Stirling Engine

3x3 Learning Objectives

Major ideas

1. The first law of thermodynamics is both a statement of conservation of energy and the possibility to interconvert thermal and mechanical energy (as well as other forms of energy).

2. The second law of thermodynamics limits the efficiency with which thermal energy can be converted to mechanical energy in a closed thermal cycle. The maximum achievable efficiency is the Carnot efficiency stated in terms of temperatures of hot and cold baths employed in a thermal cycle.

3. A method for enabling the Stirling cycle to better approach ideal Carnot efficiency is the use of a "regenerator" to absorb and then later release thermal energy during parts of the cycle.

Major equipment

1. A cleverly-designed transparent expansion/compression cylinder with electrical heat source and circulating coolant operates in a closed cycle, and linkages translate the reciprocating motion into circular motion of a flywheel and stretching and release of a spring.

NOTE: In the second week of doing the experiment, you might like to explore some modeling of the mechanics of the Stirling engine using the following (NOTE: this is not yet a prelab; see below for the actual prelab document.) 3_1 Stirling Engine 2-Apparatus.ipynb .

(While the above document should automatically link to the piston and crank drawing pistonandcrank.png , you might want to separately view and download this file.)

2. Sensors measure quantities that allow pressure and volume to be sampled throughout the thermal cycle. One or more temperature sensors may also be employed but presently do not directly measure the working gas temperature. However, the pressure and volume can be used to estimate the gas temperature (describe how).

3. An Arduino micro-controller board reads the sensors and, in turn, passes data onto a supervising computer using programs running on both the Arduino (coded in C) and the computer (coded in Matlab).

Alternates (if you have already learned and presented all of the above)

4. A method makes non-contact measurement of AC current.

5. (Not yet implemented) Methods can be devised to obtain and measure useful output work from the engine.

Data analysis

(In all of the following, be able to comment on estimates of uncertainties.)

1. Describe how the rotating sensor is calibrated and, using this calibration, converted into volume readings. Also, plot estimated working gas temperature versus volume and - if you wish - versus any other relevant thermodynamic quantity that you wish to estimate.

2. Describe a method for computing the area within a closed cycle on the pressure-volume (p-V) "indicator diagram".

3. Describe how raw efficiency is estimated using the area of the pV cycle and other measurements. How then is the ideal efficiency inferred from cycle temperatures? How well do these compare, i.e. how closely does the system approach ideal and how is the difference explained?

Prelab

Here is a link to the Stirling engine prelab as a Jupyter document to download and run on your own computer. This document automatically should link to a plot of the pressure-volume (pV) diagram but here is a direct link to download this drawing Stirling pV digram.jpg.

Here is a link to a version of the prelab that can be rendered online, but you will not be able to run any of the embedded code.

Experiment guide

See the provisional experiment guide in the attached document Stirling Engine v0_5.pdf . Note: The sensors and measurement section in this document is out of date - we no longer use the PASCO system. See below for information regarding the new sensors and data acquisition.

There are two sensors that we will use to acquire data from the Stirling Engine apparatus (an AMT-203 rotarty encoder and Honeywell HSCDANN1.6BASA5 pressure sensor). Both sensors are connected to an Arduino UNO and communicate via an SPI bus. The code that is running on the Arduino can be found here.

The Arduino is connected to the PC via USB cable. On the PC, we will use MATLAB to read the output from the Arduino and plot/analyze/store the data. The MATLAB code that is written to acquire the Arduino data can be found here (it should also be located in a folder on the Desktop named "COPY THIS DIRECTORY - RENAME YOUR COPY" - please do so). This code does function, but is in development. The file "MainScript.m" is written to plot live data from either the encoder OR the pressure sensor (not both simultaneously). There are two sections within the script where you can change the data to be displayed (by changing which line is commented out).

To stop collecting data, you must click the "Stop" button that is on the bottom of the plot window. Closing the window without clicking "Stop" will result in an error, and additional measures must be taken to collect more data.

After you have properly stopped acquiring data, you may then investigate the variable "data" - a four column array that contains all the data from the previous session. You may then use the "csvwrite" function to output your data (please refer to the MATLAB help documentation for the proper syntax).

References

Wikipedia article

https://en.wikipedia.org/wiki/Stirling_engine

Simon, R. A. (1983), "Stirling's cycle and the second law of thermodynamics," Am. J. Phys. 51, 496-499.

Bizarro, J. P. S. (2012), "The thermodynamic efficiency of heat engines with friction," Am. J. Phys. 80, 298-305.

Crane, H. R. (1990), "The Stirling Engine - 173 Years Old and Running," Phys. Teach. 28, 252-253.

Spence, R. D., and C. L. Foiles (1982), "Stirling engines for demonstration," Phys. Teach. 20, 38-39.

Deacon, C. G., R. Goulding, C. Haridass, and B. deYoung (1994), "Demonstration experiments with a Stirling engine", Phys. Educ. 29, 180-183.

Thompson, F. (1980), "An inexpensive non-contacting linear transducer," Phys. Educ. 15, 244-246.

Thompson, F. (2010), "Stirling engine gets revisited" Phys. Educ. 15, 229-230.

Haywood, D., "An introduction to Stirling cycle machines" retrieved 22 Sep 2015.

http://www.occc.edu/gholland/Thermo/Stirling_Intro.pdf

W. R. Martini, Stirling Engine Design Manual, 2nd ed. (pdf), NASA Report CR-168088 (1983), retrieved 21 Sep 2015.

Thermodynamic properties of air

E. W. Lemmon et al., "Thermodynamic properties of air and mixtures of nitrogen, argon, and oxygen from 60 to 2000K and pressures to 2000MPa", J. Phys. Chem. Ref. Data, v.29, no.3 (2000) pp. 331-386.

http://www.nist.gov/data/PDFfiles/jpcrd581.pdf

Thermopedia: thermodynamic properties of air

http://www.thermopedia.com/content/553/

Leybold instruction sheets and apparatus specifications

Instruction sheet 388 182: hot air engine

http://www.ld-didactic.de/documents/en-US/GA/GA/3/388/388182e.pdf

Leybold immersion pump 388 181

http://www.leybold-shop.com/immersion-pump-388181.html

Transformer for providing heater power

Mains coil, 56222 (for 115V)

(Can't find documentation)

Coil, 50 turns, extra-low voltage, 56218