External Combustion Engine With Stirling Open Cycle.pdf

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

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.

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

EXWST

3-4 COLNTERFLOU HEATING

*-S HEATING IN CONWSTION CHWlEER

5-6 EXPWION

6-7 &OTING IN CONBUSTION CHR"ER

8-9 REGENERATION

74 P~R~LLEL

FLOU nEnTING

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-.

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. Figure 2 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

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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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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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)

Fig. I - Entropy qeneration number veraus heat

excbanwer tube nuaber and regenerator layer nuaber

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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