Mean Effective Pressure calculations

[russkey]

Hello all,

I've put together this calculation of Mean Effective Pressure. I couldn't find this sort of estimation in the Steam Engine Design book by Lindsay Publications. I would love to get a second opinion on the math, though.

Any comments?

http://russkey.tumblr.com/post/12141995522/mep

[barts]

I think the relationship you're using for expansion of steam is wrong for adiabatic expansion.
Compare your estimate with values from a steam table.

- Bart

[fredrosse]

The equations presented assume a nearly perfect steam engine with no clearance volume. Real engines have clearance volume ranging anywhere from about 5% and up. Analysis of the clearance volume, plus the point where the valve gear starts compression on the exhaust stroke are both very relevant to the analysis of MEP

Attached PV diagram shows a diagram with clearance volume, and partial compression in the exhaust stroke.

[russkey]

I think the relationship you're using for expansion of steam is wrong for adiabatic expansion.

Bart: You are correct. I'm assuming isothermal expansion, which is the relationship I've found in two books so far (at least for the initial rough estimates at the very theoretical level).


fredrosse: This is calculation is mostly aimed at a more numerical design approach for my rotary steam engine which I have not finished yet. I wanted something that would give me an idea of what sort of theoretical maximum MEP I might have, given the various physical conditions I'm modeling in my design spreadsheet. Since this engine does not use the normal slide valve (its an electronically controlled solenoid valve)(which might be compared to a corliss valve, perhaps?) I don't want to burry myself in the details of clearance volume just yet.

So while I do understand that this is not really going to give me the rigorously correct answer, I wanted something more in the ballpark than just assuming 0.4*P_boiler (or the like).

[fredrosse]

Isothermal Ideal Gas Model: P * V = Constant

Adiabatic Ideal Gas Model: P * V^gamma = Constant

For air, gamma = about 1.4, for steam, about 1.25 - 1.3

Note that even a rotary engine will have to have some clearance volume on both the inlet and exhaust ports.

[barts]

I think the relationship you're using for expansion of steam is wrong for adiabatic expansion.

Bart: You are correct. I'm assuming isothermal expansion, which is the relationship I've found in two books so far (at least for the initial rough estimates at the very theoretical level).
.

Isothermal (constant temperature) expansion is only achievable at very slow rates w/ net heat input (e.g. jacketed cylinders & heads). My thermo texts all state that piston expansion at normal rates approximates adiabatic (constant entropy) expansion.

I'd look for steam state equations, and use a computer to solve this rather than attempting a closed-form solution by over-simplifying the problem.

http://www.nist.gov/data/PDFfiles/jpcrd338.pdf suggests a solution... this would permit modeling if you write code... there are also spread sheets extensions that make this easy, but I've never used 'em.

- Bart

[artemis]

MEP Factor = that number which, when multiplied times the ABSOLUTE pressure, will give the mean effective pressure used in the PLAN/33000=HP formula.

For general purposes, the above chart gives a MEP Factor. Since you're talking about the vane/rotor engine, you don't need to figure in clearance volume but you should use ABSOLUTE pressure (measured from perfect vacuum - usually 15 psig is used for ease) - if you're planning on 100 psi at the cylinder, then the absolute pressure is 115 psia. So multiply the 115 psia times the MEP Factor, then subtract the back pressure (the pressure "left in the cylinder" above absolute zero at end of the stroke). This will give you the MEP for that cutoff. I don't have the actual formula to hand but the chart will give you enough info that you can interpolate between the given cutoff points. Also note the great economy (even when exhausting to the atmosphere, 15 psia) at say 65% cutoff: MEP Factor = (0.9300 x 115) - 15 = 91.95 MEP. 35% less steam by volume for a pressure decrease of only 8.05 psi.

[russkey]

AHA!
There's the confirmation I was hoping for. I've juggled the equations a bit (updated the pdf: http://russkey.tumblr.com/post/12141995522/mep ) (and removed the illogical +P_b term in Eq. 5 and on) and came up with a formulation that only depends on the input pressure, back pressure, and the ratio of expansion. When I try to replicate the table you posted, artemis, I get the exact same multiplier values using my formula. So my analysis matches the theoretical calculation presented in that table.
Thanks!

[barts]

Also note the great economy (even when exhausting to the atmosphere, 15 psia) at say 65% cutoff: MEP Factor = (0.9300 x 115) - 15 = 91.95 MEP. 35% less steam by volume for a pressure decrease of only 8.05 psi.

This works well... but keep in mind that the more expansion is done, the bigger the impact of valve gear wiredrawing, problems w/ counterflow heat transfer, etc.

If you want to use 10% or 5% cut-off, you'll need a uniflow design to gain any benefits.

BTW, here's some computer software that will compute steam table parameters:

http://freesteam.sourceforge.net/

- Bart