Post by Teh Man! on Mar 29, 2006 11:52:05 GMT -5
The first thing you need to do is decide the maximum level of boost you want to run. Most stock import engines with proper fueling and tuning can handle at least 7 to 10 psi on 92-octane pump gas. Some very strong engines, like the Nissan SR20DE, can withstand up to 20 psi if enough fuel is provided and detonation is controlled. If you plane on running race gas, figure at least a few safer psi. If you are building your engine as well, lower the compression to a turbo-friendly 8 to 8.5:1 compression, then figure you can run 14 to 18 psi on pump gas and more than 20 on race fuel. This is general information; much depends on how good your tuning is, how big your budget is and how much intestinal fortitude you how. Let's do a compressor match on an SR20DE. First, we'll assume we're running 20 psi of boost, the maximum a stock SR20 with race fuel can safely take. We'll also assume pressure drop across the intercooler is 1.5 psi. This is a good generalization, but if you have a Spearco intercooler, you can reference the pressure drop in the company's comprehensive catalog.
From this information, you can calculate absolute pressure out of the compressor (Pco):
Pco = 20 psi + 14.7 psi + 1.5 psi = 36.2 psi
You can assume atmospheric pressure is 1 bar, or 14.7 psi: from this, you can calculate the pressure ratio, or Pr. So in our case:
Pr = Pco / Atmospheric Pressure
Pr = 36.2 psi / 14.7 psi = 2.463
Next, we guess what the post-intercooler temperature might be. We'll use 130 degrees F as a starting point, as we have found this is fairly representative of what we have measured with many turbocharged cars with a fairly good aftermarket intercooler.
We will now calculate the approximate density of the air after the compressor and intercooler, or Di:
Intake Air Density (Di) = Boost Pressure + Atmospheric Pressure / R x 12 x (460 + Intake Temp.)
Di = 20 + 14.7 / 53.3 x 12 x (460 + 130) = 0.0009195 ib/in^3
What's all that come from? R is constant from the ideal gas law. You don't really have to know that it means, just that it is 53.3. The 12 is there to keep the units in inches (trust me on this one), and 460 is to convert degrees Fahrenheit to degrees Rankin, an absolute temperature scale. You don't need to understand this, just always plug these into the equation.
From this we can calculate Mf or the mass flow rate of the engine at the rpm where we want to do the match:
Mass Flow Rate (Mf) = Di x displacement x (rpm / 2) x Volumetric Efficiency
For volumetric efficiency, we can assume 90 percent, which is typical for the most modern, four valve DOHC sport compact engine. For an old school, two valve engine, you might want to plug in 80 percent.
Again plugging in our number:
Mf = 0.0000.19 x 122 x (7500/2) x 90 = 37.84 lb/min
Now we need to find the corrected mass flow, or CMf, to get is in the ballpark:
Corrected Mass Flow (CMf) = Mf x (Square Root of- compressor inlet tem / 545)/(Atmospheric Pressure/Corrected Comp. Inlet Press.)
Note: 545 Rankin is 85 degrees Fahrenheit (Rankin is absolute temperature, used in many engineering calculations, 0 degrees R is absolute zero), which also happens to be the standard temp Garrett uses in its compressor maps. For matching to Garrett compressors, we use this figure. We will also use it for our ambient temp just to make things easier for us. You can subtract the actual temperature you want to use from 545, but we figured 85 degrees is a good, rough estimate of average underhood intake temp and it makes our math easier. Convert your ambient temp degrees from Fahrenheit to Rankin by adding 460 to the number. As for the ambient air pressure, it is 14.7 psi. Garrett uses 13.95 psi as the corrected compressor inlet pressure, considering the pressure drop across your typical air filter.
To find CMf for our imaginary engine:
CMf = 37.84 x (Square Root of-545 / 545)/(14.7 / 13.95) = 35.9 lb/min
Now you have your pressure ratio of 2.46 and your mass air flow of 35.9 pound/minute. Next, plot these points on the compressor map to compare how well your engine matches up to it.
If you want to plot more points, you can do so by plugging in different rpm values, remembering that no turbo is going to produce 20 psi at idle. We would figure for something between 4,500 to 7,500 rpm for the SR20DE. For a high-revving VTEC B18C, it might be between 5,000 to 8,500 rpm. Like I said before, you want to stay away from the surge line and fall across the areas of maximum efficiency.
Perhaps the most important thing to be aware of when matching compressors is avoiding surge. Surge is where the air backs up in the compressor and oscillates violently back and forth in the compressor wheel. This happens when the engine's swallowing capacity is exceeded by the compressor's output, causing the air to back up in the intake tract. The mechanics of surge is when the pressure after the compressor exceeds the energy of the radial velocity component of the compressor wheel output, which causes the airflow in the compressor wheel to back up. The airflow backs up, the pressure after the compressor drops and the airflow resumes. In severe surge, this can become a violent oscillation that destroys the thrust bearing of the turbo and even causes mechanical failure of the wheel. Surge can be felt as something as mild ad a slight fall in power to a violent jerking while driving. It also makes a faint thrumming noise that can be heard over the engine.
From this information, you can calculate absolute pressure out of the compressor (Pco):
Pco = 20 psi + 14.7 psi + 1.5 psi = 36.2 psi
You can assume atmospheric pressure is 1 bar, or 14.7 psi: from this, you can calculate the pressure ratio, or Pr. So in our case:
Pr = Pco / Atmospheric Pressure
Pr = 36.2 psi / 14.7 psi = 2.463
Next, we guess what the post-intercooler temperature might be. We'll use 130 degrees F as a starting point, as we have found this is fairly representative of what we have measured with many turbocharged cars with a fairly good aftermarket intercooler.
We will now calculate the approximate density of the air after the compressor and intercooler, or Di:
Intake Air Density (Di) = Boost Pressure + Atmospheric Pressure / R x 12 x (460 + Intake Temp.)
Di = 20 + 14.7 / 53.3 x 12 x (460 + 130) = 0.0009195 ib/in^3
What's all that come from? R is constant from the ideal gas law. You don't really have to know that it means, just that it is 53.3. The 12 is there to keep the units in inches (trust me on this one), and 460 is to convert degrees Fahrenheit to degrees Rankin, an absolute temperature scale. You don't need to understand this, just always plug these into the equation.
From this we can calculate Mf or the mass flow rate of the engine at the rpm where we want to do the match:
Mass Flow Rate (Mf) = Di x displacement x (rpm / 2) x Volumetric Efficiency
For volumetric efficiency, we can assume 90 percent, which is typical for the most modern, four valve DOHC sport compact engine. For an old school, two valve engine, you might want to plug in 80 percent.
Again plugging in our number:
Mf = 0.0000.19 x 122 x (7500/2) x 90 = 37.84 lb/min
Now we need to find the corrected mass flow, or CMf, to get is in the ballpark:
Corrected Mass Flow (CMf) = Mf x (Square Root of- compressor inlet tem / 545)/(Atmospheric Pressure/Corrected Comp. Inlet Press.)
Note: 545 Rankin is 85 degrees Fahrenheit (Rankin is absolute temperature, used in many engineering calculations, 0 degrees R is absolute zero), which also happens to be the standard temp Garrett uses in its compressor maps. For matching to Garrett compressors, we use this figure. We will also use it for our ambient temp just to make things easier for us. You can subtract the actual temperature you want to use from 545, but we figured 85 degrees is a good, rough estimate of average underhood intake temp and it makes our math easier. Convert your ambient temp degrees from Fahrenheit to Rankin by adding 460 to the number. As for the ambient air pressure, it is 14.7 psi. Garrett uses 13.95 psi as the corrected compressor inlet pressure, considering the pressure drop across your typical air filter.
To find CMf for our imaginary engine:
CMf = 37.84 x (Square Root of-545 / 545)/(14.7 / 13.95) = 35.9 lb/min
Now you have your pressure ratio of 2.46 and your mass air flow of 35.9 pound/minute. Next, plot these points on the compressor map to compare how well your engine matches up to it.
If you want to plot more points, you can do so by plugging in different rpm values, remembering that no turbo is going to produce 20 psi at idle. We would figure for something between 4,500 to 7,500 rpm for the SR20DE. For a high-revving VTEC B18C, it might be between 5,000 to 8,500 rpm. Like I said before, you want to stay away from the surge line and fall across the areas of maximum efficiency.
Perhaps the most important thing to be aware of when matching compressors is avoiding surge. Surge is where the air backs up in the compressor and oscillates violently back and forth in the compressor wheel. This happens when the engine's swallowing capacity is exceeded by the compressor's output, causing the air to back up in the intake tract. The mechanics of surge is when the pressure after the compressor exceeds the energy of the radial velocity component of the compressor wheel output, which causes the airflow in the compressor wheel to back up. The airflow backs up, the pressure after the compressor drops and the airflow resumes. In severe surge, this can become a violent oscillation that destroys the thrust bearing of the turbo and even causes mechanical failure of the wheel. Surge can be felt as something as mild ad a slight fall in power to a violent jerking while driving. It also makes a faint thrumming noise that can be heard over the engine.