Analysis of aerodynamic problems with geometrically unspecified boundaries using an enhanced Lagrangian method

摘要

This paper presents solutions for several 2-D aerodynamic problems with geometrically unspecified boundaries. These solutions are obtained with an enhanced Lagrangian method based on stream function and Lagrangian-distance coordinates, which includes special procedures to substantially improve the numerical resolution of the shock waves and for the numerical implementation of the aerodynamic conditions defining the geometrically unspecified solid or fluid boundaries. The method is first validated for flows with specified solid boundaries by comparison with exact analytical solutions and with previous computational results obtained by numerical methods using Eulerian formulations. In all cases, this enhanced Lagrangian method displayed a very good accuracy and computational efficiency and a sharp numerical resolution of shock waves. Then this method is used to obtain solutions for problems with geometrically unspecified boundaries, such as: (i) indirect problems of determining the geometrical shape of airfoils and nozzle walls for a specified pressure distribution; (ii) supersonic nozzle design problem for a specified uniform flow at the nozzle outlet based on reflection-suppression condition; (iii) analysis of flexible-membrane airfoils; and (iv) analysis of jet-flapped airfoils.