Stirling engine - Experiments, Silnik Stirlinga, Dokumenty

[ Pobierz całość w formacie PDF ]
R
Stirling engine
LEP
3.6.04
Related topics
First and second law of thermodynamics, reversible cycles,
isochoric and isothermal changes, gas jaws, efficiency, Stirling
engine, conversion of heat, thermal pump.
Optional accessories for solar motor work
Accessories f. solar motor work
04372.03
1
Support base -PASS-
02005.55
1
Extension coupling, hinged
02045.00
1
Support rod, stainl. steel, 500 mm
02032.00
1
Principle and task
The Stirling engine is submitted to a load by means of an
adjustable torque meter, or by a coupled generator. Rotation
frequency and temperature changes of the Stirling engine are
observed. Effective mechanical energy and power, as well as
effective electrical power, are assessed as a function of rota-
tion frequency. The amount of energy converted to work per
cycle can be determined with the assistance of the pV dia-
gram. The efficiency of the Stirling engine can be estimated.
Problems
1. Determination of the burner’s thermal efficiency
2. Calibration of the sensor unit
3. Calculation of the total energy produced by the engine
through determination of the cycle area on the oscilloscope
screen, using transparent paper and coordinate paper.
Equipment
Stirling engine, transparent
04372.00
1
4. Assessment of the mechanical work per revolution, and cal-
culation of the mechanical power output as a function of the
rotation frequency, with the assistance of the torque meter.
5. Assessment of the electric power output as a function of
the rotation frequency.
6. Efficiency assessment.
Motor/generator unit
04372.01
1
Torque meter
04372.02
1
Chimney for stirling engine
04372.04
1
Meter f. stirling engine, pVnT
04371.97
1
Sensor unit pVn for stirl.eng.
04371.00
1
Syringe 20ml, Luer, 10 pcs
02591.03
1
Rheostat, 330 Ohm , 1.0 A
06116.02
1
Set-up and procedure
Experimental set up should be carried out as shown in Fig. 1.
The base plate (mounting plate) of the Stirling engine must be
removed, so that the latter can be fixed on the corresponding
mounting plate of the pVn sensor unit. The incremental trans-
mitter of the pVn sensor unit is firmly connected to the axle of
the Stirling engine. The latter is then fixed upon the large base
plate.
Digital multimeter
07134.00
2
Connecting cord, 500 mm, red
07361.01
2
Connecting cord, 500 mm, blue
07361.04
3
Screened cable, BNC, l 750 mm
07542.11
2
Oscilloscope, 20 MHz, 2 channels
11454.93
1
Thermocouple NiCr-Ni, sheathed
13615.01
2
Graduated cylinder, 50 ml, plastic
36628.01
1
Raw alcohol for burning, 1000 ml
31150.70
1
Fig. 1: Experimental set-up: Stirling engine.
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany
23604
1
R
LEP
3.6.04
Stirling engine
Before switching on the pVnT meter, make sure it is connect-
ed to the pVn sensor. Connect the p and V exits respectively
to the Y and X oscilloscope channels.
4. Effective mechanical energy
In order to load the engine with a determined torque, the scale
of the torque meter is fixed on the large base plate, and the
inner metallic piece of the pointer is fixed on the axis before
the flywheel. Friction between the pointer and the set-on
metallic piece can be varied by means of the adjusting screw
on the pointer. Adjustment must be done carefully, to make
sure that the pointer will not begin to oscillate.
Start carrying out measurements with a low torque. After each
adjustment, wait until torque, rotation frequency and temper-
atures remain constant. All values and the pV diagram are
recorded.
After having been switched on, the pVnT meter display shows
“cal”. Both thermocouples must now be set to the same tem-
perature, and the “Calibration
D
T
”-button depressed. This
calibration of the temperature sensors merely influences the
temperature difference display, not the absolute temperature
display.
The upper display now shows “OT”, which means “upper
dead centre point”. At this point, the engine is at its minimum
volume. Now bring the working piston down to its lowest posi-
tion by turning the engine axle, and press the “calibration V”
button. Wrong calibration will cause a phase shift in the vol-
ume output voltage, and thus lead to a distortion of the pV
diagram. The three displays should now be on, showing 0
revs/min, and the actual temperatures for T
1
and T
2
.
5. Effective electric power
Replace the torque meter through the engine/generator unit.
The small light bulb may not be inserted. The slide resistor is
connected to the generator output, as shown in Fig. 2, and
adjusted to the highest resistance value. Before starting to
perform measurements, the Stirling engine without load
should have approximately the same rotation frequency and
temperatures as at the beginning of the previous series of
measurements paragraph 3). The string is then wound around
the Stirling engine flywheel and the large generator strap
wheel. Voltage, current intensity, rotation frequency and tem-
peratures are recorded, once rotation frequency and temper-
atures have steadied. Resistance is decreased stepwise, and
further measurement values are recorded. Repeat the series of
measurements using the small generator strap wheel.
1. Thermal output of the burner.
The amount of alcohol in the burner is measured before and
after the experiment with a measuring glass (or a scale). The
corresponding duration of the experiment is recorded with a
watch or clock.
2. Calibration of the pressure sensor
The pressure sensor must be calibrated so that the pV dia-
gram can be evaluated quantitatively. This is carried out by
means of a gas syringe.
The flexible tube is removed from the mounting plate, and the
voltage corresponding to atmospheric pressure p
0
is deter-
mined with the oscilloscope. The latter should be operated in
DC and Yt mode, with calibrated Y scale. The piston of the air-
tight gas syringe is drawn out (e. g. up to 15 or 20 ml), and the
syringe is connected to the flexible tube. The pressure (volt-
age) display on the oscilloscope screen is varied through iso-
thermal in- crease and decrease of the syringe volume. The
actual pressure inside the syringe can be calculated.
Theory and evaluation
In 1816, Robert Stirling was granted a patent for a hot air
engine, which is known today as the Stirling engine. In our
times, the Stirling engine is used to study the principle of ther-
mal engines because in this case the conversion process of
thermal energy to mechanical energy is particularly clear and
relatively easy to understand.
At present, the Stirling engine is undergoing a new phase of
further development due to its many advantages.
Thus, for example, it constitutes a closed system, it runs very
smoothly, and it can be operated with many different heat
sources, which allows to take environmental aspects into con-
sideration, too.
3. Presentation and drawing of the pV diagram
The oscilloscope is now operated in the XY mode, with cali-
brated scales.
Place the lighted burner below the glass cylinder, and observe
the temperature display. When the temperature difference has
reached approximately 80 K, give the flywheel a slight clock-
wise push to start the engine. After a short time, it should
reach approximately 900 revs/min, and a Stirling cycle ought
to show on the oscilloscope screen.
Before carrying out measurements of any kind, wait until tem-
peratures T
1
and T
2
, as well as the rotation frequency, are
approximately constant. The lower temperature should now
be about 70 °C.
Rotation frequency and temperatures are recorded. Voltages
corresponding to maximum and minimum pressures are read
from the oscilloscope. The pV diagram is copied from the
oscilloscope to a sheet of transparent paper. Make sure to
look perpendicularly onto the screen when doing this. The Y
axis ground line is drawn, too. Transfer the diagram to co-ordi-
nate paper, in order to be able to determine the diagram sur-
face.
Fig. 2: Wiring diagram for the connection of the rheostat
(slide resistor).
2
23604
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany
R
Stirling engine
LEP
3.6.04
Fig. 3a:
pV
diagram for the ideal Stirling process.
Theoretically, there are four phases during each engine cycle
(see. Fig. 3a and 3b):
1) An isothermal modification when heat is supplied and work
produced
V
1
R
V
2
p
1
R
p
2
and
T
1
= const.
2) An isochoric modification when the gas is cooled:
T
1
R
T
2
p
2
R
p
3
and
V
2
= const.
3) An isothermal modification when heat is produced and
work supplied:
V
2
R
V
1
p
3
R
p
4
and
T
2
= const.
4) An isochoric modification when heat is supplied to the
system:
T
2
R
T
1
p
4
R
p
1
and
V
1
= const.
According to the first law of thermodynamics, when thermal
energy is supplied to an isolated system, its amount is equal
to the sum of the internal energy in- crease of the system and
the mechanical work supplied by the latter:
d
Q
= d
U
+
p
d
V
It is important for the Stirling cycle that the thermal energy
produced during the isochoric cooling phase be stored until it
can be used again during the isochoric heating phase (regen-
eration principle).
Fig. 3b: Functioning of the transparent Stirling engine.
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany
23604
3
R
LEP
3.6.04
Stirling engine
Thus, during phase IV the amount of thermal energy released
during phase II is regeneratively absorbed. This means that
only an exchange of thermal energy takes place within the
engine. Mechanical work is merely supplied during phases I
and III. Due to the fact that internal energy is not modified dur-
ing isothermal processes, work performed during these phas-
es is respectively equal to the absorbed or released thermal
energy.
2. Calibration of the pressure sensor
The pressure sensor measures the relative pressure as com-
pared to the atmospheric pressure
p
0
. The volume modifica-
tion of the gas syringe allows to calculate the modification of
pressure, assuming that the change of state is isothermal, with
p
·
V
= const.
At the initial volume
V
0
, pressure is equal to the atmospheric
pressure
p
0
Table 1 shows an example of measurement for
which
p
0
was assumed to be normal atmospheric pressure
(1013 IlPa). The volume of the small flexible connecting tube
(0.2 ml) can be considered to be negligible.
Since
p
·
V
=
n
·
R · T
,
where v is the number of moles contained in the system, and
R
the general gas constant, the amount of work produced dur-
ing phase I is:
W
1
= – n ·
R · T
1
· ln (
V
2
/
V
1
)
Table 1
(it is negative, because this amount of work is supplied).
Consequently, the amount of work supplied during phase III is
Compression
Expansion
V
ml
p
hPa
p

p
0
hPa
U
V
V
ml
p
hPa
p

p
0
hPa
U
V
W
3
= + n ·
R · T
2
· ln (
V
2
/
V
1
)
|
W
1
|
>
W
3
because
T
1
>
T
2
20 1013
0
2.35
15 1013
0 2.35
19 1066
53
2.51
16
950 – 63 2.15
18 1126 113
2.71
17
894 – 119 1.99
The total amount of work is thus given by the sum of
W
1
and
W
3
. This is equal to the area of the pV diagram:
17 1192 179
2.89
18
844 – 169 1.85
16 1266 253
3.10
19
800 – 213 1.71
15 1351 338
3.40
20
760 – 253 1.59
W
t
=
W
1
+
W
3
W
1
= –
n
·
R · T
1
· ln (
V
2
/
V
1
) +
n
·
R
·
T
2
.ln (
V
2
/
V
1
)
W
1
= – n ·
R
· (
T
1

T
2
) · ln (
V
2
/
V
1
)
Fig. 4 shows the output voltage of the pressure sensor as a
function of pressure. The slope of the regression line is:
Only part of this total effective energy Wt can be used as
effective work
W
m
through exterior loads applied to the
engine. The rest contains losses within the Stirling engine.
U
= 3.04 · 10
-3
V
hPa
p
The maximum thermal efficiency of a reversible process with-
in a thermal engine is equal to the ratio between the total
amount of work I
W
1
I and the amount of supplied thermal
energy
Q
1
= –
W
1
The voltage corresponding to atmospheric pressure
p
0
is 2.35 V
Caution!
Sensitivity of the pressure sensor may undergo large
fluctuations. However, linearity between
U
and
p
is assured for
all cases.
h
th
=
W
t
/
W
1
h
th
=
·
R
· (
T
1

T
2
) · ln (
V
2
/
V
1
)
·
R
·
T
1
· ln (
V
2
/
V
1
)
h
th
=
T
1

T
2
T
1
Carnot found this to be the maximum thermal efficiency for
any thermal engine, which can only be reached theoretically.
One sees that efficiency increases with increasing tempera-
ture differences.
1. Thermal power of the burner
Duration
D
t
= 60 min
Amount of alc6hol burned
D
V
= 29 ml
Alcohol density
r
= 0.83 g/ml
Specific thermal power
h = 25 kJIg
This allows to determine the mass of alcohol burnt per sec-
ond:
m
= 6.69 · 10
-3
g/s
t
as well as the thermal power of the burner:
P
H
= 167 W.
Fig. 4: Characteristic curve of the pressure sensor.
4
23604
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany
R
Stirling engine
LEP
3.6.04
3.
pV
diagram surface
The oscilloscope’s X measuring range is of 0.5 V/div.
ThepVnTmeasuring device displays the following voltages for
the Stirling engine volumes (
V
min
,
V
max
are equipment constants):
Fig. 5: Real pV diagrams (a) without, and (b) with exterior load.
V
min
= 32 cm
3
R
U
min
= 0 V
V
max
= 44 cm
3
R
U
max
= 5 V
D
V
= 12 cm
3
R D
U
= 5 V
Thus, the scale factor for the X axis is 2.4 cm
3
/V or respective-
ly 1.2 cm
3
/div.
With the used pressure sensor, the oscilloscope’s Y measuring
range was 0.2 V/div (with other pressure sensors it may be
0.5 V/div). Based upon the pressure calibration of Fig. 4, one
finds a scale factor of 329 hPaIV or respectively 66 hPa/div for
the Y axis.
Reading the voltages for maximum and minimum pressures
with the oscilloscope being operated in the DC mode, the
pressure values for the
pV
diagram can also be expressed in
Pascal. In general, the ground line will be situated near
p
0
.
For other Stirling engines, the pV diagram may have a some-
what different shape. Thus, for example, the surface is a func-
tion of supplied thermal power and engine friction at equilibri-
um rotation frequency.
Fig. 5 shows two real
pV
diagrams for a Stirling engine with
and without load (Fig. Sa: no load, Fig. Sb: with a load of
18.3 · 10
-3
Nm). Assessed surface values are given in table 2.
Fig. 6: Mechanical energy as a function of rotation frequency.
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany
23604
5
[ Pobierz całość w formacie PDF ]