Lbs per min calculation, compounds

jmd025

jmd025

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When you are calculating density ratio in order to get lbs/min for a compound setup, do you simple find the DR for the primary PR, and add it to the DR for the secondary PR? Or am I way off base? When I figured it that way the number looked somewhat correct. Thoughts?
 
Or take the cfm calculation from the primary, and then use it with the DR of the secondary to get total cfm and lbs/min. That sounds better.
 
This is my contribution to the Compound Ninja Arts.
Heres the math as best as I can figure, from the information I have. Math courtesy of Jeff Hartmann who wrote the "Turbocharging Performance Handbook". If anyone sees anything that seems wrong feel free to comment, I did my best.

I currently have a fresh fully rebuilt engine, everything was checked and necessary components machined. It's got a .5mm overbore, obviously decked block and head, as well as full OEM rebuild. Studs overtorqued, in the "Keating" procedure.

Stage 1 (Large Turbo):
Garrett GT3582R Dual Ball Bearing
( http://www.turbobygarrett.com/turbobygarrett/catelog/Turbochargers/GT35/GT3582R_714568_2.htm )
The map wouldn't link directly just hit enlarge.

Stage 2(Small Turbo):
To be determined.

Anyone who know whats up tell me where I'm off.... and I'm going to go after 50 psi, reasons being
1.A pressure ratios of 2.2 is dead center for max efficiency on my GT3582R.
2. Two stages both working at 2.1 Pressure Ratios (PR) should produce "roughly" 49.98 psi of boost. Close to the intended 50.

PR = (boost + atmosphere)/atmosphere
PR = (50+14.7)/14.7
4.4 total engine PR

Square root of 4.4 = 2.1
Pressure ratio of 2.1 for each stage.

Variables To Be Considered:
So with a 4BT with a .5mm overbore in my case... 242 CID
Running at about 3500 rpm max
assuming 80% Volumetric Efficency
70 Degree ambient temperature
Compressors considered 75% efficient

First calculate airflow of the engine in the Naturally aspirated state.

Airflow(cfm)=(CID x RPM X 0.5 x VE)/1728

(242 x 3500 x .5 x .80) / 1728 = 196 CFM

196 CFM x .076 (conversion factor CFM to Lb/min) = 14.9 Lb/Min

14.9 Lb/Min is the air requirement of a Naturally aspirated 4B at 3500 RPM

Next we go to the Requirements of the second stage of turbo charging.
Your small turbo if you will.

It must produce 14.9 Lb/Min at a Pressure ratio(PR) of 2.2

Then you compute the Density Ratio(DR) to determine flow in the small turbo.

key: _ designates sub for the variable.

DR = (T_1C/T_2C) x PR

T_1C = Inlet Temp Absolute (Absolute means temp relative to absolute zero)

T_2C = Outlet Temp in Rankine (rankine: degrees Farenheight from absolute zero)

So:
T_1C= 70*F + 460 (conversion to Rankine) = 530*R

T_2C= T_1C + (((T_1C x PR^0.283) - T_1C)/CE)

T_2C = 530 +(((530 x 2.1^0.283) - 530)/0.78)

T_2C = 688.755*R

So:
T_1C=530*R
T_2C= 688.755*R
PR=2.1

DR(Density Ratio)= (530/88.755)x2.1 = 1.1596
So the small turbo must flow:
AF_small= DR x CFM of the NA 4B
14.9 lb/min x 1.61596 = 24.078lb/min

AF_small = Air flow through small turbo
AF_small = 24.078
Comparing the GT3582R Map I see that at a PR of 2.1 and 24 lb/min I will be about 72% efficient and close to the surge area. Hmm, lets see if it could work as my big turbo?

Assuming no intercooling between stages....Which I will later calculate and use....

I'll post the recalculation of the DR with interstage intercooling used....later

AF_Big = Air flow in larger turbo

Af_Big = AF_small x DR

AF_Big = 24.078 x 1.61596 = 38.909 lb/min

This is at 79% efficency on the GT3582R map at a 2.1 PR.

My turbo is a "perfect" large turbo for a 50 psi Compound Setup. Now to find a small turbo. Perferably in a GT series housing. I'd like to see how it performs using two ball bearing turbos, hopefullly creating really rapid spoolup


Cut and pasted from a year or two ago. You should be able to get your answers in there. Give you a rout idea. You'd have slightly higher cfm with an inter cooler. I didnt have the calculations with an inter cooler handy.

Also this is dated I ended up with a k27 over a k16. 200-250 hp 4bt.
 
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Start with desired HP, and work backwards from there. Also, the best turbo setup for spoolup and horsepower might not keep EGT in check without water.
 
JQmile said:
Start with desired HP, and work backwards from there. Also, the best turbo setup for spoolup and horsepower might not keep EGT in check without water.
Click to expand...


I tried starting with that route but all the formulas geared toward working off hp first seemed gasoline oriented and I seemed to get strange numbers.
 
Yeah, math can do that to you. Don't forget to size turbos with the peak cfm at the top right of the compressor map.
 
What do you use for air/fuel ratio in your calculations? Do you use a different AF for a street and a comp build? AF is a much greater variable than in a gas application.....

What about a BFSC? Use a higher than stock figure or cummins factory numbers?
 
I've fooled around with that stuff, but again, the gas stuff doesn't really translate. Based upon dyno figures, some of the numbers are way wonky, like at 3,500rpm, the VE on a stock 5.9L 12V is only like 60%, which is terrible...way worse than I ever might have guessed.
 
Im not sure if my question got answered?? Lost

Do you add the to density ratios and use the total to compute overall lbs/min, or do you compute primary Turbo cfm output, and then use that cfm x secondary density ratio?

Sorry if the 2nd post somehow actually explained that, and I didn't follow. I can post up my math if that's needed.
 
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PV=nRT
PV/RT=n
n*MW=mass
MW= molar weight
work the math and you can get PR and mass flow.

Work with bar and kg/s - all metric units if possible, then convert to lb/min or CFM as needed. Math is so much more friendly that way.
 
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i can work this for single stage all day, Im simply asking what is the proper way to "add" the lbs/min the primary is producing to the lbs/min the secondary is producing, to get total lbs/min......

I havent found a good resource book or website that deals with compounds.
 
jmd025 said:
i can work this for single stage all day, Im simply asking what is the proper way to "add" the lbs/min the primary is producing to the lbs/min the secondary is producing, to get total lbs/min......

I havent found a good resource book or website that deals with compounds.
Click to expand...

If you just deal with straight pressure ratios and ignore the temp rise it will be close enough, from what I have seen so far.
 
What you need is the corrected mass flow.
I was actually right in the middle of trying to verify my math when I saw this thread and got the answer from a guru - tdimeister(and verified via PM).
TDIClub Forums
mcorr = m*sqrt(T1/298)/(P1/1)

Here, T1 is the compressor inlet temperature in Kelvins and P1 is the compressor inlet pressure in bar divided ambient (1 bar).
Click to expand...

I wrote a spreadsheet with all of this but no-one has verified it yet. won't post it until I have a smart individual check it out.
 
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JQmile said:
If you just deal with straight pressure ratios and ignore the temp rise it will be close enough, from what I have seen so far.
Click to expand...

so, theoretical numbers,

primary PR 1.68
secondary PR 2.21

359 x 0.5 x 3400 / 1728 = 353.2 cfm x 85% =300.22 cfm NA

Primary density ratio 1.480
Secondary density ratio 1.900

So do we go:
300.22x1.48=444.3 cfm (primary) then 444.3cfm x 1.900 = 844.2cfm x .068 = 58.2 lbs/min

OR
1.480+1.900= 3.38
so 300.22x 3.38 = 1014.7 cfm x .069 = 70lbs/min

???

Thats all I was getting at
 
So do we go:
300.22x1.48=444.3 cfm (primary) then 444.3cfm x 1.900 = 844.2cfm x .068 = 58.2 lbs/min

[/QUOTE]

That Is the correct process for the end result as far as I know. The above calculations in my first post were looked over by an engineer, and tho they are not the best or most direct formulas, he did confirm their validity.
 
jmd025 said:
When you are calculating density ratio in order to get lbs/min for a compound setup, do you simple find the DR for the primary PR, and add it to the DR for the secondary PR? Or am I way off base? When I figured it that way the number looked somewhat correct. Thoughts?
Click to expand...


Since this is a semi-black art that no one that knows wants to share, I'll add my interpretation. They do not add. If you want your overall density ratio, you calculate it using the initial air properties (ambient temp and pressure) vs. the final air properties (after both stages and intercooler/s). You have to take into account the temperature and pressure change going through the primary turbocharger/s and intercooler (if applicable) before the air enters the secondary turbo. Make sure you are using absolute pressures in all of your calculations and account for pressure drops through the system at various points (intercooler, piping, etc.)

For example, on something I worked out last year, I had a primary setup with a DR of 1.78 before the intercooler and 2.2 after intercooling. My secondary DR was 1.89 after the turbo and 2.52 after intercooling. The combined DR for the system was 5.63.
 
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If you want to get me all the details on your motor, compressor maps, etc, I can post up some maps and info that output from my excel spreadsheet.

volumetric efficiency
desired PR from each turbo, or maybe just overall pressure and I can adjust as I see fit on the maps
max RPM
displacement(5.7L?)
approximate expected spool(I can use the compressor maps too to approximate)


Zombiefab - I'm an engineer and I glazed over as soon as I saw how you started doing it and didn't want to even try and figure out what you did.
 
I just made some numbers up, I'm simply trying to understand the mathematics of this particular instance. I can understand it if the parts of the formula are explained and I can work an example problem
 
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