## tisdag 17 mars 2020

### DigiMat Web Education

The Corona crisis asks for school mathematics education on the web.

DigiMat Basic is web based
which will soon be available on edX as MOOC as an expansion of DigiMat Pro now running as
DigiMat is constructive mathematics opening to interactive learning in both individual and group form,  without need of traditional class room teacher instruction,

Stay tuned! The World is not what it used to be.

## tisdag 3 mars 2020

### Drag Crisis and Slip at Reynolds Number 1 million

This is a continuation of the previous post identifying three types of contact between a fluid and a fixed smooth solid wall:
1. laminar slip/small skin friction
2. laminar no-slip
3. turbulent no-slip
where DFS Direct Finite Element Simulation uses 1 while standard CFD uses 2 and 3.

No-slip forms a thin boundary layer connecting fluid with zero velocity on the wall with free flow velocity away from the wall. Slip allows fluid particles to glide along a smooth solid wall without boundary layer at small skin friction.

Standard CFD uses no-slip with thin boundary layers beyond direct computational resolution thus requiring wall models for turbulent flow, which have shown to be elusive. Standard CFD therefore is not truly predictive and thus not very useful.

DFS uses slip/small friction as an effective boundary condition, which does not form a boundary layer. This makes DFS computable, with true predictive capability demonstrated.

The appearance of slip/small friction connects to the so called drag crisis observed to occur in slightly viscous bluff body flow with drag drastically dropping at a Reynolds number $Re\equiv\frac{UL}{\nu}$ of around 1 million (or 500.000), where $U$ is typical flow speed, $L$ typical length scale and $\nu$ kinematic viscosity. With $U=1$ and $L=1$, the drag crisis thus connects to $\nu\approx 10^{-6}$ or $Re =10^6$.

For Reynolds numbers below drag crisis the effective boundary condition can be viewed to be no-slip, which forces early separation into a large turbulent wake and large drag.  For Reynolds numbers above drag crisis separation is delayed to form a narrow wake with small drag,  which the analysis of DFS shows to connect to the appearance of an effective slip/small friction boundary condition.

Let us seek to follow this transition, thus starting before drag crisis with a laminar no-slip layer of width $d=\sqrt{\nu}$ and shear $\frac{1}{\sqrt{\nu}}$ with free stream velocity $U=1$, and corresponding Reynolds number based on $L=d$ of size $\frac{1}{\sqrt{\nu}}$.

A laminar no-slip layer is an example of shear flow, which shows to develop into a turbulent no-slip layer for Reynolds numbers of size $10^3$ as described in detail in the book Computational Turbulent Incompressible Flow. This connects to a drag crisis at $\nu =10^{-6}$ with $\sqrt{\nu}=10^{-3}$.

In a first step a laminar no-slip low shear layer thus develops into a turbulent no-slip high shear layer which in a second step can develop into an effective slip/small friction condition as an effect of plastic yield in high shear turbulent flow, with a corresponding maximal shear force of size $\sqrt{\nu}=10^{-3}$ appearing as small skin friction of size 0.001.

The transition from laminar no-slip to turbulent no-slip to slip can be followed in the flow over a convex surface which as laminar no-slip flow separates, because the pressure gradient normal to the boundary is small in a laminar shear layer,  and so develops into a turbulent no-slip layer which can reattach by effectively forming a slip layer with pressure gradient preventing separation.

Summary: Drag crisis connected to slip occurring at a macroscopic Reynolds number of about $10^6$ with a shear of $1000$ and corresponding skin friction $0.001$, can thus be connected to
• transition from laminar no-slip at $Re =10^6$ to turbulent no-slip with shear exceeding $10^3$,
• transition from turbulent high shear with layer to effective slip skin friction $0.001$ as an effect of visco-plastic flow.

## måndag 2 mars 2020

### Laminar Slip Layer vs Turbulent No-Slip Layer: Change of Paradigm

 A turbulent no-slip  boundary layer is uncomputable and lacks mathematical model. A troublesome concept. Modern fluid dynamics has been obsessed with the problem of tackling this problem, without success. The result is CFD which is not predictive  and thus not very useful.

DFS Direct Finite Element Simulation as a new paradigm in Computational Fluid Dynamics CFD exhibits a new basic phenomenon of
• laminar slip boundary layer
to be compared with the basic elements identified by Prandtl as the Father of modern fluid mechanics of:
• laminar no-slip boundary layer,
• turbulent no-slip layer.
The appearance of a laminar slip boundary is connected to the so called drag crisis occurring in bluff body slightly viscous flow such as air and water at a Reynolds number $Re\approx 500.000$ with the drag of a bluff body drastically dropping beyond $500.000$.

The reduction is the result of delayed separation with reduced wake as an effect of a shift from a laminar no-slip boundary layer, which trips the flow to early separation,  to effectively a laminar slip boundary layer, which allows a different form of separation as 3d rotational slip separation without tripping.

The appearance of a turbulent no-slip layer is typically artificially induced in experiments through a transversal ribbon/strip attached to the body thus effectively changing the shape of the body, which trips the flow into separation and turbulent wake. The idea is that this way force the experiment to fit with a preconceived notion by Prandtl of a turbulent no-slip boundary layer, but this is against the most basic principle of science to fit theory to observation and not the other way around.

The result of using an effective laminar slip boundary condition without any artificial tripping, is that fluid flow beyond the drag crisis is computable by DFS because impossible computational resolution of thin turbulent boundary layers required in Prandtl CFD,  is no longer needed. A non-computable turbulent no-slip boundary is thus replaced by a computable laminar slip layer.

DFS shows to accurately predict fluid flow beyond the drag crisis by computing best possible turbulent solutions of Euler's equations as first principle physics without parameters with slip as wall model and a turbulence model as emergent from computation. This makes CFD computable from being uncomputable to all Prandtl followers, and thus represents a veritable change of paradigm.

A key to the breakthrough is the concept of laminar slip boundary layer of a fluid which is viscous-plastic with fluid particles sliding along a smooth wall with skin friction coefficient of size 0.001 at drag crisis and decreasing beyond.

DFS shows that slightly viscous flow is not Newtonian with a constant (small) viscosity since the emergent turbulence model in DFS does not reflect a constant viscosity, nor does the viscosity-plastic slip boundary condition.

This gives perspective on the Clay Navier-Stokes problem which concerns a Newtonian fluid seemingly without relevance for slightly viscous flow as the main challenge of fluid mechanics.

## fredag 28 februari 2020

### Banach Documentary: Digital Math: Body and Soul

Together with Per Enflo and Johan Jansson I participate in a documentary about the great Polish mathematican Stefan Banach, to be shown in Polish TV in March. The film was shown to an invited audience at Fokus in Östervåla Fokus 22/2 followed by a discussion about Banach and our connections to his work. The historical event is recorded at the Per Enflo web site and featured on Icarus Digital Math.

The film has appeared in festivals of documentary film and will be shown at KTH in the Spring and maybe also on Swedish State Television. Stay tuned.

The title of the film is
• Banach: Between Spirit and Matter
with a connection the inscription on the grave stone of Steinhaus, who discovered Banach's talent and became his teacher:
• Mathematics connects Soul to Matter
which is basically the same as the leading theme of the series of books:
as made clear in the film.

### DFS: Change of Paradigm in CFD

DFS Direct Finite Element Simulation is change of paradigm of Computational Fluid Dynamics CFD by correctly predicting the forces acting on a body moving through a slightly viscous fluid such as air or water with the shape of the body as only input, through computation of best possible solutions to Euler's equations expressing first principle physics without parameters.

DFS takes CFD out of the conundrum of finding turbulence and wall models, which despite efforts over more than 100 years has not led to true predictive capability. Standard CFD is typically fitted to match observation but does not deliver correct prediction without prior (wind tunnel) observation and so is not very useful for design.

DFS combines the Euler equations in the fluid domain with a slip boundary condition on the smooth wall of the body modeling vanishing viscous skin friction. DFS shows to correctly predict drag as form/pressure drag within experimental precision and thus shows that the contribution from skin friction is negligible. This is in direct contradiction to standard CFD which attributes $50\%$ or more of drag to skin friction for slender bodies.

As an example we consider the case of drag and lift coefficients $C_D$ and $C_L$ for the basic test case of a long Naca0012 wing, as function of angle of attack $\alpha$. DFS delivers the following results for $0\le \alpha\le 15$ well below stall:
• $C_L(\alpha ) \approx = 0.1\times\alpha$,
• $C_D(\alpha ) \approx = 0.004 + 0.001\times\alpha$.
This fits wind tunnel experiments (without artificial tripping) by Ladson within experimental precision.

The Ladson value $C_D=0.005$ for $\alpha =0$ instead of $0.004$ with DFS, stands out as a limit case for which extrapolation from $\alpha\ge 2$ as in DFS may well be more relevant than direct measurement with tripping as an issue ($C_D=0.008$ with tripping).

We see a linear variation of both $C_L$ and $C_D$ with the angle of attack $\alpha$ as an expected effect of changing geometry.  For lift it connects to effective downwash scaling with $\alpha$ and for drag with an effective frontal area also scaling with $\alpha$

The efficiency of the wing is measured by the lift $L$ to drag $D$ quotient $\frac{L}{D}=\frac{C_L}{C_D}$ ranging from 33 for $\alpha =2$ over 60 for $\alpha =6$ to 75 for $\alpha =15$, thus with steadily increasing $\frac{L}{D}$ before stall.

The common view is that for a short wing $C_D$ has a contribution scaling with $C_L^2$ thus quadratically in $\alpha$  due to a wing tip effect, which suggests that for a long wing $C_D$ is constant as being dominated by skin friction, however without support in observation.

Summary:
• DFS shows that for slightly viscous flow beyond the drag crisis for Reynolds number around $500.000$, total drag is mainly form/pressure drag with a very small (at most $10\%$) contribution from skin friction.
• Standard CFD attributes instead $50\%$ or more to skin friction for an airplane or ship.
The consequence for design is a change of paradigm from an old standard bogged down by unsuccessful attempts to decrease skin friction, to a new standard focussing on form, where possibilities for improvements are many.

The dogma of $50\%$ skin friction is upheld by tripped experiments where e.g. a ribbon is fastened on the body transversal to the flow to generate turbulence increasing drag which is then attributed to skin friction, while it effectively instead corresponds to a change of form. This way observation is fitted to theory prescribing massive skin friction, while in correct science theory is fitted to observation.

## onsdag 19 februari 2020

### Prandtl's Tripped Science vs Boeing Max

 Prandtl making tripped experiments

 Danger of tripping

Ludwig Prandtl is viewed as the Father of Modern Fluid Mechanics because he offered a resolution of the pressing problems of fluid mechanics in the beginning of the 20th century including d'Alembert's paradox through his discovery of the laminar and turbulent boundary layer in wall bounded fluid flow.

The legacy of Prandtl is described in Prandtl-Essentials of Fluid Mechanics edited by Herbert Oertel, Springer 2004, with the following introduction
• The development of modern fluid mechanics is closely connected to the name of its founder, Ludwig Prandtl.
• In 1904 it was his famous article on fluid motion with very small friction that introduced boundary-layer theory.
• His article on airfoil theory, published the following decade, formed the basis for the calculation of friction drag, heat transfer, and flow separation.
• Prandtl was particularly successful in bringing together theory and experiment, with the experiments serving to verify his theoretical ideas.
• It was this that gave Prandtl’s experiments their importance and precision. His famous experiment with the tripwire, through which he discovered the turbulent boundary layer and the effect of turbulence on flow separation, is one example.
• The tripwire was not merely inspiration, but rather was the result of consideration of discrepancies in Eiffel’s drag measurements on spheres.
• Two experiments with different tripwire positions were enough to establish the generation of turbulence and its effect on the flow separation. For his experiments Prandtl developed wind tunnels and measuring apparatus, such as the Göttingen wind tunnel and the Prandtl stagnation tube.
• His scientific results often seem to be intuitive, with the mathematical derivation present only to provide service to the physical understanding, although it then does indeed deliver the decisive result and the simplified physical model.
• According to a comment by Werner Heisenberg, Prandtl was able to “see” the solutions of differential equations without calculating them.
To give the highlighted parts perspective recall that when I was awarded the Prandtl Medal in 2014 by ECCOMAS, I stated that I would receive the medal under the condition that it would be expressed that the New Theory/Computation of Flight developed together with Johan Hoffman and Johan Jansson showed that Prandtl had misled modern fluid mechanics into a fruitless search for the origin lift and drag of an airplane wing in a boundary layer so thin that it could never be resolved in computation. This was not allowed to be expressed and the result was that I did not accept to receive the medal. The story can be read here.

The New Theory of Flight supported by refined computations since 2014 shows that contrary to Prandtl wall bounded slightly viscous flow can be modeled by a slip boundary condition without any boundary layer, which makes the flow computable as time variable turbulent flow. There is thus now massive evidence that Prandtl was wrong, seriously wrong.

Signs that there is something fishy with Prandtl's boundary layers as the origin of drag and lift can be seen in the above highlights:
1. Prandtl use a tripwire to change the flow to fit what he could "see" without mathematics and computation.
2. His results were intuitive.
The effect of artificially tripping the flow in experiments has led to the misconception that skin friction drag is a major part of total drag with form/pressure drag a minor part, viewed to be relevant  also for an airplane wing without tripping device. The New Theory gives hard evidence that this is seriously misleading by computing drag and lift with slip in close accordance to observations.

The lesson is that if you rely on intuition rather than correct mathematics and are ready to trip experiments to fit, then you can end up with something with little connection to reality. Evidently Prandtl did so. The consequences are severe with the Boeing Max debacle a result of misconceived engineering computation following Prandtl.

PS The following question/answer appears on FAQ at Secret ion Flight:

Q30: Why is the flow tripped by a wire, strip or ribbon in wind tunnel measurements of drag of wing, when a real wing does not have any tripping device and the tripping thus appears to be artficial?

A30: The rationale presented is that the tripping will force the development of a turbulent boundary layer with substantial skin friction,  which according to Prandtl should be present. The tripping is thus done to artificially fit reality to theory, which is opposite to the basic principle of science to fit theory to reality. In the New Theory, which fits with untripped experiments, the flow of air meets the wing with a slip boundary condition modeling vanishing skin friction.

## tisdag 18 februari 2020

### Fundamentals of Aerodynamics by John D Anderson as Old Theory of Flight

The book Fundamentals of Aerodynamics by John D Anderson describes the standard theory of flight as Old Theory of Flight with basic ingredients expressed in Chapter 4:
• The purpose of this chapter is to present theoretical methods for the calculation of airfoil properties.
•  In most of this chapter we will deal with inviscid flow, which does not lead to predictions of airfoil drag; indeed, d’Alembert’s paradox says that the drag on an airfoil is zeroclearly not a realistic answer.
• However, if we lived in a perfectly inviscid world, an airfoil could not produce lift.
• Indeed, the presence of friction is the very reason why we have lift. These sound like strange, even contradictory statements to our discussion in the preceding paragraph.
• What is going on here? The answer is that in real life, the way that nature insures that the flow will leave smoothly at the trailing edge, that is, the mechanism that nature uses to choose the flow shown in Figure 4.18c, is that the viscous boundary layer remains attached to the surface all the way to the trailing edge.
• Nature enforces the Kutta condition by means of friction. If there were no boundary layer (i.e., no friction), there would be no physical mechanism in the real world to achieve the Kutta condition.
• So we are led to the most ironic situation that lift, which is created by the surface pressure distribution—an inviscid phenomenon, would not exist in a frictionless (inviscid) world. In this regard, we can say that without friction we could not have lift.
We read that the Old Theory is strange, contradictory, not realistic and ironic. The New Theory of Flight presented on Secret of Flight shows that this characterisation is correct. It is now time to allow the Old Theory to retire since it is physically incorrect and no longer is needed as a facade when there is a physically correct theory.

## måndag 17 februari 2020

### DFS vs standard CFD: Form vs Skin Friction Drag

Direct Finite Element Simulation DFS, as a new revolutionary methodology/software for Computational Fluid Dynamics CFD, computes best possible turbulent solutions to Euler's equations as first principle physics without parameters.

DFS gives results in close agreement with observations as true prediction without adjustment of parameters to match each computation with observation in non-predictive mode. In particular, DFS uses a slip boundary condition on a smooth solid wall as a model of vanishingly small skin friction.

DFS thus computes the drag of a bluff body as form/pressure drag with vanishingly small contribution from skin friction, in close agreement with observation.

For a Naca0012 airfoil at zero angle of attack DFS delivers a drag coefficient $C_D =0.006$ as form/pressure drag, which fits well with untripped measurements (red) by Abbott and von Doenhoff:

The figure also shows measurement (blue) by Ladson with artificial tripping not present for a real wing with larger $C_D\approx 0.008$, thus not applicable to a real wing which does not carry any tripping device.

We now compare DFS with standard CFD where we find the following account in the standard reference Fundamentals of Aerodynamics 5th ed by John D Anderson p. 381 with reference in particular to Lombardi, G., Salvetti, M. V. and Pinelli, D.: Numerical Evaluation of Airfoil Friction Drag, J. Aircraft, vol. 37, no. 2, March–April, 2000, pp. 354–356:
• total drag 0.00623
• skin friction drag 0.00534 ($85\%$ of total)
• DFS: form/pressure drag $95-100\%$ of total drag.
• Standard CFD: form/pressure drag $15\%$ of total drag.
We see a vast difference of form/pressure drag with a factor 6! There is no way both DFS and standard can be correct.

We have massive evidence that DFS without parameters gives correct drag. The conclusion can only be that standard CFD does not capture anything like the truth.

Standard CFD includes turbulence and wall models with many parameters, with the wall model delivering large skin friction ($85\%$) of total drag. The parameters are then adjusted to give total drag in accordance with observations, which means that form/pressure drag comes out as a small portion ($15\%$) of total drag.

The conclusion can only be that standard CFD is not useful, acknowledged by many users, since by the necessity of parameter fitting is not predictive and does not capture true physics.

The reason standard CFD does not capture physics is rooted in the wall model used, which prescribes a separation pattern which is not physical. In DFS the separation is not prescribed by a model and instead follows the physics.

It is clear that aerodynamic design will be very different if based on predictive DFS with form/pressure drag dominating skin friction drag, instead of as now non-predictive standard CFD postulating dominating skin friction in contradiction with physics.

It is the same story in ship hydromechanics with a current consensus of $70\%$ skin friction drag and  correspondingly small form/pressure drag, misleading design into (resultless) efforts to reduce skin friction.

PS More precisely John D Anderson reports the following results from Lombardi at al for NACA0012 at zero angle of attack at $Re =3\times 10^6$:

We see standard CFD delivering skin friction drag even larger than observed total drag.

### Good Example: NRK Denies Denial

Klimarealsitene reports that Norwegian State Radio NRK has declared a new Strategy on Climate Alarmism:
• Dekningen skal i hovedsak handle om hvordan, og ikke om, det skal handles for å tilpasse seg eller dempe den globale oppvarmingen.
• De stadfester at menneskeskapte klimaendringer er reelt, og at NRK skal legge dette til grunn for journalistikken.
• NRK skal være oppmerksomme på den «falske balansen». Hvis de slipper til klimafornektere, skal de stille de rette motspørsmålene.
In English:
• NRK is to report only about how to stop global warming, not if it is needed or meaningful.
• NRK declares that humans control the climate.
• Climate denialism will only be allowed to be voiced if directly countered with complete denial by NRK
We now await Swedish State Radio SR to follow with a similar declaration to meet the mission of public radio, although effectively such a policy is already implemented.

## söndag 16 februari 2020

### Strong State: Scaring or Comforting?

 Swedish Social Democracy 2020: Stronger Safer
A Strong State pretending to have a mission, can use one of two basic strategies:
1. Fear-Mongering: Imminent Threat! Alarm! The State protects you.
2. Comforting: No Threat! No Alarm! The State takes care of you.
There are many examples of 1. through history collapsing to state terror. Swedish Social Democratic Society peaking in the 1950s is an example of 2.

Today we see a Swedish Social Democratic Society, which has switched mode from 2 to 1, in the name of climate alarmism set on a road supported by a new climate law to be the first fossil free welfare state by 2050 in another great leap forward, as an example of a new brave world to be followed by the entire world.

Once that new brave world is reached, Swedish Social Democratic Society will return to mode 2. Only 30 years of great leap state terror with the end as usual justifying the means.

But is climate alarmism starting to crack already today? Yes, there are signs like this one.

### Theoretical Pole Vault Limit for Duplantis?

Duplantis says that $6.30$ is not impossible. What does theory say? Inertial energy is $m\times \frac{v^2}{2}$ with $m$ mass in $kg$ and $v$ speed in $\frac{m}{s}$, and potential energy is $m\times g\times H$, where $g =9.81\,\frac{m}{s^2}$ is gravitational constant and $H$ is height in $m$.

Duplantis horisontal speed is 10 which gives an inertial energy of $m\times 10^2/2$, which if completely converted into potential energy corresponds to $H=5$. This requires the pole to be fully elastic as well as the ground support for the pole. Duplantis uses a very stiff pole and so may reach the height 5.00 from the pole alone. The remaining height must come from the arms. Since the limit of high jump using the legs is about 2 $m$, it is apparently possible to reach 1.18 $m$ with the arms alone.

Another way is to recall that a human being can develop 1 hp momentarily and thus lift 75 $kg$ 1 $m$ during 1 $s$. So 2 $m$ may be impossible, and thus 7.00 $m$ may be the theoretical limit?

## måndag 10 februari 2020

### Letter to Scientific American on New Theory of Flight

To: Scientific American

Att: Article by Ed Regis: No One Can Explain Why Planes Stay In The Air

Yes, it is true, that there is no scientific explanation to be found within the established aerodynamics community in academics and industry, why it is possible to fly.

But there is an explanation as a New Theory of Flight developed outside the established aerodynamics community based on mathematics and computation, which allows accurate prediction of full flight characteristics of an aeroplane and which is well documented in articles, books and open source software.

The New Theory is presented in full on the web site  Secret of Flight and summarized in compact form in this flyer.

Basic scientific documentation consists of
We invite Ed Regis to go through this material and consider a follow up article in Scientific American, which we offer to contribute or write together.

The fact that the aerodynamics community despite massive efforts over 100 years has not been capable of explaining why planes stay in the air is an unbelievable story, yet true. The debacle of the Boeing 737 Max is an expression of the limitations of conventional theory and computation, in particular concerning the dangerous phenomenon of stall.

The New Theory of Flight explains the physics of generation of lift and drag of a wing including stall supported by solid mathematical analysis and computation, and more generally allows the computational simulation of the full flight characteristics of an airplane.

But New Theory is not welcomed by the aerodynamics community since it threatens making established routines obsolete. An article in Scientific American could be instrumental in breaking the silence and allow progress.

The New Theory of Flight offers an exciting story of historic dimensions which could also capture the interest of a broad public.

We hope to get in direct contact with Ed Regis to have a discussion of the subject and how to proceed.

Sincerely

Johan Jansson assoc prof scientific computing KTH Stockholm
Claes Johnson prof em applied mathematics KTH Stockholm
Ridgway Scott prof em mathematics and computer science UChicago

## fredag 7 februari 2020

### Scientific American: No One Can Explain Why Planes Stay in the Air. We can.

Scientific American sends the shocking message:
• No One Can Explain Why Planes Stay In The Air.
Yes, it is true that there is no scientific explanation to be found within the established aerodynamics community in academics and industry why it is possible to fly. Without proper understanding the design of airplanes has to rely on trial and error and the Boeing 737 Max debacle gives harsh evidence of the danger of this approach.

But there is an explanation as a New Theory of Flight developed outside the established aerodynamics community based on mathematics and computation which allows accurate prediction of full flight characteristics of an aeroplane and which is well documented in articles, books and open source software, and which the reveals the Secret of Flight for scientists and engineers and is also understandable to the general public.  Take a look an get enlightened!

I will now take contact with Scientific American and suggest a follow up article presenting the New Theory of Flight. Attention is needed.

To connect to the Scientific American article check out Old Theory, a travesty.

## torsdag 6 februari 2020

### Euler's Dream, Einstein's Ideal and Leibniz' Best Possible of Worlds

DFS Direct Finite Element Simulation offers a veritable breakthrough in Computational Fluid Dynamics CFD in the form of best possible solution of Euler's equations expressing first principle physics in the form of Newton's 2nd Law and incompressibility.

DFS is a realisation of Euler's dream formulated in 1755:
• All of aero/hydrodynamics is captured in the equations I have formulated, Euler's equations.
DFS is a realisation of Einstein's ideal:
• Mathematical model of physics without parameters.
DFS closely connects to Leibniz's grand vision:
• The real world as the best of all possible worlds as the most perfect world being richest in phenomena from simplest laws.
DFS in particular offers a solution to the problem of computing/simulating/modeling turbulent flow with turbulence as an expression of instability of slightly viscous flow preventing exact conservation of momentum and mass in both physics and computation as the essence of turbulence.

DFS generates turbulent flow as complex phenomena from simple laws and as such is best possible.

Standard CFD in the form of RANS generates simple non-turbulent phenomena from complex laws and as such is the opposite.

A short presentation of the DFS breakthrough is given here with further material on Secret of Flight.

## onsdag 5 februari 2020

### Skin Friction is Small

DFS with slip (zero skin friction) correctly predicts lift and drag within 2-5 percent to observations for Reynolds numbers Re beyond the drag crisis that is Re bigger than about 500.000 of relevance for flight. This shows that the contribution from skin friction to drag at high Re is at most 2-5 percent. In DFS drag is pressure/form drag with zero skin friction, in close agreement with observation.

This is in direct contradiction to a widespread belief in the fluid dynamics community that skin friction is 50 percent or more of total drag for streamlined bodies. The support comes from flat plate experiments where the flow by an attached transversal ribbon trips the flow and thus creates drag, which is translated to arbitrary streamlined body without ribbon claiming that the ribbon drag on the flat plate becomes skin friction on the body. Compare with this post.

The logic is missing and the 50% skin friction drag is an artefact from tripped experiments combined with the fact that standard CFD has been fitted to a preconceived artefact of 50% skin friction thus lacking true prediction.

To see how deeply rooted the belief in 50% skin friction is at e g Airbus, take a look at this picture:
(also note that predictive CFD is claimed to require 800.000 years of computing) as presented by Philipp Schlatter KTH:

When will Boeing and Airbus open to DFS and turn into a new era of predictive CFD?

## lördag 1 februari 2020

### Are Greenhouse Gasses Warming or Cooling?

 Infrared atmospheric window to the right of the peak. The dip under the peak is the effect of CO2 which changes very little upon doubling of CO2. Compare with Will Happer's diagram in PS below.
This is a comment to recent posts:

The basic dogma of CO2 alarmism is that a bit more CO2 as a "greenhouse gas" in the atmosphere will have such a big warming effect that the Earth will pass a "tipping point" into a "run-away greenhouse effect" into extinction of human civilisation.

Are then the greenhouses gasses in the atmosphere (mainly water vapour and a bit CO2) warming or cooling? The answer is: they are both cooling and warming.

They are cooling in the sense of infrared radiation into outer space as emission from the "top of the  atmosphere" at an effective emission level of 5 km and temperature -18 C, balancing the radiative input from the Sun.

They are warming in the sense of allowing the Earth surface temperature, by a gravito-thermodynamic  effect with lapse rate of 6.5 C/km, to be 33 C warmer than that at the top of the atmosphere. This is then a combined total effect of thermodynamics with gravitation and radiation,

The "radiation only" effect can be estimated to be 1/3 of the total effect by seeing that the radiative heat exchange between an Earth surface and top of the atmosphere is 2/3 thermodynamics and 1/3 radiation. This gives a greenhouse effect from radiation of about 9 C with thus a surface temperature  of + 6 C, which is the grey body temperature of an Earth without greenhouse gasses.

The greenhouse gasses thus have the double role of radiating into outer space as a cooling effect and together with thermodynamics+gravitation of keeping the Earth surface at a higher temperature than the top of the atmosphere as a warming effect.

To compare with an Earth without greenhouse gasses is not so relevant, but to compare with the warming effect of a fully opaque is enlightening. Recalling that the step from the the semi-opaque atmosphere of the Earth to a fully opaque atmosphere corresponds to completely closing the "infrared atmospheric window" from 5/6 shut, leaving a total effect of 9/5 thus less than 2 C. Since doubling of CO2 is far from closing the window, its effect as climate sensitivity can not be bigger than 1 C, probably much smaller.

PS Below is Will Happer's picture (from COP25 Madrid There is No Climate Emergence) of the spectrum of outgoing infrared radiation showing that doubling of CO2 as represented by the difference between the black and red curves visible only in the CO2 ditch below the peak, is at most 3 W/m2, which gives less than 1 C warming by Stephan-Boltzmann.

## fredag 31 januari 2020

### Atmosphere Effect of 33 C vs Radiation Effect of 9 C

 Greta's Vision: Transforming the Earth into a green planet.
A recent post gives evidence that the so called greenhouse effect as the total effect of the presence of greenhouse gasses in the atmosphere of the Earth is +9 C, rather than the claimed +33 C as the corner stone of CO2 alarmism asking for a new fossil/carbon free society and a complete restructuring of human civilisation.

The +33 C comes from an idea that the infrared radiation from the Earth with its atmosphere into outer space at 0 Kelvin, takes places from an effective emission level of 5 km above sea level at a temperature of -15 C. This fits with a lapse rate of 6.5 C/km as en effect of both thermodynamics including gravitation and radiation.

Out of the 340 W/m2 received from the Sun, 240 W/m2 is absorbed by the Earth + atmosphere and so has to be radiated to outer space at 0 K, which according to Stephan-Boltzmann's law for a black body corresponds to a temperature of 255 K, thus defining the effective emission level to be 5 km.

The +33 C then comes from comparing the temperature of 255 K at the effective emission level with the temperature on the surface of the Earth of 288 K, and the difference is then proclaimed to be the greenhouse effect as 33 = 288 - 255 C.

But this is not correct, because it attributes the total effect of the atmosphere, being an effect of both thermodynamics and radiation, to radiation alone. But there are strong arguments that the total effect is 2/3 thermodynamics and 1/3 radiation (in any case without domination of radiation), which fits with the idea of +9 C as the effect from radiation alone, which is what should be called the greenhouse effect, if rules of logic are followed.

By identifying a total atmosphere effect with a radiation effect, a large greenhouse effect of +33 C comes out. Correcting this fundamental mistake reduces the greenhouse effect by a factor 3 and thus changes alarm into no-alarm.

The dooms-day vision of CO2 alarmism can thus be replaced by hope of a better future for in particular all poor people of the world, who would have no place after the complete restructuring. Recall Greta's answer to the question of what has to be changed according to climate alarmism: Everything!

With a greenhouse effect of +9 C the surface temperature of an Earth without greenhouse gasses would thus be + 6 C, which incidently(?) is the mean annual temperature of Sweden! This supports a widespread idea that Sweden is country of mean values and as such the right norm.

 Annual mean temperature in Stockholm recovering from Little Ice Age from 6  to 7 C. As high temperature in 1930s as today. Variation from year to year 4 C.

## måndag 27 januari 2020

### Boeing 737 Max: Perspective and Questions

The BNP of Sweden is about 500 billion USD, and that of the US 18 000 billion USD, about 40 times as big reflecting a population of 10 million in Sweden and 300 million in the US.

Today nearly 1000 Boeing Max are grounded each one selling for 100 million USD with a total of 100 billion USD grounded, about 20% of the BNP in Sweden and 0.5% of the BNP of the US.

The yearly revenue of Boeing is about 100 billion and the total stock value 200 billion USD.

Questions:
• Will the Max ever fly again? What happens with Boeing if not? If half of the total value is lost?
• Why did the Boeing engineers design an airplane which showed to have a tendency to stall?
• Was it because they used standard CFD (computational fluid dynamics) software which could not predict stall?
• What new CFD software will be required to get the Max in the air?
PS Boeing 797/NMA Is Going Back To The Drawing Boards:
• Boeing has shelved all of its plans for the ‘797 NMA’ and has been asked to return to the drawing board by its new CEO.
Will the 737 Max also be returned to the drawing board?  Compare with this post.

## tisdag 21 januari 2020

### The True Total Greenhouse Effect is +9 C, not +33 C

 Misconception: Without greenhouse gasses the Earth would be a frozen snowball at  -18 C.
What is the warming effect of the radiative action of the Earth atmosphere on the temperature of the surface of the Earth, the so-called greenhouse effect?  See also following post and this one.

What would thus the temperature be if the atmosphere was fully transparent without the so-called greenhouse gasses water vapour and CO2, thus without effects of (infrared) radiation? This would be like an Earth with no atmosphere.

And the other way around: What would the temperature be if the atmosphere was fully opaque?

These questions connect to earlier posts such as this, and these if you want to browse. For a revelation of the mystery of black body radiation, see the web site Computational Black Body Radiation.

The standard answer propagated by global warming alarmism is that the greenhouse effect is +33 C. It is claimed that with a fully transparent (or no) atmosphere, the Earth would be a frozen ball at -18 C instead of the observed +15 C with a difference of 33 C.

The presence of greenhouse gasses is thus what makes the Earth livable. The message is that the greenhouse effect is big = 33 C and as such will lead to dangerous global warming of 3 C upon a small increase of CO2 as the "best estimate" of IPCC, as 1/10 of an estimated big greenhouse effect.

This is the very basis of climate alarmism demanding a stop to emission of CO2 to prevent the Earth + atmosphere passing a tipping point into a run-away greenhouse effect approaching the surface temperature of Venus with its atmosphere filled with CO2, that is a roaring Hell at 462 C.

This is the apocalypse waiting unless we cut down CO2 emissions from human activity to zero and form a fossil free world following the lead of Sweden now transforming into the first fossil free welfare state as required by the New Swedish Climate Law.

To check the alarm signal of 33 C let us recall Stephan-Boltzmanns radiation law for a grey body:
• $Q = \epsilon\sigma T^4$
connecting radiance $Q$ at temperature $T$ in Kelvin K into a background at 0 K, through Stephan Boltzmann's constant $\sigma$ with $0\le\epsilon\le 1$ a coefficient of emissivity with a black body characterised by $\epsilon =1$.

Assuming absorptivity=emissivity (according to Kirchhoff's law), we can use the SB-law to compute the temperature $T$ of a grey body at a certain distance $D$ from the Sun knowing that the temperature $T_S$ at the emitting surface of the Sun (acting like a black body) is 5778 Kelvin K. What is needed is the ratio $q=R/D$ with $R$ the radius of the Sun, with $q^2$ the dilution effect depending on distance/area. All grey bodies at the same distance from the Sun would then have the same surface temperature (compare with discussion here).

For the Earth $q =0.00465047$ which gives the surface temperature $T_E$ through the following formula resulting from the above SB-law:
• $T_E = (0.25*q^2)^{0.25}*5778 = 279$ K
with the first factor $0.25$ the ratio between projected surface to total surface of a sphere. The temperature of the Earth as a grey body with fully transparent (or no)  atmosphere, would thus be 279 K or +6 C.

For Mars with a very thin almost transparent atmosphere and with a distance to the Sun equal to 1.524 astronomical units, the formula gives 225 K, to be compared with observed about 228 K with then a small 3 C greenhouse effect. The two small moons Phobos and Deimos of Mars are reported to have about the same temperature of 233 K.

For Mercury essentially without atmosphere with a distance to the Sun of 0.4 au, the formula gives 440 K, just as observed with zero greenhouse effect.

The mean value of max and min temperatures of Ganymede, the largest of Jupiter's moons with a very thin atmosphere of Oxygen, is -125 C, which fits well with the formula with a distance of 5.2 au, again with zero greenhouse effect.

For Titan the largest moon of Saturn at a distance of 9.6 au the formula gives 90 K to be compared with an observed surface temperature of 94 K, thus with a very modest greenhouse effect of 4 K from an atmosphere somewhat denser than that of the Earth consisting mainly of nitrogen.

For Pluto with average au = 40 the formula gives 44 K = - 229 C in agreement with observed temperature varying between - 223 and - 233 C.

For the Moon (without atmosphere) rotating once every month, it is more natural to use the formula with the factor 0.25 replaced by 1 representing maximal (instead of mean) temperature to get +121 C fitting fairly well with observed maximal temperature  +127 C.

We thus see that the formula works (surprisingly or not) very well for Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres, and so we may expect it to serve also for an Earth without atmosphere:

The recorded mean temperature on the Earth surface is 288 C with gives a total atmosphere effect of +9 C, from fully transparent (or no) 279 K to observed 288 K with greenhouses gasses present into a semi-opaque atmosphere.

The total greenhouse effect is thus at most 9 C, instead of the 33 C as the corner stone of global warming alarmism.

The observed greenhouse effect of 9 C would then represent an observation of the total effect of the atmosphere on surface temperature, including both radiation and thermodynamics with gravitational lapse rate. Observation and not speculation.

Of course, the assumption that for the Earth without atmosphere emissivity=absorptivity, can be debated, since absorption and emission occurs at vastly different light frequencies, but yet may serve to get a rough estimate of the greenhouse effect (with Mercury, Mars, Ganymede, Pluto and the Moon essentially without atmospheres as observational support of the formula).

The temperature 255 K (-18 C) behind 33 C comes from an application of the SB-law assuming absorptivity = 0.7 and emissivity = 1 with questionable logic.

We can go one step further and predict what the temperature $T_E$ would be with a fully opaque
atmosphere by extrapolation from the present observed situation with the "infrared atmospheric window" acting as fully transparent atmosphere letting through 1/6 of the total emitted (infrared) radiation from the Earth surface directly into outer space. Closing the window from 5/6 to fully shut into a fully opaque atmosphere could then have an effect of $9/5$ C, less than 2 C. This is the observed variation of temperature after the last ice age.

The ultimate effect of making the atmosphere fully opaque would thus be less than 2 C and so the possible effect from more CO2 would thus be much smaller.

This argument thus supports an idea that climate sensitivity as the temperature increase upon doubling of CO2 from preindustrial level, is less than 1 C. This is based on observation of temperature 288 K (15 C) and atmospheric window 5/6 shut combined with the SB-law. Pretty basic and undisputable.

One can argue that the observations used in the argument include "feed-back" (from convection and evaporation). This is  to be compared with another common argument based on (invented) "radiative forcing without feed-back" as 1 C, which is inflated to 3 C by free invention of thermodynamic feed-back.

We can see the reduction of the basic greenhouse effect from 33 C to 9 C with a factor of 3-4, as a
reduction of the "best prediction" of climate sensitivity by IPCC of alarming 3 C into non-alarming 1 C. It may be as simple as that, to give the hope back to the people of the world.

PS1 In recent work by Nikolov and Zeller (referring to work by Volokin and ReLlez) the greenhouse effect is claimed to be whopping +90 C. A coming post will explain the origin of this utterly alarming  (misleading) number. Nikolov and Zeller do not start out very promising: Thermal enhancement of 90 K creates a logical conundrum...appears inexplicable..Stay tuned...

PS2 The infrared atmospheric window is indicated in blue in the following picture:

PS3 The thick CO2 atmosphere of Venus is fully opaque, while the very high surface temperature of +462 C is a thermodynamic effect of high pressure from gravitation and not any "greenhouse effect" from CO2.  For a Venus without atmosphere the grey body formula gives +60 C.

## söndag 12 januari 2020

### On Real Simulation

 The painter, the painting and the nude physical origin.

Icarus Digital Math will be launched under the banner:
• automated real simulation.
Here "real" signifies that the simulation can serve as true prediction of reality and "automated" that the key elements of the simulation
1. mathematical modeling in terms of differential equations
2. discretisation in terms of algebraic equations
3. computational solution of algebraic equations,
are carried out in the form of computational software, such as FEniCS.

The term "real simulation" may seem like an oxymoron with an apparent contradiction between reality as ”what is” and simulation as ”what is computed/imagined”. But the relation between reality as god-given physical origin and simulation as man-made mathematical model or picture, is in fact very complex and as such an important aspect of both science and arts.

The postmodernist philosopher Baudrillard coined the concept of ”hyperreality” with the image filling the empty place of a non-existing origin, as true reality with Disneyland as example.

The computer scientist Dijkstra similarly elevated the model as the "abstract machine" more true than the "physical machine":
• Originally I viewed it as the function of the abstract machine to provide a truthful picture of the physical reality. Later, however, I learned to consider the abstract machine as the true one, because that is the only one we can think ; it is the physical machine's purpose to supply a working model, a (hopefully) sufficiently accurate physical simulation of the true, abstract machine.
It also comes to full expression in the Copenhagen Interpretation of Quantum Mechanics with the observer intimately coupled with the observed reality, in particular deciding the fate of Schrödinger's cat in the process of observation.

In arts, the relation between the painter, the picture and the model is also filled with deep meaning, connecting to Plato's allegory of the cave with shadows forming the reality.

## onsdag 8 januari 2020

### Boeing Flight Simulator?

The Guardian reports:
• Boeing now recommends 737 Max flight simulator training for pilots.
• Decision is a reversal of company’s long-held position that computer-based training alone was adequate.
In order for a flight simulator to correctly prepare pilots to handle real flight, the simulator must represent reality, which requires CFD (computational fluid dynamics) software capable of predicting the real reaction of the airplane upon control input from the pilot, including the critical phenomenon of stall which must be avoided. Standard CFD does not have this capability since it is based on prescriptive modeling.

Without CFD the action of an airplane, beyond simply guessing, will have to be discovered from extensive experience in real flight, where extreme situations such as stall are hazardous to test and thus must be avoided.

DFS Direct Finite Element Simulation is new CFD software based on first principle physics without prescriptive modeling, which has shown to be truly predictive of complex flight dynamics including stall, beyond the capability of standard CFD.

The design debacle behind the two 737 Max crashes can be connected to the use of standard CFD without stall prediction.

The question is now if Boeing is going to use DFS to design the intended upgrade of the automatic stall prevention system MCAS and the flight simulator preparing pilots to handle 737 Max with MCAS. Or if Boeing will continue to rely on standard software without stall prediction.

See also: Boeing employees’ frightening internal messages released in 737 Max investigation:
• Would you put your family on a Max simulator trained aircraft? I wouldn’t.
• This airplane is designed by clowns who in turn are supervised by monkeys.

## lördag 4 januari 2020

### Automated Flight Based on Predictive Flight Simulation

WSJ reports:
• MAX Crashes Strengthen Resolve of Boeing to Automate Flight.
• Boeing, Airbus and industry experts for long have planned more technology to prevent pilot error.
• Boeing Co. is increasingly committed to transferring more control of aircraft from pilots to computers after two crashes exposed flaws in an automated system on its 737 MAX that overpowered aviators in the disasters.
• Executives at Boeing and other makers of planes and cockpit-automation systems for some time have believed more-sophisticated systems are necessary to serve as backstops for pilots, help them assimilate information and, in some cases, provide immediate responses to imminent hazards...
Jetliners have auto-pilot systems relieving pilots from routine flight control when cruising, while a fighter jet like the JAS Gripen requires automatic control to handle the built-in instability allowing quick turns.

An auto-pilot is like a cruise-control on a car set to maintain a given speed as an option for steady cruising, without true capability to replace the pilot under variable conditions. Not so sophisticated.

The forward canard of JAS Gripen is used to automatically stabilise the flight, which is too delicate for manual pilot control. The interaction between the pilot and the control system carries the danger of PIO pilot induced oscillations, which caused two early JAS crashes before the software was tamed to slower turns.

The two Boeing 737 Max crashes were caused by the MCAS control system installed to help the pilot  stay away from stall in climb at full throttle after start by automatically pointing the nose down upon input from a single angle of attack sensor. But the sensor failed and MCAS forced the plane into the ground. Not so sophisticated.

So, Boeing is now searching for "more-sophisticated systems to respond to imminent hazards" in different forms of automated flight.

Development of automated flight would be greatly helped if predictive computational simulation of the dynamic action of an airplane from controls including throttle, rudder, elevators, slats, flaps and spoilers, was possible, since it could replace difficult time-consuming real flight testing.

Standard software for CFD Computational Fluid Dynamics is not truly predictive, since it hinges on wall and turbulence models, which are prescriptive rather than predictive, and thus do not well serve this purpose.

But there is light in the tunnel (for Boeing): DFS Direct Finite Element Simulation is new unique CFD software offered by Icarus Digital Math allowing prediction of the full dynamic flight characteristics of an airplane from first principle physics, without wall and turbulence models.

DFS thus opens the possibility to construct a flight simulator based on first principle physics, which is truly predictive and as such can contribute to the development of (safe) automated flight.