a primary reason for reducing cutoff quickly is to minimize back pressure due to exhaust steam.
Assume it is an exponential decay, looking for the time-constant
You sure as hell won’t find it that way; the residual heat in the steam makes it re-expand in volume as the pressure comes off, and this occurs throughout the mass of steam in the tract in addition to the pressure differential from the exhaust valve opening.
If you look at the continuous flow in a Steamotive plant, you will appreciate the shape and dimensions of that outsize exhaust plenum…
You tune the exhaust, modify the port unshrouding and opening, and get longer expansion from admission cutoff to exhaust. If you were wondering why we grouse about having different exhaust duration and timing relative to admission – something a regular radial valve gear does with difficulty if at all – thinking about this should be enlightening.
interested in pressure, not volume. doesn’t the pressure decrease when allowed to expand?
i fyou can’t answer how quickly the pressure decreases, can you explain how quickly it expands?
Ideal gas in a cylinder would expand out following a pressure gradient, and you would look at the flow resistance along the exhaust tract relative to pressure and mass flow to figure out what the resistance to free expansion would be. Note that much of the design of internal-combustion exhaust systems will give you formulae for this “assuming that the water of combustion stays a vapor”.
Steam is different because its latent heat of condensation is so large. That means that you get nucleate condensation at lower pressure (which scotches getting much expansive work in LP cylinders of unsuperheated compounds) but the nuclei happily revaporize at exhaust release – expanding spherically, so the exhaust volume chokes the tract rather than inducing flow down it. That is much of the ‘back pressure’ effect associated with high speed/short events, as the expanded mass of admitted steam all has to ‘clear’ during the time the exhaust valve is open. (The mass remaining in the cylinder when the valve is close to shrouding closed then contributes to compression, and thence to admission on the following return stroke in a DA, so it is not trivial to understand).
for those that might be interested …
the plots show cylinder pressure (red), residual exhaust pressure (green) and zero (gray), for speeds of 1, 2, 4, 8 and 16 rev/sec which correspond to 5.5, 11, 21 and 43 mph for 60" drivers.
the plots show that at higher speeds, the residual exhaust pressure is relatively high for much of the cylinder cycle. At low speeds, the exhaust pressure has sufficient time to decrease such that the effective pressure, cyllinder pressure - exhaust pressure is relatively high over the entire cylinder cycle
the initial exhaust pressure depends on cutoff, so decreasing cutoff reduces the initial exhaust pressure and effective pressure.
added resulting sinusoidal force at the driver (cyan). T****he force plot shows that the back pressure from the exhaust has less effect at the beginning and end of each cylinder cycle.
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Interesting plot. What would be highly interesting here would be to see some indicator diagrams of exhaust pressure overlaid at the same cyclic rps and adjusted to the same scale dimensions.
I suspect you will find more than a little broadening of the curve as exhaust mass flow per second changes, particularly at high speed where the cutoff begins being lengthened again. I would repeat that a useful mathematical representation is likely to be an empirical set of curves for a particular ‘instantiation’, like all those irritating factors in Lawford Fry’s boiler analysis, rather than a clean set of exponential decays.
Someone like Ed should find and post a couple of the accounts of the ‘automatic cutoff control’ developed in the early 1920s (I always suspected as part of the automatic-train-control scenario). That used back pressure as the control signal for adjusting cutoff.
you need to look at a Carnot cycle for a steam engine. Steam cut off during stroke varies puposely. keeping a train moving requires less steam then when starting BUT you are missing that the inlet valve and exhaust valve are both shut before the end of piston stroke allowing the piston to be cushioned as end of stroke pressure builds up. So pressure disipates during the piston stroke but builds again before the end of the stroke
i’m aware of this (i.e. lead). it is a minor detail for my purposes
not being aware of back-pressure was a major oversight.
There is no “Carnot cycle” for a steam engine. Carnot is for an ideal gas under optimal thermodynamic conditions.
I do not think you quite understand how a typical double-acting steam engine does its business. The thing he is concerned with is the steam flow during ‘release’, which is the period the valve is open to exhaust near the end of the stroke. In typical long lap/long travel valve motion, one idea is to reduce valve unshrouding by having the ‘exhaust edge’ already moving at high speed by the time it starts crossing the port edge. A good piston valve opens an annular space into the defined exhaust-tract volume, and this gives an increasingly large area through which the steam in the cylinder can blow to equilibrium. But there is no real ‘tuned port’ kind of scavenging action (as there is in some forms of IC engine) where the induced mass flow of exhaust is so great that it ‘pulls’ steam out of the cylinder near the end of port opening. Any such effect causes more of the condensed nuclei in the cylinder (and port and passage) to flash back to vapor rather than for the steam mass to be drawn.
The ‘cushioning’ is provided by the steam and vapor remaining in the cylinder after the (long-travel) valve has traversed the exhaust port and closed it off again… during the previous stroke to the one we’re looking at exhaust expansion from. That compression not only ‘cushions’ piston reversal but keeps the port and passage pressure relatively high in the part of the return stroke up to the start of admission in the
if you didn’t see this on MRH, we captured our algorithms in a Java app
What is the multiphysics simulation for modeling the valve, tract, and changes in steam quality for the duration of an exhaust event in this app?
You might have to brute-force it with numerical approximations for a range of loads and cutoff conditions – perhaps quantized by % cutoff within the normal engine working range.
You will NOT get much, if anything, coherent out of using a simple exponential decay function, especially if you are using the result to calculate energy or entrainment characteristics in a model of a front end.
how much error would there be?
.
so the error is of no concern for my needs
Look at an indicator card for your chosen cyclic and cutoff setting, and note the point where the exhaust begins to open at that cutoff. (This will automatically, if a bit unhelpfully empirically, give you the back-pressure effect on the exhaust release).
If you are lucky, the cylinder pressure and tract pressure will equalize before the valve fully closes to steam. That pressure will determine much of your compression characteristics – for cushioning of the ‘return’ stroke, blowoff if excessive, etc.
You can then do curve fitting to get the best constants if you don’t want a double-salient (or more complex) algorithm.
I suspect you might not need many of these fitted curves to be a ‘library’ for use in the app.
Of course I can’t help but wonder if you could dust off Charlie Dockstader’s programs and figure out what curves are needed when changing the various lengths of elements in those examples…
Weren’t those some cool programs! I haven’t used mine in a long time and wonder if they still work through the many Windows updates?
Yes! They still work!!!