Graphic courtesy of Dr. Israel Urieli of Ohio University.

The gas circuit is the heart of the Stirling engine.  It is in this part of the Stirling that all of the thermodynamic processes take place.  The heat is transferred from the outside source (external combustion or heat source) into the gas through the Heater. This heat is temporarily stored in the Regenerator on the way to the Cooler where some of the remaining heat is removed from the gas (rejected).  Referring to the diagram above, the portion of the engine between the Expansion space and the Compression space is the Gas Circuit.

In this section we will be working with the principles of Scaling and Similarity in the form used by Dr. Allan J. Organ in his recent book The Regenerator and the Stirling Engine.  This is not an exact procedure or formula but is a method of  Scaling (resizing) a gas circuit for a Stirling engine which shares Similarity of performance with well documented existing Stirling engine designs.  This is accomplished by choosing certain thermodynamic ratios measured on a variety of Stirling engines and then constructing another engine of different Scale (size) by using these ratios and holding them as constant as possible in the design of the new Scaled gas circuit.

These principles are embodied in the program written by Dr. Organ's associate in the mRT organization Scalit.  Scalit performed the arithmetic operations needed to create a gas circuit from the ratios of historical engines.  It was found to contain errors in its coding which caused Dr. Organ to withdraw the program from use.  It is to be replaced by Scalit II but we have not yet obtained a copy for testing.  During this period of time SESUSA members created a spreadsheet in Excel to perform these arithmetic operations.  This spreadsheet may be downloaded from the SESUSA mailing list Files section or from this web page. 

In the previous section, we developed a Stirling engine approximation from the Beale equation and determined the rough parameters defining the engine size, power, pressure and speed.  We will now use the Gas Circuit Scaling spreadsheet to create a gas circuit to support the engine  we desire to build. 

You may have noticed that we have not discussed efficiency up until this point.  This is because the maximum efficiency of a Stirling engine is set by the temperature ratio of the gas in the heater and cooler.  All of the Similarity and Scaling engines used as the original engines have a temperature ratio of approximately 3:1 (in degrees Kelvin absolute).  This results in a maximum theoreticalefficiency of about 67 %.  If the mechanical efficiency of the mechanism can render half of the theoretical efficiency in overall operation, it is considered an excellent design.  Using a recouperator to recover (recoup) the heat from the exhaust into the incoming fuel mixture can raise the efficiency of the burner to levels which make this possible.   Building a low friction mechanism is a challenge and art meets science in the process but is a necessary ingredient of a successful design.

Speaking of friction. The friction of the gas flowing theough the pipes and channels of the gas circuit is a major component of the losses incurred. Air in particular requires a gas circuit that must balance heat transfer with gas friction losses. The small size of the openings needed for good heat transfer result in higher frictional losses in the process. This loss factor is also dependent on the speed of the gas flowing through the passages. The swept volume also contributes to the issue as there are more grams of gas per cycle flowing through the gas circuit as the swept volume increases. This means that the larger the volume and the higher the RPM, the greater the complexity of the gas circuit. Upon examining the similarities of the prototype engines by graphical analysis we discover that there is a linear relationship for volume vs. rpm which can be transferred to the derivative engine to give us an upper limit on the RPM. For air this is RPM~4060/(Vsw^-3) In word form it is RPM equals (approximately) 4060 divided by the cube root of swept volume. The chart is on page 169 of The Regenerator and the Stirling Engine by Dr. AJ Organ

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