NoSeeUm

I wished I understood the exhaust side a bit better. Ideally, with properly matched compressors you would want to run with the pressure ratios also matched.

So at 60 psi boost and with the PR's matched at about 2.45, then the cold pipe pressure would be 18 psi. The pressure differential across the secondary would then be 42 psi. So this should be the ideal air side set-up.

But then..... Please check to see if my thinking is correct.

To make it simple, lets say each turbo above is running at a ratio of 1.15 TIP/COP (Compressor Outlet Pressure). That means the secondary needs about 21 psi TIP and that the primary needs about 49 psi TIP or in this case properly named Turbine Differential Pressure (TDP). Or about 70 psi total at the exhaust manifold. My guess is that in this set-up the secondary could begin choking exhaust gas flow, but I have not done the "corrected gas flow" calculation. Still, I would think it likely be choking the flow at higher Hp / RPM. I don't think the secondary would overspeed though, because it is still running at a PR of 2.4 which is generally very acceptable for most compressor maps I have seen.

Under that above set-up the secondary definately would need a waste gate sized to maintain 49 psi TDP, but not much lower. Other wise boost and / or charge air density would begin to drop as the primary loses motive force. I think this would be a fairly good example of a waste gate control system that utilizes TIP differential in some fashion. And assuming a fairly consistent TIP/COP ratio then cold pipe pressure and MAP could be used as it is much cleaner, as Hohn (I believe) is describing.

Now lets say we set up the twins to run with the cold pipe pressure 50% of MAP. The PR's end up being 3.4 for the primary and 1.7 for the secondary. At the same ratio of 1.15 that would be 35 psi TIP / TDP for each turbo, which is still 70 psi total at the exhaust manifold. However, notice how much lower the secondary TDP is. So picking a primary compressor that runs efficienctly at a 3.4 PR would be something to really look at. Other wise total efficiencty would drop due to a lower charge density.

Jim

HOHN

Some people think you can go too big on the wastegate. I personally think that this is basically impossible because a gate that's closed flows zero. So of course, I assume that you can actually keep the huge gate from blowing wide open and staying there.

Otherwise, you have to balance gate size (total bypass flow) against turbine and housing flow.

jmo

XLR8R

Jim, did you mean to say that the secondary needs 49psi & the primary needs 21psi?

Otherwise, you have the general idea - however, I think the problem with using static equations to describe dynamic fluid flow rears it's head again, especially when discussing hot side concepts.

The exhaust manifold pressure isn't simply divided between TIP & TDP in a discrete fashion - instead, it is shared by both turbines, albeit in preferential order favoring the secondary turbine. 70psi TIP to a secondary WG'd at 49psi won't leave 21psi of TDP available for the primary turbine, since the WG couples TIP to the primary turbine... yet it wouldn't be 70psi either, due to piping losses, thermal energy degradation, etc. That's why it's easier to use corrected gas flow for hard numbers. I prefer to think of gas flow through an internal combustion engine in view of relative amounts of gas molecules, since the process is simply a heat-producing chemical reaction which relies on a recipe dictated by the laws of physics.

In the pursuit of HP, here's a culinary analogy: 1st, we want to use a recipe large enough to bake the size cake we need; 2nd, we do what we can to make it taste better.

Though I am resigned to it - I really dislike using relative terms such as PSI, CFM, velocity, *F, etc. to quantify gas flow, at least in the arena of high HP engines. They are all just different ways of describing the qualities of the gas in question! The amount & type of molecules present in the gas is of primary import, followed by their characteristics as noted above on a secondary level.

Whoever has the most molecules wins!

XLR8R

Justin, I agree that there's no such thing as too much wastegate - at least not in theory. Assuming it's operation is properly controlled, the biggest pitfall is turbulence if not executed well from a flow standpoint.

NoSeeUm

Yes, I meant to say the secondary needs 49 psi TDP and the primary needs 21 TDP. The secondary needs 49 TDP to support the PR of 2.45 or 42 psi compressor differential pressure. This is of course, holding the TIP/COP (actually TDP/CDP) ratio the same for a point of disccussion.

Each compressor needs xxx amount of motive force delivered by the turbine. This motive force, in a round about way, is derived from the pressure differential across the turbine. As soon as you open a waste gate you drop this differential pressure and the turbine loses motive force.

In the case of twins, when secondary waste gate opens the PR balance between the two compressors begins to shift toward the primary. IMO too large of a secondary waste gate and the set begins to lose benefits of componunding compressors. Imagine the primary running at a 4+ PR and the secondary running at just a hair over a 1 PR. It is my guess that in that case the secondary becomes truly a blockage on both the air and exhaust sides.

Here are the examples from above and one more, all at 60 psi boost:

Matched PR's
Primary - 18 psi @ PR = 2.45
Secondary - 42 PSI @ PR = 2.45

Matched Pressures
Primary - 30 psi @ PR = 3.4
Secondary - 30 PSI @ PR = 1.7

A Large Secondary Waste Gate
Primary - 45 psi @ PR = 4.7
Secondary - 15 PSI @ PR = 1.3

To find the TDP simply multiply by 1.15 for our example. I had to realize that secondary turbine is not choking exhaust flow for the same reason that secondary compressor is not choking air flow. Because like you said, the gas is under pressure for both instance and the density characteristics have changed. This is why I wished I understood, the "corrected gas flow" concept a bit better. Maybe some day....

Jim

XLR8R

We have to differentiate between when and how much the top WG bypasses... cracking at too low of boost kind of defeats the purpose of twins. Once the top turbo is seeing max desired drive pressure, you want ALL excess hot gas flow to bypass directly to the big turbine.

NoSeeUm

This is why I have read of some waste gates controlled by cold pipe and total boost pressure differential?

Jim

HOHN

I disagree. If you bypass all of the hot flow to the large turbine, the drive power to the secondary collapses and you lose the compounding at the compression stage. Then the top charger becomes somewhat restrictive to the intake flow because it's not "swallowing" the air as fast as it should be.

If you bypass all the gasflow to the big turbine, then you really should have a similar bypass on the compressor side as well. Then you lose all compounding, and it's really just a two-stage turbo setup, not a compound turbo setup.

Jim mentioned a little confusion on "corrected gas flow", so I think clarifying that might help a bit with wastegate operation.

When you "correct" gas flow across a turbine, you are adjusting a certain mass flow rate across a turbine to account for 1) temperature changes 2) pressure changes.

For example, if I have 20 lb/min going into a turbine at 800º at 20psia, and I get 20lb/min at 800º and 20psia out the other side,then it's pretty clear that we have done no work.

The energy to drive the turbine shows up as a change in pressure and temp. Just as we can determine the electical energy dissipated by a resistor when we know the resistance and voltage drop across it (or current through it), so it is with the turbine.

So, when we correct for turbine gas flow, we are adjusting for pressure and temperature both drop across the turbine. (technically, I think this is delta enthalpy).

That's why when you "correct" for a higher PR, the mass flow drops a bunch. If you have a PR of 3 across the turbine, then it makes sense that the mass flow rate out of the turbine is a lot less than it 3 was going in.

Just like if I pinch a garden hose in the middle--I will have more pressure upstream, and less flow (relative to unpinched) downstream of the point where I pinched it


That's why we see reports of the paradox of a larger primary housing actually improving spoolup. The lower resistance of the larger housing increases the delta enthalpy across the small turbine, increasing the work applied to it and thus spoolup.

Exploring the inverse makes this a little clearer. What if you had two indentically sized turbines in a row? You'd have NO compounding at all, because the secondary turbine would have no pressure drop across it because it primary has the same resistance to flow as the scondary. NO change in energy means no work done.

So we now arrive at some general rules of thumb:
1) the closer the size of the turbines are to each other, the more workload (as measure by PR) is transferred to the primary and the less wastegate flow is required.

2) the farther apart the turbines are in size, the more workload will be transferred to the secondary. Wastegate flow will increase, and therefore reduce overall efficiency. However, this inefficiency enhances spoolup.


So, putting practical application to this, let's say you want a smallish primary that's oriented for peak power. Using a GT42 with a slightly tighter housing, you'd want something more like a Silver series charger up top to increase the turbine flow and transfer workload to the GT42. This combo will make more power than a smaller turbo up top, but it will also sacrifice spoolup to do so.

But if peak power and efficiency are less important than spoolup and response, I want a smaller top charger on top of a big turbo with a larger housing.

So how to pick the right sized turbo/turbines based on operating PR? (see next post, this is getting too long)

XLR8R

I said all excess hot gas flow... secondary still has all the drive HP available that you want it to.


Could you restate the 3rd paragraph more clearly?
The 2nd turbine, flow-wise, in your example would still show a pressure drop across it since it poses a restriction to flow.

HOHN

Let's say we want to make 600hp from a GT42, which can be done. For maximum efficiency (and power) from the GT42, we select the largest housing available for it, the 1.44 A/R.

Now, we've see on the compressor map that the GT42 can deliver the required ~80lb/min we calculated we'd need. It can even do it at a PR of 2.5.

We've also calculated that if we operate both primary and secondary compressors at a PR of 2.5, we'll have enough total PR to cram 80 lb/min into the cylinders at a mere 2800rpm (assuming even passable CAC effectiveness-- intake temps 280º or lower).

So we start with a large charger that we want to operate at a PR of 2.5. It will be delivering 80lb/min to the engine, so we assume we'll have at least that much coming back out (uncorrected).

The pressure ratio we want at the top charger is also 2.5. Here's what we have to do:
1) "correct" the flow going into the GT42
2) calculate the "corrected flow" for at a PR of 2.5
3) Select a top charger based on the results and the turbine map of the small turbo.


These calculations will require some assumptions about EGT, since you have to know temps at different stages to correct the gas flow. We also make the assumption that TIP-CDP, or that we're basically 1:1 on our compressor vs turbo operating pressures-- maybe naive, but this is achievable.

I personally assume I want <1200º going into the top charger, and that the top charger will have a discharge temp <800º.

So I begin with 80lb/min coming OUT of GT42 at peak power. So, we run a few iterations on the spreadsheet to figure out the massflow (based on the correction formula) of what the inlet massflow is at 800º inlet, a PR of 2.5, and an outlet mass flow of 80lb/min.

My calculations tell me that the inlet mass flow is 49.87lb/min when "corrected" for this PR (call it 50). Let's look at the turbine map to see if this is enough flow to push the GT42 to a PR of 2.5:


Cool, the turbine only needs ~45lb/min corrected to be pushed to this level, so we are good to go. We'd actually have enough to drive the larg4r GT45 with the biggest housing, but we don't need that much compressor and we're favoring spoolup at the 600hp point.

So now I need a top charger that will allow 45lb/min to flow out of it at an operating PR of 2.5 and an inlet temp of 1200º. What is the corrected mass flow going *in* to the top charger?

The formula gives us a result of 32.2 lb/min at a PR of 2.5


So we need a top charger that on the turbine side is as close as we can get to 32.2lb/min at a PR of 2.5--but no less. If we go too small, we only have a 5lb/min buffer to keep the big turbine operating were we want it. If we go too big, the PR across the top charger will be too low and we won't have the boost levels we seek.

Since Garrett is the only one that publishes the turbine maps, I'm limited to picking a Garrett turbo.

Do they have anything near 32.2lb/min at a PR of 2.5? YES!


Selecting the GT35 with the largest housing gives us a couple neat things. First, it has a high (56) trim compressor which will flow well with less rotational inertia relative to a lower trim wheel. Second, the larger housing/small turbine combo gives us both passable spoolup and decent efficiency. The Ni-resist housing is extra durable and takes extreme temps.

Look, ma-- no wastegate with this setup!


Now, I have made a LOT of assumptions and simplifications, and this may or may not pan out this way in reality. I got away with ignoring turbine efficiency and doing a lot of extra calculations because having the turbine maps is almost like "cheating". The heat loss in the hot piping and such is a factor, but we had enough buffer to the larger turbo that this should be acceptable.



One last thought: the major "fly" in this ointment is that the combination of turbos and such is only ideal for the boost pressures and PRs in question. If I lay into it and want to push another 15-20psi of boost out of this, the calculations change radically, and the turbo selection might be WAY off.

The compressor side of each charger will work together pretty well. I think that I've been doing things backwards for awhile in choosing a turbo based on compressor maps. I think you need to start with a compressor map for the primary based on the max HP you want-- after that, it's all about the HOT SIDE!


Submitted for discussion...

jmo

HOHN

Sorry about that-- EXCESS, indeed!!

It's little like trying to see a skinny tree behind a large Redwood. If the flow capability of the second turbine is equal or less than that of the first, the first turbine essentially contributes zero restriction and hence does no work.

Not true? If not, what I am missing?

XLR8R

Just because you can't see the tree doesn't mean it isn't there...

Every gas turbine acts a "net" to capture a certain percentage of energy which passes through it, so the 1st turbine (secondary turbo) would get the same size slice of a bigger pie compared to the 2nd turbine (primary turbo).

I think it would require quite a large disparity in hot sides - with their conventional order in the exhaust path reversed - to create a situation in which excessive restriction through the (too small) primary turbine manifests itself in a significant manner at the inlet of the secondary turbine. This of course assumes no secondary WG - it wouldn't be able to crack in any event in this scenario.

For hot-side purposes, one could make the case for a larger turbine 1st in the exhaust flow (followed by a smaller turbine 2nd) for compounds, since the larger volume & energy from the manifold would naturally fit better into the larger "container" of the large turbine... and the cooler, less voluminious mass of hot gas would "fit" better into the smaller downstream turbine. Obviously, a host of other factors effect turbocharger sizing & order, but sometimes it helps to break the model down into it's various processes.

Hope all will forgive the blasphemy!

Tate

You still have to deal with volumes. Even though the gases have cooled and contracted a bit, the pressure has dropped significantly, so you you have a greater volume. If you put the large turbine first, since it is relatively open and not a great restriction, the gases will pass through it easily. They now come to the second, smaller turbine and get backed up. Pressure goes way up in the hot pipe, and inside the manifold. You now have very little differential across the big turbine because of the bottle neck that is the small turbine. Same reason you stage compressors the way we do, big to small. Its just the opposite with turbines.

HOHN

OH, it's stil there, it just doesn't matter anymore. Just like the restriction of a 1/2" fitting is a non-issue if it's downstream of a 3/8" fitting, right?

That's the problem, the energy available to each turbine is not the same. The first turbine doesn't get a bigger pie, because the size of the pie is a function of the pressure differential across the turbine.

It's funny you should bring up reversing the turbine order, because I was just thinking of that yesterday.

But once I started to truly grasp how "corrected mass flow" works, it explains when the turbines have to be arranged the traditional way.

The PR of the primary's turbine will correspond to a flow difference (in cfm) between inlet and outlet. At a PR of 1, inlet and outlet flows are the same, but as PR comes up, inlet flow is reduced relative to outlet flow.

Turbine flow corrects upwards for higher temps, but downward for higher PRs.

So simply correcting for higher temps will crank up the mass flow number. Let's say we have 20lb/min going to a turbine that we have weighed somehow and know that it's actually 20lb/min. Yet, accounting for a temp of 600F compared to the 59F cranks this up to 28.59ln/min. This "correction" isn't correcting the weight of the flow-- the actual mass is still 20lb/min. Instead, we're correcting for the ENERGY of that mass. We're saying that 20lb/min at 600F has as much energy as 28.6lb/min at the reference of 59F.

Now that we understand that the "correction" is actually for energy, not mass, it makes sense that a higher PR drops the flow down. Because the total energy is the mass, the density (temp) and pressure, when we increase the pressure, we are "storing" some of the energy as pressure, and thus we will have less "corrected flow".

Going back to our 20lb/min at 600F-- we "correct" it up to 28.6lb/min for the higher temp, but if we increase the PR to 2, the mass flow drops down to 14.3lb/min, even at the same 600F inlet temp. To get our 20lb/min back at a PR of 2, we'd have to have the temp around 1615F!! In other words, the elevated PR of 2 has removed enough energy from the flow that we would have to increase the temp by over a THOUSAND DEGREES to get it back!

What a turbine map is telling us is basically how the turbine will affect flow sent to it. At first (low flow), the turbine poses essentially no restriction. Then, as flow increases, the turbine begins to pose a little of a restriction, and the operating PR will climb above 1. As it does, this offsets a portion of the increased flow you are sending to the turbine.

As a result, the lines on the turbine map level off at a certain point. What's happening as you transition from the left side of the turbine map to the right side is this: at first the increased flow shows up as higher flow and almost no increase in PR. Then it migrates to a region where you get some of each-- both higher mass flow and a higher PR. Finally, it levels off on the right to a region where your attempt to increase mass flow results only in a PR increase and no change in mass flow.

(refer to turbine maps posted earlier)

Justin

HOHN

I thought I would continue posting some tidbits for search feature reference.

Earlier, I calculated and selected turbos based on 80lb/min total mass flow (600hp) and balanced PRs at each turbo (2.5PR each).

So I was curious what would happen to the turbo selection if you wanted to change the pressure balance between the turbos?


For example, what if you run a primary that can't deliver the required airflow at only a PR of 2.5-- what if it needs 3.0?

The GT42 is a good candidate for this since it has an impressively fat compressor map at a PR of 3. It's also slightly more efficient in making 80lb/min at 3:1 compared to 2.5:1.

This variation of our earlier calculation means that the inlet flow to the GT42 is now just 42lb/min. We can no longer use the 1.44 A/R housing, and we have to drop down to the 1.15 A/R housing, losing efficiency.

We also end up having to go larger on the top turbo (GT4088) to drop the PR down.

So we end up with more lag with this system in our effort to shift workload to the primary.

~~~~~~~~~~~~~~~~~~~~~~~~

If we shift the PRs the others direction and drop the primary down to 2:1, here's how it plays out.

First, we find that the GT4202 is no longer big enough to flow what we need. To get 80lb/min at the low PR of 2, we need to step up to the GT4508:


Looking where 80lb at PR of 2 falls makes this about the perfect compressor do to this job.

On the hot side, we calculate that 80lb/min out of the primary is 62lb/min going in. At this low of a PR, we'd have enough flow to push even a GT47 with its largest housing!

Anyway, the top turbo now can proportionally a little smaller. How small? How about a turbine that's 28lb/min at 3:1? The GT35 is again a candidate here, but we can go with the midrange size housing (.82 A/R) rather than the largest 1.06.

So the irony here is that by going with a larger primary and shifting workload to the secondary, we end up with earlier spoolup from the smaller secondary with its medium housing size.

The danger, of course, is that the GT35's map is sorta narrow at 3:1, so it might not be very effective on the compressor side.


~~~~

So it appears to me that the main problem of dropping the primary's PR is that the primary has to be much larger to do the job. You end up with space limits. The other thing is that the turbine housings are smaller than needed, even the biggest ones. With a PR of 2 in this case, the primary truly is "loafing".

The upshot is that by using a larger primary, you will never outgrow it. Buy a big primary with a large housing and as you need more HP, just go to larger and larger secondary turbos.

This "big primary" setup also seems to improve spoolup because you're using a little smaller turbo up top. This should improve overall response.

The other lesson that seems to be in the numbers is to "go big". Not only on the primary turbo, but also on the housings. You have to keep that flow moving, and with a small housing you just bottleneck the whole thing.

Heck, a GT4718 look like a great choice if it wasn't so stinking huge! It would take awhile to outgrow that primary, plus the huge map covers a large range.

JMO