How does the engine produce aerodynamic lift at high angle of attack?

Question

This answer asserts that "at high angle of attack the engine is producing aerodynamic lift". In the context of that answer, we are concerned about the increased torque that raises the nose of the aeroplane with respect to the center of gravity, so we should narrow down our interpretation of the otherwise vague word "lift" as the force component that is perpendicular to the wing or fuselage of an aeroplane. We define the angle of attack as the angle between the fuselage and the incoming airflow direction at infinity (shorthand word for "reasonably far away"). It is very different from the angle of the fuselage makes with the horizontal at high speed while very close to the latter at very low speed. It puzzles me in two ways.

1. It claims the engine itself produces fuselage-perpendicular force in addition to the thrust parallel to the fuselage and wing, despite the thrust of the engine is directed parallel to the fuselage and thus the wing. How is that perpendicular force produced?

2. It claims that fuselage-perpendicular force thus produced is dependent on the angle of attack. How does that work?

I would like to see a technical elucidation of this claim or some references supporting or refuting it, best if they come with mathematical derivation.

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Edit:

Some answers below observe that when the plane moves, without engine turned on, against the airflow, part of the airflow curves downwards to conclude that a net force perpendicular to the fuselage is exerted. It is not that simple as looking at part of the flow stream, since part of the flow stream goes upwards above the separating point. The net force is the integration of all the pressure on the whole surface, and the pressure on the opposite side of the object presses in the opposite direction. In fact, in a potential flow, the D'Alembert's paradox shows that the net pressure is exactly zero. Of course, real airflow is not potential flow, but this refutes the overly simple rationale of using downward airflow to derive the fuselage-perpendicular force.

However, when the engine is turned on, especially at high power. The situation may be different so long as the airflow is consistently flowing in the downward direction long after exiting the engine. The momentum of the airflow through the engine may overwhelm other parts of the airflow. But the argument must be more sophisticated than just the downward direction of the airflow.

Answer 1

Anything, even a metal plate creates "lift" when it is under an angle with an air flow. Lift isn't a magical attribute to "wings", it is just a physical consequence of the law of conservation of momentum: when you push a stream of air down, the reactive force is upwards.

the fuselage/engines also act as minor lifting surfaces: when they are under an angle they, inefficiently, redirect the airflow downwards.

For the engine this is also a bit due to the definition of thrust: thrust equations consider an inlet in the same direction of the thrust vector. So the inlet & compressor redirect the flow "downwards" under high angles of attack. - This effect has to show up somewhere: as a lift force generated by the engine.

Answer 2

Thankfully, you have a very clearly worded question. Unfortunately, though, the simple mathematical derivation you desire is not within the scope of a regular answer here (and would be everything but simple).

I agree that some of the other answers confuse lift and thrust, but I think this has more to do with definitions and unclear concepts. So let me first get the definitions out of the way:

Lift is defined as the fraction of the aerodynamic force which is perpendicular to the direction of flow at infinity. This direction is equal (but opposite) to the direction of movement if no wind is present. So per definition the lift of all aircraft components points in the same direction.

Thrust is defined… — well, there is no common definition that would be as simple as the one for lift. Thrust is created by accelerating air. But the same is true for lift, so we need to define a boundary which separates the acceleration which is interpreted as lift and the one which is interpreted as thrust. This is bookkeeping — you need to meticulously add up all pressures acting on all surfaces of the aircraft and then decide which to call lift and which to call thrust.

A lot happens around the intake lips of fan engines, especially at low speed. The intake diameter is dimensioned for a compromise between take-off, when a lot of air is sucked into the engine and high-speed flight when some of the air flowing toward the engine will spill over the intake lips, to flow around the nacelle. In case of the 737 MAX, the compromise was shifted to a smaller diameter in order to keep nacelle size manageable. Therefore, on the 737 MAX you get a lot of suction on those intake lips. The intake is slightly angled in order to support even flow at high angle of attack, so the intake is already doing quite some flow bending. This flow bending is lift - or is it? The vertical component of thrust is also the result of this flow bending.

What is important is where this happens - the engines on the MAX have been shifted quite a bit forward, so this lip suction has a large, destabilizing lever arm. And the suction grows with angle of attack - disproportionally even, due to the angled intake. In the end, this is where most of the destabilizing moment comes from, and it sure is perpendicular to the fuselage.

EDIT: Now I've had some time for the more mathematical answer desired by @Hans, but I will not dig deeper than fist-order-of-magnitude calculations because solid figures are hard to come by. For example, I did not find the mass flow figures for the 737 MAX's CFM LEAP 1B engines, but this source (thanks @mins!) should be close enough. The 485 kg/s cited there for 145 kN thrust should scale to 436 kg/s for the 130 kN of the LEAP 1B. Next assumption: The airplane's angle of attack is +15° (remember, no flaps when MCAS is active!) so the change in flow direction effected by the intake is 436 kg/s by 15°. This work has to be done at the intake face because once the flow is inside the intake it flows with the angle of the nacelle already. The intake dimensions are the third piece of guesswork here and I assume 1.7 m at the intake face. The last assumption is the air density; I use 1.15 kg/m³ for what follows.

This now allows us to calculate the incoming impulse: 436 kg = 379 m³ flow through an area of π·0.85² = 2.27 m². This needs a flow speed of 167 m/s (Mach 0.5 at sea level - looks very credible).

Next, the intake lips need to add a downward acceleration to a vertical speed component of sin(15°)·167 = 43.2 m/s. The reqired force for this is 436 kg/s·43.2m/s = 18.84 kN, and it all has to act on the intake lips. To put that into perspective: A fully loaded 737 MAX 9 has a mass of maybe 80 tons, so it weighs around 785 kN. Since we have two engines, the total force required for flow bending at the intake faces is 4.8% of the aircraft weight. At the increased lever arm of the new engine location this is already causing a noticeable nose-up pitch.

Answer 3

It is not only the engine thrust producing lift at high angles of attack. The lower surfaces of the engine nacelle ALSO produce aerodynamic lift at high angles of attack.

Even at idle thrust there is additional aerodynamic lift being produced. All engine nacelles do this.

The problem with the B737 MAX is that the engine nacelles are placed farther forward and and have a greater lifting “moment” than previous engines used on the B737.

Answer 4

An engine produces additional lift when it is under high angles of attack (and high thrust) because it causes the airflow to curve downwards. For an aircraft that flies a horizontal path at high angle of attack, the airflow approaches the engine horizontally and leaves the engine in a downward angle, close to the negative angle of attack.

In order to make the flow turn downwards, the engine must exert a downward force on the airflow. According to the third law of Newton,there is an opposite force on the engine. The component of this force that is perpendicular to the incoming undisturbed airflow is the additional lift force caused by the engine.

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One way to analyse the thrust of an engine is to look at the rate of change of momentum of the air flowing through and around the turbine.

Momentum is the product of mass and velocity: $\vec{p} = m \vec {V}$ As you see, momentum it is a vector quantity.

The rate of change of momentum $\dot{\vec{p}}$ of a mass is equal to force on the object.

By analysing the change of momentum of the air flowing around the engine, we can determine the thrust vector of the engine.

In the image below, the engine's axle is perfectly aligned with the incoming flow of air. I choose an imaginary volume around the engine, such that the static pressure at the boundary is equal to the static pressure far ahead of the engine. Because the boundary pressure = $p_0$ at every point on the boundary, the integral of pressure over the surface of the volume, the resulting net force would be zero.

The top and bottom boundaries are chosen to be along the streamlines.

The left boundary is experiencing a constant influx of air; the flow is uniform across the left boundary.

The right boundary is experience a constant outflux of air; the flow in non uniform due to the difference in flow velocity in the core and the bypass section of the engine.

The influx of mass through the left boundary is equal to the outflux of mass through the right boundary; I neglect the burned fuel here.

The influx of momentum through the left boundary $\dot{\vec{p}}_{in}$ is equal to $\dot{m}\vec{V} = \iint_{l} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The outflux of momentum through the right boundary $\dot{\vec{p}}_{out}$ is equal to $\iint_{r} \rho (\vec{V}\cdot\hat{n}) \vec{V} dA$

The difference between the inflow of momentum (indicated by the blue vector below the drawing) and the outflow of momentum (indicated by the red vector below the drawing) is the force exerted on the volume of air. The thrust (indicated by the black vector) is the reaction force.

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When we now introduce an angle of attack, the bounding volume will change shape. Also the influx and outflux momentum will be different. What is most important is that the thrust generated is no longer purely axial; the thrust vector develops a transverse component. This is the additional lift (and a bit of drag) that the engine creates a high angle of attack.

When the engine is mounted well in front of the centre of gravity, a high angle of attack / high thrust situation will cause an upward pitching moment. This is the case in the Boeing 737 MAX where this effect was changing the handling characteristics at high angles of attack. To make sure the handling would be similar to earlier 737 models, Boeing introduced the - now infamous - Maneuvering Characteristics Augmentation System (MCAS).

Answer 5

It is admirable to seek the higher plane of sophistication to gain greater understanding.

First, air is compressible, so D'Alembert is out. Probably would not be true if velocity was great enough for cavitation, but I did consider sailing battleships blunt end first to see if more energy could be recovered as flow is pulled back into the trailing edge. There is also some evidence that air curling up and towards the front of a thin undercambered wing (or a jib sail) gives it almost magical lift properties through recovery of drag energy.

But as far as the engine creating lift force 90 degrees from its thrust (making definition of lift even more specific), we may be talking impossibility without deflection of the airstream by some other physical structure. Tilting the engine out of the direction of travel does create some interesting ideas, but does the pitching or lifting tendency exist without the cowling around the fan?

It will be interesting to see (beyond software) what they do to solve this. They might want to take a look at an RB-57 Canberra.