SESM2021: Introduction to Energy Technologies

Coursework I

Student name: Eleni Tsigkogianni 24467669

For the attention of Prof. Kai Luo

 A. Describe the principles of Stirling engines.

The stirling engine was created by Robert Sterling in 1816. An external combustion engine
with a closed regenerative thermodynamic cycle that produces energy by the periodic
compression and relief of the air captured in the engine at different level temperatures.

The main difference with other engines is that:

1. Stirling engine encloses a specific amount of gas (e.g. Helium, Hydrogen, Nitrogen)
that doesn’t leave the chamber. This way the gas could be used many times
2. Also the flow of the gas between the hot and cold space is done without using
valves.

There are five parts that make a stirling engine:

a) Compression space (CS): It is always being kept with the help of the cooler. There is
a piston that moves the imprisoned gas between towards the cooler.
b) Cooler (C)
c) Regenerator (R): This is the most important part of the engine that exists between the
heater and the cooler. It is a metal cylinder which it contains a thermal laminate
material in the form of perforated sheets or beads. This material forms the matrix of
the regenerator and absorbs and delivers heat. When the gas is transferred from the
expansion space to the compression space a part of the internal heat is being
absorbed by the matrix of the regenerator. When the gas returns from the
compression space to the expansion space with the help of the piston the part of
internal heat that had been kept by the regenerator is returned to the gas.
d) Heater (H): It can work with fossil fuels, solar energy, nuclear energy or any other
kind of renewable energy.
e) Expansion space (ES): It is always being kept warm with the help of the heater. There
is a piston that moves the imprisoned gas between towards the heater.

Types of Stirling engines

There are three basic types of stiriling engine:

1. Alpha: They have two pistons in separate cylinders that are connected in series with
the heater, the regenerator and the cooler. One piston moves the gas in the cylinder
with high temperature and the other piston moves the gas in the cylinder with the low
temperature.

2. Beta: It contains only one power piston and a displacer

which is in the same cylinder as the piston. The displacer
can move freely in the cylinder. Its purpose is to transfer
the gas from the heater to the cooler and back. It does not
Picture
absorb any energy from the gas.1: Stirling engine type Alpha

Picture 2: Stirling engine type Beta

 3. Gamma: It is very similar to the beta engine. The
main difference is that the power piston and the
displacer are in different cylinders. This type of
stirling engine produces lower compression ratio but
is simpler that the other stirling engines.

Stirling cycle Picture 3: Stirling engine type Gama

When a gas trapped in a cylinder moves towards the warm part of the cylinder the pressure
raises and it tends to expand and it produces energy through the work. On the other hand,
when a gas is forced to go to the cool part of the cylinder is cooled down and compresses
consuming energy. When the gas expands it produces more energy than it consumes when it
compresses.

A. Isothermal compression process 12

The piston in the cylinder with the

low temperature moves to a random
position moving the gas to the
regenerator having a steady low
temperature.

Diagram 1: Isothermal compression 12

B. Constant volume heating process

23

The piston in the cylinder with the low

temperature keeps on moving until the
whole gas passes through the
regenerator. Simultaneously the piston in
the cylinder with the high temperature
moves on the opposite direction to a
random position keeping the volume
constant. The heat that was captured to
the regenerator is now transferred to the
gas. Because the volume is constant the Diagram 2: Constant volume heating 23
rise of the temperature causes rise to the
pressure.

C. Isothermal compression process 34

Because of the high pressure the gas

expands and moves the piston in the
cylinder with the high temperature.

Diagram 3: Isothermal compression 3 4

 D. Constant volume cooling process 41

The piston in the cylinder with the high

temperature moves to the left and the gas
passes through the regenerator. There the
heat is kept and the gas continues to the
cylinder with the low temperature. Because
the volume is constant and the temperature
of the gas falls then the pressure also falls.

Diagram 4: Constant volume cooling 41

B. For the same high and low operating temperature limits, compare the
efficiencies of petrol, Diesel and Stirling engines.

As it is given to us from the data we have the following equations:

T1 = T2 = T3’ = T3’’ = TH

T3 = T4 = T1’ = T1’’ = TL

There are many parameters involved in these three cycles which makes it difficult to compare
them. So for that reason we will assume that some of these parameters are kept the same for
all the cycles. Besides the same high and low temperature limits we will assume that otto
cycle and diesel cycle work under the same compression ratio.

Stirling efficiency:

T3 TL
η s=1− =1−
T1 TH

Diagram 5: T - S Stirling diagram

 The efficiency of the ideal otto cycle under the cold-air-

Τ '4 −Τ '1
standard assumptions is: ηο = ' ' (1) we can
Τ 3 −Τ 2
calculate the efficiency also from the equation
1
ηο =1− k−1 (a) but we will use the first one since it is
r
simpler.
Because the processes 1 – 2 and 3 – 4 are isentropic we
Τ '1 Τ '4 '
' ' Τ3
have = →Τ 2 =Τ 1 ' (2)
Diagram 6: T - S Otto diagram Τ '2 Τ '3 Τ4

We insert equation number (2) to equation number (1):

Τ '4−Τ '1 Τ '4 −Τ '1 Τ '4 −Τ '1 Τ '4

ηο =1− '
=1− =1− =1−
' ' Τ3 Τ '3 Τ '4 −Τ '1 Τ '3 Τ '3 ( Τ '4−Τ '1 ) TH
Τ 3 −Τ 1 '
Τ4 Τ '4 Τ '4

Because Τ '3 is the maximum temperature that this cycle operates we have Τ '2<Τ '3. Also
' ' '
because Τ 1 is the lowest temperature that this cycle operates we also have Τ 4 >Τ 1. So if we
T L Τ '4
compare the fractions of the stirling efficiency and from otto efficiency we have: < and
TH TH
as a result we get η s> ηο.
 The efficiency of the ideal otto cycle under the cold air standard assumptions is:

Τ '4' −Τ ''1
ηd =1− '' ''
k (Τ 3 −Τ 2 )
V3
Cutoff ratio: r c =
V2
As a result the efficiency becomes:
r kc −1
ηd =1−
1
r k−1 [ ]
k ( r c −1 )
(b)

As we can see the difference between the efficiencies of otto

Diagram 7: T - S Diesel diagram
r kc −1
and diesel (equations (a) and (b)) is the part
[
k ( r c −1 )].

Because we are working under the cold-air-standard assumptions this quantity is

always greater than 1. As a result because we have assumed that they are working
under the same compression ratio ηo > ηd .

As a result η s> ηο >η d

Although, in reality, the compression ratio of diesel is much higher than in otto and therefore it
has better efficiency.

C. Conceptually design a Stirling engine that uses renewable energy sources.

As we have already mentioned, for a stirling engine to work we need a thermal and a cooling
source. The heat for the thermal source can be provided by many different renewable sources
such as solar energy, waste heat, biomass and others. We will implement a very simple
design of stirling engine using solar energy.

Our engine is consisted by two containers. On the top of the first container there is a small
solar heating panel which helps warm the air. The second container has double walls and in
between the walls there is ice which is used to reduce down the temperature of the air. The
sun rays are collected by the solar heating panel which warms water. The water is circulated
in the walls of the container and the heat is transferred to the air that is trapped inside.
Because the temperature rises the air is expanded and is transferred through a tube to the
second container. There the temperature gets lower again due to the ice that is in between
the double walls. As a result the air is compressed again. The constant change of the volume
of the air is making the two pistons in the containers to move producing mechanical energy
which is transferred and through a bar making a fan to turn.
One of the latest applications of stirling engine was designed by MSI hardware company in
Taiwan. In a world where reduce of energy consumption is needed more and more
companies are trying to find energy saving solutions. MSI designed and produced the “Air
Power Cooler” which is used to cool down the processor. This cooler takes advantage of the
heat that is being produced by the motherboard of the computer while it works.

The stirling engine is placed on top of a chipset and from the heat that is produced the air in
the engine is getting heated. Because the air is getting warm it gets lighter and moves from
the bottom to the top and pushes the piston which makes the fan to turn. Once the air
reaches the top it gets cold and heavier so it goes down again and pushes the piston to its
first position. According to MSI this device can transform 70% of the heat power to air power.

Picture 4: MSI's Stirling Engine-based cooler

References

1. Yunus A. Cengel, Michael A. Boles. Thermodynamics an engineering approach. Mc

Graw Hill Inc 3rd edition, 1998.
2. M. David Burghard. Engineering Thermodynamics with Applications. Harper & Row
publishers 2nd edition, 1982.
3. Terzakis Konstantinos. Optimazation of Adiabatic Analysis for Stirling Engines -
Factors Effecting Efficiency. Diploma thesis, Athens February 2008.
4. E. D. Rogakis, N. A. Mpormpilas. Stirling engine: Old but also very new.
5. www.msi.com
6. www.animatedengines.com