Title screen

[References: p. 873-875 (29 tit.)]

In the framework of the ideal gas model, variational gas dynamics problems on optimum nozzle design are solved using a direct method. The model problems are two classical axisymmetric problems: the design of a supersonic nozzle with a corner point in the minimum cross section and a uniform exit characteristic and the design of a subsonic nozzle part with a plane sonic line in the minimum cross section. It is supposed that in both problems, the optimum nozzle profile must be a monotonic function. A priory information on the monotonicity of the desired profile is shown to be the one that allows a considerable increase in solution efficiency. A functional with a minimum corresponding to the optimum nozzle profile is selected taking into account the required monotonicity. For comparison, the desired nozzle profiles are described by polynomials and quadratic, cubic and rational splines. The varied variables are either profile expansion coefficients in terms of basis functions or the parameters to be interpolated. It is demonstrated that the problem solving is more efficient where the nozzle profile is represented as a monotonic function at each step of minimization. It is found that consideration of the peculiarities of the nozzle profile does much to determine the changeable part of a wind tunnel. In this problem, more efficient profile descriptions are those based on logarithmic functions and cubic splines with irregular nodes.