Choosing the right turbos (math heavy)This is where the fun begins. Well, for me at least as I love crunching numbers and toying around with figures. So you've decided you want to put the work in and run compound turbos, now you just need to figure out which ones you want.
I will assume that anyone who plans to use this already knows how to read a compressor map. If you don't, google it and learn on something more basic than this. You should have a reasonable understanding, otherwise this will get ugly fast.
Disclaimer here as well. I'm not sure if this is all right... use it at your own risk. I'm surprised how much air can flow given these numbers, but I've combed it over and over and it seems good. I have no references to cite, mostly a bunch of chicken scratch in a binder that I actually wrote this off of, but I think I read something on compounding maps by TDI Meister, who's both on here and TDI Club, so I'll say that credit for a lot of it goes to him
First step, how much power do you hope to make? Make sure there's overhead! I'll use my engine setup as an example the whole way through here.
If I make 180whp, I'll be stoked. I use a conversion factor of 1.15, which gives me 207hp at the crank. So, I'm going to figure out how much air it takes me to get 220hp crank. That would be 191 at the wheels which for now is more than enough power for me. All of this being at 4500rpm
I'm half addicted to a website called not2fast.com with a great calculator for figuring out power numbers if you know what info to give it. The most difficult figures to know are BSFC, AFR and VE. Here's a table of values that I use. I came upon these values from pulling my own sources and if anything seems off, I would gladly be corrected!
AFR
17.5:1
BSFC
<4000rpm - .34
4000-4500rpm - .37
>4500rpm - .40
VE
<3500rpm - 80%
3500-4000rpm 75%
4000-4500rpm - 70%
>4500rpm 65%
I realize stoich for diesel is around 14.5:1, but you'll be puking black smoke like mad and likely melting something at that point. I remember reading somewhere that TDI's begin to smoke at about 18.5:1 and IIRC, IDI's burn better due to the prechamber being more efficient than the TDI's design. With that, I expect a haze at 17.5:1
The BSFC I averaged out from a myriad of sources. Who knows if I'm right, but the numbers seem to make sense.
These VE numbers may seem low, but given the feel of these engines, either the BSFC or VE definitely tank after 4000rpm
After all of that, I was left with a manifold pressure of 35psi, pressure ratio of 3.52, mass flow of 23.6lb/min, 323CFM. Also, a BMEP of 332.6. Fairly high for my compression ratio (~20.5:1), but nothing stupid. Also, for reference, 220hp at 4500rpm is 255ftlbs of torque.. not bad for a 2400lb car!
http://www.not2fast.com/turbo/glossary/turbo_calc.shtml?FeetASL=370&Tamb=25&Bore=79.5&Stroke=95.5&nCyl=4&RPM=4500&VE=70&Boost=35&Ec=75&Eic=80&PdropIC=1.5&TambIC=25&wiPercentMethanol=50&wiRate=100&wiTemp=21&SFC=0.37&AFR=17.5&maxInjectorDutyCycle=85 Now, the first turbo to size up is the LP turbo. It's drawing ambient air, so it's fairly simple to figure that one out. I had spent a while looking and kept going to smaller and smaller LP turbos, realizing that some monster down there isn't what I really want. I ended up going for a fairly simple option, a K24-2470. It's reasonably efficient up to a PR of 2.1, so I'll use that as it's PR. In a compound setup, the PR's multiply, so 3.52/2.1 leaves a PR of 1.68 for my HP turbo at max boost (35psi).
Not2fast.com has lots of compressor maps available, including one for a K24-2470. It's flow is actually rated in m^3/s, not lb/min, but using not2fast's simple conversion, (23.6lb/min)/162=.146m^3/s. Plotted on the compressor map puts it right where I want it to be at full boost. Now the easy one is done.
HP turbo becomes a little bit tougher because compressor maps are measured with ambient air as the input, but our HP turbo is taking in already compressed air. I'm still using the K14 that my engine came with so I only had to buy one turbo. Fortunately everything is nice and linear, so the equation to correct the mass flow isn't too tough. m2=m1*sqrt((T/Tmap)/(P/Pmap))
Temperature is the inlet temp divided by the temp used on the map, both converted to degrees Kelvin. Pressure is absolute inlet pressure divided by pressure used on the map, in whatever unit you want, as long as they're the same.
Temperature would be very difficult to calculate, so I just use the not2fast calculator from above, change the boost to a PR of 2.1 and use the temperature that spits out; 16.2Psi giving me an outlet temp of 126*C. Now, lets throw those numbers into our equation.
m2=m1*sqrt((T/Tmap)/(P/Pmap))
m2=23.6*sqrt(((126+273)/293)/(30.9/14.7)
m2=23.6*sqrt(1.362/2.102)
m2=23.6*sqrt(.6480)
m2=23.6*.805
m2=19.0
So, plotting 19.0lb/min, which converts back to .117m^3/s with a PR of 1.68 once again puts me very near the middle of the compressor map, even a bit low, just on the edge of the 76% island. Before I actually figured it all out, I was afraid my turbos would be too small, but assuming all this math is correct, I have tons of overhead!
One problem I've run into is that I don't know how to control a turbo by PR. I've been planning to run the K14's wastegate as the difference between my intermediate charge pipe and intake manifold. The problem I run into there is that for 35psi, that's a differential of 19psi. Meaning, for my K14's wastegate to open, it'll need to be making 19psi on top of what the K24 is making. That's not so bad once it's already getting compressed air, but that's a PR of 2.3 drawing from ambient which is off the compressor map. If anyone knows a way around this, please let me know, otherwise I'll have to do testing on it and figure something out. I only plan to run 30psi at the manifold for now at least, so it's not a huge problem, the K14 set at 15psi isn't too bad, but I'd like to control it better if I could.
Just out of curiosity, I extrapolated the numbers a bit to see what I could actually do. If I come across a good deal on a TDI long block and a cummins 4BT pump, I'll probably swap that in and run some big numbers. Using the link above, changing the boost up to 50psi, I get 278hp at the crank, 30.0lb/min flow and PR of 4.4. K24 would see PR of 2.3 @ .185m^3/s and K14 would see PR 1.91 @ .144m^3/s. Both of those are still near 75% eff! VERY close to the limit of the K24 though. To go higher than that, throwing the K24 on as the HP turbo and something capable of 35-40lb/min at PR of ~2.3 would put you in the 300+whp range at 60psi. Although, the TDI may flow better, so you might be able to do in the 300's on 50psi but bigger flow numbers. Garret GT30R maybe?
Topic: Compound Turbocharging for Dummies (Read 49252 times)
