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Optimization of a Space Heating Solar System
by
Mashal Kara
A thesis submitted in conformity with the requirements for the degree of Master of Engineering
Graduate Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by Mashal Kara 2011
ii
Optimization of a Space Heating Solar System
Mashal Kara
Master of Engineering
Graduate Department of Mechanical Engineering University of Toronto
2011
Abstract
With the rapid evolution of technology and globalization, our society has become highly
dependant on the production of energy. As the threat of diminishing fossil fuels and the impact
these technologies have on the environment, the need for renewable energy has become evident.
In this project, we attempt to optimize an existing space heating solar technology using
Computational Fluid Dynamics (CFD) software. Through a series of simulations and the
construction of different predictive models, we were able to determine the optimal thickness,
flow rate and pipe diameter for a space heating solar system. During our research we discovered
that after optimizing the thickness of the panel we were unable improve the results by placing
obstructions to increase the average flow paths length. These obstructions created too large of a
resistance for the benefit they could offer. Further studies and experimental trials are needed to
fully understand how each parameter affects the power output of the system and the power
needed to run the system.
iii
Acknowledgments
I would like to start by thanking my supervisor Professor William L. Cleghorn, for his
continuous support in helping this project come to life. I would also like to thank my industrial
partner Thomas Gehring for giving me the opportunity to work on a project for the betterment of
future generations.
I would like to thank Donna Liu for her administrative assistance, advice and immense support
throughout my graduate studies. I would also like to thank the University of Toronto and the
Department of Mechanical and Industrial Engineering for creating a platform where students are
able to work on meaningful projects.
iv
Table of Contents
Acknowledgments.......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Symbols or Abbreviations ................................................................................................... v
1 Introduction ................................................................................................................................ 1
1.1 Background ......................................................................................................................... 1
1.2 Objectives and Concept ...................................................................................................... 2
1.3 Assumptions........................................................................................................................ 4
2 Calculations................................................................................................................................ 6
3 Results ........................................................................................................................................ 9
4 Parameter Optimization ........................................................................................................... 13
4.1 Regression analysis ........................................................................................................... 13
4.2 Factorial analysis of turbulent data ................................................................................... 14
4.3 Thickness analysis ............................................................................................................ 15
4.4 Flow path optimization ..................................................................................................... 17
5 Conclusions .............................................................................................................................. 22
6 Recommendations .................................................................................................................... 23
References..................................................................................................................................... 25
v
List of Symbols or Abbreviations
A Cross sectional area
Cp Specific heat
D Pipe diameter
dh Hydraulic diameter
L Panel length
€
m•
Mass flow rate through the system
N1 Number of fans in series
N2 Number of fans in parallel
P Static pressure
Pgen Power generated by the system
Pin Power input to the system
Pout Power output from the system
Q Volumetric flow rate of air through the system
RE Reynolds number
t Panel thickness
Tout Temperature out of the system
Vin Velocity in the inlet pipe
v Kinematic viscosity
1
1 Introduction
1.1 Background
Energy emitted from the sun varies with altitude, as we move towards the north, the intensity and
duration of solar radiation reduces. Solar energy can be captured in a few different ways; the
main ones are to convert it into electricity or heat.
Electricity generating solar panels, or photovoltaic solar panels, convert the energy from the sun
into usable electricity. The most efficient systems feed the power generated into the grid so as to
avoid losses due to energy transfer and storage. Most photovoltaic systems are able to generate
on average 150-160 Watts of electricity per square meter of panel from the 1000 Watts per
square inch emitted by the sun. This technology is less than 20% efficient [1].
Solar thermal technologies capture the energy of the sun to heat a medium such as water or air
before it is used. At the moment, solar water heaters are very popular as they are able to deliver
over 300 Watts of energy per square meter of panel at an efficiency of over 30% depending on
the size of the system. However, these systems require large hot water tanks to store the heated
water before use. The installation of these tanks is rather expensive and reduces the payback
period for the system. This technology is highly used in countries within 45 degrees of latitude
from the equator. Further north, the effectiveness of this kind of system is reduced due to the
lack of sun. The efficiency is also reduced further from the equator as cold temperatures in the
winter increases the energy lost in storage [2].
Solar energy can also be used to heat air and feed it to the ventilation system of the building thus
reducing the load carried by the furnace. These systems are only useful in parts of the world
where heating is required in the winter. They yield similar energy performances as solar water
2
heater technologies. Since the energy is used as soon as it is generated, these types of systems do
not require any storage, and thus have very few losses due to storage and energy transfers. At the
moment, this type of solar technology is not very popular, as it hasn’t been significantly
promoted in the regions where it can be of value [3].
1.2 Objectives and Concept
The objective of this project is to design a lightweight, self-installable and efficient space heating
solar panel. We will attempt to optimize its efficiency using ANSYS 12.1’s FLUENT module to
simulate the flow as it enters and exits the solar collector. Each time, we will vary key
parameters and flow paths and observe the effects on the power output and input. We will first
optimize physical parameters by performing a set of simulations. Using the data collected during
the simulations, we will apply statistical tools such as a Multiple Linear Regression (MLR) and a
Factorial Analysis to model the power input and output as a factor of the three main parameters.
This model will then be optimized to obtain the settings that yield the highest power generated.
Then, based on the optimized settings, we will determine the best flow path by creating
obstructions throughout the panel [4].
Figure 1, represents a schematic diagram of how space-heating solar systems operate.
3
Figure 1: Solar space-heating system
Air is forced by a fan from the space to be heated into the panel where it is heated and then
returned at a higher temperature. Return air can be delivered directly into a room or fed into the
ventilation ducts. The concept is simple enough for most homeowners to install the system on
their own with limited craftsmanship and tools. Figure 2 shows a technical drawing of the solar
collector panel with all critical dimensions.
Figure 2: Technical drawing of the solar collector panel
The critical parameters for the panel are the thickness (t), flow rate of air (Q) and pipe diameter
(D). Each of these parameters is believed to have an impact on the performance of the system.
Thickness: It is expected that as thickness is decreased more air will be in contact with the heat
source thus the heat transfer will be more effective. However, as thickness is reduced, the
All units in inches t
4
pressure loss across the system will increase thus increasing the cost of pumping the air through
the panel.
Flow rate: An increase in flow rate accelerates the air passing through the panel thus making the
flow more turbulent, which leads to a higher heat transfer rate and lower head loss. However, an
increase in flow also increases the required fan power because of the additional amount of air it
needs to move. Increasing the flow rate also accelerates the air velocity through the panel, giving
it less time to be in contact with the hot solar collectors, thus the temperature out of the system is
reduced, and so is the power output.
Pipe Diameter: A smaller pipe diameter causes the flow to be turbulent as it enters the panel, thus
facilitating heat transfer and increasing the power output. However, as pipes get smaller, the
pressure loss across the system increases, and more power is required from the pump [5].
It seems that to maximize the power generated by the system one would need to reduce the
thickness and diameter while increasing the flow rate until no additional gain is achieved. We
expect that as the power output increases, so would the power input. We will thus attempt to find
the optimal point where an incremental power increase does not require a larger incremental
power input to run the system.
1.3 Assumptions
For this research project, we will assume the flow is laminar when the Reynolds number is below
2300, and fully turbulent when above. Though we are aware that the flow in question may not be
fully turbulent, it is the only way to model it using Computational Fluid Dynamics (CFD)
software. For the fully turbulent flow, we will be using the standard k-epsilon model in ANSYS
FLUENT, which is governed by the following transfer functions [6]:
5
(eq 1)
(eq 2)
We have also made the assumption that all air properties remain constant throughout the
simulations, regardless of temperature change. We deemed it appropriate since the ranges of
temperatures we will be working within do not have a significant impact on air properties.
To simplify our model, we will assume that there are no losses within our system and that the
temperature of the solar collectors will remain constant throughout the simulation. Based on
experimental results, we were able to determine the temperature to be 370 K in clear sunny
weather. We will use this temperature as part of all our simulations.
6
2 Calculations Throughout our simulations, we will attempt to calculate the power output and the power input
required for the system. In order to adequately run the simulations, FLUENT requires the
velocity at the inlet pipe and the Reynolds number in the panel.
The velocity of the air as it enters the intake pipe in meters per second can be calculated as
follows [7]:
€
Vin =QA
(eq 3)
where Vin is the velocity of the air in the inlet pipe, Q is the volumetric flow rate of air through
the system, and A is the cross sectional area of the inlet pipe.
We then need to calculate the Reynolds number in the panel as it will allow us to determine
whether the flow is turbulent or laminar and select the appropriate model in FLUENT. Based on
our assumption a Reynolds number over 2300 will be assumed to be fully turbulent and can be
calculated as follows [7]:
€
RE =wdhν
where
€
dh = 2t , and
€
w =QtL
(eq 4)
where w is the average air velocity in the panel, dh is the hydraulic diameter, v is the kinematic
viscosity of air, t is the thickness of the panel, Q is the volumetric flow rate of air through the
system, and L is the length of the panel.
Given the above information, FLUENT will then output the air temperature out of the panel, the
pressure drop across the panel and the mass flow rate of air. From these data we need to calculate
the power output from the panel and the power input required from the fan.
The power output from the solar panel (Pout) can be calculated as follows [8]:
7
€
Pout = cp m•
ΔT (eq 5)
where cp is the specific heat of air,
€
m•
is the mass flow rate of air through the system, and
€
ΔT is
the change in temperature from the inlet to the outlet.
To calculate the power input requires a more complicated procedure. We first need to map the
system’s pressure vs flow rate curve. Then plot the different fan curves to see which ones
intercept the system curve at the desired point. Knowing that if multiple fans are placed in series,
the pressure they generate is to be added, and if they are placed in parallel their flow rates is to
be added. We add multiple fans in series and sets of fans in parallel to match the flow rate and
pressure drop required from the system. This concept is illustrated in Figure 3.
Figure 3: Fans in parallel and series [9]
Fans can be selected from the Digi-Key fan catalogue online [10], which provides the maximum
flow rate and static pressure as well as the electrical power of each fan. We can model the fan
curve for each fan using the data given on the Digi-Key database and the fan equation (eq 6)
below:
€
P = KQ2 + B (eq 6)
8
Where K and B are constants, P is the static pressure of created by the fan, Q is the volumetric
flow rate of air through the system.
We used fan SP101A-1123HST, which is rated to have a maximum flow rate of 105 cfm and a
maximum pressure of 0.300 inches of water. Using these data and the fan equation (eq 6) we are
able to come up with an expression relating static pressure and flow rate described in (eq 7).
€
P = −(2.675 ×10−5)Q2 + 0.3 (eq 7)
Knowing that pressure is added when multiple fans are placed in series and that the flow rate is
added when they are placed in parallel, we came up with the following expression:
€
P = N1 −(2.675 ×10−5) ⋅ Q
N2
2
+ 0.3
(eq 8)
Where N1 is the number of fans in series and N2 is the number of sets of fans in parallel.
For each simulation we used an Excel solver to find what combination of fans in series and
parallel could satisfy the system at the given flow rate. The power input was then calculated by
multiplying the electrical power of each fan (18 Watts) by the number of fans required to match
the system’s needs.
Pin= (fan power) x (# of fans) (eq 9)
Finally, the power generated (Pgen) is calculated by subtracting the power input from the power
output. This is the key metric that we will try to optimize throughout our simulations.
Pgen = Pout -Pin (eq 10)
9
3 Results We ran simulations while the three parameters were varied at the following levels:
Thickness: 1.5, 2 and 2.5 inches
Flow rate: 50, 100 and 200 cfm
Pipe diameter: 4 and 6 inches
Table 1 shows the results of a series of simulations we ran along with the necessary calculations
needed. Table 2 shows the results of the output data from FLUENT as well as the calculated
powers output. With the given data we were able to map the system curves and match them with
the necessary number of fans to obtain the power input, which is displayed in Table 2.
Table1:Simulationsetupandpreliminarycalculationresults Parameter settings Calculated Values
Trial no
t [in]
Q [cfm]
D [in]
Vin [m/s]
RE number
Model
1 1.5 50 4 2.91 1864 Laminar 2 1.5 50 6 1.29 1864 Laminar 3 2 50 4 2.91 1864 Laminar 4 2 50 6 1.29 1864 Laminar 5 2.5 50 4 2.91 1864 Laminar 6 2.5 50 6 1.29 1864 Laminar 7 1.5 100 4 5.82 3729 turb, k-ep, std 8 1.5 100 6 2.58 3729 turb, k-ep, std 9 2 100 4 5.82 3729 turb, k-ep, std
10 2 100 6 2.58 3729 turb, k-ep, std 11 2.5 100 4 5.82 3729 turb, k-ep, std 12 2.5 100 6 2.58 3729 turb, k-ep, std 13 1.5 200 4 11.64 7459 turb, k-ep, std 14 1.5 200 6 5.17 7459 turb, k-ep, std 15 2 200 4 11.64 7459 turb, k-ep, std 16 2 200 6 5.17 7459 turb, k-ep, std 17 2.5 200 4 11.64 7459 turb, k-ep, std 18 2.5 200 6 5.177 7459 turb, k-ep, std
10
Table2:Resultsoffirstbatchofexperiments FLUENT output Calculated values
Pressure loss Trial no
€
m•
[kg/s]
Tout [K] [Pa] [in H2O]
Power out [kW]
Power in [kW]
Pgen = Pout-Pin [kW]
1 0.029 320 16.29 0.0652 0.59 0.0180 0.57 2 0.029 318 5.346 0.0214 0.53 0.0180 0.52 3 0.029 321 13.46 0.0538 0.62 0.0180 0.60 4 0.029 318 3.69 0.0148 0.52 0.0180 0.50 5 0.029 321 11.66 0.0466 0.62 0.0180 0.60 6 0.029 309 2.977 0.0119 0.26 0.0180 0.24 7 0.058 320 61.48 0.2459 1.17 0.0277 1.15 8 0.058 320 18.33 0.0733 1.15 0.0180 1.13 9 0.058 318 54.02 0.2161 1.09 0.0243 1.07
10 0.058 318 13.79 0.0552 1.04 0.0180 1.02 11 0.058 317 49.53 0.1981 1.01 0.0223 0.99 12 0.058 316 11.31 0.0452 0.96 0.0180 0.94 13 0.115 316 240.58 0.9623 1.96 0.2167 1.74 14 0.114 316 71.56 0.2862 1.84 0.0645 1.78 15 0.115 315 205.83 0.8233 1.75 0.1854 1.57 16 0.114 314 55.63 0.2225 1.65 0.0501 1.60 17 0.115 314 195.09 0.7804 1.65 0.1758 1.48 18 0.114 312 45.44 0.1818 1.48 0.0409 1.44
Figures 4 to 6 represent the effect each parameter has on Pout at Pin. Note that Pout is measured
from the primary scale on the left and Pin from the secondary one on the right of each graph.
Figure4:ChangesinaveragePinandPoutatdifferentthicknesses
11
As we can see in Figure 4, the power output and the power input decrease as thickness increases.
The above result confirms our hypothesis that the total heat exchange increases as the thickness
is reduced, while the pressure drop across the system also increases. It is expected that, at the
optimal point, if thickness is reduced, the incremental power needed to run the fan would surpass
the incremental power generated by the system.
Figure 5: Changes in average Pin and Pout at different flow rates
Figure 5 confirms our hypothesis that as we increase the flow rate, the power output and the
power input increase. We see a large difference between the slope of Pin in the laminar (under
100 cfm) and turbulent (over 100 cfm) regions. This suggests that there may be a significant
difference in the behaviour of the flow as it becomes turbulent. We do expect that at the optimal
flow rate, the power needed to pass an incremental amount of flow through the system will be
larger than the incremental power generated by the system.
12
Figure 6: Changes in average Pin and Pout as at different pipe diameters
Figure 6 confirms that as the pipe diameter increases, the pressure drop across the system is
reduced. However, the data also show that the power output decreases as the pipe diameter
increases, which goes against our initial hypothesis. This can be explained by the fact that a
larger pipe diameter will have less minor losses at the entry point, which would explain the drop
in Pin. A larger pipe diameter also reduces the turbulence of the flow as it enters the panel, thus
making the heat exchange less efficient and reduces Pout.
13
4 Parameter Optimization
4.1 Regression analysis
In order to optimize the amount of power generated by the system, we performed a Multiple
Linear Regression (MLR) [11] with the results from our simulations. We attempted to model the
power output and input as a function of the thickness, flow rate and pipe diameter. The MLR
model assumes that each factor is linearly correlated to the output, which may not be the case in
our setup. Using all parameters and interactions, Minitab was able to calculate the following
coefficients for our model:
Table3:MultipleLinearRegressionanalysiscoefficients
Power
out [kW] Power in
[kW] Constant -0.81 -0.26 t 0.66 0.030 Q 0.017 0.0043 D 0.22 0.040 t*Q -0.0047 -0.00052 t*D -0.14 -0.0030 Q*D -0.0013 -0.00062 t*Q*D 0.00068 0.000059
R-squared values were used to evaluate the accuracy of the regressions. The regressions above
both have R-squared values of over 85%, which makes them significant. Using the above
coefficients, we attempted to optimize our parameters to maximize the total power generated.
Entering the coefficients into an Excel spreadsheet and applying a solver algorithm, we were
unable to find the optimal settings for the thickness, flow rate and pipe diameter. The model
suggests that thickness be reduced as much as possible, while flow rate and pipe diameter be
increased to their respective limits. It can thus be concluded that either the optimal parameter
setting was not captured within the limits of our simulations or that the above model is flawed.
14
The simulations performed were conducted using two different FLUENT models: one for
laminar flow and one for turbulent flow. There is a significant difference in the behaviour of the
flow when it is laminar or turbulent. It may be that the source of our error lies in the
incompatibility of the two different flow behaviours in a single model. At a flow rate greater than
100 cfm, the Reynolds number is greater than 2300 and the flow is assumed to be fully turbulent.
It is evident from Figure 5 that a turbulent flow yield higher performing results. In the next
section, we will attempt to optimize the turbulent parameters using a two-level full factorial
analysis in an attempt to achieve the optimal settings.
4.2 Factorial analysis of turbulent data
Using only data where the flow in the panel is turbulent (flow rate greater than 100 cfm) and
focusing on the smaller thicknesses we developed the following parameter limits for a full-
factorial analysis [11]:
Table4:Factorialanalysisparameterlimits Lower level Upper level
Thickness [in] 1.5 2 Flow rate [cfm] 100 200
Pipe diameter [in] 4 6
Table 5 displays the coefficients calculated by Minitab from the above factorial analysis.
Table5:Factorialanalysiscoefficients
Power out
[kW] Power in
[kW] Constant -0.32 -0.56 t 0.38 0.090 Q 0.016 0.0064 D 0.15 0.082 t*Q -0.0042 -0.0011 t*D -0.075 -0.010 Q*D -0.0011 -0.00092 t*Q*D -0.00043 0.00014
15
With the calculated coefficients from Table 5, we were able to create new models for the power
input and output. We tried to optimize thickness, flow rate and diameter to yield the highest
power generated using an Excel solver. We were initially able to obtain an optimal diameter of
6.8 inches while the thickness was being reduced to its lowest limit and the flow rate increased to
its highest limit. We then decided to change the ideal diameter to the closest commercially
available pipe size: seven inches. After setting the pipe diameter to seven inches and running the
solver again, the flow rate converged to 200.57 cfm, while the thickness still remained at its
lowest limit.
This analysis has allowed the optimization of pipe diameter and flow rate to maximize the
generated power of the system. It seems that the optimal thickness is not included within the
limits of our simulations thus a more in depth analysis of the thickness should be implemented.
The following section will attempt to find an optimal thickness for our system.
4.3 Thickness analysis
From the previous data analysis, it seemed that the optimal thickness for the system was not
captured within the limits of our parameters. We thus ran further simulations maintaining the
optimal flow rate (200 cfm) and pipe diameter (seven inches), while reducing the thickness in
quarter inch increments. Table 6 shows the results obtained from the simulations.
Table6:ResultsofthicknessoptimizationsimulationsFlow rate [cfm]
Thickness [in]
Diameter [in]
Power out [kW]
Power in [kW]
Pgen = Pout-Pin [kW]
200 0.25 7 3.6352 2.1712 1.4640 200 0.5 7 2.9719 0.4239 2.5480 200 0.75 7 2.5630 0.1872 2.3758 200 1 7 2.2485 0.1136 2.1349 200 1.25 7 2.0181 0.0811 1.9369 200 1.5 7 1.8604 0.0638 1.7965
16
Using Excel, we were able to plot the power output and power input versus the thickness and fit
lines to them as shown in Figure 7.
Figure 7: Lines of best fit for Power vs thickness
The two best fit lines plotted in Figure 7 were selected based on their high R2 values. We then
inputed the resulting forumulas into an Excel spreadsheet and used the solver function to find the
optimal thickness. The optimal thickness was found to be 0.48 inches. Thus, according to our
optimization, a panel with a thickness of 0.48 inches, flow rate of 200 cfm and pipe diameter of
seven inches should provide a power output of 3.07 kW, an input power of 0.51 kW for a total
power generation of 2.56 kW.
We then conducted a verification run with a thickness of 0.5 inches, flow rate of 200 cfm and
pipe diameter of 7 inches, which resulted in an output power of 2.94 kW and an input power of
0.33 kW for a total power generation of 2.62 kW. The results from the verification run are fairly
accurate when compared to those predicted from the model.
17
4.4 Flow path optimization
After having selected the optimal parameter settings for the panel, we will attempted to
determine the most effective flow path of air, while maintaining the optimal parameters for
thickness, flow rate and pipe diameter. Traditionally, the concept has been to place restrictions
on the panel to force the air to take a certain path, which will allow it to be in contact with a
larger surface of the solar collectors thus facilitating more heat transfer. As we vary the flow
path, we will analyze the streamline of the flow and temperature changes then compare the
power output and input for each design.
Looking at the base line case first, Figure 8 shows an isometric view of the model and the
streamlined flow with a colour gradient indicating changes in the flow’s temperature.
a) Isometric view b) Flow streamlines and temperature change
Figure 8: Baseline case results
18
The flow throughout the panel is steady and uniform. There doesn’t seem to be any interruptions
of flow, any abnormalities or recirculation. Temperature changes gradually as the flow
approaches to the output. There is a concentration of warmer air closer to the borders of the
panel, which may be caused by heat added due to wall friction. One can notice that the longer the
length of the streamline, the higher temperature obtained at the output. It can thus be expected
that by moving the input and output as far away from each other as possible we would be able to
increase the efficiency of the system.
Our first design, Design number 1, does not have any restrictions either but the input and output
have been placed in opposite corners of the panel to increase the average distance traveled by the
air as it enters and exits the panel. Figure 9 represents an isometric view of the model and the
streamlined flow with a colour gradient indicating changes in the flow’s temperature.
a) Isometric view b) Flow streamlines and temperature change
Figure 9: Design #1 results
Similar to the baseline design, this design displays a steady and uninterrupted flow. There is no
presence of recirculation. The results for this design are very similar to those of the baseline. It
19
seems that, again, the majority of the flow does not undergo a significant amount of heat transfer
as it rushes towards the exit. Presenting obstructions to the flow would reduce its velocity and
increase the length of the average flow path thus we would expect a higher energy output. It is
however uncertain as to how these added obstructions would affect the necessary power to
maintain the desired flow rate.
The next three designs present the flow with one, two, and three barriers to increase the average
length of a streamline and facilitate more heat transfer.
a) Isometric view b) Fluid flow and temperature change
Figure 10: Design #2 results
20
a) Isometric view b) Flow streamlines and temperature change
Figure 11: Design #3 results
a) Isometric view b) Flow streamlines and temperature change
Figure 12: Design #4 results
Figures 10, 11 and 12 show similar flow paths as we increase the number of barriers present. The
flow is forced to move from one end of the panel to the next making the average length of the
21
streamlines longer. However, we can see the formation of turbulence at each turn and areas
where the flow is being recirculated. These areas of turbulence increase the static pressure of the
system thus also increasing the power needed to run the fan.
Table 7, summarizes the overall performance of each design.
Table 7: Performance of different designs
Design number
Flow rate [cfm]
Thickness [in]
Diameter [in]
Power out [kW]
Power in [kW]
Pgen = Pout-Pin [kW]
Baseline 200 1.50 6.00 1.84 0.07 1.78 1 200 1.50 6.00 1.86 0.10 1.76 2 200 1.50 6.00 2.41 0.20 2.21 3 200 1.50 6.00 2.12 0.14 1.98 4 200 1.50 6.00 2.66 0.28 2.37
Out of all the different designs, we can see that the baseline one has the lowest power output but
the largest power generated due to its relatively low pressure rise. Though the obstructions help
to increase the power output of the system, the sharp edges create large amounts of turbulence
that require more power to operate the system. Making the edges of our obstructions more
streamlined could eliminate these areas of turbulence, however the additional manufacturing cost
associated with such changes would not justify the slight increase in performance.
It seems that though the technique of varying the flow path is helpful in practical level, it does
not have a significant impact once the thickness has been optimized. Adding obstacles to an
already optimized system will lead to a larger rise in input power than output power thus making
the fan less efficient.
22
5 Conclusions From the research explained in this report, we were able to determine that the optimal thickness,
flow rate and pipe diameter for a four feet by four feet space heating solar panel. The optimal
parameters being a thickness of 0.5 inches, a flow rate of 200 cfm and a pipe diameter of four
inches. These parameters are optimal as they maximize the amount of power one can generate
given the size of the solar panel. Should we modify any of these parameters, the total power
generation would decrease.
After optimizing the three key parameters, we discovered that there was no benefit in placing
obstructions along the flow, as it would only decrease the amount of power generated.
Obstructions along the flow do help getting a better heat transfer but also create additional
turbulences, which increase the amount of energy needed to maintain the desired flow rate. We
can thus say with confidence that it is of more value to optimize the key parameters, mainly the
thickness, to generate the maximum amount of power from a solar panel.
23
6 Recommendations Though we were able to obtain optimal parameter settings through a series of simulations, a gap
still remains to optimize this green technology. Here are a few suggestions for future
development:
• Physical verification of results: All our data were based on simulations developed
using Computational Fluid Dynamics (CFD) software. As is well known, the realities
of the physical world differ greatly from the idealized computer simulated algorithms.
It would be of immense value to verify the performance of the said optimized
parameters.
• Attempt to achieve similar results at different thicknesses: In our research, we have
optimized the thickness first thus leaving no room for additional optimization using
different flow paths. It would be of value to run various simulations at larger, non-
optimal, thicknesses while testing different flow paths to achieve similar if not greater
results. One may find that such results are possible or that the added turbulence from
the non-streamline flow would cause a significant increase in static pressure.
• Varying pipe diameter: Throughout our study, though we varied the size of the pipes,
we always maintained the same diameter for input and output pipes. We are aware,
however that the velocity of the air at the exit is higher due to the increase in
temperature. It may be of value to analyze the effects of having larger pipes at the
output so as to accommodate the flow and determine the optimal ratio between input
and output pipe size.
24
• In depth study of all parameters: In this research we made the assumption that the
relationships between the power output or power input and each parameter were
linear. Due to time constraints, we were only able to perform a detailed analysis of
the thickness parameter since we believed it had the greatest impact on the output. It
would be of value to analyze each of the two other parameters (flow rate and pipe
diameter) in more depth individually so as to gain a better understanding of their
relationship with the power output and input.
25
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