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Aerodynamicists control the flowfield through geometry definition and are always interested in possible geometric shapes that would be useful in design. This appendix provides the detailed definition of many of the classic shapes frequently specified in aerodynamics. It is not intended to be encyclopedic, but will provide a good starting point for where to obtain geometric definitions for aerodynamic shapes.
The NACA Airfoils
The NACA (National Advisory Committee for Aeronautics) airfoils were designed during the period from 1929 through 1947 under the direction of Eastman Jacobs at the NACA’s Langley Field Laboratory (now NASA Langley Research Center). Most of the airfoils were based on simple geometrical descriptions of the section shape, although the 6 and 6A series were developed using theoretical analysis and don’t have simple shape definitions. Although a new generation of airfoils has emerged as a result of improved understanding of airfoil performance and the ability to design new airfoils using computational methods, the NACA airfoils are still useful in many aerodynamic design applications. A number of references have been included to allow the reader to study both the older NACA literature and the new airfoil design ideas. Taken together, this literature provides a means of obtaining a rather complete understanding of the ways in which airfoils can be shaped to obtain desired performance characteristics.
Aren’t there already plenty of excellent books on the topic of CFD? Yes, there are … if you are a graduate student who wants to learn the intricacies of numerical methods applied to solving the fundamental equations of fluid dynamics. However, we believe that a paradigm shift has taken place in CFD, where the development of algorithms and codes has largely been replaced by people applying well-established codes to real-world applications. While this is a natural progression in any field of science and engineering, we do not believe that the paradigm shift has filtered into the academic world. In academia, undergraduates learning about aerodynamics are still going through theories and applications that were being taught 40 or 50 years ago. We believe that it is time to write a book for people who want to be “intelligent users” of CA, not for those who want to continue developing CA tools. We strongly endorse the perspective of David Darmofal and Earll Murman of MIT (see AIAA Paper 2001–0870):
Within aerodynamics, the need for re-engineering the traditional curriculum is critical. Industry, government, and (to some extent) academia has seen a significant shift away from engineering science and highly specialized research-oriented personnel toward product development and systems-thinking personnel. While technical expertise in aerodynamics is required, it plays a less critical role in the design of aircraft than in previous generations. In addition to these influences, aerodynamics has been revolutionized by the development and maturation of computational methods. These factors cast significant doubt that a traditional aerodynamics curriculum with its largely theoretical approach remains the most effective education for the next generation of aerospace engineers. We believe that change is in order.
We agree completely and believe that CA needs to be brought into the undergraduate classroom as soon as possible. That is why we have written this book!
The target audience for Applied Computational Aerodynamics is advanced undergraduates in aerospace engineering who want (or need) to learn CA in the broad context of learning to do computational investigations, while also learning engineering methods and aerodynamics. In addition, we believe that working engineers who need to apply CA methods, but who have no CA background, will also find the book valuable.
Several types of programs are used to provide insight into aerodynamics, such as airfoil, wing, and aircraft analysis, as well as various aerodynamic design programs. The number of programs available has grown a great deal over the past few years, and a number of the programs have been discussed in Chapters 2 and 5 especially. This appendix will list and describe some of the programs that are either available from the book website (www.cambridge.org/aerodynamics) or that could be used to complete various projects listed at the end of chapters in the book. In this section we will just list and briefly describe some of the programs:
FOILGEN; provides ordinates for NACA 4-digit, 4-digit modified and 5-digit airfoils
LADSON; provides ordinates for NACA 6- and 6A-series airfoils
PANELV2: an airfoil panel method
THINFOIL; an airfoil CFD program
LIDRAG: a lift-induced drag program
LAMDES; a program that finds wing camber and twist to obtain a given splanload
FRICTION; a skin friction and form drag estimation program
VLMpc; a two-surface vortex lattice program
DESCAM; an inverse design airfoil program
TRIDAG; the Thomas algorithm solution approach for a tridiagonal matrix
FOILGEN
This program is used for airfoil geometry generation. For airfoils with analytically defined ordinates, this program produces airfoil definition data sets in the format required for PANELV2. This includes NACA 4-digit, 4-digit modified and 5-digit airfoils. In addition, the NACA 6 and 6A camber lines are available. The user can combine any combination of thickness and camber lines available within these shapes. This provides a wide range of airfoil definitions. The program runs interactively, and a sample session, with inputs and outputs, is provided at www.cambridge.org/aerodynamics.
This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.
Music, calm speech, whispering leaves fluttering in a breeze are pleasant and desirable sounds. Noise, howling gales, explosions and screeching traffic are less so. A quantitative understanding of the sources of all such sounds can be obtained by careful analysis of the mechanical equations of motion. This is provided by Acoustics and Aerodynamic Sound, which serves as a short, one semester introduction to acoustics and aerodynamic sound at the advanced undergraduate and graduate level. Sound is treated as a branch of fluid mechanics, which is possible because students embarking on an advanced course in acoustics will be familiar with this topic. It is also desirable because an ability to relate acoustic events to hydrodynamic phenomena provides insight into acoustic principles, in particular into the role of vorticity in the mechanics of sound production by vibrating bodies and in the scattering and diffraction of sound.
The sound generated by turbulent flow is called aerodynamic sound. Most unsteady flows of technological interest are of high Reynolds number and turbulent, and the acoustic radiation is a very small by-product of the motion. The turbulence is usually produced by fluid motion over a solid boundary or by flow instability. Lighthill (1952) investigated aerodynamic sound by transforming the Navier–Stokes and continuity equations to form an exact, inhomogeneous wave equation whose source terms are important only within the turbulent region. He argued that sound is a very small component of the whole motion and that, once generated, its ‘back-reaction’ on the main flow can usually be ignored. The properties of the unsteady flow in the source region may then be determined by neglecting the production and propagation of the sound, a reasonable approximation if the Mach number M is small, and there are many important flows where the hypothesis is obviously correct, and where the theory leads to unambiguous predictions of the sound.
Lighthill was initially interested in solving the problem illustrated in Figure 4.1.1a, of the sound produced by a turbulent nozzle flow. However, his original theory actually applies to the simpler situation shown in Figure 4.1.1b, in which the sound is imagined to be generated by a finite region of ‘rotational’ flow in an unbounded fluid. This avoids complications caused by the presence of the nozzle. The fluid is assumed to be at rest at infinity, where the mean pressure, density and sound speed are respectively equal to po, ρo, co. Lighthill compared the equations for the production of acoustic density fluctuations in the real flow with those in an ideal, linear acoustic medium that coincides with the real fluid at large distances from the sources.
Music, calm speech, whispering leaves fluttering in a breeze are pleasant and desirable sounds. Noise, howling gales, explosions and screeching traffic are less so. A quantitative understanding of the sources of all such sounds can be obtained by careful analysis of the mechanical equations of motion. Most sources are very complex, frequently involving ill-defined turbulent and perhaps combusting flows and their interactions with vibrating structures, and the energy released as sound tends to be a tiny fraction of that of the structural and hydrodynamic motions. Our analysis must correctly and reliably account for this general inefficiency of sound generation, because small errors in source modelling can lead to very large errors in acoustic prediction.
In this book we shall consider only the simplest case in which the fluid can be regarded as continuous and locally homogeneous at all levels of subdivision. The motion of the fluid will be defined when the velocity and the thermodynamic state are specified for each of the fluid particles of which it may be supposed to consist. The distinctive fluid property possessed by both liquids and gases is that these fluid particles can move freely relative to one another under the influence of applied forces or other externally imposed changes at the boundaries of the fluid. Five scalar partial differential equations are required to determine these motions. They are statements of conservation of mass, momentum and energy, and they are to be solved subject to appropriate boundary and initial conditions. These equations will be used to formulate and analyse a wide range of problems; our main task will be to simplify these problems to obtain a thorough understanding of source mechanisms together with a quantitative description of the subsequent propagation of the sound including, possibly, its reflection, scattering and diffraction at solid boundaries.
A general introduction to acoustics is presented in this chapter; it forms the basis for the treatment of the fluid-structure interaction problems examined in the rest of the book.
An introductory account is given of the theory of the production and propagation of sound and its interactions with solid structures. It is intended for a one-semester course on acoustics at the advanced undergraduate or graduate level, and is therefore shorter than most of the standard texts – many important applications are omitted, such as speech and musical acoustics, ultrasonic imaging, and thermoacoustics. Sound is treated as a branch of fluid mechanics, which is possible because most students embarking on an advanced course are likely to have some familiarity with fluid mechanics or be sufficiently mature to assimilate the review material provided in the text. It is also desirable because an ability to relate acoustic events to hydrodynamic phenomena provides valuable insight into acoustic principles, in particular into the role of ‘vorticity’ in the mechanics of sound production by vibrating bodies and in the scattering and diffraction of sound. Any homogeneous fluid that has kinetic energy independent of moving boundaries must possess vorticity, a quantity that propagates by convection and molecular diffusion, and that therefore undergoes relatively little displacement during a typical acoustic cycle; the existence of vorticity signifies the presence of possible sources of sound, and its production occurs when sound is dissipated.
Chapter 1 forms a stand-alone introduction to theoretical acoustics, and is suitable together with material from §§2.1, 2.3, 2.4, 3.1, 3.2, 4.1–4.3, for a ‘short course’ on acoustics and aerodynamic sound. A general discussion of the Kirchhoff integral representation and generalisations is given in Chapter 2, with particular emphasis on sound sources of various types near an acoustically ‘compact’ body or section of a larger solid boundary, including the influence of surface vibration and scattering. Chapter 3 deals with the sound radiated by a baffled piston, Kirchhoff diffraction theory, and interactions of sound with apertures and perforated screens.