investigation of a solar air heater's conversion
TRANSCRIPT
Dickinson CollegeDickinson Scholar
Student Honors Theses By Year Student Honors Theses
5-22-2016
Investigation of a Solar Air Heater's ConversionEfficiency and Output Power as a Function of theGrid NumberNicole Elizabeth FronsdahlDickinson College
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Recommended CitationFronsdahl, Nicole Elizabeth, "Investigation of a Solar Air Heater's Conversion Efficiency and Output Power as a Function of the GridNumber" (2016). Dickinson College Honors Theses. Paper 243.
Investigation of a Solar Air
Heater’s conversion efficiency and
output power as a function of the
grid number.
Submitted in partial fulfillment of honors requirements
for the Department of Physics and Astronomy, Dickinson College,
by
Nicole E. Fronsdahl
Advisor: Professor Hans Pfister
Reader: Professor Robert Boyle
Reader: Professor Lars English
Reader: Professor Catrina Hamilton-Drager
Reader: Professor David Jackson
Reader: Professor David Mertens
Reader: Professor Windsor Morgan
Reader: Professor Brett Pearson
Reader: Professor Hans Pfister
Carlisle, PA
May 4, 2016
Abstract
A Solar Air Heater (SAH) is a device that converts solar energy into ther-
mal energy. Solar irradiance enters the SAH through a glazing and heats an
absorbing material—in our case several blackened, corrugated aluminum mesh
grids. The grids transfer their thermal energy to the passing air. This paper
theoretically and experimentally investigates the optimal number of grids to
maximize efficiency and minimize the return on investment for our single pass
wire mesh grid SAH. A higher number of grids increases the absorption and
output temperature, yet also increases flow resistance in the device. Our ex-
perimental and theoretical investigation finds that the conversion efficiency and
output power of the SAH increases with increasing mass flow rate. We found
that five absorber grids led to the highest efficiency values, yet due to the cost
of each absorber grid, the shortest ROI is with one grid.
ii
Acknowledgements
First I would like to thank Professor Hans Pfister for the original design of the SAH,
and John Root for working with me during both semesters. I would like to acknowl-
edge Jonathan Barrick as well for his assistance with the construction and mainte-
nance of our device. Thank you to Tyler Ralston, Sungwoo Kim, Eli Blumenthal, and
Kylie Logan for their previous work on the Solar Air Heater— in particular Tyler for
his work on the mass flow rate theory and for his assistance last semester. Lastly, I
would like to thank the Physics graduating class of 2016, Professor Robert Boyle, and
the Dickinson Department of Physics and Astronomy for their support and advice
during my entire research process.
iii
Contents
Abstract ii
1 Introduction 1
2 Nomenclature 3
3 Description of Design 4
4 Theory 7
4.1 Power Flux Balance for the Glazing . . . . . . . . . . . . . . . . . . . 7
4.2 Power Flux Balance for the Absorber . . . . . . . . . . . . . . . . . . 8
4.3 Power Flux Balance for the Back Panel . . . . . . . . . . . . . . . . . 8
4.4 Power Balance for the Fluid . . . . . . . . . . . . . . . . . . . . . . . 9
4.5 Total Power balance for our SAH . . . . . . . . . . . . . . . . . . . . 10
5 Experimental Methods 19
6 Results 21
6.1 Absorbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.2 Flow Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6.3 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
7 Analysis 27
8 Conclusion 28
9 Suggestions for Further Research 29
A Appendix 32
A.1 Other purposes for Solar Air Heaters . . . . . . . . . . . . . . . . . . 32
A.2 Other types of Solar Air Heaters . . . . . . . . . . . . . . . . . . . . . 32
A.3 Increase in SAH Research Popularity . . . . . . . . . . . . . . . . . . 33
A.4 Glazing Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
A.5 Linearizing the Radiation Thermal Loss Temperature . . . . . . . . . 34
A.6 Design details of construction . . . . . . . . . . . . . . . . . . . . . . 36
iv
List of Figures
1 Image of SAH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Absorbing Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Side view schematic of SAH . . . . . . . . . . . . . . . . . . . . . . . 6
4 Schematic of Inside of SAH . . . . . . . . . . . . . . . . . . . . . . . 6
5 Power flux distribution for the glazing . . . . . . . . . . . . . . . . . 7
6 Power flux distribution for the absorber . . . . . . . . . . . . . . . . . 8
7 Power flux distribution for the back panel . . . . . . . . . . . . . . . 9
8 Power flux distribution for the fluid . . . . . . . . . . . . . . . . . . . 9
9 Theoretical graph of efficiency as a function of mass flow rate. . . . . 12
10 Efficiency vs. Mass flow rate (SEJ 2016) . . . . . . . . . . . . . . . . 12
11 Theoretical Efficiency with Experimental Results . . . . . . . . . . . 13
12 SAH flow field without obstructions (Romdhane) . . . . . . . . . . . 14
13 Flow field image of SAH with fins (Romdhane 2007) . . . . . . . . . . 14
14 Flow field image of SAH with baffles (Romdhane 2007) . . . . . . . . 14
15 Flow field image our SAH . . . . . . . . . . . . . . . . . . . . . . . . 15
16 Pressure Drop Across SAH for 6 Grids . . . . . . . . . . . . . . . . . 16
17 Output Power vs. Mass Flow Rate . . . . . . . . . . . . . . . . . . . 17
18 SAH data collection image . . . . . . . . . . . . . . . . . . . . . . . . 20
19 Temperature Difference vs. Mass Flow Rate . . . . . . . . . . . . . . 21
20 Pressure Drop vs. Mass Flow Rate (0-6 Grids) . . . . . . . . . . . . . 22
21 Reynold’s Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
22 Darcy-Weisbach Comparison 0G . . . . . . . . . . . . . . . . . . . . . 23
23 Darcy-Weisbach Comparison 1G . . . . . . . . . . . . . . . . . . . . . 23
24 Darcy-Weisbach Comparison 2G . . . . . . . . . . . . . . . . . . . . . 24
25 Darcy-Weisbach Comparison 3G . . . . . . . . . . . . . . . . . . . . . 24
26 Darcy-Weisbach Comparison 4G . . . . . . . . . . . . . . . . . . . . . 24
27 Darcy-Weisbach Comparison 5G . . . . . . . . . . . . . . . . . . . . . 24
28 Darcy-Weisbach Comparison 6G . . . . . . . . . . . . . . . . . . . . . 24
29 Efficiency Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
30 Efficiency vs. Mass Flow Rate (0-6 Grids) . . . . . . . . . . . . . . . 26
31 Solar Air Heater research article volume . . . . . . . . . . . . . . . . 33
32 Linearized vs. Exact Power Output . . . . . . . . . . . . . . . . . . . 35
33 Transverse Cross-Sectional View . . . . . . . . . . . . . . . . . . . . . 36
34 Longitudinal Cross-Sectional View . . . . . . . . . . . . . . . . . . . . 36
35 Sidewall Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
List of Tables
1 Constants for ROI Calculation . . . . . . . . . . . . . . . . . . . . . . 26
2 ROI Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Average Temperature Differences . . . . . . . . . . . . . . . . . . . . 35
vi
1 Introduction
x Our current rate of fossil fuel consumption is altering the atmosphere and creating
climate change. By burning fossil fuels, we emit billions of pounds of CO2 into the
atmosphere, and burn them at a rate faster than what the Earth can absorb to
maintain a steady state[1]. In order to prevent further damage to the environment,
we need to focus our attention on renewable energy resources that do not emit as
much carbon and can regenerate at a sustainable rate. In order to compete with the
fossil fuel industry, renewable resources need to achieve high efficiencies and must be
inexpensive to purchase and operate.
A Solar Air Heater is a device that directly converts solar energy into thermal
energy. Solar Air Heaters are commonly used for space heating, but have other
uses such as drying fruit and water desalinization(Appendix A.1). Solar Air Heaters
intercept solar irradiance, which is then absorbed by a material inside. Ambient air
enters through the input, flows across the absorption materials, and exits as warmer,
more desirable air.
The basic idea is simple and tangible, allowing a diverse population to design and
construct a device. Solar Air Heaters can be designed at home, are commercially
available, and are academically researched. Often, “at-home” Solar Air Heater de-
signers are looking to maximize the output temperature with inexpensive or recycled
materials. On the other hand, researchers debate various mechanisms, inputs, and
absorption or insulation materials, analyzing ways to achieve the highest efficiency.
With the initial construction of the device, researchers consider the number of times
air transverses the absorption area. Single, double, or triple pass devices are often
compared, looking at improved efficiency or output temperature relative to the com-
plexity of additional passes. Another structural comparison is between passive versus
active air input. Passive solar air heaters allow air to flow in and out of the device
relying on the fact that hot air rises, whereas active solar air heaters utilize a fan to
push the air across the absorption material. This comparison assesses the efficiency
and output temperature with regard to saving electrical power and minimizing costs.
The most common and comprehensive list of design flexibility lies with the absorption
materials. Experiments have been done with fins, baffles, mesh grids, packed bed,
and various other materials and material placement in order to determine different
efficiency values and output temperatures. Often the comparisons are with complex-
ity, heat losses, flow distributions, and cost (Appendix A.2). Due to the desirability
of inexpensive and efficient renewable energy technology, the volume of research in
this area is significantly increasing on a global scale (Appendix A.3).
Professor Hans Pfister has been working on his design of a Solar Air Heater since
1
2013. Over the years his design has consistently achieved efficiency values near 80%
and has approximately a one year return on investment (based on the cost of the
device alone). Pfister’s design is a single pass air heater with mesh grid absorbers
folded into triangles. A fan at the input pushes air through the grids and a flow field
distribution manifold is built into both input and output ends to promote uniform
flow. The device has been updated to its current design with various improvements
to the frame, insulation, and air flow passage. With the improvements, the device is
now easier to manage, construct, and there is less potential for thermal leaks in the
frame.
Previous theoretical and experimental research done by Professor Hans Pfister and
Tyler Ralston has shown that an increase in the mass flow rate leads to an increase
in efficiency. We also state that low flow resistance correlates with a higher efficiency.
The flow resistance depends on the velocity of air entering the box as well as the
obstacles within the device. An increase in volume of absorbing materials increases
the flow resistance. Our flow resistance is measured using the pressure drop, and
we predict that an increase in flow resistance will return a decrease in efficiency. In
addition, we determine when our flow is laminar or turbulent. Despite additional flow
resistance, our grids serve as the absorption material in the device and are critical for
heat transfer. We predict that a higher number of grids will lead to higher output
temperatures due to increased absorption properties, which is desirable for practical
purposes. The original design included six grids which did not fluctuate in previous
experiments. This number (6) was determined by a simple transmissivity test looking
to minimize the amount of light that is transmitted beyond the grids. By looking
at the crossover between absorption and flow resistance and calculated efficiency, we
will be able to determine an optimal number of grids that maximizes the efficiency
and minimizes return on investment.
2
2 Nomenclature
Aa cross sectional area of SAH, m2
Aap aperture area of SAH, m2
AB area of bottom of SAH, m2
AG area of glazing, m2
AT cross sectional area of PVC tube,
. m2
AW area of one sidewall, m2
AW,tot total area for all side walls, m2
cp specific heat capacity of air at
. constant pressure, kJ / (kg·k)
hrad heat coefficient of radiated heat
hcond heat coefficient of conducted heat
hconv heat coefficient of convected heat
iILF current drawn by inline fan, A
I solar irradiance, W/m2
kb thermal conductivity of insulation,
. W/(m2 · K)
L Length of SAH
lb thickness of pine board, m
li thickness of insulation, m
m mass flow rate of air, kg/s
pa(i) pressure before aperture i, Pa
pb(i) pressure after aperture i,Pa
∆p pressure drop across the SAH, Pa
Pin solar power into SAH, W
PILF power consumed by inline fan, W
Psol solar power incident on glazing, W
Qfl heat flow rate to working fluid, W
Qcond conductive heat loss rate, W
Qcond,W conductive heat loss rate through
. a sidewall, W
Qrad heat loss rate due to radiation, W
Qloss total heat loss rate, W
Rb thermal resistance of pine board,
. m2K/W
RB thermal resistance of glazing, m2K/W
RG thermal resistance of insulation,
. m2K/W
Ri thermal resistance of sidewall, m2K/W
RW thermal resistance of sidewall,
. m2K/W
RW,tot thermal resistance of all sidewalls,
. m2K/W
RH relative humidity
s distance along length of SAH, m
S total length of SAH, m
TA temperature of absorber
Tamb temperature of ambient air, K
TB,i temperature of inside of back panel
TB,o temperature of outside of back panel
TF temperature of fluid
Tfl temperature of working fluid (air), K
TG,i temperature of glazing inside
TG,o) temperature of glazing outside
Tin temperature of air at intake, K
Tins temperature of air inside SAH, K
〈Tins〉 average temperature inside SAH, K
Tout temperature of air at outflow, K
vdrift drift velocity
vinput velocity at PVC input
VILF voltage across inline fan, V
ww width of sidewall, m
α albedo/relectivity of glazing
αg absorptivity of glazing
αB absorptivity of back panel
β calibration factor for Vernier Anemometer
∆T temperature difference between out-
flow and intake, K
ε emissivity
η conversion efficiency
ρ density of air, kg/m3
σ Stefan-Boltzmann constant (=5.6704·. 10−8 W/m2 · K4)
τ transmissivity of grid
τg transmissivity of glazing
τn transmissivity dependent on the
. number of grids
3
3 Description of Design
The original design by Pfister focused on ease of use and installation, low cost, and
high efficiency. Our Solar Air Heater (SAH) is a rectangular single pass active SAH
with layered black mesh grids folded into triangles.
Figure 1: This is an image of our Solar Air Heater on the roof of the Tome science building
at Dickinson College.
The flow is controlled by an inline fan that has a range of controllable velocities.
Currently our device is attached to a frame that allows us to control the angle of
incidence and the direction it faces (the angle of incidence changes the reflectivity
value therefore changing the efficiency based on the percentage of light entering the
device).
The aluminum mesh is our absorption material which converts solar energy to
thermal energy by transferring heat to the passing air.
4
Figure 2: Inside of our SAH showing the corrugated grid absorber.
The triangular folds allow the air to traverse the grids 16 times from the input
to the output. We have implemented pegs to hold the triangles in place and limit
movement vertically along the device. Our absorbing material is fairly inexpensive
($12.50 per grid), is easy to install or remove, and allows for high output temperatures.
The bottom and side walls are painted black to increase absorption.
The SAH is thermally insulated with Polyiscyanurate foam board on the bottom
and against the side walls. The Polygal double glazing provides some insulation on
the top as well. A flow field distribution manifold at the input and output of our
Solar Air Heater provides a more uniform flow field across the width of the SAH. This
unique design by Pfister has circular apertures of various diameters. As the air enters
the input at the center, the air spreads before the manifold, and due to the various
size diameters, distributes the pressure and flow evenly.
5
Figure 3: Schematic side view of our SAH design illustrating the corrugation of the absorber
grids and the location of the distribution manifolds. (Pfister)
Figure 4: Schematic of our flow distribution manifold at the input and output of our device.
(Pfister)
6
4 Theory
The efficiency of our SAH is a measure of comparing the power in from the sun
and our useful heat flow rate that we get at the output.
Due to conservation of energy, we know the power into the device must equal the
power coming out.
Pin = Pout (1)
We can analyze our SAH looking at four distinct parts — the glazing, absorbing
material, fluid, and back panel (which effectively has the same properties as the side
panels). We can consider the power distribution into and out of each part of the
device.
4.1 Power Flux Balance for the Glazing
The heat absorbed by the glazing is a combination of solar irradiance (I), radiated
heat from the absorber, convected heat from the fluid, and radiated heat from the
back panel in steady state. The heat leaving the glazing is a combination of conducted
and convected heat to the ambient air.
αgI + hrad,AG(TA − TG,i) + hconv(TF − TG,i) + hrad,BG(TB,i − TG,i)
= hcond(TG,o − Tamb) + hconv(TG,o − Tamb)(2)
Since our glazing has two layers, the inside temp of the glazing TG,i and the top
of the glazing TG,o are slightly different (with the inside temperature being slightly
higher than the outside temperature) (Appendix A.4).
Figure 5: Schematic of power flux distribution with the glazing
7
4.2 Power Flux Balance for the Absorber
The amount of solar energy absorbed by the material within the SAH is depends
on the reflectivity and transmissivity characteristics – how much is reflected and how
much light passes through. The absorber also re-radiates heat to the glazing, radiates
heat to the back panel, and convects heat to the fluid.
Iτg[1 + (1− α)(1− τg)]= hrad,A(TA − TG,i) + hrad,A(TA − TB,i) + hconv(TA − TF )
(3)
Figure 6: Schematic of power flux distribution with the absorber
4.3 Power Flux Balance for the Back Panel
The back panel absorbs heat from the solar irradiance that transmits past the absorb-
ing material and glazing, and the radiated heat from the absorber. The back panel
transfers heat to the fluid, radiates to the glazing, and conducts heat to the ambient
air.
IτgτnαB + hrad,AB(TA − TB,i)
= hconv,BF (TB,i − TF ) + hrad(TB,i − TG,i) + hcond(TB,i − Tamb)(4)
8
Figure 7: Schematic of power flux distribution with the back panel.
4.4 Power Balance for the Fluid
The thermal energy transferred to the fluid, Qfl, is the useful thermal output of the
SAH. The heat transferred to the air is convected heat from the absorbing material,
back panel, and the glazing. The most significant influence should be from the ab-
sorber, yet the temperature of the glazing and back panel can influence the inside air
temperature as well.
Qfl =
∫ z=L
z=0
[hconv,AF (TA − TF ) + hconv,BF (TB,i − TF )− hconv,FG(TF − TG,i)·]ww · dz
(5)
Figure 8: Schematic of power distribution with the fluid.
9
4.5 Total Power balance for our SAH
After analyzing the equations in sections 4.1, 4.2, 4.3, and 4.4, we can separate the
expressions into various thermal loss terms. Throughout the device we have radiation
and conductive and convective losses all driven by the temperature difference between
the average inside air temperature and the ambient air temperature.
P out = Qfl + Qcond + Qrad + Qconv (6)
The SAH receives solar power across the aperture area, yet our glazing reflects
some of it away.
P in = IAap(1− α) (7)
Conductive losses take place through the walls, bottom, and glazing of the SAH.
These losses come from the temperature difference of air within the SAH and the
ambient air. The rate at which this occurs is dependent on the area and the materials
involved (in our case the material can be measured by an insulation constant, the R
value), yet the temperature difference between two materials is what drives heat
conduction.
Qcond = (Awt
Rwt
+AB
RB
+AG
RG
)(〈Tins〉 − Tamb) (8)
The average inside temperature is calculated as the difference between the ambient
air and the temperature we get out. At the input, the air is the same temperature as
the ambient air, and increases linearly until we have the temperature at the output.
Since the temperature increases linearly, the average inside air temperature is the
average between these two values.
〈Tins〉 =Tout + Tamb
2(9)
According to Faghri et al. (2010), we can model our SAH as a grey body, radiating
energy according to the Stefan-Boltzmann Law. The radiation term is dependent on
the emissivity, the area of the aperture, and the temperature difference of the air
inside the SAH and the ambient air.
Qrad = εσAap(〈Tins〉4 − T 4amb) (10)
Lastly, we have convective losses driven by temperature differences. This equation
has a heat coefficient term which we do not have a value for at this time.
Qconv = Aaphconv∆T
2(11)
10
Our R values, area, and emissivity are constant since we are not changing the
materials or size of our device during experimentation. The only adjustable term is
the temperature difference. Therefore, in order to reduce our thermal losses, we want
to minimize the temperature difference between the inside air and the ambient air.
Our thermal output, the heat flux rate, is dependent on the heat capacity, the mass
flow rate, and the temperature difference.
Qfl = cpm∆T (12)
We can consider the heat capacity to be fairly constant, although there are slight
fluctuations dependent on temperature which are negligible in our efficiency calcula-
tions. As we increase the mass flow rate, the air spends less time in the SAH, has
less time to interact with the absorption materials, and leaves the device as cooler
air. With cooler inside air, the temperature difference between the inside air and the
ambient air decreases, reducing our conductive, convective, and radiative losses. The-
oretically then, higher mass flow rates will improve our efficiency, since our efficiency
is a ratio of useful power out and input power. Our mass flow rate is defined based
on the density, velocity, and the cross-sectional area of the PVC tube at the input.
η =Pout
Pin
=cpm∆T
IAap
=cpρATv∆T
IAap(13)
Since each heat loss term has a temperature difference defined by Equation 9, we
can create a combined heat coefficient term ( A.5).
IAp(1− α) = cpm∆T + Aaphcond∆T
2+ Aaphrad
∆T
2+ Aaphconv
∆T
2(14)
We can combine the three loss terms to create a heat coefficient describing the
thermal losses.
IAp(1− α) = cpm∆T + Aaphcomb∆T
2(15)
If we consider our power equation (Equation 6) and solve for ∆T we arrive at:
∆T =IAp(1− α)
cpm+ Aaphcomb
2
. (16)
Solving Equation 15 for ∆T we can express the efficiency as a function of mass
flow rate, by using Equation 16 to substitute for ∆T in Equation 13. This gives us a
theoretical expression for the efficiency as a function of mass flow rate.
η(m) =cpm
IAp
IAp(1− α)
cpm+ hcomb
2
=(1− α)
1 + Aaphcomb
2cpm
(17)
11
Figure 9: Theoretical graph showing efficiency as a function of mass flow rate for various
parameters changing the hcomb term. (Using Eq. 17)
Our theory shows an increase in efficiency as we increase the mass flow rate. The
experimental results taken by Pfister and Ralston agree with this theory. In addition,
our theoretical evaluation for 6 grids matches our data fairly accurately (Figure 11).
Figure 10: Efficiency vs Mass flow rate for winter and summer data. [2]
12
Figure 11: Our theoretical expression for 6 grids superimposed on the same graph as our
experimental results. [2]
Mass flow rate is not the only factor affecting the efficiency. In our theoretical
expression, the heat loss constant affects the efficiency. In order to analyze the heat
loss, we consider how to optimize the absorption material inside. We need to assess
the air flow through the device and provide an explanation for our design. Our
absorption material is an important piece of our design which we look to optimize.
We claim that our flow field distribution manifold improves our efficiency. To
begin our analysis, we compare our device to an empty rectangular box. Romdhane
provided an image of a rectangular Solar Air Heater with no obstructions and a smoke
machine image showing the flow field within.
13
Figure 12: Image of a Solar Air Heater with no fins, baffles, or any obstruction. [3]
The dark spaces in the corners indicate dead zones where there is little to no
air flow. This stagnant air has higher temperatures which increases thermal losses,
and decreases efficiency. Other researchers have proposed solutions such as fins and
baffles, which divert air in various patterns to create a more uniform flow.
Figure 13: Smoke machine image of
a SAH with aligned fins. [3]
Figure 14: Smoke machine image of
a SAH with baffles.[3]
Assessing these solutions, we believe there could be additional improvements that
further minimize the dead zones. Our flow field distribution manifold at the input and
output of the device has various sized holes aligned to redistribute the air uniformly
across the mesh. Our solution reduces dead zones (in particular in the corners),
creates a uniform flow, and provides a low pressure drop— all contributing to a
higher efficiency.
14
Figure 15: This figure shows our distribution manifold and smoke air flow through one
section of our device.
In order to quantify our flow resistance, we measured the pressure drop across
the device using an inclined manometer connected at the input and output. As the
resistance increases, particles accumulate against the materials resisting the flow.
With an accumulation of particles, we have an increase in particles per unit area
increasing the pressure before the obstacle providing resistance closer to the input.
With a lower resistance, the particles are free to flow and the pressure drop across
the device is smaller. This analysis allows us to determine the flow resistance as a
function of the pressure drop across our SAH.
As we increase the mass flow rate, we see the pressure drop increase.
15
Figure 16: Pressure drop across our SAH as a function of the mass flow rate for 6 grids.
Conceptually, the slope of the line describes the flow resistance of the SAH (a
steeper slope implying a higher flow resistance). Pressure drop is proportional to the
required fan power, so we aim for a low flow resistance to reduce the pressure drop.
Reducing flow resistance will reduce required fan power. As fan power increases, it
subtracts from our net power output. We were able to show that our fan power was
not significant enough to drastically detract from our device (as shown in Figure 17).
16
Figure 17: Data taken by Ralston and Pfister experimentally showing that efficiency in-
creases with mass flow rate. This graph includes the power of the fan, thermal output, and
net power out [2].
The original grid number was determined by a simple transmissivity test. We
layered grids until light no longer reflected back from a white surface beneath. With
further consideration, we have to analyze the absorption and flow resistance qualities
of our grids to experimentally and theoretically determine the optimal number.
Our grids serve as the absorption material therefore theoretically we want a high
number of grids to maximize the potential for absorption. Since we do not have the
heat coefficient terms for the convective losses, we use the temperature gain as a
measure of our absorption. We expect that as we increase grid number, the difference
between the output temperature and the ambient temperature should increase.
Additionally, our grids are an obstacle and affect the air flow. Our flow field
distribution manifold helps regulate the air for a laminar flow, yet additional grids
affect the turbulence. We can model the pressure drop values against the Darcy-
-Weisbach equation and measure the Reynold’s Number to see if our values follow a
laminar or turbulent flow.
The Reynold’s Number is a dimensionless quantity that utilizes the viscosity(µ),
density(ρ), and velocity(v) of the air and the hydraulic diameter (dh) of the input to
determine if the flow is laminar or turbulent. The hydraulic diameter is the diameter
measured from the wetted perimeter. In our case, air evenly flows through the input
17
so the wetted perimeter is simply our input diameter. Reynold’s Numbers greater
than 4000 suggest turbulent flow, whereas values below 2000 suggest laminar flow.
The region in between is a mixed stage between the two types of flows.
Re =ρdhv
µ(18)
The velocity used in this equation is the drift velocity of the air after the input.
The drift velocity is calculated using the ratio of the areas of the input pipe (AT ) and
the cross sectional area of the SAH (Aa).
vdrift =vinputAT
Aa
(19)
Since our fluid is not changing, our density and viscosity are constant, so an
increase in velocity leads to an increase in the Reynold’s Number. Higher Reynold’s
Numbers suggest an increase in turbulence as we change the mass flow rate. As we
change the mass flow rate, our device goes through each of these stages.
The Darcy-Weisbach equation is an equation expressing the pressure drop for lam-
inar flow. This equation is derived from considering the pressure needed to maintain
air flow [4].
∆p = fd1
2ρL
Dv2 (20)
Dimensionally, the pressure has units of energy density, so we express the kinetic
energy as:
KE
V ol=
1
2ρv2. (21)
Since we are looking at how the pressure influences the movement in the device,
we consider the pressure to be proportional to the kinetic energy density.
∆p ∼ 1
2ρv2 (22)
As we increase the length of the device, we linearly increase the potential for a
higher pressure drop. If we increase the diameter of the input, particles have more
room to flow and we reduce pressure at the input. With a proportionality factor, in
this case a friction factor (fd), and additional properties (the length and the diameter),
we obtain:
∆p = fdL
D
1
2ρv2. (23)
We expect that an increase in the number of grids will lead to an increase in
turbulence and a lower efficiency.
18
As we assess the optimal number of grids, we consider the combination of absorp-
tion properties and flow resistance measurements. With our efficiency calculations,
we should see what number of grids will provide us with the highest efficiency, a
desirable output temperature, and a short return on investment (ROI). This graph
will provide insight into which properties affect the efficiency the most.
In order to analyze our ROI, we evaluate the cost of the device as a function of
grid number compared to the return output power from the efficiency associated with
that grid number.
(Costpergrid ·No.ofGrids+BaseCost) =
SunHours · CostperkWh ·Max.Output · ConversionEfficiency(24)
This expression gives us the number of sun hours required to make the initial
investment back. To find the ROI we divide this value by the average number of sun
hours annually in the Carlisle, PA area.
ROI =SunHours
SunHoursperyear(25)
This equation will give us a value for the number of years required to make back
the initial cost.
5 Experimental Methods
The SAH is completely and fully operational and is currently set up on the roof of
Tome Science Building (Dickinson College). We have installed a LabPro device for
data acquisition. We have temperature sensors to measure the input and output
temperatures as well as a device for measuring the ambient air temperature. A
pyranometer calibrated to NIST standards is installed to record the irradiance once
every second. A calibrated Vernier anemometer measures the flow input from the fan
(our fan is 8 inches and we are able to control the mass flow rate from 0.02 kg/s to
0.07 kg/s which encompasses our operational maximum). This semester we added an
inclined manometer that allows us to measure the pressure drop. The manometer is
attached at the input and output to measure pa(i) and pb(i). our pressure drop is the
difference between the two (∆P ). In addition, we have two multimeters measuring
the fan speed and fan current. We use C-clamps to hold down a rectangular frame
which holds down our glazing. This allows us to remove the frame and glazing to vary
the number of grids. We implemented a few new designs to improve the consistency
19
of our measurements including pegs to hold the grid folds in place and stability with
the output temperature probe.
Our measurements were performed on March 26, 2016. Completing the experi-
ment within the same day reduces errors with relative humidity, cloud conditions, and
slight differences in experimental methods. For each run we measured the ambient
air temperature, output temperature, pressure drop, mass flow rate, fan current, fan
speed, fan voltage, and solar irradiance. In order to complete the data acquisition in
a timely fashion we reduced each mass flow rate recording time to 60 seconds. This
allowed the temperature to stabilize and reach a steady state. After 60 seconds, we
increased the fan voltage by approximately 5 volts and recorded the voltage read-
ing, fan current, and air speed. With our collected data we were able to determine
the efficiency, power out, net thermal power (corrected for differences in irradiance),
Reynold’s Number, pressure drop, and fan power.
Figure 18: Solar Air Heater test stand showing our set up for data acquisition.
20
6 Results
6.1 Absorbance
In order to determine the absorbance properties of the grids, we analyze the output
temperature as we alter the grid number. Since we have varying ambient air tem-
peratures, we compare the temperature gained from the ambient air, therefore the
difference between Tout and Tamb.
Figure 19: Temperature difference for each grid configuration as we change the mass flow
rate. Temperature difference is a measure of Tout-Tamb.
As shown in Figure 19, we see that as we increase the number of grids, the tem-
perature difference from the ambient air increases. We can infer that additional grids
lead to an increase in absorption.
21
6.2 Flow Resistance
In order to quantify flow resistance, we measure the pressure drop across the device.
Figure 20: Pressure drop measurements as a function of mass flow rate with changing grid
number.
There is a slight increase in pressure drop as we add grids, but it is on the order
of 5 Pascals. This suggests that the grid number hardly affects the flow resistance in
the device.
We calculate the Reynold’s Number using the properties of the air (ρ, µ ) and the
drift velocity of the air which ichanges based on fan speed.
22
Figure 21: Reynold’s Number as a function of the mass flow rate.
The Reynold’s Number increases linearly with the mass flow rate, starting in the
laminar region and ending up in the turbulent region (as indicated on Figure 21).
To further show that our pressure drop indicates that our flow is going from
laminar to turbulent, we model our data against the Darcy-Weisbach equation.In
Figures 22-28, the red line represents the theoretical equation and the blue is our
measured data.
Figure 22: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 0 Grids.
Figure 23: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 1 Grid.
23
Figure 24: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 2 Grids.
Figure 25: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 3 Grids.
Figure 26: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 4 Grids.
Figure 27: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 5 Grids.
Figure 28: Comparison of theoretical
pressure drop vs. experimental pressure
drop for 6 Grids.
Our pressure drop equations follow the Darcy-Weisbach approximation closely in
the laminar region. As we move towards 0.03 kg/s and the more turbulent region,
we see our experimental data diverging from our linear laminar approximation. Our
operational range is in the turbulent region.
24
6.3 Efficiency
With our experiment we calculated the efficiency as a result of mass flow rate and
changing grid number.
Figure 29: Raw data results for efficiency vs. time.
We have spikes in our efficiency curve due to a thermal lag before we reach steady
state at each fan speed. As we increase the speed, we decrease the amount of time
the air has to interact with the absorbing material, so the temperature decreases
inside the SAH. Before the air reaches steady state when we increase the fan speed,
the previous warmer air is still in the SAH therefore yielding a high, unrealistic,
efficiency. We recreated our efficiency graph by choosing the steady state efficiency
at each velocity, calculating the mass flow rate at each speed, and re-graphing the
efficiency as a function of the mass flow rate.
25
Figure 30: Efficiency as a function of mass flow rate for changing grid number.
Our efficiency peaks around 86% with 4 and 5 grids providing the highest efficiency
values. Additional calibration may be necessary with our flow straighenter between
the fan and the input. This has the potential to decrease our efficeincy by a few
percentage points.
Our return on investment calculations involved an average cost for 1 kWh of
electricity to run the fan, the average sun hours per year in the Carlisle area, and an
approximation for the base cost of the device.
Table 1: Constants for ROI Calculation
Max. Output 2.5 kW
Cost per Grid 12.50 dollars
Cost per kWh 12 cents
Annual SunHours 2540.4 hours
Base Cost 150.00 dollars
Using the equations from our theory (Equations 25 & 26) we were able to deter-
mine a list of return on investment values and sort them based on the fastest return
time, or the smallest number of years.
26
Table 2: Sorted ROI Values
No. of Grids ROI (years)
1 0.281
2 0.286
0 0.294
4 0.302
3 0.307
5 0.317
6 0.347
7 Analysis
By assessing the output temperature we can evaluate how much the absorption
changes with additional grids. Figure 19 shows us the temperature gained as we
change the mass flow rate given the seven discrete grid numbers. We consistently
measured the ambient temperature and output temperature for proper measurement
calculations.
The pressure drop data not only shows us how the pressure drop changes with
mass flow rate, but also shows us how it changes with different grids. This will give us
insight into change in turbulence and flow resistance with varying grids. Our analysis
involved converting the results from the anemometer (a change in alcohol volume)
into pascal measurements. In addition we utilized the Darcy-Weisbach equation to
compare our measured results and determine the type of flow. Our results follow the
linear line during laminar flow, and diverge when the Reynold’s Number begins to
show turbulent flow.
Our final results stem from the efficiency graph. Our raw results include spikes
and peak at an efficiency over 90%. This does not make sense with our glazing since
the natural albedo of the glazing is around 12% therefore maximizing our efficiency
at 88%. In order to correct for these spikes, our final efficiency is at the steady state
point at each mass flow rate. This allows us to create a new efficiency versus mass
flow rate graph (Figure 34) which correlates one efficiency for each mass flow rate for
each grid number.
We can determine the highest efficiency from these results and then consider
cost, fan power, and return on investment. Since we want the highest efficiency
from our SAH, we want to use a high fan speed that produces the maximum output
27
power before it plateaus. This minimizes our need for additional fan power therefore
reducing electricity and return on investment costs. In addition, the cost of a grid
is a significant piece of our overall design cost. Therefore, if we have very similar
efficiency values, our ROI will favor smaller grid numbers.
To find our ROI, we calculated constants used in Table 1. The maximum output
was determined from an approximated average solar power rating in Carlisle, Penn-
sylvania. The cost per grid was the value at which the original grids were purchased.
The cost per kilowatt hour the average electricity costs in the United States [5]. Our
evaluation for annual sun hours is a calculation of the average daily hours of sunlight
per day and the average number of sunny days per year in Carlisle [6]. The base cost
of our design combines approximate values of the materials required to construct the
device. This includes but is not limited to the base wood, the insulation, the spray
paint, the fan, the glazing, the frame, and the flow field distribution manifolds.
8 Conclusion
Our experiments returned three conclusions. First, thermal losses were the significant
driver for the difference in efficiency calculations in this grid number range. Having
4 or 5 grids in the device returned the highest efficiency values. Since the pressure
drop did not significantly change with grid number, we can determine that thermal
losses greatly influence the power balance equation.
Our second conclusion states that the temperature gain seems to plateau around
5 grids. With our data, the output temperature begins to level suggesting that the
absorption is constant. The temperature gained by the ambient air for 4,5, and 6
grids all are very similar values.
Lastly, our fastest return on investments occur with low grid number. Since our
base cost is low, each grid is a significant percent of the overall price. Our results
showed that 1 and 2 grids had the fastest ROI. The differences in efficiency and
output temperature with higher grid number were not significant enough to desire
higher grid number with regards to price. The base cost strongly affects the ROI.
Installation costs or change in material costs can largely affect our results. With a
higher base cost, the efficiency plays a more significant role in our ROI.
This Solar Air Heater is simple and inexpensive, yet produces desirable output
temperatures for practical use. The fan power required to operate the device is
minimal, and the ease of use and installation make this device an attractive option
for renewable energy. The low cost, high efficiency, and high output temperature with
little power in, make this device competitive with comparable fossil fuel resources.
28
Our SAH is limited in that it is best used during the day with sun hours. This
makes it ideal for day time functionality such as heating a building that operates
during the day (offices and businesses for example), or heating a well insulated stor-
age unit. In addition our design can be used for fruit drying, water desalinization,
methane producing bio-digester, or other short-term processes which allows for prac-
tical use during the day [7]. Our device is not a solution to climate change, but it
can minimize typical fossil fuel heating by providing a lost cost, efficient, high output
temperature device that does not emit CO2.
9 Suggestions for Further Research
Further research possibilities include improvements on materials including improved
insulation, better glazing, and prevention of leaks while maintaining low material
cost and ease of use. In addition, research can be done to include some heat storage
device/technique that makes the device more practical for anytime use.
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A Appendix
A.1 Other purposes for Solar Air Heaters
For reference regarding fruit drying purposes of the Solar Air Heater, refer to
Kareem et al., 2014, Dhanemozhi et al., 2013, El-Sabaii et al., 2012; and Hanif et al.,
2012.
For reference regarding water desalinization and purification, refer to Kabeel and
El-said, 2013; Yuan et al., 2011; and Fath and Ghazy, 2002.
A.2 Other types of Solar Air Heaters
For further information of theory and Solar Air Heater function in general, refer to
Ursula Eicker 2003. For simulation and mathematical modeling, refer to Tchinda
2009.
Our absorber material is a wire mesh grid. Other designs we found in our research
included primarily of fins and baffles. Fins are best described as rectangular strips
of metal used to divert air in various patterns. Romdhane shows an image of a SAH
32
with fins as shown in Figure 16 of this paper. For reference on a SAH with fins, Yeh
2013.
The other popular design involves baffles. Baffles are best described as triangular
pieces that have holes along the inside. Romdhane also provides an image of a SAH
with baffles as shown in Figure 17 in this paper. In addition, he studied baffles in
comparison to an empty SAH (2006). Chamoli (2013) studies a SAH with baffles
angled down towards the output. Sootkaew (2014) studies a SAH with much smaller
baffles lined up along the bottom panel.
In addition to different types of absorbing materials, double and single pass air
heaters have also been in competition. For reference on double-pass SAHs, refer to
Ho (2014), Ho et. al. (2015), and Chamoli (2011).
A.3 Increase in SAH Research Popularity
Solar Air Heaters are becoming increasingly popular due to the flexibility in design
and ability to achieve very high efficiency values. The research around SAHs is
increasing globally, as shown in the figure below.
Figure 31: Number of articles we found over the years referencing SAH’s.
33
A.4 Glazing Temperature
We are utilizing double layer glazing therefore there is a slight temperature difference
between the temperature on the inner layer and the outer layer. The glazing itself
transmits most of the solar energy passing through and reflects away a significant
portion as well. The remaining energy is absorbed by the glazing. In addition, the
inside layer of the glazing is receiving radiation from the back panel and absorber,
and convected heat from the fluid (increasing the temperature of TG,i. For theoretical
purposes, we combine the two temperatures (TG,o and TG,i) and consider 〈Tins〉 (the
average inside temperature) as the temperature of the glazing. The difference is
minimal, and since we do not measure TG,i or TG,o in our experiments, we utilize
〈Tins〉.
A.5 Linearizing the Radiation Thermal Loss Temperature
We consider our Solar Air Heater to be a grey body radiator, therefore we utilize the
Stefan-Boltzmann Law to measure our radiation driven by the temperature difference
between the inside air and the ambient air. When we combine the thermal losses to
create one heat coefficient term, we use the same temperature difference for each loss.
In our Stefan-Boltzmann equation, we see that there is a T4 temperature difference,
which is not equivalent to the linear expression.
In order to use Tout-Tamb in our radiation term, we linearize the temperature.
(T 4ins − T 4
amb) = (T 2ins − T 2
amb) · (T 2ins + T 2
amb) (26)
(T 4ins − T 4
amb) = (Tins − Tamb) · (Tins + Tamb) · (T 2ins + T 2
amb) (27)
From this equation, we use the Ti-Tamb term as our temperature differential, and
combine the other expressions into our radiation heat coefficient term.
hrad = εσ(Tins + Tamb) · (T 2ins + T 2
amb) (28)
Pout(exact) = σAapε(T4ins − T 4
amb) (29)
Pout(theoretical) = Aaphrad(∆T
2) (30)
In order to estimate the difference between our linearized version and our exact
measurements, we can calculate an output power for each equation and compare.
34
Figure 32: Comparing the linearized and exact power output for temperature differences
of 0K — 80K.
To begin our comparison, we start with an ambient temperature of 273K and
evaluate a temperature difference (80K) up to 353K. Theoretically, it does not matter
where we start since we are evaluating the temperature difference. Below are our
average temperature differences for each of the seven grid numbers.
Table 3: Average temperature difference for each grid number
No. of Grids Average ∆T (C)
0 48.08
1 56.54
2 57.86
3 57.02
4 62.96
5 63.39
6 60.33
Across this range of temperature differences, we see an average difference between
the exact values and linearized values to be 60.9 watts. On average, the loss from
the theoretical linearized value is 5% or approximately 46 watts, which is a fairly low
error.
35
A.6 Design details of construction
The Figures below show a detailed description of the dimensions of our SAH.
Figure 33: Transverse cross-sectional view of the new SAH design. The insulation is
improved from formerly R = 10.7 to R = 19. (Pfister)
Figure 34: Longitudinal cross-sectional view of the new SAH design. For the sake of ease
of construction, the angled intake and outflow channels were drilled horizontally. (Pfister)
36
Figure 35: Dimensions of the new sidewalls. The walls are made of Polyisocyanurate foam
boards which reduces the weight of the SAH and improve the R-value. (Pfister)
37