lördag 14 juli 2012

Making of the Prandtl Myth by Schlichting

Listen to Herrmann Schlichting forming the Myth of Prandtl as Father of Modern Fluid Mechanics

The myth of Prandtl as the Father of Modern Fluid Mechanics was shaped by his former students Theodor von Karman and Hermann Schlichting (photo) serving as aeronautics expert scientists in the US and Germany during the 2nd World War. Upon request from the Allied forces Schlichting documented Prandtl's expertise in the book Boundary Layer Theory, viewed as the bible of modern fluid mechanics. It is possible to argue that the outcome of the war was influenced by incorrect German aeronautics.

Let us analyze how Schlichting builds the Prandtl myth in the Introduction to his book in a sequence of quotes followed by comments:

Schlichting: The present book is concerned with the branch known as boundary-layer theory. This is the oldest branch of modern fluid dynamics; it was founded by Prandtl in 1904 when he succeeded in showing how flows involving fluids of very small viscosity, in particular  water and air, the most important ones from the point of view of applications, can be made amenable to mathematical analysis.

Comment: This sets the scence with boundary-layer theory opening to technological progress by mathematical analysis in the hands of Prandtl.

Schlichting: This was achieved by taking the effects of friction into account only in regions where they are essential, namely in the thin boundary layer which exists in the immediate neighbourhood of a solid body.

Comment: This is a clever circular formulation with effects of viscosity taken into account where they are essential and should be taken into account.

Schlichting: This concept made it possible to clarify many phenomena which occur in flows and which
had previously been incomprehensible.

Comment: Vague. Nothing was clarified, only further mystified.

Schlichting: Most important of all, it has become possible to subject problems connected with the occurrence of drag to a theoretical analysis.

Comment: This is the central dogma of Prandtl: Drag originates from boundary layer effects. We show that thus is incorrect by obtaining correct drag without boundary layers.

Schlichting: The science of aeronautical engineering was making rapid progress and was soon
able to utilize these theoretical results in practical applications. It did, furthermore,  pose many problems which could be solved with the aid of the new boundary layer theory. Aeronautical engineers have long since made the concept of a boundary layer one of everyday use and it is now unthinkable to do without it.

Comment: Vague. 

Schlichting: In other fields of machine design in which problems of flow occur, in particular in the design of turbomachinry, the theory of boundary layers made much slower progress, but
in modern times these new concepts have come to the fore in such applications as well.

Comment: This in an admittance that the boundary layer theory is not useful in applications.

Schlichting: Towards the end of the 18th century the science of fluid mechanics began to
develop in two directions which had practically no points in common. On the one
side there was the science of theoretical hydrodynamics which was evolved from
Euler's equations of motion for a frictionless, non-viscous fluid and which achieved a
high degree of completeness. Since, however, the results of this so-called classical
science of hydrodynamics stood in glaring contradiction to experimental results — in
particular as regards the very important problem of pressure losses in pipes and
channels, as well as with regard to the drag of a body which moves through a mass
of fluid — it had little practical importance. For this reason, practical engineers,
prompted by the need to solve the important problems arising from the rapid
progress in technology, developed their own highly empirical science of hydraulics.
The science of hydraulics was based on a large number of experimental data and
differed greatly in its methods and in its objects from the science of theoretical

Comment: This is an admittance that theory and practice do not come together.

Sclichting: At the beginning of the present century L. Prandtl distinguished himself by
showing how to unify these two divergent branches of fluid dynamics. He achieved
a high degree of correlation between theory and experiment and paved the way
to the remarkably successful development of fluid mechanics which has taken place
over the past seventy years. It had been realized even before Prandtl that the
discrepancies between the results of classical hydrodynamics and experiment were, in
very many cases, due to the fact that the theory neglected fluid friction. Moreover,
the complete equations of motion for flows with friction (the Navier-Stokes
equations) had been known for a long time. However, owing to the great mathematical
difficulties connected with the solution of these equations (with the exception of a
small number of particular cases), the way to a theoretical treatment of viscous
fluid motion was barred. Furthermore, in the case of the two most important fluids,
namely water and air, the viscosity is very small and, consequently, the forces
due to viscous friction are, generally speaking, very small compared with the
remaining forces (gravity and pressure forces). For this reason it was very difficult
to comprehend that the frictionall forces omitted from the classical theory influenced
the motion of a fluid to so large an extent.

Comment: The claim that Prandtl unified mathematical theory and practice is without substance. Prandtl was mathematically naive and his dictate that Navier-Stokes equations cannot be combined  with force boundary conditions, is incorrect. 

Schlichting: In a paper on "Fluid Motion with Very Small Friction", read before the
Mathematical Congress in Heidelberg in 1004, L. Prandtl | showed how it was possible to
analyze viscous flows precisely in cases which had great practical importance.

Comment: The paper is very short (8 sparsely typed pages) and contains no mathematical analysis, only vague speculations, which have showed to be misleading.

Schlichting: With the aid of theoretical considerations and several simple experiments, he proved that
the flow about a solid body can be divided into two regions: a very thin layer in the
neighbourhood of the body (boundary layer) where friction plays an essential part,
and the remaining region outside this layer, where friction may be neglected.

Comment: This subdivision is mathematically and physically impossible.

Schlichting: On the basis of this hypothesis Prandfl succeeded in giving a physically penetrating
explanation of the importance of viscous flows, achieving at the same time a maximum
degree of simplification of the attendant mathematical difficulties. The theoretical
considerations were even (then supported by simple experiments performed in a
small water tunnel which Prandtl built with his own hands. He thus took the first
step towards a reunification of theory and practice. This boundary-layer theory proved
extremely fruitful in that it provided an effective tool for the development of fluid

Comment: The claim that Prandtl unifies theory and practice with a maximum of mathematical simplification lacks rationale.

Schlichting: Since the beginning of the current century the new theory has been
developed at a very fast rate under the additional stimulus obtained from the recently
founded science of aerodynamics. In a very short time it became one of the foundation
stones of modern Ihiid dynamics together with the other very important
developments — the aerofoil theory and the science of gas dynamics. 

Comment: This summarizes the myth of Prandtl as the Father of Modern Fluid Mechanics. The truth is that Prandtl misled a whole century of fluid dynamicists in searching for drag and lift in a vanishingly thin boundary layer.

Schlichting: The existence of tangential (shearing) stresses and the condition of no slip near  solid walls constitute the essential differences between a perfect and a real fluid. Certain fluids which are of great practical importance, such as water and air, have very small coefficients of viscosity. In many instances, the motion of such fluids of small viscosity agrees very well with that of a perfect fluid, because in most eases the shearing stresses are very small. 

Comment: This is an admittance that the skin friction forces are small in the boundary layer and thus can be approximated by a slip boundary condition, in direct violation of Prandtl's dictate of no-slip.

Schlichting: For this reason the existence of viscosity is completely neglected in the theory of perfect fluids, mainly because this introduces a far-reaching simplification of the. equations of motion, as a result of which an extensive mathematical theory becomes possible.  It is, however, important to stress the fact that even in fluids with very small viscosities, unlike in perfect fluids, the condition of no slip near a solid boundary prevails. This condition of no slip introduces in many cases very large discrepancies in the laws of motion of perfect and real fluids. In particular, the. very large discrepancy between the value of drag in a real and a perfect fluid has its physical origin in the condition of no slip near a wall. 

Comment: This is Prandtl's dictate of no-slip which has made 20th century fluid mechanics both uncomputable and impossible to rationalize.

Foreword by Dryden: Boundary-layer theory is the cornerstone of our knowledge of the flow of air and other fluids of small viscosity under circumstances of interest in many engineering applications. Thus many complex problems in aerodynamics have been clarified by a study of the flow within the boundary layer and its effect on the general flow around the body. Such problems include the variations of minimum drag and maximum lift of airplane wings with Reynolds number, wind-tunnel turbulence, and other parameters. Even in those cases where a complete mathematical analysis is at present impracticable, the boundary-layer concept has been extraordinarily fruitfull and useful.

Comment:  Big words without real substance.

1 kommentar:

  1. The equation of motion are invented by Newton and they are made for ideal situations.They works when there is not any friction of surface and air friction.