Please Check my Calcs....

Discussion on Stirling or "hot air" engines (all types)
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samandress
Posts: 6
Joined: Wed Jan 27, 2016 5:18 am

Please Check my Calcs....

Post by samandress » Fri Feb 12, 2016 8:09 am

Hello all,
ive been planning a tin can gamma engine to be built from scratch
ive found two cans that seem to be a good starting point
and ive built an excel spreadsheet that calculates volumes
as well as calculating the stroke length of the power piston for a range of diameters Vs. a range of ratios
it even then highlights the strokes that are within 20% of its diameter so its easy to find which diameter power piston cylinder is square
so making it easy to select a power piston and tell you the stroke required so long as you know what ratio to use

ive then researched ratios used in existing models to try to inform my own ratio choise, and found the following
1:1.5 high temp gas burners only
1:7 coffee cup engine (candle or hot water)
5:1 to 8:1 range for a stove top fan engine
1:16 stove top example
1:10 to 1:20 LTD

ive also designed a crank shaft that runs on roller bearings and should be able to have an adjustable stroke on both pistons
allowing me to dial in on the perfect ratio with live testing (although there would naturally be limits as to how big an adjustment can be made)


below is the dimensions of my plan (all in mm)
displacer diameter _______ 53 (displacer length is 1/3 of stroke)
cylinder diameter ________ 61
cylinder length __________146 (just short of 3x its width as convention suggests )
end clearance ___________ 3 (displacer stops short of stroke 3mm at each end to prevent suction at the cost of dead space)
wall clearance __________ 4 ( power piston will have 4mm clearance between it and cylinder wall, regenerator fills this space later)
dead space _____________117814
displacer volume ________ 100749
cylinder volume ________ 426680
stroke volume___________ 308866

this engine is designed to be a small desktop model powered by a single candle flame


my question is... what sort of ratio would you suggest?
this is seemingly impossible to calculate, and pretty hard for me to guess,
a candle flame is quite high temp but not a much total energy output.


Do my plans and dimensions look right so far?
i know its hard to imagine from a table of numbers, but do the sizes and proportions seem like a working engine,
or is there anything that needs changing?


is the power piston ratio relative to stroke volume?
perhaps a fairly basic but important thing to ask...
when using ratios to determine the volume of one piston to another
do you use the volume of the displacer cylinder or the volume of the stroke of the displacer
which would therefor be 3x the volume of the displacer

Bumpkin
Posts: 131
Joined: Fri Mar 02, 2012 1:42 pm

Re: Please Check my Calcs....

Post by Bumpkin » Fri Feb 12, 2016 8:20 pm

Hi samandress. I think you're on the right track.
(I think the underlined is backwards, otherwse I basically agree with this table)
1:1.5 high temp gas burners only
1:7 coffee cup engine (candle or hot water)
5:1 to 8:1 range for a stove top fan engine -
1:16 stove top example
1:10 to 1:20 LTD
----------------
It would probably be helpful if we in the forum could produce some concise guidelines, but I doubt we could all agree. "Traditional" numbers exist, but everyone places their own value on tradition and what they want to do with it. That said; here's my two cents on understanding swept volume ratios:

Temporarily discounting numerous other variables; the temperature difference is what determines a successful swept volume ratio. For most of our purposes, we can assume air will increase in volume or pressure at the same rate as it increases in temperature. For this to be relevant, temperature must be measured from absolute zero, usually expressed on the Kelvin scale. For example: 100 degrees F. is not twice as hot as 50 degrees F. - In Kelvin degrees that difference is actually about 283 to 311 - around 10%. - A handy conversion tool: http://www.allmeasures.com/temperature.html So it appears an engine designed for those temperatures would need the power piston to sweep 1/10 as much as the displacer, but wait - the ratio is diluted by any "necessary evil" dead space. So accounting for regenerator and flow passage, it appears we need maybe a 1 -13 mechanical ratio to get an actual 1 - 10 swept volume ratio, but wait - temperature must differ for heat to flow, so unless the engine is static the working air can't reach the same potential as the outside temperature difference. So it appears that we need higher than a 1 - 13 mechanical ratio to optimize for a 1 - 10 temperature difference, but wait - we still need to account for compression effects. "Compression effects" is my oversimplification of adiabatic/isothermal nerd-speak, which translates to: Compressing a gas raises its temperature internally and makes it less able to absorb more heat. The opposite applies on the cooling stroke. There's "scholarly" debate on how the regenerator affects this, but it seems to me the only way to transfer the full available temperature difference into and out of the working gas would be to have zero pressure change - and zero power. So to design for a 1 - 10 temperature ratio I would start with about a 1 - 20 mechanical swept volume ratio.

All of the above is just purely-amateur :big smile: reasoning for my own rule-of-thumb: The swept volume ratio should be about half of the available temperature ratio. A higher ratio might run, but less efficiently. A lower ratio might run, but only down to the point that heat is pumping power more than power is pumping heat.

Bumpkin

Ian S C
Posts: 2221
Joined: Thu Dec 02, 2010 5:15 am
Location: New Zealand

Re: Please Check my Calcs....

Post by Ian S C » Sat Feb 13, 2016 2:26 am

You say the power piston will have a clearance of 4 mm, it won't work! 0.0127 mm/0.0005" is about the clearance for a power piston, the piston should just slide through the cylinder unlubricated, under it's own weight, and when the end of the cylinder is blocked off the piston should slow to almost a stop.
For a table top tin can motor, a power cylinder about 15 mm to 30 mm diameter, and say about 20 mm stroke would sound ok by me.
For Stirling Engine calculations, it is normal to use the Kelvin scale (-273.15*C), and the normal temperature scale used in scientific work internationally is the Celsius scale.
Ian S C

Bumpkin
Posts: 131
Joined: Fri Mar 02, 2012 1:42 pm

Re: Please Check my Calcs....

Post by Bumpkin » Sat Feb 13, 2016 9:52 am

OK. It was a Friday night and it looks like I ran on a bit. My main point would be that In the interest of science it'd be helpful to agree on some basic terminology. I'll accept whatever works best, but I prefer "swept volume" for the mentioned ratio. I think "displacer volume" can lead to some confusion. Likewise with temperature scales, where Celsius or Fahrenheit can be very misleading. Another point was that dead space changes the affect of the swept volume ratio.

Bumpkin

samandress
Posts: 6
Joined: Wed Jan 27, 2016 5:18 am

Re: Please Check my Calcs....

Post by samandress » Sat Feb 13, 2016 9:59 am

Bumkin____

i agree forums like this should easily be able to produce guide lines or at least a range of examples from working engines,
the trouble is any engine in the real world cannot be perfectly calculated before it is built,
from my own experience in studying thermodynamics and doing CFD computer modeling of it
even the latest technology is simply very good at "guessing" how fluids behave
there are simply too many interdependent variables - as you have said
which is further compounded by the mechanical aspects of the engine

http://www.solarheatengines.com/2012/02 ... g-engines/
this link deals with determining ratios based purely on volumetric ratio and temperature difference
without using the traditional ratios at all, its an interesting read but trades one problem for another,
without a running engine you cannot measure the temperature difference without all the heat exchangers and conduction are in play


Ian S C ____

sorry that was a typo, the displacer will have a clearance of 4mm (which would later be reduced with steel wool regenerator)
the power piston will most likely be a glass syringe or epoxy putty

as i was saying above, i don't believe ΔT K° can be determined before an engine is built,
without computer modeling at least it would be pointless to guess

as for 30mm x20mm stroke according to my calculator that would equate to a 1:22 ratio for my engine
which seems a bit severe for a flame powered engine





i think one of the problems is the old rule of having the displacer cylinder 3x as long as it is wide.
this is a very old rule based not on the behaviour of the gas but on the practicalities of the materials
when this rule was made the cylinders would be made of thick conductive metal, wrought iron or brass
im sceptical this rule applies to thin steel and glass walled cylinders



thanks all for your imput
- Sam

Bumpkin
Posts: 131
Joined: Fri Mar 02, 2012 1:42 pm

Re: Please Check my Calcs....

Post by Bumpkin » Sat Feb 13, 2016 10:59 am

Hi Sam.
---------
"i agree forums like this should easily be able to produce guide lines or at least a range of examples from working engines"
----------
Actually the only guidelines I'd like to see here are basic thermodynamics and Stirling terminology. Individual thoughts and examples can be inspiring, but should never be taken as THE way. I know you understand that; as you said:
-----------
"i think one of the problems is the old rule of having the displacer cylinder 3x as long as it is wide.
this is a very old rule based not on the behaviour of the gas but on the practicalities of the materials
when this rule was made the cylinders would be made of thick conductive metal, wrought iron or brass
im sceptical this rule applies to thin steel and glass walled cylinders"
---------------
Another reason for that design is to use the length as a regenerator, but I totally agree with your assessment that other designs might better suit other materials/purposes. In fact, I've proven to my own satisfaction that as long as thermal transfer and isolation issues are satisfied, a displacer isn't even needed and can be replaced by a reciprocating regenerator. As far as I can tell, air doesn't know the difference between whether it is displaced through a regenerator or if the regenerator is displaced through it.

Bumpkin

Ian S C
Posts: 2221
Joined: Thu Dec 02, 2010 5:15 am
Location: New Zealand

Re: Please Check my Calcs....

Post by Ian S C » Sun Feb 14, 2016 1:48 am

You can of course do without the displacer all together, thermo acoustic/laminar flow engine.
Ian S C

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