Team Solaris Group 12

Senior Design (Spring 2004)

Ashmore, R. Hunter Harrelson, Dustin M.

Henry, Asegun Newton, C. Christopher

Sponsor: Dr. A. Krothapalli

I

Contents

ABSTRACT 1

1.0 INTRODUCTION 3

2.0 DESIGN SPECIFICATIONS 6

2.1 Specifications for Final System 6

2.2 Specifications for Working Model 6

3.0 CONCEPT SELECTION 9

3.1 Concept One 9

3.2 Concept Two 10

3.3 Concept Three 11

4.0 PROJECT PLANNING 14

4.1 WBS 14

4.2 Schedule 14

4.3 Project Procedures 15

5.0 SOLAR COLLECTOR 17

5.1 Model Dish 17

5.2 Large Dish 17

5.3 Analysis of Dish 19

6.0 TRACKING SYSTEM 25

7.0 FRAME 34

8.0 HEAT CONTAINMENT 38

8.1 Heat Containment Design 38

8.2 Heat Containment Model 39

II

9.0 STIRLING ENGINE 43 The Stirling Cycle 43

9.1 Stirling Engine Designs 44 9.1.1 ALPHA Type 47 9.1.2 BETA Type 48 9.1.3 GAMMA Type 48

9.2 Stirling Engine Design Selection 49

9.3 The Stirling Steele Engine 53

10.0 GENERATOR 57

10.1 DC Motors 57

10.2 DC Motor Selection 59

APPENDIX A - FLUID CONCEPT CALCULATIONS 61

APPENDIX B – WBS 66

APPENDIX C – SCHEDULE 67

APPENDIX D – SOLAR TIME CALCULATIONS 68

APPENDIX E – CAD DRAWINGS OF FRAME 69

APPENDIX F – THE STIRLING-STEELE ENGINE© 70

APPENDIX G – DC MOTOR 79

APPENDIX H – TORQUE CALCULATIONS 80

REFERENCES 81

1

Abstract

As fossil fuel technologies become obsolete, from the depletion of fuel sources,

the demand for alternative energy technologies, such as solar power, fuel cells, and wind

power, will grow. The main reason these alternative energy sources have not been more

widely utilized, is because fossil fuels are relatively low cost compared to the initial setup

price for the alternative sources, as well as the lack of availability of efficient alternative

energy devices.

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 sun’s 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 a parabolic

reflector.

2

Section 1.0

Introduction

3

1.0 Introduction

The sun is an excellent source of radiant energy, because it emits electromagnetic

radiation with an irradiance of 1367 W/m2 on the earth’s surface. Of this solar radiation

reaching the earth, most is comprised of radiant energy ranging in wavelengths between

0.3 and 2 µm. The radiant energy incident to the earth’s surface is comprised of two

types of radiation - beam and diffuse radiation.

The purpose of a focusing solar collector is to increase the intensity of the solar

radiation 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,

2))(4(156.1F

DECR m= (1.1)

where Dm is the dimension of the collector and F is the focal length. Figure 1.1 shows a

ray diagram for the concentration of light for a parabolic reflector.

Figure 1.1 A Parabolic Reflector Concentrates Solar Irradiance at its Focal Point

By focusing the solar irradiance to a particular point, the system is capable of producing

sufficiently high temperatures in order to employ a heat engine cycle that will generate

electrical power efficiently.

This idea of using the sun’s heat as a source of power is not a new one. This

concept has dated as far back as 1000 A.D. with the development of focusing mirrors. It

is also noted that Leonardo da Vinci proposed to build a concave mirror four miles in

4

diameter on an excavated bowl-shaped recess in the ground that would serve as a source

of heat and power for commercial enterprises. 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 at a distance of about 30 feet.

Figure 1.2 German Burning Mirror of the 1700's

By utilizing the high intensity 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 that

usually uses and external combustion process, which in this case it is replaced by external

solar heating. 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.

5

Section 2.0

Design Specifications

6

2.0 Design Specifications

2.1 Specifications for Final System

According to our sponsor, Dr. A. Krothapalli, Team Solaris’ final design needed

to be capable of producing an optimum amount of electricity. Originally, our sponsor

required that the working system generate 1 kW of electricity, which was to be generated

from a Stirling engine that obtains its heat from a solar collector. The solar collector, as

instructed by our sponsor, was to be made from a military surplus satellite dish. Another

constraint, which was also placed on the project, is that the dish must track the sun

throughout the course of the day. The generation of electricity from this system is

accomplished by harnessing the sun’s energy with the use of a reflective parabolic dish,

which must track the position of the sun throughout the day and then reset itself at night

under its own power. The dish was to be coated in aluminized Mylar because of its

reflectivity, workability, and relatively low cost. The Stirling engine uses the heat at the

focal point of the dish to change heat energy to mechanical energy. A DC

motor/generator was to 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. This whole

design and construction of the project was to be done for less than $5000. Due to this

budget constraint, the requirements were renegotiated into a small-scale fully functional

model of the system.

2.2 Specifications for Working Model Complications arose involving the acquisition of a cost-efficient Stirling engine

that was suitable for our needs and feasible when considering the amount of time it would

take to have this engine up and running. It was because of these complications that we

were instructed to initially build a working model of the system that would be operational

7

by our sponsor's stated due date. This working model was to serve as an exact scaled-

down replica of the final system in every respect. The requirement for electrical output

was decreased to a more reasonable 40 Watts of usable energy.

8

Section 3.0

Concept Selection

9

3.0 Concept Selection

3.1 Concept One

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 frame design, as shown in Figure 3.1.

Figure 3.1 Design 1 – Solar energy is redirected from the focal point Before we could choose this design, testing was required to make sure the optics

ideology behind it would prove to be functional. 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

10

transferred the light to the focal point of the reflector. However, because the light from

the first reflector was not incident at an angle parallel to the second reflector's axis most

of the light diverged from its focal point. This difficulty in alignment for effective

radiation transfer subsequently resulted in a lack of intensity at second focal point. Thus

the simplest and most favored design idea failed.

3.2 Concept Two

This design concept, as shown in Figure 3.2, utilizes a heat containment unit filled

with a working fluid such as molten salt, which would 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 is similar

to Design 1 in that the supports at the focal point do not have to support much stress.

Figure 3.2 Design 2 – Use of working fluid to transfer heat

Through careful analysis this design was found to be infeasible for several reasons.

The expense of high temperature piping and high temperature pumping equipment would

cause this component of the system to drain the budget. In order to design a system with

fluid heat transfer, a working fluid would have been needed that could be maintained in a

11

liquid phase at a high temperature so that it could be circulated using a pump. A few

options were investigated, but did not seem to work well within the constraints of this

project. Water could be used, but in order to keep it in a liquid phase it would have to be

maintained at a high pressure which was undesirable due to safety concerns and

infrastructure costs. Molten salt was investigated as it can be maintained in its liquid

phase between 200° C and 600° C; however the consequence of this option was that it

would also return to a solid at night while still within the piping system which would

have presented reheating and corrosion issues. Thermal heat transfer oils and compounds

were also investigated, however they were limited in their temperature stability as most

could not exceed 400° C. Another issue with pumping a fluid to the focal point came in

trying to develop an interface between the heat containment and fluid. This difficulty

arose from the need for a fin design that would provide enough heat transfer to the fluid

so that in steady state operation the fluid could be reheated to its maximum temperature

after losing heat to the engine. The calculations concerning this issue are given in

Appendix A, which show that the forced convective heat transfer would be insufficient to

raise the temperature of the fluid for the desired operation. Due to the cost and

complexity of controlling a working fluid, and finding a non-industrial pump system that

could withstand high temperatures, this design was not chosen.

3.3 Concept Three

This particular design consisted of the Stirling engine and generator located at the

focal point. 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 3.3 shows a

drawing of Design Concept 1.

12

Figure 3.3 Design 3 – Components of system located at focal point

Since Design 2 failed, and we chose to

go with Design 3, the temperature at the

focal point needed to be determined. This

was done with a k-type thermocouple. It

was found that the temperature at the focal

point would reach 700°F (370°C) without

any problem. This proved to be an adequate

amount of heat for the Stirling engine, which had been located for use on the project;

with the operating temperatures of the Stirling engines ranging from 300°F (148°C) to

1200°F (650°C).

13

Section 4.0

Project Planning

14

4.0 Project Planning

4.1 WBS

The Work Breakdown Structure (WBS) Chart displays the structure of the project

showing how a project is organized into a summary (phase) and detail levels. The WBS

was 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 was 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 B. 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.

4.2 Schedule

The schedule for Team Solaris can be found in Appendix C. 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.

15

4.3 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

blackboard.

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.

Meetings:

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.

16

Section 5.0

Solar Collector

17

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.

5.1 Model Dish The dish we chose to use for the working model portion of the project is a 24-inch

diameter parabolic reflector. This is the same parabolic reflector that was used to gather

temperature readings when design analysis began in the fall. Through testing, it was

determined that this dish could reach temperatures upwards of 700°F without any

problems, making it highly adaptable to the requirements of the Stirling engine.

5.2 Large Dish

The set-up of the final product will include a 12-foot diameter television-

broadcasting dish made of fiberglass that can be broken down into six equal sections.

The dish was donated to the team by the WCTV Channel Six of Tallahassee. Unlike the

parabolic reflector used in the model set-up, this larger dish is not reflective and thus

must be coated with some sort of highly reflective material in order to collect a maximum

amount of radiation reflected off the dish surface to the focal point. In selecting a

material, we had to focus on radiation properties. It is known that the radiation incident

to an object must be absorbed, reflected or transmitted. Different amounts of radiation are

18

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 modes.

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. After a search for

this material, aluminized Mylar was chosen based not only on its high reflectivity (0.83)

and emissivity (0.76), but also because of its thickness and texture, which are similar to

that of household wallpaper. This makes application fairly simple by using some sort of

spray or contact adhesive. This particular material was also readily available and cheap,

which made it a fairly simple choice for the design. To apply the Mylar to the fiber glass

surface of the satellite dish a double sided adhesive tape was used. After trial and error

the method that resulted in the smoothest adhesion was when the adhesive was rolled

onto the dish in strips. After the strips were laid Mylar sheets cut into squares were

patterned over each section.

19

5.3 Analysis of Dish

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

the dish.

Radius

HypotenuseDepth

Focal Point

Figure 5.1 12-foot Dish Geometry and Focal Length

By measuring the labeled radius and hypotenuse of the dish the depth could be back

calculated using Pythagorean Theorem.

22 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)( (5.4)

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.

2RadiusDeptha = (5.5)

20

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.

afl

⋅=

41 (5.6)

where fl is the focal length, which establishes the position of the focal point. The

measurements for the twelve-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 twelve-foot dish and shows the corresponding calculated values.

Table 5.1 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.

21

Figure 5.2 Sun Diameter and Distance Affect on Concentration Ratio

Figure 5.6 shows that the angle θs 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 θs and the area of dish. The angle θs is determined from

the diameter of the sun and distance to the earth given by the following equation.

sin( )SrR

θ = (5.7)

Where r is the sun radius and R is the distance from the sun using this equation the angle

θs can be calculated as 0.27 degrees. The maximum concentration ratio for a circular

collector is given by the following equation.

2

2 2

1maxsin ( )

C

fp

A RCA r sθ

= = = (5.8)

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.

22

Figure 5.3 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

twelve-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.

23

0.04 0.06 0.08 0.1 0.12 0.14

2000

4000

6000

8000

Focal Area Diameter (m)

Con

cent

ratio

n R

atio

8000

400

C dish d fp( )

6in1.5in d fp

Figure 5.4 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 became more important.

24

Section 6.0

Tracking System

25

6.0 Tracking System

In order to achieve the greatest potential of the sun’s energy at all times, a system

capable of tracking the sun’s movement across the sky is required. 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. The 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 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 differs from standard time due to the spatial extent

of time zones, and as a result 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,

))2sin(04089.0)2cos(014615.0)sin(032077.0)cos(001868.0000075.0(2.229

BBBBE

−−−+=

……

(6.1)

where

26

365360)1( −= nB (6.2)

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 (6.3)

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

the 365th day of the year, the correction to standard time is –2.64 minutes, 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 D shows how this calculation was

performed and Figure D-1 of Appendix D 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 6.1 shows the relations of

the different angles used in determining the suns position in the sky.

27

Figure 6.1 Angles related to position of sun and view showing azimuth angle

To simplify the tracking system design only one axis of motion will be used. The

parabolic reflector will be aligned with the sun's position at maximum altitude and will

rotate on an axis perpendicular to the plane passing through that position. Figures 6.2,

6.3 and 6.4 illustrate this.

Axis of Rotation

Figure 6.2 West Elevation View of Solar Path with Aligning Axis of Rotation

28

Axis of Rotation

Figure 6.3 Solar Path 38 Degree View Point with Aligning Axis of Rotation

Axis of Rotation

Figure 6.4 3D Elevation of Solar Path with Aligning Axis of Rotation

By taking the average maximum altitude of the sun for a given month the

parabolic reflector can be aligned to it and the system can follow a prescribed path. This

is a simple method of tracking the sun whereby the altitude angle should be reset to the

appropriate average angle for a given month. By doing this the reflector can be pointed

29

at the sun throughout the entire day using one axis of motion and no sensor feedback

control. The rate at which the sun will move across the sky can be simply expressed with

negligible error in terms of the earth's 24 hour/per day cycle. Taking the shape of the

earth at Tallahassee's location to be a circle and the earth rotating at 360 degrees/24

hours, the sun's angular velocity with respect to the dish's axis of rotation will be

approximately 15 degrees per hour. The tracking system can be set to run at a series of

discrete locations as it can advance 1 degree every 4 minutes. The rotational system will

be driven by an electromechanical actuator assembly, which will be attached to the frame

and controlled by a computer program in Lab View. Figure 6.5 shows a picture of this

actuator assembly and it illustrates the actuator pushing directly on the dish's frame. As

the actuator extends its lower portion is allowed to rotate. This allows it to push on the

dish away from its rotational axis causing it to rotate.

Figure 6.5 Actuator Assembly

30

To read and control the position of the dish a potentiometer was attached to its

rotational axis. The changing resistance is fed back to the Lab View program to

determine when the actuator should be stopped. Figure 6.6 shows the setup for analyzing

the torque requirements for the system.

Effective Distance

Rotating Shaft θEffective

Weight

Figure 6.6 Torque Requirement Analysis

For the actuator to move the reflector assembly the moment produced from its

own weight (including the engine) at the position corresponding to the angle theta must

be overcome. The term, effective weight, is used for several reasons including the fact

that the moment that must be overcome by the actuator assembly is based on the

unknown inertia of the reflector assembly. The inertia that will be overcome to

accelerate the unit is modeled as a mass at some effective distance that produces an

overall moment that must be overcome for the system to move. This effective moment is

the product of the effective distance and weight, which also include the internal frictional

torque losses and errors in estimating reflector inertia as well as the location of the engine

center of mass. Therefore as the reflector assembly moves through angle θ the required

torque changes. The required torque is given by the following equation,

31

)cos(θτ ⋅⋅= effeff dw (6.4)

where the required torque is given by τ, the effective weight and distance are

given by weff and deff respectively and the angle theta corresponds to that shown in Figure

6.6. Figure 6.7 shows the Lab View program which is run in version 7.0 and requires

three analog inputs and two analog outputs (0 - 10 Volts).

Figure 6.7 Lab View Tracking System Software

As labeled on the software itself, it is setup to calculate the sun's position, through its

altitude and azimuth angles. It is also setup to record the temperature of the heat

containment as well as the power output from the alternator. The system rotational angle

is calculated from the potentiometer input, which determines where the system is

oriented. The program also has an indicator to show when the batteries are powering the

actuator. The program is designed to be able to run at any time of day, as it begins with a

dialog box shown in figure 6.8.

32

Figure 6.8 Tracking System Start Dialog Box

Figure 6.8 shows what information is required to run the system. The current day of the

year time and location as latitude and longitude are required to determine the sun's

current location. The system then outputs a 10 Volt signal to close a relay switch and turn

on the actuator. The actuator moves until it reaches the desired location corresponding to

the sun's current location. After the initial calibration procedure is complete a timer runs

and updates the system to move the dish one degree every four minutes. This update uses

the feedback from the potentiometer to determine when the actuator should be turned off.

33

Section 7.0

Frame

34

7.0 Frame

For the chosen design, the heat containment and engine are located at the focal

point of the dish. A frame was 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 motion control, explained in the previous section,

will allow the altitude angle to be set manually. This manual setting will require

adjustment each month so that the dish can point at an elevation appropriate for

maximum solar radiation. In order to accomplish this, again a similar design will be

implemented on the model that resembles that of the large scale version.

35

Figure 7.1 Large Scale Frame For 12-foot Satellite Dish

The large 12-foot satellite dish frame incorporates two axis of motion, which are used to

adjust the azimuth and altitude angles. The lower square tubing assembly can be used to

control the altitude, which will be manually adjusted each month. The higher bracket

assembly can rotate in a direction that is perpendicular to the axis of the lower bracket.

This higher bracket assembly will be used to adjust the rotation, which is aligned to the

sun's path in co ordinance with the earth's rotation.

Figure 7.2 Model Size Frame for 24 inch Dish

36

Figure 7.2 shows a schematic for the model size frame, with the same setup for motion

control. This smaller frame will be used in the same way the large-scale model rotates.

Figure 7.3 Model Frame

Figure 7.3 shows the aluminum frame for the small-scale frame, with the dish supported

by latches. The large-scale frame has its own attachments the link to the back of the 12-

foot dish, which differ in geometry but serve the same function as the latches in Figure

7.3. Drawings of the frame for the system are located in Appendix E.

37

Section 8.0

Heat Containment

38

8.0 Heat Containment

8.1 Heat Containment Design

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 that is spread over the heating side of the engine. By building a

thermal buffer that can absorb radiation, store thermal energy and deliver it to the engine,

an effective thermal capacitor 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 material such as steel or

copper will make up the bulk of the system to achieve the high thermal conductivity, and

will 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 it is intuitively confirmed that a black coating would be appropriate for it

absorption characteristics. The black nickel oxide would be the most effective candidate

when comparing the ratio of its absorptivity and emissivity, however this plating process

can be expensive and difficult to find. 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,

39

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 design.

8.2 Heat Containment Model

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,

however to minimize stresses due to thermal expansion the same material housing the

pistons, stainless steel, will be used as the heat containment. 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 with cloud interference. To determine the systems time constant, the following

energy balance must be evaluated to determine the transient temperature profile of the

reservoir.

dtdTCpmQnetQoutQin ⋅⋅==− (8.1)

Where Qin is the heat supplied by the collector, Qout represents the convective and

linearly approximated radiation losses, m is the mass of the reservoir, Cp is the specific

heat of the metal and dtdT 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 to reduce model complexity, where T is an

overestimated 1200°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 3.5 kilowatts. Using these assumptions and reductions this

differential equation can be solved, where the result has the following form.

3TA ⋅⋅⋅σε

40

−⋅⋅+= ⋅⋅

−

∞RthCpm

t

eRthQnetTtT 1)( (8.2)

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.

( ) 13 −⋅⋅⋅+⋅= TAAhRth σε (8.3)

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.

Figure 8.1 Thermal Reservoir Heat Loss Resistance Circuit

41

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.

0 50 100 150 200 250 300 3500

100

200

300

400

500

600554.744

25

Temp t( ) 273−

333.3330 t

60

Figure 8.2 Heat Capacitor Transient (min) Temperature (°C) Profile

The solution to Equation (8.2) yields Figure 8.4, which is the transient response of

the temperature reservoir. The denominator in the exponential of equation (8.2) gives the

system time constant which is .576 hours such that the time to steady state is

approximately 2.88 hours. Assuming the sun rises in morning, the reservoir should reach

steady state well before the sun reaches its maximum flux 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 more than an hour after the heat input is diminished at sunset.

According to the simulation the reservoir should supply the heat to the engine above

500°C.

42

Section 9.0

Stirling Engine

43

9.0 Stirling Engine

The Stirling engine is a closed-cycle, regenerative heat engine which uses an

external combustion process. This process involves heat exchangers, pistons, a

regenerator, and a gaseous working fluid contained within the engine to convert heat to

mechanical work.

The regenerator is an important feature of the Stirling engine because it is used to

store energy from the gas as it passes through to the cooler, and gives energy to the gas as

it flows back through the regenerator on its way to the heater. It is this, the regenerator,

which makes the Stirling engine work.

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 that is also a quiet running engine, thus addressing noise pollution concerns.

The Stirling Cycle

The cycle consists of four internally reversible processes; isothermal compression

at the cold temperature source (Fig 9.1, 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.

44

Figure 9.1 P-V Diagram of Stirling Cycle

9.1 Stirling Engine Designs

There are two basic categories of Stirling engines. The first, a displacement type

engine, is the simpler of the two (Fig 9.2).

Figure 9.2 Displacement type Stirling Cycle

45

In the displacement engine there are two pistons as shown in Figure 1. The

smaller piston is the power piston, and the second, larger piston, is the displacer piston.

All of the power for this model is provided by the power piston, whereas the displacer

piston provides no power, but functions as a billow to move the air between the hot and

the cold sides of the air compartment. The power piston for this model is 90 degrees out

of phase from the displacer piston.

The displacer type Stirling engine has four simple steps (Figure 9.2):

1) Step one: Heating

2) Step two: Expansion

3) Step three: Cooling

4) Step four: Contraction

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.

The second model, which works on the same principles as the displacement type

engine, is a little more intricate and is known as a two-cylinder engine (Fig 9.3).

46

Figure 9.3 Two-piston Stirling Engine Model

This model contains two pistons which are 90 degrees out of phase from one

another. However, in this model, power is supplied by both pistons along with the

displacement of the gas. The same basic process occurs with this model as does with the

displacement model. Once again, starting from the top of Figure 9.3, 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

47

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.

Variations of this two main Stirling engine designs are subclassified as Alpha

(two-cylinder type), Beta (displacement), and Gamma (displacement) type Stirling

engines.

9.1.1 ALPHA Type The Alpha engine (Fig 9.4) 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.

Figure 9.4 Alpha type Stirling Engine

The Alpha engine can also be compounded into a compact multiple cylinder

configuration, thus 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.

48

9.1.2 BETA Type The Beta engine (Fig 9.6) 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. This happens in a series starting with the cooler,

regenerator, and then the heater. The Beta configuration is the classic Stirling engine

configuration and has enjoyed popularity from its inception until today.

Figure 9.5 Beta Type Stirling Engine

9.1.3 GAMMA Type Gamma type engines (Fig 9.7), like Beta engines, are also a displacement type

engine. They have a displacer and power piston, similar to Beta engines, but in different

cylinders. This allows for a convenient and complete separation between the heat

exchanger 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.

49

Figure 9.6 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. (also see Figure 9.13)

9.2 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. Affordability is the key here.

The first problem is that most all Stirling engines capable of producing an output

of 1kW are in the prototype stage. The few that are not 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 reprogram the control computers and

succeed in mounting the engine in the correct orientation at the focal point, the immense

50

cost would still be an issue. The lowest priced, complete, 1kW unit, that is for sale is

about 3 times the budget of this project.

Several companies are working on Stirling engine units which operate in the 1kW

range, but they do not like revealing too much about them. Most of these people base

their entire livelihood on these engines, so of course they are not going to let your

average person obtain their plans. Stirling Technology Company (STC) is one such

company with a commercially available 1kW system.

Figure 9.7 Stirling Technology Company’s RG-1000W generator

When first searching for Stirling engine designs, plans were easily found for

working models. The idea of scaling up one of these model designs was tossed around.

A Japanese inventor, by the name of Koichi Hirata, developed the design the team had in

mind to scale up. The plans for the model can be found online and is said to run at

speeds up to 3,000 rpm. Figure 9.9 shows the completed model.

51

Figure 9.8 Alpha type model Stirling engine rated at 3000 rmp

Another design (Figure 9.10) by the same inventor is a rotary displacer prototype engine.

It was decided against this design since it is a very new design, and no data is available

about it.

Figure 9.9 Prototype rotary displacer Stirling engine.

52

The Stirling engine process is fairly simple in principle; however getting one to

work properly is an art. There are many factors that make a difference in the

performance of a Stirling engine. For example, something as seemingly miniscule as a

small temperature gradient in the piston wall is enough to cause the efficiency of the

engine to drastically decrease.

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

design that is a proven.

The original design chosen for this project was that of a gamma type Stirling

engine designed by a Dieter Viebach of Germany. This particular Stirling engine had a

mechanical work output of 500 Watts and an electrical output of 450 Watts. These plans

were sold at a moderate cost of 65 euros, or $79 USD. Figure 9.11 shows the plans for

this particular engine.

Figure 9.10 Viebach ST-05 G Stirling Engine without Generator

53

This design was originally chosen because of reviews which were received about

Viebach’s design by group of hobbyists called the German Study Group. They had

created various multiple variations of Viebach’s design, which run off of heat sources

ranging from biomass to solar heat.

Once the plans were received, one issue remained at hand, the plans were in

German. Time was spent trying to get the drawings translated, but it soon became an

issue of time to get it done. Thus another Stirling Engine design had to be chosen.

The final Stirling engine design chosen for use on this project was one by a

Ronald J. Steele. This engine is of the gamma type Stirling engine family, and is a

copyrighted design, called The Stirling-Steele Engine.

9.3 The Stirling Steele Engine

This Stirling-Steele Engine consists of four gamma type Stirling engines daisy

chained together. This particular design, however, is unique in that it requires only one

crank through per piston (Figure 9.12) where as other Stirling engines require two (Figure

9.13).

Figure 9.11 The Stirling-Steele Engine Copyright © Steele, 1994

54

This is done by driving the displacers by linear rods that are attached to the top of the

power pistons. The rods then pass through a sealed bulkhead while the displacer

cylinders are ported to the power piston cylinders. The displacer cylinders are ported 90

degrees behind the power piston cylinders, as shown in Figure 9.12. This is how the

Stirling-Steele Engine is capable of requiring only one crank through per piston. In

comparison to the Stirling-Steele Engine, a standard gamma type Stirling engine has two

pistons where each one is contained in its own cylinder. Figure 9.13 shows a diagram of

a simple displacer type gamma engine.

Figure 9.12 Gamma type Stirling engine in its simplest form.

Stages: 1) The displacer is at top dead center (TDC), and the power piston is half way up

and compressing the working gas through the port into the cold space. 2) Working gas is fully compressed as the displacer starts down and ‘displaces’ the

gas from the cold side to the hot side of the displacer cylinder.

3) The working gas is in the hot side and is rapidly expanding, passing the lose fitting displacer piston through the port and forcing the power piston down.

4) The power piston is a bottom dead center (BDC), and the displacer is half way

up with the working gas filling the cold side of the displacer cylinder where it will rapidly contract and allow the cycle to start again.

55

Other advantages to Ronald J. Steele’s Stirling engine, the Stirling-Steele engine, are that

it is easy starting, smooth running, and has good low end torque. This works well for the

required application of mounting a Stirling engine at the focal point of a parabolic

reflector.

The Stirling-Steele Engine has a displacement of 37.6CC with a maximum

wattage output of 20 Watts with a working fluid of air at 20psi, and 40 Watts with a

working fluid of Helium at 40psi. The Stirling-Steele Engine is also shown to have a

maximum free rpm of 1800rpms or 188.5 rad/sec. Assuming that the maximum rotations

per minute is reached for both air and helium, this particular engine is capable of

generating 0.078 ft-lbf (air) and 0.175 ft-lbf (helium) of torque. A complete list of

specifications for the Stirling-Steele Engine is in Appendix F.

56

Section 10.0

Generator

57

10.0 Generator Part of the original requirements for this project was to produce 1 kW of electricity from

a solar powered Stirling engine. However, due to time constraints, rarity of 1 kW output

Stirling engines, and budget, a scaled down model was allowed. This model still is

required to output an optimum amount of electricity in comparison to the mechanical

output of the engine.

The engine being used for this system is the Stirling-Steele 37.6 CC Engine. This

engine has a maximum wattage output of 20 Watts with a torque rating of 0.078 ft-lbf

when the working fluid is air. Because of this, a generator which required less than 0.078

ft-lbf or torque is needed. Also, the actuator for the entire Solaris system runs off of 24

VDC. Thus, a DC motor was decided upon for use in electricity generation.

10.1 DC Motors

A DC (Direct Current) Motor works by a current being passed through a coil in

magnetic field. The current is supplied by a power source, such as batteries, through the

commutator. The electric current then passes through a coil in the magnetic field,

producing a magnetic force, which produces a torque that turns the motor (Figure 10.2).

The magnetic force which is produced acts perpendicular to the wire and the magnetic

field (Figure 10.1). The commutator keeps the coil turning in the same direction by

reversing the current on each half revolution.

58

r

Commutato

Figure 10.1 Magnetic Interactions and Current Flow of DC Motor

Figure 10.2 Interaction between permanent magnet and coil to produce torque

59

This ultimately keeps the torque turning in the same direction. This shows that by

applying an electrical current to the motor, that work is output. Thusly, if the process is

reversed, and work is input to the motor, an electrical current will be generated.

The idea behind this is to couple the output shaft, which is now ultimately the

input shaft, of the DC motor to the output shaft of the Stirling engine. This will in turn

apply a torque to the shaft of the DC motor causing the coil to spin within the permanent

magnetic field. An electrical current, which in this particular case will be 24 VDC, will

be generated and stored in batteries.

10.2 DC Motor Selection

The particular Stirling engine in use, The Stirling-Steele Engine, has a maximum

torque output of 0.078 ft-lbf with air as the working fluid. The Stirling engine also has a

maximum angular momentum of 1800 rotations per minute. The DC motor to be used

for this application needed to be capable of generating a 24 volt direct current. This

current constraint is due to the tracking system, discussed in Section 6.0.

Of the 24 volt direct current motors which were readily available, there were very

which matched the selected criterion. This is due do the extremely low torque output of

the Stirling Engine. The DC motor selected is a ‘Miniature DC Gear-motor’ (Figure

10.3) obtained from McMaster-Carr.

Figure 10.3 Miniature DC Gear-motor

This motor was selected because of its low torque rating of 15 in-ounces, and should be

capable of producing 24 VDC. (Note that complete specifications of the selected DC

motor can be found in Appendix G.)

60

Appendices

61

Appendix A - Fluid Concept Calculations

Acpipe πD2

2⋅:= vel .131:= νoil T( ) 2 1011

⋅ T 6.4214−⋅:= velf zfluid vel⋅:=

νoil νoil Test( ):= νoil 1.546 10 7−×=

ρ oil T( ) .398− T⋅ 985.69+:= Cpoil T( ) 3.5599 T⋅ 835.55+:= koil T( ) 7− 10 5−⋅ T⋅ .154+:=

mdot vel Acpipe⋅ ρ oil Test( )⋅:= mdot 0.046= Refvelf l⋅

νoil:= Ref 3.873 105

×=

µoil T( ) νoil ρ oil T( )⋅:= Proil T( )µoil T( ) Cpoil T( )⋅

ρ oil T( ):= Vdot

mdotρ oil Test( )

:= Vdot 6.43 10 5−×=

mdot1gpm 6.395 10 5−⋅ ρ oil Test( )⋅:= mdot1gpm 0.046=mdot

mdot1gpm1.006=

ρ oil 320 273+( ) 749.676=

NuoilLam T( ) .664 Ref( )1

2⋅ Proil T( )( )

1

3⋅:= NuoilTurb T( ) .037 Ref( )

4

5⋅ Proil T( )( )

1

3⋅:=

Nuoil T( ) NuoilLam T( ):=

β1

Test:= β 1.512 10 3−×= δ l:=

Forced Convection

Tsurf 700:= g 9.8:=

TestTsurf 350+ 273+

2:= zfluid 1:= σ 5.67 10 8−⋅:= Tinf 26 273+:=

Tin 326 37− 273+:= Tout 326 273+:= TmTin Tout+

2:= Tin 562= Tout 599= Tm 580.5=

αbchrome .87:= εbchrome .09:= αanodized .11:= εanodized .84:= εpolished .03:=

12 inches long 6 inches wide 1 inch diamter pipe

l .3048 1.5( )⋅:= w .30481012

:= Acon l w⋅( ) 4⋅ 2w w⋅+:= Vol w w⋅ l⋅:= D .025:=

.5 in/s fluid velocity

62

Fluid concept calculations cont’d

Grg β⋅ Tsurf Tinf−( )⋅ δ

3⋅

νoil2

:= Ra Gr Proil Test( )⋅:= Ra 1.171 1010×= Nu .54 Ra .25( )

⋅:=

hNu koil Test( )⋅

δ:= h 41.847=

hf T( )Nuoil T( ) koil T( )⋅

l:= hf Test( ) 7.692=

hoil hf Test( ):= Nutotal Nuoil Test( )( )3 Nu( )3+

1

3:=

hoilNutotal koil Test( )⋅

δ:= hoil 41.934=

63

Fluid concept calculations cont’d

hair h:=h 13.075=h

Nu kf⋅

δ:=

Nu .54 Ra .25( )⋅:=Ra 1.176 108×=Ra Gr Prf⋅:=Grg β⋅ Ts Tinf−( )⋅ δ

3⋅

ν f2

:=

β 4.837 10 3−×=β

1Tf

:=Prf 0.734=kf 0.019=ν f 7.652 10 6−×=

Prf linterp T Pr, Tf,( ):=kf linterp T k, Tf,( ):=ν f linterp T ν, Tf,( ):=

Tf 206.75=TfTs Tinf+

2:=Ts 388.5=Ts Test 273−( ):=

Pr

724

717

714

712

711

710

708

707

706

703

700

10 3−⋅:=k

223

246

253

261

268

275

283

290

297

331

363

10 4−⋅:=ν

1.14

1.40

1.48

1.57

1.67

1.77

1.86

1.96

2.06

2.60

3.18

10 5−⋅:=T

250

280

290

300

310

320

330

340

350

400

450

:=

g 9.8:=δAp

:=p 2 l w+( )⋅:=A l w⋅:=Tinf 25:=

Natural Convection

64

Fluid concept calculations cont’d

Tin 562= Tout 599= ∆T Tout Tin−:=

∆T 37=

0 500 1000 1500 20001 .105

5 .104

0

5 .104

g Tw( )

Tw

Twall root g Tw( ) Tw, 273, 2000,( ):= Twall 762.884= Twall 273− 489.884=

Qrad Twall( ) 1.002 103×= Qair Twall( ) 3.115 103

×=

Qoil Twall( ) 4.539 103×= Qoilneeded 4.988 103×=

∆ToilQoil Twall( )

mdot Cpoil Tm( )⋅:= ∆Toil 33.672= ∆T 37=

Qengine1000.20

:= Qengine 5 103×= ∆TengineQengine

mdot Cpoil Tm( )⋅:= ∆Tengine 37.088=

Heat containment Model

Qsun 1000:= Ddish 3.6576:= Adish πDdish

2

2

⋅:= Qin Qsun Adish⋅( ) αbchrome⋅:=

Tw 273 274, 2000..:= Tinf 26 273+:= Test Tm:= Qin 9.141 103×=

Qrad Tw( ) εbchrome σ⋅ Acon⋅ Tw4 Tinf

4−

⋅:= number of fins nf 5:=

Qair Tw( ) hair Acon⋅ Tw Tinf−( )⋅:= Atotal Acon:=

Qoilneeded mdot Cpoil Tm( )⋅ Tout Tin−( )⋅:= Qoil Tw( ) hoil Atotal⋅ Tw Tm−( )⋅:=

g Tw( ) Qin Qrad Tw( )− Qair Tw( )− Qoil Tw( )−:=

Cpoil Tm( ) 2.902 103×= mdot 0.046=

65

Fluid concept calculations cont’d Because Q oil is less than Oil needed this system would not be able to heat up the

fluid to its maximum heat transfer. A more complicated design and analysis would have

to be employed to use fins to increase the convective area. However, these fins would

also serve to decrease the velocity of the fluid in contact with the fins. This design would

not provide enough convective heat transfer to keep the fluid at its maximum

temperature.

66

Appendix B – WBS Responsible Input Output

Team"""

Team"

Asegun Books and Model Information Working Estimates

Chris and Dustin Smaller dish and stirling engine

Temperature and Heat Transfer

EstimateTeamTeam

"""

ChrisForms, Vendor

Location, Trip Plan, Setup Location

Begin Assembly, Perform Tests and

Calculations

Team Mylar and AdhesiveRun actual test to

calculate temperature and heat transfer

DustinCurrent components

and design optimization scheme

Optimized, robust functioning design

Chris and Hunter

Current design, motors, dish

infastructure and supports

Optimized radiation input

Team"""

HunterLocate Vendor and determine optimal

design

Begin Assembly, Perform Tests and

Calculations

Asegun Fluid Selection and Vendor Location

Calculations of heat storage and final

optimization of design

Dustin and HunterLocate Vendor and

obtain required specs and output

Begin system tests for efficiency, cycling,

and fatigue

Asegun and Chris

Locate Vendor, RPM Requirement

correlated with engine output

Meet 1kW requirement; begin work on robustness

and consistencyTeam

"""

Team""

Team

4.0 Product Development

3.0 Design

2.2 Calculations

5.1 Assembly

3.3.7 Heat Storage

3.3.8 Stirling Engine

3.3.9 Generator

3.3.5.a Windows 20003.3.5.b Labview3.3.5.c C++

5.2 Testing6.0 Delivery of Product

5.0 Construction of System

4.1 Drawings4.2 Ordering/Obtaining Parts4.3 Machining

3.3.6 Parabolic Mirror

3.3.2 Aluminized Mylar

3.3.3 Frame

3.3.4 Tracking System

3.3.5 Operating System

3.1 Materials Selection3.2 Materials Location3.3 Components

3.3.1 Parabolic Dish

2.2 Initial Testing

2.3 Concept to Prototype

1.1.1 Needs Statement1.1.2 Product Specifications

2.0 Research and Conceptualization2.1 Design Concepts

Activity1.0 Meet with Sponsor

1.1 Customer Needs

67

Appendix C – Schedule

68

Appendix D – Solar Time Calculations

0 100 200 300 40020

10

0

10

20E as a function of time of year

Time of year (Days)

Equa

tion

of T

ime

(Min

utes

)

E n( )

n

solartime n( )8.448

16.7

13.66

-2.872

27.7365.122

7.991

14.402

11.97815.105

-2.237

26.808

6.847

=

solartime n( ) 4 Lst Lloc−( ) E n( )+ standardtime+:=E n( )

-2.9045.348

2.307-14.224

16.384

-6.23

-3.3623.05

0.626

3.753

-13.58915.456

-4.505

=

E n( ) 229.2 0.000075 0.001868cos B n( )( )+ 0.032077sin B n( )( )− 0.014615cos 2B n( )( )− 0.04089sin 2B n( )( )−( ):=

B n( ) n 1−( )360365⋅:=

n 1 31, 365..:=

standardtime 12:=Lloc 84.28deg:=Lst 75deg:=

solartime 2.638−=

solartime 4 Lst Lloc−( ) E+ standardtime+:=

E 13.99−=

E 229.2 0.000075 0.001868cos B( )+ 0.032077sin B( )− 0.014615cos 2B( )− 0.04089sin 2B( )−( ):=

B n 1−( )360365⋅:=

n 365:=

standardtime 12:=Lloc 84.28deg:=Lst 75deg:=

Solar time for Tallahassee

69

Appendix E – CAD Drawings of Frame

Figure E-1 Front view of CAD dish and frame

Figure E-2 Back view of CAD dish and frame

70

Appendix F – The Stirling-Steele Engine©

Height 10 "Weight 5.25 lbs.Cooling retrofitted for waterHeater Surface Area 19 sq inchesCooler Surface Area 24 sq inchesRegenerator Surface Area 17 sq inchesRegenerator Type annularBore 0.8750 X 4Stroke 1"Displacement 37.6 CCEngine Type 4-cylinder gamma typeMaximum Wattage Output 20 Watts @ 20 psi air

40 Watts @ 40 psi heliumMaximum RPMS 1800 rpm

The Stirling-Steele Engine

Table F-1 Specifications for the Stirling-Steele Engine

71

The Stirling-Steele Engine cont’d

Figure F-1 Isometric view of Engine Figure F-2 Bottom few of crank-case

Figure F-3 Side cut-away view of engine showing inline pistons

72

The Stirling-Steele Engine cont’d

73

The Stirling-Steele Engine cont’d

74

The Stirling-Steele Engine cont’d

75

The Stirling-Steele Engine cont’d

76

The Stirling-Steele Engine cont’d

77

The Stirling-Steele Engine cont’d

78

The Stirling-Steele Engine cont’d

79

Appendix G – DC Motor

rpm Torque (in-oz) Full Load Amps917 15 0.66

Miniature DC Gearmotor

Table G-1 Specifications of DC Motor

Figure G-1 CAD of DC Motor being used

80

Appendix H – Torque Calculations

τhelium = 30.144 in-ozτair = 14.976 in-oz

.157 192⋅ 30.144=.078 192⋅ 14.976=

τhelium 0.157ft lbf⋅=τair 0.078ft lbf⋅=

τhelium 0.212N m⋅=τheliumPHelium

ω:=τair 0.106N m⋅=τair

Pairω

:=

Calculated assuming that the maximum free rotation of 1800 RPMs is reached for both air and helium.

P ω τ⋅Power = Rotation x Torque

ω 188.496radsec

=ω 1800RPM:=

RPM2π

60sec:=PHelium 40W:=Pair 20W:=

Maximum Wattage Output: 20 Watts @ 20 psi Air40 Watts @ 40 psi Helium

Maximum Free RPM: 1800 RPM

Torque output of Stirling-Steele Engine

81

References

1.) Krothapalli, A., Dr. Energy Conversion Systems I & II. Florida State University. Website: www.eng.fsu.edu/~kroth

2.) http://www.stirlinghotairengine.com/about.htm

3.) www.precision-d.com/stirling/proposal.html

4.) http://www.ent.ohiou.edu/~urieli/stirling/engines/

5.) http://www.ent.ohiou.edu/~urieli/stirling/engines

6.) Solo http://www.stirling-engine.de/engl/solare_energiesysteme.html

7.) Sandia Labs http://www.energylan.sandia.gov/sunlab/contacts.htm

8.) STM Power http://www.stmpower.com/Contact.asp

9.) Tamin Enterprises http://www.tamin.com/company.htm

10.) Sunpower http://www.sunpower.com/contact/contact.html

11.) STC http://stirlingtech.com/about/contact.shtml

12.) WhisperGen http://whispertech.co.nz/contact.html

13.) Japanese Inventor http://www.bekkoame.ne.jp/~khirata/

14.) Sunmachines http://www.sunmachine.de/english/main.html

15.) http://www.visualsunchart.com/

16.) Steele, Ronald J. The Stirling-Steele Engine. Website: www.stirlingsteele.com

82