Radiator efficiency

Daggerr said:

The ".... 40 per cent intercooling ...." that Lovesey mentions in his Merlin paper is not an exact number, but merely a rough indication. 35 to 40 % was their objective when they designed the intercooler.

Note also that Lovesey does not call it efficiency of effectiveness.
The efficiency of any heat exchanger is normally defined by the formula that Simon Thomas posted.

The intercooler does not know and does not care what the temperature rise over the supercharger is.
Its performance is only determined by the inlet temperatures of the hot and cold fluids, its heat exchange area A, and its overall heat transfer coefficient U (which depends on fluid velocities and physical properties). When these are all known one can easily calculate the outlet temperatures of the hot and cold fluids.

According to p169 of "The Merlin in Perspective" (RRHT HS2) the Merlin 61 has a full throttle altitude of 23500 ft while delivering +15 psi boost.
So that means that the supercharger must be delivering a pressure ratio of 5.0
At -32 oC ambient and an adiabatic efficiency of about 69 % that would result in a supercharger outlet temperature of 173 oC, which corresponds with a temperature rise of 205 oC.
At an intercooler outlet temperature of 100 oC (according to Hooker) the "percent intercooling" (as defined by Lovesey) is then (173 - 100)/205 = 36 %.

I used an assumed supercharger efficiency of about 69 % to get the 205 oC rise quoted by Lovesey. Probably a few percent too high but the above calculation is just to check whether the numbers quoted by Lovesey and Hooker are plausible.

If the Merlin 61 flies at a different altitude than 23500 ft the ambient temperature will be different, and so will the supercharger outlet temperature, as well as the intercooler outlet temperature, and the newly calculated "percent intercooling" will likely also differ from the 36 % above.

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Daggerr :
69% efficiency doesn't seem too high - turbochargers from my misspent youth had sweet spots in the mid-70s
Thanks for point out my error - it was 205*C temperature rise, not temperature of 205*C - duh...

My 'hang up' is still (IMHO) that the denominator in the formula is for the cooling medium - as you say they delta temperature of the supercharger doesn't matter. And while the heat exchanger area and heat transfer coefficient determine the outlet temperature, it is just the outlet temperature which matters.

With updated numbers (173-100)/.4 = 182.5*C as output fluid temperature needs to be <173*C, that would suggest input temp of -9.5*C; that's a plausible number.
And yes, your results will vary if you fly at different altitude/temperature/power level, etc, etc.

z42 said:

As for the material of the radiator core, I'm not sure that makes much difference for the heat transfer. Copper (and brass AFAIU) used to be a common radiator material, but has largely been replaced by aluminum due to it being lighter and cheaper. Aluminum however requires additional anti-corrosion additives in the coolant.

I think the big advantage of copper is that it's easier to join the parts together with brazing or soldering.

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The P-51B cooling system ran into corrosion issues because it switched to aluminum for the radiator. Rolls Royce was not in favor of aluminum but the problem of differential materials was resolved.

Shortround6 said:

I will also note that radiators themselves were undergoing some radical changes.
View attachment 787638
Hurricane radiator. There are no fins like on a car. There is a "tank" with hundreds of hexagonal tubes running from front to back.
Oil coolers were made the same way.
View attachment 787639
So there was a lot of variation on the amount of area exposed to air vs the amount air exposed to the liquid coolant from radiator to radiator which was going to affect the "efficiency". Not all car makers could make aircraft radiators.

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The biggest change was pioneered by Rolls Royce. Fin and tube radiators are much more efficient. Air is much worse at heat transfer than water hence the fins dramatically increase the air side surface area.

Daggerr said:

The ".... 40 per cent intercooling ...." that Lovesey mentions in his Merlin paper is not an exact number, but merely a rough indication. 35 to 40 % was their objective when they designed the intercooler.

Note also that Lovesey does not call it efficiency of effectiveness.
The efficiency of any heat exchanger is normally defined by the formula that Simon Thomas posted.

The intercooler does not know and does not care what the temperature rise over the supercharger is.
Its performance is only determined by the inlet temperatures of the hot and cold fluids, its heat exchange area A, and its overall heat transfer coefficient U (which depends on fluid velocities and physical properties). When these are all known one can easily calculate the outlet temperatures of the hot and cold fluids.

According to p169 of "The Merlin in Perspective" (RRHT HS2) the Merlin 61 has a full throttle altitude of 23500 ft while delivering +15 psi boost.
So that means that the supercharger must be delivering a pressure ratio of 5.0
At -32 oC ambient and an adiabatic efficiency of about 69 % that would result in a supercharger outlet temperature of 173 oC, which corresponds with a temperature rise of 205 oC.
At an intercooler outlet temperature of 100 oC (according to Hooker) the "percent intercooling" (as defined by Lovesey) is then (173 - 100)/205 = 36 %.

I used an assumed supercharger efficiency of about 69 % to get the 205 oC rise quoted by Lovesey. Probably a few percent too high but the above calculation is just to check whether the numbers quoted by Lovesey and Hooker are plausible.

If the Merlin 61 flies at a different altitude than 23500 ft the ambient temperature will be different, and so will the supercharger outlet temperature, as well as the intercooler outlet temperature, and the newly calculated "percent intercooling" will likely also differ from the 36 % above.

Click to expand...

The 40% intercooling is a measure of how close the water temperature can get to the air temperature. Ideally the water and air temperature would be equal but the heat exchanger would be infinitely large (literally). The approach temperature is defined as the temperature difference between the two fluids as they leave the heat exchanger. The trade off for a heat exchanger design is that each degree you lower the approach increases the surface area required as compared to the preceding degree (diminishing returns). For example in my cooling tower design book there is a graph of tower size vs approach temperature. A 15 F approach is assigned as unity. To go to a 5 F approach would increase the size of the tower by a factor of 2.3. Conversely an approach temperature of 25 F would almost halve the size of the tower down to 0.6. The 40% would represent the compromise between the temperature of the air entering the engine vs packaging.

don4331 said:

Aside: Should we be including oil cooling in our radiator efficiency discussions - as noted if you let water/glycol get too warm minimizing the 'radiator' size, you increase the size of the oil cooler.

And oil coolers come with their own set of issues - mainly what I know as 'coring' where the oil in the outer tubes gets cooled so much that its viscosity increases and flow reduces - which quick becomes a feedback loop. The result is the only oil flowing through the oil cooler is going very fast through limited tubes and not efficiently cooling.​

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Good point. I think if you want to take full advantage of the higher boiling point of pure ethylene glycol cooling you'd need at the very least different lubricants as well that can work at an engine operating temperature approaching 190C, or even higher if pressurized cooling is used. Probably other engine components would need to be changed as well. And with higher CHT what advantage you get in reducing the size of the radiator perhaps gets eaten away by less detonation margin? I don't think even in Formula 1 was anything like this tried back when innovation was less restricted than today.

As for oil coolers, yes that's another interesting issue. IIRC some liquid cooled engines didn't have separate air-oil coolers but rather an oil-water heat exchanger and thus piggybacking on the main water cooling circuit, maybe even integrated into the engine block. Maybe it was Jumo 211/213?

I have an old text book on engine design, rather basic as it is only about 470 pages not including the index
There are several pages on intercoolers and since this was an American book most temperatures are given in F and they are looking at things from the intercooler between stages (cooling between turbo and engine supercharger) and not cooling between engine supercharger and intake valve.
US army wanted the intake air to the engine supercharger to never exceed 100d F at rated altitude to simulate a hot day sea level condition, they wanted 90d F most of the time. As the war went on and the turbos and fuel got better they could use the turbo to raise the intake pressure at the carb for more power but this often meant problems as the intercooler was not designed to deal with a greater mass of hotter air. All US service intercoolers were air to air. So the US was looking at a different design specification than the British (or Germans?).
They wanted not more than 1.25in Hg pressure drop through the intercooler at normal sea level rated power. The total drop in pressure from the outlet of the 1st stage to the carburetor may not exceed 1.75in Hg. The air flow may be taken at 0.110lb/(bhp)(min). The entire system must take 20 psi without damage or leaking as an indication of ability to withstand backfires.
There are two simple charts ( and several not so simple) with one showing the required air flow to get into the target area of cooling. This is by ratio of cooling air to engine air.
At a 1:1 ratio they figured about 40 degrees F of cooling of the intake charge. at a 2:1 ratio they could get about 60+ degees of cooling and at 3:1 a smidge over 70 degrees. 5:1 got about 76-77 degrees and the diminishing returns meant most intercoolers were designed to be between 1:1 to 3:1.
The other simple chart shows the temperature rise through an Auxiliary supercharger that is trying to maintain 29.92 in Hg (standard sea level pressure) that is 65% efficient.
You will get a 100d F rise at about 12,000ft and a 175 degree rise by 20,000ft. But of course the air is cooler at altitude. At 20,000ft on a standard day the air is 71 degrees F cooler than sea level.
What happens in the engine supercharger is not addressed in this chapter.

There are chapters on both liquid cooling and on air cooling of engines. Book was published in 1943 so perhaps actual secret stuff was not mentioned?

Book is

and if you can get it for 15-20 dollars it seems like a good deal if you are interested in this stuff.

Yup, just as I remember things about discussion of heat exchangers and exchanging heat, it cant be that complicated can it? Oh yes it can.