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Old August 19th, 2006, 04:30   #5
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Default Part 3: Turbo Matching Basics

Now, knowing what you are reading in the map in front of you, the heart of turbo matching involves, quite simply, matching what the engine is capable of taking in, and what the turbo is able to supply, throughout their respective operating ranges.

All you’re doing is plotting points of (boost) pressure versus mass flow rate of the engine (which, among other things, are dependent on engine RPM; engine geometry – bore, stroke, cylinder count, and in more detail, piston speed, L/R ratio, etc.; and volumetric efficiency, which are affected by valve size, timing, lift, port/manifold cross-section, length, design, etc.). Note that this has nothing to do with the turbocharger; here we’re only concentrating on the engine, and if we add a turbocharger, it does not materially affect the volumetric efficiency of the engine, which is defined as:

Volumetric efficiency -- The percentage mass of air that is actually trapped in the cylinders divided by the mass of air that would be theoretically be able to be trapped for the given swept volume of the cylinders at the same prevailing conditions.
The part that I highlighted in bold shows the importance that we’re dealing with a MASS flow, not a VOLUME flow (as discussed in my previous post about turbocharger flow rates), while the italicized part focuses on the fact that volumetric efficiency is a function of the natural breathing capability of the engine (i.e. RPM, geometric and design parameters of the engine), and is NOT significantly affected by externalities like the addition of a turbocharger. That means, for the purposes of calculation, the volumetric efficiency value of the engine DOES NOT CHANGE even if you have 3 bars of boost compared to simply atmospheric!

From here, I have found a very useful online turbo calculator here:

Below is a screenshot of parameters I inputted into the calculator a TDI engine running 2.87 bars of boost:

Here, I had the benefit of extensive test data and information for the R-TDI engine:

And just to repeat for review's sake:

Thanks to the above information, for example, I am able to determine manifold boost pressure (2.87 bar – 27.5 PSI), compressor outlet temperature (191*C), post-intercooler temperature (49*C), and play around with compressor efficiency (65%), intercooler efficiency (83%) and IC pressure drop (1.5 PSI) to get numbers that 1) agree with the test data first and foremost; 2) agree reasonably with the compressor map; and 3) are REASONABLE and REALISTIC values!

Without all this information, I can only use intuition to arrive at a set of REASONABLE and REALISTIC initial values for compressor efficiency, intercooler efficiency, IC pressure drop, and volumetric efficiency. Then I superimpose the initially-calculated pressure ratio – labelled (3) in the turbo calculator worksheet – and LBM air flow (4) onto the compressor map; interpolate the compressor efficiency and iteratively recalculate values on the worksheet until I come to an acceptable convergence with final values.

Note: In the worksheet, ignore the fields for Air:Fuel Ratio and the results for HP, Torque, BMEP and Injector sizing, as they are not at all applicable to Diesel engines!

After all is said and done, I arrived at a mass flow rate at maximum power conditions (27.5 PSI of boost @ 4000 RPM) of 22.37 lb/min, which agrees well with the R-TDI VNT-20 turbo map above (make it an exercise for yourselves to identify the operating point on the map at maximum power).

And here is where I want to make a little plug about something I have been arguing about for years: Even when the R-TDI in this paper is operating at full power and max. boost (190HP @ 4000 RPM @ 27.5 PSI boost), the mass flow, whether you choose my numbers or the numbers in the VW map, is around 22-23 lb/min (10kg/min).

I have debated about the use of massively-sized turbos which can flow many times that capacity. I have explained that volumetric efficiency by definition is independent of boost pressure, and that it is instead a function of engine geometry and design, and has nothing to do with the turbocharger.

That said, the 1.9L R-TDI engine utilizes almost ALL of the useful operating range of the VNT-20 turbo in this example, from right at the ragged edge of surge, until choking and overspeeding @ >180000 RPM.

Sure, there is much to be gained by an even larger turbo than the VNT-20 to move the choke threshold to the right, but in so doing, the WHOLE map moves to the right, including the surge line. It is wishful thinking that you can have a big turbo and not have to worry about surge in the low-end!

All this work was for just one operating point. You will then do the same process for different RPMs at max. boost to get full-load values (but remember that all of the values like compressor/intercooler efficiencies, pressure drop, volumetric efficiency, etc. will NOT remain constant) and you may also choose to calculate part-load scenarios as well.

Lastly, here is a very small listing of book titles I have read that would be good references to learn more about this subject:
- Watson & Janota: Turbocharging the Internal Combustion Engine
- McInnes: Turbochargers
- Challen & Baranescu: Diesel Engine Handbook
- Heywood: Internal Combustion Engine Fundamentals

Damn, I can’t believe I have spent more than 4 hours on this!!!

TDIMeister's German-imported 1998 Audi A4 Avant TDI quattro

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Last edited by TDIMeister; December 15th, 2007 at 16:02.
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