ENHANCEMENT OF THE POTENTIAL FLOW MODEL

Toward the end of Chapter 1 (Section 1.8) it is postulated that many flowfields of interest to the low-speed fluid dynamicist lie in the range of high Reynolds number. Consequently, for attached flowfields, the fluid is divided into two regions: (a) the thin inner boundary layer, and (b) the mainly inviscid irrotational outer flow. Chapters 2-13 are entirely devoted to the solution of the inviscid outer flow problem, which indeed is capable of estimating the resulting pressure distribution and lift due to the shape of the given solid boundaries. For the solution of the complete flowfield, however, viscous effects must be considered too, which for the attached flows will provide information such as the displacement thickness and the skin friction on the solid surface—or the drag force component due to this surface friction. Also, more advanced viscous methods should be capable of indicating whether the flow will have a tendency to detach (e. g., predicting location of separation points, or lines). The objective of this chapter is to provide a brief survey of some frequently occurring low-speed flowfields and to help the student to place in perspective the relative role of the potential-flow methods (presented in this book) and of the viscous effects in order to comprehend the complete real flowfield environment. Additionally, several simplified enhancements to the potential-flow model that account for some viscous effects will be surveyed.

The modifications presented in this chapter will begin with methods of

calculating the wake rollup, which from the classical potential-flow solution point of view was denoted as a “slight nonlinear effect.” The rest of the presented improvements (or modificatons) deal with efforts to include the effects of viscosity and some of them are logical extensions to the potential – flow model. Some others (e. g., modeling of two-dimensional flow separation) will clearly fall into the “daring and imaginative” category and their impor­tance is more in providing some explanation of the fluid-mechanical phenom­ena rather than being in such a stage that they can predict unknown flowfields.

In the following discussion, for the sake of simplicity, mainly the lifting characteristics of the experimental observations and the resulting flow models are presented. In a limited number of cases the drag force also is discussed but important effects such as side forces, moments and possible crosscoupling of the aerodynamic loads is omitted in favor of brevity. Therefore, the treatment of the various topics in this chapter is by no means complete or comprehensive and the reader is encouraged to further investigate any of the following topics in the referenced literature.