Analyzing Failure in an Alpha
Type Stirling Engine
Abstract: This analysis using ABACUS software will help to understand the failure of an air
cylinder undergoing the normal stresses and strains of a Stirling
engine cycle. This cycle includes
changing pressures and temperatures of the working fluid inside the cylinder several times per
Analysis done by
An Son Leong
Stirling Engine Background:
The Stirling engine is a closed cycle
heat engine with a gaseous working fluid. Essentially,
it is powered by the temperature difference between the hot and cold side of the engine.
Thermodynamically, the Stirling cycle consists of four parts:
The working fluid inside the syste
m is compressed
2) Heat Addition
Heat is added to the system and the gas expands
The gas expands against the piston, doing work
4) Heat Removal
Heat is removed from the system and the cycle starts all over again
Stirling Engine and Stirling Cycle was patented by Reverend Robert Stirling in 1816.
It is very efficient, approaching Carnot
however the engines are plagued by several
issues. They are not very versatile and have trouble adapting to temperature differences that
they were not designed for. It is also hard to vary the speed of the engine
. The engines fell out
of favor because of
advances in steam engine technology. Since the 60’s various companies
have researched Stirling engines for automobiles, power generation, etc but the engines have
never been developed commercially until recently. Due to their high efficiency and their abil
to run off of any heat source, several initiatives have been made to develop Stirling technology.
NASA developed a Stirling engine to generate power for a deep space probe using plutonium as
a source of heat. A California company has developed a 25 kW
generator that runs off of
sunlight focused by a parabolic mirror.
This project is an extension of a project for a class in which the authors are enrolled. The
objective was to design a Stirling engine that could run off of a low temperature
Typical commercial Stirlings run off of a temperature difference that can exceed 1000 degrees
Fahrenheit and pressures of up to 100 atm.
The Stirling engine designed by the authors was
designed using off the shelf air cylinders for a first gene
ration demonstration model. The
temperature difference is 85 degrees Fahrenheit. That is, the cold side will be kept a constant
60 degrees and the hot side a constant 145 degrees. Originally, the design called for the
working fluid to be pressurized with h
elium at 10 atmospheres with th
e system at maximum
volume, as cycle efficiency increases as pressure increases. This means that the system will see
pressures of 30 atm when the gas is compressed.
The air cylinders ordered are rated to withstand 250 psi, o
r approximately 17 atm
before the seals on the pistons burst. The question was then posed that if the seals were not
the limiting factor, how much pressure could the cylinder withstand without failure? What
effect does temper
ature have on the stainless ste
el cylinder? These questions are relevant
because they will allow the authors to optimize the design of the first generation engine
without compromising the structural integrity of the engine. The picture below is the engine
designed by the authors.
The two air cylinders are connected by brass tubing that allows transfer of the gas
between hot and cold sides. Notice the copper piping that surrounds the hot and cold cylinders.
This will circulate water at a given temperature to keep each cylinder at
the designated hot or
cold temperature. The two steel flywheels will store the kinetic energy required to compress
the gas and begin the cycle over again.
The objective of this structural analysis is to find the criteria for failure in our air
cylinders. We will know the project is successful when the Stirling designed by the authors is
safely operated as a result of the structural analysis done by ABACUS.
Two simple models were developed
to analyze the air cylinder. The picture on t
shows the top down profile of the cylinder with x and y symmetry. The picture on the right
of the cylinder and will show how the c
ylinder will deform lengthwise
The radial model was subject to four boundary conditions: It is assumed to have x and y
symmetry, the temperature of the inside of the cylinder is forty degrees
room temperature (assumed to be zero) and the outside of the cylinder is as
sumed to be 50
degrees warmer than the ambient temperature. The difference between inner and outer wall
temperature is because of the assumption that not all the gas will be the maximum hot or cold
temperature. This is because the temperature exchange is h
appening at a very high frequency.
The model for the length was also subject to four boundary conditions: X symmetr
ends of the cylinder are
constrained against movement, and the same inner and outer wall
temperature of 40 and 50 degrees
For the given model, it was found that pressure had a much greater effect on the failure
cylinder than temperature. Given the cylinder dimensions, it was found that failure will
the top edge of the model
in the area where the threads connect
the air cylinder
. This failure occurs
at an internal gauge pressure of
, much less than the
rated pressure of the cylinder. This could be because the dimension of the top of the cylinder
given in the part schematic drawings and was inaccurately represented in our mode
An assumption was made that the top and bottom wall were the same thickness as the side
wall of the cylinder. On the next page a
re the analysis for the radial and length mo
del at failure.
It is assumed the model fails when any node reaches the yield stress for stainless steel of
approx 250 MPa.
Notice the red at the top and bottom of the length model for a stress of 272
MPa. Notice also tha
t the radial stress at the inside
f the cylinder is a mere 200 MPa.
ABACUS is also capable of producing graphical results that relate to temperature. For
the purposes of this analysis, the two plots shown are heat flux and nodal temperature.
temperature plot of the
radial section is shown here. Notice the outer and inner walls are 50
and 40 degrees above the ambient temperature, with a fairly linear distribution in between.
This is a result that one would expect. When the heat flow vectors are plotted, the vectors al
point radially inward as heat is flowing from hot to cold. It is not shown here because the vector
plot is very messy and difficult to read.
The plots of the nodal temperature and heat flux for the length model are shown above. Notice
the upper half of the cylinder has become the hot temperature and the lower half has become
the ambient temperature. The heat flux plot matches up nicely with this result, as one can see
that a lot of heat is flowing out of the lower half of the cylinder.
This analysis shows that the air cylinder will fail at an internal gauge pressure of .5
atmospheres or 50 kPa. This is much less than the 17 atm promised by the manufacturer. As
shown above, the failure occurs at the
ends of the cy
re it is constrained against
deflection. This is a realistic constraint, as the design of the engine does not allow it to translate
in any direction. However, the analysis could be somewhat flawed because of the lack of
accurate dimensions provided in the
Needless to say, during test runs of
the engine it will not be run at gauge pressures higher
than 50 kPa.
This same analysis can be
done for the second generation engine to help determine how thick the cylinder walls need to
be to withs
tand a higher working pressure that will increase efficiency.