Blowing between two objects -- Why is the pressure low?

[boneh3ad]

A wing does not act like half a venturi. Instead if the wing is not stalled, then the air flow tends to follow a convex surface. The curved path of the air is associated with centripetal acceleration and a pressure gradient perpendicular to the streamline, with the lower pressure on the inside of the curve. The pressure gradient perpendicular to the flow also affects acceleration of air in the direction of flow, but to apply Bernoulli to the inside flow versus outside flow requires separating the flow into multiple streamlines.

It's certainly true (and important) to note that a wing is not like half of a Venturi, as has been discussed at great length on this site before. However, your statements about streamline curvature and the resulting conclusions are not accurate. It is certainly true that curved streamlines, as with any other curved path, require a centripetal force and that force is provided by a pressure gradient. The pressure therefore decreases in the direction of the center of curvatures. However, this pressure gradient points exactly normal to the flow direction and the only role it plays in accelerating the flow is that of the centripetal acceleration, i.e. it changes the velocity of the flow since it "causes" curvature, but it doesn't change the magnitude of the velocity. If there is any tangential acceleration to the flow, it is not related to the streamline curvature through the centripetal acceleration.

Additionally, in situations such as an airfoil where the typical frame of reference is a uniform free stream moving over an airfoil, then every streamline starts with the same total pressure and Bernoulli's equation applies everywhere, not just along a single streamline and regardless of your so-called streamline curvature effect. The exception is when a streamline enters the boundary layer region, at which point viscosity is non-negligible and Bernoulli's equation no longer applies.

You are referring to laminar flow. Laminar flow is important mainly to prevent airflow separation from the wing upper surface which creates turbulence, decreases velocity and results in loss of pressure differential, i.e, lift (wing stall).

Quite the opposite, actually. laminar flow is exceptionally susceptible to boundary-layer separation/stall, which turbulent flow is much more resistant to separation. In situations where high angle of attack maneuvers are common (e.g. fighter jets) there are often elements of the design intended to ensure turbulent flow over the wings so that separation does not occur.

There are indeed multiple streamlines if measuring pressure gradient and velocity across the wing surface and the free air stream. At the wing surface the velocity is lower due to parasitic drag and higher at some point just above the surface- a gradient.

For air blowing over a stationary airfoil, the flow velocity at the surfaces isn't just lower. It's zero. This is not due to "parasitic drag", but due to viscosity, which leads to one component of total drag: skin friction drag. If you instead imagine stationary air with a wing moving through it, this is the equivalent of the wing dragging some of the air along with it since the flow velocity relative to the surface must be zero at the surface.

For now it is easier to work in the frame of reference of a stationary wing with air moving over it. The two frames are equivalent anyway. So, at the surface the velocity is zero, and a short distance away, the velocity is the same as that predicted by inviscid theory, often called the edge velocity. The relatively thin region near a surface that features the smooth change from zero to the edge velocity is called the boundary layer. As luck would have it, nature loves us and the pressure gradient in the wall-normal direction through the boundary layer is very nearly zero, so when we do simple inviscid simulations to come up with the edge velocity, we can treat that corresponding pressure as if it was touching the surface anyway.

Because of the above it is important keep the wing surface very clean in order to support the laminar flow efficiency.

Keeping the boundary layer laminar over the wings of a transport/cargo plane (i.e. one that doesn't do a lot of high angle maneuvering) would be very nice in terms of efficiency. In fact, it's estimated that laminarizing the boundary layers on the wings of a Boeing 737 would result in a 15% fuel savings. However, this process is extraordinarily more complicated than just keeping the wing surface clean. Even if it was that simple, that would be nigh on impossible in any real-world situation.

To be more complete though, one has to factor in equal and opposite action. deflection of airflow beneath the wing creates an equal and opposite force contributing to lift. This however is more prominent during low speed high angle of attack (angle of airfoil to airflow).

This is literally always the case, not just during high angle of attack situations. The momentum change of of the air due to the deflection caused by the wing is exactly equal to the forces on the wing, both lift and drag. This is always true. The Bernoulli explanation and the flow deflection explanation are not two different mechanisms contributing to lift. They are, in fact, two sides of the same coin, and each individually can account for 100% of the lift.

The primary lifting moment comes from entrainment of the air just behind the highest area of effective camber creating low pressure.

Given that a symmetric airfoil (with zero camber) can generate lift, that should tell you that camber is not required for lift, and therefore cannot be somehow fundamental to lift.

 

[rcgldr]

... pressure gradient perpendicular to the streamline, with the lower pressure on the inside of the curve. The pressure gradient perpendicular to the flow also affects acceleration of air in the direction of flow ...

your statements about streamline curvature and the resulting conclusions are not accurate. It is certainly true that curved streamlines, as with any other curved path, require a centripetal force and that force is provided by a pressure gradient. The pressure therefore decreases in the direction of the center of curvatures. However, this pressure gradient points exactly normal to the flow direction and the only role it plays in accelerating the flow is that of the centripetal acceleration.

Thanks for getting back to this thread.

Wouldn't the pressure gradient in the direction of flow correspond to the changes in pressure related to curvature of flow? Wouldn't the lowest pressure and highest velocity of flow occur at the point of greatest centripetal acceleration (above a wing), a coexistent relationship?

 

[boneh3ad]

Thanks for getting back to this thread.

I get to be pretty busy at the end of the semester. I neglected basically the entire forum for the last few weeks.

Wouldn't the pressure gradient in the direction of flow correspond to the changes in pressure related to curvature of flow? Wouldn't the lowest pressure and highest velocity of flow occur at the point of greatest centripetal acceleration (above a wing), a coexistent relationship?

Not necessarily. The pressure gradient in the direction of the flow, by definition, is tangential to any curves in the streamlines and is therefore not coupled in any way to the associated centripetal acceleration. Now, the pressure and velocity fields are coupled, so the two can't be completely separated, but any acceleration in the streamwise direction must come from a streamwise pressure gradient, not the stream-normal pressure gradient that accompanies curved streamlines. In fact, the lowest pressures over an airfoil do not tend to correspond exactly with the areas with the largest streamline curvature. The largest curvature is at the leading edge where the flow rapidly deflects out of the way of the airfoil. This also happens to be where the highest pressure typically occurs. Of course, there are also low pressure regions that are in the vicinity of high curvature as well. The important takeaway is that you can't assume high curvature means low pressure. All you can assume is that there is a negative pressure gradient in the direction of the center of pressure.

 

[Capn'Tim]

I think you misunderstood (or I poorly worded) when I said "The primary lifting moment comes from the entrainment of air just behind the highest area of effective camber" I was not speaking to the entire lifting moment of the wing. I was intending to infer to the lift generated by that portion of the aerodynamics apportioned to the Bernoulli effect. I full well realize there are other contributors. Synopsis statements sometimes don't adequately convey intended meaning. In reality the force vector of the wing is a composite of all the pressure points along the chord line of each given section, and when those pressure points are aggregated and averaged it tends to be a point somewhere to the rear of the peak camber (with exceptions like super-critical design for example). As to the value of camber itself, with little exception nearly every viable wing design incorporates camber. Yes you can make a flat plate fly, but it is terribly inefficient and economically useless. Yes some supersonic aircraft utilize wing designs with very little if any perceptible camber, but from low speed high lift designs to high sub-sonic super critical designs there is always camber. The question is how much? And what combination of negative and positive camber over the length of the chord to effect the final "effective camber". to meet the design goals?
On another note though, looking back at my old dusty Aerodynamic primer books from the early 1970's I realize they didn't have it quite right! I am a professional and as such always learning and willing to change my thinking when either proven in error or a better explanation comes along. The venturi example is indeed a poor descriptor of the Bernouli effect as it applies to airfoils. And even NASA still is saying that the Bernouli effect causes acceleration which results in low pressure (though the explanation that the difference in pressure at the entry side of the restriction vs the exit side seems more appropriate to me). Though NASA gives recognition to both Bernouli and to Newtonian contribution to lift, they say the true cause is neither of these but the downward deflection of airflow that makes a wing fly! So there we go... :)
Best Regards!

 

[boneh3ad]

I think you are back on the correct track, but there are still a few things you are saying that are at best misleading. For instance:

The venturi example is indeed a poor descriptor of the Bernouli effect as it applies to airfoils. And even NASA still is saying that the Bernouli effect causes acceleration which results in low pressure (though the explanation that the difference in pressure at the entry side of the restriction vs the exit side seems more appropriate to me).

This may be part of the issue. There really isn't such a thing as "the Bernoulli effect." Bernoulli's princple, or the Bernoulli equation, is essentially just an equation describing the relationship between pressure and velocity in an inviscid, incompressible flow. It says nothing about cause and effect. It is simply a statement of conservation of energy (originally and most straightforwardly, although you can also cast it in terms of conservation of momentum). In other words, if you know the velocity distribution around an airfoil, you can use that to relate the velocity to the pressure, and then use the pressure to explain and/or quantify lift. This is, in fact, a quite common method of calculating lift. It does not, however, tell you anything about why the air moves faster in certain locations. Similarly, it doesn't tell you why the flow speeds up in a Venturi tube, only that the acceleration accompanies a decrease in pressure and vice versa. It is actually conservation of mass that explains why the flow speeds up in a Venturi tube.

Though NASA gives recognition to both Bernouli and to Newtonian contribution to lift

Bernoulli and Newton do not both "contribute" to life. Rather, each one can independently be used to describe lift. Using Bernoulli's equation, you can say the pressure distribution resulting from the velocity field will provide a net upward force that we call lift. Using Newton, you can say that any deflection of the air downward by the wing requires force, and the equal and opposite reaction to this is the upward force we call lift. If you used either of these to actually calculate lift, they would give the same answer. Both Newton and Bernoulli can completely and on their own explain all of lift. They are not independent contributions.

they say the true cause is neither of these but the downward deflection of airflow that makes a wing fly! So there we go... :)

The downward deflection of air is the Newtonian explanation of lift, and is, at its heart, probably the most fundamental method of qualitatively explaning lift while simultaneously being the most useless method for quantifying lift.

 

[Capn'Tim]

Bernoulli and Newton do not both "contribute" to life. Rather, each one can independently be used to describe lift. Using Bernoulli's equation, you can say the pressure distribution resulting from the velocity field will provide a net upward force that we call lift. Using Newton, you can say that any deflection of the air downward by the wing requires force, and the equal and opposite reaction to this is the upward force we call lift. If you used either of these to actually calculate lift, they would give the same answer. Both Newton and Bernoulli can completely and on their own explain all of lift. They are not independent contributions.

It is fair to say that neither airflow deflection (Newtonian) or the velocity/pressure (Bernouli) by themselves account for lift independently of each other. Nor do the two when aggregated accurately reflect the lift of a given airfoil. This much is evident through wind tunnel testing as both independently fall short of predicting the true lift of a given airfoil. Hence, all airfoils require wind tunnel testing regardless the intensity of calculation expended in the design. My recount of the NASA position was not a direct quote... rather than deflection they say curvature in a downward direction (when applied to overcoming gravity specifically). Like weather prediction which escapes exact and accurate results, aerodynamics remains to some degree dependent on observation after the fact. The entire truth of first causes remains somewhat elusive else there would be far less vigorous discussion :)

I am not a scientist or an engineer. I am a practitioner of applied science in aviation. As such I focus on trying to understand the physics principals at work vs the science itself. Most pilots unless they have a background in physics don't feel compelled to fully understand the principals at work, focusing on the other myriad of subjects they must apply in doing their work.

Some decades ago when I was a much younger gentleman, I was flying into Hong Kong Kai Tak on a B747 Classic as the First Officer. I was flying with the #1 Captain who was also a training captain. We were slated to do the famous IGS Approach into Rwy 13. Unfortunately there was a thuderstorm parked on the approach area that made that approach too dangerous to complete. The captain elected to do a downwind approach to land on Rwy 31 with a 10 knot tailwind. Windshear Advisories were in effect due to the storm. As such the captain elected to carry an additional 20 knots of airspeed during the approach due to the prospect of encountering windshear ( which in retrospect was incorrect since any windshear we encountered would likely be performance increasing rather than decreasing). In any case, this decision resulted in an increase of ground speed with the tail wind of about 30 knots. Our target approach speed at maximum landing weight was 157 knots ... A groundspeed of 187 knots (215 mph) crossing the landing threshhold. When the Captain tried to set the aircraft down it resisted touchdown due to increased ground effect and we floated some distance additionally down the runway before the Captain spoke an expletive and applied full speed brakes to kill the lift! The aircraft fell unceremoniously onto the runway and using moderate to heavy breaking we came to a stop within the remaining 6000 feet of runway with a few hundred feet to spare. As we turned off the runway I asked the captain if we shouldn't have the Flight Engineer check the brake energy charts. His response was that it was not necessary because the aircraft would sit over night in HKG... Right then and there I realized the captain had not grasped the physics reality of bringing 630,000 lbs of mass to rest within 6000 feet! The total inertial energy had to go somewhere, and that somewhere was massive heat in the braking assembly! What is not comprehended by many is that the majority of the heating does not occur at the brake surfaces (frictional heating) but deep within the brake assembly itself as the brakes absorb all that energy. It takes about 15 minutes for the heat to migrate to the surface of the assembly. To make an even longer story short, by the time we reached the gate the aircraft was on fire as the bimetallic brake assemblies melted, dripped onto the asphalt and created combustion - fire! We could have lost the whole aircraft if the fire dept had not been prompt and did a good job. As it was we lost 5 brake assemblies and three tires to the incident. Later in my hotel room I ran the brake energy chart and it ended in the RED ZONE with a danger note " Evacuate the aircraft immediately as brake fire will occur".

 

[boneh3ad]

It is fair to say that neither airflow deflection (Newtonian) or the velocity/pressure (Bernouli) by themselves account for lift independently of each other. Nor do the two when aggregated accurately reflect the lift of a given airfoil. This much is evident through wind tunnel testing as both independently fall short of predicting the true lift of a given airfoil. Hence, all airfoils require wind tunnel testing regardless the intensity of calculation expended in the design. My recount of the NASA position was not a direct quote... rather than deflection they say curvature in a downward direction (when applied to overcoming gravity specifically). Like weather prediction which escapes exact and accurate results, aerodynamics remains to some degree dependent on observation after the fact. The entire truth of first causes remains somewhat elusive else there would be far less vigorous discussion :)

I am sorry, but you are objectively incorrect here according to the previous 100+ years of aerodynamic research. If you know the pressure field accurately, you know 100% of the lift. If you know the velocity field accurately, then through the Bernoulli equation, you know 100% of the lift. If you somehow knew the change in vertical momentum in the flow resulting from the wing (i.e. if you quantified the downwash/flow deflection) then you know 100% of the lift. That is fact.

Lift is "easy". Drag is why you really need wind tunnel testing. Lift-induced drag is relatively easy to quantify, but viscous drag is essentially impossible to calculate, and so must be measured. The biggest problem in calculating drag is laminar-turbulent transition. Viscous drag increases by an order of magnitude when the boundary layer is turbulent, so knowing the transition point accurately is important to predicting drag, but that's something that we generally cannot do computationally at this point in time. There's also the matter of the wake and any separation that might occur, which will affect drag in a way that is difficult to calculate.

In short, you can get lift pretty easily and completely from pressure, velocity (Bernoulli), or downwash (Newton), but drag remains impossible to accurately calculate and requires testing. Even wind tunnels only get you so far. Eventually you will need full-scale flight testing to make sure it works as intended.

I am not a scientist or an engineer. I am a practitioner of applied science in aviation. As such I focus on trying to understand the physics principals at work vs the science itself. Most pilots unless they have a background in physics don't feel compelled to fully understand the principals at work, focusing on the other myriad of subjects they must apply in doing their work.

I am an engineer who does wind tunnel testing for a living. I promise that the above is true. The physics principles at work are, generally, conservation of mass, momentum, and energy. Newton's laws can be used to derive the conservation of momentum equations that describe fluid flow (the Navier-Stokes equations) and any change in momentum requires force. Therefore, deflecting the flow requires a force exerted by the wing, and the equal and opposite force on the wing is lift. If you have another source of upward force, I invite you to try to discuss how it arises and why it doesn't also contribute to the flow deflection.

Similarly, if you have some pressure distribution on the wing that predicts and upward force, then there must be a balancing equal and opposite force assuming the wing is at steady, level flight. That opposite force is what deflects the air flow, and again, if you are trying to say that there is some other force in addition to this integrated pressure field, then I invite you to consider what that force may be and why it doesn't show up in the pressure field, since pressure is how a fluid transmits normal force to a surface.

Some sources:
How Does an Airplane Work: A Primer on Lift, an Insight I wrote for this site
https://www.amazon.com/dp/0078027675/?tag=pfamazon01-20
https://www.amazon.com/dp/1259129918/?tag=pfamazon01-20
https://www.amazon.com/dp/0521665523/?tag=pfamazon01-20