PROLOGUE

There is no doubt that rational design (i.e., based on first principles) of flow-control devices is always preferable to a trial and error approach. Rational design of course is not always possible owing to the extreme complexity of the equations involved, but one tries either analytically or, more commonly to date, numerically. The search for useful compliant coatings, discussed in Chapter 7, is a case in point. The window of opportunity for a successful coating is so narrow that the probability of finding the right one by experimenting is near nil. Fortunately, the analytical and numerical tools to guide the initial choice for a transition-delaying compliant surface are currently available. On the other hand, the flowfield associated with a typical, deceivingly simple vortex generator for airplane wings is so complex that its design is still done to date more or less empirically.

The proper first principles for flow control are those for fluid mechanics itself. The principles of conservation of mass, momentum, and energy govern all fluid motions. Additionally, all processes are constrained by the second law of thermodynamics. In general, a set of partial, nonlinear differential equations expresses those principles, and, together with appropriate boundary and initial conditions, constitute a wellposed problem.