The author of this article is a turbo engineer for Garrett. I'm submitting it because it is an informative read and therefore is beneficial to the community.
Compressor Efficiency and More
by Khiem Dinh
Compressor efficiency is a term thrown around whenever people mention forced induction, but what does it really mean? How does it affect an engine's performance? And what role does air temperature play in all of this? The cool thing about thermodynamics is that we can explain effects with equations. Using basic compressor equations, we'll put some numbers to the affects of air temperature and compressor efficiency on compressor power requirements and air temperature increase.
Some fundamental compressor equations are below.
I like working in SI units because doing calculations with English units sucks! So, mass flow rate is in kg/sec, the average constant specific heat value for air I used is 1.007 kJ/kg*k, and k for air is 1.4. The specific heat of air actually varies with temperature, but the change is basically nothing within the range of temperatures we're using, so I'm assuming a constant value. After calculating all the values in SI units, it is a simple conversion to English units. The table and chart I generated assumes: air inlet temperature of 298K/24.85C/76.7F, and 100% compressor efficiency (isentropic compression).
Looking at the chart and table above, it becomes very obvious that increases in mass flow rate and pressure ratio require more power. Also, the graph shows lines of constant power. For a given compressor power, you can get a lot of flow and little pressure ratio, a lot of pressure ratio and little flow, or somewhere in the middle. To get a feel for what the numbers mean in the real world, we'll use 2.0L 4-cylinder engine as an example.
Automotive engines of this displacement and cylinder count will make roughly 500hp with a mass flow rate of 50lbs/min and a pressure ratio of 2.75, or about 25psi of boost. Looking at the table, a 100% efficient compressor would require 51.1hp! Looking at the compressor map for a GT3076, it shows a compressor efficiency of ~72% at this point. So the actual power requirement becomes 71hp. A GTX3582 has a compressor efficiency of 77% resulting in a power requirement of 66.4hp. That extra hp required over a 100% efficient compressor ends up as extra heat in the air. More efficient is better!
The other variable in the equation that's very important, but many people seem to neglect in the practice of building turbo cars, is the temperature of the air going into the compressor. Many people have the misconception that performance is unaffected because the intercooler will cool the air enough regardless of the air temp going into the turbo. What they are neglecting is the fact that compressor performance improves with cooler air. Said another way, it gets worse with taking in hotter air. Using values of 50lbs/min and a PR of 2.75, the table below shows compressor power required, change in temperature of the air (Delta T), and the exit temperature of the air based on the inlet temperature of the air.
Hotter air in equals mo' hotta air out! Takes more power too. Translation? Laggy turbo.
Notice that the hotter the air going into the compressor, the more power is required to compress it. Also, the increase in the air temperature is greater. Of course, this results in the final temperature being even hotter. I think comparing air inlet temps of 77F and 122F is reasonable; 77F being ambient air temp and 122F being the temp if you ingest air from the engine bay. So by sucking up the hotter engine bay air instead of cooler air from the front of the car, the compressor power required increases by 4.3hp, or about 8%. The difference in the temperature coming out of the compressor is a toasty 60.1F making the intercooler work that much harder.
Of course, there's no such thing as a perfect compressor, so let's see what happens with a 60% efficient compressor; this is often where the tuner industry operates as they try to squeeze as much power as possible out of turbos. Looking again at 77F and 122F inlet temps, the power and temperature differences are now 7.1hp and 70.2F!
Crappy compressor efficiency means supa dupa hotta air! You could boil an egg on it. Mo' laggy too.
So now we know how crappy compressor efficiency and sucking in hot air increase the power required of a compressor to move and squeeze air. But where does that power come from? A supercharger gets it off the crankshaft of the engine and a turbocharger uses a turbine wheel in the exhaust. If you go by old school nomenclature, what we call a turbocharger was referred to as a turbo supercharger. So basically a special type of supercharger with a turbine wheel to get work out of the exhaust. Anyways, we like turbos because they use otherwise wasted energy. Going back to the very first chart, a perfect compressor doing 100lbs/min at a pressure ratio of 4 would need almost 150hp. Given the option of taking that from the engine crankshaft or the exhaust energy, we'll take the exhaust energy. That's the reason why pretty much every diesel engine and the majority of gasoline engines use turbos instead of superchargers. So does the turbo engine make 150hp more than the supercharged engine? The answer is no because the turbine wheel and turbine housing create back pressure in the engine reducing its volumetric efficiency. But a turbo engine will still make significantly more power than a supercharged engine given the turbo is properly sized.
Sizing of the turbine wheel is important so as to get the maximum efficiency from it. Our worst case scenario of the 2.0L engine, 60% efficient compressor, 50lbs/min mass flow rate, 2.75 PR, and 122F air inlet temperature requires 92.4 hp of shaft power from the turbine to drive the compressor wheel. A 100% efficient turbine wheel would need to get 92.4 hp worth of energy out of the exhaust. However, like compressor wheels, there’s no such thing as a 100% efficient turbine wheel.
Throw in some moderate turbine efficiency and you end up needing a lot of exhaust power to spin a compressor.
Plugging in a value of 60% for turbine efficiency, we can see how much energy needs to be pulled from the exhaust based on the temperature of the air going into the turbo. The difference in power required going from 77F and 122F is a lag inducing 11.9 hp, or about 8%.
So what have we learned? Maximizing compressor and turbine efficiencies reduces the exhaust energy required to get a turbo going. Sucking in colder air instead of hot air also makes compressors happy. The final conclusion to all of this is that math is cool, stay in school!