regen vs volume ratio graph

[matt brown]

I came across this today and don't recall ever posting this, but it's interesting.

regen vs Vr.png (88.34 KiB) Viewed 9188 times

Note that increasing the volume ratio decreases regen issues. Also note that 1.0 regen has a tad more than .60 eff, so this relates to a cycle where Tmax=750k and Tmin=a tad less than 300k.

Now, considering Tmin=300k we can call this a plot for thermal ratio (Tr) = 2.5

As I've often claimed, once the volume ratio (Vr) = 6 you can nix regen (not worth the chase) but this really is a function of Vr:Tr not simply Vr. So, if you look at this graph and hipshoot some Vr/Tr values, you can easily see regen effect pending regen eff vs Vr.

The main takeaway is that the crappier your regen eff, the more you benefit from increasing Vr.

[Bumpkin]

I’m sure I’ve posted this here somewhere before, but this reminds me of noticing how mid to lower temperature engines of higher displacement ratios suffer less from dead space than higher compression high temperature engines. Of course it’s still a penalty, but low enough that alternate architectures can make sense.

Bumpkin

[matt brown]

I’m sure I’ve posted this here somewhere before, but this reminds me of noticing how mid to lower temperature engines of higher displacement ratios suffer less from dead space than higher compression high temperature engines. Of course it’s still a penalty, but low enough that alternate architectures can make sense.

Bumpkin

Yes, I remember you posted such in past year and rightly so. Notice in that graph that the no regen curve (orange) is over .30 eff by 5:1 volume ratio which is only twice this 300-750k thermal ratio. Without checking (calcs) I'll guess that typical 300-600k thermal cycle would require 6:1 volume ratio for similar .30 eff which ain't bad when you consider the best NASA has achieved.

Once we nix regen, we can also nix isothermal heating and cooling and go straight for Otto. Checking my handy adiabatic index for air, a 3:1 volume ratio will have a 4.6 pressure ratio and 1.55 thermal ratio which leaves enough 'overhead' for input from a 2:1 thermal ratio (300-600k). And lest I forget, this has .35 eff.

So, Bumpkin, did you notice what I just said...a 300-600k Stirling cycle with 6:1 volume ratio is .30 eff vs a 300-600k Otto cycle with 3:1 volume ratio is .35 eff. The Otto will be less powerful per rpm, but there's a world of difference between 3:1 and 6:1 volume ratios. The main advantage the Stirling has is output on the Tmin side of cycle which nixes lubrication, insulation, etc issues, but will still likely suffer from phasing issues. Meanwhile, the Otto reverses all of these issues.

[VincentG]

What does the dashed black line represent?

[Fool]

I'm not sure that I'm reading the graph correctly. It looks as if, for Vr of 5, going from no regeneration to 0.9 factor, there is an increase of 26%. IMHO that is an immense increase.

[matt brown]

Great question, I have no idea. I noticed this and the "work" callout prior posting, but couldn't figure it out. I have this graphic in a separate graphics folder and clueless what paper it came from (buried amongst others). So, it's a mystery unless someone can figure it out...

[matt brown]

I'm not sure that I'm reading the graph correctly. It looks as if, for Vr of 5, going from no regeneration to 0.9 factor, there is an increase of 26%. IMHO that is an immense increase.

Yep, you're reading this right. The real standout is that zero to 1.0 regen doubles eff at Vr=5 vs zero to 1.0 regen triples eff at Vr=2.

This graph is just another way of expressing regen 'load' (ratio of ideal source to ideal regen heat) where the more work that can be obtained per each regen cycle remarkably increases cycle eff as regen eff declines.

I'm assuming this is diatomic (air) and embarrassed I don't know at a glance (I'm out of shape) but monatomic has a slightly better graph. The main reason helium performs better is not due to heat transfer rate, but due to lower regen load where .80 regen for both monatomic and diatomic may appear the same, yet .20 regen heat loss for monatomic is less real heat than .20 regen heat loss for diatomic (due different Cv heats). Per previous posts in past, regen load has no effect on eff when regen eff=1.0 but when regen<1.0 things get nasty fast. Within any given thermal ratio, the only two tricks are (1) using monatomic gas (2) increasing the volume ratio.

[Tom Booth]

What does the dashed black line represent?

"Specific work" whatever that means.

PDF from Google reverse image search:

https://ojs.cvut.cz/ojs/index.php/MECCA ... /7573/6041

[Fool]

Thanks Tom and Matt. I think I get this graph. Specific power is power per unit mass. I assume the mass of the gas enclosed, but could be the mass of the whole system. As Vr increases the power per pound also increases.

Also it appears that a better regenerator is better, and as the Vr increases passed 3 the efficiency benefit from compression ratio curve flattens. Making 4, 5, and 6 or more relatively moot for efficiency gains. But, important for power density gains, since it is increasing fairly linearly at that point. Maybe?

[matt brown]

Awesome job Tom !!! I have 1000s of white papers on my computer and largely unsorted.

Scanning the article, Tr=2.57 and gas is air. I don't get the dotted line...look at Vr=3 and note .90 regen blue curve (~.53 total eff) is way above this dotted line which crosses near .70 regen green curve (~.43 total eff). The only thing I can conclude is that the dotted line is max work per Vr for this thermal cycle.

Remember that this graph is deceptive, and per previous post it's not the Vr that matters, but Vr/Tr. And Vr/Tr is the crude relationship which needs some "math treatment", since Vr=4 with Tr=2 yields Vr/Tr=2 which is only an acceptable approximation for midrange SE. Meanwhile, LTD type values with Tr=1.1 (300-330k) would require Vr=2.2 to achieve similar Vr/Tr=2 which is bogus. However, if we used Tr-1 and Vr-1 for LTD with Tr=1.1 and Vr=1.2 then Tr-1=.1 and Vr-1=.2 thereby Vr/Tr=.2/.1=2 and we're almost hunky dory. Yeah, I know, that probably lost most of the guys who needed it most. Bottom line is there's a Vr:Tr relationship, but exactness is unknown (not high on my to do list).

[matt brown]

I think I get this graph. Specific power is power per unit mass. I assume the mass of the gas enclosed, but could be the mass of the whole system. As Vr increases the power per pound also increases.

Yep, you nailed it. Earlier it seemed like a fly in my soup, but now it's obvious (regen stuff always grabs me).

Also it appears that a better regenerator is better, and as the Vr increases passed 3 the efficiency benefit from compression ratio curve flattens. Making 4, 5, and 6 or more relatively moot for efficiency gains. But, important for power density gains, since it is increasing fairly linearly at that point. Maybe?

Be sure to read the paper that Tom linked this graph to. Specific power is the power per mass, but this will be offset by specific output (aka power per cube). As always, it's finding a balance among various competing issues.

[VincentG]

Hey Matt, why can't we use the cold sink in an otto scheme to have a high isothermal compression ratio of lets say over 5:1? Dump all heat of compression into the sink and then heat that dense cold air up asap, then open cycle exhaust to whatever cogeneration scheme we can think up. Then the only "wasted" heat would be from compression work, and we could cogen that too really.