On vortex transport in turbine channels

The system of equations of motion and continuity describing the steady state vortex flow of a nonviscous incompressible fluid represents a quite difficult problem concerning the construction of a numerical method of solution and the application of physical boundary conditions. Such a system, written in terms of the velocity vector, pressure, density and total energy, can be written so that the equations correspond with the classical problem of finding a velocity field from a specified divergence and vortex field, which can be solved by the method of integral equations. The vortex transport equation is algebraic with respect to the velocity vector fields and can be used to determine the vortex field in a turbine channel by an iterative technique with the appropriate boundary conditions. The distributions of the current functions is known and the total energy at any point in the channel is defined by a given function. One feature of this analytical solution is the use of a family of current surfaces for the coordinate system. The efficiency the vortex field determination throughout the entire internal region of a channel because the labor involved in setting up the current surface system of coordinates is payed back by an analytical function which defines the vortex field everywhere in the region.