|Stirling Engines: How They Work
(Non Technical Terms)
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
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
On to Spreadsheet Calculations