On the determination of the shape of a supersonic nozzle taking into consideration the variation of aircraft flight conditions: PMM vol. 34, n≗6, 1970, pp. 1067–1075

Abstract

The problem of designing the superior part of a fixed-area propelling nozzle of optimum shape for a certain trajectory, taking into account the variation of flight and engine operation conditions is considered below. The aircraft is assumed to be a material point of variable mass, and its drag at any instant is considered to be equal to the corresponding stationary value. The same approach is used in the analysis of flow in the nozzle. This implies that at any instant pressure and other parameters are defined (in a coordinate system of the nozzle) by equations of stationary flow in conditions prevailing at the nozzle inlet at the particular instant. Besides the over-all results, a detailed investigation is made of two cases in which the use of the derived optimum conditions simplifies the solution of the problem. The first case occurs when throughout the flight the Mach number distribution at the nozzle inlet remains unchanged. It is found that in this case the optimum contour belongs to a family of contours corresponding to the solution of a variational problem with specified conditions. The second case is that of a plane and “short” nozzle with the flow at its inlet remaining throughout the whole flight uniform and supersonic. In this case the generatrix of the optimum nozzle is a straight line. The problem of shaping the supersonic part of a plane or axisymmetric nozzle for maximum thrust at specified flow at its inlet and given external conditions has, to a great extent, been recently solved [1–4]. The formulation of the problem given in the following is due to the fact in many applications the variation of flight conditions and of parameters at the inlet to the considered part of the nozzle is quite extensive, and that the flow at the inlet may vary not only because of changing flight conditions but, also, owing to the control of engine operation. We note, incidentally, that the control of the operation mode is a problem of its dealt with in numerous publications (see, e.g. [5–7].