torsdag 2 augusti 2012

Text Book Theory of Flight: Schlichting 1979

We continue the overview of text book theory of flight, now with Aerodynamics of the Airplane by Schlichting and Truckenbrodt, 1979:
  • In many technical applications, viscous flow can be neglected in order to simplify the laws of fluid dynamics (inviscid flow). This is down in the theory of lift of airfoils (potential flow).
  • To determine the drag of bodies, however, the viscosity has to be considered (boundary-layer theory).
  • The theory of inviscid, incompressible flow has been developed mathematically in detail, giving, in many cases, a satisfactory description of the actual flow, for example, in computing airfoil lift at moderate flight velocities. On the other hand, this theory fails completely for the computation of body drag. 
  • Only a very few comprehensive presentations of the scientific fundamentals of the aerodynamics of the airplane have ever been published. The study of the aerodynamics of the airplane requires a thorough knowledge of aerodynamic theory.
  • The lift can be obtained in very good approximation from the theory of inviscid flow.
  • Lift production on an airfoil is closely related to the circulation of its velocity near-field. 
  • There is higher pressure on the lower surface, lower pressure on the user surface. It follows, from the Bernoulli equation, that the velocities on the lower and upper surfaces are lower or higher, respectively. With these facts in mind it follows that the circulation differs from zero. The velocity field can be thought to have been produced by a clockwise-turning vortex that is located on the airfoil. This vortex, which apparently is of basic importance for the creation of lift, is called the bound vortex of the wing.
  • If the magnitude of the circulation is known, the Kutta-Zhukovsky formula, is of practical value for the calculation of lift….The circulation cannot be determined uniquely from theoretical considerations, so it is necessary to look for empirical results. The magnitude of the circulation can be derived from experience, namely, that there is no flow around the trailing edge. This is the Kutta condition.
  • It is seen that the viscosity of the fluid, after all, causes the formation of circulation and, therefore, the establishment of lift. Viscosity of the fluid must therefore be taken into consideration temporarily to explain the evolution of lift, that is, the formation of the starting vortex. After the establishment of the starting vortex and the circulation around the wing, the calculation of lift can be done from the laws of frictionless flow using the Kutta-Zhukovsky equation observing the Kutta condition.
We see that lift is connected to circulation which is determined by the Kutta condition. We see how inviscid theory is combined with viscous effects into a mix generating lift but no drag, which however does not describe actual physics.

See also Critical review of Aerodynamics of the Airplane by Schlichting and Truckenbrodt.

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