UMEÅ UNIVERSITY 2013-11-20 Department of Physics Leif Hassmyr

Updated versions 2017-10-30: Joakim Ekspong

Hot Air Engine, Type Stirling

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Hot Air Engine, type Stirling - contents The object with this experiment is to make you familiar with cyclic processes, pV-diagrams, efficiency, refrigerators, heat pumps, hot air engines etc. Task 1: Study the pistons’ movement and correlate them to the different points in the theoretical pV-diagram. Draw at page 12-14 (Appendix 1-Appendix 3) the positions and movement of the pistons in figure 9 when the gas is at the points A, B, C, D in figure 8. Also, show with arrows in both figures 8 and 9 how heat is transported away and delivered to the system in the three cases: See example at page 14 (Appendix 3). 1. Refrigerator. 2. Heat pump. 3. Hot air engine. Task 2: Study the Stirling Engine as a refrigerator and heat pump when the engine is driven by an electric motor and the flywheel can rotate both clockwise and counter clockwise. (See experiment I and II, page 6-8). Answer the questions about the cooling and heating processes: a) Record the temperature of 1 cm3 water in a test tube. b) How much water freezes instantaneously after the super cooling? (Tip: Compare the specific heat capacity of water with heat needed to form ice) c) Explain the difference when you compare the slopes of the curve just before the freezing with the slope just after the freezing. d) Why is the time it takes for water to freeze different from the time it takes to melt ice? Task 3: Study the Stirling Engine as a Hot Air Engine and record a pV-diagram. a) Figure of the pV-diagram with measured data and units on the axis. b) Determine the thermodynamic work and the hot temperature TH from the pV-diagram. Task 4: Study the Stirling Engines useful power by applying diferent loads. Figure of useful efficiency as a function of the number of revolutions/sec. Comments. Task 5: Draw a power distribution scheme (see page 10). Comments

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Part A: Description of the Processes

The idealised Stirling process is described in the pV-diagram below.

Figure 1 pV-diagram of the idealized Stirling cycle

The ideal Stirling cycle consists of two isothermal and two isochoric processes and can be described like following: Let us determine the thermal efficiency for an ideal Stirling process when the working fluid is an ideal gas (pV = nRT). Assume quasistatic frictionless conditions at every step. The work involved when a gas changes from state A to B is: 𝑊!!! = 𝑝𝑑𝑉!

! In an ideal gas, where the internal energy U = f(T), we know according to the first law of thermodynamics that ΔU = Q + W = 0 in an isothermal process. The first law of thermodynamics then becomes 𝑄!!! = −𝑊!!! According to figure 1: 1 → 2 : The gas is isothermally compressed at the temperature 𝑇! and the work W1-2 = 𝑛𝑅𝑇!𝑙𝑛

!!!!

is done on the gas while the heat QC is taken away. 2 → 3 : The gas is heated at constant volume (isochoric) to the temperature 𝑇! by supplying the heat QR . No work is done. 3 → 4 : The gas expands isothermally at the temperature TH and does the work W3-4 = 𝑛𝑅𝑇!𝑙𝑛

!!!!

. The heat QH is absorbed during this process. 4 → 1 : The gas is cooled at constant volume to the temperature TC . No work is done and the heat QR is taken away.

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and as V Vb a< , 𝑄! = 𝑄!!! = 𝑛𝑅𝑇!𝑙𝑛

!!!!

and 𝑄! = 𝑄!!! = 𝑛𝑅𝑇!𝑙𝑛

!!!!

Concerning processes 2-3 and 4-1: As V=constant and 𝑑𝑄𝑑𝑇 !

= 𝐶!

is valid for the isochoric processes we get dQ = Cv · dT or 𝑄!!! = 𝐶!(𝑇! − 𝑇!) and 𝑄!!! = 𝐶!(𝑇! − 𝑇!) respectively. That is, 𝑄!!! = −𝑄!!! which gives 𝑄!!!+𝑄!!!= 0 The efficiency can be written as

( )( )baH

baC

H

C

H

CH

H VVRTnVVRTn

QQ

QQQ

Qw

/ln'/ln'

11 −=−=−

==η

or η = −1 TTC

H

.

We see that the efficiency for the cycle is the same as for the Carnot cycle. This is possible if we can keep the heat 𝑄!!! stored in the machine. This heat should later be returned to the gas as the heat 𝑄!!!. In practice this is achieved with the so called regenerator. If the heat 𝑄!!! is transported away with the cooling water one would have to supply the heat 𝑄!!! externally and then the efficiency would not be the same as for the 'Carnot-machine'. The efficiency can also be improved by lowering the low temperature 𝑇! or by raising the high temperature 𝑇!, but it is impossible to reach an efficiency equal to 1. Note that this is not caused by mechanical shortcomings as friction. This can be derived for all reversible processes, in which there are no losses. Part B: Description of the Machine A sketch of the machine is found in figure 2. The main parts are a precision cut glass cylinder (1) with two movable pistons (2) and (3) attached to a flywheel (4). In the upper part of the cylinder there is a heating arrangement (heated tungsten spiral (5)) and the lower part is surrounded by a plastic cooling jacket (6) with inlet and outlet for the cooling water (7). The displacing piston (2) transports the gas from the warm to the cold part of the cylinder (and the other way around).

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The working piston (3), which moves with a 90 degrees phase difference relative to the displacing piston, compresses the gas and thus controls the volume. The working piston isolates the gas from the surroundings and work is taken away or delivered via this piston.

Figure 2 Schematics of different parts of the Stirling engine used in the lab

The displacing piston is made of a heat resisting glass and the bottom of it is sealed with a water-cooled metal plate with radial slots that allows air to pass during heat exchange. This piston has been given a special shape with an axial cavity filled with copper wool as the regenerator (8). The purpose of the copper wool is to absorb heat when the gas passes to the colder part of the cylinder and to emit heat when the gas passes in the opposite direction. In this way heat is conserved and the efficiency increases. The pistons are connected with piston rods to a heavy flywheel (4) to give the machine a smooth running. At the rod of the working piston (9) there is an outlet (10) for measuring the pressure in the cylinder via a channel in the piston rod. The outlet is connected to a pV-indicator for producing a pV-diagram of the process. The flywheel has a key groove for connections to other machines (for example an electric motor). A handle can temporarily be attached to the flywheel. Then one can turn the flywheel around manually and make a detailed study of the process. The pV-indicator (figure 3) consists of a mirror assemblage (11) which is possible to rotate in both horizontal and vertical directions. The volume variations of the working gas are transferred via a string (12) to the horizontal movement of the mirror holder (13). The pressure variations are transferred via a thin PVC-tube (14) to the vertical movement. By lighting the mirror in an appropriate way one can observe simultaneous variations in pressure and volume of the gas, i.e. we have a pV-diagram for the process.

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Figure 3 A schematic of the pV-indicator

Part C: The Pistons Movement Relative the pV-diagram (Task 1) Turn the flywheel manually and check that the movable piston moves freely. Study the pistons’ movement and correlate them to the different points in the theoretical pV-diagram. Draw at page 12-14 (Appendix 1-Appendix 3) the positions and movement of the pistons in figure 9 when the gas is at the points A, B, C, D in figure 8. Also, show with arrows in both figures 8 and 9 how heat is transported away and delivered to the system in the three cases: See example at page 14 (Appendix 3). Think about where the hot and cold reservoirs are in each case and how it would affect the pV-diagram. 1. Refrigerator. 2. Heat pump. 3. Hot air engine.

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Part D: The Experimental Procedure For practical reasons it is best to do the experiments in the following order. I. Refrigerator. II. Heat pump. III. Hot air engine. General instructions Turn on the cooling water and check that it flows. Lubricate the machine if neccessary according to the supervisors instructions. Note: only silicon oil! Always check that the machine runs without any part touching other parts by turning the flywheel manually. If the cooling water is lost: Turn off the filament current within three seconds. Put the protection cover over the heated filament when it is removed. Always position the displacement piston at the lowest configuration when the machine is turned off. Never leave the machine running unattended!!!! Experiment I and II: Refrigerator and heat pump (Task 2). In these two experiments one uses the arrangement shown in figure 4 and figure 5.

Figure 4 Arrangement of the Stirling engine, used as a refrigerator and heat pump. Note the external motor connected to the

flywheel.

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Figure 5 An image of the arrangement in experiment I and II. It is important to use the Plexiglass protection.

The flange with the heating filament is changed to a flange to which you can attach a test-tube. The machine is driven by an electric motor and the flywheel can rotate both clockwise and counter clockwise. In this experiment you should analyse and explain what's happening with help of the Stirling cycle's pV-diagram. Further, you should demonstrate and investigate the machine's use as a refrigerator and heat pump. Experiment I: Cooling of Water Fill the test tube with 1 cm3 of water. Measure the temperature in the test-tube with a thermo-couple (type K, 40µV/K). (Important: The thermocouple should not touch the glass!). Note: The Plexiglas protection must be mounted. Turn on the machine as a refrigerator. Study how the temperature depends on time with the help of a t/y-printer (set to measure temperatures from -25 ºC to +100 ºC and the timescale: 0.5 mm/sec). Wait until the temperature reaches -20 ºC.

Plexiglass protection

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Experiment II: Heating of Water When the temperature in the test tube is around -20 °C, change the direction of revolution for the flywheel. Heat to about +50 ºC. Observe and compare the cooling and heating processes. Experiment III: The hot Air Engine Task 3: Study the hot air engine and record a pV-diagram. Note: Turn the flywheel so that the displacing piston ends up in its lowest position when the motor has stopped. Otherwise there is a risk for overheating and thereby cracking. For a demonstration how thermal energy is converted to mechanical energy the machine is set up as in the figure 6.

Figure 6 A schematic of the Stirling engine setup during the brake test.

Mount the flange with the heating filament so that the heating filament never touches the displacing piston. Check that the cooling water flows. Connect the heating filament (1Ω) to the source. A suitable filament current is 15 A. Check that the displacing piston is in its lowest position. Start the machine by manually turning the flywheel. Record the pV-diagram by the help of the pV-indicator

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When the motor does not do any work, the thermodynamical efficiency (𝜂!!!) is determined from calculations in the pV-diagram as following

𝜂!!! = 1−𝑛′𝑅𝑇!𝑙𝑛 𝑉! 𝑉!𝑛′𝑅𝑇!𝑙𝑛 𝑉! 𝑉!

= 1−𝑇!𝑇!

= 1−𝑄!𝑄!

Determine TH if TC = 20 ºC. One problem is to determine the scale of the pressure. It must be determined by static measurements. The instructor gives the necessary instructions. The volume scale can be determined as one knows that 3

min 130 cmV = and 3max 270 cmV = .

Task 4: Determine the useful Power and useful Efficiency – brake test The brake test is done by putting a friction band of copper over the wheel attached to the outgoing axis. In one end a suitable weight is put and in the other one measure how large the frictional force is with help of a dynamometer. The number of revolutions per second is measured with the help of a stroboscope. The power Pout is determined from the relation Pout = ωτ , where ω is the angular velocity and τ is the torque. Useful efficiency:

ηoutout

inin

PP

P U I= = ⋅,

Determine η for at least 5 different loads where the largest load gives a number of revolutions that is approximately half of the unloaded number of revolutions 𝑁 < !!

!, and plot ηout as a

function of the number of revolutions/sec. It is important to make this measurement fast. (Otherwise the temperature of the engine is raising and the efficiency is changing) Note: Be careful when adding loads. Do not put on as high load so that the motor nearly stops. The gas will get extremely hot and the glass cylinder can easily break.

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Task 5: Draw a power distribution scheme Draw a power distribution scheme like the one in figure 7 below, for the maximum Pout –value when you apply loads on the Stirling engine. Give the powers in Watt and draw the width of the arrows in proportion to the power.

Figure 7 Power distribution scheme of the Stirling engine with important energy losses included.

Heat losses to the surroundings = Pin - QH ·n Losses in the Stirling cycle = QC ·n Frictional losses = W ·n - Pout

(n = number of revolutions/sec) Pout

Pin

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Hot Air Engine, Type Stirling Contents for the report 1. Figures with the positions and movements of the pistons as well as pV-diagrams and

energy flows (see example page 14) for: a) Refrigerator. b) Heat pump. c) Hot air engine. 2. Answers to the questions about the cooling and heating processes:

a) Figure of the temperature as a function of time for 1 cm3 water in a test tube during cooling and heating. b) How much water freezes instantaneously after the super cooling? c) Explain the difference when you compare the slopes of the curve just before with

the slope just after the freezing. d) Why is the time it takes for water to freeze different from the time it takes to melt ice?

3. a) Figure of the pV-diagram with measured data.

b) Determination of TH from the pV-diagram. Comments. 4. Figure of useful efficiency as a function of the number of revolutions/sec. Comments. 5. Power distribution scheme. Comments.

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Appendix 1 Refrigerator

Figure 8 Theoretical pV-diagram for the Stirling cycle

Figure 9 Glass cylinders for studying the piston movements

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Appendix 2 Heat Pump

Figure 8 Theoretical pV-diagram for the Stirling cycle

Figure 9 Glass cylinders for studying the piston movements

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Appendix 3 Hot Air Engine

Figure 8 Theoretical pV-diagram for the Stirling cycle

Figure 9 Glass cylinders for studying the piston movements The working piston is not moving. The displacing piston moves up. The heat QR is given off by the gas to the regenerator.

D

Working piston

Displacement piston

QR