Stetsyuk P.I., Tkachenko O.V., Khomyak O.M., Gritsay O.L.
Constructing the external contour of the frankl nozzle using s-shaped curves with quadratic distribution of the curvature

A mathematical model, an algorithm, and a software are developed for the problem of constructing an S-shaped curve passing through two given points with specified tangent inclination angles and providing a tangent inclination angle at a point with a given abscissa. To control the inflection point of the S-shaped curve with quadratic distribution of curvature in natural parameterization, the tangent inclination angle at the point with the known abscissa is used. The algorithm is based on the modification of the method with space dilation in the direction of the difference of two successive generalized gradients. Computational experiments have shown the efficiency of the developed algorithm for constructing the external contour of a Frankl-type nozzle. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: external nozzle contour, natural parameterization, nonsmooth optimization, quadratic curvature, r-algorithm, S-shaped curve, Nozzles, Computational experiment, Generalized gradients, Inclination angles, Inflection points, S-shaped curves, Computational efficiency

Cite:
Stetsyuk P.I., Tkachenko O.V., Khomyak O.M., Gritsay O.L. (2020). Constructing the external contour of the frankl nozzle using s-shaped curves with quadratic distribution of the curvature. Cybernetics and Systems Analysis, 56 (6), 120–135. doi: https://doi.org/10.1007/s10559-020-00317-7 http://jnas.nbuv.gov.ua/article/UJRN-0001169469 [In Ukrainian].