Understanding Aerodynamics

Arguing from the Real Physics

Doug McLean

• Publisher: Wiley
• Year: 2012
• ISBN:
  9781118454220
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Aeronautic & Astronautic Engineering
• Index: Technology & Engineering

Much-needed, fresh approach that brings a greater insight into the physical understanding of aerodynamics

Based on the author's decades of industrial experience with Boeing, this book helps students and practicing engineers to gain a greater physical understanding of aerodynamics. Relying on clear physical arguments and examples, Mclean provides a much-needed, fresh approach to this sometimes contentious subject without shying away from addressing "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience. Motivated by the belief that engineering practice is enhanced in the long run by a robust understanding of the basics as well as real cause-and-effect relationships that lie behind the theory, he provides intuitive physical interpretations and explanations, debunking commonly-held misconceptions and misinterpretations, and building upon the contrasts provided by wrong explanations to strengthen understanding of the right ones.

• Provides a refreshing view of aerodynamics that is based on the author's decades of industrial experience yet isalways tied to basic fundamentals.
• Provides intuitive physical interpretations and explanations, debunking commonly-held misconceptions and misinterpretations
• Offers new insights to some familiar topics, for example, what the Biot-Savart law really means and why it causes so much confusion, what "Reynolds number" and "incompressible flow" really mean, and a real physical explanation for how an airfoil produces lift.
• Addresses "real" aerodynamic situations as opposed to the oversimplified ones frequently used for mathematical convenience, and omits mathematical details whenever the physical understanding can be conveyed without them.

Chapter 1

Introduction to the Conceptual Landscape

The objective of this book is to promote a solid physical understanding of aerodynamics. In general, any understanding of physical phenomena requires conceptual models:

It seems that the human mind has first to construct forms independently before we can find them in things. Kepler's marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone but only from the comparison of the inventions of the intellect with observed fact.

—Albert Einstein on Kepler's discovery that planetary orbits are ellipses

 

Einstein wasn't an aerodynamicist, but the above quote applies as well to our field as to his. To understand the physical world in the modern scientific sense, or to make the kinds of quantitative calculations needed in engineering practice, requires conceptual models. Even the most comprehensive set of observations or experimental data is largely useless without a conceptual framework to hang it on.

In fluid mechanics and aerodynamics, I see the conceptual framework as consisting of four major components:

1. Basic physical conservation laws expressed as equations and an understanding of the cause-and-effect relationships those laws represent,

2. Phenomenological knowledge of flow patterns that occur in various situations,

3. Theoretical models based on simplifying the basic equations and/or assuming an idealized model for the structure of the flowfield, consistent with the phenomenology of particular flows, and

4. Qualitative physical explanations of flow phenomena that ideally are consistent with the basic physics and make the physical cause-and-effect relationships clear at the flowfield level.

By way of introduction, let's take a brief look at what these components encompass, the kinds of difficulties they entail, and how they relate to each other.

The fundamental physical conservation laws relevant to aerodynamic flows can be expressed in a variety of ways, but are most often applied in the form of partial-differential equations that must be satisfied everywhere in the flowfield and that represent the local physics very accurately. By solving these basic equations, we can in principle predict any flow of interest, though in practice we must always accept some compromise in the physical accuracy of predictions for reasons we'll come to understand in Chapter 3.

The equations themselves define local physical balances that the flow must obey, but they don't predict what will happen in an overall flowfield unless we solve them, either by brute force numerically or by introducing simplified models. There is a wide gulf in complexity between the relatively simple physical balances that the equations represent and the richness of the phenomena that typically show up in actual flows. The raw physical laws thus provide no direct predictions and little insight into actual flowfields. Solutions to the equations provide predictions, but they are not always easy to obtain, and they are limited in the insight they can provide as well. Even the most accurate solution, while it can tell us what happens in a flow, usually provides us with little understanding as to how it happens or why.

Phenomenological knowledge of what happens in various flow situations is a necessary ingredient if we are to go beyond the limited understanding available from the raw physical laws and from solutions to the equations. Here I am referring not just to descriptions of flowfields, but to the recognition of common flow patterns and the physical processes they represent. The phenomenological component of our conceptual framework provides essential ingredients to our simplified theoretical models (component 3) and our qualitative physical explanations (component 4).

Simplified theoretical models appeared early in the history of our discipline and still play an important role. Until fairly recently, solving the “full” equations for any but the simplest flow situations was simply not feasible. To make any progress at all in understanding and predicting the kinds of flow that are of interest in aerodynamics, the pioneers in our field had to develop an array of different simplified theoretical models applicable to different idealized flow situations, generally based on phenomenological knowledge of the flow structure. Though the levels of physical fidelity of these models varied greatly, even well into the second half of the twentieth century they provided the only practical means for obtaining quantitative predictions. The simplified models not only brought computational tractability and accessible predictions but also provided valuable ways of “thinking about the problem,” powerful mental shortcuts that enable us to make mental predictions of what will happen, predictions that are not directly available from the basic physics. They also aid understanding to some extent, but not always in terms of direct physical cause and effect.

So the simplified theoretical models ease computation and provide some degree of insight, but they also have a downside: They involve varying levels of mathematical abstraction. The problem with mathematical abstraction is that, although it can greatly simplify complicated phenomena and make some global relationships clearer, it can also obscure some of the underlying physics. For example, basic physical cause-and-effect relationships are often not clear at all from the abstracted models, and some outright misinterpretations of the mathematics have become widespread, as we'll see. Thus some diligence is required on our part to avoid misinterpretations and to keep the real physics clearly in view, while taking advantage of the insights and shortcuts that the simplified models provide.

We've looked at the roles of formal theories (components 1 and 3) and flow phenomenology (component 2), and it is clear that the combination, so far, falls short of providing us with a completely satisfying physical understanding. Physical cause-and-effect at the local level is clear from the basic physics, but at the flowfield level it is not. Thus to be sure we really understand the physics at all levels, we should also seek qualitative physical explanations that make the cause-and-effect relationships clear at the flowfield level. This is component 4 of my proposed framework.

Qualitative physical explanations, however, pose some surprisingly difficult problems of their own. We've already alluded to one of the main reasons such explanations might be difficult, and that is the wide gulf in complexity between the relatively simple physical balances that the raw physical laws enforce at the local level and the richness of possible flow patterns at the global level. Another is that the basic equations define implicit relationships between flow variables, not one-way cause-and-effect relationships. Because of these difficulties, misconceptions have often arisen, and many of the physical explanations that have been put forward over the years have flaws ranging from subtle to fatal. Explanations aimed at the layman are especially prone to this, but professionals in the field have also been responsible for errors. Given this history, we must all learn to be on the lookout for errors in our physical explanations. If this book helps you to become more vigilant, I'll consider it a success.

This completes our brief tour of the conceptual framework, with emphasis on the major difficulties inherent in the subject matter. My intention in this book is to devote more attention to addressing these difficulties than do the usual aerodynamics texts. Let's look briefly at some of the ways I have tried to do this.

The theoretical parts of our framework (components 1 and 3) ultimately rely on mathematical formulations of one sort or another, which leads to something that, in my own experience at least, has been a pedagogical problem. It is common in treatments of aerodynamic theory for much of the attention to be given to mathematical derivations, as was the case in much of the coursework I was exposed to in school. While it is not a bad thing to master the mathematical formulation, there is a tendency for the meaning of things to get lost in the details. To avoid this pitfall, I have tried to encourage the reader to stand back from the mathematical details and understand “what it all means” in relation to the basic physics. As I see it, this starts with paying attention to the following:

1. Where a particular bit of theory fits in the overall body of physical theory, that is, what physical laws and/or ad hoc flow model it depends on; and

2. How it was derived from the physical laws, that is, the simplifying assumptions that were made;

3. The resulting limitations on the range of applicability and the physical fidelity of the results; and

4. The implications of the results, that is, what the results tell us about the behavior of aerodynamic flows in more general terms.

The brief tour of the physical underpinnings of fluid mechanics in Chapters 2 and 3 is an attempt to set the stage for this kind of thinking.

How computational fluid dynamics (CFD) fits into this picture is an interesting issue. CFD merely provides tools for solving the equations of fluid motion; it does not change the conceptual landscape in any fundamental way. Still, it is so powerful that it has become indispensable to the practice of aeronautical engineering. As important and ubiquitous as CFD has become, however, it is not on a par with the older simplified theories in one significant respect: CFD is not really a conceptual model at the same level; and a CFD solution is rightly viewed as just a simulation of a particular real flow, at some level of fidelity that depends on the equations used and the numerical details. As such, a CFD solution has some of the same limits to its usefulness as does an example of the real flow: In both cases, you can examine the flowfield and see what happened, and, of course, a detailed examination of a flowfield is much easier to carry out in CFD than in the real world. But in both CFD and real-world flowfields, it is difficult to tell much about why something happened or what there is about it that might be applicable to other situations.

Before we proceed further, a bit of perspective is in order: While correct understanding is vitally important, we mustn't overestimate what we can accomplish by applying it. As we'll see, the physical phenomena we deal with in aerodynamics are surprisingly complicated and difficult to pin down as precisely as we would like, and it is wise to approach our task with some humility. We should expect that we will not be able to predict or even measure many things to a level of accuracy that would give us complete confidence. The best we'll be able to do in most cases is to try to minimize our unease by applying the best understanding and the best methods we can bring to bear on the problem. And we can take some comfort in the fact that the aeronautical community, historically speaking, has been able to design and build some very successful aeronautical machinery in spite of the limitations on our ability to quantify everything to our satisfaction.

Chapter 2

From Elementary Particles to Aerodynamic Flows

Step back for a moment to consider the really big picture and ponder how aerodynamics fits into the whole body of modern physical theory. The tour I'm about to take you on will be superficial, but I hope it will help to put some of the later discussions in perspective.

First, consider some of the qualitative features of the phenomena we commonly deal with in aerodynamics. Even in flows around the simplest body shapes, there is a richness of possible global flow patterns that can be daunting to anyone trying to understand them, and most flows have local features that are staggeringly complex. There are complicated patterns in how the flow attaches itself to the surface of the body and separates from it (Figure 2.1a, 2.1b), and these patterns can be different depending on whether you look at the actual time-dependent flow or the “mean” flow with the time variations averaged out. Even in flows that are otherwise steady, the shear layers that form next to the surface and in the wake are often unsteady (turbulent). This shear-layer turbulence contains flow structures that occur randomly in space and time but also display a surprising degree of organization over a wide range of length and time scales. Examples include vortex streets in wakes and the various instability “waves,” “spots,” “eddies,” “bursts,” and “streaks” in boundary layers. Examples are shown in Figure 2.1c–f, and many others can be found in Van Dyke (1982). Such features usually display extreme sensitivity to initial conditions and boundary conditions, so that their apparent randomness is real, for all practical purposes. The “butterfly effect” we've all read about doesn't just apply to the weather; the details of a small eddy in the turbulent boundary layer on the wing of a 747 are just as unpredictable.

Figure 2.1 Examples of complexity in fluid flows, from Van Dyke (1982). (a) Horseshoe vortices in a laminar boundary layer ahead of a cylinder. Photo by S. Taneda, © SCIPRESS. Used with permission. (b) Rankine ogive at angle of attack. Photo by Werle (1962), courtesy of ONERA. (c) Tollmien-Schlichting waves and spiral vortices on a spinning axisymmetric body, visualized by smoke. From Mueller, et al. (1981). Used with permission. (d) Emmons turbulent spot in a boundary layer transitioning from laminar to turbulent. From Cantwell, et al (1978). Used with permission of Journal of Fluid Mechanics. (e) Eddies of a turbulent boundary layer, as affected by pressure gradients. Top: Eddies stretched in a favorable pressure gradient. Bottom: Boundary layer thickens and separates in adverse pressure gradient. Photos by R. Falco from Head and Bandyopadhyay (1981). Used with permission of Journal of Fluid Mechanics. (f) Streaks in sublayer of a turbulent boundary layer. From Kline, et al (1967). Used with permission of Journal of Fluid Mechanics

How does all this marvelous richness and complexity arise? It is natural to expect that complexity in the flow requires complexity in the basic physics and that complex behavior in the flow must therefore have its origin at a “low level,” in the statistical behavior of the molecules that make up the gas or in the behavior of the particles that make up the molecules. But this natural expectation is wrong. Instead, the complexity we see arises from the aggregate behavior of the fluid represented by the continuum equations. In fact, the essential features of everything we observe in ordinary aerodynamic flows could be predicted from the equations for the continuum viscous flow of a perfect gas, that is, the Navier-Stokes (NS) equations, provided we could solve them in sufficient detail.

But there are two caveats that must accompany this sweeping claim. The first is that although the NS equations are a high-fidelity representation of the real physics, they are not exact. Imagine comparing a real turbulent flow with the corresponding exact solution to the NS equations, starting at an initial instant in which the theoretical flowfield is exactly the same as the real one in every detail. We would find that the NS solution matches the detailed time history of the real flow only for a short time and then gradually diverges from it. Detailed time histories of flows, however, are rarely of much interest in aerodynamics, where a statistical description of the flow nearly always suffices. In a statistical sense, we expect that a real flow and the corresponding NS solution would be practically indistinguishable. The second caveat is that even this less ambitious claim of statistical equivalence is nearly impossible to evaluate quantitatively. For one thing, exact solutions to the NS equations are not practically available for anything but the simplest of flows, and agreement for these simple cases doesn't prove much. For all other flows, especially turbulent flows, we must settle for numerical solutions. Numerical calculations that fully resolve the turbule...