Senior Design 1 (ME-498)

(Stirling Engine)

Supervisors: Dr. Waqar Ahmed KhanDr. Mohammad Nadeem khan

Prepared by

students: ID

1- Abdulrahman Abdullah Alaniz 341101778

2- Khaled Abdullah Alawlah 341100699

3- Abdulaziz Houran Alaniz 341101426

2017/2018

1. Introduction

1.1 What Is A Stirling Engine._?

The simplified engine uses two

cylinders. An external heats one cylinder source and the other is cooled by an

external cooling source. The gas chambers of the two cylinders are connected,

and the pistons are connected to each other mechanically by a linkage, that

determines how they will move in relation to one

Another.

ALPHA-TYPE STIRLING ENGINE

Beta type Stirling Engine

Gamma type Stirling Engine

Processes of compression, heating, expansion, and

cooling (See Figure 2-I

Figure 2-I Processes of compression, heating, expansion.

How an automobile internal combustion engine works. Shows Figure 2-2

In this engine, a gas-air mixture is compressed using work stored

in the mechanical flywheel from a previous cycle. Then the gas mixture is

heated by igniting it and allowing it to burn. The higher-pressure gas mixture

now is expanded which does more work than was required for the compression and

results in network output.

The working gas is compressed, and

then it passes through a steady-flow regenerative heat exchanger to

exchange heat with the hot expanded gases. More heat is added in the gas

heater. The hot compressed gas is expanded which generates more energy than i,

required by the compressor and creates network. To complete the cycle, the

expanded gas is cooled first by the steady flow regenerative heat exchanger and

then the additional cooling to the heat sink.

In the first example (Figure 2-2),

the processes occur essentially

In one place, one after the other

in time. In the second example (Figure 2-3), these four processes

all occur simultaneously in different parts of the machine. In the Stirling

machine, the processes occur sequentially but partially overlapping in time. Also,

the processes occur in different parts of the machine but the boundaries are

blurred. One of the problems vanish has delayed the realization of the

potential of this kind of thermal machine is the difficulty in calculating with

any real degree of confidence the complex processes which go on inside of

a practical Stirling engine.

A heat engine is a Stirling engine

for the purpose of this project when:

1. The working fluid is contained in

one body at nearly a common

Pressure at each instant during the

cycle.

2. The working fluid is manipulated so that

it is generally compressed in the colder portion of the engine and expanded generally

in the hot portion of the engine.

3. Transfer of the compressed fluid

from the cold to the hot portion of the engine is done by manipulating_ the

fluid boundaries without valves or real pumps. Transfer of the expanded hot

fluid back to the cold portion of the engine is done the same way.

4. A reversing flow regenerator (regenerative

heat exchanger) may be used to increase efficiency.

The general process shown in Figure

2-I converts heat into mechanical

energy, The reverse of this process

can take place in which mechanical energy is converted into heat pumping. The

Stirling engine is potentially a better cycle than other cycles because it has

the potential for higher efficiency, low noise and no pollution,

Figure 2-4 shows a generalized

Stirling engine machine as described above.

That is, a hot and a cold gas space

is connected by a gas heater and cooler and regenerator. As the process

proceeds to produce power, the working fluid is compressed in the cold space,

transferred as a compressed fluid into the hot space where it is expanded

again, and then transferred back again to the co!_ space, Net work is generated

during each cycle equal to the area of Lhe enclosed curve.

Figure 2-4 PV Diagrame

1.2 Major Types of Stirling

Engines

1-ALPHA-TYPE

2-

BETA-TYPE

3- GAMMA-TYPE

Figure 2-5 shows the various design areas that must be addressed

before a particular kind of Stirling engine emerges. First some type of

external heat source must be determined. Heat must then be transferred through

a solid into a working fluid. There must be a means of cycling this fluid

between the hot and cold portion of the engine and of compressing and expanding

it. A regenerator is needed to improve effi_iency, Power control is obviously

needed as are seals to separate the working gas from the environment. Expansion

and compression of the gas creates net indicated power which must be transformed

by some type of linkage to create useful power. Also the waste heat from the

engine must be rejected to a suitable sin

SEALS

HEAT

SOURCE

SOLID-GAS

HEAT TRANSFER

FLUID

TRANSPORT

REGZNERATOR

POWER

I

TAKEOFF

GAHSE-SAOTLID I

TRANSFER

USEFUL POWER

HEAT SINK

WORKING

FLUID

ENGINE

CONTROL

Stirling Engine Design Option Block Diagram Figure 2-5.

Uses two pistons (See Figures 2-4 and 2-6). These pistons mutually compress

the working gas in the cold space, move it to the hot space where it is expanded

and then move it back. There is a regenerator and a heater and cooler in series

with the hot and cold gas spaces. The other two arrangements use a piston and

displacer. The piston does the compressing and expanding, and the displacer

does the gas transfer from hot to cold space. The displacer arrangement with

the displacer and the power piston in line is called the betaarrangement, and the piston offset from the displacer, to allow a simpler mechanical

arrangement, is called the gamma-arrangement. However, all large size Stirling

engines being considered for automotive applications employ what is variously called the Siemens, Rinia or double-acting

arrangement..

By a heater, regenerator and cooler, as in the alpha-type of Figure

2-6. In the Siemens arrangement, there are 4 alpha-arrangement working spaces

with each piston double-acting, thus the name. This arrangement has fewer parts

than any of the others and is, therefore, favored for larger automotive scale

machines.

Figure 2-9 shows an implementation of the Siemens arrangement used

by United Sterling. United Stirling places 4 cylinders parallel to each other

in a square. The heater tubes are in a ring fired by one burner. The

regenerators and coolers are in between but outside the cylinders. Two pistons

are driven by one crankshaft and the other gives two pistons. These two crankshafts

are geared to a single drive shaft. One end of the drive shaft is used for auxiliaries

and one for the main output power

Figure 2-6. Main Types of Stirling Engine Arrangements.

Figure 2-7. A Riina, Siemens or Double-Acting Arrangement

1.3 Overview of Report

The main objective of this

project is to design and fabricate Stirling engine, particularly to generate

electricity.

To this end in Section 3,

two engines have performance data and all pertinent dimensions given (fully

described). In Section 4 automotive scale engines, for which only some

information is available, are presented. Section 5 is the heart of the report.

All design methods are reviewed. A full list of references on Stirling engines

to April 1980 is given in Section 7. Sections 8 and 9 are personal and

corporate author indices to the references, which are arranged according to

year of publication. Section 10 is a directory of people and companies active

in Stirling engines. Appendix A gives all the property values for

the materials most commonly used in Stirling engine design. The units

employed are international units because of the worldwide character of

Stirling engine development. Appendix B gives the nomenclature for the body of

the report. The nomenclature was changed from the first edition to fit almost

all computers. Appendices C, D

And E contain three original

computer programs. Appendix F presents a discussion of non-automotive

present and future applications of Stirling engines.

2. Gamma Type Stirling Engines

Gamma type

engines have a displacer and power piston, similar to Beta machines, however in

different cylinders. This allows a convenient complete separation between the

heat exchangers associated with the displacer cylinder and the compression and

expansion workspace associated with the piston. Thus, they tend to have

somewhat larger dead (or unwept) volumes than either the Alpha or the Beta

engines.

Figer 2-9 overview of stirling engine.

There are four stages for gamma type:

1-Heating :

2-Expansion

3-Cooling

4-Compression

Pv diagram of gamma:

4. Stirling Engine Analysis

The Schmidt theory is one of the

isothermal calculation methods for Stirling engines. It is the most

Simple method and very useful during

Stirling engine development.

This theory is based on the

isothermal expansion and compression of an ideal gas.

2. ASSUMPTION OF SCHMIDT THEORY

The performance of the engine can be

calculated using a P-V diagram. The volume in the engine is

Easily calculated by using the

internal geometry. When the volume, mass of the working gas and the

Temperature is decided, the pressure

is calculated using an ideal gas method as shown in equation

(1).

pv =mRT

The engine pressure can be

calculated under following assumptions:

(a) There is no pressure loss in the

heat exchangers and there are no internal pressure differences.

(b) The expansion process and the

compression process changes isothermal.

(c) Conditions of the working gas is

changed as an ideal gas.

(d) There is a perfect regeneration.

(e) The expansion dead space maintains

the expansion gas temperature – TE, the compression dead

Space

Maintains the compression gas

temperature – TC during the cycle.

(f) The regenerator gas temperature

is an average of the expansion gas temperature – TE and the

Compression gas temperature – TC.

(g) The expansion space – VE and the

compression space – VC changes following

a sine curve.

Alpha-type Stirling Engine

The volumes of the expansion- and

compression cylinder at a given crank angle are determined at first.

The volumes are described with a

crank angle – x. This crank angle is defined as x=0 when the

Expansion piston is located the most

top position (top dead point).

The expansion volume – VE is

described in equation (2) with a swept volume of the expansion piston –

VSE, an expansion dead volume – VDE

under the condition of assumption (g).

The compression volume – VC is found

in equation (3) with a swept volume of the compression piston –

VSC, a compression dead volume – VDC

and a phase angle – dx.

The total volume is calculated in

equation (4).

By the assumptions (a), (b) and (c),

the total mass in the engine – m is calculated using the engine

Pressure – P, each temperature – T,

each volume – V and the gas constant – R.

The temperature ratio – t, a swept

volume ratio – v and other dead volume ratios are found using

The following equations.

The regenerator temperature – TR is

calculated in equation (11), by using the assumption (f).

When equation (5) is changed using

equation (6)-(10) and using equation (2) and (3), the total gas

Mass – m is described in the next

equation.

Now;

The engine pressure – P is defined

as a next equation using equation

The mean pressure – Pmean can be

calculated as follows:

c is defined in the next equation.

C

= B/S

As a result, the engine pressure –

P, based the mean engine pressure – Pmean is calculated in

Equation

On the other hand, in the case of

equation (16), when cos(x-a)=-1, the engine pressure – P

becomes the minimum pressure – Pmin,

the next equation is introduced.

Therefore, the engine pressure – P,

based the minimum pressure – Pmin is described in

equation

Similarly, when cos(x-a)=1, the

engine pressure – P becomes the maximum pressure – Pmax.

The following equation is introduced.

The P-V diagram of Alpha-type

Stirling engine can be made with above equations.

4.1 Stirling Cycle, Zero Dead

Volume, Perfect Regeneration

The Stirling cycle is defined as a

heat power cycle using isothermal compression and expansion and constant volume

heating and cooling. Figure 5-2 shows such a process. Specific numbers are

being used to make the explanations easier to follow and allow the reader to

check to see if he is really getting the idea. Let us take 100 cm_ of hydrogen

at 10 MPa (~100 arm) and compress it isothermally to 50 cm3. The path taken by

the compression is easily plotted because (P(N))(V(N)) is a constant. Thus, at

50 cm3 the pressure is 20 MPa (~200 atm). The area under this curve is the work

required to compress the gas and it is also the heat output from the gas for

_he cycle. If the pressure is expressed in Pascals’ (Newton/sq. meter)(1 arm =

IQs N/m 2) and if the volume is expressed in m _, then the units of work

are (N/m_)(m 3) = N,m = Joules = watt seconds. For convenience, mega

pascals (MPa) and cm 3 will be used to avoid very large and very small numbers.

4.2 Stirling Cycle, Zero Dead

Volume, Imperfect Regenerator

Stirling engines require

highly efficient regenerators. Consider an annular

gap around the displacer which acts

as gas heater, regenerator and cooler (see Figure 5-3). Assume that this

engine operates in a stepwise manner and that this annular gap

has negligible dead volume. Let E be the regenerator effectiveness

during the transfer, For the transfer from cold space to hot

space:

HEATER (T H)

REGENERATOR

COOLER (T c)

Cold

HOT

SPACE SPACE

DISPLACER

Figure 5-3. Simple Stirling Engine with

Annular Gap Regenerator

Where

Equations 5-12 and 5-11 are the

same, just different nomenclature. Note that for E = I, both Equations 5-11 and

5-12 reduce to the Carnot equation, Equation _-6.

Rallis (77 ay) also derived a formula for the Ericsson cycle

efficiency:

Equation 5-13 also reduces to

Equations-6 when E = 1, that is, for perfect

Regeneration. To attain Carnot

efficiency, the compression and expansion ratio

must be the same. Rallis shows these

using cycles, which will not be treated here.

Rallis also gives a useful formula for the network per cycle for

the Stirling cycle:

For instance, for the numerical example

being used here

which is the same as obtained previously.

5. INDICATED ENERGY, POWER AND

EFFICIENCY

The indicated energy (area of the P-V

diagram) in the expansion and compression space can be

calculated as an analytical

solutions with use of the above coefficients. The indicated energy in the

expansion space (indicated expansion

energy) – WE(J), based on the mean pressure – Pmean, the minimum

pressure – Pmin and the maximum pressure – Pmax are described in

the following equations.

The indicated energy in the

compression space (indicated compression energy) – WC(J) are described in

the next equations

The indicated energy per one cycle of this engine – Wi(J) is

The indicated expansion power –

LE(W), the indicated compression power – LC(W) and the indicated

power of this engine – Li(W) are

defined in the following equations, using the engine speed per one

second , n(rps, Hz).

LE =WEn

LC =WCn

Li =Win

The indicated expansion energy – WE

found equation (23) means an input heat from a heat source to the

engine. The indicated compression

energy – Wc calculated by equation (24) means a reject heat from the

engine to cooling water or air. Then

the thermal efficiency of the engine – ? is

calculated in the next

equation.

This efficiency equals that of a

Cornot cycle which is the most highest efficiency in every thermal

engine.

The steady heat transfer from a hot

to a cold environment, the time rate of heat transfer may be

represented by

q

= hA(TH

? TC

)

Where A is the surface area of the

material that separates the two environments and across which the

heat flows and h is the heat

transfer coefficient, a property of the material separating the two

environments

Efficiency

of an Ideal Stirling Cycle

The equation for work (represents

energy out of the system) :

For isothermal expansion process,

the heat input is given by:

The efficiency is defined by:

6. The operating

principles of Stirling engine

In its simplest description,

a Stirling engine consists of a cylinder containing a gas and a piston

recovering the mechanical energy.

First

observation : the gas used is confined, it’s always the same. Another feature:

energy is supplied from outside of the cylinder, from where the

designations “hot air engine” or “external combustion engine” which

one can read sometimes.

This is a gradual process by

studying the following steps:

5.1- the

four basic phases

5.2- The

displacer function

6.1 The four basic phases

The thermodynamic cycle of

the Stirling engine is very simple : it includes 4 phases during which the gas

undergoes the following transformations

5.1.1. An isochoric heating (with

constant volume) :

The burner (the hot source) provides thermal energy. We easily imagine

that the pressure and the gas temperature increase during this phase.

We can see the temperature change starting from the image

on the left

6.1.2. An isothermal expansion (at

constant temperature):

The

volume increases whereas the pressure decreases. It is during this

transformation that driving energy is produced.

We can see the change in pressure by moving the piston to

opposite directions

6.1.3. An isochoric cooling :

The projected water (the cold source) recovers thermal energy. The

temperature and the pressure decrease during this phase.

We can see the temperature change to cold due to the water

flowing

6.1.4. An isothermal compression:

The pressure of gas increases whereas its volume decreases. One

must provide mechanical energy to gas for this period.

We can see the change in volume and

pressure if the temperature is confirmed

6.2. The

displacer function:

The realization of an engine such as

the one described above would be difficult : kindle the burner, extinguish it,

sprinkle, then stop cooling, with many successive thermal shocks….

This is why one will introduce an artifice

providing solutions to these problems: the displacer. This last modifies

neither the pressure nor the volume of gas, but requires it to be near the hot

source located at the top, or near the cold source located at the bottom.

Explanations through drawings:

6.2.1. Isochoric heating:

The

volume remains constant, but the displacer, while going down, sends the gas

from the lower part (cold) to the top (hot).

6.2.2. Isothermal expansion:

The displacer follows the engine

piston during the expansion so that the gas remains in contact only with the

hot source

6.2.3. Isochoric cooling:

The volume remains constant, but the displacer, while going up,

sends the gas from the higher part (hot) to the lower part (cold).

6.2.4. Isothermal compression:

The displacer, during compression, remains at the top so that the

gas is always in contact only with the cold source.