Journal of Beijing Institute of Technology, 2015, Vol. 24, No. 3
Experimental study on compression stroke characteristics
of free鄄piston engine generator
ZUO Zheng鄄xing( 左正兴) ,摇 XU Da鄄tao( 许大涛) 苣 ,摇 FENG Hui鄄hua( 冯慧华)
( School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China)
Abstract: The compression stroke characteristics of free鄄piston engine generator were studied. The
numerical model of the compression stroke was established based on thermodynamics and dynamics
equation, and the leak loss, heat loss and friction loss were considered. Through solving numerical
equations, the in鄄cylinder pressure of compression stroke under different compression ratios was cal鄄
culated, energy transfer and conversion process was analyzed, and the calculated results were exper鄄
imentally verified. The results showed that the actual effective output of electronic energy and the
compression energy stored in the compressed gas accounted for about 70% . The compression energy
gradually increased with the increasing compression ratio. When the compression ratio was more
than 7郾 5, the actual compression energy increased slowly and the energy error between simulation
and test decreased.
Key words: free鄄piston engine generator; compression stroke; experimental study; energy conver鄄
sion
CLC number: TK 441摇 摇 Document code: A摇 摇 Article ID: 1004鄄 0579(2015)03鄄 0321鄄 07
摇 摇
A free鄄piston engine generator is a novel
power mechanism, which is a combination of the
piston of free piston engine and the mover of line鄄
ar generator. It does not have a connecting rod as
in a traditional engine, which can make the kinet鄄
ic energy of piston爷 s linear motion output to the
external load conversion device directly, so it has
a broad application prospect in the electric
field [1] . Moreover, it has many advantages such
as compact structure, high power density, wide
fuel types and emissions of good quality. There鄄
fore, it has gradually become the focus of re鄄
search in recent years [2 - 7] .
The cylinder gas organization of a free鄄piston
engine generator is significant different from a
crankshaft engine because of its special piston
Received摇 2013鄄 12鄄 27
Supported by the National Natural Science Foundation of Chi鄄
na (51006010) ; the Program of Introducing Talents of Disci鄄
pline to Universities ( B12022)
苣 Author for correspondence
E鄄mail: xudatao2010@ 163. com
DOI: DOI: 10. 15918 / j. jbit1004鄄0579. 201524. 0306
motion. A free鄄piston engine generator can freely
adjust the engine working stroke, which directly
affects the combustion process and perform鄄
ance [6] . In the thermodynamic cycle of cylinder
gas, the compression stroke is one of the key fac鄄
tors influencing the startup, the subsequent work鄄
ing process and the combustion.
Based on a developed free鄄piton engine gen鄄
erator and considering the leak loss, heat loss and
friction loss, we established a mathematical mod鄄
el of compression stroke. The compression stroke
under different compression ratios conditions was
analyzed. The simulation results and experimental
results were compared, and the changing charac鄄
teristics of the in鄄cylinder pressure and compres鄄
sion energy were analyzed. Make sure the influen鄄
cing factors of the whole process so as to obtain a
more accurate model of compression stroke, it is
essential for in鄄depth research on the performance
and the establishment of stable control strategy of
free鄄piston engine generator, and it can provide
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Journal of Beijing Institute of Technology, 2015, Vol. 24, No. 3
reference in order to improve the startup process
the continuous inductive power can be obtained
1摇 Structure
characteristic
of
free鄄piston engine generator
strong coupling characteristics of both sides cylin鄄
摇 摇 The load device of a free鄄piston engine gener鄄
characteristics before the burning is essential for
of engine.
ator is the linear generator connected with the
to achieve energy conversion.
However, the
der have also brought difficult problems on stable
control of combustion. So compression stroke
combustion stability.
generator mover and the free piston. The kinetic
2摇 Analysis of compression stroke
tion is directly converted into electrical energy by
2郾 1摇 Dynamic modeling
in this research is a two stroke dual鄄piston op鄄
gine generator refers to the free piston moving
structure is shown in Fig. 1. Two pistons and the
center of the cylinder. In this process, the free
energy of piston obtained from the fuel combus鄄
electromagnetic energy conversation. The object
posed鄄type free piston engine generator.
The
mover of a linear generator are rigidly attached to
constitute a piston assembly though a connecting
rod.
The compression stroke of a free鄄piston en鄄
from one side to the other side of the top dead
piston is commonly affected by the cylinder gas
pressure, the electromagnetic force, the friction
force and the gas pressure of the scavenging box,
as shown in Fig. 2. Assuming that the gas pres鄄
sures of both sides of the scavenging box are e鄄
qual, they are offset mutually. Therefore, the
movement process of free piston can be ex鄄
pressed as
m
Fig. 1摇 Free鄄piston engine generator configuration
When the free鄄piston engine generator is
starting, the motor drives the mover and the free
piston to move in order to achieve the fundamen鄄
tal conditions of mixture combustion. Mixed gas
is provided by the fuel system and enters the cyl鄄
inder though the inlet. When the piston is closed
to the top dead center of one side, compression
stroke is about to the end, the control system im鄄
d2 x
= ( PL - PR ) A - Fe - Ff
dt2
(1)
where m is the mass of the moving parts, inclu鄄
ding free piston mass, motor mover mass and
connecting rod mass; x is the displacement of the
piston assembly; P L , P R are the pressures in the
left and right cylinders; A is the top area of the
piston; F f is the friction force; F e is the electro鄄
magnetic force introduced by the linear genera鄄
tor.
plements the spark plug ignited, and the combus鄄
tion of this side cylinder is realized. Meanwhile,
the motor is converted into generator mode.
Then, the gas explosion pressure promotes the
piston backward movement to conduct the work鄄
Fig. 2摇 Free body diagram of free鄄piston engine
ing process. The other side cylinder is turned into
the
scavenging
and
subsequent
compression
stroke, and the piston is pushed back after the
cylinder combustion. Thus, both sides of the cyl鄄
inder are ignited alternately; free piston can move
continuously between the two dead centers, and
generator
2郾 2摇 Compression energy modeling
Compression energy refers to overcoming the
cylinder gas pressure and store energy in the star鄄
tup process of the first stroke, when the exhaust
port is closed by the free piston until it moving to
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ZUO Zheng鄄xing( 左正兴) et al. / Experimental study on compression stroke characteristics . . .
the top dead center.
2郾 3摇 Friction energy modeling
engine generator, due to the leak loss, the cylin鄄
from the piston ring and the piston skirt portion.
process. In the compression stroke, applying the
the force is small compared to the other parts.
In the actual working process of free piston
der thermodynamic process is a mass transfer
law of mass conservation for the cylinder gas
dm V
dm L
= dt
dt
The friction force of free piston mainly comes
Also, there is friction force at the piston pin, but
According to the simplified empirical formula of
(2)
where m V is the gas mass of combustion cham鄄
ber; m L is the mass of leak loss. According to the
the piston ring pack friction force [2] , the friction
force can be represented by
Ff =
仔B2
p
8 fmep
(8)
energy conservation equation, the energy chan鄄
where p fmep = A m Sn, A m = 150 kg·m - 2·s - 1 , B is
dE C dQ dW dm L
=
h
(3)
dt
dt
dt
dt
where E C is the total energy of in鄄cylinder gas; Q
length, p fmep is the mean effective friction force, n
ging of cylinder gas can be expressed as
is the outflow or inflow energy of in鄄cylinder gas;
W is the output work; h is the enthalpy flow. In
addition, due to the gas work dW = PdV, and
E C = m L u, after the differential we have
mV
du dQ
dV P dm V
=
-P
+
dt dt
dt V dt
(4)
Combined with the differential expression of
the ideal gas state equation
P
dm V
dV
dP
dT
+V
= mV R
+ TR
dt
dt
dt
dt
dP ( 酌 - 1) dQ P酌 dm V P酌 dV
=
+
dt
V
dt m V dt
V dt
is the frequency of reciprocation of the piston as鄄
sembly. The friction energy loss of a compression
stroke is
Ef =
(6)
where P, V are the gas pressure and volume of
combustion chamber; c P , c V are the constant
stant; T is the gas temperature of in鄄cylinder gas.
During the time of free piston moving from
the upper edge position of the exhaust port to the
top dead center, the thermodynamic changing of
combustion chamber is expressed as the effective
compression process. In this case, the gas energy
increment of combustion chamber is
Ep =
乙
x Lg
x Le
PdV
(7)
where x Lg is the position of top dead center; x Le is
the upper edge position of exhaust port.
L
0
F f dx
(9)
The electromagnetic force of a linear genera鄄
tor is proportional to the simplified velocity [5] .
Assuming that the electromagnetic force constant
is c, we can have
Fe = c
dx
dt
(10)
Without considering the load energy loss and
other losses, the generator output power can be
considered as the output energy of the system,
which is equal to the work done by the electro鄄
magnetic force in one cycle. The generator output
energy can be expressed as
pressure specific heat and constant volume specif鄄
ic heat; u is the internal energy; R is the gas con鄄
乙
2郾 4摇 Linear generator energy modeling
(5)
According to the thermodynamic relation:
R = c P - c V , 酌 = c P / c V and u = c V T, we yield
the bore of the cylinder, S is the maximum stroke
Ee =
乙
L
0
F e dx
2郾 5摇 Heat loss energy modeling
(11)
The energy loss caused by the heat exchange
among the internal wall surface of combustion
chamber has a great impact on thermal efficiency
for free鄄piston engine generator, which is an im鄄
portant phenomenon occurred in the engine com鄄
bustion system. Though the engine heat balance
experiment, we can find that about 1 / 3 the re鄄
leased heat from fuel combustion is wasted
though heat transfer [8] . However, the emitted
heat at different times in an engine working cycle
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Journal of Beijing Institute of Technology, 2015, Vol. 24, No. 3
is not all affecting the heat efficiency. When the
piston is near the top dead center of compression
stroke, the work capacity of cylinder gas is re鄄
duced directly by the heat loss that the gas to鄄
wards to the wall surface. Therefore, it has a
1
ïì Pe 酌 2酌 1 - Pe
ïï Po
酌 -1
Po
í
酌 +1
ï 12
2 2(酌 -1)
,
ï酌 酌 +1
î
( ) {
(
berg [9] :
q = h h A cyl ( T - T w )
·
h h = 130V - 0郾 06
( 10p )
0郾 8
5
(12)
T - 0郾 4 ( V A + 1. 4) 0. 8 (13)
where h h is the heat transfer coefficient, A cyl is
the in鄄cylinder surface area in contact with the
gas, T w is the average temperature of the in鄄cylin鄄
[ ( ) ]}
1
2
Pe
2
,
>
Po
酌 +1
(
)
Pe
2
臆
Po
酌 +1
)
)
(
酌
酌 -1
酌
酌 -1
(16)
great impact on the thermal efficiency. In鄄cylin鄄
der heat transfer is modeled according to Hohen鄄
酌 -1
酌
Thus, the leak loss energy of a compression
stroke can be described as
EL = h
3摇
乙
t
0
(17)
·
mdt
Simulation and experimental
studies
3郾 1摇 Experimental prototype
The basic structure parameters of a free鄄pis鄄
der surface face, V A is the mean piston velocity.
ton engine generator are determined by the princi鄄
乙
Tab. 1. In the simulation model, the compression
The heat loss energy of a compression stroke is
Qh =
t
0
·
q dt
2郾 6摇 Leak loss energy modeling
(14)
ple of prototype design and selection, as listed in
polytropic coefficient m c is taken as 1郾 30 [2] .
Tab. 1摇 Specifications of a free鄄piston
As there is a gap between the free piston and
the in鄄cylinder wall surface in the free鄄piston en鄄
gine generator, the in鄄cylinder mixture will inevi鄄
tably incur leakage phenomenon. The leakage of
engine can be considered as one鄄dimensional
steady flow, the gap area can be treated as a
gradual retractable nozzle. According to the conti鄄
nuity equation, the mass flow that the gas goes
though arbitrary cross鄄section is same. Leak mass
flow rate is calculated as [10]
·
m=
At P
Rm T
y( P o ,P e ,酌)
(15)
where A t is the gap area between the piston and
cylinder, R m is the mixed gas constant, y( P o ,P e ,
酌) is the flow function, P e is the outside pres鄄
sure. When the in鄄cylinder pressure is higher, the
flow presents a supercritical state, the in鄄cylinder
gas flows though the gap at the local sound
speed, the leak flow only depends on the in鄄cylin鄄
der gas state and the size of gap area, and it has
nothing to do with outside gas state. The leak
flow function can be expressed as
y(Po ,Pe ,酌) =
engine generator
B / mm
S / mm
m / kg
x Le / mm
34
45
5. 0
28
P0 / MPa c / ( N·s·m - 1 )
0. 1
80
摇 摇 Based on the test platform of the free鄄piston
engine generator, a group of motor was added to
this system and the controllable motor reciproca鄄
tion was utilized for the system test. The test pro鄄
totype was shown in Fig. 3. It consisted of the en鄄
gine subsystem, the linear motor subsystem and
the control and test subsystem. The test equip鄄
ments were as follows: the engine cylinder and
cylinder head were selected from a two鄄stroke
model aircraft engine, the cylinder body and con鄄
necting rod were designed independently, and the
linear motor was selected from a commercial flat
motor. The displacement of piston assembly was
collected by a grating displacement sensor. The
in鄄cylinder pressure was collected by a Kistler gas
pressure sensor, and the measured pressure was
relative values. Compared with the collected dis鄄
placement and pressure, the changes of in鄄cylin鄄
der pressure of compression stroke were ob鄄
tained.
— 324 —
ZUO Zheng鄄xing( 左正兴) et al. / Experimental study on compression stroke characteristics . . .
in鄄cylinder gas pressure of compression stroke un鄄
der different compression ratios are shown in
Fig. 4. It can be found that there is a gap between
the simulation and experimental curves. In the
first half of the compression stroke, the two
curves are very close when the in鄄cylinder pres鄄
sure is smaller. With the deepening of compres鄄
Fig. 3摇 Prototype of free鄄piston engine generator
According to the fundamental characteristics
of compression stroke, the system simulation
model was established with Matlab / Simulink, and
simulation and experimental research were con鄄
ducted.
3郾 2摇 Experimental results
creases, and the simulated pressure increases fas鄄
ter than the experimental measurements.
As
shown in Fig. 5a, the in鄄cylinder peak pressure of
simulation is greater at the same compression ra鄄
tio. If the compression ratio is bigger, the value
The simulation and experimental results of
摇 摇 摇
sion stroke, the in鄄cylinder pressure gradually in鄄
error
摇 摇 摇 摇
between
simulation
and
Fig. 4摇 Changes of in鄄cylinder gas pressure of compression stroke in different compression ratios
Fig. 5摇 Peak pressure and compression energy in different compression ratios
— 325 —
experiment
Journal of Beijing Institute of Technology, 2015, Vol. 24, No. 3
becomes bigger. The reason is that due to the
the compression, the higher the temperature. The
ring is used to seal between the piston and the
mount of energy loss.
smaller cylinder bore of the prototype, one piston
heat transfer energy loss will cause a certain a鄄
cylinder, so a certain amount of leak area is exis鄄
3郾 3摇 Energy conversion process
therefore, it becomes the main source of the
ton engine generator refers to the process of the
of in鄄cylinder gas is bigger.
nal energy of gas at the same with the output of e鄄
merical integration of the cylinder pressure. The
considering the leak energy loss, heat energy loss
ratios is shown in Fig. 5b. With increasing com鄄
stroke, the total energy can be calcualted as
ted in it. Effective seal measures can爷 t be done,
The energy conversion process of a free鄄pis鄄
leak. The leak is more significant if the pressure
electrical energy of motor converting to the inter鄄
The compression energy is obtained by nu鄄
lectrical energy. According to the above analysis,
compression energy under different compression
and friction energy loss in the whole compression
pression ratio, the compression energy gradually
移 E = Ep + Ef + Ee + EL + Qh
increased. The differences between simulation
and experiment are that, when the compression
ratio is more than 7郾 5, the increasing rate of com鄄
pression energy becomes slow with increasing
compression ratio, which is similar to the chan鄄
ges in the experimental results of peak pressure.
The compression energy from experiments is quite
different from the theoretical values. Fig. 6 shows
the error of experimental and simulation values.
It can be seen that the compression energy error
gradually decreases as the compression ratio in鄄
creases, and the energy error ratio also gradually
decreased. The main reason is that higher com鄄
pression ratio results in greater leak energy loss,
(18)
Based on the design parameters of free鄄piston
engine generator,the necessary energy and its dis鄄
tribution relationship can be obtained by using nu鄄
merical integration methods, as shown in Fig. 7.
From Fig. 7, the compression energy of gas and
output energy of generator occupy the main parts
in the compression stroke; about 42% energy is
as the generator output; the leak loss and heat
loss are larger and the friction loss is smaller.
More energy should be used to increase the inter鄄
nal energy of gas by appropriately reducing the
output of the electrical energy so as to improve
the startup performance of the engine.
but the increasing rate is less than the increasing
rate of compression energy. Meanwhile, the peak
pressure increased as the compression ratio in鄄
creases, and the friction force between the piston
ring and the cylinder also increases, causing a
greater friction energy loss. Further, the bigger
Fig. 7摇 Energy conversion distribution of compression stroke
4摇 Conclusions
淤 Due to the leakage between the piston ring
and the cylinder and the heat of the cylinder wall,
Fig. 6摇 Compression energy error and error ratio
there are differences between experiment and
— 326 —
ZUO Zheng鄄xing( 左正兴) et al. / Experimental study on compression stroke characteristics . . .
simulation of in鄄cylinder gas pressure in the actual
Warrendale, PA, USA: Society of Automotive Engi鄄
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