Matt, it is fairly simply in theory but complicated in application.
Click the technical tab for a picture of a compressor map
The map looks like a halbred axe blade and you want to keep your compressor operating within all the lines. The line on the left angling left to right upward is the surge line. The lines that go horizontal and angle down to from left to right indicate RPM. The line at the top is maximum RPM. The line at the right is maximum air flow. The circles inside show compressor efficientcy. The vertical axis is Pressure Ratio and the horizontal axis is Air Flow Rate.
Compressor efficientcy is related to an Ideal Gas law, which basically states that if you raise the air pressure in a compressor, the air will get hotter. The very best condition would be 100% efficientcy, which is impossible. But at 100% you would still heat the air, but you would heat it the least. So for example if the compressor is 75% efficient you would be heating the air more. That is the purpose of the circles. A value of 60% is generally represented as the worst compressor efficientcy and typically defines the right lines of the map.
PR means Pressure Ratio. PR is the way that compression pressure is described for an air compressor. Roughly equate Compressor Pressure to Boost Pressure.
PR formula:
PR = ( Inlet Pressure + Compressor Pressure ) / Inlet Pressure
Single Turbo:
For sea level PR = ( 14. 25 psia + 30 psia ) / 14. 25 psia = 3. 1
For 4000' PR = ( 12. 5 psia + 30 psia ) / 12. 5 psia = 3. 4
Compare the higher PR for the same pressure. That means the air will be hotter.
Compound turbos:
Primary PR = ( 14. 25 psia + 20 psia ) / 14. 25 psia = 2. 4
Secondary PR = ( 20 psia + 30 psia ) / 20 psia = 2. 5
So with twins the air temperature ends up being quite a bit cooler for the same boost pressure. Both compressors are running at the more efficient sections of their maps.
Look at the compressor map, any time you pick a point to the left of the surge line you will be begging for trouble. To sustain a given pressure the compressor must spin at a corresponding RPM. To spin the compressor you need to spin the turbine using exhaust gas. The Hp generated by the turbine and the Hp used by the compressor are essentially equal. More RPM requires more Hp.
Now under the condition where the compressor discharge pressure is high and the turbine Hp is low. Like when the driver of the truck just lifted is foot. The compressor loses driving force to maintain the appropriate RPM. Now the air pressure can not be sustained by the compressor and it backflows through the compressor.
One thing to keep in mind. The engine uses a set quantity of air every revolution. If you double the boost pressure you double the quantity of air it will consume. Typically the quantity of air is normalized to make the comparison easier. By that I mean it corresponds to the amount of air the engine would consume if the air pressure where not raised or the air charge temperature were not elevated. Basically for comparison, it would be the amount of air the compressor is sucking in.
So say for example that an engine consumes 100 CFM of ambient air at 1000 RPM with no boost. Now just for example, if you raise the boost pressure to 14. 25 psi at a compressor efficientcy of 100% it consumes 190 CFM. Now if you throw in a less ideal compressor of 70% efficientcy the air it consumes might go to 175 CFM.
Another concept you must understand, if you don't already is Density Ratio. It is also a ratio and based upon the air temperature before and after it is compressed as well as the air pressure before and after it is compressed. In a nutshell, the higher the pressure is and the lower the temperature is means the higher the density is. More dense means more molecules of air for the same volume. A compressore running at a higher efficientcy has a higher Density Ratio. So the engine will consume a set volume of air per revolution, but physically more air goes in at a higher DR.
Not sure you really wanted to know any of this, for my part it just gets me more confused.
Argh... My fingers hurt.
Jim