Check your schedule!
This is a reminder that Experiment 2 does not necessarily follow Experiment 1.
You need to login to your course homepage on Sakai and check your lab schedule to determine the experiment rotation that you are to follow.
My Lab dates: Exp.2:... Exp.3:... Exp.4:... Exp.5...
Note: The Lab Instructor will verify that you are attending on the correct date and have prepared for the scheduled Experiment; if the lab date or Experiment number do not match your schedule, or the review questions are not completed, you will be required to leave the lab and you will miss the opportunity to perform the experiment. This could result in a grade of Zero for the missed Experiment.
To summarize:
• There are five Experiments to be performed during this course, Experiment 1, 2, 3, 4, 5. • Everyone does the first experiment on their first scheduled lab session.
• The next four experiments are scheduled concurrently on any given lab date.
• To distribute the students evenly among the scheduled experiments, each student is assigned to one of four groups, by the Physics Department. Your schedule is shown in your course homepage on Sakai.
2:
first name (print) last name (print) brock id (ab13cd) (lab date)
Experiment 2
The Stirling engine
A friendly reminder: Is this your scheduled experiment? See the previous page.
In this Experiment you will learn
• some of the principles of thermodynamics, power, work, coefficient of performance; • that the work performed by an engine can be measured using a P-V diagram; • about thermal inertia and the times required for a heat engine to reach equilibrium; • to apply different methods of error analysis to experimental results.
Prelab preparation
Print a copy of this Experiment to bring to your scheduled lab session. The data, observations and notes entered on these pages will be needed when you write your lab report and as reference material during your final exam. Compile these printouts to create a lab book for the course.
To perform this Experiment and the Webwork Prelab Test successfully you need to be familiar with the content of this document and that of the following FLAP modules (www.physics.brocku.ca/PPLATO). Begin by trying the fast-track quiz to gauge your understanding of the topic and if necessary review the module in depth, then try the exit test. Check off the box when a module is completed.
FLAP PHYS 1-1: Introducing measurement FLAP PHYS 1-2: Errors and uncertainty FLAP PHYS 1-3: Graphs and measurements FLAP MATH 1-1: Arithmetic and algebra
FLAP MATH 1-2: Numbers, units and physical quantities
WEBWORK: the Prelab Stirling Test must be completed before the lab session
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! Important! Bring a printout of your Webwork test results and your lab schedule for review by the TAs before the lab session begins. You will not be allowed to perform this Experiment unless the required Webwork module has been completed and you are scheduled to perform the lab on that day.
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! Important! Be sure to have every page of this printout signed by a TA before you leave at the end of the lab session. All your work needs to be kept for review by the instructor, if so requested. CONGRATULATIONS! YOU ARE NOW READY TO PROCEED WITH THE EXPERIMENT!
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The Stirling Engine
It is said that the plight of poor workmen, often injured by the explosions of the early steam engines were the inspiration for Rev. Robert Stirling’s engineering efforts that led to the development of what we now call “the Stirling engine” in 1816. However, Rev. Stirling’s life-long interest in engineering, his father’s profession, suggests that the technical challenges fascinated him as well. He is the author of several patents, from the “Heat Economizer” (regenerator) to various optical devices, his “air engine” being the most famous.
Stirling engines are typically external combustion engines, as opposed to the open-cycle internal com-bustion engines prevalent today. The Stirling cycle involves moving a working fluid, typicallly a gas, between two reservoirs that are maintained at different temperatures, mediating the heat transfer from the hot to the cold side and extracting mechanical work in the process. In this way, the Stirling engines are very similar to the idealized heat engines textbooks on Thermodynamics.
The designs of Stirling engines vary considerably, but they all share the inherent safety of a much lower operating pressure of the working gas, and fairly high heat-to-work conversion efficiency, especially compared to a standard gasoline engine. Their dynamic properties — the ability to rev up quickly, for example — are quite poor, so they are not well suited for motor vehicle use, but there are marine engines, hand-held toys, and deep-space probe electrical generators that all use Stirling engines.
Figure 2.1: The U10050 Stirling Motor. Reproduced from the 3B Scientific manual.
The engine used in this lab is a displacement-type engine that uses two separate pistons, connected to a common flywheel (see Fig. 2.1). One piston is the working piston; it fits snugly into the cylinder and maintains the seal on the working gas. The other, a displacement piston, is moving freely inside its cylinder, shifting the working gas through the gap between the piston and the cylinder from the hot to the cold end of the cylinder, and back again. The full Stirling cycle can be approximately divided into four parts:
1. the gas is shifted to the hot end by the displacement piston; it expands as it heats up, and pushes the working piston which in turn rotates the flywheel;
2. the displacement piston moves, shifting the gas toward the cold end; heat is lost from the gas; 3. cooled gas is re-compressed by the inertia of the flywheel pushing the working piston.
4. with the gas compressed by the working piston, the displacement piston shifts it to the hot end, where the heat is absorbed into the gas.
Figure 2.2: The Stirling cycle. Reproduced from the 3B Scientific manual.
The four parts of the cycle are illustrated schematically in Fig. 2.2.
On the left, four snapshots 1–4 show the relative positions of the displacement (A) and working (B) pistons that correspond approximately to the four parts of an idealized Stirling cycle.
On the right, A more realistic plot of the positions of the two pistons during the continuous rotation of the flywheel. The grey region in part 2 shows the part of the cycle where the working piston is near its lowest point and the gas volume is approximately at its maximum. The area above the dashed line represents the fraction of the total volume that is above the displacement piston, in thermal contact with the hot end of the cylinder.
Since it takes less work to compress the gas when it is cold (against lower gas pressure) than the work done by the gas on the piston when it is hot (gas exerting higher pressure over the same piston travel distance), there is a net conversion of heat into mechanical work.
Dividing the cycle into four discreet parts is an idealization. A more realistic plot is shown in the right-hand frame of Fig. 2.2, where the positions of both pistons vary continuosly throughout the cycle. Both pistons are attached to the same flywheel, but at 90◦ to each other. As a consequence, the solid and
the dashed line are a quarter of a cycle out of phase with each other.
Figure 2.3: The pV -diagrams of the Stirling cycle. The idealized cycle in the left frame is made up of four distinct parts. In a realistic Stirling engine the parts of the cycle are not completely separate, and the pV -diagram looks more like the one in the right frame.
Fig. 2.3 illustrates the thermodynamics of the Stirling cycle. As we follow along the curve made by the measured pairs of (pi, Vi), the area on the pV -diagram inside the cyclical trajectory of the working cycle
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of the engine represents the amount of mechanical work performed by it: W =X i Fi∆xi= X i (piA)∆xi = X i pi(A∆xi) = X i pi∆Vi
The work is being done by the gas on the flywheel along the upper curve, and by the flywheel on the gas along the lower curve; the difference is the net work done by the engine. In our example, one can estimate graphically the area inside the curve of Fig. 2.3 (right frame) to be about three–four large squares, 20 kPa by 0.25cm3
= 0.25 × 10−6m3
, and therefore, about 15–20 mJ per cycle.
Stirling engines, in general, have excellent coefficients of performance (CoP), reaching as high as twice the thermal efficiency of internal-combustion gasoline engines. When used to drive electric generators, as in this experiment, the thermal efficiency, though high, is just one of many of the CoP’s that need to be multiplied together to get the overall CoP: that of the mechanical efficiency of the flywheel-piston system, that of the conversion efficiency of mechanical into electrical energy, etc.
The overall efficiency of the process of conversion of the internal chemical energy of the fuel into the usable electrical energy that can turn on a lighbulb, is only of the order of 10%. Increasing the difference in the operating temperatures of the hot and cold ends, changing the working gas, or the compression ratio, can dramatically affect that number, but the cost and complexity of the engine may also increase.
Stirling engines, long a domain of tinkerers and enthusiasts, are making a comeback. Six Swedish submarines are equipped with Stirling engine propulsion units, enabling them to conduct long-range dives fueled by a chemical source of energy that does not involve a conventional burning of liquid fuel, without the use of nuclear power. Long-range space probes make use of a Stirling-cycle electric power generators fueled by the heat of radioisotope heat sources. Combined heat-and-power generators based on a Stirling engine are commercially available in the 100 kW power range, and their miniature cousins may one day replace laptop and cell phone batteries.
The Stirling engine as a heat pump
The many advantages of the Stirling engines are well described in the excellent Wikipedia article (recom-mended reading), one of which is their flexibility: their ability to act as heat pumps as well as engines.
If one uses an external motor to drive the Stirling engine through its thermal cycle, the net effect is the reverse conversion from mechanical energy into thermal one, heating up one end and cooling down the other end of the cylinder: following the pV -curve of Fig. 2.3 in the counterclockwise direction means a change of sign of the difference between the upper and lower halves of the cycle.
Even more interesting is the ability of the Stirling engine to reverse the direction of this heat flow, if the direction of rotation of the engine is reversed. Thus the same Stirling-cycle thermal pump can act as a heat source in winter and a cooling device in the summer!
Procedure
The Stirling Engine U10050 used in this experiment is a single-cyclinder demonstration model made of glass and clear plastic so that the movement of the internal components can be easily seen. Typically, the Stirling Engine is used as a heat engine; an alcohol flame is applied to the round end of the glass tube icontaining the displacer piston and the engine uses some of this heat energy to perform mechanical work. If the engine is connected to a direct current (DC) generator, some of this mechanical energy is converted to electrical energy. As a heat engine, the Stirling Engine will always turn in the same direction, following the heat cycle shown in Figure 2.3.
In this experiment, the Stirling engine is used as a heat pump, the opposite of a heat engine. A DC voltage is applied to the electric motor that rotates the flywheel and moves the pistons. The electrical energy is expended to transfer heat and thus to create a temperature difference between the two ends of the cylinder. The direction of the transfer of heat depends on the direction of rotation, and thus the engine
can heat as well as cool the round end of the glass tube, relative to the other end that has a large metal heat reservoir attached to it, which is in turn exchanging heat with the surrounding air.
The heat pump system consists of the following parts (please refer to Fig. 2.1 for Stirling engine parts): 1. a glass displacer piston that pumps air between the hot and cold sides of the engine. The piston is enclosed by a glass tube with a brass socket at each end; these are the temperature monitoring points of the engine;
2. a brass working piston that compresses the gas or is pushed by the expanding gas, making the conversion between mechanical and heat energy;
3. a driveshaft with balancing cams and linkages that converts to rotary motion the reciprocating motion of the working piston and also drives the displacer piston;
4. a flywheel on the driveshaft that provides rotational inertia to couple different parts of the Stirling cycle and to maintain a consistent rotational speed through the cyclical variations in the gas pressure inside the engine;
5. a direct current (DC) motor/generator that drives the engine flywheel by means of a rubber belt. 6. a DC power supply that is used to vary the rotations per minute (RPM) of the motor by varying the
applied voltage;
The operation of the engine is monitored with a variety of sensors. This data is sent to the PhysicaLab software and is displayed as a pV (pressure-volume) diagram. The work done per cycle, engine RPM, and the power output of the heat pump are also measured and reported by the software. Here is a summary of the sensors:
• the absolute pressure p inside the engine is monitored with a pressure sensor that outputs a reading in Pascals. This sensor typically has a resolution better than 1% of the range of pressure experienced by the engine;
• the temperatures T1 and T2 at each end of the displacer cylinder are measured in◦C. These sensors
are currently not installed on the engine;
• the volume change V , in m3, is calculated from a series of markings on the flywheel of the engine that determine the angle of rotation relative to a reference mark that represents the start of a pV cycle when the volume is at a maximum.
Part 1: Coefficient of performance
In this exercise you will estimate the coefficient of performance of the stirling engine heat pump. As the heat pump requires some time to reach a new operating equilibrium after a change in RPM is made, you should pay close attention to the behaviour of the engine during this time. You should document how the work done per cycle and engine power values change during these transitional periods after a change in RPM is made; you should also note and explain any systematic changes in these variables as the engine RPM is increased from a manimum to the maximum. You will be required to discuss these issues as part of your discussion.
• Review and identify all the parts of the apparatus in front of you. Rotate the engine slowly by turning the flywheel clockwise abd then counterclockwise and note the relative movement of the working piston to the displacer piston. The two pistons are offset by 90◦.
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• Connect the two wires between the DC electric motor and the power supply, red to red and black to blue. The voltage that is applied to the motor is adjusted by turning a knob and monitored on the corresponding digital display in volts (V). The current flowing through the motor is shown on the other meter in Amperes (A). Be sure that the current limit knob is turned fully clockwise.
1. Check that the switch next to the motor is pointing downward, then turn on the power supply and increase the voltage to around 5.5 V. The engine should start to rotate and the 7-segment display should show the current engine RPM. Lets define rotation as CW when the flywheel rotates clockwise as viewed from the side with the markings; CCW defines a counter-clockwise rotation.
? In which direction is the heat pump turning?
2. Close any running PhysicaLab programs, then start a new session by clicking on the Desktop icon or by typing physicalab followed by the Enter key. Login with your email address; you will email yourself all graphs for later inclusion in your lab report.
Click on the SE input to select the Stirling Engine interface. Press the Get data button to begin graphing pV cycles. In this mode, the data collection parameters are ignored; the graph updates at a rate that is determined by the speed of the engine.
3. To output a steady set of values, the Stirling engine needs some time to adjust thermally to the new operating conditions. Capture a copy of the pV cycle at the start of this equilibration process by pressing the Stop button to temporarily freeze the graph display, then click Send to: to email yourself a copy of the graph.
4. Let the engine equilibrate for several minutes, until the RPM, work and power values appear steady, then record for each variable the maximum and minimum value that occurs over the course of 60 seconds in order to determine a nominal error estimate ∆(X) = (Xmax −Xmin)/2 for the three
quantities:
∆(RP M ) = ... = ... = ...
∆(Pse) = ... = ... = ...
∆(W ) = ... = ... = ... 5. Email yourself a copy of the graph representing the pV cylce of an equilibrated Stirling engine.
? Are there any notable differences in these two graphs?
? Review the data set in order to match the data points to the oval display of the corresponding pV cycle. At which point of the oval does the pV cycle begin?
? For a given value of volume V , there are two corresponding pressure values p. Does the lower or higher pressure value occur first during the cycle?
? Is the pV cycle being drawn in a clockwise or counter-clockwise direction? Is this what you expect?
? Feel the ends of the displacer cylinder, near the brass plugs. To which side is heat being pumped?
V (V) I (A) Pm (W) RPM W (J) Pse (W) COP
Table 2.1: Stirling heat pump data for Part 1
6. Record in Table 2.1 the motor voltage V and current I displayed on the power supply, then calculate the electrical power Pm used by the motor to turn the heat pump. Estimate the errors in V and I
as ∆(V ) = 0.01 V and ∆(i) = 0.01 A.
7. Record from the pV graph the heat pump RPM and work done per heat pump rotation, then calculate the power output Pse of the heat pump at the current RPM.
8. Determine the COP for the heat pump at the current RPM: COP = Pse/Pm.
9. Increase the voltage by 1 V and repeat the equilibration and data recording procedure up to a voltage of 12.5 V. When the table is complete, terminate the transmission of data but keep the engine running. Be sure to allow enough time for the engine to settle to a thermal equlilbrium as determined from the previous estimate of this required settling time.
10. You will now plot a curve representing the coefficient of performance for the heat pump as a function of RPM. Enter your values for COP and RPM in the data window, then select Scatter plot and press Draw . Email yourself a copy of the graph.
? How does the COP vary with RPM? Is there a value of RPM where the COP seens to be a maximum?
Part 2: Heat Pump equilibration
The Stirling Engine should currently be in equilibrium at V = 12.5 V. You will now observe how the heat pump RPM, Work and Power converge to new values following a change in the voltage of the driving motor from 12.5 V to 5.5 V. To do this, you will record the elapsed time t, RP M , W and P every thirty seconds for a period of fifteen minutes.
• Check that the clock at the bottom right corner of the Desktop is displaying time in seconds. If not, right click on the Clock, select Properties and set the Format to display seconds.
• Restart the graph update. Wait until the seconds advance to zero, the decrease the voltage to 5.5 V and begin recording data in Table 2.2, as outlined above, until the table is filled.
15 t (s) RPM W (J) Pse (W) t (s) RPM W (J) Pse (W) t (s) RPM W (J) Pse (W) 30 330 630 60 360 660 90 390 690 120 420 720 150 450 750 180 480 780 210 510 810 240 540 840 270 570 870 300 600 900
Table 2.2: Stirling heat pump parameter convergence data
• Turn off the power supply, then switch the two wires at the power supply. Turn power supply back on and set the voltage to 5.5 V as before. The heat pump should begin to rotate in the opposite direction.
As you wait for the engine to equilibrate, graph as a function of time the three variables in Table 2.2.
? Looking at the convergence graphs, how long does it take for the Stirling engine to equilibrate?
? Is this time representative of the equilibration time required as you step through the 1 V changes in Table 2.1?
Part 3: Coefficient of performance, opposite direction
V (V) I (A) Pm (W) RPM W (J) Pse (W) COP
• Repeat the above steps and record your data in Table 2.3. Make notes of all the observations, as in the previous section, to include in your lab report.
? Feel the ends of the displacer cylinder, near the brass plugs. To which side is heat being pumped?
? Does the lower or higher pressure value occur first during the cycle? Is the pV cycle being drawn in a clockwise or counter-clockwise direction? Is this what you expect?
IMPORTANT: BEFORE LEAVING THE LAB, HAVE A T.A. INITIAL YOUR WORKBOOK!
Lab report
Go to your course homepage on Sakai (Resources, Lab templates) to access the online lab report worksheet for this experiment. The worksheet has to be completed as instructed and sent to Turnitin before the lab report submission deadline, at 11:55pm six days following your scheduled lab session. Turnitin will not accept submissions after the due date. Unsubmitted lab reports are assigned a grade of zero.
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