Rarefied Gas Dynamics - Science topic

The article is just click-bait; if somebody doesn't understand how the lift is created he/she haven't developed the most basic concepts of fluid dynamics. I'm trying to explain how the aerodynamic forces are generated around a body; excerpt from a course I'm working on:

"According to the kinetic molecular theory of gases ... static air exerts a pressure of about 101kPa on any object at sea level, created by the collisions between the object’s surfaces and air molecules ... this pressure changes when the air is not static but it moves around the object ... the random movement of the molecules changes, their random speed vectors gaining a component induced by the macroscopic air movement. ... This change of the random movement of the molecules is causing variations of pressure in the air volume, and acting over the object surfaces are creating forces, termed aerodynamic forces."

The article focuses on inability of common layman "lift theories" to account for the decrease of pressure and speed increase on the upper wing surface. I'm trying to correct this using some common sense.

Let's imagine a flat barn door (our "wing"), flying at an angle, through static air. Let's imagine the air molecules are un-moving grains of sand as a first approximation. In such a case the wing interacts only with the "molecules" that is able to hit, in the direct path of the wing. On the top region, the "wing" is not interacting with the "molecules", a void is created between the "wing" and the "molecules". This model is called "Newtonian sine-squared law of lift" and developed by - Newton in 1687. Interesting fact, this model is not at all accurate for normal flight, but it is accurate at hyper-sonic speeds and/or very low temperatures and pressures, such as space vehicles re-entry, as the molecular speeds are much lower than the aircraft speed.

Well, let's replace now the grains of sand with air molecules that are moving, according to the kinetic molecular theory of gases, at typical air at room conditions, the molecules are moving at about 500 m/s. A wing flying e.g. at 100 knots, about 50 m/s, is much slower. The void between the wing and the free stream is quickly filled by air molecules that are "pushed" in by elastic collisions with other air molecules. Since the air molecules are moving in the void in a global downward general direction, this has a macroscopic effect of increasing the airspeed. Since the total kinetic energy needs to be conserved, less molecular speed is available for collisions and that accounts for decreasing the pressure over the top of the wing. According to Bernoulli this is correct, as Bernoulli law is an energy conservation law, as applied to fluids. Since accelerating air downward is creating an upward lift force , the Newton's second law is also correct. So Bernoulli's and Newton's laws are actually the interpretation of the same physical phenomena.

Hopefully this short introduction dispels some misconceptions of how "no one can explain lift"

check Fig 4

I think it is better to focus first on the meaning of the sound velocity. It is a thermodynamic-based quantity that gives a statistical lecture of the microscopic collisions that happen at a certain temperature due to the molecular agitation. Similarily the macroscopic flow velocity u is a statistical resultant of the collisions at microscopic level. In terms of the mathematical character of the PDE, an elliptic field would transmit instantaneously (infinite velocity) a disturbance. Actually, this model is an approximation used for incompressible flow motion where acoustic waves propagating at a>>u are decoupled from the convective velocity. From a more complete and real physical description, the sound velocity a can be greater than u but not infinite. That means that waves (both acoustic and convective) travel at a finite speed and following particular directions. This turns out in the hyperbolic/parabolic character of the PDE.

Go to the definition of discharge coefficient in https://en.wikipedia.org/wiki/Discharge_coefficient

Several techniques are possible. There is the Direct Simulation Monte Carlo method.  Code and papers/books can be found at either Graeme Bird's website

or Alejandro Garcia's website

The main disadvantage is that his method is computationally intensive. There have been attempts to speed up the approach using Information Preserving methods (use ensembles rather than individual molecules). Details can be found by Google-ing "Information Preserving DSMC", OSIP-DSMC, or DSMC-IP.  I am unsure of the availability of code, but a 1D example appears to be explained in "Microfluid Mechanics: Principles and Modeling (Nanoscience and Technology)". One can also use solutions of the BKG equation to determine "slip" corrections to Couette and Poiseuille flow, which is a common practice in MEMS. This approach has been shown to produce results that agree with DSMC simulations, although the velocity profiles will not agree unless one uses approaches which I personally have some issues with (i.e., have to assume different slip for Couette and Poiseuille). See "Microflows and Nanoflows: Fundamentals and Simulation" by Karniadakis et al for details, although original work goes back to Cercignani and Loyalka. Finally, one could use Lattice Boltzmann techniques. I have never used them, but my former PhD advisor has. Free code such as OpenLB, Palabos, and lbm-c is available. The latter appears to be compatible with GPU computing. I cannot comment on the codes themselves OR the utility/accuracy of LBM, but know that one needs to be very careful with boundary conditions. Some people I know love the technique, others are skeptical of the results they produce.