Questions About Stagnation Temperatures
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Questions About Stagnation Temperatures
Okay, stagnation temperatures are the areas on the plane where the air is slowed all the way down to zero right? How much of an airplane's nose and leading edge experiences these temperatures? I'm guessing it couldn't be too much considering most of the air would be slowed down to a lower mach number, but not all the way to zero.
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From: Brighton
Not quite there.
Stagnation points are the places where the airflow stops. That's where the stagnation temperature is reached.
Where?
A point on the nose;
A line down the leading edge of each flying surface;
A line round the intake lip of each engine;
(In the case of the second and third, only if the leading edges are perpendicular to the local airflow) for example.
And, yes, elsewhere there is a lesser but variable amount of kinetic heating.
How much heating? Rule of thumb, stagnation temperature increase above ambient in Celcius is TAS(knots)squared/100
example: 500 kt TAS, increase 25 deg C.
Stagnation points are the places where the airflow stops. That's where the stagnation temperature is reached.
Where?
A point on the nose;
A line down the leading edge of each flying surface;
A line round the intake lip of each engine;
(In the case of the second and third, only if the leading edges are perpendicular to the local airflow) for example.
And, yes, elsewhere there is a lesser but variable amount of kinetic heating.
How much heating? Rule of thumb, stagnation temperature increase above ambient in Celcius is TAS(knots)squared/100
example: 500 kt TAS, increase 25 deg C.
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From: Blighty (Nth. Downs)
kenparry,
That rule of thumb for estimating the increment to be applied to SAT to get TAT seems very neat and simple.
For the record, did you mean:
[TAS/100]^2
(where TAS is in knots) ?
Chris
That rule of thumb for estimating the increment to be applied to SAT to get TAT seems very neat and simple.
For the record, did you mean:
[TAS/100]^2
(where TAS is in knots) ?
Chris
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From: outside the box
Adiabatic temperature change vs Kinetic Heating
First.
At stagnation point, the flow is at zero speed relative to the body for a very small layer of molecules at the surface of, f.ex., the leading edge. This means that this amount of still, warmer air is too small and will not affect the main airflow.
Now about stagnation temperature.
The air is a compressible mix of gases which changes characteristics as speed is increased. At subsonic speeds the air is thought to be isentropic and therefore the first law of thermodynamics can be applyed. That is that as the dynamic pressure decreases (velocity/IAS) the static pressure and temperature of air is increased and vice versa. All this happens adiabatically, meaning without any energy loss (heat) from the system. Because of all this, the stagnation temperature will be equall to Total Air Temperature.
TAT=SAT+Ram Rise
So Ram Rise is what we measure with the rule of thumb mentioned above..
(The exact formula is RR=TAS^2/2Cp , TAS in kt, and Cp is the specific heat for constant pressure, so a more exact rule of thumb would be
RR=[TAS/87]^2 ) These equations do NOT take account for Kinetic heating
Ofcourse there is always some friction from the air and this is what is called Kinetic Heating/Aerodynamic Heating but for subsonic speeds this is almost negligible. The modern TAT measuring probes have a recovery factor q=0.98, so the ADC of the aircraft multiplyes the above equation with q to get the correct TAT.
At supersonic and hypersonic speeds the equations used for measuring TAT are different as the air starts behaving as a non isentropic fluid.. Meaning that the Stagnation temperature will not be equal to TAT..
Jetpipe.
At stagnation point, the flow is at zero speed relative to the body for a very small layer of molecules at the surface of, f.ex., the leading edge. This means that this amount of still, warmer air is too small and will not affect the main airflow.
Now about stagnation temperature.
The air is a compressible mix of gases which changes characteristics as speed is increased. At subsonic speeds the air is thought to be isentropic and therefore the first law of thermodynamics can be applyed. That is that as the dynamic pressure decreases (velocity/IAS) the static pressure and temperature of air is increased and vice versa. All this happens adiabatically, meaning without any energy loss (heat) from the system. Because of all this, the stagnation temperature will be equall to Total Air Temperature.
TAT=SAT+Ram Rise
So Ram Rise is what we measure with the rule of thumb mentioned above..
(The exact formula is RR=TAS^2/2Cp , TAS in kt, and Cp is the specific heat for constant pressure, so a more exact rule of thumb would be
RR=[TAS/87]^2 ) These equations do NOT take account for Kinetic heating
Ofcourse there is always some friction from the air and this is what is called Kinetic Heating/Aerodynamic Heating but for subsonic speeds this is almost negligible. The modern TAT measuring probes have a recovery factor q=0.98, so the ADC of the aircraft multiplyes the above equation with q to get the correct TAT.
At supersonic and hypersonic speeds the equations used for measuring TAT are different as the air starts behaving as a non isentropic fluid.. Meaning that the Stagnation temperature will not be equal to TAT..
Jetpipe.
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From: London, GB
No, it is used in lieu of the Mach number owing to a rearrangement of the conventional form, T0/T1 = 1+[(γ-1)/2]*M^2, noting M^2 = u^2/(γ R T1) in a calorically perfect gas.
Cp can be written γR/(γ-1) and the expression u^2/2cp = T0-T1 is consistent with this. Rewriting as [u/sqrt(2cp)]^2 you'll see that expressing u (TAS) in knots requires you to scale sqrt(2cp) accordingly (i.e. by 3600/1852 for the conversion from m/s to kts) to achieve the same result.
Cp for air (at room temperature - i.e. vibrational modes frozen out) is about 1004.5 J kg^-1 K^-1 so you can play with the numbers to see where the approximate constant of 87 comes from.
Cp can be written γR/(γ-1) and the expression u^2/2cp = T0-T1 is consistent with this. Rewriting as [u/sqrt(2cp)]^2 you'll see that expressing u (TAS) in knots requires you to scale sqrt(2cp) accordingly (i.e. by 3600/1852 for the conversion from m/s to kts) to achieve the same result.
Cp for air (at room temperature - i.e. vibrational modes frozen out) is about 1004.5 J kg^-1 K^-1 so you can play with the numbers to see where the approximate constant of 87 comes from.
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From: outside the box
Since equations link airspeeds to eachother
- EAS=TAS sqrt(ρ/ρ0)
- M = TAS/sqrt(γ R T)
The Ram Rise equations are linked in the same way. We choose for which airspeed we want the TAT-SAT equation to be solved for, TAS, Mach or EAS.
- TAT - SAT = TAS^2 / 2Cp
- TAT - SAT = 0.5 M^2 (γ-1) SAT
- TAT - SAT = (ρ0/ρ) EAS^2 / 2Cp
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Jane-DoH, as I wrote in previous post, these equations can only be applied for subsonic speeds to get an exact answer. I guess we could use them to answer your example with some kind of correcting factor ''q'' as the aerodynamic heating at M 2.0 is still low. But then we would be assuming laminar isentropic flow for supersonic airspeeds which is quite wrong, however as i said, we should end up with an answer close to what we would have if we used the correct (quite complex) equations for super/hypersonic speeds..
So what do we know, M=2.0 and SAT=220 Kelvin
TAT - SAT = 1/2 M^2 (γ-1) SAT q
(a reasonable value for q at M 2.0 would be i think 3-5%, q= 1.03-1.05)
TAT - SAT = 0.5*4*(1.4 - 1)*220*1.05
TAT - SAT = 184.6 degrees of Ramrise
TAT= 184.6 + SAT = 404.6 K = 131 Celsius, would be heating up the leading edges of the aircraft..
Hope this helps
Jetpipe.
So what do we know, M=2.0 and SAT=220 Kelvin
TAT - SAT = 1/2 M^2 (γ-1) SAT q
(a reasonable value for q at M 2.0 would be i think 3-5%, q= 1.03-1.05)
TAT - SAT = 0.5*4*(1.4 - 1)*220*1.05
TAT - SAT = 184.6 degrees of Ramrise
TAT= 184.6 + SAT = 404.6 K = 131 Celsius, would be heating up the leading edges of the aircraft..
Hope this helps
Jetpipe.
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Jetpipe
I did not know that
Where do you derive "q" from?
Understood. What formula is that out of curiousity?
Jane-DoH, as I wrote in previous post, these equations can only be applied for subsonic speeds to get an exact answer.
I guess we could use them to answer your example with some kind of correcting factor ''q'' as the aerodynamic heating at M 2.0 is still low.
But then we would be assuming laminar isentropic flow for supersonic airspeeds which is quite wrong, however as i said, we should end up with an answer close to what we would have if we used the correct (quite complex) equations for super/hypersonic speeds..
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From: france
supersonic aerodynamics
JD,
it might be the formula of Raleigh for supersonic speeds :
Pt-p/p =[ 166,92158M^7/(7M^2-1)^2,5]
-1
Pt = Total Air Pressure
p = Static Air Pressure
M^7 = Mach to the power 7
M^2 = Mach to the power 2(square)
^2,5 = power 2,5
/ = diveded by. ...
hope this helps, but don't try to commit this formula to memory.
bm.
it might be the formula of Raleigh for supersonic speeds :
Pt-p/p =[ 166,92158M^7/(7M^2-1)^2,5]
-1 Pt = Total Air Pressure
p = Static Air Pressure
M^7 = Mach to the power 7
M^2 = Mach to the power 2(square)
^2,5 = power 2,5
/ = diveded by. ...
hope this helps, but don't try to commit this formula to memory.
bm.
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From: New York & California
blackmail
And this gives you the "q-factor" or does it give you the stagnation temperature? I don't see any temperature figures in there...
BTW: How do you determine total air-pressure? Can I just set it as an "x-value" and then fill in the rest, then solve for it?
JD,
it might be the formula of Raleigh for supersonic speeds :
Pt-p/p =[ 166,92158M^7/(7M^2-1)^2,5] -1
Pt = Total Air Pressure
p = Static Air Pressure
M^7 = Mach to the power 7
M^2 = Mach to the power 2(square)
^2,5 = power 2,5
it might be the formula of Raleigh for supersonic speeds :
Pt-p/p =[ 166,92158M^7/(7M^2-1)^2,5]
-1 Pt = Total Air Pressure
p = Static Air Pressure
M^7 = Mach to the power 7
M^2 = Mach to the power 2(square)
^2,5 = power 2,5
BTW: How do you determine total air-pressure? Can I just set it as an "x-value" and then fill in the rest, then solve for it?
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From: London, GB
these equations can only be applied for subsonic speeds to get an exact answer
And this gives you the "q-factor" or does it give you the stagnation temperature? I don't see any temperature figures in there...
BTW: How do you determine total air-pressure? Can I just set it as an "x-value" and then fill in the rest, then solve for it?
Last edited by selfin; 20th April 2011 at 23:53.
