Liquid piston engines by Gupta, Aman Narayan, Sunny Sharma, Shubham

Liquid Piston Engines

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Liquid Piston Engines

Aman Gupta, Shubham Sharma, and
Sunny Narayan

This edition first published 2017 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA
and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-32295-5

Cover images: Irrigation, Elswarro | Dreamstime.com. Plant, lofoto | Dreamstime.com
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Cover design by Kris Hackerott

Set in size of 11pt and Minion Pro by Exeter Premedia Services Private Ltd., Chennai, India

Printed in the USA

10 9 8 7 6 5 4 3 2 1

Contents

Abstract ix

List of Symbols xi

1 Introduction 1
1.1 Background 1
1.2 Types of Stirling Engines 2
1.3 Stirling Engine Designs 4
1.4 Free-Piston Stirling Engines 6
1.5 Gamma Type Engine 18
References and Bibliography 27

2 Liquid Piston Engines 29
2.1 Introduction 29
2.2 Objectives 32
2.3 Brief Overview of Pumps and Heat Engines 33
2.4 Heat Engine 38
2.5 Clever Pumps 42
2.6 History and Development of Stirling Engines 45
2.7 Operation of a Stirling Engine 48
2.8 Working Gas 53
2.9 Pros and Cons of Stirling Engine 53
2.10 Low Temperature Difference Stirling Engine 54
2.11 Basic Principle of a Fluidyne 55
2.12 Detailed Working of a Fluidyne 57
2.13 Role of Evaporation 61
2.14 Regenerator 61
2.15 Pumping Setups 62
2.16 Tuning of Liquid Column 63
2.17 Motion Analysis 64
2.18 Losses 65
2.19 Factors Affecting Amplitude 66
2.20 Performance of Engine 67

v

vi Contents 67
70
2.21 Design 71
2.22 Assembly 72
2.23 Calculation 74
2.24 Experiments 76
2.25 Results 78
2.26 Comparison Within Existing Commercial Devices 79
2.27 Improvements 80
2.28 Future Scope 80
2.29 Conclusion 83
2.30 Numerical Analysis
References and Bibliography 87
87
3 Customer Satisfaction Issues 88
3.1 Durability Issues 88
3.2 Testing of Engines 89
3.3 Design of Systems 89
3.4 Systems Durability
References and Bibliography 91
91
4 Lubrication Dynamics 93
4.1 Background 94
4.2 Friction Features 94
4.3 Effects of Varying Speeds and Loads 95
4.4 Friction Reduction 96
4.5 Piston-Assembly Dynamics 102
4.6 Reynolds Equation for Lubrication Oil Pressure 104
4.7 Introduction 105
4.8 Background 110
4.9 Occurrence of Piston Slap Events 114
4.10 Literature Review 117
4.11 Piston Motion Simulation Using COMSOL 120
4.12 Force Analysis 131
4.13 Effects of Various Skirt Design Parameters 132
4.14 Numerical Model of Slapping Motion 133
4.15 Piston Side Thrust Force 133
4.16 Frictional Forces 143
4.17 Determination of System Mobility
4.18 Conclusion

Contents vii

5 NVH Features of Engines 145
5.1 Background 145
5.2 Acoustics Overview of Internal Combustion Engine 146
5.3 Imperial Formulation to Determine Noise Emitted
from Engine 149
5.4 Engine Noise Sources 151
5.5 Noise Source Identification Techniques 154
5.6 Summary 157
References and Bibliography 158

6 Diagnosis Methodology for Diesel Engines 161
6.1 Introduction 161
6.2 Power Spectral Density Function 162
6.3 Time Frequency Analysis 162
6.4 Wavelet Analysis 163
6.5 Conclusion 164
References and Bibliography 165

7 Sources of Noise in Diesel Engines 167
7.1 Introduction 167
7.2 Combustion Noise 168
7.3 Piston Assembly Noise 168
7.4 Valve Train Noise 170
7.5 Gear Train Noise 170
7.6 Crank Train and Engine Block Vibrations 171
7.7 Aerodynamic Noise 171
7.8 Bearing Noise 171
7.9 Timing Belt and Chain Noise 172
7.10 Summary 174
References and Bibliography 175

8 Combustion Based Noise 179
8.1 Introduction 179
8.2 Background of Combustion Process 
in Diesel Engines 180
8.3 Combustion Phase Analysis 183
8.4 Combustion Based Engine Noise 184
8.5 Factors Affecting Combustion Noise 186
8.6 In Cylinder Pressure Analysis 187
8.7 Effects of Heat Release Rate 187
8.8 Effects of Cyclic Variations 188
8.9 Resonance Phenomenon 189

viii Contents 189

8.10 In Cylinder Pressure Decomposition Method 192
8.11 Mathematical Model of Generation of 193
199
Combustion Noise 199
8.12 Evaluation of Combustion Noise Methods
8.13 Summary 203
References and Bibliography 203
204
9 Effects of Turbo Charging in S.I. Engines 205
9.1 Abstract 206
9.2 Fundamentals 207
9.3 Turbochargers 208
9.4 Turbocharging in Diesel Engines 208
9.5 Turbocharging of Gasoline Engines 213
9.6 Turbocharging 213
9.7 Components of Turbocharged SI Engines 222
9.8 Intercooler 223
9.9 Designing of Turbocharger 223
9.10 Operational Problems in Turbocharging of SI Engines 224
9.11 Methods to Reduce Knock in S.I Engines 225
9.12 Ignition Timing and Knock
9.13 Charge Air Cooling 225
9.14 Downsizing of SI Engines
9.15 Techniques Associated with Turbo Charging 231
of SI Engines Boosting Systems
233
10 Emissions Control by Turbo Charged SI Engines
235
11 Scope of Turbo Charging in SI Engines
237
12 Summary 237
237
13 Conclusions and Future Work 238
13.1 Conclusions 240
13.2 Contributions
13.3 Future Recommendations 243
References and Bibliography
247
List of Important Terms
249
Bibliography
251
Glossary

Index

Abstract

Engines and pumps are common engineering devices which have become
essential to the smooth running of modern society. Many of these are very
sophisticated and require infrastructure and high levels of technological
competence to ensure their correct operation. For example, some are com-
puter controlled, others require stable three-phase electrical supplies, or
clean hydrocarbon fuels. The first part of the project focuses on the iden-
tification, design, construction and testing of a simple, yet elegant, device
which has the ability to pump water but which can be manufactured easily
without any special tooling or exotic materials and which can be powered
from either combustion of organic matter or directly from solar heating.

The device, which has many of the elements of a Stirling engine, is a
liquid piston engine in which the fluctuating pressure is harnessed to pump
a liquid (water). A simple embodiment of this engine/pump has been
designed and constructed. It has been tested and recommendations on
how it might be improved are made. The underlying theory of the device is
also presented and discussed.

The second portion deals with noise,vibration and harshness perfor-
mances of internal combustion engines. Features of various sources of
noise and vibrations have been discussed and major focus has been on
combustion based noise and piston secondary motion.Various equations
of piston motion were solved and effects of various parameters on it were
analyzed.

ix

List of Symbols

Symbol Definition Units
V Volume cm3
P Pressure Bar
T Temperature Kelvin
R Gas Constant J/K-mol
v Voltage Volt
I Current Ampere
Q, V Volume flow Rate cm3/s
Qe Heat Absorbed Joules
A Tube Area cm2
q Charge coulomb
Cp Specific Heat J/Kg-K
η Kinematic Fluid Viscosity m2/S
ω Frequency Hz
Rt Radius Of Tube cm
X Fluid Displacement cm
ρ Fluid Density kg/m3
U Heat Transfer coefficient W/m2-k
L,l Tube length cm
g Acceleration due to gravity m/s2

xi

Liquid Piston Engines. Aman Gupta, Shubham Sharma, and Sunny Narayan.
© 2017 Scrivener Publishing LLC. Published 2017 by John Wiley & Sons, Inc.

1

Introduction

1.1 Background

The Stirling engine system was studied years ago. Such engines have merits
the basis of sealings, materials, heat transfer rate, size, and weight issues.
During past years the major focus has been on various designs of Stirling
engine systems.

This engine is based on a heated reciprocating system. The gas receives
heat and expands at constant temperature. Rate of transfer is higher, which
is a major drawback of these engines. In contrary the internal combustion
(IC) engine is operated by combustion of air-fuel mixture which results
in higher heat and pressure rise which is converted to useful work. The
temperature varies with the combustion and piston motion. As the heat is
supplied externally the following varieties of sources can be used:

Heat from gaseous, liquid, or solid fuel
Solar energy
Recycled Waste heat

1

2 Liquid Piston Engines

Cooling in a Stirling engine cycle can be done in the following ways:

Convection cooling
Use of cooling fluids like water, ethylene glycol, or a mixture

Reversible nature of Stirling engine differentiates it from IC engines.
Combustion outside results in lower emissions as well as less noise and
vibration.

Solar energy may also be harnessed using parabolic dish.
As a smaller number of fuel types or heat sources are available, a Stirling
system may be designed as such. This system may use solar heating as the
primary heat source, as well as a natural gas burner as an auxiliary unit
during nights and cloudy periods.

1.2 Types of Stirling Engines

Using basic concepts of heat engineering many designs of Stirling engines
have been proposed over past years. These engines may be classified on the
basis of mechanical design features as:

Kinematic designs: These engines operate on basis of crank-
shaft and linkage mechanisms in which the motion of the
piston is limited by configuration of linkages.
Free-piston designs: In these engines the oscillatory motion
of the piston in a magnetic field generate electric power.
Pressure gradient cause tuned spring-mass-damper motion
of displacer. Such machines are simple to operate but more
complex on basis of dynamics and thermodynamics. For
cooling purposes, the piston may be driven by a motor.

Stirling engines may also have alpha, beta, or gamma configurations
which are discussed as follows:

Alpha engines which are seen in Figure 1.1 have two separate pis-
tons that are linked and oscillate showing some phase lag. The working
gas moves to and fro passing through a cooler, regenerator, and a heater
between the cylinders. These engines are kinematic engines which need
proper sealings.

Beta engines that are seen in Figure 1.2 have a displacer-piston arrange-
ment that are in phase with one another. The displacer pushes the gas to
and fro between the hot (expansion area) and cold ends (compression

Regenerator Introduction 3
Hot end
Gas motion
Cold end

Crank shaft

Figure 1.1 Alpha engines. Heater
Hot end
Displacer Regenerator

Cold end Cooler

Power piston

Figure 1.2 Beta engines.

Cold end Cooler Power
Displacer Regenerator piston

Hot end Heater

Figure 1.3 Gamma engine.

area). As the working gas moves, it passes through a cooler, regenerator,
and heater. Beta engines can be either kinematic or free-piston engines.

Gamma engines which are shown in Figure 1.3 have a system wherein
the displacer and power pistons operate in separate cylinders. The displacer
moves the working gas to and fro between the hot and cold ends. The cold

4 Liquid Piston Engines

area has cold side of the displacer and power piston. As the gas moves, it
passes through a cooler, a regenerator, and a heater. These engines can be
either kinematic or free-piston type.

1.3 Stirling Engine Designs

The power piston in the engine is connected to an output shaft by linkages.
Kinematic design of the engine has following merits:

Coordination of various parts for proper motion during
start-up, normal operation, and fluctuations of loads.

Some disadvantages of such a design include:

Need of lubrication due to rotating parts.
Need of more maintenance.
Proper sealing needed.

Some of the novel designs of kinematic engines are discussed next.

Wobble-plate Mechanisms
The wobble-plate that is seen Figure 1.4 has a wobble plate which is in a
sliding contact with the crankshaft pivoted by connections to pistons as
well as connecting rods. This ensures straight travel inside the cylinder
with out rotation. The thrust is transferred to the crank at an offset angle

Crank
shaft

Piston

Wobble
plate

Figure 1.4 Gamma engine.

Swash Introduction 5
plate
Power piston
Crank
shaft Power piston

Figure 1.5 Swash plate engines.

to wobble plate which acts as a double-acting engine using the power
stroke of one cylinder to compress the cold gas for the adjacent cylin-
der. The power piston for one cylinder is the displacer piston for another
cylinder.

The Z-crank shape that the same to the wobble plate design has pis-
tons connected directly to the crankshaft. Pivot points are made in order to
ensure axial motion of the piston in the cylinder. Such design is more com-
pact as compared to a single-piston Stirling engine. However these engines
have certain demerits:

Cyclic load and wear of pivots is quick as they are under
compression and bendings.
Piston-lubrication is a major issue. Oil flow may cause fouling
and lesser external heat transfer so reducing the efficiency.

Swash Plate Drive mechanisms – This drive has may same features as
wobble plate. Bearings are used to connect the swash plate to the crank-
shaft and rotates with the crankshaft, but the wobble plate which remains
fixed is attached to the shaft. This design has many merits:

Quiet operation, better sealings with lesser lubrication
problems.
Design of swash plate may be changed for better stiffness
and power transfer.
The balancing of swash plate can be done built by adding
additional sets of pistons. This in turn increases the power
output and reduces the power-to-weight ratio.

Rhombic Drive – In this mechanism, yokes connect the power piston
and the displacer piston. These are linked to twin crankshafts by means
of connecting rods, as seen in Figure 1.6. In this drive mechanism power

6 Liquid Piston Engines Displacer
piston
Regenerator

Power Yoke
piston power

Connecting Gear
rod

Displacer york Crank
disc

Figure 1.6 Rhombic drive engine.

piston and the displacer piston move with constant lag. The rhombic drive
has many benefits:

The engine has less vibrations due to complete balance of
various lateral forces.
These engines operate at higher power outputs due to higher
pressures.
Many units can move at same time in order to provide power
to a multi-cylinder engine.

1.4 Free-Piston Stirling Engines

These engines have two oscillating pistons that are not connected as seen in
Figure 1.7. The displacer piston has a smaller mass compared to the power
piston. The heavier piston moves undamped. Motion of the displacer is
simulated by springs or by the compressible working gas. The springs
placed between the displacer and the power piston provide harmonic oscil-
lations of the displacer. These oscillations are maintained by temperature
difference, and so the system operates at the natural frequency.

The power in a free-piston system is generated by a linear alternator.
Recently some of the designs have been using a hydraulic drive to run the
crankshaft. Use of these hydraulics is good in engines having more torque
which reduces the lateral forces in such systems.

Heater Introduction 7
Regenerator
Hot end
Cooler Displacer
Cold end

Alternator

Electric
output

Figure 1.7 Free piston engine.

Free-piston systems have major advantages:

Less lateral forces and lubrication needs due to absence of
rotating parts.
Less maintenance.
Properly sealed units prevent loss of the working gas.

These systems have following disadvantages:

Need of complex calculations to ensure proper working.
Lower response time as compared to kinematic and IC
engines.
Piston position is an important parameter to control system
as oscillations may become unbalanced.

The Alpha configuration of engine is the simplest form having two pis-
tons and two cylinders connected by a regenerator. Both these cylinders are
normal to one another connected by a flywheel. The hot piston is in contact
with located high-temperature source while the cold piston is with the low-
temperature reservoir. The pistons are arranged in a manner that the linear
motion is converted to rotatory motion and a constant phase difference is
maintained. The pistons are joined at a common point on flywheel.

As compared to the other basic designs the alpha type engine has greater
volume due to higher compression ratios.

8 Liquid Piston Engines

Figure 1.8 An Alpha Stirling engine.

Cold end

Hot end
Figure 1.9 Alpha engine - Transfer phase.

WORKING OF ENGINES: working of a Stirling engine can be divided
into four operations steps that are similar to I.C. engine. Heat is added
and removed at constant temperatures. The working of I.C. Engines occurs
on the basis of Otto and Diesel cycles, respectively. Mechanisms of these
engines is complex as motion is based on movements of multiple pistons.
Working of an Alpha Stirling can be analyzed as follows:
1. Transfer of working gas from cold side to hotter side:
Flywheel moves clockwise, the hot piston moves towards right hand side
towards Dead Centre and the cold piston moves up towards Top Dead
Centre (TDC) as seen in Figure 1.9.

Introduction 9

Cold end

Hot end
Figure 1.10 Alpha engine - Power stroke.

The regenerator connects both pistons and operates at hotter
temperatures.

The pistons move in such a manner that the change in the engine vol-
ume is minimum and heat addition occurs at constant volume.

Towards end of the process, the working gas will be hotter and the major
portion of remains in the hot cylinder. This is similar to suction stroke.

2. Power stroke
As flywheel roates by 90°, the majority of the working gas is now in the hot-
ter cylinder and volume of the engine is minimum.

The fluid receives heat from a hot source. It expands moving the fly-
wheel further. This is similar to power stroke of the engine and all energy
is derived from this stroke.

As the hot piston moves towards right side due to gas pressure, the gas
expands, with a portion passing through the regenerator.

As the heat added to the system at constant temperature it is converted
to work, with a little rise in temperature. A perfect isothermal processes
will cause a phase change.

This may be compared to the power stroke.
The working fluid expands to about three times its original volume.
The flywheel turns by another quarter rotation and the hot piston starts to
move to Dead Centre. The cold piston moves downwards. The regenerator
gets heated up as the hot fluid passes by.
Heat rejection occurs at constant volume and can be seen as the exhaust
stroke of the engine.

10 Liquid Piston Engines

Figure 1.11 Alpha engine - Transfer stroke.

Figure 1.12 Alpha engine - compression stroke.

3. Compression stroke
The crank moves by quarter of rotation. The cold piston is at the bottom
dead center location and the hot piston moves towards inner dead center.

The working gas has major portion in the cold cylinder which cools
down rejecting heat to cold reservoir. As the cold piston moves to the top
dead center, volume is reduced and the working gas is compressed.

During Isothermal Compression the working gas rejects heat and gets
compressed. There is minimum change in the internal energy and work
needed is also minimum. Towards the end of the process, almost all the gas

Hot Introduction 11
cylinder
Cold
cylinder

Triangle
connecting
rod

Figure 1.13 Ross engine.

Expansion Heater
space Regenerator

Cooler
Compression
space

Figure 1.14 Double-acting engine.

is in the cold piston, so volume reduces to about one-third of its original
and the cycle goes on.

This final stroke may be compared to action of a supercharger or turbo-
charger. There is no need of compression inside the power piston.

This mechanism was first proposed by Andy Ross. This linkage makes
design more compact as connecting rods move in a straight line. This in
turn reduces the force on the pistons and thus improves performance of
the engine. Wear is less due to less friction and life is also increased.

The double-acting-engine has four cylinders. The pistons act as the
expansion space of one engine and at the same time as compression space

12 Liquid Piston Engines

Pistons Bearing

Power shaft
Figure 1.15 Rocking yoke.

Pistons
Gears

Power Crank shaft
shaft

Figure 1.16 Gear mechanism.

of a neighbouring one. Thus this is the same as four Alpha engines. Sir
William Siemens has done major work to develop these engines.

The cylinders are connected in a circular manner with cold and hot
regions of neighbouring cylinders connected by a reservoir. Hence the out-
let of the last cylinder is connected to the first one. So this system is more
compact and with high specific power output. All the pistons move at a
phase difference of 90°.

Maintaining the phase difference between the pistons and harnessing
power is complicated.

All the above mentioned mechanisms face problems due to excessive
side thrust and excessive wear and they have lower life and reliability.

Introduction 13

Swash plate Heater tubes
drive Combustor
Regenerator
Cooler

Piston

Figure 1.17 Swash plate mechanism.

Expansion Heater
space Regenerator

Valve Cooler

Compression
space

Manifold

Turbine

Figure 1.18 Beal engine.

William Beale later designed an engine in which a turbine was used to har-
ness power out.

Such mechanism that is seen in Figure 1.18 uses gas compressors to run
turbines. Double-acting compressors may be used for more pulses of air
per cycle but at lesser specific power of the engine. Uniform loading and
lesser thrust force also increases life of the engine.

WORKING: Working of the double acting Stirling engine can be under-
stood from the design of Alpha Stirling engine. Various engines in alpha
design can have the same stroke. For that the phase lag between any two
adjacent pistons must be 90°.

14 Liquid Piston Engines

As shown in Figure 1.18, first see the first piston moving downwards. The
engine between the last and the first cylinder may be considered as a fourth
engine. The first and second piston move downwards at the same time, this
transfers the working gas to the hotter side with negligible change in volume.

Hence the first engine is working on Isochoric heat transfer in work-
ing fluid. The second one is vicinity of the BDC and third piston moves
upwards. The second one is in power stroke, and the volume of fluid is
maximum. Similarly, other engines are in transfer stroke which moves
fluid from hot to cold end. A Beta configuration of engine has a displacer
and piston in same cylinder with a 90° phase difference. Robert Stirling
was first to invent a Beta Stirling engine that was an inverted beam engine.
It was similar steam engine having a beam linkage.

These are more suited for space limited applications, but output is lower
than other engines. Use of a regenerator is complex in absence of insula-
tion between the hot and cold ends. There is loss of RPM of the engine and
hence its output.

WORKING: The basic working of a Beta Stirling engine is similar to that
of Alpha Stirling engine. The difference lies in the way the working gas

Figure 1.19 Beta engine.

Piston Compression Expansion
space space
Displacer

Beta engine

Regenerator

Cooler Heater
Figure 1.20 Beta engine in working.

Introduction 15

moves in the cylinder. Displacer causes motion of the working gas and also
hinders the use of wire gauss/mesh.

For an Alpha engine system, it is easy to see engine strokes. For every
quarter rotation of a stroke was finished.

However, for a Beta Stirling engine the four strokes may not be easily
distinguished. The piston reaches in vicinity of dead center positions near
end of strokes. As the transfer strokes are at constant volume, there is a
small change in volumes.

A vertical configuration of a Beta engine is seen in Figure 1.21.
Clockwise quarter movement of crank results in transfer stroke which
results in working fluid motion from the cold end towards hot end. Power
and compression strokes show a major changes in volumes, whereas trans-
fer stroke show a minimum changes.

The displacer is ahead to piston by a quarter of stroke without change
in volume.

It helps in motion of fluid between the hot and cold ends.
As seen in Figure 1.22, the displacer is at dead center while the power
piston moves right. The left part of figure shows the position of piston and
displacer at the start of the stroke, whereas the right part of figure shows their
positions at the termination of the stroke that are opposite at initial and then
in same phase. The piston motion is small due to a small changes in volume.
Heat addition occurs at constant volume in the Stirling cycle. As a
regenerator is not present in cylinder, it is usually placed between the cold
and hotter sides of the engine. These devices have lesser efficiency. In Some
cases heating is done from conduction of heat from hotter side of cylinder
so there is no need of a regenerator.

Transfer of working fluid from
hot to cold end

Expansion stroke Compression stroke

Transfer of fluid from
cold to hot end

Figure 1.21 Vertical beta engine.

16 Liquid Piston Engines

Figure 1.22 Working of beta engine.

Figure 1.23 Working of beta engine – expansion.

From the diagrams we can predict the motion of the piston and dis-
placer at the end of each stroke.

Towards the end of the transfer stroke as a major portion of the work-
ing gas is present in the hotter side of the system and the power piston
moves towards dead center. The flywheel turns by 90° and the gas expands
at constant temperatures getting heat expands which results in motion of
power piston towards dead center. The beta design gives lesser output as
compared to alpha one.

From the figures it is clear that power piston moves by a larger amount
whereas the displacer moves only a short distance which denotes power
stroke.
3. Transfer of working fluid from hot end to cold end -towards the end of
the expansion phase, the displacer moves towards inner dead center, while
the piston is at outer dead center. The flywheel rotates by another 90°. The
hot fluid passes in the gaps of the displacer and moves towards the cold
side. The motion of the displacer is more than the piston.

The fluid loses heat to cylinder walls at constant volume.

Introduction 17

Figure 1.24 Transfer stroke – Beta engine.

Figure 1.25 Compression stroke - beta engine.

Rhombic
linkage

Flywheel

Displacer Power piston

Figure 1.26 Rhombic drive – Beta engine.

4. Compression stroke
After that flywheel moves by another quarter cycle as most of the work-
ing fluid is now near the colder section of the cylinder. The piston and the
displacer move towards inner dead center as volume is reduced. The fluid
is compressed at constant temperatures in contact with the cold reservoir.
At the end of the this stroke, the transfer again starts and the cycle repeats.

The Rhombic drive has a single cylinder with two separately moving
pistons. The Beta design was designed by Rolf Meijer of Philips company,
in the 1960s.

18 Liquid Piston Engines

Unlike the conventional engines, the connecting rods in this drive
are rigid which makes its operation smooth and lesser vibrations. So the
engine is quieter as thrust force is reduced resulting in lesser wear. In spite
of these merits this linkage is difficult to assemble.

1.5 Gamma Type Engine

A Gamma design of engine has a displacer-type Stirling engine, having
power piston in a separate cylinder. This arrangement allows complete
separation between the heat exchangers and working space. Displacer
cylinder diameter is bigger than the power piston diameter and so larger
unswept volumes are seen as compared to Alpha or Beta designs.

Though two separate cylinders are present only one is sealed. Power pis-
ton remains isolated from the reservoirs. So sealing is easier compared to
Alpha designs. Issues of sealing are important as closer tolerance that fit
are needed for effective working of the engine. As sealing of the Gamma
engine is easier these are easily manufactured.

As the heat exchangers are placed on the larger displacer cylinder their
placement is easier. Better heat exchangers can be designed as the area
available is much larger. Due to this flexibility in the design with use of
water-cooled having cooling jackets, have been made.

Gamma engines are a major focus of work due to its ease of manufac-
ture. Two types of these engines known as the Ringbom engines and the
Low Temperature Engines have been made. The Low Temperature designs
are most popular.

On the other hand, the Gamma engines have the minimum specific
power as during the expansion is incomplete as only a portion of fluid

Figure 1.27 Gamma engine.

Introduction 19

reaches the hot region. As a result, some of portion of expansion occurs in
the compression space. As compression ratios are lower so, these engines
are used in case need of separate cylinders.

WORKING: working of a Gamma Stirling design is similar to that of a Beta
Stirling engine. The displacer moves in a separate cylinder, whereas the
power piston moves in separate cylinder. Both these cylinders are linked in
order to allow passage of the working fluid between them.

2. Transfer stroke
At the onset of the stroke, major portion of the working fluid is present
in the compression space. The displacer moves up towards the top dead
center, whereas the piston moves downwards. The piston motion is lesser
when compared to movement of the displacer as heat addition occurs at
constant volume.

Compression Displacer Expansion
space space

Gamma engine Regenerator
Piston
Cooler Heater

Figure 1.28 Gamma engine working.

Piston
Displacer
Figure 1.29 Gamma engine – transfer stroke.

20 Liquid Piston Engines

Figure 1.30 Gamma engine – expansion stroke.

3. Expansion Stroke
After the flywheel moves by a quarter of cycle, during the start of transfer
stroke most of the working gas is in the expansion area near hot reser-
voir. At the start of the stroke, the displacer moves up to top dead cen-
ter, whereas the piston moves upwards. As the gas expands, piston moves
upwards during power stroke of the engine.

As partial expansion occurs in the compression space, power produced
is lesser.

The flywheel rotated by another 90˚, the working gas expands and most
of it is near the hot reservoir. The displacer is now moving towards the BDC
while the piston is moving upwards to its TDC. As the displacer moves
down it pushes almost all the working fluid to the compression region of
the cylinder.

4. Compression stroke
As the flywheel has moved by another 90˚, most of the working fluid is in
the compression space. As the piston moves down towards BDC, the effec-
tive volume inside the cylinders is reduced. The working fluid which is
now in contact with the cold reservoir is compressed. Not all the working
fluid is in contact with the cold reservoir as the compression space extends
into the power piston cylinder which is not in contact with any thermal
reservoir. This increases the work required in compression and the effect is
reduced specific power output. If the cold reservoir is the atmosphere, this
effect is somewhat negligible.

Introduction 21

Figure 1.31 Low temp engine.

Figure 1.32 Sneft engine.

The compression ratios for a Gamma Stirling engine are much smaller
compared to other types as the swept volume of the power cylinder is much
smaller compared to the total volume of the engine.

In many cases foam is used to make displacer which also has some
effects of regeneration. The cylinder of displacer that has smaller diameter

22 Liquid Piston Engines

encloses cylinder. Power piston and cylinder are placed on the top plate of
the displacer. In such cases air acts as working gas. The power produced is
lesser of order of 1W. Such a model seen in Figure 1.32 works at a tempera-
ture difference of about 40 °C.

Ringbom design of engines are also Gamma type Stirling in which just
the piston is connected to the flywheel.

The displacer always has a large clearance near dead center positions
that is denoted by stops. Such an engine makes a sound in dispalcer and is
called as thumper engine.

Higher gas pressures pushes the displacer to move up and down.

WORKING: In a Ringbom engine, mean operating pressure is same as the
atmospheric pressure and works in the absence of a mechanical linkage.

The figure shown above is near end of the compression stroke, as pres-
sure inside the cylinder rises which transfers major portion of fluid in the
compression area. As the displacer cylinder pressure rises, the force acting
on it also increases.

The pressure on the top and bottom of displacer is nearly equal. But
the forces are not equal as push rod is present near top. This results is an
upward force having magnitude equal to pressure acting on pushrod area.
As this force is more than the displacer weight, the displacer piston moves
up. As the compression goes, the rise in pressure is more which lifts dis-
placer upwards.

The piston and displacer motions of Ringbom engine are shown in
Figure 1.33.

1. Transfer of fluid from cold to hot end:
Displacement of the working fluid occurs towards the hotter side as the
displacer piston moves up.

Also remember Pmax> Patm > Pmin.

2. Expansion or power stroke
At the onset of this stroke, the pressure is maximum. The piston starts
moves downwards, which causes gas to expand. As the pressure falls, dis-
placer starts to slow down and comes to stop producing thumping sound.
As this stroke ends the pressure falls below the ambient pressure and the
displacer moves downwards.

3. Transfer of working fluid from hot to cold end.
As the pressure inside the displacer cylinder further drops the transfer
stroke begins. The displacer moves with down wards acceleration and
the working fluid is moves to the cold end. At the end of this process,

Displacer Introduction 23

Guide for displacer push rod
Piston

Figure 1.33 Ringbom engine. Displacer
Displacer push rod
Piston

Figure 1.34 Cut out section.

24 Liquid Piston Engines

Power piston
Displacer rod

Displacer piston
Displacer cylinder

Heat plate

Figure 1.35 Free-piston engine.

theoretically the pressure will be least and the displacer will be downwards,
while the piston starts to move upwards.

4. Compression stroke.
As the piston starts to move upwards for the compression stroke, the pres-
sure inside the engine starts to increase. The displacer decelerates and soon
stops. As the pressure exceeds the displacer weight, it moves upwards.

Free-Piston Stirling engine is the general term given to those which
have pistons which are not mechanically connected to a flywheel. There are
types that even have liquid pistons or diaphragms to do the job of mechan-
ical pistons. Since there is no connecting rod and flywheel arrangement to
convert the linear motion of the piston into rotary motion, some co-axial
devices have to be used to harness the produced work. The most com-
monly used co-axial device is the linear alternator. Another application of
the free-piston Stirling engines is to function as a pump, as linear motion
of the piston can be easily integrated for that purpose.

W. T. Beale has done pioneering work in free-piston type engines which
can overcome the lubrication problem. Many of these engines use springs,
gravity or inertial masses in order to supply the energy needed for the
compression.

WORKING: Ringbom Stirling is a form of free piston engine. In these
engines, gravity powers the compression stroke. Either springs or inertial
masses may be also provided to give necessary energy. Displacer motion is
similar to the Ringbom engine.

Introduction 25

(a) Extended rod (b) Inertial mass (c) Sprung motor/alternator
Engine

Heat
pump

(d) Duplex (e) Spring to piston (f) Casing reaction (harwell)

Cold Hot

(g) Fluidyne (h) Alpha (three to six cylinders)

Figure 1.36 Various free engines.

Figure 1.37 Transfer stroke – free engine.

26 Liquid Piston Engines

Figure 1.38 Expansion stroke – free engine.

Figure 1.39 Transfer stroke – free engine.

Transfer of fluid from cold to hot end:
Initially, the pressure inside cylinder is higher and displacer moves
upwards. The working gas moves towards hotter end of the engine.
2. Expansion or power stroke:
During the onset of the expansion stroke, the pressure inside is highest due
to which power piston moves down thus there is an increase in the volume.

Introduction 27

Figure 1.40 Compression stroke – free engine.

The gas expands further causing a fall in pressure. At the end of the stroke
the power piston moves down.
3. Transfer of fluid from hot to cold end:
As pressure falls near to the atmospheric pressure, the displacer moves
downwards and hence the working gas is moved to the cold region. This
process continues till the displacer stops at BDC.
4. Compression stroke:
The piston mass powers the compression with initial contribution due to
atmospheric pressure, but later its effect becomes lesser. During the fall
of piston under gravity, the volume reduces and working fluid gets com-
pressed. The piston decelerates towards the end of stroke reaching the
bottom dead center at the end of the stroke.

References and Bibliography

1. Stirling engine assessment, EPRI, paolo alto,CA;2002,1007317. http://www.
engr.colostate.edu/~marchese/mech337-10/epri.pdf

2. http://docslide.us/documents/stirling-engine-assessment.html
3. http://www.vineethcs.com/pdf/Stirling%20Engines-A%20Begineers%20

Guide_rev_2.pdf

Liquid Piston Engines. Aman Gupta, Shubham Sharma, and Sunny Narayan.
© 2017 Scrivener Publishing LLC. Published 2017 by John Wiley & Sons, Inc.

2

Liquid Piston Engines

2.1 Introduction

Water is an important civic amenity needed for survival. Oceans are the
major source of the water cycle, covering about 71% of the global area,
whereas about 3% of freshwater is found as polar ice and glaciers. Some
major sources of water on earth and their abundance is shown in the
figures below.

To account for our basic needs, about 20–50 liters of water are needed
every day for the use of a single person. The constant growth of the human
population has exposed many citizens in the developing nations of Africa
and Asia to an acute shortage of pure and usable water. A United Nations
report estimates that about 27% of the population in Africa and 65% in
Asia are compelled to use contaminated water unfit for daily use [5]. The
graphs presented here clearly show the water stress on human populations.

A major source of water available on earth is surface water in the form
of freshwater rivers, streams, ponds, etc. But the majority of water bodies
are being polluted due to industrial or human activities, leaving the global

29

30 Liquid Piston Engines

Fresh 3% Ground Rivers 2%
water
Saline 31.3% Swamps
97% 11%
Ice caps
and glaciers Lakes
68.7% 87%

Total water Fresh water Fresh surface
water

Figure 2.1 Percentage of water sources on surface of earth.

80% 1980 1990 2000
60%
40%
20%

0%
1970

Figure 2.2 Percentage of global population exposed to water shortage.

America Euurope
65% 2%

Africa
27%

Asia
65%

Figure 2.3 Percentage of population exposed to polluted water.

population exposed to water-borne disorders. According to an estimate,
about 2 million tons of waste are being dumped into water bodies and
about 6,000 children die due to water-borne disorders each day [6]. This
situation can be visualized in some of the pictures shown below.

Liquid Piston Engines 31

Figure 2.4 Sources of polluted water in underdeveloped nations.

Renewable groundwater sources on a national basis

Annual withdrawals
(cubic kilometers)

0–5
5–20
20–100
More than 100
No data

Figure 2.5 Global groundwater withdrawal.

In such conditions groundwater can be a good way of meeting the needs
of the population. Groundwater makes up 31% of the total freshwater sup-
ply on this planet. Groundwater is available in porous aquifers. An aquifer
is a permeable rock from which the groundwater can be extracted easily. It
needs to be pumped out by a suitable mechanical pump running on elec-
tricity or a fuel-operated engine [8]. Global usage of groundwater can be
seen clearly from the data presented herein.

Due to scarcity of fossil fuels, there is a need to look out for alternative
sources of energy, including renewables like wind, solar power, geothermal
power, etc. Harvesting of solar energy is a good way to meet the future
energy demands of our society. The average yearly solar flux reaching earth
is 174 PW. About 30% of this is reflected back by clouds, atmosphere and

32 Liquid Piston Engines

the surface of earth. The remaining 70% is used to heat water in oceans and
on the surface of earth [9].

Solar flux can be used in an indirect or a direct way. The indirect way
includes use of bio-mass, wind or solar thermal pond, whereas the direct
one includes use of photo voltaic cells or utilization of solar flux for raising
vapor cycle to run a heat engine.

Alternatively, solar energy can be used to run a liquid piston fluid pump
for raising groundwater, thus avoiding the use of polluted water from
polluted water bodies. These pumps can also be used for the irrigation
of crops. Liquid piston engines are a good choice to tap vast solar power.
Their operation dates back to the early 19th century when the Humphrey
engine was first used. These engines have many advantages over modern
conventional engines. They do not need complex mechanisms like crank
or cylinder, are noiseless in operation and simple to construct. There is
no need for lubrication in the absence of sliding parts. However, various
designs require heat input and output at vastly different temperatures;
hence the construction material must be able to resist corrosion as well as
high temperatures [10].

2.2 Objectives

To design and fabricate a novel heat pump which is affordable in the devel-
oping world, hence create the awareness for alternative low-cost energy
sources.

Imcoming solar radiation
100%

Top of atmosphere 30%
Lost to space

19%
Absorbed

in the
atmosphere

51%
Absorbed
at surface

Figure 2.6 Solar energy balance.

Liquid Piston Engines 33

2.3 Brief Overview of Pumps and Heat Engines

Pumps – convert mechanical energy into fluid energy.

Turbines – exactly the opposite, convert fluid energy to mechan-
ical form.

Classification of pumps – based on the method by which mechan-
ical energy is transferred to the fluid –

Positive-displacement pumps

Kinetic pumps
Under positive-displacement
These pumps discharge a given volume of fluid for each stroke
or revolution.
Energy is added intermittently

Reciprocating action – pistons, plungers, diaphragms, and bellows.

Rotary action – vanes, screws, lobes.

Types of positive displacement pumps
Peristaltic pumps

Fluid captured within flexible tube
Tube is routed between rollers – rollers squeeze tube and
move liquid as parcels

Rotary Gear
Vane
Positive Screw
displacement Progressing cavity
Lobe of cam
Reciprocating Flexible tube (peristaltic)

Piston
Plunger
Diaphragm

Kinetic Radial flow (centrifugal)
Axial flow (propeller)
Mixed flow

Jet or ejector type

Figure 2.7 Pump types.

34 Liquid Piston Engines

Vane Cam ring
Vane slot

Suction Discharge Outlet
Rotor Inlet Discharge manifold

Figure 2.8 Vane pumps. Drive
shaft

Piston Discharge

Suction Suction manifold
(b) Double acting—duplex
(a) Single acting—simplex
Figure 2.9 Simple and double-acting pumps.

Avoids Contact of Liquid with Mechanical Parts

Kinetic Pumps

Transforms kinetic energy to static pressure – adds energy via rotating
impeller

Fluid enters through the center of an impeller and is thrown outwards
by the vanes

Jet

Used for household water systems.
Composed of centrifugal pump and jet assembly
Suction is created by the jet in the suction pipe

Liquid Piston Engines 35

Discharge Intake Discharge Intake Discharge

Flow
rate

1 Revolution Time
(a) Single-acting pump—simplex

Side #1 Discharge Intake Discharge Intake Discharge
Side #2 Intake Discharge Intake Discharge Intake

Flow
rate

Time

1 Revolution
(b) Double-acting pump—simplex

Figure 2.10 Discharge rates.

(a) Peristalic pump with variable-speed (b) Peristalic pump with case open to

drive system show tubing and rotating drive rollers

Figure 2.11 Peristaltic pumps.

Comparisons between the two types:

Characteristic Positive-d isp lacem en t Kinetic

Flow rate Low High
Pressure rise High Low
Self-priming Yes No
Outlet stream Pulsing Steady
Works with high viscosity fluids Yes No

36 Liquid Piston Engines Outlet

Outlet Fluid
inlet
Fluid
inlet

(a) Radial-flow impeller (b) Mixed-flow impeller
Outlet
Fluid
inlet

(c) Axial-flow impeller (propeller)
Figure 2.12 Kinetic pumps.

(a) Pump and motor

(b) Cutaway of pump (c) Radial-flow impeller

Figure 2.13 Centrifugal pumps.

Pump selection depends on –

Discharge
Head requirement
Horsepower requirements of the pump

Liquid Piston Engines 37

Discharge pipe
Motor
Impeller

Suction Pressure
pipe pipe

Diffuser

Nozzle

Foot valve
with
strainer

Figure 2.14 Jet pumps.

40
Capacity

Pump capacity (gal/min)30 Volumetric
Input power (hp)efficiency
Efficiency (%)20Overall100
efficiency Input 80
power 60
40
10 20
0
0 0 500 1000 1500 2000

Discharge pressure (psi)

Figure 2.15 Performance curves.

As pressure increases there is a slight decrease in capacity due to inter-
nal leakage from the high-pressure side.

Power needed varies linearly with pressure.
Volumetric efficiency = flow rate delivered/theoretical flow
rate (90 to 100%). Theoretical flow rate is based on displace-
ment per revolution times the speed of rotation.

38 Liquid Piston Engines

200Total head (ft) 60
150 Total head (m) 50
100 40
500 1000 1500 1000 30
50 Pump capacity (gal/min) 20
00 10

2500

0 2000 4000 6000 8000 10000

Pump capacity (L/min)

Figure 2.16 Centrifugal pump performance curves.

Capacity decreases with increasing head.

At “cut-off ” head flow is stopped completely and all energy
goes to maintaining the head.
Typical operating conditions well below “cut-off ” head.

Overall efficiency = power delivered to fluid/power supplied to pump.

2.4 Heat Engine

The onset of industries had led to rapid development of the steam engine.
Heat can be transformed into useful work and vice versa. This is the main
feature for working of an engine. A refrigerator is also another form of
engine since it transfers heat from a cold body to a hot one. In this portion
major features of the Carnot engine have been discussed.

The first and second law of thermodynamics are as follows:

First Law – Energy remains constant in a system i.e.

ΔEth = W + Q.

Second Law says that all macroscopic processes are irreversible.
Heat can itself move from a hot to a cold body, but reverse process is

impossible.
The area under p–V denotes done is done by an ideal gas. This work is

positive when the energy is out of the system.

Liquid Piston Engines 39

Heat from hot
to cold body

QH Copper bar QC

FIRI ICI

Hot reservoir at Cold reservoir at
Th Tc

Figure 2.17 Heat engine.

Hot reservoir Th

System Qh

Copper bar as
system

Qc

Tc
Cold reservoir

Figure 2.18 Energy transfer.

The first law of thermodynamics can be expressed as:

Q + WS = Eth

Energy that is transferred inside a system as heat that is stored inside and
which causes an increase in thermal energy. A reservoir of energy shows a
larger transfer of thermal energy without a significant change of its thermal
energy. Hot and cold reservoirs have temperatures that are denoted as TH
and TC.

The energy transfer diagram of a heat engine has been shown in
Figure 2.17. A copper bar is a system that serves as a path of heat transfer
between a hotter and a cold body. Amount of heat transferred from the res-
ervoir is denoted by QH, whereas the heat transferred out is denoted by QC.

From the previous equation we have

Q = Eth + WS

Where Q is the net heat to system. Assuming that the work done is zero.
As the bar is at steady state, ΔEth = 0. So QC = QH.

40 Liquid Piston Engines

As seen in Figure 2.19, heat is flowing from a body at colder temperature
to one at hotter. Such a process is against the second law of thermodynamics.

The process may be compared to action of two stones reaching a higher
temperature as we rub them together and then place them in water.

Work done on the stones causes an increase in their energy equal to the
work done. i.e. W = ΔEth. As these stones contact cold water the heat flows
to the water, i.e.

ΔEth = QC.

This process can be fully efficient as all the energy supplied to the system
is ultimately transferred to the water as heat. The reverse cannot take place
without need of external force as seen in Figure 2.20.

Second law forbids this action

Hot reservoir Th
Qh

System Copper bar as
system

Qc

Tc
Cold reservoir

Figure 2.19 Heat flow.

Hot reservoir Th

Qh

System Copper bar as
W system

Qc

Tc
Cold reservoir

Figure 2.20 Work efficiency.

Liquid Piston Engines 41

The arrangement shown above has a gas placed in an insulated box hav-
ing a piston with mass M. The base is heated as it has no insulation. The
gas expands that lifts piston by distance Δx at constant temperature. The
change in internal energy is null due to this fact and so the first law of
thermodynamics can be written as WS = Q. As the piston reaches top most
position its lift stops. As the system works in a closed cycle, so its efficiency
is full as seen in Figure 2.22.

Heat Engines and Refrigerators

An engine is a device that gets heat QH from a hot source, does some
work, and then rejects heat QC to a cold source. This process is shown in
Figure 2.23 as engine connects to both sources.

The whole cycle may be written as

Eth net = 0, E = Q + W = Q – WS = 0.
or Wout = Qnet + QH – QC

Insulation M

Piston

Gas
X

Flame

Figure 2.21 Iso thermal process. Th

Hot
system

Qh

W out

Figure 2.22 Perfect engine.