Design of Liquid Piston Stirling Engine
Design of Liquid Piston Stirling Engine
Design of Liquid Piston Stirling Engine
1
Abstract
An alpha-type Liquid Piston Stirling engine with a maximum power output of
23W and an efficiency of 3.4% was designed, built and instrumented for demonstration
purposes. Based on in-depth research and design optimization, engine parameters were
determined and a particular design was drafted. All the engine parts were manufactured
in the Engineering Department’s machine shop. The design was modified following
initial testing and modified to improve performance. During the final two weeks of the
project different sensor types were added to enable real-time data collection and
processing. Furthermore, sufficient data was taken to characterize the fluidyne system.
There is still a lot of work to be done in order to realize our initial project goals and it is
our hope that the engine will be improved upon extensively in the coming years.
2
Acknowledgements
We owe Professor Carr Everbach a great deal of gratitude for his expertise, support
and advice during the entire process but more especially during the initial stages of
the project in getting us onto the right track. Secondly, we would like to thank Mr.
Grant Smith ‘Smitty’ for his help in machining several system components, in
ordering several system parts and directing us when it came to using the machines in
the departmental shop. Professor Fred Orthlieb was also very invaluable in moving
the project forward and his help in machining some of the system pieces when Smitty
was away is very much appreciated. To our E14 students, Paul Agyiri ’07 and Lauren
’07, we say thank you for testing the regenerative materials in order suggest what the
best material is for the purposes of our project. Finally to our peers, engineering
faculty members and friends who kept pushing us on, we say thank you.
3
Table of Contents
1. Introduction …………………………………………………………….. 6
1.1 Background Information …………………………………………….. 6
1.2 Project Objectives & Goals …………………….…………………….. 6
1.3 Why a Liquid Piston Stirling Engine……………………………………8
1.4 Liquid Piston Stirling Engines- A Historical Overview ..........................8
1.5 Basic Operation of a Stirling Engine……………………………………9
1.6 Basic Operation of the liquid piston Fluidyne Engine………………….13
1.7 Effects of Evaporation and Mean Pressure……………………………...14
1.8 Applications……………………………………………………………...15
1.9 Report Organization……………………………………………………..16
2. Theory …………………………………………………………………….. 16
2.1 Working Fluid and Pressure …………………………………….. 16
2.2. Operating Temperatures ........................…………………………….. 16
2.3 Displacer Frequencies……………………………………………….. 17
2.3.1. Derivation of Operating Frequencies…................................ 17
2.4 Tuning of Liquid Columns…………………….…………………….. 18
2.4.1. Derivation of Tuning Column length given Frequency………18
2.5 Power Output…………………………………………………………...21
2.6 Losses…………………………………………………………………...22
2.6.1. Viscous Losses………………………………………………..22
2.6.2. Power Losses in Fluid Flow…………………………………..23
2.6.3. Kinetic Flow Losses…………………………………………..23
2.6.4. Heat Losses……………………………………………………24
2.6.5 Shuttle Losses………………………………………………….25
2.6.6 Other Losses that could affect System………………………...25
2.7 The Regenerator and its Operation……………………………………...26
3. Design Process …………………………………………………………………...28
3.1 Our Design……………………………………………………………….28
3.1.1 Engine System Parameters………………………………………30
3.2 Components of the System………………………………………………32
4
3.2.1 Heat Exchanger…………………………………………………32
3.2.2 PVC…………………………………………………………….33
3.3.3 Displacer………………………………………………………..33
3.3.4 Pumping Column……………………………………………….34
3.3.5 Regenerator……………………………………………………..34
3.3.6 Connections…………………………………………………….34
3.3.7 Tuning Column…………………………………………………36
3.3.8 Unistrut Structure………………………………………………36
3.3.9 Summary of Design and Parameter sizes……………………....36
4. Construction and Assembly …………………………………………….. 38
4.1. Introduction …………………………………………………….. 38
4.2. Machine Shop Work Details …………………………………….. 38
4.2.1. Displacer……………..…………………………………….. 39
4.2.2. Six inch to three quarter inch end caps………………….........40
4.2.3. The Tuning Column …………………………………….. 40
4.2.4. The Regenerator …………………………………….. 40
4.2.5. The Heat Exchanger……………………….. ………………. 42
4.2.6. Carbide Silicate/Fibre Funnels……………………………… 43
4.2.7 Unistrut………………………………………………………..43
4.2.8 Insulating Float………………………………………………..44
4.2.9 Modifications…………………………………………………45
4.3. Data Acquisition System…………………………………………….. ..46
4.3.1. The Pressure Transducer……………………………...……...46
4.3.2 Thermocouples. .……………………………………..............47
4.3.3 Proximity Sensor……………………………………………..47
5. Results and Discussion…………………………………………………………47
6. Conclusions……………………………………………………………………..57
7. Further Work…………………………………………………………………...58
8. References………………………………………………………………………62
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1. INTRODUCTION
6
Fig 1.1 below shows the crude methods most rural folks in Africa obtain their water and
attempt to purify them. As is evident for one or more of these images, water supply is
generally unhygienic and the means of accessing water is not as efficient as it could be.
Woman pouring water into pot to be purified/sterilized by sunlight Women standing next to a well, typically 20-30 feet in depth
Fig 1.1: Pictures of rural water supply and storage
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A very important objective of this project, as was mentioned in the goals section in
this report, is to design and develop a system that can easily be constructed given the
limitations of a developing society. With this in mind, there is the need to choose a
design that incorporates constructional simplicity; a fluidyne system provides this. It
can be constructed using relatively simple and inexpensive materials. In our case,
PVC tubing, which are primarily cheap and also come in different standard sizes, can
sufficiently accommodate the needs of a Fluidyne System. A liquid piston Stirling
engine can therefore be built without the need for sophisticated machining which is
definitely a plus.
A second major advantage of liquid piston Stirling engines is that they are silent
during operation. Compared to mechanical-piston Stirling engines as well as other
pumps, fluidynes are extremely silent during operation which is an added benefit.
One does not have to concern themselves with losses as a result of moving parts
(mechanical pistons). In fact the only predominant losses that lower the efficiencies
considerably of fluidyne systems are viscous losses. The oscillating liquid must be
viscous enough to be able to sustain oscillations got a long period of time. The
engines’ efficiency ranges from 3-6%. Despite the low efficiency, the constant
supply of solar energy all year round will be enough to power the engine to serve the
needs of villages in a typical rural setting.
8
liquid-output piston avoids the need for a sliding mechanical seal, which has been a
continuing problem for crankshaft Stirling engines.
Most of the early interest has centered around the use of Fluidyne machines to pump
water. Like any other Stirling engine, the liquid piston engine can also be operated as a
refrigerator or a heat pump and several people have proposed exploiting this.
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Ideal engine operation
P T
1 Actual engine operation
QH 1 2
TH
2
4 TC
3 4 3
QC
V s
1 – 2: Isothermal Expansion
The working gas (air in our case) expands as heat QH is transferred to the
expansion space of the engine. The gas expands and does work (usually work is
done on a power piston), causing the engine volume to increase and the pressure
to decrease. Assuming isothermal conditions (T=TC), the heat transferred to the
working gas is exactly QH=WE, where WH is the work done on the power piston.
2 – 3: Isochoric Displacement (Cooling)
The working gas is moved through the regenerator at the maximum engine
volume. Heat is transferred from the working gas to the regenerator, causing the
pressure, temperature and entropy of the gas to decrease.
3 – 4: Isothermal Compression
The cooled working gas is compressed (usually by a power piston) in the
compression space, and heat QC is sunk to the cold reservoir at constant
temperature TC. Consequently, the engine volume decreases, while the engine
pressure increases. Assuming isothermal conditions (T=TC), the heat sunk to the
surroundings is exactly QC=WC, where WC is the work done by the power piston
on the working gas.
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4 – 1: Isochoric Displacement (Heating)
The working gas is moved through the regenerator at the minimum engine
volume. Heat is transferred from the regenerator to the working gas, causing the
pressure, temperature and entropy of the gas to increase.
Figure 3.1.a) A typical alpha-type Stirling engine. b) A typical beta-type Stirling engine.
1
The Ross yoke drive mechanism is discussed at
http://www.ent.ohiou.edu/~urieli/stirling/engines/engines.html
11
source: http://www.ent.ohiou.edu/~urieli/stirling/engines/engines.html
Each of the three engine types has certain advantages and disadvantages. The
primary disadvantage of alpha type is a requirement for perfect sealing for two pistons.
Also, the configuration of the two pistons at an angle to each other can be cumbersome
for construction, especially for demonstration engines.
Beta engines offer potential significant advantages, especially in terms of
efficiency and size, but are technically complex. The requirement of a coaxial displacer
and power piston makes for difficult machining of the engine. This requirement also
increases friction in the engine because the displacer necessarily slides in and out of the
power piston. Moreover, the mechanical drive mechanism used to convert translation of
the pistons into rotation of the output shaft is a difficult design problem to say the least.
Finally, while a beta demonstration engine would be interesting, the coaxial piston
motion and regenerator position make it difficult to see Stirling cycle principles at work.
Gamma engines are best equipped for educational purposes. With two parallel
cylinders attached to a common crankshaft (see Figure 3.2 below), it is relatively easy to
discern the four stages of the Stirling cycle, and to study the functions of the displacer,
power piston and regenerator in each thermodynamic process.
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1.6 Basic Operation of the Liquid Piston Fluidyne Engine
The liquid piston Stirling operates quite differently from the generic Stirling engine
described above. The most obvious is the fact that the mechanical pistons are replaced by
water. Therefore, as the hot side is heated, the increased air pressure raises water on the
cold side and lowers water on the hot side. The left-hand U tube which has one end
heated and the other end cold functions as a displacer; and the right-hand tube, which has
one end open to the atmosphere, works as the output, or power, piston; this configuration
is generally known to be the gamma configuration.
When the water in the displacer is set oscillating- by manually rocking the system to
jumpstart-from one limb of the U tube into the other limb and back, it is obvious that at
one point in the cycle, top dead air in the cold end will correspond to bottom dead air in
the hot end; this situation is illustrated in the left hand part of fig 1.5.1 overleaf, in which
most of the air trapped above the water in the displacer is in the hot left-hand limb. Most
of the air is therefore hot, so its pressure will rise, which tends to force the tube to move
from right to left as the arrow indicates in the figure below;
Cold
Hot
Displacer Output
13
Half a period later, the displacer water will have swung back into the other limb, so that
the cold surface is at the bottom dead center, which is the situation at the right hand side
of fig 1.5.1. Most of the air is therefore in the cold side of the machine, so its pressure
will fall, pulling the water in the output column back from left to right.
Cold
Hot
Displacer Output
The most important factor in Stirling engine design is the efficiency losses due to non-
idealities. Due to imperfections, the efficiencies of Stirling engines are significantly
lower than the ideal ones. The non-idealities include adiabatic losses and heat losses from
mechanical components.
14
the mean pressure of the working fluid to increase the pump’s pumping capability and its
efficiency and minimize the evaporation by designing a float which will rest on top of the
liquid column in the hot side of the engine.
1.7 Applications
The engine output power has been extracted and used for pumping, including
irrigation pumping. Three simple ways to use the Fluidyne output to pump water have
been identified.
The first is known as series coupling which simply requires a T piece placed at the
end of the output column and two non-return valves. On the inward stroke of the
output liquid when the gas pressure inside the engine is low, liquid is drawn in
through the lower non-return valve. On the outward stroke, liquid is forced out
through the upper valve. However, the presence of the T piece (pumping line) in
series with the output column of the non-return valves may upset the tuning of the
system because with the non-linearities associated with the valves, the behavior of
the output tube as a resonant, oscillating system may be seriously affected.
The drawbacks that have just been highlighted could be remedied by placing the
pumping system in parallel with the output column. The volume of liquid moving in
the output tube can be greater than the volume passing through the pump, so that
there need not be a close correlation between the pumped volume and the engine
stroke which in the series configuration, has to be the case. Secondly, nonlinearities in
the flow through the pump will have relatively small effects on the oscillation of the
larger amount of liquid in the output line. In this case, the output line does not do any
work directly, except to overcome its own losses, but merely oscillates at a frequency
tuned to that of the displacer, thus giving rise to relatively large pressure variations
within the engine for pumping purposes. For this reason, the “output tube” is usually
referred to as the “tuning line” or the “tuning column” highlighting the fact that its
main function is to have a large, resonant oscillation and not to provide a direct output
mechanism.
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1.8 Report Organization.
The report has been broken down into several sections. This first part has been a
general introduction to the broader topic of Stirling engines and has narrowed our
scope focus to Fluidynes. The theory section (section 2) explains the theory
underlying our design as well as the model equations and concepts that are pertinent
to our system .The next section (section 4) discusses the design process and the
considerations that were important in arriving at our system’s parameters. Section 5
discusses the construction and assembly of the different parts of the engine after
which this paper presents and discusses our results, draws relevant conclusions and
recommends ways to improve on the existing design. The appendices then follow.
2. THEORY
2
Elrod, 1974; Geisow, 1976.
16
between 120 - 300 º C for a machine which incorporates design simplicity like ours and
uses relatively available and inexpensive materials for construction, insulation and
jointing. The cold side temperature can be maintained at water’s ground level
temperature of about 10 º C.
2g
ω= rad/s (2.3.3)
LD
1 2g
or f = Hz (2.3.4)
2π LD
17
Fig.2.3.1 Simple Displacer U-Tube
A displacer length of less than 1 ft may be impractical for the however, one in the
range of 1-2m, corresponds to frequencies of 0.5-0.7Hz, which are common in most
practical engines.
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Fig 2.4.1: Tuning column configuration with merged cylinders
Fig 2.4.1 shows a representation of the tuning column that represents a merged cylinder
machine. It has liquid length Lt and a cross-sectional area, At. One end is open to the
atmosphere. The other end terminates in the displacer.
Displacing the water in the open end of the tuning column downward by an amount χ
does two things. First, it raises the liquid at the other end by an amount χ. Secondly, it
reduces the value of gas above the working space by an amount At χ. Both effects give
rise to a pressure difference across the tuning column tending to force it back toward
equilibrium position.
If the gas is initially at a pressure Pm and at a volume where the tuning column is at a
mid-stroke, Vm, the space above the liquid is isothermal as we would like it to be in an
ideal Stirling engine, then the pressure will rise by an amount p, where:
PmVm = (Pm + p)(Vm - At χ) (2.4.1)
according to the ideal gas law. Therefore,
Vmp = (Pm + p)At χ (2.4.2)
Stirling engines usually have a relatively low compression ratio, so that p is generally
fairly small compared to Pm. Consequently, an approximation for p = At Pm χ/Vm.
For a merged cylinder configuration as has been shown in Fig. 2.4.1, the pressure
difference between the liquid surface in the displacer and the open end of the tuning
column is:
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Pm At χ ρ g χ At
+P = + ρ gχ + (2.4.3)
Vm 2 Ad
Gas
Tuning Displacer
compressi
liquid liquid
on
level level
lowered raised
Most of the pressure difference will act across the tuning column, generating an angular
velocity which is equal to
At Pm [1 + At / 2 Ad ]g
ω= ( + )rad / s (2.4.4)
Vm ρ Lt Lt
Or
At Pm [1 + At / 2 Ad ]g
f = 1/ 2π ( + ) Hz (2.4.5)
Vm ρ Lt Lt
The compressibility of a perfectly isothermal gas is equal to Vm/ Pm where Vm and Pm are,
respectively, the initial volume and pressure. The compressibility of a perfectly adiabatic
gas is Vm/ γPm , where γ is the specific ratio of the gas. For a mixed isothermal-adiabatic
volume, we can simply calculate the overall compressibility of the working gas from the
weighted average of the mean isothermal and adiabatic volumes, Vi and Va.
ΔP − Pm
= (2.4.6)
ΔV V + Va
i γ
Substituting equation 2.4.6 into equation 2.4.5 gives an approximate formula for the
natural frequency of the tuning line in a Fluidyne machine with mixed isothermal and
adiabatic spaces.
1 π Rt2 Pm Rt2
ft = (1/ 2π ) [ + g (1 + )] (2.4.7)
Lt ρ (V + Va 2 Rd2
i γ
Where Rd is the diameter of the displacer and Rt, the diameter of the tuning column.
Equation 2.4.7 can be rearranged to give a simple relation between the tuning column
length, Lt and its radius Rt for any given frequency of operation f.
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π Rt2 P0 Rt2
{ } + g[1 + 2 ]
ρ [Vi + Va γ ] 2 Rd
Lt = (2.4.8)
4π 2 f 2
3
By West, 1971.
21
thermal insulation around the heat-exchanger as well as other system parts that are good
thermal conductors.
2.6 Losses
The liquid piston Fluidyne engine has no rotating or sliding solid parts, and therefore no
mechanical friction. It, however, suffers from the viscous and other losses associated with
flowing fluids, especially flowing liquids and air. In addition, just like in the more
conventional Stirling engines, it suffers from the fact that the gas spaces are, in general,
neither perfectly isothermal nor perfectly adiabatic.
Rt 2π f ρ (2.4.11)
η
is much greater than unity. f is the frequency of the oscillation, Rt , the diameter of the
tube and ρ , η are the density and viscosity, respectively, of the fluid. Substituting the
parameters for water at room temperature, and using a frequency of 0.52 Hz, which is the
operating frequency of our fluidyne, we find that the radius parameter becomes
Rt 2π *0.52*10
3
(2.4.12)
0.001
With a design choice where the radius of the tuning column is 0.05m, the radius
parameter, R = ٭90.37 which implies that our cylinders can be treated as wide when we
calculate viscous effects of water flow.
Closely related to viscous flow is the resistance coefficient which is defined as the
pressure drop per unit length divide by the mean flow velocity. For nonturbulent
oscillating flow in wide tubes, as we have determined above, the resistance coefficient is
given as:
R = 2 ρωη Rt (2.4.13)
22
It is obvious, therefore, that the pressure drop for a given flow rate increases only as the
square root of the viscosity η .
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Element K
90˚ smooth bend 0.15-0.25
90˚ mitre bend 1.0
Sharp edge contraction 0.5
Sharp edge enlargement 0.2
Table 4.2.1: Minor pipe loss coefficients
The total pressure drop due to all the bends, constrictions, enlargements, etc, in the
system will be obtained by summing the contributions from each of them individually.
With this in mind, the minor pipe loss can be expressed as:
πρ f 3Vo3
Ek 0.42ΣK (2.4.17)
2 Rt4
The minor pipe losses increase with the cube of the frequency and the cube of the swept
volume. Also, as the tube diameter is decreased, the kinetic losses increase more rapidly
than do viscous losses.
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2.6.5 Shuttle Losses
This is the heat loss due to the motion of the displacer piston. In the stationary state, the
temperature of the piston will be approximately equal to that of the adjacent cylinder
wall. When the piston moves, each section of its surface moves to confront a new part of
the cylinder wall, at a different temperature. Heat is transferred between the two adjacent
surfaces at different temperatures. The formula for calculating the shuttle losses4 is:
π s 2 k ΔTD
Qs = (2.4.19);
8 Lg
where s = stroke
k = thermal conductivity of the gas between the piston and cylinder
ΔT = temperature difference between the hot and cold end of piston
D = piston diameter (or cylinder insider diameter)
L = Length of piston
g = gap between piston and cylinder
It is evident that this equation is frequency-independent. The reason is that if the
frequency is, for example, increased, the time available for heat transfer is during each
motion of the piston is proportionally reduced. Therefore, the amount of heat transferred
during each cycle is inversely proportional to the frequency. The total amount of heat
transferred per unit time is therefore equal to the amount transferred per cycle multiplied
by the number of cycles. One of these factors varies inversely with frequency, and the
other, directly with frequency. The overall effect is therefore independent of the
frequency.
4
Equation is discussed in Martini’s Design Manual, (1978)
25
meniscus is close while the gap is open at the top. As the pressure in the cylinder varies,
gas flows into and out of this volume. Since the lower end of the gap is kept cold by the
oscillating liquid column, extra heat must be added to this gas as it leaves the space. This
loss is however pretty small in Fluidyne machines; we will therefore ignore it for the
purposes of our design.
Another minor heat loss source comes from the fact that extra heat input may be needed
because of the inefficiency of the regenerator. The regenerator, as it will be explained
shortly, reheats the gas as it returns to the hot cylinder. Since there is a great possibility
that it will not be perfectly effective, extra heat must be supplied from the heater which
could lead to the system being less efficient.
Finally, the heat that is stored in the hot components of the engine must be supplied by
the heat source which means that if it does not go into heating the air but rather the hot
pieces of the device, then it represents a lost energy source which could make the system
a less efficient.
5
Description of the regenerator adapted from external source. E90 Report by Milos Ilak’04 and Jesse
Hartigan ’04.
26
impedance to the flow of the working gas through the regenerator itself. This is usually
achieved by using arrays of tubes, wire meshes, or by using porous materials with high
heat capacity through which the flow of the working gas is forced. In practical engines,
there is often a significant tradeoff between the gains in efficiency due to the regenerative
action and the flow losses. The flow rate of the working gas can be reduced greatly,
which causes losses to the power output. For small engines, these losses can be higher
than the potential benefits of a regenerator. Also, the passages in the regenerator may add
to the dead space in the engine, reducing the power output and efficiency further.
However, even with no regenerator, some regenerative action will still be provided by
different engine elements. In the case of an engine that contains a displacer for example,
the thin annulus of air around the displacer can provide some regenerative action.
Figure 2.7.1 shows a sample regenerative displacer piston which would not cause
an increase in the dead space or flow losses, since the displacer would have to exist in
order to provide reciprocating motion to the power piston as described earlier in this
section. The temperature gradient is considered negligible in the longitudinal direction,
and high heat transfer rates to and from the regenerator are assumed in the radial
direction. One way of achieving this highly anisotropic thermal conductivity is to make
the regenerator matrix out of light plastic in which radial highly conductive wires are
embedded.
Displacer
movement
Tcold
Thot
Figure 2.7.1. a) Heat transfer occurring from the hot air to the regenerator as the air moves towards the
cold space.
27
Air flow from cold Heat out of
Air passage side to hot side regenerator
Displacer
movement
Thot
Tcold
Figure 2.7.2. b) Heat transfer from the regenerator to the working gas as the cold air moves towards the hot
space.
3. DESIGN PROCESS
In this section, we discuss the design process, the reasons for the design decisions
made and the design parameters we chose and calculated, based on the equations
derived under the theory section.
28
components of our design include the displacer, tuning column, heat exchanger and
the regenerator, all of which can easily be constructed from relatively simple and
inexpensive materials
2) Machining Simplicity
As stated above, liquid pistons generally incorporate constructional simplicity which
implies that machining the various pieces in place is not necessarily a difficult task.
Unlike with Stirling engine designs which utilize mechanical pistons, there is really
no reason to achieve picture-perfect machining on any part of the system. In some
mechanical pistons for instance, it is imperative that the displacer and the output
piston be aligned perfectly so that no significant friction effects develop.
3) Instrumentation Easiness
Our design incorporates various testing devices that make it easy to collect relevant
data on our system as well as to characterize it. The design incorporates various
sensors as well as other analog measurement devices in order to realize the above
mentioned objective.
29
Fig 3.1.1: Design diagram of our fluidyne pump
Swept Volume
The next design parameter to determine is the engine-displacement, or swept , volume.
The Beale number 6 Bn enables us to generate a fairly good estimate. It offers a simple
relationship between mean cycle pressure, operating frequency, engine displacement and
power output.
Power = Beale number * mean pressure * frequency * displacement
W = Bn PfVo (3.1.2)
6
Walker, 1979
30
For our system, we have a target performance of 0.5m3 / hour . Therefore, with a
pumping arm of length 10 feet (3.05 metres), the theoretical power output through this
head for our system is given as:
0.5m3 / hour *103 *3.05m *9.81/ 3600 = 4.16Watts (3.1.3)
Fluidyne machines tend to be approximately 4-6% efficient. We therefore expect to
provide an input power of approximately 70 watts.
The swept volume, from equation 3.1.2 is therefore expected to be:
4.16
= 1131.37cm3 (3.1.4)
0.005*1*0.52
This is the total volume change during each cycle of the engine. However, in the case of
an alpha configuration machine with the hot and cold pistons moving with approximately
equal strokes and about 90° out of phase, the total volume change is 2 * (the swept
volume of either piston). Therefore for our particular design, each piston should have a
displacement of 1131.4 cm3.The projected stroke, which is the amplitude of the
oscillations can then be expressed as
sπ 0.152
= 1131.37 *10−6 m3 (3.1.5)
4
This equation yields a stroke of 6.23cm.
Dead Volume
The optimum compression ratio in a Stirling engine is about 2:1. For an alpha
configuration machine, if both pistons have a swept volume V and differ in phase by 90°,
the total volume of the working gas in the cylinders, excluding clearance spaces is given
by:
1 π
V (1 + cos(ωt − )) (3.1.6)
2 4
If the unswept volume available for clearance space, heater and regenerator is VD, then the
compression ratio, i.e., the ratio of the maximum to the minimum is equal to 2 when VD =
1.12V. The unswept/dead volume of our system is therefore calculated to be
approximately 1267cm3.
31
Other miscellaneous design parameters
At a frequency of 0.52 Hz, the number of strokes per hour is expected to be 0.52*3600 =
1877/hour. To be able to pump 0.5m3/hour requires 0.5/1877 = 266cm3/stroke.
The pumping system is gas-coupled to the Fluidyne by means of an air-filled pipe. The
mean volume of air in this pipe must be at least 133cm3 because this is the anticipated
volume swept in each column during half cycle. To minimize dead volume so as to
maintain a relatively high compression ratio, the air-filled couple was designed to have a
volume close enough to 133cm3. The mean volume must be at least this value, rising to
266cm3 and falling to zero during each stroke. This implies that we have a remaining
dead volume of about 1134cm3 to allocate between the heat exchanger, regenerator as
well as for clearances and connecting pipes.
32
rolled into a coil and placed inside the exchanger. The outer surface of the coil was
placed in such a manner at to be in contact with the inner surface of the cylindrical 8in
copper tube. The thermal expansion of copper is 17*10-6/C.
Nichrome wire will be used as a heat source within the heat exchanger during the actual
operation of the system. The gage of the wire being used is 29 AWG (0.0113 in dia.) and
it will be to maintain the temperature inside the exchanger between 350 – 450 degrees
Fahrenheit. Fluidyne machines tend to be 3-4% efficient so it was determined that 70
watts input power would be needed. To maintain the desired temperature, 100 – 150
watts will be the power input to the wire to achieve the temperatures desired within the
exchanger.
The nichrome wire will be wrapped around a 1.5 in x 1.5 in x 6 in long piece of ceramic
block, which will be centered inside of the copper heat exchanger. The ceramic will be
utilized because it can withstand temperatures of up to 1400 F. In addition, the ceramic
provides a way to situate the nichrome wire inside the heat exchanger without the wire
touching the copper casing, thereby; shorting the wire and limiting the amount of heat
that can be generated.
3.2.2 PVC
The tubing used in constructing the major part the system is PVC (Polyvinyl chloride)
material. This material is a widely-used plastic that is commonly used for similar
applications as that of this project. In addition, PVC is relatively easy to assemble and
cheap. The melting point for PVC is 212 C and has a heat transfer coefficient of 0.16
W/m k. The three parts of the system that consist primarily of PVC are the displacer,
tuning, and pump tubing.
3.2.3 Displacer
To achieve a flow rate of 0.5 m3/h the displacer tubing was constructed to be. To move
0.5 m3/h of water the number of strokes per hour for the hot and cold spaces was
calculated to be 1877. The displacer has two chambers; one chamber is the hot space the
33
other chamber is the cold space. The volumes of both chambers were derived to be 231
cm3. The hot and cold chambers are adiabatic and isothermal volume spaces,
respectively.
3.2.5 Regenerator
The liquid piston Stirling engine is a alpha configuration model; therefore, a regenerator
component will be included in the system operation. The regenerator typically consists
of a mass of wires and is located between the reservoirs (hot space and cold space). Two
types of regenerative material will be tested and analyzed and the most efficient of the
two materials will be in the final system operation. The materials being tested are small
rocks and steel brillo pads. When the air is moving between the hot and cold sides its
heat is transferred to and from the regenerator. The regenerator contributes to the
efficiency of the Stirling cycle by storing and releasing the heat to and from the air. The
regenerator has a volume of 1400 cm3 (85 in3) and will be situated above the cold space
and to the right of the heat exchanger. The regenerator is an isothermal volume space.
3.2.6 Connections
The volume for the tubing used to connect the respective components and the clearances
in the system was calculated to be 210 cm3 (12.8 in3). The total volume consisted of an
adiabatic space of 109 cm3 (6.62 in3) and an isothermal space of 101 cm3 (6.18 cm3).
34
Table 1: Mean Volume of Adiabatic and Isothermal Spaces
Component Parts Isothermal cm3 Adiabatic cm3
Hot Cylinder 266
Cold Cylinder 266
Regenerator 1400
Heater 925.8
Pump 133
Clearance/Connections 101.3 108.5
Total 2693.1 501.5
Isothermal Volumes
Heater
Regenerator
Heater
Regenerator Connections
Adiabatic Volumes
Connection
s
Hot Cylinder
Hot Pump
Cylinder Connect ions
Pump
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3.2.7 Tuning/Output Column
The tuning line will reach it maximum amplitude of movement in output when the
frequency of the pressure variations is about equal to the natural or resonant frequency of
the water oscillating in the output column. To achieve the appropriate length of the
tuning line the total isothermal and adiabatic volume spaces, table 1, were used in
equation 2.4.8. The length of the tuning line was calculated to be 7.13 cm3 (23.4 in3).
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Float-cylinder gap 3.5mm
Tuning column diameter 50mm
Tuning column length (determined from 23 feet
equation 2.4.8)
Pump-arm mean volume 133cm3
Regenerator internal volume 1440 cm3
Heater inner volume 1440 cm3
Dead space Volume 3250 cm3
Swept volume 7000 cm3
Heater Temperature Max. 400 °C
Cold Temperature 10 °C
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4. CONSTRUCTION & ASSEMBLY
4.1 Introduction
This section will provide details on the design, fabrication and construction process as
well as the decisions that we made to improve on the original design. A couple of pages
are been dedicated to explaining exactly how we constructed the various engine parts
because we believe there is the need to document this process should there be a desire, in
the future, to improve on the existing design. Please refer to the appendix to see the
various crude sketched, with dimensions, of the different engine parts.
The construction of the engine parts, after the design decisions had been made, took the
most time primarily because one member of the group had no prior experience with the
machine shop which meant that we needed to spend some time learning how to use the
machines in the shop. We got under way around the second the second week of the
semester and completed all the engine parts that constituted our initial design by mid
April. We are currently in the process of testing several engine parameters to see if there
are any design decisions we may have to alter. As an example, we have just decided to
set up a better and more effective heat exchanger and have machined pieces that enable
us to utilize a nichrome wire rather than our original idea which will be explained shortly.
We have also incorporated a pressure transducer into the design to enable us get a sense
of the pressure variations within the system. The circuitry for this device is however, yet
to be completed. Additionally, thin wire thermocouples have been placed in the hot and
cold spaces inside the system.
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All the parts were fabricated using standard machinery – Bridgeport milling machines
and lathes, band-saws, drill presses, a belt sander, etc. For the more sophisticated parts,
we sought the assistance of Grant Smith and Professsor Orthlieb. However, for most of
the engine components, we made them and gained useful insights and experience in the
process.
The machinist, Mr. Grant Smith, ordered and or provided the materials that were
necessary in advancing the project. The table below shows the ordered system
components and the approximate cost.
Material/Part Cost/$ 7
PVC Tubes (6”, 2”, 1”,¾”) 70.00
Transparent PVC 10.00
Six inch T 15.00
Carbide Silicate Board 15.00
High Temp. RTV 15.00
Copper Foil 20.00
Nichrome Wire 15.00
Phenolic 20.00
Plastic End Caps 10.00
Pressure Transducers 10.00
Thermocouples 15.00
TOTAL 220.00
Table 4.2.1: Engine Part costs
4.2.1 Displacer
The displacer, U-tube, which is made of 6 in ID PVC was cut to the desired lengths using
the band saws, after which the ends were beburred with the belt sander. The length of six
inch tubing on the hot side is 3 ft while that on the cold side of the displacer is 2ft. A 6
inch ‘T’ connects from one of the two six inch elbows at the lower ends of the displacer,
7
The figures given here are all approximate.
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which give the U-shape of the displacer, to the tuning line and the rest of the hot engine
column
40
students determined the temperature of both the hot air at the top, and the cold air at the
bottom and how they varied respectively as they moved through the regenerator. In
addition, they looked at the velocity profile of the air as it moved through the regenerator
to determine the effect different regenerative materials have on the speed of air in the
system. Table 4.2.2 below shows the results of their experiments. Based on the data
presented here, there is no obvious ideal choice for our regenerative material. Different
materials registered different ideal results. For example, the medium sized pebble yielded
the highest hot cycle temperature difference, while the 2 pads of steel wool yielded the
largest cold cycle temperature difference. The small pebbles on the other hand recorded
the biggest hot and cold cycle speeds which, as the data suggests, does not vary much
among the different possibilities.
Hot Cycle
Normalized Cold Cycle
Temperature Temperature Hot Cycle Cold Cycle
Material Difference Difference C Speed m/s Speed m/s
We made the decision to use the medium size quartzite pebble primarily because of its
high temperature difference at the hot side of the engine. The cold size temperature
difference in our system was not a big issue since we are of the strong opinion that the
cold chamber really is not as cold as we would have wanted it to be. Secondly, the hot
and cold cycle speeds recorded are high enough compared to the other materials that we
would not have to worry much about kinetic flow losses.
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The graph below therefore shows the relationship between air speed and the stage in the
cycle for the medium bebble. As is evident from it, the high temperature difference and
the approximately constant cold and hot cycle speed makes it an ideal regenerative
material for our system.
80
60
40
20
-20
-40
-60
-80
-100
-2 0 2 4 6 8 10
Time (s)
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glued to the copper tube with high temperature RTV which has the advantage of being
able to withstand extremely high temperatures.
For the purposes of testing and empirically knowing the exact amount of heat input into
the system, we are going to replace the copper coil within the heat exchanger with
nichrome wire. This would be coiled around a rectangular block of carbide silicate
material 1.5 * 1.5 * 6 inches. A ½ inch hole was drilled through the center of the block
through which a solid rod which would be used to hold the block in place. To do this,
holes are drilled through the copper, screws are put through these holes which then press
firmly on the rod, to hold it in place.
phenolic
Copper
tube
Fig 4.2.1: Picture of the heat exchanger
4.2.6 Unistrut
Given the size of the system, as well as the fact that it will not stay put without a support
frame, we designed a Unistrut support frame to hold the displacer portion of the system in
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place. The frame has two triangular truss-like members and a rectangular base. The
triangular members are separate by about 8 inches, giving enough room to hold the
machine in place. At the base, the rectangular cross section also provides enough room
for the lower portion of the engine. The entire frame is supported at the base by two
straight pieces that run across the ground as can be seen in Fig 4.2.2. One inherent
drawback of the current unistrut design is the face that it does not lend itself to being able
to move the machine around a whole lot which is an issue that could be addressed in the
future.
End Caps
Unitstrut
Frame
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4.2.8 Modifications
4.2.8a Heater
The initial heater used during the first run of the system was replaced with another heater
that was of similar design. The initial heater was taken from a blow dryer and contained
a built in cut-off switch as a safety precaution in case of over heating. The cut-off switch
did not allow for the heat exchanger to reach the necessary temperatures of 300-350oC
needed for operation. The blow dryer heater was replaced with a heater that was
composed of a nichrome coil wrapped around a ceramic base. The new heater was
powered by a veriac whose maximum input power was 664 watts.
Figure 4.2.8c Machined ceramic material used to smooth the transitions of the fluid in the pipe.
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4.3 Data Acquisition System:
To be able to quantify and measure the system’s performance as well as the various
parameters, it has been equipped with pressure transducers, thermocouples and very soon,
will incorporate anemometers. These will be used in conjunction with some data
acquisition system in order to observe the engine’s operation.
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Fig. 4.3.1: 316L Pressure Transducer
4.3.2 Thermocouples
The thermocouples are to be used to monitor the engines temperature. These highly
sensitive thermocouples are attached to the system via the heat exchanger. They are also
put into the dead spaces in the hot chamber. They rely on the voltage differential between
the wires to provide a temperature reading. The calibration has been programmed into the
reader to the extent that the output voltage, i.e., the voltage difference between the two
wires translates directly to a temperature value.
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Figure 5.1 Picture of system; the red arrows show where leakage occurred; the white arrow show where
frictional losses were observed.
The leakage of the moving fluid, in our case air, was observed to have occurred at the top
and bottom of the heat exchanger and the top of the hot cylinder. The red arrows in
figure 5.1 indicate the locations where air was observed to leak. The manner in which the
leakage was detected was through hearing whistling sounds at the stated locations during
the operation of the system. The leakage of air could be a result of the following:
1. large temperature changes in the heat exchanger – may have opened sealed holes
in exchanger
2. pressure variations in the system – the forces due to the pressure could have
created small openings at the connections
3. inadequate method and application of sealing material – because of the difficulty
in determining where the leakages were some openings may have been omitted
Not only did the leakages contribute to the system’s inability to sustain oscillation, the
frictional losses were a second set of problems. The frictional losses in the system are
mostly due to fluid flow. The system contains many entrances and exit losses at the
transitions between:
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1. displacer and the tuning column
2. the displacer and ¾ connections
3. the ¾ connections and the heat exchanger and regenerator
The locations of where the frictional losses took place in the system could be viewed in
figure 5.1.
During the initial test run the peak pressure during free oscillation was observed to be
2.5kPa.
Figure 5.1.1 Using heat device from hair dryer the maximum pressure recorded was 8kPa and the
maximum pressure during free oscillation was 2.5kPa; the decay time constant was 5 seconds.
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The three initial peak pressure values in figure 5.1.1 are 8kPa and correspond to the
forces used to jumpstart the system. During free oscillation the time constant was
calculated to be approximately 5 seconds. The oscillations eventually decayed
exponentially to zero soon after trying to jumpstart the system.
Figure 5.1.2 Graph of temperature variations inside hot cylinder; max temperature during free-
oscillation was observed to be 30oC.
The temperature ranged between 27oC and 30oC. The low temperature range of the hot
cylinder shows the inefficient heat transfer between the heat exchanger and the hot
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cylinder. Although the thermo-couple in the heat exchanger did not work during the
initial run we have assumed the temperature in the heat exchanger to have greatly
exceeded 37oC and thus the temperature range of the hot cylinder should have reached a
maximum temperature far greater than the recorded temperature shown in figure 5.1.2.
As stated earlier, the heater device inside the heat exchanger cut off when it reached a
certain threshold temperature and may have contributed to the low heat transfer between
the exchanger and the hot cylinder. The cutting off of the heater made the heat transfer
highly inefficient.
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Figure 5.2.1 The maximum pressure during free-oscillation was found to be 2.5kPa; the oscillations
decayed exponentially with a decay time constant of 40 seconds
The max pressure value during free-oscillation was recorded to be 2.5kPa and the decay
time constant was observed to be 40secs. The reinforced sealing of the system using
RTV reduced the amount of air leakage and thus allowing the pressure variations to be
sustained for a longer period of time.
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The maximum output power was calculated to be 23 watts. The oscillations of the
system during the final run were sustained much longer than the oscillations of the initial
test run.
Figure 5.2.3 Heat exchanger temperatures varied between 125oC and 400oC.
During the period of free-oscillation the maximum temperature recorded was 375oC and
the minimum temperature recorded was observed to be 125oC. The wide swing in the
temperature inside the heat exchanger shows that the heater was effective in delivering
the desired amount of power and thus the temperature range between 300 – 350oC, target
temperature range, was achieved.
53
While the system was oscillating the high temperatures experienced inside the heat
exchanger caused significant deformation of the outer PVC casing. The thermal
resistance of PVC was found to be 212oC. To add further thermal protection for the PVC
material a ceramic paper lining was laid on the inside wall of the heat exchanger. As the
temperature of the heat exchanger approached the thermal resistance of the PVC material
it began to become soft. This lining of ceramic paper helped in protecting the PVC casing
from the extreme temperatures, but as the test progressed the PVC casing, nonetheless,
began to deform.
The deformation of the heat exchanger may have affected the integrity of the system and
may have contributed to the opening of seals that were reinforced with RTV and taping.
Although the findings of figure 5.2.3 suggests that air was moving into and out of the
exchanger at different temperatures, openings in the exchanger due to the high
temperatures that the heater produced and the low thermal resistance of PVC could have
contributed negatively to the pressure variations during operation.
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Figure 5.2.4 Temperature varied between 23oC and 37oC in the hot cylinder.
As air moved in and out of the hot cylinder temperature variations were recorded. The
occurrence of temperature differences during free-oscillation in the hot cylinder shows
that air at room temperature and warm air were entering the component. Because the
temperatures entering the cylinder were not close to the temperatures in the heat
exchanger, the air in the heat exchanger did not reach the maximum temperatures that the
heater in the exchanger reached. In other words, the air circulating in the system did not
reach the maximum temperatures of 300-350oC.
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The poor heat transfer between the heat exchanger and the hot cylinder may be due to a
number of reasons, of which is the most probable cause for the inefficient heat transfer is
the low dead space volume. By increasing the dead space volume the mass of air moving
in the system could be increased; thereby, allowing more air to be heated by the heater at
any given time in the system. The increased air volume would thus allow for the
temperature increase in the hot cylinder. Thus, the heat transfer between the heat
exchanger and the system would be improved. The dead space volume could be
increased by increasing the diameter of the connections, from ¾ inch PVC piping to 1 or
even 2 inch PVC piping.
Additionally, the transitional elements used to smooth the transition from the different
diameter piping contributed to the improvement of the system operation. The transition
elements, made from ceramic material, were placed at the entrance and exit between the
displacer and tuning column and between the ¾ connections and the heat exchanger.
More transition elements could have been placed between the displacer and the ¾
connection piping, which may further cut down the frictional losses in the system.
A foam float was placed inside the hot cylinder above the water level to minimize
evaporation of the water. The foam helped in keeping the water from entering the
connections and thus into the heat exchanger, a situation that would negatively effect the
system operation because the water level in the system would decrease and increase the
volume of the hot cylinder. The increase hot cylinder volume would decrease the system
efficiency because the transfer of heat into the volume space was not ideal, as shown by
the low temperature range of the hot cylinder, see figure 5.2.4.
Furthermore, the cold water bath on the cold side did not provide a proper heat sink for
the space. Because PVC is a bad thermal conductor the heat entering the cold chamber
was not removed and thus did not provide a more extreme temperature difference in the
system. The greater the temperature differences in the liquid stirling engine the greater
the efficiency of the system during operation.
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5.2.6 Tuning Column
The data collected from the tuning column can be viewed in table 5.2.6. The flow in the
column was observed to be laminar with a fluid velocity of .63 m/s.
6. Conclusions
Given our project objectives we feel that the opportunity to work on this endeavor greatly
enhanced our appreciation and awareness of the resources and technologies that we take
for granted daily. Our goal of developing a liquid piston stirling engine that was capable
of producing and output power of 5 watts or 3.5 % efficiency was somewhat realized.
The design and materials used to construct the system were kept to a mechanical
simplistic model to allow for better integration in developing societies. Although certain
aspects of the system proved to be difficult problems the attempts to overcome them
brought about many success and setbacks. Our interest and analysis of the liquid piston
stirling engine may inspire future work on the system which would advance our last
objective, which was to raise greater awareness of fluidyne engines as a low cost energy
source for applications found in developing societies.
We have learned a great deal on the operation of the stirling engine, more specifically the
liquid piston stirling engine. Hopefully, the experience gained working on this project
57
will affect our futures in regards to advancing technologies that would benefit the most
underprivileged our communities and societies. We also enjoyed working along side our
advisor Prof. Carr Everbach, and technician Grant Smith. In addition, we learned a great
deal from Prof. Fred Orthlieb, who was very instrumental in helping us acquire many of
the materials and parts needed.
7. Further Work
To enhance the performance of the engine and improve on its efficiency, further
improvements could be made to the existing engine. These improvements will
compliment the successes of this project to make the
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improved. One way to achieve this is by possibly placing the heater insider the
hot chamber. This will ensure that the air in the hot cylinder is heated directly.
Alternatively, heat transfer could be improved by placing thermal fins to facilitate
conduction.
where all pressures are gage pressures. The pressure increase in the engine would
increase as well, increasing the work per cycle.
The main drawback of pressurization is leakage of the working gas (air in our
case) due the greater effect of imperfect sealing at higher pressures. Sealing
imperfections not evident currently may appear if a compressor is used to raise
the mean pressure. In addition, caution should be exercised in pressurizing since
both the PVC tubes could crack.
59
4. Addition of thermocouples inside the cold cylinder as well as velocity sensors in
connecting tubes
To better characterize the engine, additional sensors should be incorporated into the
system. In addition to the thermocouples that have been placed in the heat exchanger
and in the hot cylinder, one should be placed inside the cold cylinder to monitor the
temperatures there. Secondly, to get an accurate sense of the speed of air flow in the
system during each cycle, velocity sensors should be implemented inside the hot and
cold chambers. This will be useful in providing the speed of the air flow in the system
which is necessary for fluid dynamics’ analysis. Knowledge of the speed of air flow
will also be useful in determining kinetic flow losses in the engine.
60
pumping line and measure performance, the engine design must be improved upon to
function more efficiently.
7. Fulfill primary project goal
The end product for this project should be a solar-powered water pump, with the
water that has been pumped, heated with focused sunlight. It is our hope that this
objective will be pursued in the near future to ensure that all the goals/objectives of
this project are met.
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8. References
- West, C.D. 1983. Liquid Piston Stirling Engines. Van Nostrnad Reinhold Publishing.
- Ilak Milos, Hartigan Jesse, 2004, Design and Development of a small Stirling Engine.
- URL: <www.wikipedia.com>
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