SPACE HEATING DESIGN OPTIONS FOR
ANHEUSER BUSCH’S STORAGE FACILITY
Manuel A. Leija
B.S., California State University, Sacramento, 2007
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2009
SPACE HEATING DESIGN OPTIONS FOR
ANHEUSER BUSCH’S STORAGE FACILITY
A Project
By
Manuel A. Leija
Approved by:
______________________________, Committee Chair
Professor Timothy Marbach
_____________________________
Date
ii
Student: Manuel A. Leija
I certify that this student has met the requirements for format contained in the University format
manual, and that this Project is suitable for shelving in the Library and credit is to be awarded for
the Project.
____________________________________, Department Chair
Professor Susan Holl
Department of Mechanical Engineering
iii
___________________
Date
Abstract
of
SPACE HEATING DESIGN OPTIONS FOR
ANHEUSER BUSCH’S STORAGE FACILITY
by
Manuel A. Leija
Statement of the Problem
This project investigates the use to solar energy to heat Anheuser Busch’s storage
facility in Fairfield, California, specifically using solar (Trombe) wall and an evacuated
tube collector design considerations. This warehouse is currently using 25 steam heated
air units that constantly malfunction. Anheuser Busch demands a solution to this
problem by finding an alternative system that will meet the heat load requirements while
at the same time utilize renewable energy sources. Using preexisting solar radiation data,
as well as the facility constraints, an optimal solution will be presented.
Sources of Data
The hourly solar radiation data was collected from the National Solar Radiation
Data Base for the Travis Field Air Force Base in Fairfield, California for 2005. The
hourly temperature and wind velocities were taken from Weather Underground, a website
that has historical data for various locations from 2006 to present. Microsoft Excel was
used to perform the calculations necessary to present the solution.
iv
Conclusions
The most optimal solution for this project was the Trombe wall design. The
October 4th heat load demand is 35 MW and the wall capacity is 7 MW. This only meets
20% of the heat demand and the other two selected days were even less, therefore
auxiliary heat must be supplied. The evacuated tube collector’s smallest storage tank is
859 m3 (227,000 gallons), which is an impractical and costly design.
________________________________, Committee Chair
Professor Timothy Marbach
_______________________
Date
v
ACKNOWLEDGMENT
I would like to acknowledge the faculty at California State University, Sacramento for
providing me with the proper tools and education for allowing me to finish this project. I
would especially like to acknowledge Professor Marbach for instilling in me a passion for
renewable energy and alternative technology. This desire allowed me to explore new
heights with energy design that was not only challenging but exciting as well. I also
would like to acknowledge William Bennett and Anheuser Busch for allowing me to help
them with a project that may be a major influence to other companies.
vi
TABLE OF CONTENTS
Acknowledgment ............................................................................................................... vi
List of Tables ..................................................................................................................... ix
List of figures ...................................................................................................................... x
Nomenclature .................................................................................................................... xii
Chapter
1. BACKGROUND AND INTRODUCTION .................................................................. 1
1.1 History of Solar Energy ........................................................................................... 2
1.2 Solar Contribution to Other Renewable Energy Sources ........................................ 4
1.3 Solar Applications .................................................................................................... 5
2. SOLAR COLLECTORS ................................................................................................ 7
2.1 Unglazed Solar Collectors ....................................................................................... 7
2.2 Glazed Collectors ..................................................................................................... 9
2.3 Evacuated Tube Collectors .................................................................................... 11
2.4 Concentrating Collectors ....................................................................................... 12
3. COMPUTATIONAL SETUP AND PROCEDURE ................................................... 15
3.1 Assumptions........................................................................................................... 15
3.2 Trombe Wall Analysis ........................................................................................... 16
3.3 Evacuated Tube Collector Analysis ....................................................................... 23
4. ANALYSIS OF THE DATA ....................................................................................... 28
4.1 Trombe Wall Data.................................................................................................. 29
vii
4.2 Evacuated Tube Collector Data ............................................................................. 30
5. FINDINGS AND INTERPRETATIONS .................................................................... 33
5.1 Further Research .................................................................................................... 33
5.2 Conclusions ............................................................................................................ 34
Appendix A: Solar Radiation Data for the Three Selected Days..................................... 36
Appendix B: Calculation Tables ...................................................................................... 37
Appendix C: Miscellaneous Charts ................................................................................. 52
Appendix D: Charts Used for Determing Specific Data for Trombe Wall Analysis....... 66
Bibliography ..................................................................................................................... 69
viii
LIST OF TABLES
Table 1: Assumed Values for Trombe Wall Analysis ..................................................... 16
Table 2: Assumed Values for Evacuated Tube Collector Analysis ................................. 16
Table 3: Solar Wall Data Calculated for Selected Days .................................................. 29
Table 4: Evacuated Tube Data Calculated for Selected Days ......................................... 31
Table 5: Yes or No Comparison Table of Both Design Methods .................................... 33
Table 6: Hourly Solar Radiation Data and Temperature for Three Selected Days ......... 36
Table 7: Evacuated Tube Collector Analysis for October 4, 2005 .................................. 37
Table 8: Evacuated Tube Collector Analysis for November 2, 2005 .............................. 39
Table 9: Evacuated Tube Collector Analysis for December 16, 2005 ............................ 41
Table 10: Trombe Wall Analysis for October 4, 2005 .................................................... 43
Table 11: Trombe Wall Analysis for November 2, 2005 ................................................ 46
Table 12: Trombe Wall Analysis for December 16, 2005 ............................................... 49
ix
LIST OF FIGURES
Figure 1: Unglazed Solar Collector Used for Pool Heating ............................................... 8
Figure 2: Glazed Flat-Plate Solar Water Collector ............................................................. 9
Figure 3: Glazed Flat Plate Solar Air Collector ............................................................... 10
Figure 4: Solar Wall (Trombe Wall) With Opening for Circulation ............................... 11
Figure 5: Evacuated Tube Collector ................................................................................ 12
Figure 6: Line Focus (Parabolic Trough) Collectors ....................................................... 13
Figure 7: Point Focus Line Collectors ............................................................................. 14
Figure 8: CM6B Pyranometer Measuring Device ........................................................... 22
Figure 9: Direct Applied Solar Storage System ............................................................... 23
Figure 10: Indirect Applied Storage System .................................................................... 24
Figure 11: Evacuated Tube Collector Area v. Useful Collector Gain for October 4, 2005
........................................................................................................................................... 52
Figure 12: Collector Efficiency v. Useful Collector Gain for October 4, 2005............... 53
Figure 13: Useful Collector Gain v. Heat Used by Load for October 4, 2005 ................ 54
Figure 14: Useful Collector Gain v. Heat Used by Load for November 2, 2005 ............ 55
Figure 15: Useful Collector Gain v. Heat Used by Load for December 16, 2005........... 56
Figure 16: Isotropic Model v. Anisotropic Model for October 4, 2005 .......................... 57
Figure 17: Isotropic Model v. Anisotropic Model for November 2, 2005 ...................... 58
Figure 18: Isotropic Model v. Anisotropic Model for December 16, 2005 ..................... 59
Figure 19: Total, Beam, and Diffuse Hourly Radiation Components for October 4, 2005
........................................................................................................................................... 60
x
Figure 20: Total, Beam, and Diffuse Hourly Radiation Components for November 2,
2005................................................................................................................................... 61
Figure 21: Total, Beam, and Diffuse Hourly Radiation Components for December 16,
2005................................................................................................................................... 62
Figure 22: Hourly Heat Loss from Building for October 4, 2005 ................................... 63
Figure 23: Hourly Heat Loss from Building for November 2, 2005 ............................... 64
Figure 24: Hourly Heat Loss from Building for December 16, 2005 .............................. 65
Figure 25: Transmittance of One, Two, Three, and Four Covers for Three Types of Glass
........................................................................................................................................... 66
Figure 26: Effective Incidence Angle of Isotropic Diffuse Radiation and Isotropic
Ground-Reflected Radiation on Sloped Surfaces ............................................................. 67
Figure 27: Typical (τα)/(τα)n Curves for One to Four Covers ......................................... 68
xi
NOMENCLATURE
Symbols
Ab
Ac
Ai
f
GT
I
Ib
Id
Io
kT
K
L
Rb
S
Ta
Ti
Ts
Ts+
U
Qu
VT
Building Surface Area (m2)
Solar Collector Receiving Area (m2)
Anisotropy Index
Modulating Factor
Total Irradiance (Wh/m2)
Total Hourly Irradiance (J/m2)
Hourly Beam Irradiance (J/m2)
Hourly Diffuse Irradiance (J/m2)
Extraterrestrial Hourly Radiation (J/m2)
Hourly Clearness Index
Glass Extinction Coefficient (m-1)
Glass thickness (m)
Ratio of Beam Radiation on a Tilted Plane to that on the Plane of Measurement
Absorbed Solar Radiation (J/m2 or W/m2)
Ambient Temperature (°C or °F)
Inside Temperature (°C or °F)
Storage Temperature at the Beginning of the Hour (°C or °F)
Storage Temperature at the End of the Hour (°C or °F)
Overall Heat Loss Coefficient (W/m2K)
Useful Energy Gain for the Solar Collector (J/m2 or W/m2)
Tank Volume (m3 or gallons)
Greek Symbols
αn
Absorptance of a Plate at Normal Incidence
β
Tilt Angle of Solar Collector (Degrees)
η
Efficiency of Solar Collector
θ
Angle of Incidence (Degrees)
θe
Effective Angle of Incidence (Degrees)
ρg
Ground Reflectance
τ
Transmittance
(τα)b Beam Transmittance-Absorptance Product
(τα)d Diffuse Transmittance-Absorptance Product
(τα)g Ground Transmittance-Absorptance Product
(τα)n Transmittance-Absorptance Product of a Plate at Normal Incidence
xii
1
Chapter 1
BACKGROUND AND INTRODUCTION
With the increase in human population during the last few decades there has been
a large increase in energy consumption. This energy is used in almost every aspect of a
person’s life and therefore must be supplied when demanded. Today approximately three
quarters of the energy supplied comes from fossil fuels, i.e., coal, oil and natural gas
(Boyle 6). Allowing this to continue in this manner may seem sufficient for the time
being; however concern begins to arise when the longevity of this supply comes into
question. At current consumption rates, proven world coal reserves should last for about
200 years, oil for approximately 40 years and natural gas for around 60 years (BP, 2003).
The sustainability of fossil fuels and nuclear fuels, or lack thereof, is what brought about
the development of renewable energy technology. An energy source is said to be
sustainable if it is not substantially depleted by continuous use, does not emit pollutants
or other environmental hazards, and does not produce health hazards or social injustices.
There are a few renewable sources that are more sustainable than the previous mentioned
fossil and nuclear fuels. Solar power, hydropower, wind power, wave power, tidal
power, bioenergy and geothermal energy all fall under the category of renewable energy
and although they are not 100 percent sustainable they essentially cannot be depleted,
their use produces significantly less greenhouse gases, as well as fewer health hazards.
Solar energy and its applications are the premise of this paper and therefore will be
discussed more so than any other renewable energy source.
2
The sun is a sphere of intensely hot gaseous matter with a diameter of 1.39 x 109
meters and is approximately 1.5 x 1011 meters from the earth (Duffie, 3). This sphere can
be thought of as a fusion reactor with its gases held together by gravitational attraction
and it is the fusion of hydrogen into helium that produces the energy radiating from the
sun. Basically, as four protons combine to form a helium nucleus mass is lost during the
reaction and converted to energy. This energy at the sun’s center has a temperature of
many millions of degrees and the radiative and convective processes this energy goes
through to get to the surface causes the temperature to drop to about 6000 K. This
thermal radiation emitted from the sun is what promotes life and growth for all the
organisms on the earth. Thermal radiation can be considered as consisting of
electromagnetic waves and much like all waves have specific characteristics such as
wavelength and frequency that follow them. Although the electromagnetic spectrum has
wavelengths that run from 10-5 to 104, thermal radiation covers wavelengths from about
10-1 to 102 with frequencies of 1012 to 1016. These wave characteristics can be used to
accurately predict other properties that are used for solar design such as emissivity,
absorptivity, and reflectivity. Emissivity is the amount of heat flux that is allowed to be
emitted by an object and is usually a property of the material. Absorptivity is the amount
that can be absorbed and reflectivity is the amount that can be reflected. All these
properties limit the amount of solar energy the collector can actually use.
1.1 History of Solar Energy
Ancient Greeks and Romans would use their architectural talents to design their
buildings in order utilize the energy from the sun to heat and light indoor spaces. They
3
would face the house towards the south and later realized that installing glass would help
entrap the heat inside the building for longer periods of time. This passive design would
offset the need to burn wood which was often in short supply. To this day many people
use this same technique in their homes or business for space heating and lighting. Since
then many designs have been made to use solar for various processes and as technology
improved so did the efficiencies and equipment used to collect and store this energy. In
the 1760s a Swiss naturalist by the name of Horace de Saussure said, “It is a known fact,
and a fact that has probably been known for a long time, that a room, a carriage, or any
other place is hotter when the rays of the sun pass through glass.”(Perlin) In order to
show the effectiveness of trapping heat with glass, Horace built a box out of pine,
insulated the inside and covered the top with glass. He also put two smaller boxes inside
the larger one. After exposing this apparatus to the sun for awhile, Horace noticed that
the boxes inside were heated to 109° C (228° F). Unsure of the phenomenon behind this
he still proclaimed that this “hot box” could have practical applications and later was the
stepping stone to solar collector design. The first water heaters available were simply
tanks of water placed behind a normal window. In 1891 Clarence Kemp combined the
“hot box” method with the old method of exposing metal tanks to the sun to patent his
own solar water heater he called The Climax. Combining the two methods increased the
tanks ability to collect and retain solar heat. The only disadvantage to The Climax was
that the heat collector and the storage tank were all one unit and exposed to the
environment. This meant that during the night the heat would leave the tank and there
would not be hot water in the mornings for bathing. In 1909, William J. Bailey of
4
California designed and patented a thermosyphon solar water heater (Boyle, 36). This
new system was broken into two parts, a heating element that was exposed to the sun and
an insulated storage tank that was tucked away in the house. This allowed water to
remain hot overnight due to the reduction in heat loss. Using the sun to heat water started
to become more widespread around the globe, however as natural gas prices dropped and
fossil fuels became cheaper everywhere, solar heating decreased because it started to
become less cost effective. It wasn’t until the oil crisis in the 1970s when solar started to
make its way back into the homes of many residences. Now more people are turning to
solar for their water and space heating needs and are either installing new systems on
their preexisting homes or incorporating them into newly built houses.
1.2 Solar Contribution to Other Renewable Energy Sources
Solar energy can be either directly used or indirectly used. Direct use involves
solar energy to be absorbed through solar collectors for hot water or spacing heating,
passively through walls and windows for heating and lighting, concentrated by mirrors to
produce high temperatures or through photovoltaic cells to produce electricity. Solar
radiation can be converted to useful energy indirectly, via other energy forms (Boyle, 12).
When solar radiation reaches the earth part of that radiation is absorbed by the oceans
warming them. This creates water vapor in the air which later condenses and forms rain.
This rain is fed into rivers, where this water flow can be used to turn turbines and create
electricity. This is known as hydropower and it currently provides about a sixth of the
world’s electricity. Due to the tilt of the earth, solar radiation falls more perpendicular in
the tropical regions than the polar regions, hence heating the tropics much more than the
5
poles. This heat imbalance causes heat to flow from the tropics to the poles creating
wind. Wind power uses turbines to harness the energy potential from the wind
converting it into electricity. When winds roll across the ocean, waves are created.
These oceanic waves can be used to generate electricity similar to that of wind power.
One last indirect form is bioenergy. Through photosynthesis in plants, solar radiation
converts water and atmospheric carbon dioxide into carbohydrates which form the basis
of more complex molecules (Boyle, 13). Biomass in the form of wood or other biofuels
is usually burned and the steam created turns a steam turbine to create electricity. Solar
plays an important role in energy generation, not only directly but indirectly as well.
1.3 Solar Applications
Since this project involved direct use of solar energy, more emphasis will be put
on the types of direct uses instead of indirect uses. When discussing solar energy and its
applications, it is customary to distinguish between the different types of systems. The
types of systems are active solar heating, solar thermal engines, passive solar heating and
day lighting. An active system always involves solar collectors to gather the solar energy
and is often used to heat water or small spaces. Solar thermal engines are essentially an
extension of active solar heating. They use carefully designed collectors to get
temperatures high enough to drive steam turbines for electricity generation. Passive
systems generally are systems that absorb the solar energy directly into the building to
heat a space and reduce the dependence of mechanical heating systems. Usually the
collector is an integral part of the building. Day lighting is exactly what the name
suggests. Windows or openings are used to bring in the suns natural light in order to cut
6
electrical costs. Although active and passive systems are stated here as two different
solar collection systems, in practice however, these two are not clear cut but rather blend
into each other with a range of possibilities in between. This project studied the effects
of both active and passive systems and therefore will discuss the technology for those
types of systems.
7
Chapter 2
SOLAR COLLECTORS
There are different types of solar collectors and depending on the application the
collector will need to be sized accordingly. Solar energy collectors absorbs solar
radiation, converts it into heat and then transfers this heat to a collector fluid which is
usually air, water, or oil. The fluid that receives the heat can then be delivered to the
desired location to either be used instantly such as heating a room or water, or it can be
stored in a tank for later use when no solar radiation is available. They are essentially
specialized heat exchangers.
Collectors can be unglazed, glazed, evacuated, and of the concentrating type.
Unglazed and glazed collectors are generally used for low temperature collection while
evacuated and concentration collectors are for high temperature situations. Some of these
collectors are stationary while others are non-stationary. Stationary collectors generally
have the same area for collecting radiation and absorbing radiation. Non-stationary
collectors generally track the sun and have concave surfaces that allow the radiation to be
concentrated to a smaller absorbing area. Stationary collectors were used for the analysis
of this project, specifically evacuated tube collectors and vertical flat plate collectors, i.e.,
a Trombe wall.
2.1 Unglazed Solar Collectors
Unglazed solar collectors are simply an absorber plate with tubes running through it
for the fluid. They do not have a glass cover and there cannot block the reradiated energy
8
from the absorber plate. Without a glass cover the absorber plate is exposed to the
environment and therefore is subject to convection and radiation losses. This is why they
are low temperature collectors. The most common type of unglazed collectors are those
used for swimming pool heating. Since the pool should be maintained around 70-80
degrees Fahrenheit it is not necessary and often considered overkill to use a glazed
collector.
Figure 1: Unglazed Solar Collector Used for Pool Heating
9
2.2 Glazed Collectors
Glazed collectors are those with glass coverings and are often referred to as flat plate
collectors. This glass can be single sheets or multiple sheets. Putting a glass cover over
the absorber plate allows visible light and short wave radiation to be transmitted but
blocks long wave radiation. The energy being reradiated by the absorber plate has long
wavelengths and cannot be transmitted through the glass therefore becoming trapped
between the glass and absorber plate allowing for more absorptivity. These collectors are
also subject to radiation losses and convection losses. However, the convective losses in
flat plate collectors are significantly less compared to unglazed type because the type of
convection between the plate and glass is natural convection and not forced convection
like the unglazed collectors. Flat plate collectors can have water flowing through tubes
or the gap can be filled with air. Either way the fluid is heated and then transferred to
perform its desired task.
Figure 2: Glazed Flat-Plate Solar Water Collector
10
Figure 3: Glazed Flat Plate Solar Air Collector
Another type of glazed collector that is often overlooked is a solar wall, or Trombe
wall. Named after French inventor Felix Trombe in the late 1950s, the Trombe wall is
essentially a vertical flat plate collector that uses air as its transfer medium. It has a glass
covering and the wall of the building is converted to an absorber plate by adding to it a
selective material that has a high absorptivity property and a low emissivity property.
The air inside the wall can transfer heat by natural convection or by forced convection. If
the wall has no gaps in it, then the heat inside the wall rises due to buoyancy effects.
After some time the entire air space will be heated with the hotter temperatures towards
the top of the wall. This heat is then conducted through the wall and then convectively
warms the room on the other end of the wall. Another way to heat a room with a Trombe
wall is to allow gaps in the upper and lower part of the absorber wall. This creates a
11
forced convection effect. This forces the warm air to flow out the upper gap into the
room warming it and replacing the air in the wall with cooler air from the room. This
continuous circulation will warm the room quicker than the just by natural convection
alone. Glazed solar collectors are continuously being improved to increase efficiencies
and reduce size and cost.
Figure 4: Solar Wall (Trombe Wall) With Opening for Circulation
2.3 Evacuated Tube Collectors
Evacuated tube collectors are used for high temperature applications because of their
design and are therefore more costly. They consist of a tube with a metal strip running
along the center of the tube as the absorber plate. Inside the tube air is evacuated and a
vacuum exists. This vacuum suppresses all convective losses and the only heat loss is
due to radiation. This device uses a heat pipe to carry the collected energy to the water
12
that circulates along a header pipe at the top of the array of tubes. A heat pipe is a device
that takes advantage of a boiling fluid to carry large amounts of heat. A hollow tube is
filled with a liquid at a pressure chosen so that it can be made to boil at the hot end but
the vapor will condense at the cold end (Boyle, 37). This carefully designed tube has a
thermal conductivity many times greater than if it was just made of a solid tube and are
therefore able to transfer large amounts of heat.
Figure 5: Evacuated Tube Collector
2.4 Concentrating Collectors
Concentrating collectors are mostly used to generate steam in order to produce electricity.
There are parabolic trough collectors, or line focus collectors, and point focus collectors.
Both types of collectors focus the radiation directly onto a specific area in order to
maximize the amount of absorbed energy. The line focus collectors are a parabolic
13
trough made of a highly reflective material that is designed to focus all the suns energy
on to a pipe that runs along the focal center of the trough. The concentrators can remain
still or be allowed to move in order to track the sun throughout the day.
Figure 6: Line Focus (Parabolic Trough) Collectors
Point focus collectors operate on the same principle as the line focus collectors
except these focus all energy on a point instead of a tube along the center. They look like
satellite dishes with a tip in the middle where water runs in and out. These collectors are
14
also allowed to track the sun except these are able to do it in two dimensions as opposed
to one dimension like the parabolic trough collector.
Figure 7: Point Focus Line Collectors
15
Chapter 3
COMPUTATIONAL SETUP AND PROCEDURE
When sizing equipment for solar applications there are many different variables that
need to be considered. Solar analysis can be done using thermal simulation software
such as Transys or Fluent, or it can be done analytically using design equations and a
numerical program such as Microsoft Excel. The analysis done for this project was done
using the latter method. The equations used for this analysis were provided by John A.
Duffie and William A. Beckman in their textbook “Solar Engineering of Thermal
Processes.” Although this project involved separate analysis of a Trombe wall and an
Evacuated Tube Collector, some of the equations used for one method may be used for
the other.
3.1 Assumptions
Before starting any of the analysis, several assumptions needed to be made. The
absorptance of the plate at normal incidence (αn), the ground reflectance (ρg), and the
glass extinction coefficient and thickness factor (KL). Due to the complexity of their
numeric values, these variables had to be assumed but were made from previous design
problems. Table 1 has the assumed values for the Trombe wall analysis.
16
Absorptance, αn
Reflectivity, ρg
Glass Factor, KL
0.90
0.3
0.0125
Table 1: Assumed Values for Trombe Wall Analysis
The collector analysis also had to have some assumed values. The desired inside room
temperature, the collector efficiency (η), and the heat loss from the tank all needed to be
assumed also because of the difficulty of the calculations. Below is a table of these
assumptions and their values.
Desired Room Temp.
Collector Efficiency
Tank losses
21° C (70° F)
0.5
0
Table 2: Assumed Values for Evacuated Tube Collector Analysis
Similar to the Trombe wall analysis, these assumed values were based off of previous
design considerations for real world systems.
3.2 Trombe Wall Analysis
As mentioned before a Trombe wall is essentially a flat plate collector attached to the
south side of a building wall. The sun gives off radiation which is transmitted through
the glass and abosorbed onto the absorbed plate heating it to temperatures higher than the
ambient. As more radiation is emitted more heat is produced making the space a heat
17
source with a heat flux on the wall. Since the adjacent room to the wall is at a lower
temperature than the air space in the wall, heat will flow into the room warming it up.
One of the first things necessary for the analysis is to find how much heat is absorbed
onto the absorber plate. This is denoted by S and is the sum of the beam, diffuse and
ground radiation.
 1  cos  
 1  cos  
S  I b Rb  b  I d  d 
   g I  g 

2
2




(3.1.1)
There are many different variables in this equation but each one is necessary and has its
own way of being determined. The first term is the beam radiation contribution. Ib is the
hourly beam radiation and can be found by subtracting the diffuse component from the
total component. Rb is the ratio of beam radiation on a tilted surface to that on a
horizontal surface and the equation is given by:
Rb 
cos 
cos  z
(3.1.2)
where,
cos   sin  sin  cos   sin  cos  sin  cos   cos  cos  cos  cos 
 cos  sin  sin  cos  cos   cos  sin  sin  sin 
(3.1.2a)
and,
cos z  cos  cos  cos   sin  sin 
(3.1.2b)
18
The variables presented in equations 2a and 2b are the angles that describe the geometric
relationships between a plane of any particular orientation relative to the earth at any time
and the incoming beam solar radiation (Duffie, 12). ϕ is the latitude which runs north or
south of the equator, north being positive. δ is the declination which is the angular
position of the sun at solar noon with respect to the plane of the equator and can be
calculated as:


  23.45 sin  360
284  n 

365 
(3.1.2c)
where n is a specific day out of the year based on a 365 day cycle. β is the slope, γ is the
surface azimuth angle, ω is the hour angle and can be calculated as 15° per hour with the
morning being negative and the afternoon being positive. θ is the angle of incidence and
θz is the zenith angle. The last component of the beam contribution is the transmittanceabsorptance product and is a property of the glass. The transmittance is found using
figure 25 in the appendix. This figure gives the transmittance for one, two, three, or four
glass covers. Knowing the angle of incidence, the glass extinction coefficient and the
glass thickness, the transmittance can be determined. The absorptance of the plate at
normal incidence was a given variable and did not need to be found. The transmittanceabsorption product can now be found and is given by:
 n  1.01  n   n
(3.1.3)
19
Figure 27 in the appendix is the graph for determining the transmittance-absorption
product for beam, diffuse and ground radiation. This graph is of typical   /  n
curves for one to four glass covers. However, in order to use this graph the incidence
angle for each component must be determined. Figure 26 gives the effective incidence
angle for diffuse and ground radiation knowing the slope of the collector. It can be seen
that vertical collectors have a slope of 90° and therefore the diffuse and ground incidence
angles are the same. The beam incidence angle can be found using equation 2a and
rearranging to solve for θ.
Looking back at equation 3.1.1, it can be seen that all components have been
found or given and the only two remaining components are the diffuse hourly radiation
and the total hourly radiation. The ground reflectance also still remains to be solved but
there is not an equation available to determine this value. This is found either by testing
methods or the same value can be used for a similar location. The diffuse radiation can be
found by using this set of equations:
Id

I

1.0 .09 kT
for k T  0.22
.9511.1604kT  4.388kT2 16.638kT3 12.336kT4 for 0.22 kT  0.80 (3.1.4)
where kT is known as the hourly clearness index and is found by this equation:
20
I
Io
kT 
(3.1.4a)
and I is the total incident hourly solar radiation and Io is the extraterrestrial hourly
radiation and is found by:
Io 
12  3600

360n 

Gsc1  0.033 cos

365 

  2  1 


 cos  cos  sin  2  sin 1  
sin  sin  
180


(3.1.4b)
where n is the day of the year and Gsc is the solar constant of 1367 W/m2. All variables
in equation 1 have been found and can now be used to determine the total amount of
energy absorbed for each hour of the day. Summing up the total absorbed radiation for
the 24 hours gives the total heat capacity for the Trombe wall for that specific day.
This analysis was performed based on the isotropic sky model. This model states
that it can be assumed that the combination of diffuse and ground-reflected radiation is
isotropic. With this assumption, the sum of the diffuse from the sky and the groundreflected radiation on a tilted surface is the same regardless of orientation, and the total
radiation on a tilted surface is the sum of the beam contribution and the diffuse on a
horizontal surface (Duffie, 90). However, an improvement was made to this model by
Liu and Jordan (1963), to where the radiation on a tilted surface was the sum of the beam,
diffuse and ground-reflected radiation. This model was used in this analysis because it is
21
easier to calculate the radiation on a tilted surface. Other models do exist and one of
them is the anisotropic sky model. This model accounts for horizon-brightening and the
circumsolar diffuse radiation on a tilted surface. Hay and Davies (1980) account for the
circumsolar diffuse radiation but not the horizon-brightening. It was Reindl (1990) who
account for the horizon-brightening proposed by Klucher (1979) and is referred to as the
HDKR model. This model gives the absorbed radiation as:
 1  cos   
3   
S  I b  I d Ai Rb  b  I d 1  Ai  d 
 1  f sin  
2


 2 
 1  cos  
 I g  g 

2


(3.1.5)
Most of these variables were used in the isotropic model and do not need further
explanation. However, there are two new variables that appear and they are the
anisotropy index, Ai, and the modulating factor, f and are given as:
Ai 
f 
Ib
Io
Ib
I
(3.1.5a)
(3.1.5b)
22
It is said that these new equations when used in conjunction with equation 5 will give
better results. Both models were used in the Trombe wall analysis just to confirm to
accuracy of the results with each other.
The “I” component in the last part of equation 1 is the total radiation that was
given by the sun for that hour before it gets absorbed by object. This value cannot be
calculated by any equation but can only determined through testing measurements.
Usually an instrument such as a pyranometer is used to measure the radiation given off
by the sun. The detectors for these instruments must have a response independent of
wavelength of radiation over the solar spectrum. In addition, they should have a response
independent of the angle of incidence of the solar radiation (Duffie, 48).
Figure 8: CM6B Pyranometer Measuring Device
Most solar data is measured with these types of instruments. The data that was used for
this project was provided by the National Renewable Energy Laboratory. The data by
23
NREL is the hourly radiation data for the entire 12 month period of 2005. This hourly
data has units of W-h/m2, but in order to use this for our purpose this value must be
multiplied by 3600 seconds (3600 seconds per hour) to get J/m2. Once the total absorbed
radiation for the day is calculated, then this value is multiplied by the total wall area to
get the total amount of heat the wall will provide for that day in J.
3.3 Evacuated Tube Collector Analysis
The second analysis done for this project is that of an evacuated tube collector. It
is important to investigate other means of supplying space heating other than a Trombe
wall. An evacuated tube collector was chosen to be the device that would supply this
heat requirement. Most collectors are used as direct systems. These are systems where
the tube fluid transfers heat directly to the working fluid. The working fluid is generally
stored in a tank a used whenever hot water is demanded.
Figure 9: Direct Applied Solar Storage System
24
Indirect systems do not use the working fluid directly. The heated water is stored in a
tank and then when heating is required, the working fluid removes the heat and uses it for
another purpose. Most indirect systems are used for space heating where the storage
fluid is water and the working fluid is air.
Figure 10: Indirect Applied Storage System
25
Both systems involve a storage tank and this tank limits the amount of heat that can be
utilized. The solar collector will absorb a fraction of the incoming radiation in itself, but
the tank will have to store that heat so it can be used at times when solar energy is not
readily available. This meant that it was not necessary to design the evacuated tube
collector, but instead use the collector efficiency. When sizing a storage tank it is
necessary to decide whether or not to go with the unstratified tank or the stratified tank
model. The unstratified model seemed satisfactory for this project since once in
equilibrium the tank would be large enough that stratification would have little effect.
The heat capacity of water, or any liquid for that matter, operating over a finite
temperature difference is given by:
Qs  (mC p ) s Ts
(3.2.1)
where Q is the total heat capacity, m is the mass of the water, Cp is the specific heat and
ΔTs is the temperature difference. Now including all parts of the system, the collector,
the tank, and the load, the energy balance on this unstratified tank is:
mC 
p s

dTs
 Qu  Ls  UAs Ts  Ta'
dt

(3.2.2)
where Qu is the useful energy from the collector, Ls is heat removal from the load, and U
is the overall heat loss coefficient from the tank to the ambient. The variables above are
26
either properties of the fluid or the ambient and can be determined fairly easily. The
useful energy from the collector and the heat removal from the load are also easily
calculated but may take on different forms. For this project they were stated as such
respectively:
Qu    Ac  I T
(3.2.3)
And
Ls  hw  A  Tdesired  Ta 
(3.2.4)
Equation 3.2.2 can be integrated over a time to determine the performance of the
collector-storage system. However this integration can be quite complex and rigorous
due the time dependence of some of the variables, therefore it is often necessary to use
numerical integration methods. Euler integration is a simple enough method to solve this
time dependent system and this is done by rewriting the temperature derivative as
T

s

 Ts / t and solving for the tank temperature at the end of each time increment.
Rearranging equation 3.2.2 and incorporating Euler integration will give a useful energy
equation that can used to find the temperature of the tank at the end of each hour.
Ts  Ts 

t
Qu  Ls  UAs Ts  Ta'
mC p s


(3.2.5)
27
This equation is often used on a 1-hour time basis and Ts for one hour becomes the Ts
for the next. Further analysis can be done to determine the size of the heat pipe, mass
flow rate of the water, and the velocity of the air passing over the heat exchanger. More
importantly, however, is the sizing of storage tank. The size of the tank will determine the
amount of heat that can be stored, considering all losses, and therefore a tradeoff between
tanks size and cost will ultimately determine the feasibility of the project.
28
Chapter 4
ANALYSIS OF THE DATA
As mentioned earlier, the data was given by NREL as hourly data radiation for the
entire year of 2005 for the Travis Airforce Base in Fairfield, California. Attempting to
analyze all the data given would be impractical and cumbersome, therefore three days of
that year were taken into consideration. First the data was broken down into five of the
coldest months for that location and year: Janurary, February, October, November and
December. Next, out of these five months, the three days that were considered were the
warmest day, an average temperature day, and the coldest day: October 04, 2005,
November 02, 2005 and December 16, 2005. Table 6 in the appendix gives the solar
radiation in Wh/m2 for each hour of those days.
29
4.1 Trombe Wall Data
Dates
10/4/05
11/2/05
12/16/05
Heat Load Desired
35 MW
42 MW
92 MW
S/day (Isotropic)
7.88 MJ/m2
4.81 MJ/m2
811 kJ/m2
Total S for wall
7 MW
4.3 MW
720 kW
% of Load Met
20%
10.2%
.78%
S/day (Anisotropic)
8.63 MJ/m2
5.30 MJ/m2
838kJ/m2
Total S for wall
7.7 MW
4.7 MW
744 kW
% of Load Met
22%
11.2%
.8%
Table 3: Solar Wall Data Calculated for Selected Days
Using the equations in section 3.1, the total absorbed energy for the wall was
calculated for each hour. These values were then summed up and multiplied by the wall
area to get a total amount of absorbed energy for the entire south facing wall of the
facility. The total surface area of the south wall, subtracting the surface area for 21
loading dock doors, is 3196 m2. This data alone gives the total heat capacity of the wall,
however it is still meaningless unless it is compared to the heating demand for the
Anheuser Busch facility. To calculate this heat demand, the heat loss for this warehouse
had to be determined. Normally, heat losses from buildings involve convection losses to
the outside and conduction losses through the walls. Conduction through the walls was
30
ignored because convection losses generally are larger than conduction losses. The
building heat loss are just the convection losses in this situation and is defined as:
Qh  hw AT 
(4.1.1)
where hw is the heat transfer coefficient and is determined that for forced convection
conditions over buildings this coefficient is expressed as:
 8.6V 0.6 
hw  max 5, 0.4 
L


(4.1.1a)
The variable V is the wind velocity in meters per second and L is the cube root of the
building volume in meters. For this project, the average wind velocity for the three days
was less than one. Therefore, the determining coefficient to use in equation 4.1.1 is 5
W/m2K. Using this information and the total surface area of the building, the total heat
loss for each hour was found and then summed up to give a daily heat loss of 35 MW, 42
MW, 92 MW for October, November and December respectively. It can be seen from
table 3 that the solar wall cannot meet the heat demands required by this facility for any
of the selected days, furthermore, it would only have 11 hours of sunlight to do so.
4.2 Evacuated Tube Collector Data
31
Date
10/4/05
11/2/05
12/16/05
Qu for Collector
38.8 MW
46.7 MW
102 MW
Heat Load Desired
38.7 MW
46.6 MW
102 MW
Collector Area
15100 m2
31200 m2
380000 m2
% Roof Covered
33%
68%
> 100%
900 m3
1279 m3
4542.5 m3
(238,000 gallons)
(338,000 gallons)
(1,200,000 gallons)
Tank Volume
Table 4: Evacuated Tube Data Calculated for Selected Days
The data for the evacuated tube system was calculated using equation 3.2.3.
Before this set could be generated, a start temperature had to be assumed otherwise there
would not be any starting data to put into the equation. The ambient temperature at 1:00
am was used as the tank temperature for that hour. Simply putting this, as well as the
other variables in table 4, into the equation yielded the final temperature after each hour
for that day. The two variables that can be changed in order to validate this option for
this project are the collector area and the tank volume. The area was increased until the
useful energy for the collector was equal to the heat loss from the building. This was the
minimum collector area allowed that ensured that the heating load for the building was
satisfied for that day. The tank volume was increased so that way the temperature in the
tank at the end of any hour was not lower than its freezing point. Temperatures below
this point will not flow and there would be no heat transfer allowed until the fluid’s
32
temperature increased. Looking at table 4 it can be seen that for each of the three days
the useful energy gain was either greater or equal to the building heat loss. If it is to be
assumed that this is precisely what is supposed to occur, then the data shows that the
equivalent collector area and tank volume necessary to produce this are also correct,
except for the day in December. On this day the collector area exceeds the size of the
roof and therefore the heat load cannot be met. The main concern, however, is the
volume of the tank necessary for each day. These volumes are extremely large and it
may be difficult for the design engineer to find a company with the capabilities to make a
tank of such extreme proportions and even if there is a company out there willing to take
on such a feat, the question of cost and space arises. Is it really economically beneficial
to install a system such as this with a tank this size and if so, is there room on site for
such an eyesore? This is just the beginning of concerns that the design engineer and the
customer might have
33
Chapter 5
FINDINGS AND INTERPRETATIONS
The appendix contains the excel sheets used to generate the data for the analysis
and any other information that may have been briefly mentioned. The final table below
briefly compares the two design methods and shows the options for heating the
warehouse. This table is expressed as a yes or no evaluation as opposed to a numerical
comparison which is shown in table 4 and table 3 in the above section.
Trombe Wall
Evacuated Tube Collector
Dates
10/4/05
11/2/05
12/16/05 10/4/05
11/2/05
12/16/05
Was the heat load met?
No
No
No
Yes
Yes
Yes
Is the design feasible?
Yes
Yes
Yes
Yes
Yes
No
Is this method
Yes
Yes
Yes
No
No
No
recommendable?
Table 5: Yes or No Comparison Table of Both Design Methods
5.1 Further Research
Although the analysis for this project included some lengthy and detailed
equations, there is still more that can be done in order to determine the most optimal
solution to the problem. First and foremost, a cost analysis should be done. Due to the
specifications of the problem, cost was ignored because most companies that design these
34
types of systems need to be on site in order to obtain accurate sizes and in turn give
accurate costs. Unfortunately, most companies cannot afford to waste time on a project
that will not guarantee them the contract. Second, instead of just using a numerical
analysis program such as excel to determine the necessary data; another type of program
should be used to compare the results. A simulation program such as Fluent or Transys
should be used in order to handle the more complicated issues such as variable heat
fluxes and infiltration. Third, the assumed variables should be varied and possibly
measured so that way the analysis is as accurate as possible. Projects similar to this one
are tedious and time consuming and usually require the work of several engineers. Since
there is a lot of money invested into these types of systems a very thorough analysis must
be done, however, what has been done here is good first step in determining the
feasibility and complexity.
5.2 Conclusions
The information obtained from this report and the data presented here has paved
the way for future analysis and further research into the design of space heating for
Anheuser Busch’s Fairfield facility. Based off the obtained information the most optimal
solution would have to be the solar wall. Even though the heat load was not met by this
method, it appears to be more realistic than the alternative. Large tanks are too difficult
and expensive to manufacture. To accommodate for the extra heat loss, an auxiliary
heater system will have to be used. If there is a necessity to be completely sustainable,
then another renewable system, such as geothermal, might be able to be incorporated to
cover the excess heat loss.
35
APPENDICES
36
APPENDIX A
Solar Radiation Data for the Three Selected Days
10/4/2005
11/2/2005
12/16/2005
Hours
Gt (Wh/m2)
Ta (°F)
Gt (Wh/m2)
Ta (°F)
Gt (Wh/m2)
Ta (°F)
1:00 AM
0
56.9
0
54.8
0
45.4
2:00 AM
0
57
0
54.1
0
41.7
3:00 AM
0
57.1
0
53.7
0
39.2
4:00 AM
0
57.3
0
53.6
0
37.3
5:00 AM
0
56.9
0
53.6
0
36
6:00 AM
0
57.2
0
53.9
0
35.3
7:00 AM
33
56.8
4
54
0
36
8:00 AM
193
58.1
82
54.3
6
36.2
9:00 AM
390
59.3
237
55
38
39.8
10:00 AM
563
61
315
55.8
60
42.1
11:00 AM
687
64.3
417
57.5
76
46.2
12:00 PM
749
66.8
422
60.3
85
50.7
1:00 PM
744
65.5
529
62.1
86
51.4
2:00 PM
675
65.8
423
61.8
77
51.9
3:00 PM
545
64.6
318
62.1
62
50.8
4:00 PM
367
62.2
198
61.5
41
49.9
5:00 PM
169
60.3
51
60.9
9
46.8
6:00 PM
21
59.8
0
61
0
46.1
7:00 PM
0
59
0
60.5
0
44.4
8:00 PM
0
57.8
0
60.4
0
43.4
9:00 PM
0
57.8
0
60.3
0
41.3
10:00 PM
0
58.7
0
58.6
0
40.8
11:00 PM
0
57.3
0
56.5
0
40.9
12:00 AM
0
56.7
0
58.6
0
46.6
Table 6: Hourly Solar Radiation Data and Temperature for Three Selected Days
37
APPENDIX B
Calculation Tables
VT (gallons)
238000
VT (m3)
900.9280036
AC (m2)
15100
AB (m2)
57791.8
U (W/m2K)
5
T inside (°C)
21
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Gt (Wh/m2)
0
0
0
0
0
0
33
193
390
563
687
749
744
675
545
367
169
21
0
0
0
0
0
0
I (J/m2)
0
0
0
0
0
0
118800
694800
1404000
2026800
2473200
2696400
2678400
2430000
1962000
1321200
608400
75600
0
0
0
0
0
0
Qu for the day
38776800
Ta (F)
56.9
57
57.1
57.3
56.9
57.2
56.8
58.1
59.3
61
64.3
66.8
65.5
65.8
64.6
62.2
60.3
59.8
59
57.8
57.8
58.7
57.3
56.7
Ta (C)
13.8
13.9
13.9
14.1
13.8
14.0
13.8
14.5
15.2
16.1
17.9
19.3
18.6
18.8
18.1
16.8
15.7
15.4
15.0
14.3
14.3
14.8
14.1
13.7
Heat used for the day
38688399.44
Ts
13.8
11.8
9.9
7.9
6.0
4.1
2.1
0.4
0.0
1.2
3.9
8.0
12.9
17.6
21.8
24.9
26.4
26.2
24.8
23.2
21.3
19.5
17.8
15.9
Table 7: Evacuated Tube Collector Analysis for October 4, 2005
38
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ts+
11.8
9.9
7.9
6.0
4.1
2.1
0.4
0.0
1.2
3.9
8.0
12.9
17.6
21.8
24.9
26.4
26.2
24.8
23.2
21.3
19.5
17.8
15.9
13.9
efficiency
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Qu (J/hr)
0
0
0
0
0
0
896940000
5245740000
1.06E+10
1.5302E+10
1.8673E+10
2.0358E+10
2.0222E+10
1.8347E+10
1.4813E+10
9975060000
4593420000
570780000
0
0
0
0
0
0
1.396E+11
Heat used (J/hr)
7455142200
7397350400
7339558600
7223975000
7455142200
7281766800
7512934000
6761640600
6068139000
5085678400
3178549000
1733754000
2485047400
2311672000
3005173600
4392176800
5490221000
5779180000
6241514400
6935016000
6935016000
6414889800
7223975000
7570725800
1.39278E+11
Heat loss (J/hr)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 7: Evacuated Tube Collector Analysis for October 4, 2005 (Continued)
39
VT (gallons)
338000
VT (m3)
1279.469182
AC (m2)
31200
AB (m2)
57791.8
U (W/m2K)
5
T inside (°C)
21
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Gt (Wh/m2)
0
0
0
0
0
0
4
82
237
315
417
422
529
423
318
198
51
0
0
0
0
0
0
0
I (J/m2)
0
0
0
0
0
0
14400
295200
853200
1134000
1501200
1519200
1904400
1522800
1144800
712800
183600
0
0
0
0
0
0
0
Qu for the day
46737600
Ta (F)
54.8
54.1
53.7
53.6
53.6
53.9
54
54.3
55
55.8
57.5
60.3
62.1
61.8
62.1
61.5
60.9
61
60.5
60.4
60.3
58.6
56.5
58.6
Ta (C)
12.7
12.3
12.1
12.0
12.0
12.2
12.2
12.4
12.8
13.2
14.2
15.7
16.7
16.6
16.7
16.4
16.1
16.1
15.8
15.8
15.7
14.8
13.6
14.8
Heat Used for the day
46602665.39
Ts
12.7
11.1
9.4
7.7
5.9
4.2
2.5
0.8
0.0
0.9
2.7
5.7
9.1
13.8
17.4
19.9
21.0
20.6
19.7
18.7
17.7
16.6
15.4
14.0
Table 8: Evacuated Tube Collector Analysis for November 2, 2005
40
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ts+
11.1
9.4
7.7
5.9
4.2
2.5
0.8
0.0
0.9
2.7
5.7
9.1
13.8
17.4
19.9
21.0
20.6
19.7
18.7
17.7
16.6
15.4
14.0
12.8
efficiency
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Qu (J/hr)
0
0
0
0
0
0
224640000
4605120000
1.331E+10
1.769E+10
2.3419E+10
2.37E+10
2.9709E+10
2.3756E+10
1.7859E+10
1.112E+10
2864160000
0
0
0
0
0
0
0
1.6826E+11
Heat used (J/hr)
8668770000
9073312600
9304479800
9362271600
9362271600
9188896200
9131104400
8957729000
8553186400
8090852000
7108391400
5490221000
4449968600
4623344000
4449968600
4796719400
5143470200
5085678400
5374637400
5432429200
5490221000
6472681600
7686309400
6472681600
1.6777E+11
Heat loss (J/hr)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 8: Evacuated Tube Collector Analysis for November 2, 2005 (Continued)
41
VT (gallons)
1200000
VT (m3)
4542.494136
AC (m2)
380000
AB (m2)
57791.8
U (W/m2K)
5
T inside (°C)
21
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Gt (Wh/m2)
0
0
0
0
0
0
0
6
38
60
76
85
86
77
62
41
9
0
0
0
0
0
0
0
I (J/m2)
0
0
0
0
0
0
0
21600
136800
216000
273600
306000
309600
277200
223200
147600
32400
0
0
0
0
0
0
0
Qu for the day
102600000
Ta (F)
45.4
41.7
39.2
37.3
36
35.3
36
36.2
39.8
42.1
46.2
50.7
51.4
51.9
50.8
49.9
46.8
46.1
44.4
43.4
41.3
40.8
40.9
46.6
Ta (C)
7.4
5.4
4.0
2.9
2.2
1.8
2.2
2.3
4.3
5.6
7.9
10.4
10.8
11.1
10.4
9.9
8.2
7.8
6.9
6.3
5.2
4.9
4.9
8.1
Heat Used for the day
101938313.9
Ts
7.4
6.7
5.8
4.9
3.9
2.9
1.8
0.8
0.0
0.5
1.8
3.8
6.2
8.8
11.0
12.6
13.5
13.1
12.4
11.6
10.8
10.0
9.1
8.2
Table 9: Evacuated Tube Collector Analysis for December 16, 2005
42
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ts+
6.7
5.8
4.9
3.9
2.9
1.8
0.8
0.0
0.5
1.8
3.8
6.2
8.8
11.0
12.6
13.5
13.1
12.4
11.6
10.8
10.0
9.1
8.2
7.5
efficiency
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
Qu (J/hr)
0
0
0
0
0
0
0
4104000000
2.5992E+10
4.104E+10
5.1984E+10
5.814E+10
5.8824E+10
5.2668E+10
4.2408E+10
2.8044E+10
6156000000
0
0
0
0
0
0
0
3.6936E+11
Heat used (J/hr)
14101199200
16239495800
17684290800
18782335000
19533628400
19938171000
19533628400
19418044800
17337540000
16008328600
13638864800
11038233800
10633691200
10344732200
10980442000
11500568200
13292114000
13696656600
14679117200
15257035200
16470663000
16759622000
16701830200
13407697600
366977930000.00
Heat loss (J/hr)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table 9: Evacuated Tube Collector Analysis for December 16, 2005 (Continued)
43
Latitude
38.249
Τ
0.82
(τα)d=(τα)g
0.6186654
αn
0.9
(τα)n
0.74538
ρg
0.3
θe
59
KL
0.0125
(τα)/(τα)n
0.83
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Hour Angle
-165.0
-150.0
-135.0
-120.0
-105.0
-90.0
-75.0
-60.0
-45.0
-30.0
-15.0
0.0
15.0
30.0
45.0
60.0
75.0
90.0
105.0
120.0
135.0
150.0
165.0
180.0
Gt (Wh/m2)
0
0
0
0
0
0
33
193
390
563
687
749
744
675
545
367
169
21
0
0
0
0
0
0
I (J/m2)
0
0
0
0
0
0
118800
694800
1404000
2026800
2473200
2696400
2678400
2430000
1962000
1321200
608400
75600
0
0
0
0
0
0
I0 (J/m2)
0
0
0
0
0
0
214427
1183644
2052620
2762135
3263839
3523540
3523540
3263839
2762135
2052620
1183644
214427
0
0
0
0
0
0
Date
n-value
declination
Wall Area
10/4/2005
277
-5.400668
3186.723
kT
0
0
0
0
0
0
0.55403
0.58700
0.68400
0.73378
0.75776
0.76525
0.76014
0.74452
0.71032
0.64367
0.51401
0.35257
0
0
0
0
0
0
Id (J/m2)
0
0
0
0
0
0
112876.3
658093.7
1317569.3
1892949.7
2304532.2
2510691.4
2495162.6
2267173.0
1836571.7
1244663.0
384319.2
73201.1
0
0
0
0
0
0
Table 10: Trombe Wall Analysis for October 4, 2005
44
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ib (J/m2)
0
0
0
0
0
0
5923.7
36706.3
86430.7
133850.3
168667.8
185708.6
183237.4
162827.0
125428.3
76537.0
224080.8
2398.9
0
0
0
0
0
0
Rb
0.64098
0.62533
0.59219
0.52150
0.32846
-1.26854
1.62008
1.14859
1.03063
0.98198
0.96027
0.95394
0.96027
0.98198
1.03063
1.14859
1.62008
-1.26854
0.32846
0.52150
0.59219
0.62533
0.64098
0.64565
θ
121.4
117.4
111.2
103.5
94.9
85.8
76.5
67.5
59.4
52.6
48.0
46.4
48.0
52.6
59.4
67.5
76.5
85.8
94.9
103.5
111.2
117.4
121.4
122.8
(τα)/(τα)n
0
0
0
0
0
0.06
0.38
0.66
0.86
0.92
0.95
0.95
0.95
0.92
0.86
0.66
0.38
0.06
0
0
0
0
0
0
(τα)b
0
0
0
0
0
0.04472
0.28324
0.49195
0.64103
0.68575
0.70811
0.70811
0.70811
0.68575
0.64103
0.49195
0.28324
0.04472
0
0
0
0
0
0
Table 10: Trombe Wall Analysis for October 4, 2005 (Continued)
S (J/m2)
0
0
0
0
0
0
48659.2
288788.1
594959.8
863771.5
1057070.4
1152309.9
1144988.1
1036460.5
833050.7
550869.2
278167.7
29523.1
0
0
0
0
0
0
7878618
45
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ta (C)
13.8
13.9
13.9
14.1
13.8
14.0
13.8
14.5
15.2
16.1
17.9
19.3
18.6
18.8
18.1
16.8
15.7
15.4
15.0
14.3
14.3
14.8
14.1
13.7
Heat loss (W)
1862150.8
1847715.6
1833280.3
1804409.7
1862150.8
1818845.0
1876586.1
1688927.5
1515704.2
1270304.4
793940.3
433058.3
620716.9
577411.1
750634.4
1097081.1
1371351.4
1443527.8
1559010.0
1732233.3
1732233.3
1602315.8
1804409.7
1891021.4
34789019.4
Ai
0
0
0
0
0
0
0.027626
0.031011
0.042108
0.048459
0.051678
0.052705
0.052004
0.049888
0.04541
0.037287
0.189314
0.011187
0
0
0
0
0
0
f
0
0
0
0
0
0
0.223301
0.229848
0.248114
0.256983
0.261148
0.262436
0.261559
0.258857
0.252841
0.240686
0.606887
0
0
0
0
0
0
0
Total S for the wall for 10/4/05
6996044.27
7 MW (Isotropic)
7667171.839
7.7 MW (Anisotropic)
Table 10: Trombe Wall Analysis for October 4, 2005 (Continued)
S (J/m2)
0
0
0
0
0
0
51805.984
310036.59
648698.33
947790.11
1163629.3
1269025.6
1260746.2
1138619.1
910830.15
594278.4
309727.4
29223.294
0
0
0
0
0
0
8634410.5
46
Latitude
38.249
τ
0.82
(τα)d=(τα)g
0.6186654
αn
0.9
(τα)n
0.74538
ρg
0.3
θe
59
KL
0.0125
(τα)/(τα)n
0.83
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Hour Angle
-165.0
-150.0
-135.0
-120.0
-105.0
-90.0
-75.0
-60.0
-45.0
-30.0
-15.0
0.0
15.0
30.0
45.0
60.0
75.0
90.0
105.0
120.0
135.0
150.0
165.0
180.0
Gt
0
0
0
0
0
0
4
82
237
315
417
422
529
423
318
198
51
0
0
0
0
0
0
0
I
0
0
0
0
0
0
14400
295200
853200
1134000
1501200
1519200
1904400
1522800
1144800
712800
183600
0
0
0
0
0
0
0
I0
0
0
0
0
0
0
344239.4
607681.4
1461150.3
2158004.6
2650755.1
2905821.5
2905821.5
2650755.1
2158004.6
1461150.3
607681.4
0
0
0
0
0
0
0
Date
n-value
declination
Wall Area
11/2/2005
306
-15.666098
3186.723
kT
0
0
0
0
0
0
0.041831
0.485781
0.583924
0.525485
0.566329
0.522813
0.655374
0.574478
0.530490
0.487835
0.302132
0
0
0
0
0
0
0
Id
0
0
0
0
0
0
14345.8
282293.8
808361.7
1080369.0
1424684.4
1447716.9
1792071.5
1444066.7
1090142.5
681504.4
173935.6
0
0
0
0
0
0
0
Table 11: Trombe Wall Analysis for November 2, 2005
47
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ib
0
0
0
0
0
0
54.21
12906.23
44838.32
53631.04
76515.60
71483.12
112328.49
78733.33
54657.45
31295.58
9664.37
0
0
0
0
0
0
0
Rb
0.405220
0.370015
0.298398
0.157687
-0.159241
-1.268539
12.837653
2.418627
1.723912
1.493373
1.398808
1.372102
1.398808
1.493373
1.723912
2.418627
12.837653
-1.268539
-0.159241
0.157687
0.298398
0.370015
0.405220
0.415910
θ
111.33
107.71
102.09
94.93
86.69
77.76
68.51
59.33
50.69
43.26
38.02
36.08
38.02
43.26
50.69
59.33
68.51
77.76
86.69
94.93
102.09
107.71
111.33
112.58
(τα)/(τα)n
0
0
0
0
0.04
0.34
0.65
0.86
0.94
0.96
0.96
0.97
0.96
0.96
0.94
0.86
0.65
0.34
0.04
0
0
0
0
0
(τα)b
0
0
0
0
0.029815
0.253429
0.484497
0.641027
0.700657
0.715565
0.715565
0.723019
0.715565
0.715565
0.700657
0.641027
0.484497
0.253429
0.029815
0
0
0
0
0
Table 11: Trombe Wall Analysis for November 2, 2005 (Continued)
S
0
0
0
0
0
0
6111.14
134727.08
383388.42
496738.85
656599.91
659722.83
843508.12
672147.45
509473.13
325480.13
130952.51
0
0
0
0
0
0
0
4818849.5
48
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ta (C)
12.7
12.3
12.1
12.0
12.0
12.2
12.2
12.4
12.8
13.2
14.2
15.7
16.7
16.6
16.7
16.4
16.1
16.1
15.8
15.8
15.7
14.8
13.6
14.8
14.3
Heat loss
2165291.7
2266338.6
2324079.7
2338515.0
2338515.0
2295209.2
2280773.9
2237468.1
2136421.1
2020938.9
1775539.2
1371351.4
1111516.4
1154822.2
1111516.4
1198128.1
1284739.7
1270304.4
1342480.8
1356916.1
1371351.4
1616751.1
1919891.9
1616751.1
41905611.4
Ai
0
0
0
0
0
0
0.00015749
0.02123847
0.030687
0.02485214
0.02886559
0.02459997
0.03865636
0.02970223
0.02532777
0.02141845
0.01590368
0
0
0
0
0
0
0
f
0
0
0
0
0
0
0.06135814
0.20909394
0.22924467
0.21747112
0.22576454
0.21691734
0.24286553
0.22738294
0.21850424
0.20953552
0.22943012
0
0
0
0
0
0
0
S
0
0
0
0
0
0
6220.74038
148486.214
425322.642
542181.688
719203.045
717536.899
937178.487
739558.403
559673.733
358878.622
151597.097
0
0
0
0
0
0
0
5305837.57
Total S for the wall for 11/2/05
4279035.327
4.3 MW (Isotropic)
4711470.276
4.7 MW (Anisotropic)
Table 11: Trombe Wall Analysis for November 2, 2005 (Continued)
49
Latitude
38.249
Τ
0.82
(τα)d=(τα)g
0.6186654
αn
0.9
(τα)n
0.74538
ρg
0.3
θe
59
KL
0.0125
(τα)/(τα)n
0.83
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Hour Angle
-165.0
-150.0
-135.0
-120.0
-105.0
-90.0
-75.0
-60.0
-45.0
-30.0
-15.0
0.0
15.0
30.0
45.0
60.0
75.0
90.0
105.0
120.0
135.0
150.0
165.0
180.0
Gt
0
0
0
0
0
0
0
6
38
60
76
85
86
77
62
41
9
0
0
0
0
0
0
0
I
0
0
0
0
0
0
0
21600
136800
216000
273600
306000
309600
277200
223200
147600
32400
0
0
0
0
0
0
0
I0
0
0
0
0
0
0
0
149813.2
975088.6
1648923.2
2125396.2
2372036.8
2372036.8
2125396.2
1648923.2
975088.6
149813.2
0
0
0
0
0
0
0
Date
n-value
declination
Wall Area
12/16/2005
350
-23.3716512
3186.723
kT
0
0
0
0
0
0
0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0
0
0
0
0
0
0
Id
0
0
0
0
0
0
0
21319.7
135072.7
213453.5
270430.2
302447.3
305963.2
273946.2
220480.9
145589.2
31764.9
0
0
0
0
0
0
0
Table 12: Trombe Wall Analysis for December 16, 2005
50
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ib
0
0
0
0
0
0
0
280.29
1727.31
2546.53
3169.82
3552.74
3636.83
3253.79
2719.13
2010.81
635.05
0
0
0
0
0
0
0
Rb
0.252026
0.207628
0.119555
-0.045199
-0.380529
-1.268539
-7.772577
5.186074
2.700507
2.122074
1.908971
1.851056
1.908971
2.122074
2.700507
5.186074
-7.772577
-1.268539
-0.380529
-0.045199
0.119555
0.207628
0.252026
0.265656
θ
103.73
100.41
95.18
88.43
80.53
71.85
62.70
53.44
44.49
36.52
30.63
28.38
30.63
36.52
44.49
53.44
62.70
71.85
80.53
88.43
95.18
100.41
103.73
104.88
(τα)/(τα)n
0
0
0
0.02
0.22
0.56
0.8
0.91
0.95
0.97
0.98
0.98
0.98
0.97
0.95
0.91
0.8
0.56
0.22
0.02
0
0
0
0
(τα)b
0
0
0
0.014908
0.163984
0.417413
0.596304
0.678296
0.708111
0.723019
0.730472
0.730472
0.730472
0.723019
0.708111
0.678296
0.596304
0.417413
0.163984
0.014908
0
0
0
0
S
0
0
0
0
0
0
0
9585.32
57780.48
89980.04
113463.09
126757.39
128446.62
115456.91
94114.55
65806.16
9889.31
0
0
0
0
0
0
0
811279.86
Table 12: Trombe Wall Analysis for December 16, 2005 (Continued)
51
Hour
1:00 AM
2:00 AM
3:00 AM
4:00 AM
5:00 AM
6:00 AM
7:00 AM
8:00 AM
9:00 AM
10:00 AM
11:00 AM
12:00 PM
1:00 PM
2:00 PM
3:00 PM
4:00 PM
5:00 PM
6:00 PM
7:00 PM
8:00 PM
9:00 PM
10:00 PM
11:00 PM
12:00 AM
Total
Ta (C)
7.4
5.4
4.0
2.9
2.2
1.8
2.2
2.3
4.3
5.6
7.9
10.4
10.8
11.1
10.4
9.9
8.2
7.8
6.9
6.3
5.2
4.9
4.9
8.1
6.3
Heat loss
3522207.8
4056313.1
4417195.0
4691465.3
4879123.9
4980170.8
4879123.9
4850253.3
4330583.3
3998571.9
3406725.6
2757138.1
2656091.1
2583914.7
2742702.8
2872620.3
3320113.9
3421160.8
3666560.6
3810913.3
4114054.2
4186230.6
4171795.3
3348984.4
91664013.9
Ai
0
0
0
0
0
0
0
0.0018709
0.00177144
0.00154436
0.0014914
0.00149776
0.00153321
0.00153091
0.00164904
0.00206218
0.00423895
0
0
0
0
0
0
0
f
0
0
0
0
0
0
0
0.11391295
0.1123679
0.10857952
0.10763645
0.10775099
0.10838296
0.10834227
0.11037434
0.11671922
0.14000112
0
0
0
0
0
0
0
S
0
0
0
0
0
0
0
9978.39688
59821.0096
92914.6668
117079.418
130788.558
132576.785
119211.641
97354.4092
68624.0356
9707.88102
0
0
0
0
0
0
0
838056.802
Total S for the wall for 12/16/05
720399.1618
744176.5154
720 kW (Isotropic)
744 kW (anisotropic)
Table 12: Trombe Wall Analysis for December 16, 2005 (Continued)
52
APPENDIX C
Miscellaneous Charts
Figure 11: Evacuated Tube Collector Area v. Useful Collector Gain for October 4, 2005
53
Figure 12: Collector Efficiency v. Useful Collector Gain for October 4, 2005
54
Figure 13: Useful Collector Gain v. Heat Used by Load for October 4, 2005
55
Figure 14: Useful Collector Gain v. Heat Used by Load for November 2, 2005
56
Figure 15: Useful Collector Gain v. Heat Used by Load for December 16, 2005
57
Figure 16: Isotropic Model v. Anisotropic Model for October 4, 2005
58
Figure 17: Isotropic Model v. Anisotropic Model for November 2, 2005
59
Figure 18: Isotropic Model v. Anisotropic Model for December 16, 2005
60
Figure 19: Total, Beam, and Diffuse Hourly Radiation Components for October 4, 2005
61
Figure 20: Total, Beam, and Diffuse Radiation Components for November 2, 2005
62
Figure 21: Total, Beam, and Diffuse Radiation Components for December 16, 2005
63
Figure 22: Hourly Heat Loss from Building for October 4, 2005
64
Figure 23: Hourly Heat Loss from Building for November 2, 2005
65
Figure 24: Hourly Heat Loss from Building for December 16, 2005
66
APPENDIX D
Charts Used for Determing Specific Data for Trombe Wall Analysis
Figure 25: Transmittance of One, Two, Three, and Four Covers for Three Types of Glass
67
Figure 26: Effective Incidence Angle of Isotropic Diffuse Radiation and Isotropic
Ground-Reflected Radiation on Sloped Surfaces
68
Figure 27: Typical (τα)/(τα)n Curves for One to Four Covers
69
BIBLIOGRAPHY
Books:
Boyle, Godfrey, 2004: Renewable Energy, Power for a Sustainable Future, Oxford
University Press Inc., New York.
Duffie, John A. & Beckman, William A., 2006: Solar Engineering of Thermal Processes,
John Wiley & Sons, Inc., Hoboken, New Jersey.
Modest, Michael F., 2003: Radiative Heat Transfer, Academic Press, San Diego, Ca.
Internet Sites:
National Solar Radiation Data Base, “USAF #745160-Travis Field AFB, CA (CLASS
II)”
<http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/hourly/siteonthefly>
Wunderground.com, Temperature Historical Data
<http://www.wunderground.com/weatherstation/WXDailyHistory>
BP Statistical Review of World Energy, BP.
<http://www.bp.com/centres/energy2002/index.asp>
Perlin, John, “Solar Evolution: The History of Solar Energy”
<http://www.californiasolarcenter.org/history_solarthermal.html>
Journal Articles:
Kalogirou, Soteris A., 2004: “Solar Thermal Collectors and Applications”, Progress in
Energy and Combustion Science