Method of Characteristics for Design of Centrifugal Pump Geometry

The method of characteristics leads to the blade geometry of a centrifugal pump. The method is built taking the advantage of the governing equations of fluid mechanics written in a non-orthogonal coordinates system. The coordinate system is based on an analytically described boundary of a centrifugal pump. Some of the information concerning the designed geometry should be introduced in advance. The mass conservation equation needs the information of the blockage factor resulting from the blading thickness. In the momentum conservation equation the body force replaces the blading force together with the friction force. In the energy conservation equation the dissipation effects are represented by a loss coefficient. It is shown that while simplifying the body force vector, the set of equations reduces to a hyperbolic system which allows applying the method of characteristics. The shapes of surfaces representing the designed blading can be built from the trajectories of fluid particles.