Instead of the theory of operation and mathematical explanations regarding heat transfer co-efficients, effective surface areas etc., we’ll look at the effects of charge cooling.
The pressure, temperature and volume of a fixed mass of gas are related by a rule of physics called the Ideal Gas Equation:
PV/T = Constant,
where P = absolute pressure, V = volume and T = absolute temperature.
All it really says is that if you change any one of these parameters, at least one of the others will change too.
Another way to write this is: P1V1/T1 = P2V2/T2,
where, say, P1, V1 & T1 describe our ambient air entering the air cleaner and P2, V2 & T2 describe the air coming out of our turbocharger compressor.
You might think that, as it’s called the “ideal” gas equation, it doesn’t really apply in the real-world but at the low-ish pressures and temperatures we’re talking about, it’s pretty accurate. [Though for super-high pressure steam boilers in power stations, for example, the mathematics can get quite a bit trickier.]
Now, we’ll modify the Ideal Gas Equation a bit to suit our purposes. [Any theoretical physicists out there, please just come along with us for a while, OK?]
As mentioned earlier, the equation applies to a fixed mass of gas. In our case let’s say this is the mass of air drawn in through the air cleaner of our engine in one second, while we’re driving at full throttle and heavy load. The volume of our air is related to the mass of our air by the equation:
V = m/d, where m = mass (grams) and d = density (grams/Litre),
and so, if we replace “V” in our equation, we get: P1m1/T1d1 = P2m2/T2d2.
As the mass of air leaving our turbocharger is the same as the mass of air entering it, m1 = m2 and our equation becomes:
P1/T1d1 = P2/T2d2
We can rearrange this to:
d2 / d1 = post-turbocharger density/pre-turbocharger density = P2/P1 x T1 /T2.
Before we go on, we do need to clarify our pressure and temperature measurements. We discussed the concept of absolute pressure in the first article of the series, that is, pressure above an absolute vacuum. So, to convert from gauge pressure (or boost pressure) to absolute pressure, we need to add 14.7psi or 1.0Bar.
A similar thing applies to temperature. Zero degrees Celsius is obviously not as cold as anything can even get. In fact, that temperature is -273.15°C or Absolute Zero. To convert from Celsius temperature to absolute temperature, we need to add 273.15 to the Celsius temperature.
The units of absolute temperature are Kelvin (K), so 0°C is the same as +273.15K and 25°C is 298.15K etc.
Absolute pressure and absolute temperature are the units we need to make use of our gas equations.