Here are some calculations for the compressor wheel I am currently using in my MB.
First off: This compressor will for sure outflow the GT23 tubine by far!
This is only compressor calculation with normal 20 degrees celcius ambient air temperature.
I chose high volumetric efficiency of 96%, this may be lower in real, but to compensate i chose high lambda of 1.2
I am aware that this is pure THEORETICAL calculation, real world will quite sure create more losses, this calculation shall only be a rough estimation.
Formula used:
CFM = L x rpm x VE x PR / 5660
L = Displacement
rpm = well....rpm *g*
VE = volumetric efficiency
PR = Pressure ratio
"CFM" is US measuring unit, "cubic feet per minute" , and is used in some compressor maps.
CFM / 14.27 = lb/min
lb / 0.45359 = kg
Our comp-map is in m³/sec so we have to convert from weight to volume. Typical weight of ambient air is about 1.2kg/m³ at 20 degrees celcius.
PR = requested boost plus ambient pressure plus pressure losses
.
I have calculated plotting points for following rpm steps:
1500/2250/2500/3000/3500/4000/4350
2250 shall be our point of highest torque, and highest power shall be from 3500-4350
To go sure we don't come left to surge line, there is also 1500rpm calculated and a "starting point" with 20% from max. flow at PR1
Displacement in Liter 3.222
VE 96%
Plot 1 (Requested boost in intake manifold is 1.45bar + Ambient +0.15 losses = PR2.6))
3.222 x 1500 x 96 x 2.6 / 5660 = 213.13 CFM = 14.93lb/min = 6.77kg/min = 0.113kg/sec = 0.094m³/sec
Plot 1 = 0.094 / PR 2.6
Plot 2
3.222 x 2250 x 96 x 3.2 / 5660 = 393.47 CFM = 27.57lb/min = 12.50kg/min = 0.208kg/sec = 0.173m³/sec
Plot 2 = 0.173 / PR 3.2
Plot 3
3.222 x 2500 x 96 x 3.1 / 5660 = 423.53 CFM = 29.68lb/min = 13.46kg/min = 0.224kg/sec = 0.187m³/sec
Plot 3 = 0.187 / PR 3.1
Plot 4
3.222 x 3000 x 96 x 3.1 / 5660 = 508.23 CFM = 35.61lb/min = 16.15kg/min = 0.27kg/sec = 0.224m³/sec
Plot 4 = 0.224 / PR 3.1
Plot 5
3.222 x 3500 x 96 x 3.0 / 5660 = 573.81 CFM = 40.21lb/min = 18.24kg/min = 0.304kg/sec = 0.253m³/sec
Plot 5 = 0.253 / PR 3.0
Plot 6
3.222 x 4000 x 96 x 2.65 / 5660 = 579.28 CFM = 40.59lb/min = 18.41kg/min = 0.306kg/sec = 0.256m³/sec
Plot 6 = 0.256 / PR 2.65
Plot 7
3.222 x 4350 x 96 x 2.4 / 5660 = 570.53 CFM = 39.98lb/min = 18.13kg/min = 0.302kg/sec = 0.252m³/sec
Plot 7 = 0.252 / PR 2.4
Starting point for surge line: 20% of plot 6.
0.256 / 5 = 0.05 / PR 1
These data can be filled into the compressor map now:
Now we got our airmass. Lets see what fuel we need....
A 6 Cylinder 4 stroke engine has 3 combustion strokes per revolution.
This means @ 1500rpm:
1500 x 3 / 60 = 75 combustion strokes per second
2250 x 3 / 60 = 112.5T/sec
2500 x 3 / 60 = 125 T/sec
3000 x 3 / 60 = 150 T/sec
3500 x 3 / 60 = 175 T/sec
4000 x 3 / 60 = 200 T/sec
4350 x 3 / 60 = 217.5 T/sec
Lets calculate with Lambda 1.2.
When we converted from kg/sec to m³/sec for the plotting points above we also used factor 1.2 so we can use these numbers from above calculations.
At 1500 rpm these where 0.113Kg/sec or 0.094m³/sec. So we use 94g/sec. Divide by Lambda 1: 14.7 . 94/14.7 = 6.394g = 6394mg Diesel, divided through 75 combustion strokes per second = 85mg or 101mm³/stroke (Diesel densitiy is calculated with 0.84)
So here are the other points:
1500rpm: 94g/sec air and 85mg / 101mm^3 Diesel
2250rpm: 208g/sec air and 125mg / 149mm^3 Diesel
2500rpm: 224g/sec air and 122mg / 145mm^3 Diesel
3000rpm: 270g/sec air and 122mg / 145mm^3 Diesel
3500rpm: 304g/sec air and 118mg / 140mm^3 Diesel
4000rpm: 306g/sec air and 104mg / 123mm^3 Diesel
4350rpm: 302g/sec air and 94mg / 112mm^3 Diesel.
So if we look at stock program:
we see,the engine need 72mm³/stroke (60.5mg) for 470Nm in point of highest torque, this equals to 6.52Nm/mm³ or 7.77Nm per mm3.
At 2250 rpm we have 125mg/149mm³ which would lead to about 970Nm with a clean lambda of 1.2
About 60mm³ the stock engine needs at highest power rpm for the 197hp, in upper calculation our result is about 120mm³, so this would also give about TWICE the stock power ~ 400hp.
What a pity the GT23 turbine wont flow these amounts of exhaust gas :-(
But impressive what this "little" compressor could do, if coupled with a right sized turbine....
Regards, Alex