Introduction

The flow considered in this chapter is assumed to be steady, incompressible, inviscid, and irrotational. The body immersed in the flow is assumed to be a body of revolution at zero angle of attack. An understanding of incompressible flow around bodies of revolution at zero or small angle of attack is important in several practical applications, including airships, aircraft and cruise-missile fuselages, submarine hulls, and torpedoes, as well as flows around aircraft engine nacelles and inlets. This type of flow problem is best handled in cylindrical coordinates (x, r), as shown in Fig. 7.1. Recall that r and θ lie in the y-z plane.

Because the flow fields discussed in this chapter are axisymmetric, the flow properties depend on only the axial distance x from the nose of the body (assumed to be at the origin in most cases) and the radial distance, r, away from this axis of symmetry. The flow properties are independent of the angle θ. As a result, we may examine the flow in any (x-r) plane because the flow in all such planes is identical due to the axial symmetry. It is convenient to develop the defining equations initially in cylindrical coordinates (i.e., dependence on x, r, and θ) and then to simplify them for axisymmetric flow (i.e., dependence on x, r only).

Preface

This textbook presents the fundamentals of aerodynamic analysis. Major emphasis is on inviscid flows whenever this simplification is appropriate, but viscous effects also are discussed in more detail than is usually found in a textbook at this level. There is continual attention to practical applications of the material. For example, the concluding chapter demonstrates how aerodynamic analysis can be used to predict and improve the performance of flight vehicles. The material is suitable for a semester course on aerodynamics or fluid mechanics at the junior/senior undergraduate level and for first-year graduate students. It is assumed that the student has a sound background in calculus, vector analysis, mechanics, and basic thermodynamics and physics. Access to a digital computer is required and an understanding of computer programming is desirable but not necessary. Computational methods are introduced as required to solve complex problems that cannot be handled analytically.

The objective of this textbook is to present in a clear and orderly manner the basic concepts underlying aerodynamic-prediction methodology. The ultimate goal is for the student to be able to use confidently various solution methods in the analysis of practical problems of current and future interest. Today, it is important for the student to master the basics because technology is advancing at such a rate that a more directed or specific approach often is rapidly outdated. In this book, the basic concepts are linked closely to physical principles so that they may be understood and retained and the limits of applicability of the concepts can be appreciated. Numerous example problems stress solution methods and the order of magnitude of key parameters. A comprehensive set of problems for home study is included at the end of each chapter.

Introduction

This chapter examines the role of viscosity in the flow of fluids and gases. Although the viscosity of air is small, it must be included in a flow model if we are to explain wing stall and frictional drag, for example. The four preceding chapters are concerned with the analysis of airfoils, wings, and bodies of revolution based on an assumption of inviscid flow (i.e., negligible viscous effects). The inviscid-flow model allowed analytical solutions to be developed for predicting, with satisfactory accuracy, the pressure distribution on bodies of small-thickness ratio at a modest (or zero) angle of attack. However, the inviscid-flow model leads to results that are at odds with experience, such as the prediction that the drag of two-dimensional airfoils and right-circular cylinders is zero. This contradiction is resolved by realizing that actual flows exhibit viscous effects.

Viscosity is discussed from a physical viewpoint in Chapter 2. In Chapters 5, 6, and 7, the existence of viscosity is acknowledged when it is necessary to advance an analytical derivation for an inviscid flow. Also, viscous effects are called on, with words like viscous drag and separation, when comparing the predicted and observed behavior of airfoils and wings. However, no analysis in this textbook has been developed thus far that provides the required detailed physical basis for these effects.