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Senior Design 1 (ME-498)

(Stirling Engine)

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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



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




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


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





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    
























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



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
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


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


Figer 2-9 overview of stirling engine.

There are four stages for gamma type:

1-Heating :










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.




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


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


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

















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.


= B/S


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



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




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


        HEATER (T H)                            
COOLER (T c)                          

SPACE                                                                                       SPACE

















Figure 5-3. Simple Stirling Engine with
Annular Gap Regenerator


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


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.






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).



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




This efficiency equals that of a
Cornot cycle which is the most highest efficiency in every thermal


The steady heat transfer from a hot
to a cold environment, the time rate of heat transfer may be

represented by

= 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


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.

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):

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

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:




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.

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