## Stirling Cycle Machine Analysis (Spring 2012)<http://www.ohio.edu/mechanical/stirling/me422.html>

ME 422 (Class #15543)/ ME522 (Class #15545) = 3 credit hours.
Prereq: MATH344, ME328, CE340, and/with ME412, or Permission

The course structure is based on the book 'Stirling Cycle Engine Analysis', I Urieli & D M Berchowitz. (1984). This book is out of print, however some copies are available in Stocker Room 296. Much of the material that is in the book has been updated and placed on this web site, so that you will not need to refer to the text for this course. The book included FORTRAN code of the computer simulations, however all the programs have been updated and rewritten in MATLAB, a convenient interactive language which allows direct graphical output - essential for Stirling cycle analysis.

The course will develop around the analysis and computer simulation of single phase, piston/cylinder thermal power and refrigeration systems including thermodynamics, heat transfer and fluid flow friction.

Requred Course Outcomes

Depending on the class size, each student will be responsible for the simulation of a specific machine (engine or refrigerator). This will require understanding, adapting, modifying and using the basic MATLAB computer simulation program which will be provided to each student. There will be no formal laboratory work, however each student will be responsible for devising or obtaining basic data for their specific simulation.
During the quarter we will attempt to visit a number of companies involved in Stirling cycle machine development in Athens (Sunpower, Stirling Technology, Stirling Ultracold (previously: Global Cooling) as well as Andy Ross in Columbus.
We will also discuss aspects of parameter analysis and Stirling cycle machine design using these analysis techniques.

Tentative syllabus:

• Background and Introduction
Basic Engine Configurations
Here we define the Alpha, Beta, and Gamma engine configurations and show typical examples of usage.

• Isothermal Analysis.
We define and analyse the Ideal Isothermal model of a Stirling engine, and discuss its limitations. One amazing (but obviously incorrect) conclusion of this analysis is that all three heat exchangers are redundant, and only contribute dead space! Nevertheless we can obtain important insights of a specific design, particularly when we augment the solution with Allan Organ's particle mass flow analysis.
1. Develop the Ideal Isothermal equation set including the energy analysis
2. The Schmidt closed form solution
3. Develop and test computer program modules 'define'(MATLAB version)

We find that the Ideal Isothermal model predicts that the heat exchangers of a Stirling engine are redundant, thus we cannot seriously use this model to predict the ideal performance of a real machine. We thus turn to an alternative model - the Ideal Adiabatic model. Unfortunately we find that there is no closed form solution to this model and we have to resort to computer simulation. Nevertheless we can gain various insights from using this model in particular with regards to the importance of the regenerator.
1. Develop the Ideal Adiabatic equation set
2. Develop the method of solution of the Ideal Adiabatic equation set
3. On the numerical solution of ordinary differential equations
4. Develop and test computer program modules 'adiabatic'(MATLAB version)
5. Case Study - The D-90 Ross Yoke-drive Engine

• Simple Analysis.
This analysis approach uses the Ideal Adiabatic model as a basis to predict the real performance of the three heat exchanger sections, particularly with regards to heat transfer and pressure drop. This can then be used to do parametric analyses on specific machines.
1. Regenerator heat loss analysis
2. Heater and Cooler heat transfer analysis
3. Pumping work loss in all three heat exchangers
4. Defining the relevant Scaling Parameters
5. Develop and test computer program modules 'simple'(MATLAB version)

• Scaling Parameters and Stirling Engine Design
This section is based on the significant work by Dr Allan Organ of mRT - Regenerative Thermal Machines. If time allows we will define and examine the various scaling parameters defined by Dr Organ as relevant to Stirling engines, and discuss how to use these in developing a design methodology. (Update 2013: Unfortunately the website by Dr Organ no longer exists)

There will be no final examination. Grade will be determined by a final presentation and report on individual research, analysis, and computer program modules developed, as well as a discussion of the results obtained. The final report is due by Tuesday, June 5, 2012.
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The course includes a set of tutorial computer program modules for simulating specific Stirling engine configurations. These have been transcribed to the MATLAB language, and the complete set of m-files will be provided. The MATLAB program conveniently allows direct graphical output of the simulation results. One of your tasks will be to augment these modules to simulate and design the specific engine assigned to you, thus you will need to become familiar with the entire simulation package. Currently the engine modules are for Alpha machines, including a Sinusoidal drive, a Ross Yoke-drive and a Ross Rocker V engine. The heat exchanger types include tubular, annular gap, and slot heat exchangers, and the regenerator matrix types include screen mesh and rolled foil matrices. Working gas types include air, helium, and hydrogen.