Corruption of Modern Physics 14: Prandtl’s Boundary Layer Theory
Ludwig Prandtl is named Father of Modern Fluid Mechanics motivated by his boundary layer theory with a no-slip boundary condition as key element, which has dominated fluid mechanics since the 1920s.
No-slip means that a fluid meets a fixed solid boundary with zero velocity thus creating a boundary layer connecting free flow velocity away from the boundary with thickness scaling with ν−−√ with ν fluid viscosity of typical size 0.000001.
A typical boundary layer is thus very thin of size 0.001 which requires so many mesh points in computation that the required computational power is far away still today. In addition, small viscosity fluid mechanics is turbulent with small scales also asking for resolution.
Father Prandtl with his no-slip boundary condition thus forced modern fluid mechanics into a fruitless search for wall models seeking to circumvent the need of boundary layer resolution, which made modern fluid mechanics into a nightmare of wall modeling.
How could this be?
The reason is that with the no-slip condition Prandtl could present a resolution of d’Alembert’s Paradox remaining unresolved since its formulation in 1755, with the paradox comparing prediction of zero drag or resistance to motion in theoretical potential flow satisfying a slip boundary condition as a model of small skin friction of size 0.001 allowing the fluid to slide without friction along a solid boundary, with observation of real flow with substantial drag.
As noted by Nobel Laureate Hinshelwood, this made fluid mechanics from start into a joke when divided into
- practical fluid mechanics or hydraulics observing phenomena which cannot be explained (non-zero drag)
- theoretical fluid mechanics explaining phenomena which cannot be observed (zero drag).
Prandtl suggested to resolve the paradox by declaring potential flow satisfying Euler’s equations for slightly viscous flow as an illegal solution because of violation of the no-slip condition.
This simple trick brought relief to fluid mechanics from start viewed as a joke, but it came with the side effect of making fluid mechanics instead into a computational night-mare. From ashes into the fire.
In 2010 I published together with Johan Hoffman a real resolution of d’Alembert’s paradox in the prestigious Journal of Mathematical Fluid Mechanics, which showed that the reason the zero-drag potential solution with slip cannot be observed, is that it is unstable and so is replaced by a turbulent solution of Euler’s equations with slip but non-zero drag from a turbulent wake.
Main drag is thus not an effect of skin friction as Prandtl claimed, but from free flow turbulence as shown in the fig above.
This work changed the premises for fluid mechanics freeing it for the computational impossibility of no-slip, since slip does not generate any boundary layer.
The full potential is exposed in Euler Right! Prandtl Wrong? including a revelation of the Secret of Flight.
Take a look and free yourself from the prison of no-slip.
See more here claesjohnson
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Jerry Krause
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Hi Claes and PSI Readers,
PSI Readers because Claes has not respond to my comment to his article of 11/8. So I do not know if he is monitoring his PSI comments.
Claes wrote: “A typical boundary layer is thus very thin of size 0.001”. What he did not write is the units that must define the thickness of the boundary layer. Whether a m, a mm, a micrometer?
Chemists study “the chemistry of surfaces) which by definition must be due to the atoms (molecules) on a surface. It does not matter what the atoms (molecules) beneath this surface are because external atoms (molecules) coming into constant with this surface must first contact these surface atoms (molecules).
Now an instrument called an IR Thermometer has been invented and one can make the following experiment. Point this instrument at a surface being illuminated by the sun and read the temperature. Then, without changing anything except placing an opaque barrier to shade the surface. Again read the instrument’s temperature and note how rapidly the surface temperature has decreases. Than remove the barrier and note haw rapidly the temperature increases to its previous value.
The only way to explain what is observed is that only an atomic layer, or two, is being heated by the direct solar radiation and the surface is only being heated by the diffuse indirect solar radiation which doesn’t cast an observable shadow.
Hence, maybe the “boundary layer’ is much thinner than Ludwig Prandtl was imagining and reasoning .
Have a good day, Jerry
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Howdy
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“A typical boundary layer is thus very thin of size 0.001 which requires so many mesh points in computation that the required computational power is far away still today”
Since 1920, or maybe 1755? Are you kidding me? Talk about stuck in the past. So no new developments in free flowing liquids then? Difficulty for the sake of it.
Just aim for the smoothest skin regardless. Smooth skin, smooth flow. If I want maximum air flow in a cylinder head I remove as much restriction as possible and smooth the surfaces, otherwise I get mini turbulences that slow the flow (parasitic?). An aircraft flies more efficiently when it’s smooth and clean. Fast flowing hydraulics like minimal bends etc. It’s demonstrated all over the place. What’s the big deal.
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