THE ROLE OF A LENGTH CONSTRAINT IN THE DESIGN OF MINIMUM-DRAG BODIES

The key role of a constraint on the Length of a designed body is demon strated by taking the example of symmetric profiles which achieve mini mum wave drag in a supersonic flow. As a result of this an optimal bod y can contain a rear-base which emerges as a section of a boundary ext remum. By assumption, there is no gas flow around the rear base, and t he ''base'' pressure p(+) which acts on them is specified and is indep endent of the form of the required contour and the ordinate y. When de signing profiles, in addition to their length, it is customary to spec ify the area of the longitudinal section F and other isoperimetric con ditions. Even when p(+) = 0, which, naturally, does not occur, it is n ow necessary to introduce a rear base for extremely small F. When p(+) > 0, a base appears earlier still. The replacement of the optimal con tours with a rear base by a ''pseudo-optimal'' contours with a sharp e dge leads to an increase in drag of tens and hundreds of percent. Spec ial attention has been paid to cases in which p(+), due to heat supply in the base domain, for example, exceeds the free-stream pressure. He re, there is always a rear base and, when F < F-o, where F-o depends o n p(+)/p(infinity), the form of the optimal contours is the same as in the problem without a specified F In this case, the optimal configura tion is a hollow or partially hollow ''checkmark''. (C) 1998 Elsevier Science Ltd. All rights reserved.