Turbo Tech: Generating Compressor and Turbine Maps

,

Well, you don’t and therefore bundle their inefficiencies together into one value on the turbine map.  So by changing the bearing system in a turbocharger, you change the efficiency values on the turbine map.  What do these turbine efficiency values look like?  Unfortunately, none of the turbo manufacturers make them publicly available from what I can find.  Another very important value not shown on the turbine map is pressure ratio for a given speed line and flow rate.  Turbine pressure ratio and efficiency are both dependent on the compressor wheel attached on the other end along with the turbine housing (A/R and volute shape design being variables).  Why don’t the manufacturers show this data?  Probably because for each turbine wheel, the turbo manufacturers would have to make a map for every combination of compressor wheel, turbine housing, and bearing system out there.  For example, the standard Garrett GT30, 60mm turbine wheel can be paired with four different compressor wheels (GT3071/GT3076/GTX3071/GTX3076) and a LOT of turbine housings (T3 flanged, T4 flanged, divided, all in different A/Rs).  That’s over thirty turbine maps right there for one turbine wheel.

While the general public does not get to see the details of a turbine map, those details are critical for proper turbocharger matching for OEM applications.  The major challenge in determining turbine efficiency is accuracy of measurements of the exhaust.  The properties of the exhaust gas must be very accurately measured before and after the turbine wheel.  By measuring the properties of the exhaust, we can determine the value for its internal energy.  Knowing the values of internal energy pre and post turbine along with the mass flow rate allows us to determine how much power went into the turbine wheel.

Here is another way to look at the power flow through a turbo.  We have exhaust flow going into the turbine with an energy state of E1.  The turbine extracts energy, E3, out of the exhaust flow; the energy the turbine can’t extract from the exhaust flow leaves the turbine at state E2.  The more efficient a turbine, E3 becomes larger and E2 becomes smaller.  Conversely, the less efficient the turbine, E3 is lower and E2 is higher.  Not all of E3 makes it to the compressor as some energy is lost due to friction in the bearing system, E4.  E5 is the end result going into the compressor after taking into account bearing losses and turbine inefficiency.  E7 consists of actual compressor work and compressor inefficiency.  The more efficient the compressor operates, the higher the pressure ratio and/or mass flow rate.  Compressor inefficiency generates heat (do not want) increasing the temperature instead of increasing the pressure or mass flow rate (do want).  On a gas stand, we can measure properties at E1, E2, E6 and E7 allowing us to calculate E5.  Knowing E5 gives us a secondary method to verify overall turbine efficiency (turbine efficiency bundled with the bearing power loss as we have no easy way to separate the two).

So now we know some of the parameters we need to measure, but how do we measure them?  Also, how accurate do we need to be in the measurements?  This is where we need to do a little sensitivity analysis and an error stack-up.  Sensitivity deals with how much the result changes based on one parameter changing.  For example, here is an equation: Y = A * B^3.  If A = 1 and B = 1, then Y = 1.  If A = 2 and B = 1, then Y = 2.  However, if A = 1 and B = 2, then Y = 8!    So as you can see, for the same change in B, the end result drastically changes as compared to the same change in A.

When running any type of test where measurements are taken, there’s always a margin of error.  Electronic transducers are commonly used to measure pressures and temperatures and they come in different levels of accuracy.  They also have a limited range of temperatures in which they will work correctly.  As you can probably guess, the higher the accuracy and temperature capability of the transducers, the more they cost.  The accuracy is most often given as a percentage of the full scale of the transducer.  For example, you can get pressure transducers with an operating range of 0-20 PSIA (pounds per square inch absolute pressure, as opposed to gage pressure) or 0-100 PSIA.  A very high accuracy transducer may have an accuracy of +/- 0.05% of full-scale whereas a less accurate transducer may be +/- 0.25% of full-scale.  For the 0-20 PSIA transducers with an accuracy of +/- 0.05%, that translates into +/- 0.01 PSI.  The 0-100 PSIA transducer with the same +/- 0.05% has an accuracy of +/- 0.05 PSI.

This chart shows the effects of various levels of error in the measurements for calculating compressor efficiency.  I assumed worst case where the directions of error for each measurement create the greatest amount of error in the final calculation.  Taking into account only temperature error, a transducer with +/- 1K accuracy means our final efficiency calculation could be off by a full two percentage points!  If you tell an engineer their compressor efficiency is 75%, +/- 2%, that is not very good; 73% is hugely different than 77%.  Aero engineers tend to stress about tenths of a percent and fight for any 1% efficiency gain they can get.  So obviously, this level of accuracy is not good enough.  I repeated the same process for calculating the magnitude of pressure reading error on the final efficiency value while keeping the temperature error equal to zero.  Finally, I combined both errors together to see the effect on the final efficiency calculation.  A temperature error of +/- 0.1K combined with a pressure error of +/- 0.001 bar creates a final error of 0.39% points which I think is reasonable.  Looking at compressor maps, the efficiencies are only given as integers, so +/- 0.39% would probably accurate enough.