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Isentropic formula for expansion/compression

Posted by kdc2 
Isentropic formula for expansion/compression
January 27, 2016 02:31PM
Hello all,

I think this has been covered many times, but can someone help clarify if the following must be in absolute (°K)

T2=T1(P1/P2) (1-1/y) y=Cp/Cv

I got this from a nasa site and there isn't any reference to units Isentropic Compression. Wiki also doesn't list units on its Isentropic process page. What am I missing?

Thank you,
Keith D
Re: Isentropic formula for expansion/compression
January 28, 2016 07:15AM
Yes, it must be absolute. Units wouldn't be listed because those you are supposed to make sure to use the units from whatever tables you're filling the formula with numbers from. A formula would only have units in it if it was one of those weird ones with a constant built in.
Re: Isentropic formula for expansion/compression
January 28, 2016 02:55PM
Thanks zimirken. I've found an example using absolute Rankine, so not forced to SI units. (not a fan here, but can deal if needed)

It also seems if using the rankine scale, psia and ft3 are my necessary units.

Another question, it seems that the constant R has worked its way out of my target equations, so would my y stay the same? Basic units are Btu/lbm*R. Gosh I wish I had more confidence setting up these equations.

Thanks again,
Keith
Re: Isentropic formula for expansion/compression
January 30, 2016 11:33AM
If you need to look at more formulas, here is my sheet for calculating the whole steam piston cycle, with macros for the steam table calculations.
Attachments:
open | download - XSteam_Excel_v2.6.xls (571.5 KB)
Re: Isentropic formula for expansion/compression
January 31, 2016 10:54PM
Nice, that is a perfect check verification. Refining the process through saturation/quality conditions. Thanks.

Guess back in 2011 I downloaded the us units version of Xsteam. Coming back slowly with better understanding.
Re: Isentropic formula for expansion/compression
February 01, 2016 01:30PM
Any ideas on how to treat a uniflow expander exhausting into a condenser? We have to assume a small pressure gradient remains between the cylinder and condenser. Would the basic assumption be to calculate the total volume at the assumed residual pressure and subtract the percentage the cylinder volume represents and use that mass?

Zimirken, I did notice your point "D" referencing the vapor fraction of point "C", but no attempt at calculating vapor fraction at "D". My assumption is that vapor fraction at "D" would need to be used to get any forward ballpark accuracy? -Cheers, Keith
Re: Isentropic formula for expansion/compression
February 01, 2016 01:52PM
On my 35 foot boat my condenser ran at 29 inches of vacuum almost all the time.
The engine was a compound running at 275 psi on the high and 50psi on the low with 175 De superheat
Rolly
Re: Isentropic formula for expansion/compression
February 01, 2016 02:48PM
Hi Rolly,

Would that be the same as saying the temperature in the vacuum condenser environment was 175°F, or how/where are you applying the 175 de-superheat nomenclature? -Keith
Re: Isentropic formula for expansion/compression
February 02, 2016 08:02AM
kdc2 Wrote:
-------------------------------------------------------

> Zimirken, I did notice your point "D" referencing
> the vapor fraction of point "C", but no attempt at
> calculating vapor fraction at "D". My assumption
> is that vapor fraction at "D" would need to be
> used to get any forward ballpark accuracy?
> -Cheers, Keith

Since C-D is just the exhaust port opening, I assumed that the vapor fraction would be the same. But now that you pointed it out, I suppose the drop in pressure would cause the steam to superheat, wouldn't it?
Re: Isentropic formula for expansion/compression
February 02, 2016 08:48AM
zimirken Wrote:
> I suppose the
> drop in pressure would cause the steam to
> superheat, wouldn't it?

That's right where/what I'm working through. It seems that I will be able to drop the pressure enough before exhaust to cause serious condensation. I do believe the exhaust event will tend to superheat. That is the balance to work through to make sure the hardware will support it and have some degree of accurate predictability. Seems the double acting, "b" side has enough rod/bore ratio that it needs less scrutiny to avoid excessive pressure drop before the exhaust event in my case.
Re: Isentropic formula for expansion/compression
February 02, 2016 09:25AM
No Superheat is the heat above the saturated temperature going into the engine. 200F above saturated is ideal. . Hot well temperature should never be above 170F but in most marine vessels it’s whatever the sea water temperature is. 170 F is as close to oxygen free water as you can get in the hot well. 29+ inches of vacuum is close to 14.5 negative psi on the underside of the piston.
In all the cars I’ve been in that had gauges on the condenser including my 1920 Stanley, the pressure ran from one to five psi on the condenser except going up a hill, then I’ve seen it go as high as 15 psi and down a good hill it drops to zero but I have never seen a negative pressure (vacuum)
Rolly
Re: Isentropic formula for expansion/compression
February 02, 2016 09:42AM
Rolly Wrote:
-------------------------------------------------------
> No Superheat is the heat above the saturated
> temperature going into the engine. 200F above
> saturated is ideal. . Hot well temperature should
> never be above 170F but in most marine vessels
> it’s whatever the sea water temperature is. 170
> F is as close to oxygen free water as you can get
> in the hot well. 29+ inches of vacuum is close to
> 14.5 negative psi on the underside of the piston.
>
> In all the cars I’ve been in that had gauges on
> the condenser including my 1920 Stanley, the
> pressure ran from one to five psi on the condenser
> except going up a hill, then I’ve seen it go as
> high as 15 psi and down a good hill it drops to
> zero but I have never seen a negative pressure
> (vacuum)
> Rolly

That's because those are absolute gauges relative to perfect vacuum as opposed to atmospheric gauges which are zero at atmospheric pressure. It only goes to 15 psi because that is when the condenser will start venting excess steam at atmospheric pressure.
Re: Isentropic formula for expansion/compression
February 07, 2016 10:27PM
Does anyone recognize this format? Has a slight Ken signature to it, but I can't remember where I got it.

Still am troubled a bit by thumbnails and such. Think something is broke. -Keith


Re: Isentropic formula for expansion/compression
February 11, 2016 06:55PM
Hi Zimirken,

What did you base your 4 and 5 iteration pressure and entropy/enthalpy and density/vapor fraction steps on if I could please inquire? Thanks, Keith
Re: Isentropic formula for expansion/compression
February 12, 2016 02:58PM
kdc2 Wrote:
-------------------------------------------------------
> Hi Zimirken,
>
> What did you base your 4 and 5 iteration pressure
> and entropy/enthalpy and density/vapor fraction
> steps on if I could please inquire? Thanks, Keith


The pressure is simply the exhaust pressure value which is entered in a green box near the top. I believe the entropy/enthalpy/density/vaporfraction for points D and E are incorrect. I forgot to take into account that the exhaust pressure drop would change these values from point C. I believe the exhaust pressure release would superheat the remaining steam and increase the vapor fraction. The spreadsheet will have to be updated to reflect this. I made this spreadsheet as part of my college senior project some 3 years ago so it might take me a bit to find the formulas.



Edited 1 time(s). Last edit at 02/12/2016 03:02PM by zimirken.
Re: Isentropic formula for expansion/compression
February 12, 2016 05:21PM
Quote
zimirken
I believe the exhaust pressure release would superheat the remaining steam and increase the vapor fraction

This is incorrect any drop in pressure will release heat not gain it. It is a cooling event all across the board. To gain superheat an increase in pressure must be reached.

By nature superheated steam is at its most vapor fraction already. Ideally to gain superheat is a function of increased heat content of fully expanded vapor which can be reached by compression also.

Jeremy Holmes



Edited 2 time(s). Last edit at 02/12/2016 05:37PM by Jeremy Holmes.
Re: Isentropic formula for expansion/compression
February 12, 2016 05:53PM
Interesting process. Seems very temperature dependent as volume heads toward infinite/vacuum vs liquid. I'm wondering if we are at 100% vapor, if dropping pressure superheats, at what point does compression condense the fluid vs adding heat to keep it from condensing?

Jeremy, superheat can be gained by throttling, isenthalpic expansion. Temperature doesn't go up, just superheat deg. Shoot, I can't see your post so running blind in an edit in which you posted before. Sigh.



Edited 2 time(s). Last edit at 02/12/2016 06:02PM by kdc2.
Re: Isentropic formula for expansion/compression
February 12, 2016 06:21PM
Hi Keith the reason for my thinking there is because of "de-superheating" which is a flash steam process. IE: injecting water into super heated steam similar to a normalizer. This will increase vapor volume. But without that added component and dropping pressure will not cause an increase of vapor. -edit- remember super heated steam is already full expanded-

Its plausible that increased vapor with superheated steam, but water must be added or like a diesel hi compression must be achieved.

Jeremy Holmes



Edited 1 time(s). Last edit at 02/12/2016 06:30PM by Jeremy Holmes.
Re: Isentropic formula for expansion/compression
February 12, 2016 06:47PM
You will have to forgive me for keeping my head buried in "flash steam" how would this effect a compound engine.
Re: Isentropic formula for expansion/compression
February 12, 2016 07:07PM
Keith you have been on the forum for many years and I have yet to see a model of your engine or a diagram of your engine cycle of your engine.

Mine is here

Four cycle flash steam engine

the exception of my engine cycle is that it re-uses live/superheated steam, also it is only single acting.

This is an exciting time for me as I am building 100 L912 Injectors and making the final modifications to my proof of concept engine.

Jeremy Holmes
Re: Isentropic formula for expansion/compression
February 12, 2016 11:33PM
Seeing your 4 cycle flash steam visually made it much easier for me to understand your concept. It reminds me in some ways of the super efficient power plants which reheat the vapor from the previous cycle. As always good luck to you!
Re: Isentropic formula for expansion/compression
February 22, 2016 09:14AM
Ok, I updated the spreadsheet. I assumed that the exhaust valve opening (points C-D) was the same as steam expansion through a throttle valve. This only made a small difference at the temperatures and pressures that I inputted, but it is more correct. Perhaps next I will add things like heat loss/gain from the cylinder walls, but for now it is complete and correct.
Attachments:
open | download - Steam Piston Engine Thermodynamic Calculator.xls (625.5 KB)
Re: Isentropic formula for expansion/compression
February 29, 2016 04:46PM
Jeremy,

It has been indeed a long time in the works. I just reread one of your replies on Nov. something 2009.

At the moment, the system is a receiverless compound, probably very close to what Bill was working on at the time too.

Next is to really nail and understand the specifics of various forced polytropic processes and work with them. Really obvious to me how we superheat with isenthalpic leaning expansion in certain cases, so the counter, basic isentropic leaning compression needs the same scrutiny so I know what's really happening. Serious work is lost during compression, so it needs to be accounted for. It was also noted before on work used to expel steam in a counterflow, but that is fractions compared to compression losses. Complicated stuff and I'm searching to get my motive back.

Zimirken, How do you base the iterations that help determine vapor fraction? They look good, certainly better than anything I have, but I have no source to reference but to try and figure out what and why your doing what your doing spinning smiley sticking its tongue out

Keith
Re: Isentropic formula for expansion/compression
February 29, 2016 07:16PM
Hi Keith yes its always a long project in the making. Im getting dangerously close to selling my injector valves. They operate on 12vdc and can be used on a number of different engine designs. I have 100 valves now...

The real key to the injector is efficient throttling, this is possible with variable lift settings. I already have 2 US utility patents on the valve.

Jeremy
Re: Isentropic formula for expansion/compression
March 01, 2016 07:31AM
kdc2 Wrote:
-------------------------------------------------------
> Jeremy,
>
> It has been indeed a long time in the works. I
> just reread one of your replies on Nov. something
> 2009.
>
> At the moment, the system is a receiverless
> compound, probably very close to what Bill was
> working on at the time too.
>
> Next is to really nail and understand the
> specifics of various forced polytropic processes
> and work with them. Really obvious to me how we
> superheat with isenthalpic leaning expansion in
> certain cases, so the counter, basic isentropic
> leaning compression needs the same scrutiny so I
> know what's really happening. Serious work is lost
> during compression, so it needs to be accounted
> for. It was also noted before on work used to
> expel steam in a counterflow, but that is
> fractions compared to compression losses.
> Complicated stuff and I'm searching to get my
> motive back.
>
> Zimirken, How do you base the iterations that help
> determine vapor fraction? They look good,
> certainly better than anything I have, but I have
> no source to reference but to try and figure out
> what and why your doing what your doing spinning smiley sticking its tongue out
>
> Keith

The vapor fraction is calculated once from the properties surrounding it at every step. The only iteration the sheet does is for the expansion step. It calculates the ending pressure, and then the specific enthalpy, and then repeats this a few times.
Re: Isentropic formula for expansion/compression
March 01, 2016 11:11PM
Why the repetition?
Re: Isentropic formula for expansion/compression
March 02, 2016 08:22AM
kdc2 Wrote:
-------------------------------------------------------
> Why the repetition?


Because unlike expanding an "ideal gas" like air, calculating the expansion of steam must be iterated because the properties change as it expands. Since the ending pressure is based on the K value, (P1/P2 = (V2/V1)^k) and the k value is based on specific isobaric heat capacity and specific isochoric heat capacity (k = Cp/Cv), and those are in turn based on one of three things: pressure and temperature, pressure and specific enthalpy, or pressure and specific entropy. Since those values all change as the steam expands, unless you want to do a huge amount of fancy math you need to iterate.

I used the starting specific enthalpy to calculate the the first estimate of the ending pressure. Then I used the first pressure estimate to recalculate the ending specific enthalpy. It's the ending specific enthalpy that you need in order to determine the ending pressure. I repeated this a few times so that it would get closer to convergence. Now that I have a more accurate ending pressure and specific enthalpy, I can calculate all the other properties of the expanded steam.

You can see the proof of this in the spreadsheet convergence:
First k	1.374	
First Estimate of Pc	2.780	bar
First estimate of h	2625.6	kJ/kg
Second estimate of Pc	3.128	bar
Second estimate of h	2646	kJ/kg
Third estimate of Pc	3.161	bar
Fourth estimate of h	2648	kJ/kg
Fourth estimate of Pc	3.164	bar




Now, the work extracted from the steam is actually really easy, since without any cylinder losses, energy is conserved. This means that if you subtract the energy of the expanded steam from the energy of the unexpanded steam, all that energy was converted to work on the piston. So for calculating the work done during the expansion phase, you don't need to know anything about the shape of the curve between the two points, you just need to know the beginning properties and the ending properties.
Re: Isentropic formula for expansion/compression
February 18, 2019 06:48PM
Bump
Re: Isentropic formula for expansion/compression
February 18, 2019 07:49PM
Hi Jeremy, I'd love to get my hands on some of those injector valves when they're ready. I've followed your project for a while, and as always I wish you luck

- Kyle
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All files from this thread

File Name File Size   Posted by Date  
XSteam_Excel_v2.6.xls 571.5 KB open | download zimirken 01/30/2016 Read message
x-steam 2011.png 39.3 KB open | download kdc2 02/07/2016 Read message
Steam Piston Engine Thermodynamic Calculator.xls 625.5 KB open | download zimirken 02/22/2016 Read message