application.
The cooling efficiency of a wet cooling tower compares the actual temperature change of
the cooling water as it falls through the tower to the maximum theoretical temperature change of
the cooling water as it falls through the tower,
𝜂CT =
Range
𝑇𝑤,in − 𝑇𝑤,out
=
Range + Approach (𝑇𝑤,in − 𝑇𝑤,out ) + (𝑇𝑤,out − 𝑇wb,in )
When the temperature of the water leaving the cooling tower is equal to the wet-bulb temperature
of the moist air entering the cooling tower, the tower is said to be 100% efficient. It is not possible
to design a perfectly-efficient cooling tower, and many industrial cooling towers are about 70-75%
efficient [2].
Like for most engineering projects, cost is an important design consideration for cooling
towers. The cooling tower will have an initial build cost, as well as an operating cost (𝐶 [$ per
hour]) to keep it functioning. Since the build cost of the cooling tower is generally a small fraction
of the total build cost of the power plant, we will only consider the operating cost. The operating
cost consists of the power draw of the equipment needed to run the cooling tower and the cost to
replace the water lost by the cooling circuit.
The final design consideration you will account for is whether the wet cooling tower is a
good choice for the cooling circuit, or if a different technology might be more practical. The
purpose of a wet cooling tower is to cool the water in the cooling circuit primarily via evaporation.
We can imagine scenarios, however, in which the cooling tower efficiency (𝜂CT ) approaches 1
despite little evaporation taking place. In these cases, the desired cooling effect is being achieved
mostly via convection, and thus a convection-based technology, like a heat exchanger, would
probably be a better choice than a wet cooling tower. To assess this criterion, we will define the
cooling tower effectiveness as
𝜖=
change in water temp due to evaporation Δ𝑇evap
=
total change in water temp
Δ𝑇total
To provide a specific value for this project, the lower limit for this cooling tower design will be
taken as 𝜖 = 0.8. Any designs with 𝜖 < 0.8 must be disregarded, no matter their apparent
efficiency or cost.
Section A. Analysis of System Scope (15 points)
The primary goal of this lab activity is to practice and analyze the techniques of
experimental design, but it is still important to develop an understanding of the basic cooling tower
physics and the overall design problem. Although the design of experiment procedure should
produce reasonable conclusions, having a rough idea of how a system works is critical for being
able to assess your results/design recommendations. That is, as an engineer you are expected
to not only solve problems and find answers, but to be able to comment on the validity of the
solutions you develop. Complete the tasks below to develop your understanding of the complete
cooling tower system.
1. (5 Points) At steady state, the cooling tower requires power to run the water pump and the air
fan. It is also necessary to replace any water that is lost to the environment, which we will consider
to be entirely via evaporation (i.e. our model (simulator in part 3) ignores the effects of drift losses
and blow down, but those effects are accounted for in the lab experiment (part 2)). Develop an
equation for the cost to run the cooling tower per hour at steady-state operation. Assume the
power plant can sell electricity at Celec = $0.12 per kilowatt-hour and that the cost of water is Cwater
= $10 per 1000 gallons. Write the equation with Qevap, the volumetric flow rate of evaporated
water, in units of L/s.
2. (5 Points) As described previously 𝜂CT ≈ 1 when 𝑇𝑤,out = 𝑇wb,in . Explain why the minimum
outlet temperature of the liquid water is equal to the wet-bulb temperature of the air entering the
tower. (Hint: What are the two primary driving forces for energy exchange between the water and
the air inside the cooling tower? Under what conditions would the water and air be in equilibrium,
with no net energy exchange between the two fluids?)
3. (5 Points) The cooling tower effectiveness, 𝜖, is given as the ratio of two temperature
differences, but neither temperature difference is explicitly defined. The total change in the liquid
water temperature (Δ𝑇total ) is just the cooling range. To determine an expression for the change
in the liquid water temperature due to evaporation (Δ𝑇evap ), consider a falling film of water exposed
to a stream of air at atmospheric pressure (Figure 2a). This falling film of water will exchange
energy with the air via both heat and mass transfer. These various energy exchanges will result
in a temperature change of the portion of water that remains liquid (Δ𝑇total). We want to
approximate how much of this temperature change is due to evaporation.
Figure 2. Detailed view of water falling over the packing material with (a) description of processes
and (b) control volume for water
To make this approximation, we imagine the water to be an adiabatic control volume (Fig. 2b)
with some total mass flow rate in (𝑀̇tot ), some mass flow rate of liquid water out (𝑚̇𝑙 ), and some
mass flow rate of water vapor out (𝑚̇𝑣 ). This is obviously not exactly what happens in this physical
problem, since there will be convection between the air and the water vapor doesn’t all evaporate
at one time, but this is a reasonable simplification that will allow us to approximate Δ𝑇evap . Using
the adiabatic CV show in Fig. 2b, show that
𝑀̇tot (ℎ𝑓@𝑇in − ℎ𝑓@𝑇out ) = 𝑚̇𝑣 (ℎ𝑔@𝑃air − ℎ𝑓@𝑇out )
Further simplify the above equation to show that
Δ𝑇𝑙 ≈
𝑚̇𝑣 (ℎ𝑣𝑎𝑝𝑜𝑟@𝑃,𝑇,𝑅𝐻 − ℎ𝑓@𝑇out )
𝑀̇tot 𝑐𝑝
where Δ𝑇𝑙 is the difference between the liquid water temperature at the inlet and outlet of the
control volume, and 𝑐𝑝 is evaluated at the average liquid water temperature. Note that Δ𝑇𝑙 is the
change in the liquid water temperature if we were to only consider evaporation; that is, Δ𝑇𝑙 =
Δ𝑇evap and we have derived an expression to approximate the temperature change of the water
in the cooling tower due exclusively to evaporation.
Section B. Measurement Requirements (20 points). Note that some of the questions in this
section are somewhat subjective (i.e., there is not a single “correct” answer). Your grade
on these questions will be based upon the ability of your arguments/rationale to convince
the grader that your answers are suitable. However, that does not mean all answer are
correct and proper engineering justification is required in all cases.
4. (5 points) For the effectiveness and efficiency equations described previously, describe how
and/or where you will get the equation inputs for each parameter. Use a table to clearly indicate
each and every parameter in both equations, the units of these parameters, how you will
determine each parameter and, if relevant, the locations of these parameters. Some ways in
which you might determine the parameters are measuring them, looking them up, specified in this
handout, etc. The best way to clearly indicate the locations of any relevant measurements will be
to draw a schematic of the water loop and add locations to this figure with corresponding point
numbers. The schematic is expected for full credit.
5. (15 points) Describe what equipment and instrumentation you will use to carry out the
necessary measurements to evaluate the effectiveness and efficiency and the reasons behind
your choices. Furthermore, the ability to remotely monitor/operate this system and store data will
be useful. Consequently, you are required to choose equipment/instrumentation with these
remote capabilities for this question.
You are also required to specify the corresponding ancillary equipment necessary to successfully
operate your equipment and instrumentation. For example, a pitot static tube does not measure
velocity directly; it needs to be operated with additional instrumentation that can read pressure.
This ancillary equipment should also include equipment to remotely operate/monitor your system
as well as store data.
Section C. Impact factors (50 points). Note that some of the questions in this section are
somewhat subjective (i.e., there is not a single “correct” answer). Your grade on these
questions will be based upon the ability of your arguments/rationale to convince the grader
that your answers are suitable. However, that does not mean all answer are correct and
proper engineering justification is required in all cases.
6. (15 points) List the factors that you think will affect the efficiency and effectiveness of the cooling
tower. Be sure to include at least 9 factors in this list. Included in this list should be the air
temperature, local pressure and wet bulb temperature, among others. Note that terms like relative
humidity cannot also be listed as factors if they are dependent variables of the other factors.
Separate these factors into two categories: high impact factors and low impact factors. Assume
that the primary objective is high efficiency. Cost is a secondary objective and should be
considered from a qualitative standpoint.
Report your answer using 2 separate tables as formatted in the example below. Describe your
rationale for why you placed each factor in the high or low impact category. Note that the width of
the right column in these tables is intentionally made large to better utilize the space on the pages
(and thereby assist in keeping you within the assignment page limit).
Example table for question 9:
High
Factors
…
…
Impact Reason
Low
Factors
…
…
Impact Reason
…
…
…
…
7. (20 points) Consider a full size (1,500 to 2,500 kW) cooling tower. For each of the factors you
listed in question 6, choose an initial value that you plan to use in your system design. These
values should be specific and quantitative. This means that you should specify actual dimensions
and materials. For example, specifying “metal” for the tube material is insufficient, but specifying
“copper” is sufficient. As another example, specifying “medium” for the tube diameter is
insufficient, but specifying “10 mm” is sufficient.
Report your answer in table-format as shown in the example below. Describe your rationale for
how you came up with these initial values. Note that the width of the right column in these tables
is intentionally made large to better utilize the space on the pages (and thereby assist in keeping
you within the assignment page limit).
Example table for question 7:
Initial
Value
of
Factor
Dry bulb temperature
= 22℃
Pressure = 1 atm
Inner diameter of flow
tube = 10 cm
Reason
…
…
…
…
…
Some additional resources to consider for cooling towers:
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http://www.proairengineering.co.za/?page_id=767
o This article highlights different types of cooling towers such as natural and
mechanical draft cooling towers and alludes to the largest end of the spectrum
for the towers, but also mentions that towers range from rooftop systems to the
larger ones for power plant. It also highlights many of the different uses of the
cooling towers
https://www.jhuapl.edu/content/techdigest/pdf/APL-V13-N03/APL-13-03-Moon_III.pdf
o This is a paper on the environmental impacts of cooling towers and some of the
sediments that build up during operation. The first figure and table, and the
background section, provide some information about the tower heights,
evaporation rates, and accompanying cooling rates.
https://www.sciencedirect.com/science/article/pii/B9781933762166500086
o Section 4.6 - Cooling Tower Operations provides some information on mass flow
rates, evaporation rates and tower height.
8. (15 points) Given that your primary objective is to maximize cooling tower efficiency, “imagine”
that you will be able perform a maximum of up to 50 “experiments.” Note that you need not do
exactly 50 experiments and that a smaller quantity may be acceptable. Cost is a secondary
objective and should be considered from a qualitative standpoint at this stage.
Choose which factors you would experimentally test and what specific levels you will choose (i.e.,
do not simply specify “small,” “medium,” and “big” for the levels of inner diameter of the tube, but
instead list actual quantitative values such as 5 mm, 25 mm, 100 mm). Present the experiments
that you will do using a similar format to the two tables shown in lecture and also indicated below.
Factor
A
B
C
D
E
F
G
Gasket Design
Front Cover Design
Front Bolt Torque
Gasket Coating
Pump Housing Finish
Rear Bolt Torque
Torque Pattern
Level
1
2
Production
New
Production
New
Low
High
No
Yes
Smooth
Ultrasmooth
Low
High
Front then Rear
Rear then Front
Table 1. An example table that describes the factors and levels chosen in an experimental design.
The table is taken from lecture and is meant for illustrative and conceptual purposes only. Note that
many of the levels are insufficiently described in this table. For example, “low” and “high” are
insufficient descriptions of the levels for front bolt torque. Format your answer in question 10 using
this table’s format.
A1
B1
A2
B2
B1
B2
C1
C2
C1
C2
C1
C2
C1
C2
D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2 D1 D2
G1
G2
E1
G1
F2
G2
G1
F1
G2
E2
G1
F2
G2
F1
Table 2. An example table that describes which factors and levels will be tested in an experimental
design. This table represents a ½ fractional factorial experiment design. The white squares indicate
experiments to be done and the grey square represents experiments that aren’t done. The table is
taken from lecture and is only for the purposes of illustrating how to format your response to this
question.
References
[1] Moran, M. J., Shapiro, H. N., Boettner, D. D., & Bailey, M. B. (2014). Fundamentals of
engineering thermodynamics. John Wiley & Sons.
[2]
https://www.chemengonline.com/cooling-towers-estimate-evaporation-loss-and-makeupwater-requirements/?printmode=1