Construction of compact nonsymmetric nozzles of maximal thrust for given lift

Abstract

The variational problem of the construction of supersonic nonsymmetric plane nozzles of maximal thrust for given lift and given restrictions on the size is solved. According to the restrictions on the size, the contours are fairly short, so that they do not interact. By virtue of this, the method of an undetermined control contour [1] can be used for the solution. It is shown that the problem is equivalent to a problem of maximal thrust (in the absence of a condition on the lift) in a coordinate system rotated through a certain angle relative to the original coordinate system and with unchanged restrictions on the size. The influence of these restrictions on the solution to the problem is investigated. It is shown that in some cases the control contour method is inapplicable, in particular, due to the possible presence of shock waves in the domain of influence of the contour. Numerical calculations illustrate the influence of the lift on the geometry and thrust. Special cases of this problem have been considered earlier. In [2], the problem of a plane contour of maximal thrust for given lift was solved and in [3] the problem of a nonsymmetric nozzle of maximal thrust without condition on the lift.