Description of the Book Content

In the text, the theory is developed for different regimes and the numerics are explained for some problems. In this respect, some computer code are available for full potential and transonic small disturbance equations. Boundary layer codes for laminar and turbulent flows are also available.

In Fig. 1.6, a road map for the materials of the book is described. The block in the middle covers steady two-dimensional incompressible inviscid flows. The generation of lift around a rotating cylinder (Magnus effect) is mathematically modeled as

a potential flow with circulation. In the text, the important notion of circulation is discussed in details from both physical and mathematical views. Without circulation, there is no lift (because of symmetry). The circulation increases the velocity on one side and retards it on the other side. The difference in velocity is associated with a difference in pressure (Bernoulli’s law), hence a lifting force is generated. An analytical closed form solution is obtained for this model. The lift is related to the asymmetry generated by the circulation and a relation between lift and the angle of the flow separation is derived. Also, the Kutta-Joukowski lift theorem is established.

Next, the Joukowski transformation is introduced to relate the flow over a cylinder to a flow over Joukowski airfoils (including the flat plate and circular arc as special cases). The celebrated formula for the lift coefficient of flat plates (or for that matter any thin airfoil) is derived. Similarly, a formula for the camber effect is obtained from the circular arc. In all cases, the Kutta-Joukowski condition at the sharp trailing edge is applied, which states that the flow leaves the airfoil smoothly to mimic the real viscous flow. The physical source of circulation (and hence lift) can be explained in terms of the vorticity of the fluid elements in the boundary layer, due to shear stresses between the layers of the fluid. The general Joukowski airfoil results are also obtained (without using complex variables) and the effect of thickness on lift is delineated.

Next, the thin airfoil theory of Glauert and Munk is discussed in details, allowing the calculation of lift (and moment) for general thin airfoils using superposition of fundamental solutions (in terms of sources for the thickness problems and vortices for the lifting problems). The above topics are covered in Chaps. 2 and 3.

Compressibility effects for two-dimensional subsonic, transonic and supersonic flows are discussed in Chap.4. Both the linearized theory and the nonlinear transonic small disturbance theory are treated in detail. For subsonic flows, the Prandtl-Glauert rule relating subsonic and incompressible flow results is derived. For supersonic flows, Ackeret theory for thin airfoils provides the lift and wave drag estimates, as well as an explanation for why we have this type of drag. For transonic flows, the failure of the linearized theories is explained and the characteristic and shock relations, based on small disturbance theory, are given. Numerical schemes to solve the nonlinear equation using the Murman-Cole method are explained and the numerical results are presented. This chapter is one of the unique features of this book.

Chapter 5 deals with two-dimensional unsteady cases for both incompressible and compressible flows.

Three-dimensional effects are studied in Chaps. 6 and 7 for high and low aspect ratio (AR) wings. For incompressible flows, Prandtl lifting line theory (1918), the Weissinger vortex lattice method and the Munk and Jones slender wing theory are covered. The concept of induced drag (or vortex drag), also called drag due to lift, is explained and it is shown that for given lift, an elliptic planform (without twist) is optimum in the sense that the induced drag is minimum (the induced drag is related to the added kinetic energy stored in the cross flow induced by the vortex sheet, that is equal to the thrust needed to maintain the wing motion). The extension to compressible flows, with low and high Mach numbers, is followed for both bodies of revolution and slender wings. Optimum shapes for supersonic projectiles are discussed, together with the transonic and supersonic area rules, as well as conical flows. Transonic lifting line theory, swept and oblique wings are also covered.

Finally, viscous effects or Reynolds number effects, are dealt with in Chaps. 8 and 9, starting with Navier-Stokes equations and incompressible and compressible boundary layer theory, including viscous/inviscid interaction procedures, and the calculation of skin friction drag and form drag (that is pressure drag due to the boundary layer interaction with the inviscid flow, which is important in the case of separation. In general, there are four types of drag, skin friction drag, induced drag, wave drag and form drag. It is difficult to separate their contributions, particularly if the shock penetrates the boundary layer).

The book contains also four special topics, including wind turbines, airplane design projects, hypersonic flows and flow analogies (electric and hydraulic). Another special feature of the book is three appendices, the first two consist of ten exams and their solutions, and the last deals with mathematical methods in aerodynam­ics, including the method of complex variables, method of characteristics and the conservation laws with shock waves and contact discontinuities.

There are already many text books available on aerodynamics (see Refs. [1-12] below) and the authors would like to add one more. The authors hope that the reader will enjoy this book as much as the authors did.