Dynamic Cylinder Deactivation

[christofoo]

Starting in #222 it became clear to me that you had a more complete and more standard definition of pumping losses than me. (Tangent; isn't there an additional separate loss which was left out required to generate the vacuum, which is also proportional to manifold vacuum? Not that it changes any arguments, all we have to say is that there is some loss and it is proportional to manifold vacuum.) Primarily, I think it was a communication roadblock. This supports the general drift of a criticism towards me; if I read on this subject more my terminology would be consistent, and the discussion would be significantly less frustrating for everyone, although I wouldn't go so far as to agree that I should have left it alone, since I maintain that my earlier arguments are intact (off the top of my head, with the exception of 2 counterpoints that I expected to be minor). EDIT: top of my head is not so accurate, rereading my first two leading arguments #185 and #191 both of my last steps may have been rendered erroneous to everyone but me. Still seems like if you followed the initial steps you could have worked out what I meant, but eh, I can relate to annoyance from someone who seems not to know what he's talking about.

And, thanks again for your patience starting around the same post.

[christofoo]

Now that we've established that there is a plausible mechanism by which DCD can reduce pumping losses, for my next 'magic' trick, I will now demonstrate that DCD and lean-burn cycles can be thermodynamically equivalent to a first order, again neglecting dynamic analysis for the moment, consistent with the analysis we already made.

It seems silly enough now, but I - seriously - thought everyone would slap their heads and say 'of course, DCD and lean burn are thermodynamically equivalent!' after reading this post:

Originally Posted by christofoo

...
DCD vs lean-burn: Why does lean-burn work and DCD not?

Suppose the lean-burn engine is operating at 25% (er, how to say this?) leanness, by which I mean stoichiometric AFR X 1.25.

Compare to DCD with 25% of cylinders deactivated, 75% at stoichiometric AFR. All else being equal, including valve timing.

If you think I'm wrong, explain to me:

1. Is there a difference in air mass flow rate?
2. Is there a difference in manifold vacuum?
3. Whatever else you think requires consideration.

Clear as mud, right? This is what it's like to be a physicist. I often don't know what about my communication is not going to jump out at you with perfect clarity. After the discussion with t vago, I feel inspired to give this a detailed step by step analysis, since I've been shown the value of doing so. (Although note that there is a mistake in the above; I should have said that the lean burn engine should be setup with stoich-AFR X 1.333 instead of 1.25 - I got 3/4 and 4/3 turned around. This will be further illustrated.)

How can I prove thermodynamic equivalence? As a very quick overview there will be three basic steps: assume a given lean burn engine, setup a similar DCD engine with the same fuel input and air mass flow rate, show that the DCD engine has identical thermodynamic parameters.

Now in detail, using the same definitions t vago used starting in #222:

1. Take a lean-burn engine as a given, with some set lean-AFR, produced work, manifold pressure, pumping loss, and available work.
2. Define lean-AFR = stoichiometric-AFR X K, where K>1 is my definition of 'how lean' the engine is. As a specific example, we're going to consider K=4/3=~1.33, because this is going to help illustrate a simple case later on, but this analysis will hold true for all values K>1 as long as we stay within both physical limits of lean-burn and DCD (hint: they may be different).
3. Setup a DCD engine with the same air mass flow rate and fuel input, and everything else the same. At this point we will not know pumping loss, or available work since we don't know the manifold pressure, but we do know that this engine will have the same produced work as the lean-burn engine. (Careful, I'm coming back to this assumption.)
4. How do we get the air mass flow rate to match the lean-burn engine? For the lean-burn engine, we have (air mass = fuel mass X K X stoich-AFR). For DCD, we need to introduce (air mass = fuel mass X stoich-AFR / duty-cycle), where (duty-cycle = number of cylinders that fire / total number of cylinders per cycle) and duty-cycle<1. You might think that duty cycle could be only certain rational numbers, like 3/4, 1/2, or 1/4, but actually duty cycle can be any number between 0 and 1 if you average over an arbitrarily large number of revolutions instead of only one revolution. So if we set the air mass of the DCD engine to equal to the air mass of the lean-burn engine, we get (fuel mass X K X stoich-AFR = fuel mass X stoich-AFR / duty-cycle), which reduces to (K=1/duty-cycle) or (duty-cycle=1/K). For example, In the special case where K=4/3 in a 4 cylinder lean-burn engine, a corresponding DCD engine would have duty-cycle=3/4, or in other words, 3 cylinders activated and 1 cylinder deactivated.
5. The fact that duty-cycle=1/K doesn't actually matter. The point is that there always exists some similar DCD engine which can have the same air mass flow rate and fuel input as the lean-burn engine. What we know is simply that this case exists. Or For any lean-burn engine with K, there exists some DCD engine with duty-cycle=1/K that has the same fuel input and air-mass-flow rate (and all other reasonable common denominators).
6. However, we know that air-mass-flow rate is dictated in an Otto cycle by manifold pressure. We want to assume common denominators between the two engines, so they both have the same number of cylinders, the same displacement, and the same valve timing. Since the two engines have the same air-mass-flow rate, and all else is equal, then the DCD engine must have the same manifold pressure as the lean-burn engine.
7. Now we can compare thermodynamic efficiency. We assumed that the two engines have the same fuel input and therefore they have the same produced work. We assumed they have the same mass flow rate and proved that this is achievable (within limits, I will return to this). (We also assumed the same displacement and valve timing.) Now we know that they have the same manifold pressure and therefore they have the same pumping loss and the same available work.
8. Therefore, a DCD engine having duty-cycle=1/K will have the same thermodynamic efficiency as a lean-burn engine with lean-AFR=stoichiometric-AFR X K.

Next I'm going to dive right into interesting implications that this proof has, and then after that I'll address the validity of key assumptions, which may or may not dovetail into some speculation about practicality of DCD.

[Frank Lee]

Geesh, it would be faster to go out to the shop and build a prototype.

[christofoo]

We can compare a 4 cylinder DCD engine at 3/4 duty-cycle to a hypothetical 4 cylinder variable-displacement engine, similarly with 1 cylinder deactivated and sealed shut. The variable displacement engine is identical except for the elimination of pumping losses in 1 cylinder, so it must be more efficient than DCD.

(A 3 cylinder engine would be even more efficient than the variable displacement engine due to reduction in mechanical friction losses.)

This means by extension that variable-displacement technology is thermodynamically more efficient than lean-burn, all other things being equal.

Seems surprising? Let's try a sanity check.

Try setting up the two engines I hypothesized with equal fuel input and equal manifold vacuum. The lean burn has more displacement than the variable-displacement engine with respect to the same fuel, so it must run leaner than stoich, which isn't so important except to illustrate that this case exists. Bottom line: lean-burn has the same produced work, the same manifold vacuum but with more displacement, so it has higher pumping loss and lower available work and therefore lower efficiency.

EDIT: one key assumption however is that the lean-burn engine has a manifold vacuum at all, which may not be true. If conditions allow manifold to be close to ambient pressure and pumping losses become negligible, then there's nothing left for variable-displacement to improve over. (But a smaller smaller fixed displacement engine would eliminate mechanical friction over a variable-displacement engine.)

(EDIT: FYI, need a break, will get back to assumptions and practicalities later on... probably.)

[t vago]

Originally Posted by christofoo

Fuel input has not changed since we started DCD. Produced work has not changed. The number of cylinders experiencing pumping loss has not changed. But manifold pressure has gone up, manifold vacuum has gone down, pumping loss has gone down.

And this means available work has gone up.

Sorry, no.

Available work has not changed, but produced work has gone up to cover the deadbeat cylinder.

It's really very simple - with DCD, you're running an internal combustion engine at stoich (or rich due to the engine computer going into limp-in mode), with what amounts to an air compressor that gets its air supply from the intake manifold, which then discharges into the exhaust stream.

Yah, pumping work will go down as compared to a normally operating otherwise identical engine, but the DCD engine will still consume more fuel than the normally operating one, because you just added an extra load to it, all other things being equal. That load is the pumping work associated with the deadbeat cylinder.

[t vago]

Originally Posted by christofoo

I do think I owe you an apology, I'll get back to that in a minute.

Don't worry about it. I really can be nice - I just don't like willfull ignorance, especially about snake-oil scams. We have to watch out that we at EM.com aren't inadvertently promoting these things, since they hurt the cause of ecomodding.

It was actually rather refreshing to post those things about lean-burn. Thank you.

[christofoo]

Originally Posted by t vago

Sorry, no.

Available work has not changed, but produced work has gone up to cover the deadbeat cylinder.

It's really very simple - with DCD, you're running an internal combustion engine at stoich (or rich due to the engine computer going into limp-in mode), with what amounts to an air compressor that gets its air supply from the intake manifold, which then discharges into the exhaust stream.

Yah, pumping work will go down as compared to a normally operating otherwise identical engine, but the DCD engine will still consume more fuel than the normally operating one, because you just added an extra load to it, all other things being equal. That load is the pumping work associated with the deadbeat cylinder.

I don't agree. The way I setup the problem, starting in #251 and not before, is to move the fuel from the deadbeat cylinder to the other 3 so that the total fuel per cycle, and hence the produced work per cycle (#239 by you), is unchanged. At that step it is an assumption, not an assertion, or I should say it is an approach to the setup rather than a derived parameter. (Because assumptions are always part of the setup, not a method for jumping to conclusions. ... in real derivations that is.)

Afterwards I balance AFR and then re-analyze losses still without changing fuel quantity per cycle, and hence not changing produced work. Again, an assumption, not an assertion.

There are three parameters that are derived, rather than assumed in the setup. The first is manifold vacuum, next is pumping loss, and the last is available work.

As additional commentary; loss for the deadbeat cylinder exists before the cylinder is deactivated, so there is no need to add a loss at this step. It is much easier to analyze pumping loss for the whole cycle rather than for each cylinder. The engine displacement does not change with DCD, which is a restatement of the cylinder's pumping loss existing before and after, but manifold vacuum does change after DCD, a necessity to re-balance AFR. So only the change in the manifold vacuum can have an effect on per-cycle pumping loss after DCD is activated. (#224 by you)

[serialk11r]

Hmmm well now that I think of it, a cylinder running with no spark/fuel can incur a higher pumping loss if the exhaust valve opens significantly later than when the air in the cylinder is at the pressure in the exhaust manifold, because the energy used to create the vacuum will be lost on top of having to push the gases out the cylinder in the exhaust stroke. At higher intake manifold pressures though, I doubt this is a problem as the exhaust valves always open a bit early anyways.

But then running any cylinder at a higher load is more efficient due to the higher temperature and pressure.

Seems like a toss-up at this point. Someone should just go deactivate 2 fuel injectors on an alpha-N based engine (in open loop) and see what happens.

[t vago]

We will agree to disagree, then. You can formulate elegant proofs, or you can observe the real world.

The entire point of having an intake manifold vacuum in the first place is to control the amount of oxygen in each firing cylinder. That's all. Pumping work is a necessary evil for a basic gasoline engine. Anything else that uses (power brakes, for instance) engine vacuum is trying to make the best of the situation.

That being said, adding any sort of load will increase the amount of required work. Engine accessories, underfilled tires, headwinds, and even ersatz air pumps made out of non-firing cylinders will increase the amount of required work. The pumping work consumed by the DCD deadbeat cylinder will have to be considered as a component of the work required by the engine, correct?

So, even considering that intake manifold vacuum will in fact become lower, the DCD engine is expending even more fuel that is not actually pushing the vehicle forward. To push a vehicle forward at some constant speed, a set amount of required power must be met by the engine. The engine must provide enough available work to meet this requirement. Plopping the pumping work of one or more dead cylinders, onto the work required to push the vehicle forward, and all the other work required by the vehicle, will not help matters.

Discussions, about balancing AFR or redefining lambda to be some other variable or drawing comparisons between DCD and lean burn, will not change this. I simply don't know any other way to point this out to you, christofoo, other than to say to you and other doubters, that you should actually go do DCD-type experiments with your engines.

[Frank Lee]

I've been unable to find a totally detailed description of Cadillac's coolant loss limp home mode- so I don't know if it reverts to open loop- but if it stays closed loop, there's your DCD. Nope it isn't being utilized for fe gains.