Design of the supersonic part of a maximum thrust spatial nozzle

The problem of obtaining the form of a spatial supersonic nozzle cross section that intersects the circular critical cross section of the nozzle and an output circuit inscribed in the given dimensions, which has the greatest thrust among all possible admissible forms. is considered. The Lagrange functional, in which all gas-dynamics equations and boundary condition are taken into account with the help of variable Lagrange multipliers, is compiled. The first variation of the functional is written out. The equations and constraints turning the first variation into zero form an adjoint problem for the Lagrange multipliers and an optimality condition. A numerical algorithm for the consistent solution of gas-dynamics equations and the adjoint problem is developed. Numerical examples are given.