Tat

[jtr]

Anyone give me an idea of what sort of wing surface skin temperature you might get compared to the actual TAT indication. Talking cruise FL's Mach .85ish?? This is re a discussion about fuel cooling on long haul.

[CJ Driver]

Temperature of airflow over the wing

I'm extrapolating from general aerodynamics, not asserting a certain answer, but I would expect the airflow across the surface of the wing to be cooler than ambient for a subsonic aircraft.

At the leading edge of the wing, there may be a degree of compression taking place, leading to a small rise of temperature (as there is when the airflow hits the nose of the aircraft, the pitot tube, the air temperatuer probe, and anything else that sticks out). But, as we all know, lift is caused by the reduced air pressure of the airflow as it accelerates across the wing - since the air adjacent to the wing is at a lower pressure than ambient air, I would expect there to be a corresponding cooling effect.

The extent of the cooling (relative to ambient) will depend on the wing geometry, and also on the speed - as you go faster the effects of friction will counteract the effects of the pressure drop, and I suspect that in supersonic aircraft the net result is a warming of the wing skin.

Comments anyone?

[John Farley]

There could be a fair amount of skin heating from the sun's rays if in the clear on top

[Blip]

Don't forget that the pressure on the upper surface of the wing is still a positive pressure, i.e. putting a downward pressure on the upper surface of the wing. It's just that the downward pressure is less than the ambient pressure.

You are right that this reduction in downward pressure on the upper surface of the wing will cause a temperature drop.

But don't forget the lower surface of the wing too. It will experience an increase in upward pressure above ambient and so will experience an increase in temperature. It's just that the amount of change in this upward pressure is less than the change in downward pressure on the upper surface.

Also there would be temperature rise due to surface friction.

The net result???

[jtr]

Appreciate the input.
If the air is still moving, then all the ram rise has not been taken out of it, thus even at an under wing point (higher pressure), I do not believe the temperature will be the same as the TAT as measured. In fact, only at the l/e stagnation point should it be the same as the TAT figure.(all ram effect accounted for)
Therefore, shouldn't it be possible for the fuel temp to fall below the TAT figure, if you sit there long enough? (discounting fuel cooled oil coolers/IDG's etc)?

[safetypee]

The discussion and any calculation of TAT may be too generalized to give a practical answer. The fuel temp in a particular aircraft will depend on many variables such as tank location, structure, location, and any fuel re-circulation. Most aircraft where fuel temp is important will have a fuel temp measurement system. In those aircraft that do not then it is necessary to establish the correlation between the measurement of TAT (including TAT system errors) and actual fuel temp, this is normally established by flight test. Thus, in extreme, it may be possible for the fuel to be colder than the indicated TAT.

[John Farley]

Now we see what you are thinking I have to say that I would guess that the radiant heating temp rise of the wing upper surface (potentially in double figures of degrees even for a light coloured shiny surface) will swamp any such aerodynamic effects. Lower surface will stay nice and cool though!

[CJ Driver]

Ram Effect, and a surprising review of lift

OK chaps, two separate corrections to the thread so far.

First, especially for Blip, one of those perhaps astonishing little revelations - on most aerofoils, the air accelerates across the top, AND across the bottom of the wing, especially at cruise angle of attack. In other words, there is low pressure both above, AND BELOW the wing. The reason that you get lift is that the pressure is rather lower above the wing than below it, so the net lift vector is upwards. For those of you who have lost your aerodynamics textbooks and are disinclined to believe me, take a ride in a fabric high wing aircraft with slightly tired coverings. Sure enough, you will see that the fabric "balloons" downwards on the bottom of the wing in the cruise - because of the low pressure below the wing.

Alternatively, just remember, in one of those witty (?) memory items, that "Lift Sucks".

And now for JTR:
RAM rise is the temperature increase caused as a direct result of compressing the air. The compression is because you are "ramming" the air against something (like a pitot tube, or a wing leading edge). Actually of course the air was stationary, and the airplane was pressing into it, but you get the idea. But that temperature rise was completely reversible (excluding effects to do with condensing out the moisture content, which for our purposes we will ignore) such that as soon as you stop compressing that parcel of air, and return it to ambient pressure, it will return instantly to ambient temperature as well - it will not "stay warm". So, in the shock wave at the wing leading edge (where compression is taking place) the temperature will be higher than ambient. Just an inch or two further back, where the air has already started to accelerate over the aerofoil, the pressure will already be lower than ambient, and so also will the air temperature.

Some further expansion on the original question:
RAT/TAT is actually only "true" at the temperature probe. That is, it is comprised of the ambient temperature (SAT or OAT), plus the ram rise caused by sticking the probe out into the airflow and thus compressing the air at the probe. Although, for example, your engine power settings might be calibrated to RAT/TAT, that doesn't actually mean that the temperature at any other point on the airframe, wing, engine inlet or whatever is actually at RAT/TAT. Local aerodynamics will mean that the compression at those points will, in general, be different, and therefore so will the local temperature rise. I agree with your suggestion however that at a few specific points on the airframe, and in particular the wing stagnation point, the temperature will also be very close to RAT/TAT.

As indicated earlier though, the air pressure surrounding the rest of the wing is not compressed, so RAT/TAT does not apply. In fact, the air surrounding the wing is at a lower pressure than ambient - that's how you are getting lift remember, because lift sucks. So not only is the air around the wing not as warm as TAT, it's actually going to be colder than SAT/OAT.

Which means your wing fuel gets very cold after a while. Unfortunately how cold is a function of not only OAT but also skin friction, insulation properties of the tank bladders (where fitted), radiation/insolation, thermal mass of the fuel, and perhaps more importantly all the heating from the fuel systems themselves.

[jtr]

I think I get the point you are making John, however the joys of long haul are such that in my last trip, I did not see the sun for the entirety of two sectors (about 24 hours airborne, give or take).

So if this is the radiant energy you are speaking of, then I see little of it.

CJ, many thanks for your detailed explanation, however, my question (yes it is a broad one) still goes unanswered.

Is there any likelihood of the fuel temp getting significantly lower than the TAT.

By way of example, I have seen temperatures in the order of
-70 SAT,
fuel temp -41.
-40 TAT

Now my concern is that with an engine shut down (744), and the flight continuing to dest, the only heat source for 50 odd tonnes of fuel is the fuel/oil heat exchanger for the operating engine. So with all that heat sink, and cold temps, surely the fuel temp could become an issue.
To give some parameters to the query, I am refering to long haul scenarios, e.g. 10+ hours in the cruise. Getting airborne with 160t or so of FOB, you can find yourself 5 or 6 hours later, with 100t of the stuff, now 60deg colder than when you left! (these are extreme, but real numbers)
Interestingly, and this may be merely a reflection of the FCOM's we are given, the A340/330 had an IDG/fuel heat exchanger that had a return to the tank (well I think it did) however the -400 has no tank heating methods that I am aware of. There is a fuel/oil heat exchanger, but it seems to be an intergral part of the engine fuel pumping system. I have a sneaking suspicion that the HYD demand pumps have a fuel cooler of some form, but cannot recollect anything about the eng HYD pumps. QAVION, you awake?

[CJ Driver]

TAT is not the determining temperature

JTR,

Sorry if I was not clear enough. In answer to your question, "Is it possible for the fuel to get colder than TAT?" - the answer is sure, why not? The point of my earlier posting is that the wing skin temperature has got very little to do with TAT, and everything to do with SAT. The temperature of the stagnation point on the leading edge might be TAT, but that isn't where you are storing your fuel. The temperature of the air over the wing skin is a function of SAT and aerodynamic lift, and in particular is COLDER than SAT (which itself is of course a lot colder than TAT). So, in your example with a cruise SAT of -70, the airflow directly adjacent to the wing skin would be colder than -70. I can't tell you how much colder because that's a function of local fluid dynamics, although you might be able to do a back-of-the-envelope guess by figuring out how much "suck" it takes, divided by the wing area, to hold your megajet up in the air, and then making a few broad assumptions about relative pressure between the top and bottom of the wing.

Even if you assume that the wing surface airflow is at SAT, since you are saying that after a long cruise the relative temperatures reach a steady state of SAT=-70, Fuel Temp =-40 then it sounds like your heat exchanger is able to maintain a 30 degree differential. All other things being equal, and taking a large pinch of salt with this, if you lost half of the heat source, you might reasonably expect to maintain 15 or more degrees of differential. (More, because heat losses would reduce as the fuel temp approaches SAT). So - and again I emphasise this is back-of-an-envelope stuff - you might expect to see perhaps -50 to -53-ish if you lost half your heat.

In practice, you may not lose half your heat when you shut down an engine. I have no idea how the system is set up, but you might find that with one shut down you actually get more heat from the remaining engine than when both are running, so that the temperature is not as bad as -50. This is right around the freezing point of Jet A1 by the way, although well below the freezing point of Jet A (which can be up to -40). Since you are already operating with the fuel at -40, I assume you are on Jet A1 already.

Finally, I know that Boeing have a software product called the Fuel Temperature Prediction Program for the 777 that models wing airflow temperature, insolation, friction warming, and contributions from the heat exchangers, fuel pumps, etc., to allow operators to plan things like polar routes. I don't know whether you have a version for your type, but just to confirm all the above waffle - in the FTPP examples I have seen, in routine ops (not OEI), the fuel temperature falls below TAT (but stays above SAT).

[jtr]

Thanks CJD, that was what I was thinking as well. The Boeing texts all refer to TAT as if it is some type of limiting factor, which was what I was having difficulty grasping, (as you can see). Queue Boeing Muzac...

...fuel temperature decreases toward TAT

TAT can be raised in one of three ways....

Thanks to all

[bookworm]

The temperature of the stagnation point on the leading edge might be TAT, but that isn't where you are storing your fuel. The temperature of the air over the wing skin is a function of SAT and aerodynamic lift, and in particular is COLDER than SAT (which itself is of course a lot colder than TAT).

I disagree with that, CJ Driver. You're ignoring the boundary layer.

The problem is that while the air at the outer edge of the boundary layer is indeed travelling at the freestream velocity (or faster if the surface is lifting), the viscosity of the air means that the velocity (with respect to the surface) falls off to close to zero at the skin.

Because of conduction through the air, it's not as simple as the skin acting like a stagnation point and the skin temperature being equal to the TAT. The skin temperature (on the assumption of a skin that is neither a source nor sink of heat) is SAT + r*(TAT-SAT) where r is a temperature recovery factor. r depends on the thermodynamic properties of air and is about 0.85. So the temperature rise, in effect due to skin friction, is 0.85 times the ram rise. It's this skin temperature that you're likely to be measuring with a simple OAT indicator, unless it's deliberately set up to measure TAT. Thus the skin temp is just 15% of the ram rise less than the TAT.

Moving to the lifting wing case, the pressures, and therefore temperatures, at the outer edge of the boundary layer do indeed decrease over both surfaces, particularly the upper surface. If you make some assumptions about the likely ratio of the peak pressure coefficient to the mean pressure coefficient, you can see that the temperature reduction is proportional to wing loading, and has some dependence on the ambient pressure.

I ran the numbers once and deduced that for typical light aircraft wing loadings, points on the skin can be 1 degC below the indicated OAT, and for big jets it can be as much as 10 degC. I'd hope that this is consistent with your FTPP.

[safetypee]

An interesting problem of low fuel temp jtr, but normally the flight manual states the limiting value (from memory JP4 is most critical). If the minimum fuel temp is reached then the aircraft must descend into warmer air; crew action required.

Even more practical, with one engine inoperative I presume that the aircraft would not sustain very high altitude (low air temp) and with drift down / cruise in warmer air at lower altitude the fuel temp problem is self correcting.

[Blip]

Thanks for that CJ Driver.

What you say makes sense really when you consider that a symmetrical airfoil at O degrees has a symmetrical reduction in pressure on both the upper and lower surfaces and as you say, at typical angle of attack at cruise speed would make for a low angle of attack.

The annoying thing is, I have checked the reference that I have (Aerodynamics for Naval Aviators. ISBN 0-89100-370-3) and it depicts Airfoil Pressure Distribution three times with diagrams.

The first on page 17 indicates both higher and lower pressure than ambient on the lower surface of the wing (the higher pressure along the forward half and the lower pressure along the rear half.)

The second one on page 19 clearly indicates higher than ambient pressure along the entire lower surface of the wing.

And on page 48 it indicates lower than ambient pressure on both the upper and lower surfaces with what you describe, that is that the pressure reduces more on the upper surface than it does on the lower surface.

No wonder there is confusion about this.

Anyway I don't want to change the subject. TAT vs fuel temperature. It's an interesting discussion.

[jtr]

Safetypee, you have now highlighted another problematic area. On occaisions, you will find yourself in the above scenario, with a low fuel temp warning (but carrying Jet A-1) and at a cruise altitude that would see a temp decrease with descent, unless you take a hit of something like 10,000'. Not an issue usually for us, as with A-1 we still have 7 degrees up our sleeve, but still an interesting situation.
Plenty of what-ifs when you start factoring in terrain, en-route airfields available etc.