Concorde engine intake "Thrust"

[goarnaut]

Trying to Post A Sketch ut It Won't Let Me...

The math is quite straightforward and can be found in any good engine text or fluid mechanics text...but that does not help us understand the physical principles behind it...


I have already given the momentum equation involved which is a statement of Newton's Second Law of Motion...which we mostly know as F = mass times acceleration...


In fact the Second Law tells us that a force results from a change of momentum...In differential form F = m * a becomes...F = m * dV / dt...which means a mass that experiences a velocity change (differential of V with respect to time) is experiencing a momentum change...


Of course momentum must be conserved...just as mass or energy must be conserved...if a car collides with another car it loses its momentum as it stops...but the other car gains momentum as it is shoved forward...


Same thing with a flowing fluid... if it goes into a control volume such as an engine intake with a certain amount of momentum...and then loses a good part of that momentum...what happens to it...?...it is transferred to the control volume...ie the engine...which is attached to the airplane...


An impulse is simply a change of momentum...when we accelerate a hot gas stream out the tailpipe we impart a change of momentum to that mass flow...the result is reacted by the engine which is attached to either an airplane or a test stand...in either case a change of momentum in the forward direction means thrust...

If we were to take an engine inlet duct (a diffusing duct that has a smaller hole at the front than at the back) and bolt it to the floor inside a wind tunnel... and then blow air at 500 mph through that duct...what do you think would happen...?


If we allowed the mount to slide back and forth...which way would it slide...forward or backward...?


What if we turned the duct around and now had the big hole at the front and the little hole at the back...?...which way would it move now...?...isn't this how a wind sock works...?...which way does it want to go...?...back of course...


And have you ever seen a wind sock where the wind is blowing into the little hole...?...and coming out the big hole in the back...?...of course not...


So why would that intake duct that is shaped just like a wind sock that is turned around front to rear want to move back...?...of course it is going to move forward...


The reason is that the impulse (change of momentum) gets bigger as we go from front to back...

Now we can work out an example like the illustration...we have an airplane flying at 250 m/s...and the inlet opening is 1 m^2...the mass flow is 100 kg/s...let's say the opening at the aft end of the duct is 1.25 m^2...which has the effect of slowing down the flow and increasing static pressure...at the same time the flow loses momentum as it slows down...


We recall that Force = mass flow * velocity...so the force at the front of the duct is 250 m/s * 100 kg/s = 25,000 newtons...a little over 5,000 lb of force...


If the flow slows down to 125 m/s at the aft end...its total force will now be 125 m/s * 100 kg/s = 12,500 N...(mass flow does not change of course...owing to conservation of mass)...


So the fluid flow has lost 12,500 lb of force...but we need to account for all the forces acting on that control volume...we see that there is pressure from the wall pushing on the fluid that is equal and opposite to the pressure of the fluid that is pressing on the wall...since pressure acts exactly perpendicular to any wall...we see that a lot of the arrows are canted in the forward (thrust) direction...this gives us a clue that the sum total of all those little arrows is going to end up as a net forward force...


We can integrate all the pressure forces across that surface and expend a lot of math...or we can just do a simple multiplication of the pressure times the area of the inlet and outlet respectively...that will give us the answer...


So we see that our static pressure at FL350 is 22,500 N/m^2 (22.5 kPa)...and our intake area is 1 m^2...so the total pressure force pushing back is 22,500 N...


At the aft end our pressure is 1.5 times higher...this is a subsonic plane and slowing down the flow from ~M0.8 to ~M0.4 will result in a static pressure increase of that amount...


Our duct exit is 1.25 m^2...so our total force at the back is 22,500 N * 1.5 * 1.25 m^2 = ~42,000 N...So we have gained nearly 20,000 N from the pressure on the engine duct inside surface...!...


We subtract the 12,500 we lost from the flow slowing down...and we are still ahead y more than 7,000 N...an engine of that mass flow would make perhaps 30,000 N total thrust so that would be a good part of it right there...nearly ¼... of total thrust...


So yes the engine inlet is making thrust...that is very real...it is just that we are used to thinking purely about thrust as mass flow times velocity coming out of the tailpipe...and that is the simplest way to account for the sum total of all the physical forces going on in the engine...


However...if you want to do a more thorough line-by-line accounting...then we must start at the tip of the engine and do this impulse analysis for each component...we would then go on and do this for the compressor...the burner...the turbine...and the jet nozzle...and we would find that the net thrust still remains the same...but it is the physical forces of pressure and momentum and impulse that do their work at each point along the way...


Regards,


Gordon.