External Combustion Engine With Stirling Open Cycle, Silnik Stirlinga, Dokumenty
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Gianni Bidhi*, Giuseppe Grazzini
,
and Adriano Milazzo
*
EXTERNAL COMBUSTION ENGINE WITH STIRLING OPEN CYCLE
**
(*I
Dipartimento di Energetica, Universitii di Firenze
Via di Santa Marta, 3, 50139 FIRENZE, Italy
( )
Dipartimento di Progettazione Architettonica, IUAV,
S. Croce, 191, 30135 VENEZIA, Italy
ABSTRACT
Industrial engines using open cycles are
generally described in terms of Otto or Diesel
cycles. We are attempting to develop an open-cycle
engine approximating the Stirling cycle, while
conserving external combustion. Our open-cycle
Stirling engine is- being built on a motorcycle V-
engine; of course the heat exchangers have been
designed from scratch. Some thermodynamic
considerations justifying the use of the open
cycle have been developed. A numerical simulation
of the proposed open cycle has been carried out.
An optimization of the heat exchanging system has
been attempted, making use of an entropic
parameter. By now, the complete design of the
experimental motor has been carried out, waiting
for experimental testing to verify the cycle
effectiveness and the optimization criteria.
Subscripts
i radiative exchange
c combustion chamber
w wall
1 IRTRODUCTION
Stirling engines are commonly built as closed
cycle engines, with all related problems of
conserving gas pressure and purity, and of heat
discharging to atmosphere.
All other industrial engines, those described
in terms of Otto or Diesel cycles for example,
have always been built as open cycle engines, even
if the reference cycles are closed; maybe the
easier construction is the main reason for their
outstanding diffusion.
In the same way we can consider to build an
open cycle engine working with
a
Stirling-style
cycle. So it is possible to utilize an existing
crankcase and the working fluid is simply air. By
this way we hope to lower engine costs, still
mantaining the peculiar advantages of a Stirling
engine, such as external combustion (that means
lower fuel quality demand), high efficency, lower
lubrificating oil consumption.
A area
C thermal capacity
k
c /c gas constant
K thermal conductivity
1 length
NTU number of thermal units
p pressure
Q heat
S entropy
t time
T temperature
v specific volume
V volume
W work
Greek symbols
E
heat exchanger efficiency
U
Boltzman radiative constant
2
TEE
OPEN CYCLE STIRLIHG EllGIllE
The choice for an open system is intended to
reduce the complexity of the engine, but is also
according to some thermodynamic considerations.
Using an open cycle we can eliminate the cold heat
exchanger, that means less volume and absence of
circulation systems for the cooling fluid, in
other words lower pumping losses.
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CH2781-3/89/0000-2407
$1.00
0
1989
IEEE
**
PQ
From thermodynamical point of view we can
observe that a reversible engine working with
finite temperature differences between the
reservoirs and the isotherms of the system has a
maximum for produced work, maximum wich is
function of the heat exchanger sizes
[l].
If ATl
and ATo are the temperature differences among the
reservoirs and the system, the heat transfers can
be assumed as
The higher value of maximum work being
achieved when the ratio of the hot to the cold
heat exchanger constant is minimum, then we would
have the maximum possible cooler size: the
atmosphere where an open engine discharges the
working air at the end of the cycle can be just
seen as an infinite surface cooler.
3 EHGIIIK
DESCRIPTION
8,
=
C1
ATl
At, and
Q,
=
CO ATo &to
(1)
where C depend on the heat transfer mechanism, and
At are the time interval of the heat transfers. If
we define
The
HORINI
350 motorcycle engine is a four
stroke two cylinder engine with 62
mm
bore and
57
mm stroke: the compression ratio is 1O:l; each
cylinder has two valves, driven by a camshaft
displaced in the crankcase. The V configuration
with a 72 degrees angle between the two cylinders
is quite favorable in order to achieve a constant-
volume heating phase,
because there is a period of
the cycle in wich the two pistons have almost the
same motion law. So we decided to use one of the
two cylinders as the cold one where the isothermal
compression takes place.
As
the engine is an open
cycle one, this cylinder has an intake valve, wich
is closed during the compression.
r
=
1
+
(C1
Atl
/
CO Ato)
(2)
it can be demonstrated that the maximum work is
Wm
=
C1 Atl T1
I1
-
(TO
/
T1)ll2l2
/
r
(3)
with an efficiency equal to
(4)
as found by Curzon and Ahlborn [2].
The efficiency is maximum for ATl
=
0, as in
Carnot conditions, but the work then is zero.
Looking at figure 1 we can see that, if maximum
work is requested, for a fixed r AT1, we need the
minimum value of r, that is 1 because of its
definition. This mean a value of CO Ato much
greater than CIAtl.
.8
.I
.8
.5
.4
.3
nm
INLET
0-
i
CONPRESS
I
ON 10-11 CMBU8TION
1-2 EXIT FRON THCCOLO CYLINDER
11-12
WEAT RELEASE
2-3
HEOTING IN
THE
REGENERATOR
AIR
INLET
io
FUEL
n~o
12
EXWST
.2
3-4 COLNTERFLOU
HEATING
*-S
HEATING
IN CONWSTION CHWlEER
5-6
EXPWION
6-7 &OTING IN
CONBUSTION
CHR"ER
8-9
REGENERATION
.1
74 P~R~LLEL
FLOU nEnTING
0
9
nm
OUTLET
Fig. 2
-
Schematic draft of the engine
Fig. 1
-
Efficiency and work produced versus
r
AT^
r
Atl
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-
81-.
1
I
0
 The cold air compressed in the cylinder is
sent through another valve into the regenerator,
wich is made of a matrix of stainless steel wire.
Then the air is heated in a counterflow tube
exchanger by the hot gas produced by a metane
flame. The heat exchange is calculated as a pure
convective one, except for the last part of the
exchanger, where the wall is directly in contact
with the flame,
so
that the radiative heat
transfer is prevailing. A special design
combustion chamber has been employed, realized
with temperature resistant stainless steel. So
heated, the air expands in the hot cylinder, where
the work output is collected by the crankshaft.
Finally the air flows again through the heat
exchanger (this time parallel flow) and leaves
part
of
the residual heat to the regenerator prior
to discharge to the atmosphere.
A
third valve is
then required to regulate the discharge phase. All
the valves have been collected on the head of the
cold cylinder, wich is close to the regenerator:
they all are moved by an overhead camshaft
trough
short rocker arms.
shows a schematic
draft of the engine.
values are requested.
A
start value for the
inlet temperature of the regenerator is used
to evaluate the recuperated heat, using the
relations of next point.
b) The effectiveness of the counterflow heat
exchanger is calculated as in
[3]
with the
formula
:
-
NTU (l-Cmin/Cmax)
where the adimensional NTU, (number of termal
units), that is the product of the overall
termal conductance by the transfer area
divided by the minimum capacity ratio Cmin,
express the size of the heat exchanger. For
parallel flow exchanger and for the
regenerator the formula is quite similar
[31.
For the regenerator we employed experimental
equations of friction factor and heat
transfer coefficient
[4]
.
The same authors
give the criteria to choose the mesh size and
wire diameter
of
the regenerator metal
matrix: in our case, using stainless steel,
we obtained a 0.05 mm wire diameter and a
1.06 mm mesh.
Once we know the thermal effectiveness we can
get the outlet temperatures from the inlet
ones simply as
4
CYCLE
DESCRIPTION
The model utilized to calculate the various
points of the cycle is a quite simple one. As in
many other models of Stirling engines compression
and expansion phases are supposed to be adiabatic,
because their duration is too short for heat
exchanging. Heating phase is not precisely
constant volume, but evaluation of the
displacements
of
the pistons is very simple. The
problem is that at the beginning is unknown the
amount of energy recuperated by the regenerator,
so that a first estimation has to be made.
a) once we know the air mass inducted from
pV-MRT, we can evaluate the conditions at the
end of compression from pv =cost. The
compression starts at bottom dead center and
is interrupted after
72
degrees, when the
valve between the cold cylinder and the
regenerator opens, and pressure drops at a
lower value due to the mixing with the
residual mass from the former cycle. Neither
this amount of residual, nor its temperature
are known at this moment, therefore start
k
where Tmax and Tmin are hot and cold inlet
temperatures respectively.
c) The temperature of combustion is also
unknown, being influenced by the amount of
heat absorbed by the cycle. So other
iterative calculation is required. The limit
of maximum aloud temperature for the
combustion chamber material (stainless
titanium steel) has to be taken in account in
this phase.
In the combustion chamber we can imagine that
the walls directly touched by the flame have
constant temperature Tw, related to the
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II
combustion temperature by the equation:
exposed in
[5].
The target function is the entropy
generation number NS
=AS
/ASmax, that is the
ratio between the entropy generated by thermal
exchange and friction irreversibilities
(7)
From the wall temperature Tw the outlet
temperature of the air is easily found, once
we know the geometry and the thermal
conductivity
K,
by the relation
A
S
=
C1
fln[l+&(r-l)l
+
l/z
ln[l-ez(r-l)/rl
Tout
=
Tw
-
(Tw
-
Tin)
(8)
(10)
Knowing the outlet temperature of the
combustion chamber, the expansion phase is
known from pV =cost. Now also the work
produced is known, and the power of the
engine can be found from the difference
between the expansion and the compression
works.
From the hot cylinder the air goes back to
the combustion chamber, where it is reheated
up to a temperature given by
(8).
Now the
whole heat absorbed by the walls of the
combustion chamber Qc is evaluable, and we
can find a new value of Tw such that Qc=Qi.
The air flows back in the heat exchanger,
whose efficiency is different than before
because now the exchange is a parallel flow
one. Anyway we can calculate by
(6)
the
outlet temperature of the exchanger, wich is
also the inlet temperature of the
recuperator. This new value is certainly
different from the one used in (a);
so
we
have to go back and do again the whole
calculation from that point. Iterations are
made till the temperature values became
stable.
The start value for the combustion
temperature Tc has to be reevaluated from the
balance
of
the combustion chamber
and the maximum entropy
1 1
A
Smax
=
Q
(-----
-
-----
)
(11)
Tinl Tina
that is generated when the whole heat Q exchanged
in the system is transferred between the two
extreme temperatures T
Improving the size of the exchanger,
expressed in terms of NTU, the number Ns has only
a minimum in the whole range of NTU; then it can
be utilized as optimization criterion for heat
exchangers design, taking into account entropy
generation.
In the expression of S we can see the
efficency
E
of the exchanger, the ratio r between
the extreme temperatures and the ratio z between
the heat capacity rates of the two streams.
The only given values are the dimensions of
the cylinder, being all the others subject to the
optimization. While the optimization goes on, the
cycle has to be calculated, wich requires an
iterative process.
The global volume of the heat exchanger and
regenerator has to be evaluated in relation to the
cylinder volume, being a big volume certainly
unfavourable for the cycle efficiency.
The revolution speed can be choiced in a
range limited by the aim for a good engine power
and by the reduction of friction and dynamic
losses.
Once we decided the values of global volume
and revolution speed, we still have
to
fix the
ratio between the exchanger and the regenerator,
and finally the number of exchanger tubes and
regenerator layers. On these two last parameters
we attempted an optimization, at three different
levels of revolution speed and of global volume.
Qext
E
Qi
+
Qout
(9)
where Qsxt is the heat introduced by the
burning fuel and Qout is the one outgoing
from the chamber toward the heat exchanger.
5
OPTIIIIZATION
To optimize the regenerator and heat
exchanger design, we make use of the criteria
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1
I
k
in!
and
Tin2*
First the cycle is calculated with a basic
design. Then another calculation is made with
improved values
of
the sizes of the regenerator
and of the heat exchanger. The variation in the
entropy generation number
NS
is registered: if the
rate of change of this parameter with the NTU
of
the exchangers is negative, further work of
optimization can be made improving the size of the
regenerator or of the exchanger. The program stops
when the rate
of
change of the entropy generation
number becomes greater or equal to zero.
References
[I] G. Grazzini, F. Gori, "Influence of thermal
irreversibilities on work producing systems,"
Rev. Gen. Therm. Fr.,No.312, dec.1987, pp.637-639.
[2] F. Curzon, B. Ahlborn, "Efficiency of a
Carnot engine at maximum power output," Am. J,
Phys., Jan 1975, V.43, pp. 22-24.
[3]
W.
Kays, A. London,"Compact heat exchangers,"
McGraw Hill, London 1964.
6
CONCLUSIONS
[4]
H.
Miyabe,
S.
Takahashi, K. Hanaguchi, "An
approach to the design of Stirling engine
regenerator using packs of wire gauzes," 17th
IECEC, 1982, pp.1839-1844.
The results of the optimization are shown in
graphic form in fig.3 and followings.
The whole possible range of revolution speeds
has
to be
explored
to
get an optimum design wich
fits for the work range of the engine. We used
1000, 2000 and 3000 rpm revolution speeds with
exchanger-regenerator system volume
of
90, 60 and
30 cm3, divided in
2/3
for the exchanger and 1/3
for the regenerator.
[5] G. Grazzini, F. Gori, "Entropy parameters for
heat exchangers design," 1nt.J. Beat Mass
Transfer, Vo1.31,
No12,
1988, pp. 2547-2554.
speed
we explored a double range of different exchanger
tubes and regenerator screens numbers. It can seen
how the optimal choice varies with the engine
speed: at 1000 rpm the optimum is achieved with 58
tubes and 32 layers, while at 2000 rpm this values
become 42 and 24 respectively.
The optimization method do
fit
the engine
design problem, as we can seehow the values with
smaller
Ips
have higher engine power. For the
experimental motor we are thinking of a speed of
about 2000 rpm with a exchanger-regenerator volume
of 30 cm
.
Further optimizations are possible on valve
timing and on the other design parameters.
(2000
rpa)
2
Fig.
I
-
Entropy qeneration number veraus heat
excbanwer tube nuaber and regenerator layer nuaber
3
Fig.
3
-
Entropy peneration nu8ber versus beat
exchanqer tuba nuaber and reqenerator layer number
Fiq 5
-
Enqine power versus tube and layer nuaber
241
1
On each value of volume and revolution
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