The document discusses the construction and working of a Stirling engine. It begins with an abstract explaining that a Stirling engine is a heat engine that operates through cyclic compression and expansion of a gas using different temperatures to convert heat into mechanical work. It then provides a brief history of the Stirling engine, explaining its invention in 1816 and various early designs. The main body of the document describes the Stirling cycle and working principles through four phases, provides a diagram of the pressure-volume relationship, and gives equations for efficiency. It concludes by detailing the design, construction, and potential applications of Stirling engines.

1. 2015
Muhammad Sajawal
Hayat
UCET University of
Sargodha
[STIRLING ENGINE
CONSTRUCTION AND
WORKING]

2. Stirling engine Construction and Working
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Stirling engine
construction and
working

3. Stirling engine Construction and Working
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Sr.
no Table of contents
Pg.
no
1 Abstract 3
2 Introduction 4
3 History 4
4 Stirling cycle & Working 4
5 PV diagram 5
6 Efficiency formulas and equations 5
7 Manufacturing, Design and Assembly 7

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Abstract: A Stirling engine is a heat engine that operates by cyclic compression and expansion
of air or other gas (the working fluid) at different temperatures, such that there is a net
conversion of heat energy to mechanical work. More specifically, the Stirling engine is a closed-
cycle regenerative heat engine with a permanently gaseous working fluid. Closed-cycle, in this
context, means a thermodynamic system in which the working fluid is permanently contained
within the system, and regenerative describes the use of a specific type of internal heat exchanger
and thermal store, known as the regenerator. The inclusion of a regenerator differentiates the
Stirling engine from other closed cycle hot air engines.
Originally conceived in 1816 as an industrial prime mover to rival the steam engine, its practical
use was largely confined to low-power domestic applications for over a century.
The Stirling engine is noted for high efficiency compared to steam engines, quiet operation, and
its ability to use almost any heat source. The heat energy source is generated external to the
Stirling engine rather than by internal combustion as with the otto cycle or diesel cycle engines.
Because the Stirling engine is compatible with alternative and renewable energy sources it could
become increasingly significant as the price of conventional fuels rises, and also in light of
concerns such as peak oil and climate change. This engine is currently exciting interest as the
core component of micro combined heat and power (CHP) units, in which it is more efficient and
safer than a comparable steam engine.

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Introduction: Like the steam engine, the Stirling engine is traditionally classified as an external
combustion engine, as all heat transfers to and from the working fluid take place through a solid
boundary (heat exchanger) thus isolating the combustion process and any contaminants it may
produce from the working parts of the engine. This contrasts with an internal combustion
engine where heat input is by combustion of a fuel within the body of the working fluid.
History: Robert Stirling was a Scottish minister who invented the first practical example of a
closed cycle air engine in 1816, and it was suggested by Fleeming Jenkin as early as 1884 that all
such engines should therefore generically be called Stirling engines. This naming proposal found
little favour, and the various types on the market continued to be known by the name of their
individual designers or manufacturers, e.g., Rider's, Robinson's, or Heinrici's (hot) air engine. In
the 1940s, the Philip’s company was seeking a suitable name for its own version of the 'air
engine', which by that time had been tested with working fluids other than air, and decided upon
'Stirling engine' in April 1945. However, nearly thirty years later, Graham Walker still had cause
to bemoan the fact such terms as 'hot air engine' remained interchangeable with 'Stirling engine',
which itself was applied widely and indiscriminately; a situation that continues.
Cycle & Working:
There are three basic configurations of stirling engine depending upon construction. The
configuration under study is gamma configuration having piston and regenerator in separate
cylinders.There are four basic phases of stirling cycle for gamma configuration of stirling engine.
 Isochoric heating: The volume remains constant, but the displacer, while going down,
sends the gas from the lower part (cold) to the top (hot). During this phase, the engine
piston moves slightly, the overall volume is minimal. In contrast, the displacer carries out
a long race and the gas is heated.
 Isothermal expansion: The displacer follows the engine piston during the expansion so
that the gas remains in contact only with the hot source. The displacer moves little. In
contrast, the operating piston carries out more than 70% of its race. It recovers energy.
 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). The displacer carries out most
of his race: the gas is cooled. The operating piston moves little.
 Isothermal compression: The displacer, during compression, remains at the top so that
the gas is always in contact only with the cold source. The displacer remains at the top:
the gas is cold. However, the piston engine performs the majority of its race: it
compresses the gas by yielding mechanical energy.

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The PV diagram: The principle of operation,
above exposed, can be represented on a
diagram called “ Pressure-Volume diagram”
or PV diagram.
On this diagram, one easily sees the four
phases detailed above, by not forgetting that
expansion and compression are at constant
temperatures (TM and Tm).
The coloured surface, ranging between the
four segments describing the cycle, is
representative of the work collected during a
cycle.
The demonstration is provided below.
At every moment, the force which is exerted on the piston is F = S x P where S is the surface of
the piston and P the instantaneous pressure.
The elementary work provided during a short time “dt” is equal to the instantaneous force
multiplied by displacement “dy "of the piston during this period “dt”.
𝑑𝑤 = 𝐹 × 𝑑𝑦
𝑑𝑤 = 𝑆 × 𝑃 × dy
or, if it is noticed that S x dy = dV , the variation in volume during the period of time "dt".
𝑑𝑤 = 𝑃 × 𝑑𝑉
On the PV diagram, this last expression is the elementary surface located under each curve.
The work is positive under the curve of expansion because dV>0. Work is negative under the
curve of compression because dV<0. The resulting work during a cycle is represented by surface
under the curve of expansion decreased by surface under the curve of compression. Therefore, it
is the surface between the curves.
Efficiency of stirling cycle: The efficiency of the engine is equal to the ratio between the
recovered mechanical energy Wnet and the heat Qtotal that is required to provide. The latter is
provided during the isochoric heating and during the isothermal expansion.
Wnet = Wexp + Wcomp
Where, see above, Wcomp will be negative after its calculation.
Qtotal = Qheat + Qexp

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Recovered mechanical energy: The work, Wnet , is equal to sum of the recovered work
(positive) during the expansion and the provided work (negative) during the compression :
Wnet = Wexp + Wcomp
Wnet = ∫exp PdV + ∫comp PdV
with P = nRT / V
we obtain :
Wnet = ∫exp (nRTmax / V) dV + ∫comp (nRTmin / V) dV
Wnet = nR (Tmax - Tmin) ln Vmax / Vmin
Provided heat:
During the isothermal expansion, the provided heat is equal to the recovered work during this
same phase:
Qexp = ∫exp PdV
Qexp = nR Tmax ln Vmax / Vmin
During isochoric heating, we have to provide :
Qheat = nCv (Tmax - Tmin)
where Cv is the constant-volume molar heat capacity of the gas when we heat it from Tmin to
Tmax.
The total provided heat is:
Qtotal = nCv (Tmax - Tmin) + nR Tmax ln Vmax / Vmin
Stirling cycle efficiency:
η = [R (Tmax - Tmin) ln Vmax / Vmin] / [Cv (Tmax - Tmin) + R Tmax ln Vmax / Vmin]
ηCarnot = 1 - Tmin / Tmax
To obtain this equality, we have to suppose that the energy useful for isochoric heating is entirely
recovered during isochoric cooling, it is the function of the regenerator studied in
the "Regenerator" page. In this case, Cv (Tmax - Tmin) disappears as we obtain:
η = [R (Tmax - Tmin) ln Vmax / Vmin] / R Tmax ln Vmax / Vmin
or, after simplification :
η = (Tmax - Tmin) / Tmax
or :
Stirling engine efficiency when there is a regenerator:
η = 1 - Tmin / Tmax
In reality, the regenerator efficiency is not equal to 100%. The Stirling engine efficiency will be
always inferior to the Carnot cycle efficiency.

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Designof stirling engine:
Construction: The gamma configuration stirling engine has following parts.
Displacer and its cylinder: The displacer is a special-purpose piston, used in Beta and Gamma
type Stirling engines, to move the working gas back and forth between the hot and cold heat
exchangers. Depending on the type of engine design, the displacer may or may not be sealed to
the cylinder, i.e. it may be a loose fit within the cylinder, allowing the working gas to pass
around it as it moves to occupy the part of the cylinder beyond. The displacer in our project is a
test tube having 16mm diameter.
The cylinder of displacer in stirling engine is a test tube having 19mm internal diameter. The 16
mm diameter displacer can move freely inside it. Basically the function of displacer cylinder is
heating gas or air inside it. When the displacer moves forward the hot air is removed from this
cylinder.
Piston and its cylinder: The function of piston and its cylinder is to get kinetic energy from
expanded air and convert it into work in the form of a closed system.
The piston of our stirling engine is made up of aluminum having 20mm diameter. The cylinder is
also made up of aluminum in which the piston is sealed. These parts are made on lathe machine.

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Flywheel: A flywheel is a rotating mechanical device that is used to store rotational energy. The
flywheel of our stirling engine is a wheel of aluminum having radius 30mm and weight equal to
0.2kg connected to both displacer and piston through connecting rods.
Connecting rods: The connecting rods are rods having 3mm diameter and adjustable length.
The lengths of rods are adjusted according to the piston and cylinder arrangement.
Heat sink: A heat sink is connected to the displacer cylinder test tube for absorbing heat from
hot working fluid (air) which is heated inside the displacer cylinder.
Applications:
Some satellites get energy through a Stirling engine. The efficiency is particularly high
considering the great differences in temperature. The hot source consists of radioactive isotopes.
The use of radioactive elements is not very ecological, it presents risks at the time of the take-off
of the rocket. The justification comes owing to the fact that solar panels can be dirtied or be
destroyed in certain zones of space, as near Mars.
When one takes advantage of energy from the Sun, one uses a reflective dish which concentrates
the sunbeams in only one point: the focus of the dish where you install the Stirling engine.
In the United States, great reflective dishes were installed in the desert with Stirling engines to
generate electricity without buying fuel! (NB: photovoltaic panels have a poor performance,
about 15%. Therefore, at equal power, their surface is larger than reflectors of a Stirling engine).

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Appendix: