Elements Of Vorticity Aerodynamics

The book opens with a discussion of the vorticity-dynamic formulation of the low Mach number viscous flow problem. Physical aspects of the velocity and the vorticity fields, their instantaneous relationship, and the transport of vorticity in viscous fluids are examined for steady and unsteady flows. Subsequently, the mathematical aspects of vorticity dynamics and issues of initial and boundary conditions for the viscous flow problem are treated rigorously using classical analyses. Coverage includes evolution of the vorticity field which surrounds and trails behind airfoils and wings, generalizations of Helmholtz' vortex theorems and the Biot-Savart Law. A theorem is introduced that relates the aerodynamic force to the vorticity moment and the applications of the theorem are reviewed. Interpretations of the Kutta-Joukowski theorem and Prandtl's lifting line theory for vorticity dynamics are presented and wake integral methods are reviewed. The virtual-mass effect is shown to be the seminal event in unsteady aerodynamics and a simple approach for evaluating virtual-mass forces on the basis of vorticity dynamics is presented. The book presents a modern viewpoint on vorticity dynamics as the framework for understanding and establishing the fundamental principles of viscous and unsteady aerodynamics. It is intended for graduate-level students of classical aerodynamics and researchers exploring the frontiers of fully unsteady and non-streamlined aerodynamics.