Practical Methods of Problem Solution

Three approaches can be used to seek solutions to problems in aerodynamics of the type defined in this chapter as follows: [11]

It is important to understand that these methods always should be used in a mutually supportive manner. Too often, we see experimentalists who steadfastly insist that their (sometimes incorrect) experimental data are a better representation of reality than what is predicted by a theoretical model. Similarly, theorists who have grown too close to their favorite analysis may criticize the work of an experimen­talist as incorrect because it does not conform to their predictions. In contrast, those who practice the “black art” of CFD sometimes insist that their numerical com­putations represent the “correct” solution without checking whether all constraints and physical models used in the “black box” are truly appropriate.

Therefore, we start our study of aerodynamics with a strong bias in favor of methods that use application of simplifying assumptions. To make this work, we must be sure of the understanding of basic principles. This method has produced many of the most useful physical insights into the underlying behavior of aerodynamic flow fields. Never­theless, we frequently see situations in which such approximations fail. It is important to learn the appropriate strategies for addressing situations that do not readily yield to the familiar and comfortable assumptions that may have worked in a similar problem solved previously. It also is imperative to learn not to misuse simple theoretical results in cases in which the underlying simplifying assumptions may be violated.

It is shown by example how to determine when an experiment is necessary or when resort should be made to strictly numerical methods. Again, our approach is to show how all of the available techniques can be used in concert to produce a powerful, adaptable problem-solving strategy. Our first encounter with the need for experimental verification is in Chapter 5 as we learn about important applications of airfoil theory in wing design. The value of the theory in formulating experiments and the need for them in validating the theoretical predictions is an oft-repeated scenario.

A valuable application of computational methods is the ability to represent complex results in easily interpreted graphical form. Therefore, even in problems that can be well represented by an approximate analytical solution, numerical evalu­ation of the results and plotting them in graphical form is needed frequently. As part of the text, students are provided with an integrated set of numerical tools to use in the manner described. Numerical methods are used frequently to extend ana­lytical models that can be used only in their original form in simplified geometries, and so on.

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