Final Design (Fall 2003)
Sponsor: Dr. A. Krothapalli
1.0 Introduction ________________________________________________________ 2
1.1 Background_____________________________________________________ 2
2.0 Project Planning ____________________________________________________ 5
2.2 WBS _______________________________________________________ 5
2.1 Schedule ____________________________________________________ 5
2.2 Project Procedures ____________________________________________ 6
3.0 Design Specifications______________________________________________ 7
3.1 Customer Needs and Specifications _______________________________ 7
3.2 Conceptual Designs ___________________________________________ 8
Design Concept 1_____________________________________________________ 8
Design Concept 2_____________________________________________________ 9
Design Concept 3____________________________________________________ 10
4.0 Concept Selection________________________________________________ 12
4.1 Selection Process ____________________________________________ 12
6.0 Solar Concentrator__________________________________________________ 22
7.0 Heat Containment System ____________________________________________ 26
8.0 Stirling Engine_____________________________________________________ 33
Two Basic Engine Designs ___________________________________________ 35
ALPHA Type _____________________________________________________ 39
BETA Type_______________________________________________________ 40
GAMMA Type ____________________________________________________ 41
Stirling Engine Design Selection _________________________________________ 42
Figure 8.9 The alpha type model Stirling engine rated up to 3000rpm. _______ 44
9.0 Tracking Control System _____________________________________________ 49
10.0 Frame ___________________________________________________________ 53
Appendix A___________________________________________________________ 55
Appendix B___________________________________________________________ 56
Appendix C___________________________________________________________ 57
Appendix D___________________________________________________________ 58
Appendix D cont’d _____________________________________________________ 59
Appendix E___________________________________________________________ 60
Appendix E cont’d _____________________________________________________ 61
Appendix F___________________________________________________________ 62
Stirling Engine References ___________________________________________ 62
As fossil fuel technologies become obsolete, mostly due to the depletion of fuel sources,
the demand for alternative energy technologies, such as solar power, fuel cells, and wind
power, grows. The reason as to why these alternative energy sources have not been more
widely utilized is that fossil fuels are relatively low cost compared to the initial setup
price for these alternative sources, and the lack of efficient devices that are readily
available for obtaining alternative energy.
Of the available alternative energy sources, the sun is quite possibly the easiest to
obtain, and is a great source of pollution free energy. The goal of our project, Solaris, is
to harness the suns energy and in turn, generate electricity. This is to be done by use of a
stirling engine/generator system which will be placed at the focal point of the parabolic
A potentially great source of radiant energy is the sun. The sun emits
electromagnetic radiation with a solar irradiance of 1367 W/m2
on the earth’s surface. Of
this solar radiation reaching the earth, it is comprised mostly of radiant energy ranging in
wavelengths between 0.3 and 2 µm. This radiant energy is then comprised of two types
of radiation, beam and diffuse radiation. If a flat surface collector is utilized, both beam
and diffuse radiation is collected, but if an optical (i.e. parabolic/focusing) collector is
used, then only beam radiation is collected.
The purpose of a focusing solar collector is to increase the intensity of the solar
radiation falling on the collector. The factor by which the solar irradiance is increased is
known as the concentration ratio, CR, which is defined in Equation 1.1,
where Dm is the dimension of the collector and F is the focal length. Figure 1.1 shows
the principle of light concentration for a parabolic reflector.
Figure 1.1 A parabolic reflector (Dm)
concentrates the solar irradiance on the
smaller collector (Di) at the focal point.
By focusing the solar irradiance to a particular point, the system is capable of producing
sufficiently high temperatures to use in a heat engine cycle to generate electrical power
This idea of using the suns heat as a source of power is not a new one. This
concept is dated as far back as 1000AD with the development of focusing mirrors by Abu
Ali al-Hasan al-Haitham. It is also noted that during the 1640s, in Rome, Father
Athanasius Kircher had shown that sunlight could be concentrated to a point to ignite
fires. Figure 1.2 shows an image of a German burning mirror of the 1700s. As shown in
the picture, the mirror is being used to set fire to a pile of wood from a distance.
Figure 1.2 Picture of ‘German burning mirror’
(Parabolic Reflector) of the 1700s.
By utilizing the high temperatures created at the focal point of parabolic reflectors,
along with a heat engine, such as a stirling engine, it is possible to efficiently generate
electrical power. A stirling engine is a closed-cycle, regenerative heat engine which uses
and ‘external combustion’ process, which in this case is solar heat. The stirling engine
works by converting heat energy to mechanical work, such as spinning a flywheel. This
mechanical work can then be converted to electrical energy by use of a generator attached
to the flywheel of the stirling engine.
2.0 Project Planning
The Work Breakdown Structure (WBS) Chart displays the structure of a project
showing how a project is organized into a summary (phase) and detail levels. The WBS
is a great way to organize a project into a schedule of duties and events that must take
place throughout the project scope. Using a WBS chart is an intuitive approach to
planning and displaying a project. As a planning tool, the WBS Chart can be used to
quickly create a project by ‘drawing a picture’.
Team Solaris’ WBS can be found in Appendix A. Our WBS shows the
relationship between each of the activities the team is undertaking, and helps to give a
clear view of the task that will be performed in this project.
The schedule for Team Solaris can be found in Appendix B. The schedule shows
the breakdown of all the project activities. The chart shows all the dates by which
activities will be started and/or completed by. All deliverables have been included in the
schedule, allowing for preparation time before they are due. The dates on the schedule
are tentative, and may be changed in order to complete the project in a timely fashion or
to account for any unforeseen problems that may arise.
2.2 Project Procedures
Documentation and e-mails:
1. All Documents will be dated as received; a copy of all documents will be
available to every team member as a hard copy, e-mail, or team folder on
2. All e-mails concerning the project will be sent to every team member regardless
of relevance to individual tasks.
3. The official copy of all documents will be held by Chris Newton, and will be
brought to every group meeting.
1. Regular meetings with the customer will be held no less then every other week to
update him on the progress of the project.
2. Regular team meetings will be held no less then once every week to update group
members on project progress.
3. All team members required to attend meetings unless notification of absence is
given 24 hours before time of meeting.
Reports and deliverables:
1. All group members will approve all reports.
2. Deliverables will be started no less then four days before they are due.
3. All team members must be present to prepare deliverables.
4. If a team member cannot be present to help in the preparation of the deliverables,
he must give notice to rest of team.
3.0 Design Specifications
3.1 Customer Needs and Specifications
According to Dr. A. Krothapalli, Team Solaris’ final design needs to be capable of
producing an optimum amount of electricity. Dr. A. Krothapalli wishes for Team Solaris
to generate 1 kW or electricity, but due to the budget, the final output is negotiable. The
electricity is to be generated from a stirling engine which obtains its heat from a solar
collector. The solar collector, as instructed by our sponsor, is to be made from a surplus
satellite dish. Another constraint, which was also place on the project, is that the dish
must track the sun throughout the course of the day. This whole design and construction
of the project is to be done for less than $5000.
Table 3.1 Wish/Demand List of Sponsor and Importance
Wish/Demand Requirement Importance
Demand Solar Collector made from large parabolic dish 10
Demand Device to be self sufficient 10
Device to have a minimum output of 1kW of
electricity after sustaining itself (batteries, servos,
Demand Dish must track the sun 10
Demand Dish must reset itself in the evening 10
Demand Type of engine to be used: Stirling Engine 10
Wish AC generator 8
The generation of electricity for this project is to be done by harnessing the suns
energy with the use of a large parabolic dish, which must track the position of the sun
throughout the day. The dish will be coated in aluminized Mylar because of its
reflectivity, workability, and relatively low cost. The dish must then reset itself at night
under its own power and be ready to operate the following day. The Stirling engine will
use the heat at the focal point of the dish to change heat energy to mechanical energy. A
DC motor/generator will be attached to the Stirling engine, either by belt, or directly on
the shaft. The generator needs to produce enough electricity to supply enough power to
sustain the system, plus generate an optimum useable amount of electricity.
3.2 Conceptual Designs
Once the needs of the customers’ ‘problem’ were understood, Team Solaris was able to
come up with several basic conceptual ideas.
Design Concept 1
This particular design consists of a parabolic dish with a stirling engine and generator
located at the focal point of the dish. Solar radiation is reflected to the focal point, onto
the expansion (heat) cylinder of the stirling engine. The one downside to this design
concept is that there is a large amount of weight that needs to be supported at the focal
point. Figure 3.1 shows a drawing of Design Concept 1.
Figure 3.1 Design Concept 1 – Components
of system located at focal point
Design Concept 2
This design concept, as shown in Figure 3.2, utilizes a heat containment unit, filled with a
working fluid such as molten salt, which will transfer the heat from the focal point of the
dish to the expansion (heat) piston of the stirling engine. The stirling engine will be
located on the ground/platform beneath the parabolic dish. This design simplifies the
design of the dish from the first concept, in that the supports at the focal point do not
have to undergo as much stress.
Figure 3.2 Design Concept 2 – Heat containment at
focal point. Use of working fluid to transfer heat to
Design Concept 3
In this design concept, the solar radiation is focused onto a concave mirror, which is then
reflected and focused downward through the center of the parabolic dish. Directly below
the dish is where the stirling engine will be located, along with a heat reservoir, if needed.
This concept is the most feasible, in that weight will not be a factor at the focal point,
which simplifies the design, as shown in Figure 3.3.
Figure 3.3 Design Concept 3 – All components of system are
placed below the center of the dish, and the solar energy is
redirected from the focal point.
4.0 Concept Selection
4.1 Selection Process
In order to choose the best concept for the design, the team looked at each option,
taking into consideration which design would be the most feasible and the simplest to
construct. With this in mind, the team chose
Concept Design 3 as its preliminary design.
Before Team Solaris would permanently
choose this design, it needed to be tested to
make sure the optics ideology behind it
would work. The testing was performed
with a 24-inch parabolic reflector and a 35-mm gold plated concave spherical mirror. An
apparatus was constructed to allow for adjustments of the mirror at the focal point. It
was found that the idea behind the optics idea
for transferring the suns energy did work, in that
it transferred the light, but failed in that it did
not transfer enough heat. Thus the simplest, and
most favored design idea failed. Not wanting to
deal with a working fluid, and a means of a pump system that could withstand high
temperatures, Team Solaris decided that Design Concept 1 was the design to go with.
Since Design Concept 2 failed, and the team chose to go with Design Concept 1, the
temperature at the focal point needed to be determined. This was done with an Omega k-
type thermocouple, and an Omega DPi8A digital display. It was found that the
temperature at the focal point would reach
700°F with out any problem. This proved to
be an adequate amount of heat for the
stirling engines which had been located for
use on the project; with the operating
temperatures of the stirling engines ranging from 300 to 1200°F.
5.0 Solar Collector
The purpose of the solar collector is to collect the radiation incident from the sun.
The parabolic shape is used to collect light from a larger area and condense it down to a
much smaller area. The reduction in area increases the radiation power density, as the
same radiation that would have been spread over a few square meters, can be collected
and spread over an area less than a square meter. This concentration of radiation is used
as a form of heating for the Stirling engine. The goal of the collector design is to
maximize its efficiency within the project budget of $5000. Using some initial guess
efficiencies for each energy conversion process, it was estimated that to produce a
kilowatt of power output from the generator, that a twenty-foot diameter dish was
needed. This option was not feasible because of cost, thus a ten-foot diameter dish was
used. The ten-foot diameter dish was obtained and required assembly. The circular
collector mesh was separated into four partitions. Each partition was supported by curved
metal supports and could be subdivided into four sub-partitions as in the following figure.
Figure 5.1 Satellite Dish Partition
The used ten-foot dish was donated to the team and therefore did not hinder the
budget, however, being undersized for the initial power requirements made many design
modifications become necessary. In order to optimize the design of the collector a
material was needed to coat the shape and serve as a light reflector. The goal was to
choose a material that could adhere to the satellite dish surface. The surface of the dish,
shown below was made of a conformable metal meshing.
Figure 5.2 Satellite Dish Metal Mesh
This mesh was the surface in which the reflective material would have to adhere
to and therefore its composition had to be factored into the material selection. To get the
maximum radiation reflected off the dish surface up to the focal point, a material with a
high reflectivity had to be chosen. The radiation incident to an object must be absorbed,
reflected or transmitted. Different amounts of radiation are transmitted and reflected for
different types of surfaces, however, the following energy conservation equation shows
how the total amount of radiation energy must be accounted for through each of the
α⋅= GGabs , τ⋅= GGtr , ρ⋅= GGref (5.1)
GGGG reftrabs =++ , 1=++ ρτα (5.2)
G is the incident radiation,α is the absorptivity, τ is the transmissivity, and ρ is the
reflectivity. Each mode of radiation takes a fraction of the incident energy such that the
sum of the coefficients is one. These three dimensionless constants are properties of any
material and for an opaque surface τ is zero and the remaining coefficients transfer all
the energy. For this application the goal is to find a material that could adhere to the
parabolic shape of the collector while also having a high reflectivity. In the search for this
material, aluminized mylar was chosen because it has the texture of wall paper and has a
reflectivity of 0.83.
Figure 5.3 Aluminized Mylar Film
This particular material was also readily available and cheap, which made it an
easy choice for the design. In addition to having a high reflectivity, the mylar also has an
emissivity of .76, which is good because a high emissivity denotes that it emits a large
portion of the radiation it absorbs. This would add back into the energy that is lost due to
Measurements of the dish dimensions were taken to calculate the equation to
describe its shape. This was needed to accurately calculate the shape and focal point of
Figure 5.4 Dish Parabola Equation and Focal Length
By measuring the labeled radius and hypotenuse of the dish the depth could be back
calculated using Pythagorean theorem.
RadiusHypotenuseDepth −= (5.3)
From this calculation the constant needed to calculate the equation of the parabola could
be determined, where the shape of a symmetric parabola is given by,
bxaxf +⋅= 2
where f(x) is the function describing the shape of the parabola, and x is the horizontal
distance from the center. The constants a and b describe the shape, where b can be made
zero by placing the bottom center of the dish at the origin. From this constraint, the value
of f(x) is equal to the depth when x is equal to the dish radius. Therefore the constant a
can be calculated using the following equation.
a = (5.5)
Once the constant is solved for, the focal point can be found. The focal length of a
parabola is the distance from the bottom to the focal point. The focal point for a
symmetric parabola lies along the axis of symmetry, and the distance above the
intersection of the axis and curve is given by.
Where fl is the focal length, which establishes the position of the focal point. The
measurements for the ten-foot dish can be applied to equations (5.3) through (5.6) and the
actual focal length can be determined. The following table indicates the measurements
for the ten-foot dish and shows the corresponding calculated values.
Table 5.5 Dish Measurements and Calculations
The calculation of the focal length is useful, however due to the dynamics
involving the sun and earth the focal point will not be an exact point as it will actually be
a focal area. The area in which the radiation is condensed is what will determine the
radiation intensity. The higher the radiation intensity is the higher the temperature of heat
reservoir will be, which supplies heat to the Stirling engine. There is a limit on the size of
the focal area as the ratio of the collector area to the focal area can be calculated as the
concentration ratio. The limit to the concentration ratio arises from the combination of the
size of the sun with its distance from the earth. There is a small variation in angle of the
incident radiation from the sun when its center is aligned with that of the dish.
Value (SI) Value (Eng)
Radius 1.524 m 5 ft
Hypotenuse 1.613 m 5.292 ft
Depth .528 m 1.732 ft
a 0.227 (1/m) 0.745 (1/ft)
fl 1.1 m 3.609 ft
Figure 5.6 Sun Diameter and Distance Affect on Concentration Ratio
Figure 5.6 shows that the angle sθ , causes a small variation in the angle at which incident
radiation impinges the collector surface. This variation causes the focal point to spread
over the area created by the rays that are not aligned perpendicular with the collector
surface. This small area creates a limit for how small the focal area can be and can be
calculated by knowing the angle sθ and the area of dish. The angle sθ is determined
from the diameter of the sun and distance to the earth given by the following equation.
s =)sin(θ (5.7)
Where r is the sun radius and R is the distance from the sun using this equation the angle
sθ can be calculated as 0.27 degrees. The maximum concentration ratio for a circular
collector is given by the following equation.
Where C is the concentration ratio, Ac is the collector area, and Afp is the area of the
focal point. The maximum concentration ratio for a circular parabolic collector is 45,000.
The purpose in calculating the actual concentration ratio is to relate it to the maximum
obtainable temperature of the receiver placed at the focal region where the relationship is
given the following figure.
Figure 5.7 Concentration Ratio vs. Temperature
It is clear from this figure that in order for the receiver temperature to be maintained in
the regime over 1,000 degrees C the concentration ratio must approach 1,000. This is a
useful calculation as will be demonstrated in the following section. Using the area of the
ten-foot dish, the necessary focal area can be determined to bring the receiver into the
1,000 degree C temperature range. The following graph shows how the concentration
ratio varies, where the focal area is described by a circle of diameter dfp. The diameter is
shown in meters and the corresponding concentration ratio is calculated.
0.04 0.06 0.08 0.1 0.12 0.14
Focal Area Diameter (m)
C dish d fp( )
6in1.5in d fp
Figure 5.8 Concentration Ratio vs. Diameter of Focal Area
From this plot it is evident that in order to get the receiver temperature in the
1,000 degree range the focal area would need to be reduced to a small circle less than
four inches in diameter (0.1m). With this in mind, the necessity of coating the dish with
the mylar effectively increased. A few different methods were explored involving
attempts to put screws through the mylar and bolt it to the metal mesh of the dish. These
methods were unsuccessful as they stressed the mylar and caused large wrinkle
deformations in the shape. These deformations would cause the radiation to deviate from
the prescribed path and would serve to increase the focal area. Different types of
adhesives were researched and a spray adhesive that was weather resistant was found.
This adhesive was then used to coat the dish with the mylar, over the screws.
Figure 5.9 Mylar Cut Around Screws
The mylar was cut into strips the size of the sub-partitions and then cut into smaller sizes.
Each piece was glued to the mesh and small slits were cut where the screws were
attached to allow the mylar to lie more flat against the mesh. After the mylar was laid the
focal area was measured, and was found to be about two feet in diameter. This large focal
area is largely due to wrinkles and imperfections in the dish’s shape. To further condense
the light a magnifying glass, or solar concentrator, were used to decrease the focal area
and increase the temperature.
6.0 Solar Concentrator
The purpose of the concentrator is to condense the light reflected off the satellite
dish. The dish is moderately effective at collecting the light, however imperfections in the
surface compounded with its loss of reflectivity from handling prevent it from creating
the necessary heating to run the engine. The goal is to design a magnifier that can focus
the light into a smaller region to increase the power density. By decreasing the focal area
the concentration ratio can be increased, and subsequently, the operating temperature of
the heat reservoir can be increased. By increasing the temperature of the reservoir the
heat to the engine can be amplified to result in an increase in efficiency. This is best
understood in relation to the idealized carnot efficiency given by,
where η in the ideal heat engine efficiency, TH is the hot temperature and TC is the cold
temperature. This relationship is useful because it gives an upper limit to the feasible
efficiency and also shows how the efficiency is increased, by increasing the difference
between TH and TC. The Stirling engine portion of the energy conversion process is
expected to be the least efficient, therefore persistent efforts must be made to boost the
engines efficiency. Subsequently the goal of optimizing this component of the design is
to capture most of the reflected radiation and significantly reduce the focal area. To do
this an optical magnifier must be used to further condense the sun’s light into a small
region of intense heating. To focus the radiation, a Fresnel lens will be used, which is a
prism ridge approximation to a magnifying glass. A Fresnel lens uses a series of ridges as
circular rings to bend light rays toward its focal point. Each ridge is an approximate prism
with the corresponding shape to focus light towards the focal point. The lens will be used
instead of a glass magnifying glass to save cost, as a magnifying glass of the size required
for this application could easily exceed the budget. The Fresnel lens, as an approximate
magnifying lens, can be made from a plastic sheet, which dramatically reduces its cost.
The following figures illustrate the manner in which it manages incoming light rays and
directs them to its focal point.
Figure 6.1 Fresnel Lens Ray Ddiagram
Figure 6.2 Fresnel Lens Characteristics
The Fresnel lens uses concentric ridges to focus the light and the density of the ridges
determines the image quality. For this application image quality is not the objective, and
therefore a low ridge density can be used for the purpose of light collection. The Fresnel
lens will be mounted below the focal point of the dish, so that the focal points for the dish
and lens coincide. For this design a Fresnel lens from Edmund Optics will be used, which
has a diameter of 18.25 inches and a focal length of two feet. The following figure
illustrates the positioning of the solar concentrating lens with respect to the dish.
Figure 6.3 Positioning of Solar Concentrator
The solar concentrator increases the operating temperature of the heat reservoir by
directly increasing the concentration ratio. The factor of concentration ratio increase is
denoted by the reduction in area given by the following equation.
ArKAi ⋅= (6.2)
Where, Ai is the initial concentrated area, Ar is the reduced area and K is the
concentration increase factor. With the initial radius approximately two feet in diameter
and reduced area approximately four inches in diameter the concentration factor is
approximately 36. This is well over ten, which would boost the temperature from the low
temperature (approximately 400 degrees C) regime to the high temperature regime
(approximately 1000 degrees C). Thus this component serves as the solar concentrator,
which intensifies the solar radiation into a small focal region. With the heat collected the
need for its containment arises. With such a high power density the energy could easily
exceed that of which a Stirling engine is designed for. Therefore the need for a thermal
buffer arises. The thermal buffer should store the intense heat and supply it to the Stirling
engine component at a rate that is acceptable.
Focal Point 2 feet
7.0 Heat Containment System
The heat containment system is needed to buffer between the solar radiation and
the Stirling engine. The need for the buffer arises from the need to supply the engine with
a consistent heat input. By building a thermal buffer that can absorb radiation, store
thermal energy and deliver it to the engine, a thermal reservoir can be achieved. A few
benefits arise from this component including absorption maximization, time constant
extension and heat loss minimization. These three characteristics are the advantages of
implementing such a system and they are the target factors in the system optimization.
To accomplish the three target goals the heat containment system will include
different materials, which are best suited for each factor in the design. These different
materials will each serve an individual purpose and will be optimally designed to
interface with each other. To maximize absorption the containment system will need to
be made of a material with a high absorptivity. This material may not have all the
characteristics that will be best for the design however a material with a high absorption
and low emissivity and high thermal conductivity will be the best to interface with the
incident radiation. To design a material for this application, a cheaper material such as
aluminum, which will make up the bulk of the system, can simply be coated or plated
with another material with the high absorption and low emissive properties needed. The
two most likely coatings are black nickel oxide and black chrome. It is known that black
surfaces approach the characteristics of the idealized black body, and therefore a black
coating is necessary. The black nickel oxide would be the most effective candidate when
comparing the ratio of its absorptivity and emissivity, however this plating can be
expensive and may prove to hinder the budget. The black nickel oxide absorptivity is
0.92, while its emissivity is 0.08. As with these characteristics, it will effectively capture
the reflected radiation and will have minimal surface radiation. The ratio of these
properties is 11.5, however for the black chrome, the absorptivity is 0.87 and its
emissivity is 0.09, yielding a ratio of 9.7. Although this ratio is smaller this coating will
be more cost effective and easily obtained, therefore it will be used as the coating in this
The heat containment system will be used as a thermal buffer and in essence it
will serve as a large thermal capacitor, because it will store the sun’s energy and provide
it at a desirable rate. The thermal reservoir will need a material with a large specific heat.
The systems time constant must be determined, so that the correct amount of mass can be
used to store enough energy in the thermal capacitor so that the system does not fluctuate
throughout the day’s operation. To determine the systems time constant, the following
energy balance must be evaluated to determine the transient temperature profile of the
CpmQoutQin ⋅⋅=− (7.1)
Where Qin is the heat supplied by the collector and concentrator, Qout represents the
convective and linear approximated radiation losses, m is the mass of the reservoir, Cp is
the specific heat of aluminum and
is the time rate of change of the temperature. The
convective losses will be for all exposed surfaces. The radiation losses will be treated as
the linearized approximation 3
TA⋅⋅⋅σε to reduce model complexity, where T is an
overestimated 1200 degrees C for the purpose of worst-case analysis. The emissivity ε
will be that of the chrome plating and the heat input will be calculated based on the
reflectivity of the mylar and absorptivity of the chrome plating. For this analysis the heat
supplied to the engine will be estimated at three kilowatts. The lost heat will be calculated
using one inch thick ceramic tile insulation with a thermal conductivity of 0.09 W/mK at
1000 degrees C. Using these assumptions and reductions this differential equation can be
solved, where the result has the following form.
eRthQinTtT 1)( (7.2)
T(t) is the transient temperature function and Rth is the thermal resistance given by the
following equation which takes into account the natural convection from all surfaces, the
radiation from all surfaces, and the conduction through the insulation.
TAAhRth σε (7.3)
h is the natural convective heat transfer coefficient, A is the surface area, ε is the
emissivity of the chrome plating, σ is Boltzman’s constant, T is the overestimated
temperature, x∆ is the insulation thickness, and k is the insulation thermal conductivity.
The thermal resistance was derived by relating the resistances from the following thermal
loss modeling circuit, which models all separate heat transfer modes in parallel.
Reservoir Temp Ambient Temp
Figure 7.1 Thermal Reservoir Heat Loss Resistance Circuit
To further optimize the heat reservoir, the thermal losses to the surroundings must
be minimized so that it can remain at the highest possible temperature. To do this only,
one face of the reservoir must absorb the radiation as the other surfaces can be insulated
from the outside air. Solarguard insulation will be used to reflect the radiation emitted by
the reservoir back onto itself. Solarguard insulation is a foil-like wrapping that can be
included in the design in between the reservoir and insulating ceramic tiles. By insulating
the reservoir the Qout term in Equation (7.1) can be minimized, which can result in a
higher operating temperature. Considering these components, optimization will lead to
greater and more efficient performance.
The geometry of the reservoir should be one that minimizes the surface area and
maximizes the mass. To do this the triangular shaped interface was selected because it
has the smallest amount of faces, and minimizes surface area. Therefore all other shapes
with the same cross sectional area will have greater surface area. In addition to optimal
geometry highly conductive thermal grease will be interfaced between the engine and
reservoir to minimize contact resistance. Subsequently the triangular shape was used as
the basis for the design and is shown in three dimensions in the following figures.
Figure 7.2 Heat Containment System
Figure 7.3 Heat Containment Front View
Using the thermal model, a transient simulation of the thermal reservoir
performance was run as it displays the time response of the system using the above
design, in which the dimensions are shown in inches.
0 5000 1 .10
Temp t( )
Figure 7.4 Heat Capacitor Transient Temperature Profile
The solution to Equation (7.2) yields Figure 7.4, which is the transient response of the
temperature reservoir. The denominator in the exponential of equation (7.2) gives the
system time constant which is 1.4 hours such that the time to steady state is
approximately 7.1 hours. Assuming the sun rises around seven o’clock, the reservoir
should reach steady state as the sun reaches its maximum flux around two o’clock in the
afternoon. This large time constant will serve to minimize fluctuations in the heat input to
the Stirling engine as it should also run for 7 hours after the heat input is diminished at
sunset. According to the simulation the reservoir should supply the heat to the engine
above 980K (700 degrees C), as this is useful information to selecting the proper Stirling
8.0 Stirling Engine
A Stirling engine is a closed-cycle, regenerative heat engine which uses an
external combustion process, heat exchangers, pistons, a 'regenerator' and a gaseous
working fluid contained within the engine to convert heat to mechanical work (motion).
The regenerator is an important feature of the Stirling engine because is used to
store energy from the gas as it passes through on the way to the cooler (low temperature
heat exchanger) and gives energy to the gas as the gas flows back through the regenerator
going to the heater (high temperature heat exchanger). It is the regenerator that makes
the Stirling Engine.
The operation of the Stirling engine is not complicated. There are no carburetors,
ignition systems, valves, or other complicated mechanisms. Stirling engines run off of the
expansion of air as it is heated, and the contraction of the same air as it is cooled. The
source of heat can be wood, fuel oil, sunlight, or geothermal sources.
Because the Stirling engine uses external combustion, it is extremely
environmentally friendly. The actual combustion process can be controlled to deliver
maximum heat with extremely low emissions. The engine’s suitability for renewable
energy sources such as geothermal, biomass and solar energy make it a true "green"
machine. It is a quiet engine, addressing noise pollution concerns.
The Stirling Cycle
The cycle consists of four internally reversible processes; isothermal compression
at the cold temperature source (Fig 8.1, curve 1), constant volume heating (curve 2),
isothermal expansion at the hot temperature source (curve 3), and constant volume
cooling (curve 4). These processes are performed on a sealed volume of working gas
which is most often air.
Figure 8.1 P-V Diagram of the Stirling cycle.
Two Basic Engine Designs
There are two basic categories of Stirling engines. The first is the simpler of the
two and is a basic displacement engine (Fig 8.2).
In the displacement engine there are two pistons. The smaller piston shown in
Figure 1 is the power piston. All of the power for this model is provided by the power
piston. The second larger piston is the displacer piston. Its function is to move the air
between the hot and the cold sides of the air compartment. It provides no power at all.
Figure 8.2 Displacement type Stirling engine cycles.
The power piston for this model should be 90 degrees out of phase from the displacer
piston. This model has four simple steps. Beginning at the top of the Figure 1, the first
step is heating. The heating is caused by the movement of the displacer piston so that
most of the gas is on the hot side. The temperature of the gas subsequently increases,
causing an increase in pressure. Because of this increase in pressure there is an
expansion of the gas causing the power piston to rise. Then, due to the 90 degree phase
shift between the two pistons, the displacer piston is moved, resulting in the cooling of
the gas. But when the gas is cooled, the pressure decreases, causing a contraction in the
gas, thereby pulling the power piston back down. Then once again, due to the 90 degree
phase shift, the displacer piston follows causing the gas to shift to the hot side of the
chamber. The temperature of the gas then increases, which completes the cycle. This is
the most basic model of the Stirling engine.
The second model works on the same principles as the displacement type but it is
a little more intricate and is known as a two-cylinder engine (Fig 8.3).
The two piston model is slightly more complex than the displacement model.
There are still two pistons, and they are still 90 degrees out of phase from one another.
However, in this model power is supplied by both pistons, and the displacement of the
gas is caused by both as well. Yet same basic process occurs as with the displacement
model. Once again, starting from the top of the illustration, the first step is the heating of
the gas in the chamber. The flywheel is turning, and thus the cold piston moves up, and
the hot piston moves down causing the gas to flow to the hot side. This then causes an
increase in the temperature of the gas. The gas therefore expands, pushing both pistons
downward. At this point the inertia of the flywheel causes it to continue rotating which
in turn raises the hot piston and pulls the cold piston downward. The gas is then pulled to
the cold side of the chamber, and the temperature of the gas is decreased. This decrease
in temperature causes the gas to contract, and therefore pulls both pistons upwards.
Then, once again, the inertia of the flywheel pulls the hot piston down and pushes the
cold piston up. Thus the gas flows to the hot side of the chamber and is heated, ending
the cycle where it began.
There are hundreds of variations of types of these two designs. They are divided
into Alpha (two-cylinder type), Beta (displacement type) and Gamma (displacement
type). Then there are the double acting engines which are alpha engines in series. These
can drive either a crankshaft drive, a swashplate drive or a cousin, the wobble drive.
The Alpha engine (Fig 8.4) is a two-cylinder type having two pistons in separate
cylinders which are connected in series by a heater, regenerator and cooler. The Alpha
engine is conceptually the simplest Stirling engine configuration, however, it suffers from
the disadvantage of both pistons requiring seals in order to contain the working gas.
The Alpha engine can also be compounded into a compact multiple cylinder
configuration (Fig 8.5), enabling an extremely high specific power output. The four
cylinders are interconnected, so that the expansion space of one cylinder is connected to
the compression space of the adjacent cylinder via a series connected heater, regenerator
and cooler. The pistons are typically driven by a swashplate, resulting in a pure sinusoidal
reciprocating motion having a 90 degree phase difference between the adjacent pistons.
Figure 8.4 Alpha type Stirling engine.
The Beta engine (Fig 8.6) has a single power piston and a displacer, whose
purpose is to "displace" the working gas at constant volume, and shuttle it between the
expansion and the compression spaces through the series arrangement cooler,
regenerator, and heater. The Beta configuration is the classic Stirling engine
configuration and has enjoyed popularity from its inception until today.
Figure 8.5 Compounded Alpha type Stirling engine.
Figure 8.6 Beta type Stirling engine.
Gamma type engines (Fig 8.7), like Beta, are also displacement type have a
displacer and power piston, similar to Beta engines, but in different cylinders. This allows
a convenient complete separation between the heat exchangers associated with the
displacer cylinder and the compression and expansion work space associated with the
piston. Thus they tend to have somewhat larger dead (or unswept) volumes than either
the Alpha or Beta engines.
Figure 8.7 Gamma type Stirling engine.
In the gamma-type engine cycle, the isothermal compression occurs as the power
piston reduces the volume of the working gas and the displacer chamber is in the cold
source state. The displacer then insulates the cold source, moving the gas in the chamber
to the hot source, resulting in constant volume heating. Isothermal expansion occurs as
the power piston moves, allowing the working gas to expand. Finally, the displacer
insulates the hot source, moving the working gas to the cold source, cooling the constant
volume of gas.
Note: During the expansion process some of the expansion must take place in the
compression space leading to a reduction of specific power. Gamma engines are therefore
used when the advantages of having separate cylinders outweigh the specific power
disadvantage. This is the type of engine that will be used for our design.
Stirling Engine Design Selection
In selecting a Stirling engine to generate our 1kW goal we quickly ran into a
problem. There are tons of available plans for model Stirling engines, but very few are
even rated over 100 W mechanical work output. It turns out that an affordable 1kW
generating system is the goal of quite a few companies right now. Affordable is the key
word here. The first problem is, almost all of them are in the prototype stage. The few
that aren’t in prototype stage are designed for use with a fuel burner and would be near
impossible to modify to mount at the focal point of a concentrating dish. Even if we
could talk them into reprogramming the control computers and succeed in mounting it in
the correct orientation at the focal point, we still have the problem of cost. The lowest
priced complete 1kW unit that is for sale is somewhere around 3 times the budget of our
There are several companies working on units in the 1kW range, but they do not
like revealing too much about them. These people base their entire livelihood on these
engines, so of course they are not going to let their plans out to anyone. Stirling
Technology Company (STC) is one company with a commercially available 1kW system.
Figure 8.8 Stirling Technology Company’s RG-1000 1kW generator
When first searching for the designs for a Stirling engine, we quickly found plans
everywhere for working models. We found a few very good designs for model Stirling
engines that had been built and tested. We thought of maybe scaling up one of these
designs. A Japanese inventor by the name of Koichi Hirata developed the design we
were thinking of scaling up. The plans for the model are all online and it is said to run at
up to 3,000 rpm. Scaling this design up to our needs sounded like a good idea. The
completed model can be seen in Figure 8.9.
Figure 8.9 The alpha type model Stirling engine rated up to 3000rpm.
Another design by the same inventor is a rotary displacer prototype. We decided against
this one since this is a very new prototype. There is no data available about it and there is
not anything that even says it will work.
Figure 8.10 The prototype rotary engine
It turns out the Stirling engine process is fairly simple in principle; however
getting one to work properly is almost an art. There are so many factors that make a
different in the performance of the engine. Even something as seemingly miniscule as a
small temperature gradient in the piston wall is enough to throw the efficiency of the
entire engine out of whack.
After talking to numerous people that center their lives on Stirling engine design,
it became clear that relying on a design that had never been tested before was out of the
question. The only logical choice was to settle for a lower power output from an engine
that is a proven working design.
After countless hours of searching, a man by the name of Mr. Dieter Viebach in
Germany was located that produces plans for a gamma type Stirling engine with a
mechanical work output of 500 W an electrical output of 450 W. These plans are sold at
the moderate cost of 65 euros, or about $79 USD. The castings are apparently available
for about $905 USD. This is of course without shipping.
Figure 8.11 Viebach Synchrongenerator ST 05 G-G 450 Watt
This engine stands a height of 600 mm, or about 23.6 inches. The surface area of
the heating side is 350 x 300 mm, which is about 13.8 x 11.8 inches. The total weight
when mostly made of aluminum casting is around 20 kg, or 44.1 lbs. The flywheel has a
mass of 7.5 kg (16.5 lbs) and a diameter of 280 mm (11 inches). The working piston
diameter is 85 mm (3.35 inches), the restrictor piston diameter is 96 mm (3.78 inches),
and the stroke is 75 mm (2.95 inches). The engine was designed with air or nitrogen as
working fluid at an operating pressure of up to 10bar (145psi). The method of heating it
arbitrary since it is a Stirling engine, but the prototype was heated with propane gas.
With a fuel flow rate of 225 gram/hour the engine produces 300 W mechanical work.
The gross calorific value for propane is 13.87 kWh/kg. The given mass flow rate equates
to 3.121 kW of heat input which is less than our estimated heat input from the
concentrating dish. There must be a source of constant water circulation to cool the
engine. If no water is delivered to a Sterling engine the temperature begins to equalize
after a matter of minutes, which soon stops the engine from running. The engine is
estimated to have an efficiency of 22%. The engine starts running at 200°C (392°F) and
produces 500W power output when near the max temperature of 650°C (1202°F). The
idling speed is approximately 800 rpm and the torque output is 8 Nm.
The cast set includes a majority of the parts necessary to build the engine. The
parts are sand-cast and therefore need further machining before they can be used in the
engine. The set includes the crankcase, quill, frame cover, cooler with guidance
restrictor, actuator, cylinder head, working piston and piston rods, restrictor, one
connecting tube elbow with flange, and one cooling water pick up flange. These parts are
all for use up to the 10 bar rated pressure. Some parts must be made in addition to the
cast parts. Standard parts like caps, seals, screws, pipe, and other miscellaneous items
must also be bought.
The following drawings are the only ones we have access to until we order the complete
drawing set. Included with the drawings is a detailed list of the additional materials
needed along with supply sources. The drawings include eleven sides text with seven
illustrations, four parts list in DIN A4 format, four detailed materials lists, one design in
DIN A2, five designs in DIN A3, 55 designs in DIN A4, four sides manufacturing and
testing instruction sheets, and one report.
Figure 8.12 Two drawings of the ST 05 G (without generator)
A group of hobbyists called the German Study Group are working on Stirling
engines. The most powerful engines they are making are based of Mr. Viebach’s gamma
type engine design. They have created multiple variations of Viebach’s design, running
off of heat sources ranging from biomass to solar heat. Below is a 1kW unit that is based
on Mr. Viebach’s design and is currently being developed by Epas Products in Germany.
Figure 8.13 EPAS Stirling BM 1000 uses biomass as a heat source
9.0 Tracking Control System
In order to achieve the greatest potential ‘harvest’ of the suns energy at all times,
we need a system capable of tracking the sun’s movement across the sky. This tracking
system needs to be capable of continually adjusting the altitude and azimuth angles of our
parabolic reflector so as to keep the reflector under maximum solar irradiance. Also, this
system should be able to ignore transient shadows and lights from fast moving sources
such as clouds, shrubbery, and birds, and also ignore oscillations of the parabolic
reflector caused by wind. They system must also be capable of returning the parabolic
reflector to its original ‘home’ position in anticipation of the next sunrise.
The sun’s position is related in terms of several different angles, but for
simplicity, its position can mainly be based on its altitude and azimuth angle. All the
sun-angle relationships, however, are based on solar time. Solar time is the apparent
angular motion of the sun across the sky, with solar noon being the time when the sun
crosses the meridian of the observer. Solar time is calculated by applying two different
correction factors to the local standard time. The first correction factor is a constant
which is a correction for the difference in longitude between the observers meridian and
the meridian on which the local standard time, Lst, is based. For the continental United
States time zones, the standard meridians are: Eastern - 75°W; Central - 90°W; Mountain
- 105°W; and Pacific - 120°W. The second correction factor takes in account the
perturbations in the earth’s rate of rotation. This second correction factor is found from
the equation of time,
)1( −= nB (9.2)
and n is equal to the day of the year, thus 1[n[365. The difference in minutes between
solar time and standard time is thus
Solar time – standard time = 4(Lst-Lloc) + E (9.3)
where Lloc is the longitude of the location in question measured in degrees west. It is also
a known fact that it takes the sun four minutes to transverse 1 degrees of longitude.
Tallahassee is located in the Eastern time zone, therefore the standard meridian, Lst, for
Tallahassee is 75°W, and its longitude is 84.28°W. For calculation purposes, considering
day of the year, the correction to standard time is –2.64minutes, thus making
12-noon Eastern Standard Time equal to approximately 11:47:36 AM solar time. This
means that the sun will cross directly overhead of Tallahassee at 12:02:64 PM Eastern
Standard Time on the 365th
day of the year. Appendix C shows how this calculation was
performed and Figure C-1 of Appendix C shows the equation of time as a function of
time of year for Tallahassee.
By knowing the solar time, you can find when the sun will be directly overhead
for that particular day, which will aid in locating the altitude and azimuth angle of the
sun. The solar altitude angle, αs, is the angular distance above the horizon, with a
maximum of 90 degrees. The azimuth angle, γs, of the sun, is the angular distance
measured along the horizon in a clockwise direction. Figure 1.1 shows the relations of
the different angles used in determining the suns position in the sky.
Figure 9.1 Angles related to position of sun and
view showing azimuth angle.
The tracking system for the collector will have two axis of motion. The system
will have 90° of altitude travel and 240° of azimuth travel. The altitude drive will range
from 0° to 90°, as measured from the horizontal, and the azimuth drive will travel from
60° to 300°. This will allow for the collector to remain in the direct sunlight throughout
the day. A single Quadrant Photodiode (4-element array) Amplification Module will be
used to control both axes. The module planned for used is Phresh Phontonics’ SiQu50-M
module. The SiQu50-M combines a Silicon Quadrant Photodiode with amplifiers and
position sensing circuitry, which provides output voltages of both the sum of the axes and
of each axis independently. The Silicon Photodiodes produce a current that is
proportional to the light falling on it. The detector is made of one monolithic piece of
Silicon, thus the response from each element will be identical. By a comparison of the
produced currents, the location of the light can then be determined. When each of the
four elements produces an equal current, the source of light is centered. The outputs for
the azimuth (X) and altitude (Y) angels can be compared as follows:
X=[(i1+i2)-(i3+i4)] 104/(i1+i2+i3+i4) (9.4)
Y=[(i1+i4)-(i2+i3)] 104/(i1+i2+i3+i4) (9.5)
This current is then converted and amplified to a useable voltage. The voltage input
needed to control the module ranges from 5 to 18 volts. The sensing area of the module
is 50 square millimeters, and has a spectral response of 400 to 100 nanometers with an
output voltage of –Vcc-3/-Vcc+3. Appendix D shows an electrical diagram of the SiQu50-
M module and a drawing of its outer casing. An issue that may need to be considered in
the future with this product is the intensity of the light beam falling on the module, which
could, if needed, be taken care of my creating a ‘mask’ for the module. All adjustments
for the tracking system should be made on a clear day so as to have few clouds to
interfere with setting procedures.
For the chosen design, all of the components of the system are located at the focal
point of the dish. A frame is to be constructed which is capable of withstanding the
forces and moments that will be experienced at the focal point of the dish. The frame
will have to securely house the heat containment unit, the stirling engine, and the
generator. It is approximated that the maximum weight to be loaded at the focal point of
the dish is 500 pounds. Because of this, it was decided that the frame should be
constructed out of carbon steel square tubing and flat bar. It may seem a bit over-kill, but
it leaves little chance for failure.
Aside from the structural design of the frame, it must also be capable of
maneuvering the dish to track the sun. The frame must move the dish in both the altitude
and azimuth directions; 90 degrees from the horizon in the altitude direction, and 240
degrees in the azimuth direction. This is to be accomplished by use of two separate linear
actuators, which work in conjunction with the Silicon Quadrant Photodiode module.
Preliminary drawings of the frame for the system are located in Appendix E.
Responsible Input Output
Books and Model
Chris and Dustin
Smaller dish and
Location, Trip Plan,
Perform Tests and
Team Mylar and Adhesive
Run actual test to
and heat transfer
Chris and Hunter
Locate Vendor and
Perform Tests and
Fluid Selection and
Calculations of heat
storage and final
optimization of design
Dustin and Hunter
Locate Vendor and
obtain required specs
Begin system tests for
Asegun and Chris
Locate Vendor, RPM
correlated with engine
work on robustness
4.0 Product Development
3.3.7 Heat Storage
3.3.8 Stirling Engine
3.3.5.a Windows 2000
6.0 Delivery of Product
5.0 Construction of System
4.2 Ordering/Obtaining Parts
3.3.6 Parabolic Mirror
3.3.2 Aluminized Mylar
3.3.4 Tracking System
3.3.5 Operating System
3.1 Materials Selection
3.2 Materials Location
3.3.1 Parabolic Dish
2.2 Initial Testing
2.3 Concept to Prototype
1.1.1 Needs Statement
1.1.2 Product Specifications
2.0 Research and Conceptualization
2.1 Design Concepts
1.0 Meet with Sponsor
1.1 Customer Needs