Can FAA Authorise an Airliner for Passenger Transportation with Negative Longitudinal Stability?

The new Boeing 737 Max came out from a hastened design process, where an existing airframe dating back to 1967 was equipped with larger more fuel efficient engines mounted further forward and higher on the wings to satisfy requirements on ground clearance. The Max showed a tendency to stall in climb and turn as an effect of the new engines apparently giving extra lift thus moving the centre of lift CL ahead of the center of gravity CG into possibly negative longitudinal stability. To compensate the software MCAS was installed with the objective to automatically pitch the nose down upon input from an angle of attack sensor. For details, see Boeing 737 Max Groundings.

It appears that the idea was to hide the MCAS to not distract the pilot, but with a malfunctioning sensor that led to the fatal crashes.

But a civil airplane for passenger transportation is required to have positive longitudinal stability (see also FAA 1962 4b.150) with then CL behind CG, which pitches the nose down on increasing angle of attack and thus, without software or pilot control, maintains stable flight without stall.

Apparently, Boeing did not have the capacity to predict the tendency to stall of the new design using Computational Fluid Dynamics CFD, and so make a redesign into airplane with better stall characteristics. DFS is CFD software with the unique capability of predicting stall.

How could then FAA authorise the Max, when it was clear from the presence of MCAS that the Max design did not fully meet a requirement of longitudinal stability?  Or was the MCAS hidden also to FAA? And how will it be possible for FAA to reauthorise the Max if the basic design is kept and only the software is updated? Is it possible to guarantee that the MCAS will always work as intended, if the flight characteristics cannot be fully explored in real life testing and neither in CFD simulation? The new DFS Flight Simulator under construction can answer this question.

The Swedish military jet fighter JAS-Gripen was designed to have negative longitudinal stability to allow quick turns, which required stabilising software. After two crashes the software was modified into slower turns, which was ok since the plane was not used for combat.

First crash:

Second crash (2.23):

Non-Scientific Speculations by 2019 Nobel Laureates

Stone Age scientists raising alarm about global cooling.

The traditional discussion on Swedish State Television with the 2019 Nobel Laureates has taken place under the usual title "Geniuses Speculate" as a gift to the Swedish people and to humanity.

The main theme was of course climate where all Laureates except one expressed their firm conviction  that science is settled on a rock-solid prediction of catastrophic global warming due to emission of CO2 from burning of fossil,  which must be stopped by all means and at any cost: By 2050 the World must be fossil free, and this is possible since people are willing to sacrifice.

The exception was Physics Laureate James Peebles who dared to say that science cannot tell if the globe is warming or cooling, in particular not because of a small change of the trace gas CO2 in the atmosphere, recalling Yogi Berra: Prediction is difficult, in particular about the future. Peebles also questioned the willingness of people to sacrifice the pleasures offered by the present fossil society.   

Peebles was then declared to be a "heretic" with the important role of giving additional support to the belief of the believers, as expressed by Medicin Laureate William G. Kaelin Jr: Since a heretic (by definition) is wrong, it helps to show what is right and therefore the heretic must be given the right to expression.

So Peebles as Laureate was allowed to express his skepticism to CO2 climate alarmism in Swedish State Television, as a unique exception from Swedish State controlled climate alarmism policy towards the goal of Sweden as the first fossil free society, since the Stone Age.

The view expressed by Laureate Kaelin can be seen as a misinterpretation of the proverb "the exception confirms the rule" attributed to Cicero in the form:

• exceptio probat regulam in casibus non exceptis

which is to be interpreted as saying that an exception requires the existence of rule as background, not that a counterexample to a scientific theory proves that the theory is correct. Laureates... 

Boeing Halts Production of 737 Max vs DFS

Boeing will halt production of troubled 737 Max airplane. It’s unclear how long the suspension will last.

Compare with CFD State-of-the-Art/NASA 2030 Vision vs DFS recalling that Boeing and its competitors are very conservative companies and penetration of CFD is gradual.

Yes, Boeing indeed took a very conservative approach when launching the new 737 Max by equipping a design from 1967 by new larger supposedly more fuel efficient engines, which had to mounted farther forward and higher to clear ground. 

The result showed to be an airplane with a tendency to stall in low-speed climb and turn, which must have come as a surprise, because the standard software for CFD Computational Fluid Dynamics used by Boeing does not have the capability to predict the complex flow dynamics of stall. 

But the design was kept by Boeing, in line with its conservative company strategy, and to fix the instability the MCAS software was installed with the objective to automatically pitch the nose down on input from an angle of attack sensor. But the system malfunctioned with catastrophic consequences. 

The idea has then, since the the 737 Max fleet was grounded in March 2019, been to improve the software to make it safe, but reauthorisation by FAA is dragging and may never come. So now the production is halted and may never be resumed. 

DFS Direct Finite Element Simulation from Icarus Digital Math  is new software for CFD with the capability if predicting full flight characteristics of an airplane including stability and tendency to stall, as a realisation already today of NASA CFD Vision 2030.  DFS comes with new mathematical theory explaining for the first time The Secret of Flight.             

DFS as new computation/theory is now being presented to Boeing towards evaluation of the new predictive capabilities of DFS and possible incorporate into the designs process. Big values are at stake.

The catch for Boeing is that if the Max requires stabilising software, then it will be very hard to demonstrate that the software always will operate as intended and thus for FAA to re-authorise. The other possibility is that in fact the software is not needed, but that requires predictive computational simulation capability at Boeing trusted by FAA, since real flight testing of extreme situations is hazardous. In both cases, both Boeing and FAA have a problem, for which the only real solution may well be to put an end to the whole story of 737 Max.

How long time would it take for Boeing to make a whole new design (for the new engine or better) meeting todays expectations, using a tool like DFS and then start production?  Two years?      

The True Explanation of the Coanda Effect

A common description of the generation of lift of a wing is through the Coanda effect as the "tendency of a fluid jet to stay attached to a convex surface" typically demonstrated by a teaspoon in the water jet from a faucet subject to a lift force:

The same argument is then used to explain the generation of lift of a wing or airfoil:

But why does a fluid have a "tendency to stay attached to a convex surface"? The standard answer going back to Prandtl's boundary layer theory, is that it is an effect of viscosity which gives a fluid a "stickiness" which makes it "stick" to a surface with zero relative velocity as a no-slip boundary condition.

The new theory of flight exposed on The Secret of Flight gives a different explanation of the generation of lift as instead an effect a slip boundary condition allowing the fluid to slide along the surface with vanishingly small skin friction and then stay attached without separation because of the following property of 2d potential flow (stationary incompressible flow without rotational motion in two dimensions as in the airfoil picture):

• Potential flow can only separate a stagnation where the flow velocity is zero.  

The reason is that the boundary of the 2d airfoil section with a slip boundary is a streamline followed by fluid particles sliding along the boundary. This means that a nearby streamline in the fluid will stay close to the boundary as long as the flow velocity is positive. The nature of flow separating at stagnation can be seen in the potential flow over the half-plane $y\ge 0$ in a $(x,y)$ 2d coordinate system with boundary $y=0$ with velocity $(v_x,v_y)$ given by

• $v_x=-x$ and $v_y=y$ with stagnation at $(0,0)$.      

We see that the flow is incompressible and is directed towards $x=0$ with $y=0$ serving as a streamline and that the flow velocity $v_y=y$ away from the boundary is small for $y$ small thus preventing separation in finite time and allowing separation only after long time as the flow approaches $x=0$ with very small velocity $v_x=-x$. We see stagnation in the separated flow at stall  in the airfoil picture above.

Summary:  Incompressible flow can stay attached to a convex surface without separation and thus generate lift of wing,

• because it satisfies a slip boundary condition,
• not because it sticks to the boundary with a no-slip.      

The consequences are far-reaching as concerns both computational simulation and understanding of slightly viscous incompressible fluid flow including flight aerodynamics.

In fact, in laminar flow with no-slip the pressure gradient vanishes close to the boundary and so the flow cannot stay attached to a convex boundary. 

Prescription vs Prediction in CFD

Recent posts compare the standard methods of CFD based on turbulence and wall models (RANS, LES and DES as a combination), with DFS Direct Finite Element Simulation without turbulence and wall models as best possible solution of Euler's equations.

DFS has shown to accurately predict complex aerodynamics such as the stall of an airplane by capturing both turbulence and flow separation from first principle physics. DFS thus predicts the full flight characteristics of an airplane with the only input being the shape of the airplane. DFS not only predicts flow separation but also makes it understandable as 3d rotational slip separation with point or line stagnation.

This is a stunning example of the ideal according to Einstein of a mathematical model capable of predicting true physics without input of physical parameters. It is like predicting the circumference of a circle with radius 1 to be $2\pi$, just much more complicated and surprising.

With the standard methods of RANS-LES prediction is replaced by prescription mediated through the turbulence and wall models containing many parameters.  As a result RANS-LES cannot truly predict flow separation since that has to be built into the wall model, by either prescribing the flow to stay attached to a smooth solid wall and separate at a corner, or separate under influence of an "adverse pressure gradient".

The main novelty of DFS is thus the possibility of true prediction, which is not possible with RANS-LES which include prescription.  This connects to Bohr's comment to Einstein's claim that God does not trow dice, in the form:

• Einstein, stop telling God what to do!

RANS-LES tells physics what to do. DFS predicts what physics does.

DFS prediction of stall of a jumbojet with flow separation on top of the
inner part of the wing, in close agreement with observation.

Flow Separation in RANS-LES and DNS vs DFS

The standard methods for CFD Computational Fluid Dynamics are RANS-LES with, and DNS without turbulence and wall models. Both RANS-LES and DNS use a no-slip boundary condition prescribing zero relative fluid velocity on a solid wall, as the corner-stone of Prandtl's boundary layer theory dominating modern fluid dynamics.

DNS is restricted to Reynolds number well below drag crisis at around $5\times 10^5$, because computational resolution of thin boundary layers is required.

RANS-LES uses a wall model prescribing the transition from zero relative velocity on a wall to free stream velocity.

Reynolds numbers for vehicle fluid dynamics of cars, airplanes and boats lie in the range $10^6 -10^9$ beyond the drag crisis.

DFS is a new method for flows beyond the drag crisis based on best possible solution of Euler's equations with a slip boundary condition as a force boundary condition expressing vanishing skin friction without boundary layer.

The drag crisis appears to represent a switch from a no-slip to effectively a slip boundary condition. In CFD with Reynolds numbers in the range $10^6-10^9$ of relevance for vehicles, it thus appears to be possible use a slip boundary condition which does not generate a boundary layer. The evidence is DFS with slip for a wide range of vehicle fluid dynamics in close agreement with observations.

DFS can be viewed as a form of DNS which works for high Reynolds numbers beyond the drag crisis, works because then the fluid effectively satisfies a slip boundary condition.

In particular DFS has shown to correctly predict the critical element of flow separation from a solid wall as 3d rotational slip separation. 

On the other hand, in RANS-LES the flow velocity is prescribed close to the wall and thus also flow separation (or non-separation) is prescribed and prescription is not prediction.

DNS with no-slip as being restricted to low Reynolds numbers, cannot predict flow separation beyond the drag crisis and and so separates on the crest of a wing and not at the trailing edge required for generation of lift (before stall).

In short, DFS represents a major advancement in CFD by allowing prediction of flow separation through the use of a force boundary condition expressing observed vanishingly small skin friction
allowing the simulation to "follow the physics", in contrast to RANS-LES where instead the simulation "prescribes/dictates the physics". The difference is huge.

In fluid dynamics according to Prandtl, flow separation is connected to the presence of an "adverse pressure gradient" retarding 2d flow to stagnation followed by separation as a 2d phenomenon. Accordingly flow separation in RANS-LES is prescribed by "adverse pressure gradients", which however not physics.  True flow separation is a 3d phenomenon which is captured in DFS.

     

CFD State-of-the-Art/NASA 2030 Vision vs DFS

DFS Direct Finite Element Simulation offers revolutionary new possibilities in CFD Computational Fluid Dynamics.

Let us give perspective to DFS starting with the survey of state-of-the-art and future prospects of CFD given by P. Spalart and V. Venkatakrishnan at Boeing as prime user of CFD, presented in 2016 before the 737 Max disaster in 2019:

1. Boeing and its competitors are very conservative companies, first of all because of their passion for safety, but also because of the extreme industrial consequences of any design mistakes.
2. Flaws uncovered during assembly or flight test of a new model cause considerable disruptions for the entry into service. The corresponding financial impacts are very large, and the possibility that the new aircraft model would be impossible to certify short of, say, a complete redesign of the wing would be a nightmare. 
3. As a result, the penetration of CFD is gradual, often involving agreement amongst large communities, from engineers to top managers to company pilots, and acceptance by government agencies such as the Federal Aviation Administration (FAA).
4. We believe automatic grid adaptation, or ‘self-gridding,’ is a very powerful ingredient of CFD; however, it has proven very difficult, and even the talent in government, industry, and academia and the competition amongst CFD code suppliers have had only modest levels of success.
5. At present, CFD and wind tunnel are used in a complementary fashion.
6. Potential new areas for CFD to contribute are in the certification of various phases of an aircraft development
7. Concerted efforts are needed if much of the database in the flight simulator is to be populated using CFD. 
8. The level of confidence in CFD when dealing with flow past complex configurations such as high lift (with leading-edge and trailing-edge devices deployed) is considerably less compared to the high-speed clean-wing area. 
9. To set the stage in our industry, we may consider the problem of calculating the flare and landing maneuver of an airliner, therefore a configuration with high-lift devices, landing gear, spoilers, moving control surfaces, ground effect, thrust reversers, and unsteadiness lasting many seconds.  More specifically, as of today a solution for this landing maneuver that is accurate to the degree needed in our industry is out of reach even with the least costly type of turbulence modelling, namely, RANS.
10. It is conceivable that computing power will someday make DNS in aeronautics possible, so that modelling proper would disappear, and the turbulence considerations would be reduced to ensuring that the grid and time resolution are adequate. 
11. In 2000, one of us boldly anticipated this to happen around 2080, but by now we are not confident of this for the 21st century, or even that it will ever happen. 
12. Our prediction in 2000 that LES would prevail in the 2045 time frame assumed wall modelling, and a few other generous assumptions. 
13. The widely expected substitution of CFD for the vast majority of ground and flight testing in the aerospace and similar industries, although announced in the 1970s, will take decades from today to complete, gradually expanding from the center to the edges of the operational envelope, from isolation to complete collaboration with other disciplines, and from innocuous to safety-critical decisions. 

In this perspective DFS offers the stunning new possibility of simulating the full flight characteristics of an airplane including critical dynamic moments of start, landing, climb, turn and stall. DFS can be be viewed as DNS in sense of capturing the critical elements of (i) turbulence and (ii) flow separation without turbulence and wall model. This is way beyond the above Boeing perspective.

And even more stunning: DFS is realised with todays super computer power in readily available open source form by Icarus Digital Math.

How is this possible? It seems way beyond the bleak perspective of a conservative Boeing. The breakthrough of DFS has been possible by circumventing the main road block to progress built by Prandtl as the Father of Modern Fluid Mechanics, namely the idea that fluid flow critically depends on the presence of thin boundary layers where a fluid meets a solid wall with a no-slip velocity boundray condition, so thin that computational resolution is impossible with any foreseeable computer power. 

Prandtl, thus claimed that both lift and drag of a wing comes from a thin boundary layer around the wing surface. This connects to the "butterfly effect" as a large effect (tornado in Texas) resulting from a vanishingly small detail/cause (butterfly in Brazil). 

Such an effect can be virtually impossible to actually verify because a vanishingly fine resolution can be needed to computationally resolve the little detail. But to disprove the reality of the effect is possible: Take away the little detail/cause/butterfly and observe that the effect/tornado is still there. 

This is what DFS does (in addition to capturing turbulence): DFS uses a slip/small friction force boundary condition without boundary layer, instead of no-slip with layer, and yet computes lift and drag of a wing in full accordance with observations, and more as full flight characteristics. 

DFS thus breaks the Spell of Prandtl which has paralysed CFD during the 20th century and in the above Boeing perspective will continue to do so during the 21st.  

In particular, DFS meets the NASA CFD Vision 2030, already today.

See also: Spalart and Strelets: Turbulence Prediction in Aerospace CFD: Reality and the Vision 2030 Roadmap with the same message as above.

Compare with:

• FAA predicted Boeing 737 Max, facing more delays, would crash 15 times over its lifetime
• FAA says it will not approve Boeing 737 MAX until 2020

The Difference Between DFS and RANS-LES, DNS and DES

The main methods in CFD Computational Fluid Mechanics are:

• DFS Direct Finite Element Simulation. 
• RANS-LES Reynolds Averaged Navier-Stokes-Large Eddy Simulation.
• DNS Direct Numerical Simulation.

The characteristics are:

• DFS: Best possible solution of Euler's equations with force boundary condition as slip/small friction without turbulence and wall model.
• RANS-LES:  Turbulence model and wall model specifying velocity profile into no-slip on wall.
• DNS: Navier-Stokes equations without turbulence/wall model with no-slip on wall.  

The capabilities/limitations are:

• DFS: Captures high Reynolds number flows (beyond drag crisis around $10^6$) with slip in large generality including separated flow, and through drag crisis with small friction.
• RANS-LES: Large difficulties of turbulence/wall modeling and flow separation. 
• DNS: Restricted to low Reynolds numbers.  

For a review of the state-of-the-art of RANS-LES and DNS (2016), see 

• On the role and challenges of CFD in the aerospace industry 

by P. R. Spalart and V. Venkatakrishnan, Boeing Commercial Airplanes Seattle.

DFS prescribes a force boundary condition on a solid wall as slip/small friction, while RANS-LES and DNS both prescribe velocities to be zero on wall as no-slip.

A force boundary condition is a so called natural or weak boundary condition, which mathematically can be imposed in variational form and as such represents a physical boundary condition, which can be controlled as slip/small friction.

On the other hand, a no-slip boundary condition on velocity is mathematically referred to as an unnatural or strong boundary condition, which is unphysical in the sense of being possible to impose in reality, only by paper and pen in a mathematical model or computer code.  

DFS captures flow separation by using a force boundary condition allowing the simulation to "follow the physics".

RANS-LES does not capture flow separation by artificially prescribing the velocity close to the wall which does not "follow the physics".

DNS for high Reynolds number flow requires computational power estimated to be reached only in 2080, as predicted by Spalart in 2000 and repeated in the above review. 

In short, DFS is the only CFD method which today can deliver simulations of high Reynolds number capturing the essential aspects of turbulence and flow separation. Compare with  Spalart's bleak perspective for RANS-LES and DNS:

• Our expectations for a breakthrough in turbulence, whether within traditional modelling or LES, are low and as a result off-design flow physics including separation will continue to pose a substantial challenge, as will laminar-turbulent transition.

As a key example, DFS allows accurate simulation/prediction of the full flight of an airplane including flow separation as stall, and thereby reveals The Secret of Flight, for the first time in the history of science, from first principle physics without turbulence and wall modeling.

RANS-LES handles separation by ad hoc prescription of velocities close to the wall, and not in true computation simulation. But ad hoc prescription is not prediction.

The difference between unnatural unphysical paper and pen velocity boundary condition comes to expression in the famous Kutta condition, where the velocity in a (potential) flow computation is artificially ad hoc prescribed to be zero (stagnation) at a sharp trailing edge of an airfoil. The separation is thus prescribed to take place at the trailing edge, which corresponds to artificially introducing a massive force to this effect, for which however the physics is lacking. The fake explanation is that the singularity of a sharp trailing edge "prevents" the flow from earlier separation with loss if lift.  With the Kutta trick lift is generated, but the physics is missing.

To come to grips with the unphysical flow separation in RANS-LES by ad hoc prescription of velocities close to the wall, remedies such as Detached Eddy Simulation DES have be tried but again relying on velocity prescription without true predictive capability.

A solid wall can force the normal fluid velocity to vanish as a non-penetration condition (ultimately realised by a force), but the tangential velocity cannot be prescribed e g as a no-slip condition; only tangential forces can be prescribed, such as zero skin friction or slip.

The change from early separation on the crest of the flow around a sphere with no-slip for Reynolds numbers below the drag crisis with massive wake, to later 3d rotational slip separation for Reynolds numbers through and beyond the drag crisis with smaller wake diameter and corresponding drastic drop of drag, can be followed in these pictures: