# FAQ

Q1: Why is slip/small friction a first principle physics boundary condition?

A1: This is because slip/small friction models the very small skin friction observed in experiments. More precisely, in experiments where the flow is not artificially tripped by ribbons or wires transversal to the flow which generate turbulent boundary layers with an order of magnitude larger skin friction than without tripping. Real wings do not have tripping devices and thus skin friction from tripped experiments feed standard CFD as RANS with too much skin friction. A slip boundary condition can be seen as a vanishingly thin film limit of a laminar boundary layer with very small skin friction. Slip makes CFD computable because impossible computational resolution of thin boundary layers is not required.

Q2: What is the turbulence model of DFS?

A2: DFS solves Euler’s equations from a principle of best possible computational solution, which acts as an automatic turbulence model, in a situation where, as an expression of the turbulent nature of slightly viscous flow, the Euler equations cannot be solved exactly. More precisely, DFS solutions have stable mean-value outputs such as drag and lift, while exact solutions such as potential flow have unstable outputs and thus are unphysical. DFS is best possible computation of turbulent flow. DFS simulates physical flow form first principle physics.

Q3: DFS uses adaptive output error control based on a dual solution to a dual problem linearised at a computed turbulent solution with very reaction coefficients as solution gradients. Why does not the dual solution blow up?

A3: This is because the coefficients are oscillating and thus drive both exponential growth and decay with a combined cancellation effect making the dual solution computable without blow up. The dual solution to a DFS solution thus does not blow up, but the dual solution of potential flow does as an expression of the instability of potential flow.

Q4: How does DFS make CFD computable?

A4: By using a physical slip/small friction force boundary condition which does not generate thin boundary layers, which are impossible to resolve computationally with foreseeable computer power. Standard CFD uses a no-slip boundary condition coming with thin boundary layers. A no-slip boundary condition is unphysical since individual fluid particles cannot be controlled and only forces can be imposed. The no-slip boundary condition was used by Prandtl to resolve d’Alembert’s paradox by claiming that potential flow with zero drag cannot be observed since it satisfies a slip boundary condition. This was a resolution on purely formal but not physical grounds. The correct resolution of the paradox is to understand that potential flow cannot be observed since it is unstable (see A3)

Q5: What is the significance of slip as zero friction vs small friction?

A5: This distinction is important in certain cases since the flow separation can be different between slip and small friction. For example the physical flow over a rotating wheel of a F1 racing car is seen to separate on top of the wheel, which is captured in DFS with small friction of sufficient strength, while DFS with slip gives later separation with reduced down-force. The switch in DFS from slip to small friction can be connected to the mesh size h with a skin friction coefficient in the small friction boundary condition bigger than h reducing the tangential velocity and thus having an effect.

Q6: Physical flow is rotational with vorticity. In standard no-slip CFD vorticity is viewed to be generated from a no-slip boundary layer. From where does vorticity come in DFS with slip?

A6: It comes from instability in accelerating slightly viscous flow named vortex stretching as the main mechanism of generation of vorticity through the vorticity equation. There is a misconception named Kelvin’s theorem that says that without rotational forcing vorticity stays small if not generated in a no-slip boundary. But Kelvin did not take the instability of the vorticity equation into account and thus his theorem is misleading.

Q7: How big is true skin friction?

A7: Standard CFD uses skin friction calibrated to tripped flat plate experiments to estimate that skin friction is 50-70% of total drag for a slender body like a wing at small angle of attack or ship moving through still water. DFS with slip computes total drag of such a body as form/pressure drag in close accordance with observation, giving strong evidence that untripped skin friction is less than 10% of total drag. This gives design a new reality to work from.

Q8: What is meant by the automated computational modeling of DFS?

A8: This is what the FEniCS software makes possible: A given mathematical model, in the form of a set of partial differential equations like the Euler equations over a given domain in space in the case of DFS, are automatically transferred into a discrete system of equations using the finite element method, which is automatically solved by linear algebra software. The finite element mesh is automatically adapted to best capturing of chosen outputs with chosen computational power. The only input is pde, geometry and forcing.

Q9: What is the connection between slip and laminar/turbulent boundary layer?

A9: The flow around a wing before stall acts as satisfying a slip boundary condition, which can be seen as a limit of the very small skin friction of a laminar boundary layer. This means that the flow without tripping “by-passes” the formation of a turbulent boundary with substantial skin friction. It is the slip which makes flight possible by making the flow follow the upper surface of a wing without separation until the trailing edge. With laminar/turbulent no-slip boundary layer the flow separates on the crest and lift is lost.

Q10: What makes an airplane fly?

A10: There are two crucial elements: (i) The flow is incompressible. (ii) The flow acts as with a slip boundary condition. The crucial flow features following from (i) + (ii) are: The flow does not separate on the crest of the upper side of the wing and before stall it does not do so until the trailing edge, where it separates as 3d rotational slip separation without pressure rise (which destroys lift in potential flow).

Q11: Are the explanations of the physics of flight found in text books incorrect?

A11: Yes. They essentially consist of Kutta-Zhukovsky circulation theory for lift without drag, and Prandtl boundary layer theory for drag without lift, unphysical theories which cannot be combined into a theory of physical flow with both drag and lift.

Q12: How is possible to design airplanes with incorrect theory?

A12: It does not matter if a theory is incorrect if it is not used, and instead design is geared by experiments in wind tunnels and experience form earlier designs, which is the current engineering practice. Experiment and experience instead of (useless) theory. But such methodology can mislead, as shown in catastrophic design of the Boeing 737 Max 8 creating an airplane prone to stall requiring software control like unstable fighter plane, software which malfunctioned and forced two planes into fatal crashes directly into the ground.

Q13: Why is Prandtl named the Father of Modern Physics?

A13: Because he presented a resolution of d’Alembert’s paradox, which had haunted theoretical fluid mechanics since its formulation in 1755, a resolution based on the concept of a thin no-slip boundary from which both drag and lift of a wing were supposed to originate. Prandtl’s resolution was viewed as relief from a trauma, but came with the side effect of making CFD impossible by demanding computational resolution of very thin boundary layers.

Q14: How is it possible the the dual linearised problem is computable for a turbulent solution with highly oscillating large reaction term?

A14: This is because of cancellation effects in the reaction term with alternating exponential growth and decay as an expression of turbulence. It reflects that meanvalue outputs such as drag and lift are computable in the presence of turbulence. If linearised at a potential solution the dual solution blows up reflecting that even meanvalue outputs (drag e g) of potential solution are unstable.

Q15: Is it meaningful to make convergence studies with excessive refinement to show that DFS captures an exact solution?

A15: No. There is no exact solution to turbulent flow as the nature of turbulence. It means that there is a true limit to the possible accuracy of meanvalues decreasing with increasing size in space and time of mean values, but not even global mean values such as drag and lift can be computed to arbitrary precision. However, with focussed adaptivity it is possible to capture the effect of even small changes of e g geometry on drag and lift.

Q16: What is the drag crisis?

A16: It refers to a drastic drop of drag e g for a circular cylinder from 1 to 0.2 at a Reynolds number of about 500.000, which reflects a change/transition from a no-slip boundary layer (laminar or turbulent) to a effectively a slip boundary condition with delayed separation and decrease of drag. The role of the dimples of a golf ball is to trigger this transition.

Q17: Is not LES also first principle physics, like DFS?

A17: No. LES as Large Eddy Simulation requires a subgrid turbulence model and in common form also a wall model in accordance with the dictate by Prandtl to use a no-slip boundary condition. DFS requires no turbulence or wall model and the turbulence modeling is done automatically by weighted momentum residual control as best possible solution of Euler’s equations in the presence of turbulence, where residuals can be zero only for unstable solutions such as potential solutions.

Q18: Is lift generated by the sharp trailing edge of an airfoil according to the Kutta-Zhukovsky theory?

A18: No, this is a misconception. It is observed since long that a wing with a rounded trailing edge (up to 2% of chord, or even 10% with some more drag) works just as fine.  This is also in accordance with DFS, which in particular shows that there is no large scale circulation around a wing as postulated by Kutta-Zhukovsky.

Q19: Does drag originate from a thin boundary layer as postulated by Prandtl?

A19: No. DFS with slip without boundary layer gives drag in close correspondence with observation as form/pressure drag. DFS shows that skin friction drag is very small in contradiction to common belief that it is half or more of total drag based on misleading artificially tripped flat plate results.

Q20: What is d’Alembert’s paradox?

A20: It is the fact noted by d’Alembert in 1755 that drag and lift of potential flow as solution to the Euler equations, is zero, which is not what is observed. Prandtl’s explanation form 1904 is that potential flow does not satisfy a no-slip boundary condition as so potential flow is not physical flow. We gave a new explanation in 2008 based on the fact that potential flow is unstable and as such cannot be observed in reality.  DFS initialised as potential flow turns into a partly turbulent flow from 3d rotational slip separation (at the trailing edge of a wing).

Q21: Why is the leading edge on a wing rounded?

A21: A wing with positive angle of attack creates from flow acceleration strong suction (lift) on the upper part of a rounded leading edge, which tapers off towards the trailing edge to zero suction,  because the flow does not separate on the crest due to an effective slip boundary condition.  2/3 of the lift comes this way from suction on the upper wing surface, and the rest from the lower pressure side of the wing. With a no-slip boundary condition the flow separates on the crest of the wing and lift is lost.

Q22: What is stall?

A22: This is when the flow separates on the (upper) suction side and lift is lost, drag increases and the wing loses functionality. This happens at a certain angle of attack (around 20 degrees) as a result of streamwise vorticity enhanced in the accelerating flow over the leading edge which causes transversal unstable opposite flow leading to 3d rotational slip separation before the trailing edge.  The MCAS control system of a Boeing 737 Max 8 was intended to automatically decrease the angle of attack (dip the nose down) to avoid stall in climb and turn after take-off at large angle of attack to counter an instability created by a change of design with bigger engines mounted further forward on the wings, which was not previewed according to standard simulation.  The MCAS did not work as intended an led to two fatal crashes before the Max was grounded possibly for ever.

Q23: A common view in the spirit of Prandtl is that not only drag but also lift somehow is an effect of viscosity making the flow stick to the wing surface satisfying a no-slip boundary condition. Is this a correct view?

A23: No. There is a fundamental difference between a no-slip and slip boundary condition as concerns both drag and lift. In particular, flow with no-slip will separate on the crest of a wing because the pressure gradient normal to the boundary is very small in a no-slip boundary layer (in Prandtl’s boundary layer equations, it is put to zero), and thus cannot accelerate the flow to follow the surface after the crest and so the flow separates. Details here.

Q24: How can it be that Prandtl even today is viewed as the Father of Modern Fluid Mechanics, when his boundary layer theory effectively has made CFD impossible?

A24: Prandtl’s no-slip boundary layer theory presented in 1904 went unnoticed until the late 1930s when it became an important element in German efforts to take a lead in aviation (in competition with England). This was before the computer and Prandtl’s boundary layer theory was viewed as a tool to simplify analytical computation with pen and paper. With the computer, Prandtl’s theory instead presented an unsurmountable obstacle by asking for impossible computational resolution of thin boundary layers. But the grip of analytical tradition was strong even in the postwar era of computing and so Prandtl’s no-slip condition and impossible CFD became the wisdom of the fluid dynamics community ruling into our time, only recently questioned by DFS. (In war time, an incorrect theory could also be used to mislead your opponent).

Q25: DFS shows (beyond the drag crisis) to predict lift and drag of a bluff body from shape alone, thus without any parameter input. How is this possible?

A25: This is because the flow before 3d rotational slip separation into a turbulent wake has a large scale structure and the turbulent dissipation in the wake can be captured without mesh refinement to physical scale.

Q26: What is the input to DFS of bluff body flow?

A26: Beyond the drag crisis it is only the shape of the body and desired output such as lift and drag and time average pressure distribution together with tolerance level or total computer time. No turbulence or wall model. DFS thus is a parameter free model and it is most remarkable that as such it delivers lift, drag and pressure distribution in close agreement with observation. A parameter free model represents according to Einstein the ideal mathematical model allowing predictions of physics without prior physical measurements. There are very few such models. A basic example is Newton’s 1st Law stating that a body which is not subject to any force will remain in rectilinear motion with constant velocity.

Q27: Standard CFD such as RANS and LES typically attributes for a streamlined body such as a wing at small angle of attack, 50% or more of total drag to skin friction. DFS computes drag of such bodies correctly with zero skin friction thus as pressure/form drag. What is going on?

A27: Std CFD is calibrated to experiments for flat plates with tripping into a turbulent boundary thus to unphysical large skin friction, as well as total drag experiments. Std CFD thus delivers 50% skin friction and 50% pressure drag, which both must be wrong in the perspective of DFS. Std CFD thus overestimates skin friction by using data from tripped experiments and underestimates pressure/form drag by not properly capturing flow separation.

Q28: What makes DFS truly predictive, while RANS-LES-DES are prescriptive and thus not truly predictive?

A28: This is because DFS does not rely on turbulence and wall models like RANS-LES-DES which prescribe the flow rather than predict from first principle physics.

Q29: In what sense is Real Flight Simulator RFS different from the flight simulators used for pilot training?

A29:  Conventional flight simulators are based on aerodynamic data (aero-data) collected from observations of flight under different pilot controls, specific for each airplane served by the simulator. This data collection is time-consuming and with a special difficulty of collecting data for extreme situations such stall and spin. With predictive DFS aero-data can be produced a much lower cost covering a much larger spectrum of flight conditions.

DFS in interactive form also opens to direct flight simulation in slow motion without precomputed aero-data.

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 idea 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/Computation, which fits with untripped real experiments, the flow of air meets the wing with a slip boundary condition modeling vanishing skin friction.