Design dimension question

[Nut]

I'm designing up a basic gamma using what I believe are Rizzo's "rules of thumb". One rule is that the swept volume ratio displacer:power is 1.5:1. Knowing my power swept volume its easy enough to work out stroke and piston diameter. However there are infinite variations obviously. What should I be aiming at? At the moment I'm leaning towards a stroke the same as the displacer (purely for ease of construction) and then a piston to suit but should I be being more scientific than that? Should I be using a particular stroke:diameter ratio? Are these engines like IC engines where power comes more so from piston diameter and torque more so from stroke?

[matt brown]

I can't imagine Rizzo suggesting (via notation) DP/PP=1.5 since this is a lofty goal similar forum member Vincent. Here's the basic equation that is best considered parity among various PVT values:

(Thigh-Tlow)/Thigh=PPvol/DPvol

Going with your DP/PP=1.5 let's say DP=30cc and PP=20cc, so what's Thigh and Tlow ?

Remembering that T must be Kelvin, let's use conv'l Tlow=300k whereby we find that Thigh=900k as in:

(900-300)/900=20/30

If you play with this above equation thru a wide range of values you'll see why common LTD where DP/PP=40 (or more) can run on such a small temperature spread (source vs sink). I'm not saying you must follow these proportions, I'm just saying that these are the relative variations (kinda an order of merit=1 thing).

I've never seen this equation before, but suspect Senft has it in one of his books (he's a math guru). I found it last year during my deep dive on gammas (I'm mainly an alpha guy).

[Nut]

Thanks Matt. I was assuming the rules were derived from Rizzo but it may have well been Senft. I have not been able to source any of their works yet so do not proclaim to have read them. The "rules" I refer to are:
1. The length of the displacer chamber = 3 times its diameter.
2. The length of the heated chamber = 2/3 of the length of the displacer chamber (cylinder).
3. The length of the cooling chamber = 1/3 of the length of the displacer cylinder.
4. Swept volume of the displacer = 1 1/2 times the swept volume of the power piston.
5. Length of the displacer = 2/3 of the length of the displacer cylinder.
6. Stroke of the displacer = 1/3 of the length of the displacer cylinder.

I will play with your equation and see what I come up with. I had never really factored in heat input per se other than knowing that I need a reasonable heat differential and minimal friction. I think a bit more appreciation of Kelvin is required (ie how it compares to celcius).

Do you have any comments on bore vs stroke once I have locked in the swept volume?

[matt brown]

(1) what size are you thinking - heating/cooling will dominate large engine issues due to geometry (surface area vs volume)
(2) regen or not - regen will complicate everything, but has a drastic effect on efficiency

Above DP/PP=1.5 with 300-900k cycle obscures regen issues. If we consider Vr=volume ratio and Tr=thermo ratio, above cycle has Tr=3 with Vr=1.666 (as in 50cc/20cc) such that Tr/Vr approaches 2. This is the nasty of SE where the heat energy between Thigh and Tlow is almost always far greater than the heat energy of an ideal expansion. The basic idea here is that when the heat between any two temperatures is constant, the more expansion work you can achieve the better or in notation Vr>Tr is waaaaay more efficiency than Vr=Tr or Vr<Tr, especially when no regen. And just to cover myself for anyone else that happens by, when Vr/Tr=6 (or more) regen isn't worth the hassle (regardless of Vr and Tr finite values).

(3) torque is more effected by charge pressure than bore/stroke, kinda like ICE with blower trumps all

[matt brown]

Just a quick glance at your list and everything looks OK except for DP/PP. I'll take a closer look after dinner and get back to you. Overall, gammas are very forgiving, but remember that an "ideal" gamma has Pmax when PP is TDC similar ICE. However, P value/s of real gamma will vary due to phasing and sinusoidal effect (per your concern).

Everything else equal (always a dangerous premise) the real SE challenge is scheming an engine with Vr>3

[Nut]

I was thinking 30mm diameter displacer with 30mm stroke. Displacer cylinder being 60mm of stainless and 30mm of air cooled copper. Displacer piped to nearby power cylinder. Cylinder being air cooled copper with a 24.3 mm graphite piston and 30mm stroke. Each side will be on seperate frame to try and reduce heat creep and all serviced by a central flywheel. I'll be using bearings wherever possible. My objective is not to build the most efficient engine in the world but rather a simple display item that is unique and runs.

I hadn't considered regen as I thought it was more of an alpha thing. In my concept the regen would end up between two cooling areas which I assume defeats the purpose.

Thanks again for your input. My knowledge of the subject is growing but it's very early days. I've learnt a lot of practical theory building my first one and its those lessons I'm trying to exploit in this creation along with more theory to get the relative sizings as close to right as I can.

[matt brown]

Basic dims appear OK, but note this graphic I whipped up...

nut gamma.png (3.93 KiB) Viewed 124 times

where the purple region would be annular regen when consider as such, otherwise part of the 2/3 "hot space" and I like these proportions. Remaining dims appear fine, except I'd reduce PP bore to 20mm whereby DP/PP=2.25 approaches a fuzzy 2 when including dead volumes. Best to consider build with options for smaller diameter PP and various phasing (with conv'l 90deg as starting reference).

Xlnt idea to use copper for cold space and conduit to PP (xlnt heat sinks), but don't think it's a good idea for PP itself, nor aluminum. Both are easy to machine and copper looks pretty, but both wear easy and lack thermal stability...increase size when heated tho theoretically not an issue for PP. And a gamma with this volume ratio will need a hefty flywheel similar an alpha due to the high pressure swing across each cycle (rpm).

I was looking around for my old solar one gamma for reference, but I can't find the bugger.

[Nut]

Thanks so much Matt. I did wonder about the copper PP cylinder. I didn't think wear would be an issue because of the graphite piston (and its only a toy, not running intermittently). But hadn't considered the expansion. I'm doing my best to come up with a modular design that is easy to swap parts in an out such as PP or a water cooled cold end. The dual flywheel makes it relatively easy to initiate a phase shift. I will take your advice on a 20mm PP, and have a go at making a copper cylinder but leave enough fat in the walls if I choose to bore it out later.

The regen image is very interesting. I'll do some more research on how it is implemented. I'm assuming its a balancing act between dead space and a conductive medium. I did think a copper ring that is insulated externally may achieve some function. Even if it doesn't make it into Version 1 I'll try and build such that it could be bolted in at a later date.

An interesting side note on phase shift. My first foray into this fascinating world is a walking beam gamma and you can change its speed (by fluke not design) by moving the horizontal postion of the beam pivot which obviously changes the phase ever so slightly and allows you to find the sweet spot for the particular heat differential at the time.

Thanks again for your help.

[matt brown]

The PP wear issue comes from non-linear forces trying to rock the piston during reciprocation. If the piston has a sharp crown edge, this edge will try to slightly dig the cylinder walls intermittently. This is never an issue with most ICE due to their relatively wide ring gap between piston and cylinder. Any scrape might result in galling cylinder, especially with soft metals. PP expansion should not be an issue since PP is on the cold side (my favorite gamma feature).

SE history is loaded with regen buzz and often akin killing a fly with a baseball bat. Regardless of thermal range, regen is a large amount of cycle energy for low volume cycles (3 and under), but when small scale, it doesn't matter.

Modular design is the way to go, more design issues, but kinda an insurance fund.