How to Go Fast Faster: The Math Behind Turbocharging. Part 7b: Intercooler Efficiency

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Part 1 is here.

Part 2 is here.

Part 3 is here.

Part 3b is here.

Part 4 is here.

Part 4b is here.

Part 5 is here.

Part 5b is here.

Part 6 is here.

Part 7 is here.

     So now that we have an intercooler, we can calculate its Internal Flow Area (in3), Intercooler Lag (sec), Intercooler Gain (%), Power Loss (%), and ultimately, the Intercooler Efficiency (%) based on some logged data and intercooler/engine specs.

     If we do not know the exact Internal Flow Area, we can always figure it out by some measuring.  We just need the Number of Channels, the Channel Width (in), and the Channel Length (in).  Here’s the easy equation:

Internal Flow Area (in3) =

Internal Flow Area

This equation is really simple.  Just multiply the three dimensions of the intercooler channels, and we get our Internal Flow Area, or basically the volume.

     With all the extra piping of an intercooler, the air takes a longer route from the throttle body all the way into the engine.  This can cause a small lag between the time you actually open up the throttle and the time the intercooled air reaches the engine.  This can be called Intercooler Lag.  To calculate that, we need the Volume/Internal Flow Area (in3) of the intercooler and the Flow Rate (cfm or ft3/min) at a certain rpm.  Then we can approximate the time by a simple equation:

Intercooler Lag (sec) = Intercooler Lag

All we’re doing is diving the Volume of the air by the Flow Rate to get the Intercooler Lag.  But we also have to multiply that by 60 to convert the minutes to seconds, and then divide by 1728 to convert the feet cubed to inches cubed.  Then its all just multiplied by 2, which is a result of the increased airflow going through the engine when going from cruise to boost.

     We can also calculate how much “more” air we’re stuffing into the cylinder by cooling and making the air more dense via the intercooler.  This is called Intercooler Gain, and to calculate that, all we need is the Absolute Temperature (o) of the ambient air, the Temperature before the intercooler (oF), and the Temperature after the intercooler(oF).  We then plug all that into this equation to find our gain:

Intercooler Gain (%) =

Intercooler Gain

So here we’re just dividing the temperature of the air before entering the intercooler by the air exiting the intercooler, ie. the change in temp caused by the intercooler.  We then just subtract by one and then multiply by 100% to get an answer in percent form.

     Unfortunately while the Intercooler Gain does indicate how much extra air should be entering the combustion chamber with the addition of the intercooler, the Intercooler Gain does not equal the same increase in power due to aerodynamic loses inside the intercooler and the piping.  This would be called Power Loss.  We can calculate the Power Loss by using  another formula here, using the Boost-Pressure (psi) of the system, and the Boost-Pressure (psi) after the installation of the intercooler:

Power Loss (%) = Power Loss

We’re adding the air pressure (more commonly called boost) to the atmospheric pressure (14.7) to find the absolute pressure.  We do this twice, as the boost pressure before the installation of the intercooler will be higher because of the aerodynamic drag in the intercooler.  We then divide the absolute pressures, subtract one by all that, and then multiply all that by 100% to find our Power Loss in percentage form.  Hopefully the intercooler won’t have lowered our boost pressure too much, resulting in a minimal Power Loss.

      The last equation in this sequence would then be the calculation of the actual Intercooler Efficiency. The Intercooler Efficiency is found by the temperature removed by the intercooler divided by the temperature rise due to the compressor.  This is similar to the Intercooler Gain, but this number is more applicable to the exact intercooler without influences from the turbo/engine/piping/etc.  This time we need the:

  • Temperature Pre-Intercooler/Post-Compressor (oF)
  • Temperature Post-Intercooler (oF)
  • Ambient Temperature (oF)

     Here’s the equation:

Intercooler Efficiency (%) =

EQUATIONPLACEHOLDER

We’re basically finding the  temperature removed divided by the temperature rise.  As our intercooler has a higher efficiency, it’ll remove more heat, and thus we’ll have a higher nominator.  We want a small as possible denominator, but we obviously can’t change that with the intercooler.  Just muliply the dividend by 100% to change the efficiency to a percentage.

     And that’s your Intercooler Efficiency.  Obviously this can only be calculated with your intercooler installed and with certain equipment, but this is a very accurate way of finding out how your intercooler is performing (considering everything else works perfectly).

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