Front sections of bodies of revolution with annular channel and nearly minimal wave drag

Abstract

A study is made of the problem of constructing the generator of the outer part of a body of revolution with annular channel that in the case of supersonic flow with attached shock wave realizes nearly minimal wave drag for fixed dimensions. The complete equations for the flow of an ideal (inviscid and non-heat-conducting) gas are used. The construction is completed by numerical solution of Cauchy and Goursat problems by the method of characteristics. Conditions of optimality are obtained by means of the method of an undetermined control contour [1]. One of the conditions cannot be satisfied, which makes the approach approximate. Nevertheless, the smooth nonoptimal generators which are obtained give compared with straight generators almost the same gain (up to 12% for the wave drag coefficient) as the optimal contours with bends constructed using an exact and much more complicated method [2]. At the same time, the gain with respect to generators that are optimal in the approximation of Newton's formula is much less (from a few tenths to 1 of a percent). It is established that the expression for the drag of optimal bodies with annular channel obtained in the framework of a linear theory [3; 4] gives in the considered problem, in contrast to the problem of an optimal rear section, not only quantitatively but even qualitatively incorrect results.