I ran your input numbers and got...

369K coming out of lp turbo.
470K coming out of high pressure turbo.

That's 377°F. If it's 70° day outside, subtract 70 from 377= 307° left to cool. Air 2 air is AT MOST 75% efficient, so 307×.75= 230.25 drop. 377° intercooler inlet temp - 230.25° drop = ~147°F air coming out of intercooler, or 337K.
337K÷288K= 1.17, sqrt of 1.17 = 1.08.
1.08x62lbs/min= 67.
Finally 67÷3.0pr= 22lbs/min.

 

Okay I've gone back through everything now and things are moving towards matching what you've told me. I was pretty surprised when my MFR out of the intercooler suddenly matched the lb/min from the beginning. I still have a few questions though to make sure I'm doing this right.

First the first step, I get the CFM of the engine in NA form and then most the calculations seem to be based on that. I do still need to find Wa though to determine PR and mass flow through the low pressure turbo right?

While I was able to match the flow rate out of the intercooler the two compressor stages were off a little bit, i.e. NA flow rate = 23.8 lb/min, stage 1 =24.8 lb/min, and stage 2 = 27.9 lb/min should these numbers all match or does it only matter for the final coming out of the intercooler?

All of these calculations are based on ideal conditions with the exception of 95% VE. I've tried crunching the numbers with some assumed losses as well, such as 1psi drop across air filter and 2 psi drop through intercooler and piping, and local baro of 14.5 psi. The ideal PR is 3.0 but when I factor in losses I get an actual of 3.4. If I use 3.4 the 2 stages get a little closer to matching, but post intercooler dips a bit. NA flow = 23.8lb/min, stage 1 = 24.5 lb/min, stage 2 = 27.2 lb/min, and post intercooler = 23.6 lb/min. Should I be assuming these losses or am I over complicating things?

The last one is kind of a dumb question I feel I should already know the answer to, but I've never really had to think about it since I've never had a question of having an additional temperature rise after a single turbo. When plotting the low pressure turbo, I obviously have a few points in the low revs that land well below where the map start (not in surge, just below the last speed line), since the compressor isn't really operating down there can you just assume 100% efficiency for temp calculations for those points? I would think that if its not actually creating boost, its probably not making much heat either.

 

That's all exactly normal, your seeing how turbos compress the air in stages, your basically watching the density increase.
For shits and gigs you can run those numbers as a single turbo, you'll see it in one step instead of 2.
Also fyi, the same equation works for the exhaust, then you can plot on turbine maps.

 

Forgot to answer the second part of your question.

Definitely not 100% efficiency but the pressure ratio is so low that it isn't adding alot of heat. Heat is a percentage of boost, if your boosting 2% then there isn't much heat either. So I guess it could look like it was close to 100%, me myself I would run the numbers how it actually is. BUT even our best numbers aren't 100% accurate, the whole idea of all of this is to get "close enough" where only some minor tweaking is necessary. It gets you away from building a random setup and then endlessly guessing and trying stuff.
It comes down to the variables and assumptions that have to be made, atmospheric conditions, ve % changing, turbine efficiency etc.
The more data you can log, egt, drive pressure, pre and post temps from compressors and ic etc, the better and faster you can dial in your setup.

 

Thanks with all your help with this. I think I have a decent plan now. The turbo sizing changed from what I was originally thinking. To stay under 30 psi and have decent efficiency it now looks like a G40-900 for primary and GT2252 for secondary.

You said the same equation works on turbine maps, but if I try using anything from here the numbers make no sense in relation to what's on a turbine map. I've never been able to find any useful information on how to read them. Every source I find says its a complicated process, but never actually attempts to explains it. Do you know of anything that would actually be helpful in learning this? Seems like they wouldn't be out there if nobody knew how to read them. haha

 

If computing the compressor side takes up 2 lines of paper, computing the turbine side takes up the whole paper. The compressor side is just matching up to the engines air demand, pretty easy.
The turbine side needs you to know the exhaust conditions (flow, pressure, and heat) so you can figure out how much energy the turbine needs. Which is dependent on what the compressor needs (pressure ratio, efficiency, ambient air temp and pressure).
Yes, it's complicated.

GENERALLY with compounds figure the turbines expansion ratio the same as pressure ratio. I'll give a quick example for ya.

So if exhaust temp is 1500°f /1088k,
1088÷288= 3.78, sq/rt 3.78= 1.94
1.94× 62lbs/min= 120. 120÷3 = 40lbs/min exhaust flow, at 1.76 expansion ratio. That point on the turbine map needs to be on a line of the turbine/ housing that you picked. If it's above the line, it means the turbine is too small for that flow point, wastegating needed.
If that point is below the line, the turbine is to large, is flow capacity exceeds what your trying to do.

We know the hp turbo has a pr rise of 1.76, so we'll just assume a 1.76 drop in exhaust drive pressure. 3.0÷1.76= 1.70 left over for the lp turbo.
We also know that there's a temp drop thru the hp turbine, figure 300°f, so 1,000°f exhaust at a 1.7 pressure ratio feeding the lp turbine.
1,000f/811k÷288k =2.82, sq/rt 2.82= 1.68
1.68×62lbs/min= 104, 104÷1.7= 61lbs/min.
Lp turbine is 61lbs/min @1.7 expansion ratio.

I didn't check this against anything, I just ran the numbers so you could get an idea of how the equations work. You'll have to use your experience to know your egts. Don't rely on the turbine numbers TOO much since your only using basic numbers in the equations. A detailed "work out" of the numbers is needed to nail down the turbine side. You have enough to use it as a guide, and with some instrumentation you could dial in your setup really quickly.
You'll be surprised how big of a lp turbine you'll need, try not to have to gate the lp charger. A wastegate adds expansion ratio, and expansion ratios multiply across the exhaust stages just like boost does. So a 2psi increase here can make for 16psi in the manifold.

 

Okay, your assumptions for the lp turbo are pretty close to my estimates, so I come out with the same numbers that you do. I know you said the lp turbo may need to be surprisingly large, but when I look at the map, that just doesn't seem feasible.

Let's go with the 61lb/min at 1.7 ratio, and plot that on the map for the G40-900. Surely a turbo that size on a 2.3L is plenty to make around 630 hp, however 61 lb/min is off the map entirely. The highest value to land on a line in the map is about 38 lb/min with the largest 1.19 A/R housing. I've heard that Garrett turbine maps are different than most, but not sure why. Is this where my issue lies, or am I missing something. The smallest turbine in Garrett's line up where 61 lb/min at 1.7 lands on the map is in their 55 series turbos which can support in the range of 2000 hp with 110+mm turbines. Surely it doesn't need to be THAT big, right??

 

Those numbers were assuming a 1:1 drive to boost ratio. Typically 1.2:1 is a good compromise between streetability and performance. Going higher will give you a quicker reacting/ spooling setup, going lower will give you the most hp/psi.
If boost is 3pr, then the exhaust is 3×1.2= 3.6pr in the manifold. Run the numbers again and you'll see the flow is lower.

Garrett typically does their maps in total-to-static pressure. Static is atmospheric pressure, total is atmospheric pressure PLUS the speed of the gas. Gas has mass, which has momentum, and so means it contributes to turbine power also.

You have to realize the lp turbo doesn't know it's feeding a 2.3L engine. It's feeding a 2.3L engine that is being fed by a turbo, which makes it look like a bigger engine. If the hp turbo is doing 1.76pr, then the lp turbo thinks it's feeding (2.3L×1.76pr=4) a 4L engine. What the usual "gotcha" moment is with compounds, is that since the pr is split, the lp turbo has to move that airflow at a pretty low pressure ratio.

 

Okay, if I'm doing this right it makes things a lot closer and brings it down to 51lb/min around 2.2 PR. The map for the G40-900 with 1.19 A/R is around 45lb/min at this point. That would just mean the lp turbo needs to be gated, but 5-6lb/min shouldn't be too substantial, right?

 

Can’t say that I understand the thought process here.

IMO the K.I.S.S. approach is almost always the way to go with a performance project. Your goals seem far from wild. And you 100% should not need a compound setup to achieve 550 hp on a 2.5 liter with reasonable spool. You can easily hit your goal with factory cubes and less rpm on one turbo. Why over complicate it?

Curious why you want to de-stroking a relatively small motor? Typically, small engines go the other way. You are giving up valuable cubic inches on a motor that will rev to 9k without being de-stroked. (but could also hit your power goal with a much lower valvetrain friendly rpm) Which also makes me question a 9000rpm goal? That will kill longevity and require light weight expensive valvetrain parts. Any specific reason you want to wind it that high?

All that said, trying something new and different is always cool in my book, However impractical.

Might head over to yellow bullet and check out Kevin’s compound 2.0 4g63 setup. He has actually built it and has real world experience and data. Though he was making 2x the power you are intending… so you could basically cut the primary turbo size in half.

https://www.yellowbullet.com/threads/compound-turbo-charging.216811/

 

Kevin did a lot of experimenting. I believe he ended up doing what I mentioned above. Or at some point he did. My buddy used that design to build his.

 

His setup worked well, until he had an intake back fire and a giant explosion in his charge pipes. He ended up removing the compound setup and just uses a large single with an intercooler. Then a little n20 to spool it. 1/3rd the cost/complexity and works better.

 

The explosion from the intake backfire was from the meth he was spraying directly into the volute of one of the turbos.
I thought he went back to a compound a couple years after the big single nos combo. Im probably wrong.

 

Yea, he was spraying in between the turbos without an IC on the compound setup. Running 100% methanol as his standard fuel and spraying almost 50% of his total fueling pre-turbo on the primary charger. It was enough to get his charge temps down around 150* by his math. Which is the boiling point of the fluid and pretty much the limit of meth as a charge cooler. If he sprayed more pre-turbo it didn't pick up power.. aka It didn't cool the air down anymore.

As far As I know after the explosion he scrapped the compound idea all together.

 

Thanks for the input, I'll definitely give that a read when I have some free time.

To answer your questions, I am de-stroking to achieve a better rod/stroke ratio (stock is 1.65 de-stroked is 1.76) which will allow the higher revs and better knock resistance because of the additional dwell at TDC. This also allow me to bump up the compression a bit from 8.2 to 9:1. It will be fully built so valvetrain will be able to support this. The reason for the higher revs is to have a wider power band. Typically people hitting this power level on a Subaru only have 2-3k rpm of fun after a turbo big enough to do this is spooled. They usually aren't really making power until 4.5-5k and redline around 7k. Because it is being de-stroked, I'll obviously lose some torque as well so running compounds is to compensate for that.

To sum it up, I want 550 whp, but I want it to be streetable, I don't want to wait forever for boost, and I don't want just a quick spike in power and then it's over. The small turbo can spool sooner to make up for the lost torque of the shorter stroke and be able to carry it through until the large turbo can spool and hold it through the rest of the rev range. I would like to have the feel of sequentials without all the additional valving and control necessary to make that happen.

 

To be clear, I’m not arguing here, just discussing. So I hope you take no offense. A high rpm screamer compound setup is unique and cool IMO. I just hope you realize none of that is necessary to make a quick spooling 550hp on a 2.5.

Your rod ratio isn’t bad to begin with at 1.65. It is perfectly capable to hit 9k rpms with a good bottom end and valvetrain. But my point was you don’t need anywhere near 9000 rpm to hit your goal with a 2.5 liter! You shouldn’t have any knock issues at those power levels so you are revving it just to be revving it. Which is ok, I just hope you don’t think either of those things are necessary.

For example: my daily for many years was a 2.0 4g63 eclipse with decent forged rods/pistons. Was 9.5:1 and I revved it to 7800. 34lbs of boost on a 60mm Holset and untouched head with valve springs. Ran OEM cams even! Spool was great and it trapped 134. Was AWD and had zero weight reduction, factory AC and all options. It was a whale at just under 3400lbs. Which is well over your power goal on a smaller motor. So I’m simply stating you don’t need some crazy high revving compound setup for 550hp and great spool with a 2.5 liter. You need E85 and a properly spec’d standard setup… that’s it.

Over camming the thing and de-stroking it will absolutely kill the bottom end and the “spool”. This is done on race cars and is the exact opposite of what you want with a “street” car. Run your base compression as high as you feasibly can. 10:1 or higher would be better w e85. Run a turbo compressor that’s not over spec’d for your power level with a relatively large exhaust wheel. This way it doesn’t peter out up top. Run very mild or even factory cams and you will easily spool at relatively low rpm.

Another big issue to address with big RPM is the trans. My trans and synchro's were NOT happy shifting over 7800 RPM. You need a worked trans to shift at big RPM. They typically need super light weight unspring 3-4 puck setups to work well too. Which also is not street friendly.

 

No offense taken. I always appreciate a good discussion.

I appreciate the input, but I have to respectfully disagree with some of what you said. What you're saying, I'm sure works great on that platform. The 4G63 is an amazing engine, however it is not a great comparison to the EJ25. The 4G63 is a slightly under-square (about 0.96) iron block inline engine with an 88 mm stroke. The EJ25 is horizontally opposed, over-square (about 1.26) with only a 79mm stroke. The R/S is similar, however with the 4G63 around 1.7. I envy what the DSM guys can do with their engines, but the Subaru is a totally different animal. It's well known in the Subaru community that these engines are very knock prone. Trying to run this boost on a Subie with 9.5:1 especially with factory R/S is likely going to be race gas only, E85 probably wouldn't be enough. As for valvetrain, I'm using stock sized valves and Stage 1 cams with Dual-AVCS so idle shouldn't even have a noticeable difference. One area where the Subie may have a 1-up though is in the trans. I have the newer 6-spd which has been shown to take some decent abuse. I'll just have to see what it can do when I get there.

I am aware I can hit that power level without going this route, but I'm am looking for a wider power band than what these engines have been shown to do on a large single turbo