Category Fundamentals of Modern Unsteady Aerodynamics

Center of Pressure (xcp)

The location at which the resultant aerodynamic moment is zero. If we consider the profile (the wing section) as a free body, this point can be assumed as the center of gravity for the pressure distribution along the surface of the profile.

1.1.3 Aerodynamic Center (xac)

This is the point where the aerodynamic moment acting on the wing is independent of the angle of attack. The aerodynamic center is essential for the stability pur­poses. For a finite wing it is the line connecting the aerodynamic centers of each section along the span.

1.1.4 Steady Aerodynamics

If the flow field around a flying body does not change with respect to time, the aerodynamic forces and moments acting on the body remain the same all the time. This type of aerodynamics is called steady aerodynamics.


1.1.1 Aerodynamics

It is the branch of science which studies the forces and moments necessary to have a controlled and sustainable flight in air. These forces are named the lift in the direction normal to the flight and the drag or the propulsive force in the direction of the flight. In addition, it studies the effect of the velocity fields induced by the motion during flight. On the other hand, the study of the forces created by the motion of an arbitrarily shaped body in any fluid is the concern of the Fluid Mechanics in general. It is necessary to make this distinction at this stage.

1.1.2 Aerodynamic Coefficients

These are the non-dimensional values of pressure, force and moment which affect the flying object. In non-dimensionalization, the free stream density p and the free stream velocity U are used as characteristic values. One half of the dynamic pressure, VipU2 is utilized in obtaining pressure coefficient, cp. As the character­istic length, half of the chord length and as the characteristic area the wing surface area are considered. Hence, the product of dynamic pressure with the half chord is used to obtain the sectional lift coefficient q, the drag coefficient cd, and the moment coefficient cm, wherein the square of the half chord is used. For the finite wing, however, the coefficient of lift reads as CL, the drag CD and the moment coefficient CM.

Flights in Earth’s

Flights in Earth’s atmosphere existed long before the presence of mankind. 300 million years ago it was performed by insects with wings, 60 million years ago by birds and 50 million years ago by bats as flying mammals (Hitching 1982). Man, on the other hand, being the most recently emerged species among the living things first realized the concept of flight by depicting the flying animals in his creative works related to mythology or real life (Gibbs-Smith 1954). Needles to say, as a discipline, the science of Aerodynamics provides the most systematic and fundamental approach to the concept of flight.

The Aerodynamics discipline which determines the basic conditions of flying made great progress during the past hundred years, which is slightly longer than the average life span of a modern man (Anderson 2001). The reason of this progress is mainly the existence of wide range of aerospace applications in mili­tary and civilian industries. In the civilian aerospace industries, the demand for development of fast, quiet and more economical passenger planes with long ran­ges, and in the military the need for fast and agile fighter planes made this progress possible. The space race, on the other hand, had an accelerating effect on the progress during the last 50 years.

Naturally, the faster the planes get the more complicated the related aerody­namics become. As a result of this fast cruising, the lifting surfaces like wings and the tail planes start to oscillate with higher frequencies to cause in turn a phase lag between the motion and the aerodynamic response. In order to predict this phase lag, the concept of unsteady aerodynamics and its underlying principles were introduced. In addition, at higher speeds the compressibility of the air plays an important role, which in turn caused the emergence of a new branch of aerody­namics called compressible aerodynamics. At cruising speeds higher than the speed of sound, completely different aerodynamic behavior of lifting surfaces is observed. All these aerodynamical phenomena were first analyzed with mathe­matical models, and then observed experimentally in wind tunnels before they were tested on prototypes undergoing real flight conditions. Nature, needless to say, inspired many aerodynamicists as well. In recent years, the leading edge

U. Gulfat, Fundamentals of Modern Unsteady Aerodynamics, 1

DOI: 10.1007/978-3-642-14761-6_1, © Springer-Verlag Berlin Heidelberg 2010

vortex formation which gives extra lift for highly swept wings at high angles of attack has been studied extensively. During the last decade, the man made flight has no longer been based on a fixed wing. The flapping wing aerodynamics which utilizes the unsteady aerodynamic concepts is used in designing and building micro air vehicles to serve mankind in various fields.

First, let us introduce various pertinent definitions in order to establish a firm convention in studying the topics of unsteady aerodynamics in general.

Fundamentals of Modern Unsteady Aerodynamics

The flying animate objects were present in earth’s atmosphere about hundreds of million years before the existance of human kind on earth. Only at the beginning of twentieth century, the proper analysis of the lifting force was made to provide the possibility of powered and manned flight. Prior to that, one of the pioneers of mechanics, Sir Isaac Newton had used ‘his impact theory’ in an attempt to for­mulate the lifting force created on a body immersed in a free stream. In late seventeenth century, his theory was a failure due to calculation of insufficient lift generation and made him come to the conclusion that ‘flying is a property of heavenly bodies’. In a similar manner, almost after two centuries, William Thomson (Lord Kelvin) whose contributions to thermo and gas dynamics are well known, then proved that ‘only objects lighter than air’ can fly!

Perhaps it was the adverse influence of these two pioneers of mechanics on Western Europe, where contributions to the discipline of hydrodynamics is unquestionable, that delayed the true analysis of the lift generation. The proper analysis of lifting force, on the other hand, was independently made at the onset of twentieth century by the theoretical aerodynamicists Martin Kutta and Nicolai Joukowski of Central and Eastern Europe respectively. At about the same years, the Wright brothers, whose efforts on powered flight were ridiculed by authorities of their time, were able to fly a short distance. Thereafter, in a time interval little more than a century, which is a considerably short span compared to the dawn of civilization, we see not only tens of thousands of aircrafts flying in earth’s atmosphere at a given moment but we also witnessed unmanned or manned missions to the moon, missions to almost every planet in our solar system and to deeper space to let the existence of life on earth be known by the other possible intelligent life forms.

The foundation of the century old discipline of aeronautics and astronautics undoubtedly lies in the progress made in aerodynamics. The improvement made on the aerodynamics of wings, based on satisfying the Kutta condition at the trailing edge to give a circulation necessary for lift generation, was so rapid that in less than a quarter century it led to the breaking of the sound barrier and to the discovery of sustainable supersonic flight, which was unprecedented in nature and once thought to be not possible! In many engineering applications involving motion we encounter either forced or velocity induced oscillatory motion at high speeds. If the changes in the excitations are rapid, the response of the system lags considerably. Similarly, the response of the aerodynamic systems cannot be determined using steady aerodynamics for rapidly changing excitations. The unsteady aerodynamics, on the other hand, has sufficient tools to give accurately the phase lag between the rapid motion change and the response of the aerody­namic system. As we observe the performances of perfect aerodynamic structures of nature, we understand the effect of unsteady phenomena to such an extent that lift can be generated with apparent mass even without a free stream. In some cases, when the classical unsteady aerodynamics does not suffice, we go beyond the conventional concepts, with observing nature again, to utilize the extra lift created by the suction force of strong vorticies shed from the sharp leading edge of low aspect ratio wings at high angles of attack. We implement this fact in designing highly maneuverable aircrafts at high angles of attack and low free stream velocities. If we go to angles of attack higher than this, we observe aerodynami­cally induced but undesirable unsteady phenomena called wing rock. In addition, quite recently the progress made in unsteady aerodynamics integrated with elec­tronics enable us to design and operate Micro Air Vehicles (MAVs) based on flapping wing technology having radio controlled devices.

This book, which gives the progress made in unsteady aerodynamics in about less than a century, is written to be used as a graduate textbook in Aerospace Engineering. Another important aim of this work is to provide the project engi­neers with the foundations as well as the knowledge needed about the most recent developments involving unsteady aerodynamics. This need emerges from the fact that the design and the analysis tools used by the research engineers are treated as black boxes providing results with inadequate information about the theory as well as practice. In addition, the models of complex aerodynamic flows and their solution methodologies are provided with examples, and enhanced with problems and questions asked at the end of each chapter. Unlike this full text, the recent developments made in unsteady aerodynamics together with the fundamentals have not appeared as a textbook except in some chapters of books on aeroelasticity or helicopter dynamics!

The classical parts of this book are mainly based on ‘not so terribly advanced’ lecture notes of Alvin G. Pierce and basics of vortex aerodynamics knowledge provided by James C. Wu while I was a PhD student at Georgia Tech. What was then difficult to conceive and visualize because of the involvement of special functions, now, thanks to the software allowing symbolic operations and versatile numerical techniques, is quite simple to solve and analyze even on our PCs. Although the problems become more challenging and demanding by time, how­ever, the development of novel technologies and methods render them possible to solve provided that the fundamentals are well taught and understood by well informed users. The modern subjects covered in the book are based on the lecture notes of ‘Unsteady Aerodynamics’ courses offered by me for the past several years at Istanbul Technical University.

The first five chapters of the book are on the classical topics whereas the rest covers the modern topics, and the outlook and the possible future developments finalize the book. The examples provided at each chapter are helpful in terms of application of relevant material, and the problems at the end of each chapter are useful for the reader towards understanding of the subject matter and its future usage. The main idea to be delivered in each chapter is given as a verbal summary at chapters’ end together with the most up to date references. There are ten Appendixes appearing to supplement the formulae driven without distracting the uniformity of the text.

I had the opportunity of reusing and borrowing some material from the pub­lications of Joseph Katz, AIAA, NATO-AGARD/RTO and Annual Review of Fluid Mechanics with their kind copyright permissions. Dr. Christoph Baumann read the text and made the necessary arrangements for its publication by Springer. Zeliha Gulgat and Canan Danismam provided me with their kind help in editing the entire text. N. Thiyagarajan from Scientific Publishing Services prepared the metadata of the book. Aydin Misirlioglu and Firat Edis helped me in transferring the graphs into word documents. I did the typing of the book, and obtained most of the graphs and plots despite the ‘carpal tunnel syndrome’ caused by the intensive usage of the mouse. Furthermore, heavy concentration on subject matter and continuous work hours spent on the text showed itself as developing ‘shingles’! My wife Zeliha stood by me in all these difficult times with great patience. I would like to extend my gratitude, once more, to all who contributed to the realization of this book.

Подпись: Ulgen GulgatDatga and Istanbul, August, 2010