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

42 Liquid Piston Engines

Qh is transfered from hot body to system
Hot Th

Heat Qh W out
engine Qc

Cold Tc

Remaining Qc= Qh-Wout
is transfered as waste heat to
cold one

Figure 2.23 Energy transfer in engine.

The efficiency defined as –

1 Qc
Qn

Maximum value of efficiency is 100 percent. But this needs Qc = 0. Such
an engine seen in Figure 2.23 is theoretical. Practically engines have lower
values of 10–40 percent.

Perfect Heat Engine

As seen in Figure 2.24. As the mass reaches its maximum it is removed
as piston in locked position with volume of the gas constant. The cooling
occurs and the gas is gets compressed to its initial phase hence completing
a cycle.

Mass is again placed and the process repeats. This process is seen as a
pV diagram in Figure 2.25. As zero work is during isochoric process so
network output = (WS)12 + (WS)3

2.5 Clever Pumps

Apart from manmade pumps nature also has many clever pumps such as
the human heart, capillary action in plants and neuron pumps in the nerve
cells of the human cerebrum.

a. Human Impulse: All animals have nerve cells known as neu-
rons present in their cerebrum. These cells transmit nerve
impulses from and to the brain which form the basis of

Liquid Piston Engines 43

Heat transfer Gas expands Piston is locked M
from fuel to lifting the and mass removed
gas mass
Pin
M M No heat

Gas Heat

Heat

Gas cools at Isothermal
constant compression restores
volume gas to initial stage

Figure 2.24 Ideal engine.

Isotherm
Heating

Qh

1 2
P
Cooling
Qc

Qc

Compression 3

V
Figure 2.25 Ideal engine P-V curve.

human reflexes, movements, emotions, and senses. Neurons
have Na+K+ATPase, which is a protein pump present in neu-
rons of the brain. It utilizes energy from ATP molecule stops
pump three sodium ions out of a cell and two potassium ions
into the cell. This causes a potential difference across cell
membranes called resting potential, which is the basic cause
of nerve impulses transmitted across neurons in the human

44 Liquid Piston Engines

body. These impulses form the basis of human stimuli. Action
of this natural pump can be seen in the figure below [12].
b. Capillary action: this effect occurs due to cohesive, adhesive
forces or surface tension and plays an important role in trans-
portation of water. Capillary action in trees helps to draw
water into roots by xylem tissue cells. Xylem cells are made of
cellulose molecules which form a chemical bond with water,
hence helping in circulation of water in a tree [13].
c. Human heart – The human heart is an excellent example of
a natural pump. It has four valves, namely tricuspid valve,
mitral valve, aortic valve, and pulmonic valve. Starting from
the right atrium, blood flows through the tricuspid valve to
the right ventricle and is sent to the lungs for oxygen enrich-
ment by the pulmonary artery. From the lungs, blood flows
through the pulmonary vein to the left atrium and from the
left atrium to the left ventricle through the mitral valve. This
enriched blood flows to the aorta through the aortic valve,
from where it is distributed to the whole body. Each valve
has a set of flaps which maintain blood flow through it [14].

Osmosis or reverse Osmosis are other naturally occurring phenomena,
which can be used to design a novel pump capable of selective pumping.

3Na+

Outside

Cell Na Na+K+ATPase K
membrane

Inside Closed Closed
(leak) (leak)
ATP ADP+Pl 2K+

Figure 2.26 Human Impulse pump.

CH2OH H OH CH2OHO H OH CH2OHO H OH
O
H H O OH H H H H O OH H H H H O OH H H

O OH H H H H O O OH H H H H O O OH H H H H O
O

H OH CH2OH H OH CH2OH H OH CH2OH

Figure 2.27 Water cellulose bonding.

Liquid Piston Engines 45

2.6 History and Development of Stirling Engines

“As you enter the past, you will find direction for the future”
—Ivo Kolin [16]

During the industrial revolution of the 18th century, the steam engine
became a primary source of power. But this device has its drawbacks. Its

Aorta Left atrium
Right atrium
Right ventricle Septum
Left ventricle

Blood vessels
Figure 2.28 Workings of a human heart.

Hydrostatic
pressure

Water Solution Water Solution

Osmosis Semipermeable Reverse osmosis
membrane

Figure 2.29 Osmosis and reverse osmosis.

46 Liquid Piston Engines
maximum efficiency is at the most 2% and there were many accidents
involving explosions. This prompted engineers to look for alternative
sources of power like Stirling engines.

A Stirling engine is a hot-air engine operating on the principle that air
expands on being heated and contracts on being cooled. These devices
have zero exhaust and are external combustion engines; hence a wide vari-
ety of fuels can be used to run a Stirling engine which includes alcohol,
bio–products, or waste gases, etc. These engines are suitable for opera-
tions which have the following needs [16]: A) Constant power output.
B) Noiseless operation. C) Long startup period. D) Low speeds.

The development of the Stirling engine is widely attributed to the
Scottish scientist Sir Robert Stirling. The first version of this engine, devel-
oped in 1815, was heated by fire and air cooled. Figures of some of these
early versions are presented in the sections below.

Later, in 1864, Erickson invented the solar-powered engine to heat
the displacer tube at the hot side. The heat was obtained by use of solar

Figure 2.30 Earliest version of a Stirling engine developed by Stirling brothers.

Figure 2.31 Alpha-type Stirling engine developed in 1875.

Liquid Piston Engines 47

reflectors. The first alpha-type engine was built in 1875 by Rider. Reader
and Hooper proposed the first solar-powered heat engine for irrigation
purposes in 1908. Following this, Jordan and Ibele designed a 100  W
solar-powered engine for pumping of water. In 1983 a low-temperature
difference Stirling engine was patented by White, which had an efficiency
of about 30%. Colin later presented a design with a low temperature differ-
ence of 15 °C, and Senft published specifications of an engine with a very
low temperature difference of 5 °C between hot and cold ends [16].

Some of the following events can be considered as important milestones
in the design and development of a Stirling engine for use as a pump:

1688: Thomas Savery develops a drainage pump which was a
liquid piston machine.

1909: Development of Humphrey pump.
1931: Malone designed and developed an engine with regenera-

tive cycle similar to a Stirling engine.
1965: Philips Company patented a Stirling engine.
1977: The metal box company developed Stirling engine for

irrigation purposes in Harwell lab.
1985: McDonnell designed an engine with parabolic reflectors

to focus solar energy, thus achieving a high temperature
of 1400 °C.

A thermal engine is a device which converts heat energy into mechanical
energy. The operation of a heat engine can be described by a simple ther-
modynamic cycle as follows:

Efficiency
W Qh Qc
Qh Qh

Figure 2.32 McDonnell engine.

48 Liquid Piston Engines W

High temprature
source

Q1
Heat engine

Q2
Low temprature sink

Figure 2.33 Heat engine.

Energy conversion process

Chemical Combustion Heat Machine Mechanical Generator Electrical
energy energy energy energy

Heat engine

Figure 2.34 Energy conversion in a heat engine.

Heat engines can be further classified as external combustion or internal
combustion engines. An engine where fuel is burnt outside the engine is an
external combustion engine, whereas in the internal combustion engine,
the fuel is burnt inside the engine. An engine operating on a Carnot or
Stirling cycle is an example of an external combustion engine while one
operating on an Otto or Diesel cycle is an internal combustion engine.
Comparison of these cycles is presented below:

2.7 Operation of a Stirling Engine

“In all places where there exists a difference of temperature, there can be a produc-
tion of motive power.”

—Sadi Carnot, 1824 [16]

In a Stirling engine the fluid is contained in a confined space; hence there
are no problems of contamination. In order to reduce the heat losses, the

Liquid Piston Engines 49

Table 2.1 Comparison of various engines.

Type of Heat Heat

combustion Cycle Compression addition Expansion removal

External Carnot Adiabatic Isothermal Adiabatic Isothermal
External Stirling Isothermal Isometric Isothermal Isometric
Internal Otto Adiabatic Isometric Adiabatic Isometric

Carnot (ideal) heat cycle P-V diagram

Pressure (P) Heat added

entropy increases

gas expands

C constants temperature
Isothermal expansion

Gas compressed D Gas expands
no heat added or lost
no heat added or lost

constant entropy constant entropy

temperature rises B temperature falls
Adiabatic compression Adiabatic expansion

Gas compressed A

heat given out

entropy falls

constant temperature
Isothermal compression

Volume (V)

Carnot (ideal) heat cycle entropy diagram

Temperature (T) Heat added
constants temperature
expansion (work done by gas)

CD

Compressed Expansion
no heat added or lost no heat added or lost

no work done constant entropy
no work done

B A

Heat extracted

constants temperature

compression (work done ON gas)

Entropy (S)

Figure 2.35 P-V& T-S plot of a Carnot cycle.

Otto heat cycle PV diagram Otto heat cycle entropy diagram
Pressure (P)
Temperature (T)C

Heat inS=0 C
Heat outexpansionV=0

Heat in D B Expansion
B Heat out (work out)
Compression D
S=0 A (work in)
compression Entropy (S)
A

Volume (V)

Figure 2.36 P-V& T-S plot of an Otto cycle.

50 Liquid Piston Engines

Expansion space
Expansion piston

Heater

Working gas (air)

Regenerator Compression space
Cooler
Compression
piston

Crank

Ross yoke linkage

Figure 2.37 Stirling engine.

mass flow rate must be low, which can be maintained by low viscosity fluid
or high working pressures. These engines are 30 to 40% efficient in a tem-
perature range of 923–1073 K [7].

A Stirling engine consists of the following components:

1. Heat source – as fuel does not come in direct contact with
the working fluid, Stirling engines can work on fluids which
may damage parts of a conventional engine.

2. Regenerator – the function of a regenerator is to prevent the
waste heat from being lost to the environment by storing it
temporarily, thus helping to achieve high efficiencies close to
an ideal Carnot cycle. A simple configuration consists of fine
mesh of metallic wires. In an ideal Stirling cycle, the con-
necting space between hot and cold ends acts as regenerator.

3. Heat sink – typically the ambient environment acts as an
ideal heat sink; otherwise the cold side can be maintained by
iced water or cold fluids like liquid nitrogen.

4. Displacer piston – it causes the displacement of working gas
between hot and cold regions so that expansion and contrac-
tion occurs alternatively for operation of engine.

5. Power piston – transmits the pressure to the crankshaft.

In a Stirling engine, hot air expands when heated and contracts when
cooled. This principle of operation was most properly understood by Irish

Liquid Piston Engines 51

scientist Robert Boyle from his results on experiments on air trapped in a
J-shaped glass tube.

Boyle stated that the pressure of a gas is inversely proportional to its
volume and product of pressure and volume occupied is a constant depend-
ing on temperature of gas.

Hence PV = NRT

Various assumptions are made in this cycle are [16]:

1. Working fluid is an ideal gas.
2. Conduction and flow resistance is negligible.
3. Frictional losses are neglected.
4. Iso-thermal expansion and contraction.

This cycle can be described by the following stages [16]:

1. Phase C–D: Iso thermal expansion – the working fluid
undergoes an iso-thermal expansion absorbing the heat from
source. The power piston moves out, hence increasing the
volume and reducing the pressure. The work done in expan-
sion of gas is given by:

We RT log VD
VC

2. Phase D–A: Power piston now reaches the outermost
position and stays there so that volume is constant. The
working fluid is passed through the regenerator where it
gives up heat for use in the next cycle. Hence its temperature
and pressure falls. No work is done during this phase.

3. Phase A–B: The power piston starts moving inwards, reduc-
ing its volume and increasing its pressure the working fluid
gives up heat to cold sink. The work done in compressing the
gas is given by:

Wc RT log VB
VA

4. Phase 2–3: The power piston is at its most inwards point and
stays there to keep the volume constant. Working fluid passes

52 Liquid Piston Engines

Pressure (P) Stirling engine heat cycle PV diagram
C

Regen heat in Heat out T=0
B Heat in expansion

D

Regen heat out

T=0 A
compression

Volume (V)

Stirling engine heat cycle entropy diagram

Pressure (P) C Heat in Expansion
D
Regen heat in Heat out
V=0 V=0
Regen heat out
B
Compression A

Volume (V)

Figure 2.38 P-V & T-S plot of a Stirling cycle.

again through the regenerator, recovering the heat lost in the
second phase; hence its pressure and temperature go up.

Wnet We Wc We R[Th Tc ] log Vmax
Vmin

But

VB = VC, VA = VD

Th Tc 4
Th

In a Stirling cycle, two Isochoric processes replace the two Iso-entropic
processes in an ideal Carnot cycle. Hence more work is available than a Carnot
cycle as net area under P–V curve is more. Thus there is no need for high pres-
sures or swept volumes. This can be seen in the figures presented below.

Liquid Piston Engines 53

p pv = C T 3 4C 4
3 4C TH

pvk = C

2 4
2C
TC
2 2C 1

1
vS

Figure 2.39 Comparison of Stirling cycle and Carnot cycle.

2.8 Working Gas

It is a gas on which the engine operates. There are several gases that can be
used to run a Stirling engine. Lighter gases having atomic mass lesser than
that of air have higher specific heat and gas constant and lower viscosity
resulting in lesser viscous losses and higher heat storing capacity [16]. This
can be seen in the following graph which was obtained by simulation by
Philip Brothers.

2.9 Pros and Cons of Stirling Engine

The Stirling engine has some merits as well as demerits, which are dis-
cussed below.

1. Merits
A. Stirling engines can be run on a wide variety of fuels
including solar energy without a need for the fuel to
come in contact with operating gas, hence avoiding
containment. Hence, even if solar energy is unavailable,
alternative fuels can be used for operations. Thus these
devices are not susceptible to fuel shortage.
B. Low and noiseless operations are possible. Hence suit-
able for submarines.
C. Lower maintenance is needed and combustion of fuel
occurs outside the engine.

54 Liquid Piston Engines

efficiency
55 %

50

45 Helium Hydrogen
40 Air

35

300 20 40 60 80 100 120 140 160

Figure 2.40 Stirling engine efficiency V/S power output for various gas.

Boiler-heat Regenerator
exchanger
Heat
Exhaust Stirling exchanger
gas engine
Heat
consumer

Fuel

Air Combustor Generator Cooler-heat
consumer

Figure 2.41 A CHP Stirling engine.

D. Can be used as a CHP unit.
E. No danger of explosion as in steam engines.
2. Demerits
A. Commercial feasibility not possible on large-scale

manufacturing.
B. Takes time to start from cold.

2.10 Low Temperature Difference Stirling Engine

These engines can run at a typically low temperature difference of less
than 100 °C between hot and cold end. With high temperature differ-
ence between hot and cold end, it is necessary to maintain long separa-
tion between hot and cold ends, whereas area of heating and cooling is

Liquid Piston Engines 55

High temperature
differential
engine

Low
temperature
differential

engine

Figure 2.42 Comparison of LTD and HTD engines.

less important. In 1980 Sneft and Kolin developed simple versions of such
engines where a cup of hot tea could be used as a heat source. The figures
below clearly distinguish between the LTD and HTD engines.

2.11 Basic Principle of a Fluidyne

The basic principle of a fluidyne is similar to a Stirling engine. A gas when
heated expands, and if its expansion is confined, its temperature rises. This
can be understood more easily by the following operations:

Initially the displacer piston is at the centre, with half of the gas in the
hot side and the other half of the gas in the cold side of the cylinder. The
pressure gauge is neutral.

As the displacer piston moves towards the cold end, the gas is displaced
towards the hot end by the connecting tube, and its temperature and hence
pressure goes up, as indicated by the gauge.

As the piston moves towards the hot side, the gas is displaced towards
the cold end, its temperature and hence pressure falls. The changes in the

56 Liquid Piston Engines

Hot Cold Pressure
end Displacer end Pressure

piston

Figure 2.43 Motion of a displacer piston in cylinder.

Hot side Cold side

Figure 2.44 Motion of displacer piston towards cold side.

Pressure

Hot side Cold side

Figure 2.45 Motion of displacer piston towards hot side.

displacer pressure can be used to drive another piston known as the power
piston. When the gas pressure is high, the power piston moves towards the
open end of the cylinder, hence doing some work which can be used to
pump water or rotate a crankshaft.

But when the gas pressure is low, the power piston returns towards its
original position for which work is needed, which is less than the work
available from the previous stroke as lesser force is acting on the piston due
to low gas pressure. Hence there is an excess of energy that can be used for
pumping operation or other tasks.

Liquid Piston Engines 57

Pressure

Hot side Cold side

Figure 2.46 Motion of displacer piston and power piston.

Pressure

Hot side Cold side

Figure 2.47 Motion of displacer piston and power piston.

By clever and innovative engineering, some of the power available from
the power piston can be used to drive the displacer piston, and so create a
variable pressure heat engine.

2.12 Detailed Working of a Fluidyne

A fluidyne can be considered a wobbling column of fluid similar to a pen-
dulum or see-saw toy.

Various Phases of Operation of a Fluidyne
a. Stage 1 – initially levels of liquid in columns is equal when
no heat is applied.
b. Stage 2 – as heat is applied at the hot end, the air at that
end is heated up and expands, moving towards the cold end
through the connecting arm. This pushes the fluid to TDC

58 Liquid Piston Engines Extreme
2
Mean
1

4 5
3

Figure 2.48 Motion of a see saw and pendulum: Gravity acts as a restoring force to bring
back to mean position.

Figure 2.49 Stages of operation of a fluidyne.

at the hot end and BDC at the cold end and the fluid out of
the output column.
c. Stage 3 – the air comes in contact with fluid at the cold end,
cools down and contracts. Once the fluid has reached its
extreme positions at both columns of the U tube, at the hot
side, the inertia of the weight of the extra risen fluid col-
umn tries to bring down the raised level of fluid to its mean
position.
d. Stage 4 – as this happens, the air is again transferred from
the cold end to the hot end through the connecting space, so
that the level of fluid overshoots the mean at the hot side and
reaches BDC, whereas at the cold end it reaches the TDC
and the fluid is again sucked back in the output column.
e. Stage 5 – inertia of weight tries again to restore the levels of
fluids equal at both ends, so that the cycle starts again.

Liquid Piston Engines 59

TDC

Mean position

S=length External heat
of stroke

BDC

Figure 2.50 Stages of operation of a fluidyne.

Initial position of fluid Inertia of weight
at TDC Initial position at BDC

Mean position
S=length External heat
of stroke
BDC

Figure 2.51 Stages of operation of a fluidyne.

Initial position of fluid Initial position
at TDC at BDC

Mean position
S=length External heat
of stroke
BDC

Figure 2.52 Stages of operation of a fluidyne.

60 Liquid Piston Engines

Figure 2.53 Stages of operation of a fluidyne. Cold
Hot

Displacer Output
Figure 2.54 General working of a fluidyne. Cold

Hot

Displacer Output
Figure 2.55 General working of a fluidyne.

Analogous to this cycle, a fluidyne operates in the same way with the left
end of the U tube acting as a displacer piston, whereas the right end acts as
the power piston. Initially most of the air is trapped in the hot side of the
engine and the top dead centre of the cold end corresponds to the bottom
dead centre of the hot end.

The temperature of air rises being in contact with the hot end, hence its
pressure rises, which tends to pump fluid out from the output tube.

Regenerator Liquid Piston Engines 61
Displacer
Pressure

Hot Cold
side side

Figure 2.56 Regenerator.

After half of the cycle most of the air is transferred to the cold side of the
machine and so its pressure falls. The cold surface is at bottom dead center
and the fluid is pulled back into the U tube.

2.13 Role of Evaporation

Evaporation leads to an increased heat input as the latent heat of evapora-
tion is absorbed by the water present in the displacer column. This leads to a
fall in the overall efficiency of the cycle. The evaporation can be suppressed
by increasing the pressure of air in the fluidyne. Stirling engines operate at
high temperatures of 700–800 °C. However, there are various losses, which
bring this temperature down to about 130–300 °C. Evaporation can be sup-
pressed by placing a float in the hot chamber [21].

2.14 Regenerator

Though this does not constitute a mandatory part of the engine, use of a
regenerator is beneficial. With the use of a regenerator, there is a steady
state fall in temperature as the gas gives up heat to the regenerator. Hence
by the time the gas goes into the cold chamber it has already been cooled.
As the gas moves into the hot chamber, it picks up the heat from the regen-
erator; thus the regenerator acts as a buffer of heat and increases the effi-
ciency of the cycle. There are several ways to design this heat exchanger.
One of the common ways is to increase the heat exchanging, keeping

62 Liquid Piston Engines Heat into
regenerator
Air flow from hot
Air passage side to cold side

Thot Tcold
Air passage
Air flow from cold Heatout of
side to hot side regenerator

Thot Tcold

Figure 2.57 Heat exchange in a regenerator.

Table 2.2 Comparison of properties of various materials for regenerator [15].

Material Fibre diameter Density Specific heat

MS Steel 30 μm 7.8 g/cc 437 (j/kg°c)
SS Wool 40 μm 7.8 g/cc 510 (j/kg°c)
SS Mesh 100 μm 7.8 g/cc 510 (j/kg°c)

the resistance to flow minimum. The material of the regenerator can be
honeycomb, wire meshes, or metallic strips made of high-capacity, heat-
absorbing materials.

The action of a regenerator and the properties of some materials suitable
for use in a regenerator can be seen below:

2.15 Pumping Setups

There are several available setups wherein pressure variations can be used
for pumping water. Commonly used pumping configuration involves a
T piece at the end of the output tube and two non-return valves. On the

Gas column Liquid Piston Engines 63
Liquid column
Valves
Gas column Pumping

line

Liquid column

Figure 2.58 Pumping configurations.

outward stroke, the fluid is forced through the upper valve whereas dur-
ing the inward stroke, the fluid is drawn through the lower non-return
valve. However, this setup has some drawbacks. Above a certain pumping
head, the work needed to pump the fluid becomes greater than the volume
change in the engine. Another configuration uses the pressure variations
in the working gas. When the pressure of gas is low, the fluid is drawn up
from the lower valve and as it rises, the fluid is expelled.

2.16 Tuning of Liquid Column

For any oscillating mechanism, the amplitude of motion is maximum
when the frequency of pressure variations on it is equal to the natural reso-
nant frequency of vibrations. The length of the output column has to be
adjusted. If the length is too long, then due to the larger mass of the col-
umn, working gas would be unable for acceleration. On the other hand,
if the length of the column is too small then there would be insufficient
pressure built up in the engine. If the displacer is left to oscillate itself, then
oscillations in the tube will die due to viscous and other losses. There are
several ways to keep the displacer in motion. One of these is the “rocking
beam mechanism”. In this mechanism, the whole machine is mounted on
a pivot-like spring. As the liquid moves back and forth, its shifting weight
causes the whole mechanism to rock like a see-saw.

64 Liquid Piston Engines

Heat in

Spring

Figure 2.59 Rocking beam mechanism.

x
x

Liquid density P

Cross sectional
area A

Figure 2.60 Displacement of fluid in a U tube.

2.17 Motion Analysis

Working fluid in our case is air at atmospheric pressure of 100 Kpa, and
to get maximum oscillating amplitude of vibrations, flow losses must be
minimum.

If the fluid raises by a distance X in one column it must fall by the same
amount in the other column. Hence the difference between volumes of two
columns is given by 2 AX

The pressure due to this volume of difference is given by 2 AXg
Mass of liquid column is given by AL
Hence force acting on column =  ALX

ALX 2 AXg
X 2X g 5

l
2g radians [21]
l sec

Liquid Piston Engines 65

2.18 Losses

There are no moving parts involved in this device, hence no friction. But
various other losses in the liquid piston engine which include:

1) Viscous losses in tube – Crandall proposed the resistance coefficient
is the ratio of pressure drop per unit length and mean flow velocity and is
given by:

r (2 )1/2

Rt

Viscous power losses are defined as the product of pressure drop and
mean velocity of flow, i.e.,

PV rLV 2
Rt2

LV 2 (2 )‰

Rt2 Rt

2) Kinetic energy losses – in addition to various viscous losses there are
flow losses occurring when the fluid changes its direction or speed at the
bends or exits, etc. The pressure drop due to a minor obstruction is given by:

P K V2
2

Hence the power loss is given by the product of pressure drop and flow
velocity.

E PV K V 2V K V3
2 2 2Rt4

Hence total loss is given by summing up individual losses and is given
by:

K Va
2 2Rt4

Where K is a factor depending upon the nature of obstruction.

66 Liquid Piston Engines

Table 2.3 Value of kinetic energy loss factor for various configurations [21].

Element K

90 smooth bend 0.15
90 sharp bend 1
Sharp contraction 0.5

3) Heat losses – This device is a low power output machine compared to
conventional Stirling engines, hence various heat losses due to conduction
must be minimized. Various components of the system can be viewed as
cylinders, for which the heat loss is given by:

Q 2 kL T
ln D2

D1

Where k is the thermal conductivity of material.

4) Shuttle losses – Liquid piston when stationary has the temperature
equal to that of its adjacent space. When this piston moves to a new region,
these are heat losses occurring due to the motion of the displacer piston
and are also known as step down losses. They are calculated by formula:

Qs S2k TD
8Lg

Where D – diameter of displacer column
L – length of displacer column

These losses are dependent on the length of the stroke, which in turn
is frequency of oscillations. The more the frequency, the less is the time
period available for heat transfer and the more are the heat losses.

2.19 Factors Affecting Amplitude

At a particular limit, the liquid piston begins to hit the cylinder top after
which the fluid goes into an area of different cross-section. If evaporation
is neglected then it is seen that the amplitude of vibrations increase as the

Liquid Piston Engines 67

temperature at hot end goes up. However, it is limited by some of following
criteria:

1. Viscous flow losses
2. Poor heat transfer limit
3. Increase in amplitude causes fluid to hit at displacer-air

column interface and move into an area of different cross
section.

2.20 Performance of Engine

Beals number depending on the temperature of heat source is an impor-
tant parameter to determine the power output of this device.

Beals number is given by ratio Power output
Pressure f displaced volume

The variation of source temperature with Beals number is shown in
graph below.

2.21 Design

In this section various factors taken into consideration while designing the
setup are discussed.

0.020Beale no.

0.015 600

0.010
0.005

300 400 500
Heater temprature in K

Figure 2.61 Variation of Beals number with source temperature.

68 Liquid Piston Engines

Air column Collecting cup
Wooden
Pumping line frame
Supports
Cold end

Hot
burner

Displacer

Reserviour

Figure 2.62 Layout of setup.

The chosen design has the following characteristics:

1. Easy to assemble.
2. Easy to transport due to small size.
3. Relative low cost.
4. Provision of cheap and ready to use fuel.

Choice of Materials

The tables shown in the following sections give an idea about the choice
of various design ideas which were evaluated on the basis of various
parameters. Red color indicates the most preferred idea, yellow repre-
sents a reasonable one, whereas the green color denotes the most pre-
ferred choice.

The aim of this design was to pump water up to a certain height using
a liquid piston engine. Initially a hair dryer was chosen as a source of heat
with copper tubes and elbow joints as material for displacer. However,
there were several problems with this setup as brazed joints were of poor
quality and a hair dryer was found to be insufficient to give the required
heat.

Hence this setup had to be discarded. There were several delays on
account of this, and time and cost were the crucial factors to implement the
design. Hence project management was needed so that all accomplished
tasks could be done within deadlines. A Grantt chart giving an overall
review of various talks related to this project is presented below:

Liquid Piston Engines 69

Table 2.4 Comparison of various design choices.

Displacer column material Cost Availability Ease of working
Glass

Plastic

Copper tube Availability Cost Required temperature
Heat source attained

Alcohol

Hair dryer

Design Choices

Oct–Nov Dec–Jan Feb March April June–July August

Literature Review
Initial design
Implementation of

initial design
Final design
Search for parts and

assembly
Testing
Writeup

Based on the above criteria, final selection was made for various design
parameters as follows:

1. Displacer piston-material must be cheap and corrosion
resistant and provide ease of assembly. Plastic tube is ideal
for this case, being cheap and readily available.

2. Wooden base for support and robustness.
3. Fuel – methylated spirit and cotton for use in burner due to

ease of use.
4. Choice of material for pumping line, burner, air column, cold

end: Copper and brass were the choices available. Thermal
conductivity of copper is 401 W/m K, whereas for brass it is
109 W/m K, Using copper can cause more heat losses to the

70 Liquid Piston Engines

ambient atmosphere. Also, copper is more prone to corro-
sion. Brass is an alloy of copper and zinc having better corro-
sion resistance than copper. Hence it is more suitable for use.

Major Components

The designed system consists of the following major parts:

a. Plastic tube for displacer column of radius pipe 0.63 cm
and length 30 cm. It consists of a hot chamber and a cold
chamber.

b. Pumping Column – Brass column of radius 0.39 cm and
height 15 cm.

c. Burner for providing the heat.
d. Collecting cup.
e. Connecting arm of length 6 cm and diameter 3 mm.
f. Air column of 5 mm diameter and length 18 cm.
g. Supporting wooden base.
h. Two balls of mild steel of diameter 5 mm which act as one

way valves.
i. Brass couple at cold end holding the collecting cup, other

end of air column and water returning tube.
j. Plastic supports at hot and cold ends.
k. 2 hose clips for effective sealing at hot and cold ends.

Cost of Components

1. Radiation foil – £4.78
2. Brass pipe – 50 p
3. Brass tap connector – 99 p
4. Copper pipe & brass couple – 50 p
5. Glue – £3

2.22 Assembly

Major steps in assembly of components are as following:

1. Machining the surface of brass tap connector (which acts as
a burner) and drill to holes for supply of air for burning

2. Joining the two ends of connecting arm by brazing with
output column and burner.

Liquid Piston Engines 71

Table 2.5 Volume occupied by various parts. Volume(cm3)

Part list 29.6
Displacer Tube 3.53
Air column 0.42
Connecting Arm 7.19
Pumping Column 6.93
Pumping Arm 0.42
Connecting Arm

Air column
8.6%

Pumping column
17.5%

Displacer
72%

Connecting
arm 1.03%

Figure 2.63 Percentage of total volume of system.

3. Machining the plastic supports and making holes equal to
the diameter of burner and brass junction to support at hot
and cold ends and fixing them by iron nails to the wooden
base.

4. Fixing the two ends of displacer plastic tube with the outlets
of burner and brass junction. Ensuring tight fitness by fixing
the supporting hose clips at the joints.

5. Joining the ends of air column with burner and brass
junction.

6. Covering the base with foil to minimize heat losses.

2.23 Calculation

Target performance parameters: pumping height = 15 cm,
pumping column diameter = 0.78 cm

72 Liquid Piston Engines

Available parameters: diameter of displacer pipe = 1.2 cm, Beals
number = 0.015

Frequency of oscillations is given by f, Hence

f8
2

2g
f l 1.57 Hz

2

Time period = 1/f = 0.63 sec
Pumping rate = Q A 2gH  = 8.19 cm3/s = 8.19 × 10 6 m3/s

Power needed to pump water =   × Q × g × H
= 1000 × 8.19 × 10 6 × 9.8 × 0.15
= 0.012 W

of pumping arm = Power needed to pump water
input power available from engine

2.24 Experiments

Experiments were done to find how different factors affect the work out-
put of the engine. Results from various experiments are discussed in the
following sections.

Devices Used
a. Thermocouple – it is based on the thermo electric or Seebeck
effect which states that a voltage is generated between junc-
tions of two different metals at different temperatures. This
voltage is proportional to the temperature difference.
b. Manometer – these are direct reading devices which can
be used for leak detection, flow measurement, and process
monitoring. They are very simple devices and no calibra-
tions are needed. The readings have accuracy of 0.5 m.

Liquid Piston Engines 73

+ Metal A
eAB Metal B

–

eAB = seeback voltage

Figure 2.64 A thermocouple.

Figure 2.65 Manometer.

Figure 2.66 Experimental setup for finding pressure and temperature.

1. To study the variation of pressure and temperature of air col-
umn with time.
Procedure – balance the level of manometer with knob, so
that air bubble is at centre, light up the flame and connect

74 Liquid Piston Engines

one end of manometer with the gap provided in the hot air
column. Note the readings at various time intervals. Plug
one end of thermocouple with the opening and other to the
meter and note readings at specified time intervals.

2.25 Results

Discussion – temperature of air in the engine was found to increase with
time as it gains more and more heat from the burning fuel. Pressure was
found to fluctuate with time as it moves back and forth from the hot side

Table 2.6 Variation of pressure and temperature of air with time.

Reading in Pressure in Bar Temperature (K) Time in
mm of Hg seconds

730 0.96 296 0
988 1.3 298 300
912 1.2 300 320
1216 1.6 305 340
912 1.2 306 360
1368 1.8 308 380
760 1 310 400
1444 1.9 311 420
745 0.98 312 440

320Temprature K
315
310
305
300
295
290

0 300 320 340 360 380 400 420 440
Time (s)

Figure 2.67 Variation of temperature with time.

Pressure mm of Hg Liquid Piston Engines 75

towards the cold side alternately through the connecting air column. Peak
pressure was found to be around 1400 mm of Hg, whereas the peak tem-
perature was found to be around 39 °C, indicating poor heat transfer to
the working gas (air).In order to reduce heat losses the connecting column
was covered with an insulation covering of PTFE tape. Further, in order to
improve the heat transfer rate, bigger connections can be used so that more
mass of air is able to gain heat from the burning fuel.

Calculation of length of stroke
Calculation of stroke of water column was difficult due to quick oscilla-
tions; however, it was theoretically found using ideal gas laws and observing
temperature and pressure at certain time intervals using manometer, stop
watch and thermocouple.

1400
1300
1200
1100
1000

900
800
700

0 300 320 340 360 380 400 420 440
Time (s)

Figure 2.68 Variation of pressure with time.

S
Hot

Case 1: No heat Case 2: Heat is applied
Figure 2.69 Osmosis and reverse osmosis.

76 Liquid Piston Engines

Table 2.7 Variation of stroke length with time.

P1 mm V1 T1 P2 mm T2 V2 V1–V2 S (cm) Time
of Hg (cm3) (K) of Hg (K) (cm3) (cm3) in cm (s) sec

733 22.6 296 988 298 16.8 5.8 2.56 300

988 16.8 298 912 300 18.32 1.52 0.67 320

912 18.32 300 1216 305 13.96 4.36 1.9 340

1216 13.96 305 912 306 18.68 4.72 2.085 360

912 18.68 306 1368 308 12.53 6.15 2.7 380

1368 12.53 308 760 310 22.7 10.17 4.5 400

760 22.7 310 1444 311 11.99 10.71 4.7 420

1444 11.99 311 745 312 23.31 11.32 4.98 440

According to gas law

P1V1 P2V2
T1 T2

Vd V1 V2 2 D2S
4

Where S is length of stroke

2) To study the variation of power output with time

Power Bn Pf Vt 0.015 1.57 Vt P 0.023 Vt P [20]

Discussion – the efficiency of the device was found to be in the order of
2–6%, which is very low, due to various poor heat transfer, leakage, viscous
and frictional losses. Some measures to improve the efficiency of the sys-
tem are discussed in the sections below.

2.26 Comparison Within Existing
Commercial Devices

University of Witwatersrand has investigated a design having a capacity
to pump 100 gallons/hour of water. The Bell corparation has also made a

Liquid Piston Engines 77

Table 2.8 Variation of efficiency of pumping column with time.

Pressure Vd (cm3) Vt (cm3) Power (W) of pump Time in
(Bar) 5.8 8.2 seconds
1.52 2.14 0.185 6.4%
0.96 4.36 6.16 0.069 2.2% 300
1.3 4.72 6.6 0.22 5.4% 320
1.6 6.15 8.69 0.27 4.3% 340
1.8 10.17 14.38 0.37 3.15% 360
1.9 10.71 15.14 0.56 2.13% 380
1.7 0.41 2.8% 400
1.2 420

6Efficiency (%)
5
4Power (W)
3
2
1

0 300 320 340 360 380 400 420 440
Time (s)

Figure 2.70 Variation of efficiency of pumping column with time.

0.6
0.5
0.4
0.3
0.2
0.1

0 300 320 340 360 380 400 420 440
Time (s)

Figure 2.71 Variation of power output with time.

78 Liquid Piston Engines

model capable of pumping 30 gallons/hour of water with an efficiency of
18% and head of 4 feet. A working liquid piston fluidyne pump has been
developed by Dr. Tom Smith and Dr. Christos Markides at the University of
Cambridge. This device is able to pump about 400 litres of water per hour
to 1M head when 600 W of heat input is supplied to it [23]. Some other per-
formance parameters of existing fluidyne pumps are presented below [21]:

The designed model shows a maximum efficiency close to that achieved
practically by existing models. Some more methods to increase the effi-
ciency are discussed in the next section.

2.27 Improvements

To increase the engine efficiency some of the following improvements can
be made in the current design:

1. Use of bigger diameter displacer tubes – it ensures a greater
amount of air flowing between cold and hot side. This can
lead to larger amplitude of oscillations due to higher pres-
sure, but smaller compression ratio whereas smaller tubing
results in a larger compression ratio.

2. Use of regenerator – The regenerator acts as a thermal sink,
releasing and absorbing heat at various stages, hence increas-
ing the efficiency of the engine. The most common method
of heat storage is to obstruct the flow of working fluid by use
of metallic mesh, porous material, array of tubes, but this
may cause flow losses.

3. Better heat exchange – in order to enhance the heat exchange
at the hot end, resistance heating can be used instead of
burning fuel along with fins for greater heat transfer.

Table 2.9 Performance parameters of existing engines.

Reference Flow rate (gallons/hr) Head (ft) Efficiency

West (1970) 100 5.3 3.5%
Goldberg (1977) 9.5 2 1%
Mosby (1978) 5.9 1 8%
Reader (1981) 2 3.3 5.2%
Pandey (1985) 2500 10 7%
Current design 5.8 (max) 0.5 6.4% (max)

Liquid Piston Engines 79

2.28 Future Scope

Parabolic mirrors can be used to focus solar energy for operation of a liq-
uid piston engine. Such a device is shown below.

Many commercial setups have been built, tested and operated by the
team of Dr. Tom Smith and Dr. Markides at the engineering department

Sun

Parabolic Target
reflector
Pumping
column

Hot Cold
side side

Reserviour

Figure 2.72 Commercial setups for solar liquid piston engine.

Table 2.10 Comparison of irrigation costs for various methods.

Mode of irrigation Cost or irrigation per hectare per day
Electric pumps £0.34–£0.55

Diesel pumps £0.29–£0.17

Photovoltaic pumps £1.27–£4.07

Liquid piston pumps £0.29–£1.07

Table 2.11 Comparison of pumping costs and efficiency of various methods.

Mode of irrigation Efficiency Pumping cost per unit power output
Photovoltaic pumps 20–40% £3.35–£10.7
Liquid piston pumps 2–4% £1.50–£3

Table 2.12 Comparison of emissions.

Mode of irrigation CO2 emissions per hectare per day (kg)
Diesel pumps 2.3–3.6
Solar P-V pumps 0.8–1.3

80 Liquid Piston Engines

of the University of Cambridge. Typical data for cost, efficiency and CO2
emissions is discussed here, assuming a lift head of 10 m [23].

Going by the reliable data obtained, the future of this technology seems
to be bright, and to tap the economic potential there are several organiza-
tions currently involved in research in the field of Stirling and liquid piston
engines. Some of these are listed below [16]:

1. STM co-operation – holders of various Stirling engine pat-
ents and developed a 40 KW engine for use in GE hybrid
vehicle.

2. Sun power – founded by Beale, pioneers in development of
cryogenic coolers of capacity 35 W–7.5 KW.

3. Infinia – developers of 1 KW free-piston engines and
cryogenic coolers.

4. SES – makers of large parabolic dish operating solar power
stations of 850 Mw capacities.

5. Thermo fluidics limited – formed in 2006 by Dr Tom Smith
of the University of Cambridge and supported by carbon
trust, is developing such pumping devices for use in Brazil,
India, and Ethiopia.

2.29 Conclusion

The most common application of the liquid piston system is in irrigation
pumping. Other important applications include drainage pumping, failsafe
cooling of nuclear reactors, cooling of combustion engine with waste heat,
and circulation of water in remote areas without use of electricity. These
devices are simple to construct and can be used easily for demonstrations
and teaching purposes.

2.30 Numerical Analysis

During charging or suction phase

ZI + q/c = Vin

Differentiating bothsides with respect to time we have:

ZC(δI/δt) + (δq/δt) = 0

Liquid Piston Engines 81

ZC(δ2q/δ2t) + (δq/δt) = 0
ZC(δ2V /δ2t) + ( δ2V /δ2t) = 0

Applying Laplace on both sides we have:

ZC(D2V ) + D V = 0
ZC[S2F(S)] + [SF(S) V (0)] = 0

F(S) V (0) 1/S+ 1
S 1

ZC

Taking inverse Laplace we have

V (t) V (0) 1 t
V (t) V (0) 1
e ZC

t

e

Where = RC
When t =

V (t) = V (0)[1   e 1] = 0.63 V (0)

b) During the discharging phase we have
ZI + q/C = 0
Z(δq/δt) + q/C = 0

Volume 0.63 –v (0)
flow rate

v– (0) T=
Time

Figure 2.73 Suction Phase.

82 Liquid Piston Engines

Z V V /C 0
t

Taking laplace

ZC[SF(S) V (0) + F(S)] = 0

V (0)
F(S) S 1

ZC

Volume
flow rate

–v (0)

0.36 –v (0)

Time period T
Figure 2.74 Discharge phase.

Volume 0.5 –v (0)
flow rate

–v (0)

0.693
Time

Figure 2.75 Total flow.

Liquid Piston Engines 83

V (t) V (0) t

e ZC

When t =
V (t) = V (0) * 0.36

When suction flow = discharge flow rate we have,

V (t) V (0) 1 t V (0) t

e ZC e ZC

t/ = 0.693
hence t = 0.693
V (t) = V (0) * 0.5

References and Bibliography

1. http://liquidpiston.com/technology/faq-2/
2. http://liquidpiston.com/technology/how-it-works/
3. http : / / w w w. p opu l ar m e ch an i c s . c om / m i l it ar y / re s e arch / a 1 5 2 3 3 /

liquidpiston-darpa-contract/
4. http://www.utsc.utoronto.ca/~quick/PHYA10S/LectureNotes/LN-18.pdf
5. http://en.wikipedia.org/wiki/Ground_
6. waterhttp://en.wikipedia.org/wiki/Water_resources#Sources_of_fresh_water
7. http://www.unesco.org/water/wwap/wwdr/wwdr3/pdf/WWDR3_Water_

in_a_Changing_World.pdf
8. http://www.engin.swarthmore.edu/academics/courses/e90/2005_6/

E90Reports/FK_AO_Final.pdf
9. http://en.wikipedia.org/wiki/Ground_water
10. http://en.wikipedia.org/wiki/Earth’s_energy_budget
11. http://www.humphreypump.co.uk/operating%20cycle.htm
12. Different pumps for irrigation systems, James Dee, FARM Note: 332,

Department of Agriculture, January 2009.
13. http://www.biologymad.com/NervousSystem/nerveimpulses.html
14. http://www.cazadero.org
15. http://www.webmd.com
16. http://www.aquatechnology.net/reverseosmosistheory.html
17. http://www.inference.phy.cam.ac.uk/sustainable/refs/solar/Stirling.PDF
18. http://ir.canterbury.ac.nz/bitstream/10092/2916/1/thesis_fulltext.PDF

84 Liquid Piston Engines

19. http://www.mpoweruk.com/heat_engines.html
20. http://www.animatedengines.com/vstirling.shtml
21. http://www.exergy.se/goran/hig/re/07/stirling.pdf
22. C. D. West, Liquid Piston Stirling Engines, Van Nostrand Reinhold, New York,

1983.
23. http://www.omega.com/temperature/z/pdf/z021-032.pdf
24. http://www.thermofluidics.com
25. http://www.mathpros.com/papers/thermodynamics/Integral_Analysis_for_

Thermo-Fluid_Applications.pdf
25. https://www3.nd.edu/~msen/Teaching/DirStudies/Engines.pdf
26. Qianfan Xin, Diesel Engine System Design (Woodhead Publishing in

Mechanical Engineering) 1st Edition,ISBN-13: 978-1845697150.
27. Gupta, Aman, and Sunny Narayan. “Electrical Analogy of Liquid Piston

Stirling Engines.” Hidraulica 2, 58, 2016.
28. Narayan, Sunny, and Vikas Gupta. “OVERVIEW OF WORKING OF

STRILING ENGINES.” Journal of Engineering Studies and Research 21.4, 45,
2015.
29. Gupta, Aman, and Sunny Narayan. “A Review of Heat Engines.” Hidraulica 1,
67, 2016.
30. Narayan, S. “Analysis of noise emitted from diesel engines.” Journal of Physics:
Conference Series. Vol. 662. No. 1. IOP Publishing, 2015.
31. Gupta, Aman, and Sunny Narayan. “Effects of turbo charging of spark igni-
tion engines.” Hidraulica 4, 62, 2015.
32. Narayan, Sunny. “Designing of liquid piston fluidyne engines.” Hidraulica 2,
18, 2015.
33. Narayan, Sunny.  Effects of Various Parameters on Piston Secondary Motion.
No. 2015-01-0079. SAE Technical Paper, 2015.
34. Narayan, Sunny. “Analysis of Noise Radiated from Common Rail Diesel
Engine.” Tehnički glasnik 8.3, 210–213, 2014.
35. Narayan, Sunny. “TIME-FREQUENCY ANALYSIS OF DIESEL ENGINE
NOISE.” Acta Technica Corviniensis-Bulletin of Engineering 7.3, 133, 2014.
36. Narayan, Sunny. “Wavelet Analysis of Diesel Engine Noise.”  Journal of
Engineering and Applied Sciences 8.8, 255–259, 2013.
37. Narayan, Sunny, and Vikas Gupta. “Motion analysis of liquid piston
engines.”Journal of Engineering Studies and Research 21.2, 71, 2015.
38. Narayan, Sunny. Modeling of Noise Radiated from Engines. No. 2015-01-0107.
SAE Technical Paper, 2015.
39. Narayan, Sunny, Aman Gupta, and Ranjeet Rana. “Performance analysis of liq-
uid piston fluidyne systems.” Mechanical Testing and Diagnosis 5.2, 12, 2015.
40. Gupta, Vikas, Sahil Sharma, and Sunny Narayan. “REVIEW OF WORKING
OF STIRLING ENGINES.” Acta Technica Corviniensis-Bulletin of Engineering
9.1, 55, 2016.
41. Singh, Amar, Shubham Bharadwaj, and Sunny Narayan. “Review of how aero
engines work.” Tehnički glasnik 9.4, 381–387, 2015.

Liquid Piston Engines 85

42. Narayan, Sunny. “A review of diesel engine acoustics.” FME Transactions 42.2,
150–154, 2014.

43. Narayan, S. “Noise Optimization in Diesel Engines.”  Journal of Engineering
Science and Technology Review 7.1, 37–40, 2014.

44. Gupta, Vikas, Sahil Sharma, and Sunny Narayan. “REVIEW OF WORKING
OF STIRLING ENGINES.” Acta Technica Corviniensis-Bulletin of Engineering
9.1, 55, 2016.

45. Singh, Amar, Shubham Bharadwaj, and Sunny Narayan. “Prikaz rada motora
zrakoplova.” Tehnički glasnik 9.4, 381–387, 2015.

46. Klangpraphan, Praphan, Pisit Yongyingsakthavorn, and
T. Soontornchainacksaeng. “Development of the Solar Liquid-Piston Stirling
Engine: Parameters Affecting the Efficiency of the Engine.” 2013.

47. Winkelmann, Anna, and Eric J. Barth. “Second Generation Controlled Stirling
Device.”

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

3

Customer Satisfaction Issues

3.1 Durability Issues

Durability is an important aspect as customers need shorter service inter-
vals and longer engine lifetime. Increase in mechanical and thermal loading
causes higher engine power density, lower emissions, and longer lifetime
which are greater issues in durability. Structural issues are also important
in view of system performance. These issues may be classified as:

fracture based performance which includes rupture and
cracking.
buckling under load.
Thermal deformations, fatigue, creep, oxidation, and
corrosion.
Cavitation issues.
Wear and oil degradation.
EGR cooler fouling, boiling, and corrosion.
Deposits leading to fouling.
Hydrogen embrittlement.

87

88 Liquid Piston Engines

Buckling is failure of parts due to higher compressive stresses. Abrupt
rupturing of bubbles formed causes Cavitation. Fouling and deposition
may occur due to coking and deposition of soot. As Hydrogen is released
embrittlement may also be caused. Shocks and deformation resistance is
lessened.

Most of the these issues occur in EGR system, turbocharger, injection
systems, skirt assembly, cylinder head exhaust manifold, and valve train.

Injector choking is also a major cause of concern due to carbon depo-
sition. Engine needs frequent overhauling due to excessive wear, oil
consumption or blow-by.

The following engine parameters are dependent upon engine durability:

Torque produced.
Speed of skirt.
Heat flux in system.
Temperature of compressor and compression ratio.
Charge inside air cooler and EGR outlet gas temperatures.
Load in values.
Piston slap.
Engine load.

3.2 Testing of Engines

In order to validate the design, testing is needed. This is done in order to
see effects of mechanical and thermal loads and fatigue. Some of these tests
include full-load test, over-fueling test and load cycle tests.

Evaluation of the sealing capacity of the cylinder head gasket by is an
important aspect of fatigue testing in which exposing of components is
done to high thermal gradients. Thermal shocking is done by changing
temperature gradient. Thermal loading may reach its peak at peak torque.
Cam stress can maximize with an increase in cranking speed.

In field tests includes evaluation by changing temperature, humidity,
altitude, speed, fuel and oil consumption, speed and torque, exhaust mani-
fold pressure, turbine outlet pressure, and fluid temperatures.

3.3 Design of Systems

Light and durable design is the major objective of design approach that
includes increase in stiffness, lowering temperature, higher strains.

Customer Satisfaction Issues 89

Engine structural parameters that need evaluation include:

Deflection, plasticity, stress, and strain.
Fatigue.
Multi-body dynamic vibration and modal analysis.
Wear and Cavitation.
Transient structural analysis.
Fluid-structure interaction.

Finite element analysis may be used to analyze complex geometry to
identify stress concentrations areas.

3.4 Systems Durability

Durability is evaluated using either deterministic approach or probabilistic
approach. A FEA simulation software like GT-POWER can analyze the
temperature distribution.

References and Bibliography

1. Qianfan Xin, Diesel Engine System Design (Woodhead Publishing in
Mechanical Engineering) 1st Edition, ISBN-13: 978-1845697150.

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

4

Lubrication Dynamics

4.1 Background

Surface topography may refer to both the shape and the roughness of sur-
face which includes the waviness and the asperity contacts. Topography
also affects the oil film thickness and the lubrication regime formed. In
the hydrodynamic or mixed lubrication type of lubrication, the influence
of roughness of surface on film thickness and pressure distribution is not
negligible. The roughness along transverse direction must increase the
load bearing capacity and the oil film thickness whereas, the longitudi-
nal one would cause reduction. Topography has an important effect on
the load carrying capability. These interactions become more dominant
as the thickness-to-roughness ratio decreases. Some of the models related
to surface topography include the following: (1) Patir and Cheng (1979)
average model, which takes into account the influence of surface rough-
ness (2) Greenwood and Tripp (1971) asperity contact model.

Topography also changes with engine operational conditions and
changes due to wear. This also affects the friction power of all the sliding

91

92 Liquid Piston Engines

surfaces. During break-down, some of the asperities are worn off leading to
smoother surfaces. This reduces frictional forces. As the wear progresses,
the engine friction reduces and then stabilizes.

Taylor analyzed the effects of surface roughness on engine friction and
wear. Zhu studied effects of surface roughness on cylinder liner, piston
skirt and piston rings.

Oil reduces friction, wear and acts as a coolant to removing the exces-
sive heat, and impurities. Additives used include anti-wear agents, friction
reducers, viscosity index improvers, detergents, anti-rust agents, and
antifoam agents. Some effects of the lubricant on engine friction include
cavitation, thermal effects, oil starvation and the changes in viscosity.

The viscosity may be used for classification of oils as given by SAE J300
(2004). Grades of viscosity include the SAE5, SAE10, SAE30, SAE40,
SAE45, and SAE50. Higher grades of oil mean higher viscosity. The multi
grades of oils use viscosity index improvers in order to stabilize the viscos-
ity. The 10W-30 means that the viscosity of the SAE10 at 15°. SAE grades
of oil may help to reduce the friction at starting without problems of low
viscosity and metal contacts.

Newtonian fluids show a linear relationship among stress and shear rate.
Under high pressures conditions, as viscosity falls and shear rate increases,
the fluids show this nature. Increases of level of soot and dispersant of oil
shows an increase in viscosity.

Vogel’s equation shows relation among temperature and pressure of oil.
The viscosity falls with increasing in temperature.

The non-Newtonian can show effects for rough surfaces. Coy and Taylor
studied the lubricant rheology, friction and wear.

Frictional coefficient decreases with a fall in viscosity in hydro dynamic
regime. So, the friction in piston skirt and bearings show lower friction,
while the valve train shows an increase. Valve train friction can be reduced
by using the oil with friction modifier. An optimum value of viscosity hav-
ing minimum engine friction exists.

Taylor showed the valve train friction losses are higher for in light-duty
engines as compared to heavy-duty engines. As the valve train friction is
dominant in the boundary lubrication, the modifier additives may be more
effective for light-duty engines.

Taylor and Kapadia found fuel consumption was less by 5 % by care-
ful choice of lubricants. Reduction in viscosity changes the lubrication
regime from hydrodynamic to boundary one. This may increase the wear
and scuffing. So, there is a tradeoff between reduction of friction and
durability.

Lubrication Dynamics 93

4.2 Friction Features

Engine friction can be analyzed by various methods like motoring and
teardown method, indicator diagram, pressurized motoring method,
Morse test, Willan’s Line method, torque method. Wakuri and Richardson
have analyzed each method in details.

As various load and speed vary various engine parts operate at differ-
ent lubrication regimes. Friction losses changes in design parameters and
operating conditions.

Stribeck diagrams show effects of duty parameter on viscosity, loading,
and sliding velocity. Lubrication regimes depend on load, speed, viscosity,
state of break-in, etc.

The piston skirt moves in a periodic sliding motion from TDC to BDC
positions. At higher speeds during middle stroke, the skirt operates in
hydrodynamic or elasto- hydrodynamic lubrication regime. During expan-
sion and compression stroke pistons operate in mixed lubrication.

An oil film is developed for surface separation. Near the dead center
positions as the sliding velocity reaches zero, there is a probability of for-
mation of mixed lubrication regime. Squeezing action may occur in piston
rings.

Forces acting on compression rings include the tension and gas pres-
sure. Tension depends on the force needed to compress the ends of the
ring. These rings operate in hydrodynamic regime at mid-stroke and in
the mixed regime near the dead centers as the gas pressure is high and the
viscosity is low. Under such condition, oil film breaks resulting in higher
wear. These rings have a tapered face to help in scraping action.

The oil ring used has thin rails in order to generate a thin oil film.
The friction on the piston skirt and the rings can show a sudden rise and
fall near dead center positions as skirt reverses direction which is impulsive
and has frequencies that excite the crankshaft resulting in a knocking noise.
This is known as ‘stick slip’ noise. Changes in Frictional coefficients may be
suppressed using modifiers and coating materials which results in reduc-
tion of ‘stick slip’ noise.
The bearings in engine have different load bearing capacities at varying
speeds. The main bearing operates in the hydrodynamic or elasto hydrody-
namic due to constant sliding velocity.
The instantaneous force acting on small-end of connecting rod can be
null. The resultant force on big end of the connecting rod as well as main
bearing of crankshaft is greater than zero. The resultant force on cam shaft
is never zero.