Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations - Ivan Dubrovskyi; Valerii Bucharskyi (Challenges and Issues of Modern Science)
A rocket engine with a standard single-section profiled nozzle provides maximum thrust only at a certain value of atmospheric pressure [1]. To expand the range of atmospheric pressure values at which the optimum engine operation mode is achieved, a dual bell nozzle can be used [2]. A typical diagram of such a nozzle is shown in Fig. 1. Its main elements are three cross-sections a, b, c and two profiled section elements a-b, b-c bounded by them. The fig. 1 shows the general case of the contour of such a nozzle, for which a corner in the generatrix is located at points a and b. In addition, the section a coincides with the critical section of the engine chamber.