Stirling engine - Experiments.pdf - Stirling dokumenty - oliv07

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

Support base -PASS-

02005.55

Extension coupling, hinged

02045.00

Support rod, stainl. steel, 500 mm

02032.00

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

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

Torque meter

04372.02

Chimney for stirling engine

04372.04

Meter f. stirling engine, pVnT

04371.97

Sensor unit pVn for stirl.eng.

04371.00

Syringe 20ml, Luer, 10 pcs

02591.03

Rheostat, 330 Ohm , 1.0 A

06116.02

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

Connecting cord, 500 mm, red

07361.01

Connecting cord, 500 mm, blue

07361.04

Screened cable, BNC, l 750 mm

07542.11

Oscilloscope, 20 MHz, 2 channels

11454.93

Thermocouple NiCr-Ni, sheathed

13615.01

Graduated cylinder, 50 ml, plastic

36628.01

Raw alcohol for burning, 1000 ml

31150.70

Fig. 1: Experimental set-up: Stirling engine.

PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany

23604

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).

23604

PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany

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

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 =

· 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

hPa

p – p 0

hPa

p – p 0

hPa

W 3 = + n · R · T 2 · ln ( V 2 / V 1 )

| W 1 | > W 3 because T 1 > T 2

20 1013

2.35

15 1013

0 2.35

19 1066

2.51

950 – 63 2.15

18 1126 113

2.71

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

844 – 169 1.85

16 1266 253

3.10

800 – 213 1.71

15 1351 338

3.40

760 – 253 1.59

W t = W 1 + W 3

W 1 = –

· R · T 1 · ln ( V 2 / V 1 ) +

· 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.

= 3.04 · 10 -3

hPa

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

= 0.83 g/ml

Specific thermal power

h = 25 kJIg

This allows to determine the mass of alcohol burnt per sec-

ond:

= 6.69 · 10 -3 g/s

as well as the thermal power of the burner: P H = 167 W.

Fig. 4: Characteristic curve of the pressure sensor.

23604

PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany

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

Stirling engine - Experiments.pdf

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