Spring 2017

Solar Powered Stirling Engine SBE 498H SENIOR CAPSTONE MEGAN MCHUGH

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Table of Contents

List of Figures ................................................................................................................................................ 3

List of Tables ................................................................................................................................................. 3

Abstract ......................................................................................................................................................... 4

Introduction .................................................................................................................................................. 5

Literature Review .......................................................................................................................................... 5

Engine Configuration ................................................................................................................................ 8

Mode of operation. ............................................................................................................................... 9

Forms of cylinder coupling .................................................................................................................... 9

Forms of piston coupling..................................................................................................................... 11

Operational characteristic: dead volumes .......................................................................................... 12

Development of the Solar Powered Stirling Engine ................................................................................ 12

The first era of solar powered Stirling engines. .................................................................................. 12

The second era of solar powered Stirling engines. ............................................................................. 12

Solar Powered Stirling Engine Optimization ........................................................................................... 14

Mean temperature differential Stirling engine optimization. ............................................................ 14

Finite-time thermodynamics optimization. ........................................................................................ 14

Multi-objective solar dish-Stirling engine optimization. ..................................................................... 15

Research Methodology ............................................................................................................................... 15

Materials ................................................................................................................................................. 15

Stirling Engine Parts and Assembly Procedure ....................................................................................... 17

Modifications ...................................................................................................................................... 17

Parabolic dish ...................................................................................................................................... 18

Measurements and Calculations............................................................................................................. 19

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Temperature and speed ...................................................................................................................... 19

Power output ...................................................................................................................................... 20

Dead volumes...................................................................................................................................... 22

Results ......................................................................................................................................................... 22

Discussion.................................................................................................................................................... 24

Summary of Data .................................................................................................................................... 24

Solar Dish Findings .................................................................................................................................. 24

Future Implications ................................................................................................................................. 25

Conclusion ................................................................................................................................................... 26

References .................................................................................................................................................. 28

Reflection .................................................................................................................................................... 33

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List of Figures

Figure 1. Idealized Stirling cycle represented in a pressure vs. volume graph. ............................................ 6

Figure 2. SunPulse Water connected to the India Mark II Water Pump (Ardron, 2010). ............................. 8

Figure 3. Alpha configuration Stirling engine (Urieli, 2012). ....................................................................... 10

Figure 4. Beta configuration Stirling engine (Urieli, 2012).......................................................................... 10

Figure 5. Gamma configuration Stirling engine (Urieli, 2012). ................................................................... 11

Figure 6. Base Stirling engine model heated by an ethanol flame. ............................................................ 17

Figure 7. Stirling engine model with extended displacer cylinder length. ................................................. 18

Figure 8. Front view of the solar Stirling engine system. ............................................................................ 18

Figure 9. Back view of the solar Stirling engine system. ............................................................................. 19

Figure 10. Materials (left to right): Neiko tachometer, SainSmart digital multimeter with thermocouple,

and welding goggles. ................................................................................................................................... 20

Figure 11. Temperature (°F) at the end of the cylinder or between the cooling fins versus time (s) for the

prototype Stirling engine. ........................................................................................................................... 23

Figure 12. Speed (rpm) for all trials versus time (s) for the prototype Stirling engine. .............................. 23

List of Tables

Table 1. Stirling Engine Parts Material List ................................................................................................. 16

Table 2. Nomenclature................................................................................................................................ 21

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Abstract

This paper provides a study on the configuration of Stirling engines and the effect using a solar

dish as a heat source on efficiency. The Stirling engine was based on the MIT 2.670 design - a Gamma

configuration, low temperature differential Stirling engine. Temperature and speed were measured for

the base model Stirling engine to determine the initial efficiency. Modifications were planned to add a

parabolic mirror as a solar dish and compare the efficiency to the initial design, however, the completed

solar Stirling engine testing and data collection is to be performed in the following summer. The work

performed by the engine was to be calculated using the Schmidt formula to then find the power output.

Results from the completion of this study would indicate how the solar dish effects the power output of

the Stirling engine.

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Introduction

In the future, power plants need to accommodate issues such as the depletion of conventional

fuels, the increase in cost of fossil fuels, the use of alternative fuels, the demand for a prime mover that

produces less air pollution and less noise, and the amount of waste heat recovery. The Stirling engine

addresses these problems as it has multi-fuel capability, high efficiency, low fuel consumption, clean

combustion, low noise levels, and low temperature operation (Thombare & Verma, 2006). The

configuration of a Stirling engine consists of cylinder couplings, piston couplings, and a mode of

operation. Previous research lists these classifications as parameters to determine the most suitable

engine geometry and arrangement (Beale, Wood, & Chagnot, 1980; Mancini & Heller, 2003; Senft, 2001;

Wood, Chagnot, & Penswick, 1980). Most Stirling engines are single or double acting, and originally the

single cylinder was the most common. Studies have developed many arrangements that include multi-

cylinder operation, which is necessary for double acting engines (Bratt, 1980; Finkelstein, 1960). The

main forms of cylinder couplings experimental works have produced include the Alpha, Beta, and

Gamma engines (Ross, 1979; Thombare & Verma, 2006). Piston couplings usually come in the rigid form,

although gas and liquid forms have been developed as well (Beale, Wood, & Chagnot, 1980; Meijer,

1958; Philip, 1987; Ross, 1979). All of these factors that make up the configuration of the Stirling engine

influence the overall power output and efficiency of the engine. The current research aims to construct

a solar powered Stirling engine, add various modifications, and test for the most efficient design by

using the recorded measurements to calculate the power output of each in order to determine to

optimal Stirling engine configuration.

Literature Review

In 1816, Robert Stirling invented the Stirling engine, a device with cyclic compression and

expansion of the working fluid at different temperature levels (Patent No. 4081, 1816). This operation,

the Stirling cycle, is also known as a closed regenerative thermodynamic cycle, and a net conversion of

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heat to work is accomplished by the volume change regulating the flow (Thombare & Verma, 2006). The

four thermodynamic processes that make up this Stirling cycle consists of isothermal expansion due to

heat from an external source (1), constant volume heat removal (2), isothermal compression (3), and

constant-volume heat addition (4); each part of the cycle is represented by the corresponding numbers

in Figure 1. Low-power range solar thermal conversion units consist of three main sub-systems: the

solar receiver, the thermodynamic gas circuit, and the drive mechanism. Stirling engines are considered

among the most effective of these units and improvements in performance can be made based on

changes in the main sub-systems (Mancini & Heller, 2003). The following literature review explores

previous studies on the development of various Stirling engine configurations, the variables that effect

the engine performance, and the Stirling cycle along with its operational characteristics.

Figure 1. Idealized Stirling cycle represented in a pressure vs. volume graph.

The main focus of the research will be optimizing a solar powered modification of the base

Stirling engine. The solar powered Stirling engine was patented in 1987 by Roelf J. Meijer. Using a large

dish facing the sun, the rays of sunlight can be reflected onto a focus point at the center of the dish to

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collect solar energy as a source of heat. The heat then powers the Stirling engine connected to the solar

dish collector and produces electricity, which makes the system a viable alternative energy source

(Patent No. 4707990, 1987). The development of the solar powered Stirling engine began as Ford Motor

Company obtained a worldwide exclusive license to research almost all applications of the Stirling

engine from N.V. Philips of the Netherlands. Philips worked on making Stirling engines for the Ford

Torino vehicles, however, the project ended early and the work continued instead at Stirling Thermal

Motors, Inc. (Meijer & Godett, 1987).

The solar powered Stirling engine has other applications as a pump, which is important as it is

cost effective and can be used for water pumping in areas of the world where there is low access to

clean water. Pumping systems employed in sunbelt countries have a maximum water cost target of 6

cents/m3, as set by the World Bank based on their study demonstrating photovoltaic pumping systems

currently cost 8.4 cents/m3 and gasoline pumping systems at 8.58 cents/m3. Sunvention Sunpulse Water

has designed and constructed a prototype solar thermal water pump as seen in Figure 2, which consists

of a solar collector directly coupled to a slow-speed Stirling engine that can be coupled to the water

pump, or anything else that requires mechanical power. TÜV labs assessed the Sunvention system and

found it works at a cost of 2.4 cents/m3 – an amount that meets the World Bank target. This means

there are a large number of applications for the solar powered Stirling engine outside of electricity

production and water pumping, since it can serve as an air pump for fish farms or to fulfill mechanical

requirements such as milling, grinding, and compressing (Ardron, 2010).

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Figure 2. SunPulse Water connected to the India Mark II Water Pump (Ardron, 2010).

Engine Configuration

The drive mechanism is important to consider when choosing an engine configuration because it

is not compatible with every arrangement. The primary role of the drive mechanism is to reproduce the

volumetric changes that occur in order to maintain the heat transfer, gas dynamic, and thermodynamic

engine requirements (Thombare & Verma, 2006). The parameters to consider when choosing an engine

configuration are important for optimization of performance. Gary Wood (Wood, Chagnot, & Penswick,

1980) of Sun-Power Corp. lists the required parameters to consider: engine cylinder layout, engine

mechanism, burner or heater type, displacer and piston construction, type and size of regenerator, and

crankshaft construction. Other basic parameters to consider include speed, displacement, and the Beale

number, which is used to characterize the performance of Stirling engines by estimating the power

output of a design based on pressure, piston volume, and engine cycle frequency (Beale, Wood, &

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Chagnot, 1980). There are three levels of classifications for Stirling engine designs: mode of operation,

forms of cylinder coupling, and forms of piston coupling. According to Senft (2001), these parameters

will determine the optimum engine geometry.

Mode of operation. The modes of operation include single acting, double acting, single phase,

multiphase, resonant, and non-resonant. A broad classification of Stirling engines only differentiates

between single and double acting. A single side of the piston is in contact with the working fluid, which

is moved from one cylinder to a second cylinder in single acting engines as invented by Robert Stirling in

1816. Multiple working spaces are used in the double acting engine, which moves the working fluid

through the use of both sides of the piston as invented by Babcock in 1885 (Thombare & Verma, 2006).

Finkelstein (1960) has described numerous arrangements and concepts for multi-cylinder operation.

Multi-cylinder engines are necessary in doubling acting arrangements because the appropriate

difference between the expansion and compression processes can only be obtained with a minimum of

three cylinders (Thombare & Verma, 2006). United Stirling designed a 40 kW four-cylinder double acting

Stirling engine with the objective of component development. Different heater head temperatures and

different working gases were used in the testing of the engine. The United Stirling P’ series established

by Bratt (1980) is the most manufactured and developed doubling acting Stirling engine.

Forms of cylinder coupling. There are three different forms of cylinder coupling: Alpha, Beta,

and Gamma. The simplest Stirling engine configuration is the Alpha engine (Figure 3), which consists of

two pistons: compression and expansion. The hot piston used for expansion is connected in series to a

heater, a regenerator, a cooler, and the cold piston used for compression. Both pistons need to be

sealed in order to contain the working gas, which is a disadvantage to the configuration (Thombare &

Verma, 2006). The classic Ross-Yoke drive and the balanced “Rocker-V” mechanism are innovative Alpha

engine designs by Ross that are used as small air engines (U.S. Patent No. 4138897, 1979). Beta engines

(Figure 4) are constructed so the piston and displacer are within the same cylinder. Separate linkages

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may connect the two pieces to a crankshaft to maintain the phase angle that is required instead of

having the piston and displacer physically touch. The top of the power piston and the bottom of the

displacer form the compression space in Beta engines. The Gamma engine (Figure 5) has the advantage

of utilizing a simple crank mechanism with the displace cylinder, cooler, heater, regenerator, and

compression cylinder connected serially. The displacer-piston arrangement is similar to the Beta engine

configuration as separate cylinders are used to house each piece. An interconnecting transfer port joins

the two cylinders, which share the compression space (Thombare & Verma, 2006).

Figure 3. Alpha configuration Stirling engine (Urieli, 2012).

Figure 4. Beta configuration Stirling engine (Urieli, 2012).

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Figure 5. Gamma configuration Stirling engine (Urieli, 2012).

Forms of piston coupling. The slider crank drive is used in twin cylinder versions of the Stirling

engine due to how easy it is to manufacture and how reliable it has proven to be. However, it is nearly

impossible to balance and the linkage does not take care of the drive mechanism problem that occurs

when the displacer and the piston are used in tandem in a cylinder (Thombare & Verma, 2006). Philip

(1987) developed the rhombic drive in the 1950s, which is dynamically balanced even in an arrangement

with a single cylinder making it the most well known and most developed of single cylinder Stirling

engines. Each assembly requires matching gear wheels, numerous moving parts, and bearing surfaces

causing the complexity of the unit to be its main disadvantage (Philip, 1987).

The swash plate is a dynamically balanced system at a fixed swash plate angle, and is mainly

used in automobile engines. Varying the angle of the swash plate creates an unbalanced effect, and also

changes the stroke of the engine, therefore providing control of the power output of the engine. Meijer

(1958) invented the method of changing the swash plate angle during operation. Related forms of piston

coupling include the Ross rocker and ringbom type. Cambridge University is investigating the use of the

Ross rocker mechanism in Stirling engines (U.S. Patent No. 4138897, 1979) while the ringbom has a

displacer driven by the cyclic gas forces and a piston that is linked to the crankshaft mechanically (Beale,

Wood, & Chagnot, 1980). Aside from the mentioned rigid forms of piston couplings there are gas forms

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such as free piston, free displacer, and free cylinder, and there are liquid forms such as jet stream,

rocking beam, and pressure feedback (Thombare & Verma, 2006).

Operational characteristic: dead volumes. The un-swept volumes in a Stirling engine are called

dead volumes and can account for up to 50% of the total engine internal gas volume (Thombare &

Verma, 2006). The power output will increase as the swept volumes increase as long as the other

factors, such as temperature and pressure, remain the same. The power output of the engine is reduced

by the amount of dead volume, however, the reduction in efficiency is dependent on the location of the

dead volumes. The optimal amount of dead volume must allow for sufficient heat transfer surfaces and

must accommodate the heat exchangers (Wu et al., 1998).

Development of the Solar Powered Stirling Engine

The first era of solar powered Stirling engines. Ericsson adapted the Stirling engine to work with

solar energy in 1870 using parabolic trough collectors to heat steam and drive the engine after his initial

invention of a solar-powered hot air engine that used a reflector to heat the displacer cylinder in 1864

(Rizzo, 1997; Jordan & Ibele, 1955; Spencer, 1989; Ericsson, 1870; Daniels, 1964). The first solar powered

hot air engine was built in 1872 by Ericsson using a spherical mirror concentrator on an open-cycle hot

air engine (Spencer, 1989). There were not many solar powered Stirling engines built during this time,

instead Reader and Hooper proposed its use in a water pumping system in 1908 (Reader & Hooper,

1983).

The second era of solar powered Stirling engines. In India, an open cycle solar powered Stirling

engine using a parabolic collector was implemented by Ghai and Khanna from 1950 to 1955; however,

there were issues with heat loss (Walpita, 1983; Spencer, 1989; Daniels, 1964). There was also a water

pumping 100 W solar powered Stirling engine described by Jordan and Ibele in 1955. Numerous studies

focused on using transparent quartz windows, and found these solar powered Stirling engines had

problems with fouling effects and heat transfer (Daniels, 1964; Spencer, 1989; Trayser & Eibling, 1967;

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Utz & Braun, 1960; Finkelstein, 1961; Gurtler, 1979; Walker, Kentfield, Johnson, Fauvel, & Srinivasen,

1983; Hull & Hunt, 1984). However, optimum heat transfer area was obtained by Walpita’s design for a

solar receiver made from 3.175 mm outer diameter spiral steel tube when the heat transfer from solar

radiation to the working fluid was analyzed (Walpita, 1983).

The Stirling engine with a concentrating collector also became more prevalent in the second era.

Ahmed et al. produced electricity using a 50 kW solar powered Stirling engine with a single membrane

dish concentrator and a working gas of hydrogen; however, there were design errors that lead to issues

with the tracking system (Ahmed, Al-Agami, & Al-Garni, 1990). Childs et al. developed a solar dish

concentrator Stirling engine electric module that worked at an efficiency of 22% for an average

production of 10 h/day when determining the most cost effective approach to solar powered desalting

technology (Childs, Dabiri, Al-Hinai, & Abdullah, 1999). Theoretical models for four different orbit

configurations were developed by Audy et al. when using a Stirling engine with a solar dynamic power

system for space station applications (Audy, Fischer, & Messerschmid, 1999).

Solar dish/engine systems are characterized by either modularity, efficiency, autonomous

operation, or the capability to work with either solar energy or conventional fuel and are systems that

convert solar energy to mechanical energy and then electrical energy (Kongtragool & Wongwises, 2003).

Solar dish/engine systems track the sun using a mirror array in order to obtain the required temperature

for efficient conversion and usually use hydrogen or helium in high temperature and high pressure

systems (Washom, 1984; Kongtragool & Wongwises, 2003). Many projects using this technology began

with the Dish/Stirling Joint Venture Program in 1991 to develop 5-10 kW dish/Stirling systems for

applications in remote areas and the Utility Scale Joint Venture Program for 25 kW dish/engine systems

in 1993 (Bean & Diver, 1992; Gallup, Mancini, Christensen, & Beninga, 1994). A 9 kW dish/Stirling solar

power system for remote power markets was also developed by Advanced Dish Development System

(Diver, Andraka, Rawlinson, Goldberg, & Thomas, 2001). Davenport et al. worked on two generations of

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a SunDish system at the Salt River Project using solar energy or methane gas collected from a landfill as

fuel. The second generation included improvements to system performance, simplicity of installation,

and reliability of the engine and dish subsystems to record a change from under 20 kW in 1998 to over

23 kW in 2002 at an efficiency of 26% (Davenport, Butler, Taylor, Forristall, Johansson, & Ulrich et al.,

2002).

Solar Powered Stirling Engine Optimization

Mean temperature differential Stirling engine optimization. Tlili, Timoumi, and Nasrallah (2008)

looked at design considerations for determining the optimal configuration for a mean temperature

differential Stirling engine using a target power source of a solar dish/Stirling engine with an average

concentration ratio and a constant heat source temperature of 320°C. The heat exchangers were

designed to have a low pressure-drop and be of high effectiveness. The paper found the optimal swept

volume is 75 cm3 for a frequency of 75 Hz for their engine and there is a definite optimal value of swept

volume ratio that maximizes the power when for a given difference temperature, operating frequency,

and dead volume. For a temperature difference of 300°C, the best operating frequency value is 75 Hz,

although it can be limited to anywhere between 35 and 75 Hz. The porosity of the regenerator can be

manipulated by changing the diameter or length of the wire and plays a significant role in controlling the

pressure drop. The volumes of the heat exchanger should be determined based on the thermal

efficiency of the engine and the pressure drop with the studying finding the optimal heat exchanger

volume to be 165 cm3 with a 0.450 m long tube that is 0.011 m in diameter.

Finite-time thermodynamics optimization. Yaqi, Yaling, and Weiwei (2011) optimized the

maximum power output and corresponding thermal efficiency of the solar powered dish-Stirling heat

engine using finite-time thermodynamics taking into considerations the factors of finite-rate heat

transfer, regenerative heat losses, conductive thermal bridging losses, and finite regeneration processes

time. They found that the maximum power thermal efficiency are effected by the absorber

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temperature, the collector concentrating ratio, and the effectiveness of the regenerator. The theoretical

guidelines presented suggest that the smallest possible heat leak coefficient is the result of a high

efficiency regenerator leading to a higher overall efficiency with the optimum absorber temperature at

1100 K and the optimum collector concentrating ratio at 1300.

Multi-objective solar dish-Stirling engine optimization. Ahmadi, Sayyaadi, Mohammadi, and

Barranco-Jimenez (2013) used finite time thermo-economic multi-objective analysis and NSGA-II

algorithm to optimize the dimensionless thermo-economic objective function, thermal efficiency, and

dimensionless power output for a dish-Stirling system building off the previous research conducted

(Ahmadi et al., 2012; Ahmadi, Hosseinzade, Sayyaadi, Mohammadi, & Kimiaghalam, 2013; Ahmadi,

Mohammadi, Dehghani, & Barranco-Jimenez, 2013). The multi-objective optimization used different

variables: heat source temperature, hot working fluid temperature, temperature ratio, and irreversible

property. They found the dish-Stirling thermal efficiency to be between 35% and 40% while Stirling

engine thermal efficiency was between 40% and 45%.

Research Methodology

Materials

The parts of the Stirling engine were manufactured in the machine shop in the Aerospace and

Mechanical Engineering building at the University of Arizona. The 23 parts constructed for the Stirling

engine were made from a variety of materials as listed in Table 1. The engine part materials were cut

from aluminum, brass, and steel.

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Table 1. Stirling Engine Parts Material List

Part Name Material

Gudgeon Block aluminum rod

Crank Web aluminum rod

Bearing Plate 21 aluminum stock

Bearing Plate 22 aluminum stock

Alcohol Burner Cap brass

Power Cylinder brass

Main Bearing Bushings (2) brass

Flywheel brass casting

Connector Link brass hex stock

Transfer Piston Guide brass hex stock

Cylinder Plate brass stock

Power Connecting Lever brass stock

Lever Connector brass stock

Lever 011 brass stock

Lever 012 brass stock

Power Piston cold rolled steel

Lever Shaft drill rod

Displacer Piston Rod drill rod

Crank Pin drill rod

Crank Web Shaft drill rod

Displacer Cylinder stainless steel

Displacer Piston stainless steel

Base zinc/aluminum casting

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Figure 6. Base Stirling engine model heated by an ethanol flame.

Stirling Engine Parts and Assembly Procedure

Modifications. The parts of the Stirling engine were constructed according to the plans laid out

by Morris (1996) with some modifications. Dimensional changes were made to the displacer cylinder

(3.38” to 6.00”), displacer piston (2.00” to 5.00”), and connecting rod (2.75” to 5.75”) and can be viewed

in Figure 7. This was done in order to accommodate the focal length range of 4.5” to 5” of the parabolic

dish used as a solar collector (Figure 8) and make sure that the sunlight is focused on the cylinder end

that needs to be heated. The base of the model was also modified to be the appropriate size with a 10-

24 screw hole to attach to the Viltrox VX-18 heavy duty tripod that served as a mount and a way to

angle the dish and cylinder towards the sun. Characteristics for future optimization testing may include

observing the changes in efficiency based on the angle of the Stirling engine, dead volumes, different

displacer sizes, and the use of a regenerator along with various regenerator materials.

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Figure 7. Stirling engine model with extended displacer cylinder length.

Figure 8. Front view of the solar Stirling engine system.

Parabolic dish. The main modification is the solar energy collector as the heat source at the

cylinder end. An 18” diameter aluminum parabolic dish was used with a theoretical focal length of 4.5”.

to secure the dish to the engine and tripod, three 1” c-clamps were connected to the rim of the mirror

and nylon rope was used to attach the clamps to the tripod as seen in Figure 9. When testing, welding

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goggles and gloves were necessary to shield the eyes and hands from the ultraviolet (UV) rays reflecting

from the parabolic mirror.

Figure 9. Back view of the solar Stirling engine system.

Measurements and Calculations

Temperature and speed. The temperature (°F) of the cylinder end and the air between the

cooling fins was measured at intervals of 5 seconds over the duration of 300 seconds total using a digital

multimeter with a thermocouple placed at the cylinder end or between the cooling fins. The speed

(revolutions per minute, rpm) of the flywheel was measured at the same intervals and recorded using a

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tachometer focused on a reflective point on the black taped flywheel. Higher revolutions per minute

served as the base level to judge the efficiency of each Stirling engine modification.

Figure 10. Materials (left to right): Neiko tachometer, SainSmart digital multimeter with thermocouple,

and welding goggles.

Power output. The power output of the Stirling engine determines its efficiency. Modifications

were made to the basic Stirling engine design in an attempt to optimize its performance. Calculations for

the power output of the solar Stirling engine were not performed during this study as there was not

enough time to collect sufficient data, however, these are still applicable for the future research to be

completed on the project. The variables used in the calculations are defined in Table 2.

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Table 2. Nomenclature

Variable Definition

α phase angle lead, displacer over power piston (°)

τ working fluid temperature ratio, TC/TH

f engine speed/cycle frequency (rps/Hz/s-1)

kP swept volume ratio, VP/VD

kS dead space volume ratio, VS/VD

kSH hot space dead volume ratio, VSH/VS

kSR regenerator dead volume ratio, VSR/VS

kSC cold space dead volume ratio, VSC/VS

kSDP total dead volume to total volume ratio, VS/(VD+VP)

kST total dead volume to total volume ratio, VS/V1

pm mean cycle pressure (N/m2)

pmax maximum cycle pressure attained (N/m2)

PI engine indicated power (W)

TC cold space working fluid temperature (K)

TH hot space working fluid temperature (K)

VD displacer swept volume (m3)

VP power piston swept volume (m3)

VS dead space volume (m3)

VSH hot space dead volume (m3)

VSR regenerator dead volume (m3)

VSC cold space dead volume (m3)

Wnet net work of the engine (J)

The work for the Stirling engine configurations constructed can be calculated using the Schmidt

formula (Eq. 1) for gamma type engines where the variables A, B, and pm are described by the formulas

Eq. 2, Eq. 3, and Eq. 4, respectively.

Wnet = pm ∗ Vp ∗ π ∗ sinα ∗(1 − τ)

√A + (A2 − B2) (1)

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A = (1 + τ) +4 ∗ kS ∗ τ

1 + τ+ kp (2)

B = √(1 − τ)2 − 2 ∗ (1 − τ) ∗ kP ∗ cosα + kP2 (3)

pm = pmax ∗ √(A − B)/(A + B) (4)

The indicated power output, PI, (Eq. 5) can then be calculated in watts by multiplying the work,

Wnet, found in the Schmidt formula with the engine speed in revolutions per second, or cycle frequency,

f.

PI = Wnet ∗ f (5)

Dead volumes. The total dead volume (Eq. 6) comprises the hot space, regenerator, and cold

space dead volumes and can be expressed in terms of total volume (Eq. 7) or total swept volume (Eq. 8).

This is another characteristic that determines Stirling engine efficiency and will be used in calculations

based on the data collected during the future research.

VS = VSH + VSR + VSC = (kSH + kSR + kSC) ∗ VS

VS = kST ∗ V1 = kST ∗ (VS + VD + VP)

VS = kSDP ∗ (VD + VP)

(6)

(7)

(8)

Results

Measurements were taken without the parabolic dish attached, but instead with a butane torch

to optimize engine performance before changing the heat source. Data was collected at 5 second

intervals for both temperature in degrees Fahrenheit, °F (Figure 11) and speed in revolutions per

minute, rpm (Figure 12) with the heat extinguished after 100 seconds.

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Figure 11. Temperature (°F) at the end of the cylinder or between the cooling fins versus time (s) for the

prototype Stirling engine.

Figure 12. Speed (rpm) for all trials versus time (s) for the prototype Stirling engine.

150

200

250

300

350

400

450

500

550

0 15 30 45 60 75 90 105 120 135 150

tem

pe

ratu

re (

°F)

time (s)

Stirling Engine Temperature Tests

Cylinder Trial 1 Cylinder Trial 2 Cylinder Trial 3

Cooling Fins Trial 4 Cooling Fins Trial 5

0

100

200

300

400

500

600

700

800

0 15 30 45 60 75 90 105 120 135 150

spe

ed

(rp

m)

time (s)

Stirling Engine Speed Tests

Cylinder Trial 1 Cylinder Trial 2 Cylinder Trial 3

Cooling Fins Trial 4 Cooling Fins Trial 5

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Discussion

Summary of Data

The data in the graphs of Figure 11 and Figure 12 represent the measurements taken of the

prototype Stirling engine as the solar powered Stirling engine was completed, however, not yet ready

for testing due to some adjustments in design that are to be made. In Figure 11, the temperatures

between the cooling fins for both trials were consistently between 160°F to 180°F. The temperature

plots for the cylinder trials all have the same downward concave parabolic shape starting and ending

between 300°F and 350°F with a peak between 450°F and 500°F. In the speed trials depicted in Figure

12, the lines all take a similar form, however, trial 1 is an outlier with the peaks and sinks during the first

60 seconds of testing likely due to human error in recording data for the first trial. The four other trials

all show the speed slowly and steadily increasing over time with some variations, and then a sharp drop

in rpm after 105 seconds, which is 5 seconds after the heat source was extinguished. Due to the facts

that there is not much collected data at the moment and that these numbers are from the prototype

model rather than the solar powered Stirling engine leaves little room for commentary on the efficiency

of the engine or the effects of the modifications on optimization. The engine works consistently with a

heat source that is hot enough, and further work on the solar dish modification will allow for the desired

result of a working solar powered Stirling engine.

Solar Dish Findings

The modified design of the Stirling engine was successful in running provided the appropriate

amount of heat, however, further changes could lead to a higher efficiency. Measurements with the

solar dish revealed that the focal point of the parabolic mirror was between 4.5” to 5” resulting in a

135°F average cylinder temperature, which is not sufficient to power the Stirling engine. Research will

continue during the summer to optimize the system. The plan is to accommodate the extra 1” length of

cylinder by adding spacers between the cooling fins and the parabolic mirror so that the end of the

M c H u g h | 25

cylinder is hit directly by the UV radiation focused at that point 4.5” out from the 1.13” diameter center

hole of the dish.

Future Implications

In April 2016, 175 countries signed the United Nations (UN) Paris Climate Agreement back in

agreeing that each nation would develop and submit their own national climate actions that would take

effect in 2020. Twelve of the UN’s 17 Sustainable Development Goals address climate change with the

goal to limit global temperature rise to well below 2 degrees (UN, 2016). Each community can take part

in addressing their individual, unique climate issues and contribute towards the global cause of

mitigating climate change. There is a need to start looking at renewable and alternative energy sources

to protect our environmental future. Arizona is an ideal location to implement solar Stirling engine

technology on a wide scale using the sun to generate electricity in a more efficient manner. Maricopa

Solar maintained Stirling engine units provided by Stirling Energy Systems designed in collaboration with

Sandia National Laboratories. These were in use for several years and produced 1.5 MW of energy at

26% efficiency, which is one of the best solar power options compared to the about 16% efficiency of

parabolic troughs or photovoltaic panels (NREL, 2013).

The production of photovoltaic panels includes critical materials such as indium and other rare

earth materials that are unsustainable sources, and PVs do not allow thermal energy storage like

concentrated solar power so they cannot work beyond the daytime. The U.S. Department of Energy

SunShot Initiative aims to make solar power nationally competitive with other forms of renewable

energy technology without subsidies by 2020. The concentrated solar power section of the SunShot

review meeting program states that their goal is “to innovate and develop next-generation CSP

technologies for low-cost collectors, high-temperature receivers and high-efficiency dry-cooled power

cycles to meet the aggressive technical targets of SunShot” with “up to $55 million over 3 years in 21

M c H u g h | 26

projects at companies, universities and national laboratories” including the University of Arizona

(Pitchumani, 2013).

The World Coal Association (WCA) website states that at our current rates of production we

have enough coal reserves to last us about 110 years, with only 52 years for oil reserves and 54 years for

gas reserves (WCA, 2017). Here in Arizona, the sun is a great choice of renewable energy source as it is

reliable here most of the year. Photovoltaic panels remain the best residential choice for solar power

generation, however, concentrated solar power Stirling engines are the most efficient choice for large

scale power plants and fulfill our need for an alternative energy source in the near future. With the

involvement of the University of Arizona in the Department of Energy’s SunShot Initiative, Tucson has

the opportunity to be a leader in this change and continue its commitment to solar power which earned

it the status as a U.S. Department of Energy Solar America City (City of Tucson, n.d.).

Conclusion

The solar powered Stirling engine has the potential to be an alternative technology that help

paves the road towards sustainable ways of generating power and energy. Underdeveloped, arid regions

of the world could use the Stirling engine to pump clean water for irrigation or air for other types of

agriculture with the additional benefit of the engine being able to serve other mechanical needs.

Increasing interest and awareness of climate change related issues gives the opportunity for a larger

variety of renewable energy technologies to be developed and suit the needs of the local environment.

Here in Arizona, the region is very suitable for the solar powered Stirling engine technology to be used

on a large scale in providing electricity. The Stirling engine constructed for this project was able to run

and with the modifications made to the solar dish, the system as a whole can be put together and solar

power will be used as the heat source instead. Further modifications to the solar powered Stirling

engine can then be made to optimize its performance. Already one of the most efficient forms of solar

M c H u g h | 27

energy conversion, the Stirling engine is an older technology that is being reapplied in ways that

contribute to the growth of sustainable technology.

M c H u g h | 28

References

Ahmadi, M.H., Hosseinzade, H., Sayyaadi, H., Mohammadi, A.H., & Kimiaghalam, F. (2013). Application

of the multi-objective optimization method for designing a powered Stirling heat engine: Design

with maximized power, thermal efficiency and minimized pressure loss. Renewable Energy. 60,

313-322.

Ahmadi, M.H., Mohammadi, A.H., Dehghani, S., & Barranco-Jimenez, M.A. (2013). Multi-objective

thermodynamic-based optimization of output power of Solar Dish-Stirling engine by

implementing an evolutionary algorithm. Energy Conversion and Management. 75, 438-445.

Ahmadi, M.H., Sayyaadi, H., Mohammadi, A.H., & Barranco-Jimenez, M.A. (2013). Thermo-economic

multi-objective optimization of solar dish-Stirling engine by implementing evolutionary

algorithm. Energy Conversion and Management. 73, 370-380.

Ahmed, A., Al-Agami, M., & Al-Garni, M. (1990). Solar powered Stirling engine with a single membrane

dish concentrator. In Proceedings of the First World Renewable Energy Congress (pp. 1202-7).

Ardron, Mitra. Sunvention SunPulse Water – Solar Thermal Pump. 2010. Print.

Audy, C.H., Fischer, M., & Messerschmid, E.W. (1999). Nonsteady behavior of solar dynamic power

systems with Stirling cycle for space stations. Aersp Sci Technol. 1, 49-58.

Beale, W.T., Wood, J.G., Chagnot, B.F. (1980). Stirling engine for developing countries. American

Institute of Aeronautics and Astronautics. 809399, 1971-5.

Bean, J.R., & Diver, R.B. (1992). The CPG 5-kWe dish/Stirling development program (Paper No. 929181).

Proceedings of the IECEC, San Diego.

Bratt, C. (1980). Design characteristics and test results of the United Stirling P40 engine. American

Institute of Aeronautics and Astronautics. 809397, 1964-6.

Childs, W.D., Dabiri, A.E., Al-Hinai, H.A., & Abdullah, H.A. (1999). VARI-RO solar-powered desalting

technology. Desalination. 125, 155-66.

M c H u g h | 29

City of Tucson (n.d.). Alternative and Renewable Energy. City of Tucson. Retrieved from

https://www.tucsonaz.gov/gs/alternative-and-renewable-energy

Daniels, F. (1964). Direct use of the sun’s energy. New Haven: Yale University Press.

Davenport, R.L., Butler, B.L., Taylor, R., Forristall, R., Johansson, S. & Ulrich, J. et al. (2002). Operation of

second generation dish/Stirling power systems. Proceedings of the ASES 2002 Solar Conference,

Reno.

Diver, R., Andraka, C.E., Rawlinson, K.S., Goldberg, V., & Thomas, G. (2001). The advanced dish

development system project. Proceedings of the Solar Forum 2001, technical paper.

Ericsson, J. (1870). Sun power; the solar engine. Contribution to the Centennial Exhibition, Philadelphia.

571-7.

Finkelstein, T. (1960). Generalized thermodynamic analysis of Stirling cycle engines (Paper No. 118A).

SAE International.

Finkelstein, T. (1961). Internally focusing solar power systems (Paper No. 61-WA-297). American Society

of Mechanical Engineers Annual Meeting.

Fletcher, J.C. (1975). U.S. Patent 3972651. Washington, DC: U.S. Patent and Trademark Office.

Gallop, D.R., Mancini, T.R., Christensen, J., & Beninga, K. (1994). The utility scale joint-venture program

(Paper No. AIAA-94-3945-CP). Proceedings of the IECEC, Monterey.

Gurtler, R.W. (1979). U.S. Patent 4173123A. Washington, DC: U.S. Patent and Trademark Office.

Hull, P.G. & Hunt, A.J. (1984). A reciprocating solar-heated engine utilizing direct absorption by small

particles. J Sol Eng Trans ASME. 106, 29-34.

Jordan, R.C., & Ibele, W.E. (1955). Mechanical energy from solar energy. In Proceedings of the World

Symposium on Applied Solar Energy, Phoenix (pp. 81-101).

M c H u g h | 30

Kongtragool, B., & Wongwises, S. (2003). A review of solar-powered Stirling engines and low

temperature differential Stirling engines. Renewable and Sustainable Energy Reviews. 7, 131-

154.

Mancini, T., & Heller, P. (2003). Dish Stirling systems: an overview of development and status. Journal of

Heat Transfer, Trans. ASME. 125, 135-51.

Meijer, R.J. (1958). U.S. Patent 2828601. Washington, DC: U.S. Patent and Trademark Office.

Meijer, R.J. (1987). U.S. Patent 4707990. Washington, DC: U.S. Patent and Trademark Office.

Meijer, R.J. & Godett, T.M. (1987). The base engine for solar Stirling power. Stirling Thermal Motors.

197-213.

Morris, S.J. (1996). Development of the machine shop instruction and the Stirling engine project for

2.670: ME Tools (Master's thesis). Massachusetts Institute of Technology, Cambridge, MA.

NREL. (2013). Concentrating solar power projects: Maricopa solar project. National Renewable Energy

Laboratory. Retrieved from

https://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectID=58

Philip, N.V. (1987). A report of Philip Stirling engine program. Eindhovan, Netherlands.

Pitchumani, R. (2013). SunShot concentrating solar power program update. Sunshot U.S. Department of

Energy Program Review Meeting. Phoenix, AZ.

Reader, G.T., & Hooper, C. (1983). Stirling engines. London: Cambridge University Press.

Rizzo, J.G. (1997). The Stirling engine manual. Somerset: Camden miniature steam services.

Ross, A. (1979). U.S. Patent 4138897. Washington, DC: U.S. Patent and Trademark Office.

Senft, J.R. (2001). Optimum Stirling engine geometry. International Journal of Energy Research. 1, 1087-

101.

Spencer, L.C. (1989). A comprehensive review of small solar-powered heat engines: Part I. A history of

solar-powered devices up to 1950. Solar Energy. 43, 191-6.

M c H u g h | 31

Stirling, R. (1816). Patent No. 4081. Edinburgh, Scotland: Chancery.

Tavakolpour, A.R., Zomorodian, A., & Golneshan, A.A. (2008). Simulation, construction and testing of a

two-cylinder solar Stirling engine powered by a flat-plate solar collector without regenerator.

Renewable Energy. 33, 77-87.

Thombare, D.G., & Verma, S.K. (2006). Technological development in the Stirling cycle engines.

Renewable & Sustainable Energy Reviews. 12, 1-38.

Tlili, I., Timoumi, Y., & Nasrallah, S.B. (2008). Analysis and design consideration of mean temperature

differential Stirling engine for solar application. Renewable Energy. 33, 1911-21.

Trayser, D.A., & Eibling, J.A. (1967). A 50 W portable generator employing a solar-powered Stirling

engine. Solar Energy. 11, 153-9.

United Nations. (2016). Sustainable development goals. United Nations: Sustainable Development.

Retrieved from http://www.un.org/sustainabledevelopment/climatechange/#programme

Urieli, I. (2012). Stirling cycle machine analysis. Ohio University. Retrieved from

https://www.ohio.edu/mechanical/stirling/

Utz, J.A., & Braun, R.A. (1960). Design and initial tests of a Stirling engine for solar energy applications

(Master's thesis). Mechanical Engineering Department, University of Wisconsin.

Walker, G., Kentfield, J., Johnson, E., Fauvel, R., & Srinivasen, V. (1983). Coal-fired Stirling engines for

railway locomotive and stationary applications. Proc Inst Mech Eng. 46, 197.

Walpita, S.H. (1983). Development of the solar receiver for a small Stirling engine (Paper No. ET-83-1).

Special study project, Asian Institute of Technology.

Washom, B. (1984). Parabolic dish Stirling module development and test results (Paper No. 849516).

Proceedings of the IECEC, San Francisco.

WCA. (n.d.). Where is coal found? World Coal Association. Retrieved from

https://www.worldcoal.org/coal/where-coal-found

M c H u g h | 32

Wood, J.G., Chagnot, B.J., & Penswick, L.B. (1980). Design of a low pressure air engine for third world use

(Paper No. 829289). Proceedings of the 17th intersociety energy conversion engineering. 1744-8.

Wu, F., Chen, L., Wu, C., & Sun, F. (1998). Optimum performance of irreversible Stirling engine with

imperfect regeneration. Energy Conversion & Management. 39(8), 727-732.

Yaqi, L., Yaling, H. & Weiwei, W. (2011) Optimization of solar-powered Stirling heat engine with finite-

time thermodynamics. Renewable Energy. 36, 421-427.

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Reflection

Completing this senior capstone project has given me the opportunity to further explore

alternative energy technologies and their efficiency. Constructing the Stirling engine required a lot of

time spent in the machine shop where I was able to hone my skills using the machinery and tools

available there. The research for the literature review allowed me to see the multitude of sustainable

research that has been performed and not yet applied in the real world, which shows that there is room

to grow in terms of efficiency and accessibility of renewable energy technology. My career plans reflect

my chosen focus for my capstone project as I have accepted a graduate student research position at the

University of Texas at Austin in the Civil, Architectural and Environmental Engineering Department

working towards my masters in Sustainable Systems. The focus of my graduate thesis project is on

building energy consumption and reduction along with sustainable building automation systems.

renewable energy technology such as the solar powered Stirling engine is a large part of that topic, and

completing this project gave me background and insight into potential paths to take the project.

Emphasizing the sustainable aspects of the solar powered Stirling engine I constructed along with the

research literature I read through would be a way to describe my capstone project to a graduate school

program. It is possible that the Stirling engine technology could become a greater portion of my

graduate thesis project depending on its applications to the building energy problems being addressed.

Overall, it has been a great experience to personally construct a solar powered Stirling engine and learn

more about alternative sustainable methods that could be the way of the future.