This book opens with a discussion of the vorticity-dynamic formulation of the low Mach number viscous flow problem. It examines the physical aspects of the velocity and the vorticity fields, their instantaneous relationship, and the transport of vorticity in viscous fluids for steady and unsteady flows. Subsequently, using classical analyses it explores the mathematical aspects of vorticity dynamics and issues of initial and boundary conditions for the viscous flow problem. It also includes the evolution of the vorticity field which surrounds and trails behind airfoils and wings, generalizations of Helmholtz’ vortex theorems and the Biot-Savart Law. The book introduces a theorem that relates the aerodynamic force to the vorticity moment and reviews the applications of the theorem. Further, it presents interpretations of the Kutta-Joukowski theorem and Prandtl’s lifting line theory for vorticity dynamics and discusses wake integral methods. 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.

The book introduces the fundamentals of fluid-mechanics, momentum theories, vortex theories and vortex methods necessary for the study of rotors aerodynamics and wind-turbines aerodynamics in particular. Rotor theories are presented in a great level of details at the beginning of the book. These theories include: the blade element theory, the Kutta-Joukowski theory, the momentum theory and the blade element momentum method. A part of the book is dedicated to the description and implementation of vortex methods. The remaining of the book focuses on the study of wind turbine aerodynamics using vortex-theory analyses or vortex-methods. Examples of vortex-theory applications are: optimal rotor design, tip-loss corrections, yaw-models and dynamic inflow models. Historical derivations and recent extensions of the models are presented. The cylindrical vortex model is another example of a simple analytical vortex model presented in this book. This model leads to the development of different BEM models and it is also used to provide the analytical velocity field upstream of a turbine or a wind farm under aligned or yawed conditions. Different applications of numerical vortex methods are presented. Numerical methods are used for instance to investigate the influence of a wind turbine on the incoming turbulence. Sheared inflows and aero-elastic simulations are investigated using vortex methods for the first time. Many analytical flows are derived in details: vortex rings, vortex cylinders, Hill's vortex, vortex blobs etc. They are used throughout the book to devise simple rotor models or to validate the implementation of numerical methods. Several Matlab programs are provided to ease some of the most complex implementations.

Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The main objective of the book is to provide an introduction to fluid dynamics in a simultaneously rigorous and accessible way, and its approach follows the idea that both the generation mechanisms and the main features of the fluid dynamic loads can be satisfactorily understood only after the equations of fluid motion and all their physical and mathematical implications have been thoroughly assimilated. Therefore, the complete equations of motion of a compressible viscous fluid are first derived and their physical and mathematical aspects are thoroughly discussed. Subsequently, the necessity of simplified treatments is highlighted, and a detailed analysis is made of the assumptions and range of applicability of the incompressible flow model, which is then adopted for most of the rest of the book. Furthermore, the role of the generation and dynamics of vorticity on the development of different flows is emphasized, as well as its influence on the characteristics, magnitude and predictability of the fluid dynamic loads acting on moving bodies.The book is divided into two parts which differ in target and method of utilization. The first part contains the fundamentals of fluid dynamics that are essential for any student new to the subject. This part of the book is organized in a strictly sequential way, i.e. each chapter is assumed to be carefully read and studied before the next one is tackled, and its aim is to lead the reader in understanding the origin of the fluid dynamic forces on different types of bodies. The second part of the book is devoted to selected topics that may be of more specific interest to different students. In particular, some theoretical aspects of incompressible flows are first analysed and classical applications of fluid dynamics such as the aerodynamics of airfoils, wings and bluff bodies are then described. The one-dimensional treatment of compressible flows is finally considered, together with its application to the study of the motion in ducts.

ELEMENTS OF AERODYNAMICS An accessible and hands-on textbook filled with chapter objectives, examples, practice problems, sample tests, and an online aero-calculator In Elements of Aerodynamics, Professor Oscar Biblarz delivers a concise and fundamentals-oriented approach to aerodynamics suitable for both undergraduate and graduate-level students. The text offers numerous problems, examples, and check tests, allowing readers to gain and cement their knowledge through hands-on practice. Using a unique blend of fundamentals, the book provides students with a new approach to high lift airfoils including examples designed to complement the theory. It covers the most vital information on incompressible and compressible flow over two-dimensional and three-dimensional wings. A companion website that includes an interactive aero-calculator and additional student resources makes this a suitable text for online, hybrid, and distance learning. Readers will also find: A concise introduction to units and notation with discussion of the proper usage of dimensionless coefficients in aerodynamics, featuring descriptions of airflow as an incompressible and compressible low-viscosity medium past streamlined wings Comprehensive re-evaluation of the fundamentals of fluid dynamics, including the differential control volume approach and formulation of lift, drag, and pitching moments for thin, attached boundary layers over slender wings at high angles of attack Practical applications of mass, momentum, and energy relations, derived from Euler’s equation, Bernoulli’s equation, and the Kutta-Joukowski theorem Selected treatment of transonic and hypersonic aerodynamic aspects, including supercritical airfoils, the non-linear small perturbation potential equation, Newtonian theory, and hypersonic lift and drag Well-suited for students enrolled in an introductory aerodynamics course as part of an engineering program, Elements of Aerodynamics will also earn a place in the libraries of physics students and those interested in basic fluid mechanics.

This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management.