Chapter 1: INTRODUCTION

1.1 Project background

This assignment is focus on designing and building a Stirling engine water proof model. This

project focus on using Carnot cycle thus help student have a better understanding on how the

Carnot cycle work.

1.2 Problem statement

To determine whether the student are able to create a working Stirling engine. On the final

testing day, student is required to show their product to the lecture to determine the success of

the project.

1.3 Research objectives

The research objectives of this project problem are for us as a student to:

1. Complete a hands-on experience by working in group to design, build and test a Stirling

engine.

2. Demonstrate the student understanding of the assumptions they choose design model

for Stirling engine with regard of heat-exchange process that allows near-ideal

efficiency in conversion of heat into mechanical movement by following the Carnot

cycle principle.

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1.4 Project scope

The scope of the project are to study about design, build and test a water proof model based

on objective to test the capability of our Stirling engine model to work. The project also

meant to deliver us the understanding of the concept of external combustion engine and how

the simple temperature phenomena can lead into power generation potential. These studies

are also for new graduates especially to have hands-on experience by working in group and

demonstrate our understanding of the assumptions of our chosen design model for Stirling

engine wit according to Carnot cycle principle.

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Chapter 2: THEORY

2.1 Introduction

A Stirling engine is a heat engine operating by cyclic compression and expansion of air or

other gas, the working fluid, at different temperature levels such that there is a net conversion

of heat energy to mechanical work. In easy word, Stirling engine is some kind of closed

cycle heat engine. This means that the Stirling engine works by converting heat into

mechanical output, and the fluid that does the mechanical work, called the working fluid, is

normally enclosed within the engine and is not mixed with any other material.

Basically, there are two major types of Stirling engines that are distinguished by the way they

move the air between the hot and cold sides of the cylinder. One of it is the two

piston alpha type design is that has pistons in independent cylinders, and gas is driven

between the hot and cold spaces. The other type of Stirling engine is a displacement type

Stirling engines, known as beta and gamma types, use an insulated mechanical displacer to

push the working gas between the hot and cold sides of the cylinder. The displacer is large

enough to insulate the hot and cold sides of the cylinder thermally and to displace a large

quantity of gas. It must have enough of a gap between the displacer and the cylinder wall to

allow gas to flow around the displacer easily.

But in our project, we constructed the beta type Stirling engine.

2.2 Beta Stirling Engine

The basic information of a beta Stirling is it has a single power piston arranged within the

same cylinder on the same shaft as a displacer piston. Its displacer piston is a loose fit and

does not extract any power from the expanding gas but only serves to shuttle the working gas

from the hot heat exchanger to the cold heat exchanger. When the working gas is pushed to

the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the

cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by

a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha

type, the beta type avoids the technical problems of hot moving seals. So, we can say that the

beta Stirling engine is much more practical than the alpha type.

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2.3 Basic component

2.3.1 A fixed mass of gas

Known as the working fluid which is normally sealed inside the engine. Ideally the gas

should have low heat capacity so it expands a lot in volume when heated. In this project, we

used air as the fixed mass or the working fluid.

2.3.2 Heat source

The source can be almost anything, since it does not come into direct contact with the

working fluid or the internal parts of the engine, so we are using the candle as the heat source.

It is really helpful and suitable for our mini Stirling engine model. Plus, it is also cheap and

easy to find.

2.3.3 A heater to transfer the heat from the heat source to the working fluid

The heater needs to be effective at transferring heat to the working fluid but at the same time

it should not introduce too much pumping loss (friction) to the working fluid. The heater also

needs to withstand the high temperature of the heat source without deforming.

2.3.4 A regenerator

The regenerator is a device that sits between the cold and hot places of the Stirling engine so

that the working fluid moves through it in both directions. The regenerator acts as a

temporary storage of heat, and its purpose is to help retain the heat within the engine instead

of letting the heat dissipate in the colder parts, thereby improving the engine’s thermal

efficiency. Ideally, the regenerator should take up as little volume as possible, introduce

almost no pumping friction, has very high heat storage capacity, and has high thermal

conductivity perpendicular (but not parallel) to the fluid flow. A cooler (ice) is to cool the

working fluid in the cold end of the engine, show in the figure that an error.

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2.3.5 Displacer piston

When there is temperature dissimilarity between upper displacer space and lower displacer

space, the engine pressure is transformed by the movement of the displacer. The pressure

increases when the displacer is located in the upper part of the cylinder and as we know, most

of the air is on the hot lower side. The pressure decreases when the displacer is moved to the

lower part of the cylinder. The displacer only moves the air back and forth from the hot side

to the cold side. It does not run the crankshaft and the engine. In other words, the connecting

rod to the displacer could be a string in this engine and it would still work.

2.4 Basic process

2.4.1 Heating

Let's start from top dead centre of the hot piston. The hot piston moves to the upper part of

the cylinder and the cold piston moves to the lower part of the cylinder during the first 90

degrees of revolution. The working air is moved from the cold space to the hot space. And

the pressure in the engine is increased.

2.4.2 Expansion

During the next 90 degrees of revolution, the two pistons both move the lower part accepting

the air pressure. The engine gets its power during this portion of its cycle.

2.4.3 Cooling

The crankshaft revolves by power stored in the flywheel for the next 90 degrees. The hot

piston moves to the lower part and the cold piston moves to the upper part. The air is moved

from the hot space to the cold space. And the pressure in the engine is decreased.

2.4.4 Contraction

The two pistons are moved to upper part by the contraction of the air during the next 90

degrees. The engine also gets power during this portion of its cycle. The two piston type

Stirling engine then repeats this cycle.

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Chapter 3: METHODOLOGY

3.1 Materials

Aluminium can

Plastic cardboard

Plastic bottle

Balloon

Bolt and nut

Ice-cream stick

Plasticine

Wire

Disc

3.2 Apparatus

Scissor and knife

Duct tape

Super glue

Candle

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3.3 Procedure

The Stirling engine created for this project is environmental friendly. Thus most of the

material use in this project is made out of recycle material.

3.3.1 Body

The body of the Stirling engine is made out of aluminium can. The top portion of the can is

cut off so that the piston can easily insert in the aluminium can. To cover up the hole in the

top portion we use a cut out of plastic cardboard. We calculate the size so that it will fit

exactly at the top of the aluminium can.

Figure 1

3.3.2 Piston 1

The piston is made by cutting out the plastic cardboard and places it inside the Stirling

engine. The cut out is offset about 1mm smaller than the aluminium can to reduce the friction

between the wall of the aluminium can and the piston. It is also to create a pressure difference

between the cold compartment and the hot compartment. The different pressure causes the

first piston to move upwards.

Figure 2

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3.3.3 Piston 2

First, the top part of a bottle is cut out. Then a balloon is cut into size and a bolt is pierce in

the balloon which is secure with a nut and some super glue. This will act as our second

piston. When the air is push by the first piston, it will cause the balloon to expand thus

pushing the shaft of the piston.

Figure 3

3.3.4 Weight

A weight has been placed at one end of the Stirling engine to provide the Stirling engine with

inertia so that it can continue moving. For this component we use a disc which the middle

hole has been cover by a piece of cardboard. It is critical to ensure the disc is placed in the

center so that the center of gravity is correct.

Figure 4

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3.3.5 Ice holder

To create a colder compartment at the top of the aluminium can we create an ice holder. It is

made by cutting a bottle where the top part and the bottom part is removed. The smaller hole

is make exactly the same size with the outer side of the aluminium can. Plasticine is used to

seal the hole between the cone shape bottle and the aluminium can.

Figure 5

3.3.6 Drive shaft

A piece of wire is bend with the correct size and specification so that the piston can move

better and freely. The wire is connect with the connecting shaft from both piston and fixed in

place by using ice-cream stick.

Figure 6

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3.3.7 Assembly

Two holes are punch at the cover of the aluminium can. The first hole is made exactly at the

center of plastic cardboard. This hole is make exactly the same size with the piston shaft to

reduce the pressure loss from the hole to the surrounding. The next hole is make lager in size

at the side part of the cover. This hole is cover by the second piston. The hole allows the air

to move freely from the can into the piston.

Piston 1 is placed inside the aluminium can. A wire is use to connect the piston to the drive

shaft. A second piece of wire is also use to connect piston 2 to the shaft. The entire air

opening is seal off to ensure we have a closed system.

Figure 7

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Chapter 4: RESULTS

4.1 Result

The result for this Stirling engine was failed. The piston failed to expand. This is because, the

mass of the piston was too heavy, and the size is big, got friction and not flexible volume.

Besides that, it is because of not enough heat source and cooling system.

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Chapter 5: DISCUSSIONS.

5.1 Problem encounter during the making process of Stirling engine

In this project our group have fail to make a working Stirling engine. This is cause by several

problem encounters during the process of making the Stirling which will be discuss later.

5.1.1 Volume

First of all the volume inside the body of the Stirling engine is too huge. Increase in volume

means more heat energy is needed to supply enough energy to the system. This causes not

enough pressure difference between the top part of the Stirling engine and the lower part of

the Stirling engine.

To overcome this problem student must first decrease the body size of the Stirling engine. By

doing so they decrease the volume in the Stirling engine. Then student must make Piston 1 fit

almost the whole inside of the body. The piston will fill up most of the space inside the body

of the Stirling engine thus reduce the volume inside the engine even more. Small volume

mean less energy require to move the piston.

5.1.2 Huge Payload

First of all to ensure the Stirling can work perfectly student needs a load to supply inertia to

the engine. The resources in the internet suggest the usage of disc since the disc is round and

will give equal amount of inertia to all direction. This will help make our Stirling engine

more stable and not shake.

However when using this method students are unable to discover to centre of the disc thus

making the distribution of inertia unbalance. The drive shaft which is not straight cause

friction between the ice-cream stick and the drive shaft need a lot of energy to overcome.

Friction from the piston and the wall of the body also need a certain amount of energy to

overcome. Due to this three reason, the total weight that needs to be overcome increase in a

huge amount however the energy produce is just too small to push the weight of the whole

system.

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To ensure the success of our project student must first try and reduce the total weight of the

system. Student must first ensure that the piston is loosely fit inside the body of the engine.

Next the drive shaft must make out of new unbend wire so that they can have a smooth and

straight wire for our drive shaft. Lastly student must ensure to determine the true centre of the

disc so that the inertia acting on the system will be in equilibrium.

5.1.3 Leakage of Pressure

Student need sufficient amount of pressure so that the Stirling engine can work properly.

However the pressure produce during the heating process has escape through the opening in

the body of the engine.

The hole at where the connecting shaft comes out is one of the examples where the air

pressure can escape. Although the hole is small, it brings great effect towards whether the

experiment is a success or a failure. Other than that the seal on the cover of the body and the

main body might also have a leakage. The balloon might also been puncture and the air

pressure leaked from there. This entire situation will contribute a huge amount of pressure

lost and thus reduce the energy within the system.

Student must ensure all of the opening is completely seal off and the opening at the

connecting shaft is make as small as possible to reduce the pressure loss. Student can use

soap water test to see if there is any hole which we did not cover completely.

5.1.4 Unsuitable material

The material use for making the Stirling engine is unsuitable. First of all is the body of the

Stirling engine. Aluminium is a good conductor of heat. That mean the heat from the bottom

of the can is easily transferred to the top of the can this causes no temperature difference in

the body of the Stirling engine. As we all know the principle which allows the engine to work

is having a temperature difference. If there is no temperature difference, then the Stirling

engine will not work.

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5.1.5 Temperature Difference

Although an ice compartment is build for our engine, student cannot put a lot of ice in it since

it might block the movement of the connecting shaft.

The ice might be too few to cool down the top part of the Stirling engine thus create too few

temperature difference. The heat transfer from the bottom might melt the ice to fast before

any changes can be observed.

When heating of the body, there is loss of heat energy to the surrounding. The condition at

UMP Pekan is windy. It blows the fire from the candle thus reduce the heat transfer to the

aluminium can. We should make wind breaker to divert the wind and reduce the heat loss to

the surrounding.

5.1.6 Regenerator

Students are unable to build a suitable regenerator for the Striling engine. This cause the

temperature from the hot end might seep into the cold compartment. Thus reduce the

efficiency of our product.

To ensure the product can work perfectly. Student must first find a way to separate the hot

compartment and the cold compartment since temperature difference will give the pressure to

move the engine.

5.1.7 Safety Precaution

It is very important that student follow certain safety precaution when conducting this

experiment. First of all student should be very careful when burning candle to supply heat to

the sterling engine. Student should use suitable stand to hold both the candle and the Stirling

engine in place. Next we are there is high pressure in the body of the Stirling engine. The

high pressure in the Stirling engine might cause the engine to explode and cause injury to

those standing nearby. Thus it is recommended that everyone should stand 15m away from

the Stirling engine so ensure the safety of bystander.

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5.2 Application in daily life

5.2.1 Application of sterling engine in our society

First of all it is a basic knowledge that Stirling engine is a very efficient system since the

principle behind moving it is through the temperature difference at two different

compartment which cause pressure difference and thus supply energy to the system. The heat

energy can be obtained from any source from the sun, from combustion, geothermal and even

the waste heat from conventional engine.

This engine is far more efficient and environment friendly if compare with gasoline engine.

There is no need to intake gaseous in every cycle thus there is no air pollution. It also does

not require to burn fossil fuel which is one of the major pollution in the world.

Although Stirling engine has many good point there is not much development in this

technology until recent year. Nowadays Stirling plays a major role in supply electricity in

space exploration shuttle since there is limited air for combustion in space.

Stirling engine can also work the other way around. When work is place into the system from

motor we can see that this engine can become an efficient heat pump or refrigerator. When

work is supply into the system one end we start to absorb heat and the other end will start

expelled heat. If you design the machine correctly, the cold end will get extremely cold. In

fact, Stirling coolers have been made that will cool below 10 degrees Kelvin. Micro Stirling

coolers have been produced in large numbers for cooling infrared chips down to 80 degrees

Kelvin for use in night vision devices.

5.2.2 Modern Stirling Engine Development

Today, there are many companies developing Stirling devices for niche markets, such as

cogeneration units and power generation using alternative fuels. Stirling engines have come a

long way from the large and heavy engines of the 19th century, thanks to advancements in

materials, manufacturing processes, and theory and analysis methods. This page contains a

handful of links to some of these companies. Click on the images to learn more about these

organizations and the engines they produce. All images and information related to these

devices are property of and are assumed to be copyrighted by their respective owners.

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STM Corporation SOLO Kleinmotoren GmbH

Stirling Energy Systems, Inc. Kockums Sweden.

Sunpower, Inc. Infinia Corporation

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Tamin Enterprises NASA Glenn Research Center

5.3 Calculation for Better Understanding

5.3.1 Propagation of heat in the air.

The equation describing the propagation of heat in a substance can be deduced from three

simple and almost obvious experimental observations. We will make the hypothesis that the

thermal conductivity and the specific heat of materials are constant. It is not the case, but it is

not very important for us: what interests us is to understand the physical mechanisms.

The first observation is that in any point of a substance, the heat flows from hot to cold. The

quantity of heat flowing per second (i.e. its current) is proportional to two things: the thermal

conductivity of the substance and the slope with which the temperature decreases at the

observed point.

δ Q = - k.S.(δ T(x,t)/δ x).δ t -------(1a)

i.e. that the quantity of heat δ Q (joule) flowing for a short time δ t (en sec) through an area S

(in square metres), is proportional to the temperature drop δ T (Kelvin degrees) found at the

location x, at time t for a short distance δ x (en m) taken in the direction of flow. The ratio δ

T(x,t)/δ x is not other than the partial derivative of T with respect to the variable x, i.e. its

slope. The proportionality factor K is the thermal conductivity of the substance (i.e. its ability

to conduct heat) and the minus sign indicates that the flow is in line with the temperature

drop.

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If one considers a small volume of tube or wire, section S and thickness Δ x, the net quantity

of heat which penetrates is equal to the one which enters at the point x, less the one which

leaves at (x + Δ x). One can write by taking account of the signs:

δ Q = k.S.{δ T(x+ Δ x,t)/δ x - δ T(x,t)/δ x}.δ t -----(1b)

The second experimental observation is that the temperature of a volume containing a

substance increases when a quantity of heat penetrates there. This increase in temperature is,

of course, proportional to the quantity of heat received and inversely proportional to the

volume, to the density of the substance which is there, and to its specific heat.

δ Q = ρ .c.δ T.S.Δ x -----(2)

i.e. that the quantity of heat δ Q (joule) which penetrated in small volume S.Δ x (m3), caused

an temperature increase δ T (K). The coefficients of proportionality ρ (the Greek letter rho)

and c are respectively the density of the substance (kg/m3) and its specific heat (J/kg/K). The

latter expresses the quantity of heat which it is necessary to raise of one degree the

temperature of one kg of the substance. For the gases which are compressible, this quantity is

different according to whether the operation is done with constant volume or constant

pressure. Below, we used the values corresponding to constant volume.

The third experimental observation is that no energy is created from nothing. The result is a

principle of continuity: the heat which penetrates in an element of volume (according to the

first observation) must necessarily correspond to that which makes increase its temperature

(according to the second observation). In other words, in the absence of a source of heat in

the volume, two afore-said heat quantities must be equal otherwise there would be creation of

spontaneous heat, which is not possible.

By equalizing the terms δ Q of the equations (1b) and (2) above:

ρ .c.δ T.S.Δ x = k.S.{δ T(x+Δ x,t)/δ x - δ T(x,t)/δ x}.δ t -----(3a)

By rearranging this equation by dividing it by δ t, by (ρ .c), by S and by Δ x:

δ T/δ t = (k/(ρ .c)).{δ T(x+Δ x,t)/δ x - δ T(x,t)/δ x}/Δ x -----(3b)

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This equation says that the temperature variation δ T (degrees) during the short period of time

δ t (seconds) i.e. the speed with which the temperature varies is proportional to the variation

of the slope of the temperature (δ T/δ x) on the distance Δ x. The coefficient of

proportionality is k/ρ .c. If Δ x approach zéro, the expression{δ T(x+Δ x,t) /δ x - δ T(x,t)/δ

x}/Δ x becomes the second partial derivative of T compared to x which is written δ 2T/δ x2.

Finally, the equation (3b) becomes:

δ T/δ t = (k/(ρ .c)).(δ ²T/δ x²) (3c)

which is the partial differential equation of heat.

Table 1

With this equation, it is possible to calculate the temperature profile, according to time, in a

tube filled with gas and finished at both ends with a hot source and a cold source. Its

resolution is not obvious. We use the famous harmonic series of Fourier. Above, you can see

the result with a hot source at 800 degrees K on the left of the tube (x = 0). Initially all the gas

is 300 degrees K.

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The equation (3c) indicates that the speed δT/δ t with which the temperature varies in a point,

is proportional to “the constant” k/(ρ .c) of the gas used. And it is there that hydrogen and

helium show a superiority compared to the air or nitrogen. In what follows, k is expressed in

watt/meter/degree K, ρ in kg/m3 and c in joule/kg/degree K.

For air : k/(ρ .c) = 0,025 / (1,29 x 718) = 0,000027 m²/sec).

For helium : k/(ρ .c) = 0,14 / (0,164 x 3116) = 0,00027 m²/sec (10 times more than air).

For hydrogèn : k/(ρ .c) = 0,18 / (0,083 x 10183) = 0,00021 m²/sec (8 times more than air).

For nitogen : k/(ρ .c) = 0,026 / (1,15 x 743) = 0,00003 m²/sec (almost like air).

Comparison with a metal:

For copper: k/(ρ .c) = 401/(8900 x 386) = 0,00012 m²/sec (4,4 times more than air).

For steel: k/(ρ .c) = 80,2/(7840 x 450) = 0,0000227 m²/sec (a little less than the air).

More quickly the heat diffuses in the gas, more easily we will be able to make run the engine

with a high speed and with a great power. When we solve numerically the equation (3c) (see

the graph), we are surprised to note that the speed of diffusion falls quickly less than 3

mm/sec! This is more than 100,000 times slower than the speed of sound or pressure. This is

really not fast. That shows that, in a Stirling engine, the totality of gas to be heated or cooled

must be in very intimate contact with the exchangers. When we design a Stirling engine, to

get a good efficiency it is necessary to take account this point.

If the engine does not run too quickly and if the exchangers are effective, it is not necessary

to use hydrogen or helium. In this case, the only way to increase the power of an engine

without changing its configuration or its initial velocity, is to increase the internal pressure of

gas. A warning statement is essential here for those which would like to test this technique on

a model. The use of air at high pressure into a Stirling engine can cause an explosion of

vapours of the lubricating oil by diesel effect and the destruction of the engine. Such an

explosion had caused the death of seasoned experimenters, for example in Philips Company.

Choose low pressure when you use air, or an inert gas such as nitrogen or helium if you want

to use high pressures.

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Finally, we must still remember that the speed of propagation of heat in the gas is not the

only factor for the efficiency and speed of a Stirling engine. There is also the transfer of heat

between the exchangers and the gas. The speed of this transfer is roughly proportional to the

difference in temperature and to the surface of the heat exchanger. The theory is highly

complex, but in practice we see that the heat exchange is inversely proportional to the density

of gas. We can still see that hydrogen and helium have a clear advantage over air or nitrogen.

5.3.2 Basic principles of thermodynamics.

To understand the operating principle of the Stirling engine, it is not necessary to know many

things. It is considered that the gas used (air, hydrogen, helium, nitrogen...) is a “perfect” gas,

i.e. that it obeys the following law: for a mass of gas given and at constant temperature, the

product of the pressure of gas by its volume remains constant. It is Mariotte's law, we can

write it like that:

PV = constant

where P represents the pressure of gas and V its volume.

If the temperature of gas is introduced, this law becomes:

PV = nRT

Where P represents the pressure of gas, V its volume, n the number of gram molecule (or the

quantity of gas)), R the universal gas constant (R = 8,314 472 J / K mol) et T the température

of the gas (expressed in Kelvin: T = t + 273, if t is the temperature expressed in Celsius

degrees).

According to the good old principle: "nothing is lost, nothing is created, and everything is

transformed" we can approach the energy exchanges during a cycle of Stirling: any loss of

calorific energy during a cycle is equal to the recovered mechanical energy during this same

cycle.

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Figure 8

On the diagram above, we see that we provide in calorific energy: Qexp + Qheat

However, we recover: Qcool + Qcomp. About the mechanical energy, we recover Wexp but

we provide Wcomp. The overall balance becomes, by stipulating that the heat energy lost was

fully transformed into mechanical energy:

Qexp + Qheat - Qcool - Qcomp = Wexp - Wcomp

This leads us to speak about mechanical efficiency: it is the ratio of recovered mechanical

energy (the engine goal, in fact) to the heat energy that we must provide:

Efficiency = ( Wexp - Wcomp ) / (Qexp + Qheat )

NB: as we can see it in the page “the regenerator”, it is not necessary to provide Qheat if a

regenerator is installed. Indeed, at this time there, we recover Qcool. If we refer to the page

“the principles”, we are able to show that the efficiency may be expressed according to the

temperatures (expressed in Kelvin) of the heat source and of the cold source, according to the

following formula:

Efficiency = 1 - Tm / TM

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5.3.3 Kinematics in a few equations.

Figure 9

We assume, first, that the movement of moving parts of the engine are the consequence of the

uniform rotation (ω = constant) of a motor shaft from 0 ° to 360 ° at each cycle. On the

diagram opposite, you can see the representation of a slider-crank mechanism.

By supposing λ small, when the covered angle is φ, the value of d is:

d = r (1-cosφ) + 0,5λ r sin2 φ

Where λ = r/L

When we know the section of the piston S, it is easy to determine the volume of gas V above

the piston at each moment, for a given φ.

V = d S

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Figure 10

When we have several pistons (alpha engine) or a piston and a displacer (beta and gamma

engines), it is advisable to take into account the phase shift dφ between the two. The above

equation becomes, for the second element:

d2 = r2 [1-cos(φ-dφ)] + 0,5λ2r2 sin2(φ-dφ)

where λ2 = r2/L2

In the same way that above, we obtain the value of instantaneous volume:

V2 = d2 S2

5.3.4 How calculate the engine.

4.1. Join together your knowledge in kinematics and thermodynamics:

If you combine your knowledge in thermodynamics and those in kinematics, you can

calculate your engine. By setting the maximum and minimum temperatures, the pressure in

the engine can be calculated for each value of rotation of the main shaft.

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Figure 11

There are several volumes to consider:

- a volume of expansion (variable).

- a volume of cooling (constant).

- a volume of regeneration of heat (constant).

- a volume of reheating (constant).

- a volume of compression (variable).

This is true whatever the type of engine, even if the diagram opposite seems show, rightly, an

alpha engine.

According to the engines, the expression of volumes of compression and expansion are not

the same.

These volumes depend on the input variable, which is the angle of rotation φ.

In the table below, for three types of engine, we have collected the expressions of the

volumes of expansion and of the volumes of compression:

Table 2

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Then, for each volume, it is necessary to apply the following relationship that adds the

various gas masses (n is the number of gram molecules in the engine)

n = Σ PVi / RTi

In this expression, i takes the following values:

- i = e for the volume of expansion, Ti = TM

- i = cool for the volume of cooling, Ti = Tm

- i = reg for the volume of the regenerator, Ti = 1/2 ( Tm + TM )

- i = heat for the volume of reheating, Ti = TM

- i = c for the volume of compression,, Ti = Tm

It should be noted that we consider that the pressure is uniform throughout the engine at any

moment.

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Chapter 6: SUMMARY, CONCLUSIONS & RECOMMENDATIONS

6.1 SUMMARY

The purpose of this project is to design, build and test a Stirling engine model with an

objective, to demonstrate the Stirling engine process which include compression and

expansion process. The goal of this project is to demonstrate understanding of the

assumptions and limitations of our design model for model performance according to the

Carnot cycle principle.

Based on some discussion among the team members, we have come out with the best

design model. All the material that was used was suggested by all team members as we are all

looking for the high quality and suitable materials.

During the test day, we prepared our model and test weather our Stirling engine can

run or not. But, unfortunately, our Stirling engine cannot run.

6.2 CONCLUSION

As the conclusion, in order to produce a Stirling engine which is functional, we need to apply

the theory of thermodynamics to the process. But there still got some problem that we can’t

solve due to the limitation of materials and sources that we got. As results, we failed to

operate our group Stirling engine. We strongly believe that we manage to produce a

functional Stirling engine if we got extra time to solve that problem.

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6.3 RECOMMENDATIONS

(i) Use large heat source that can give a higher temperature while cooling the other side.

But this will only work up until a critical temperature because of the materials we

have used.

(ii) Ensure that there is as small as possible heat-leaking, which can be assured by using

the right materials.

(iii) Use a much more practical material to design this Stirling engine so that it can

work more efficient.

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REFERENCES

FLUID MECHANICS, Fundamentals and Applications By Yunus A. Cengel and John M.

Cimbala

Retrieve from http://www.animatedengines.com/stirling.shtml

Retrieve from http://www.stirlingengine.com/

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