A finite element solution of three-dimensional inviscid rotational flows through curved ducts

A previously developed two-dimensional finite element algorithm for the solution of steady Euler equations is extended to three-dimensional problems. Starting with the general three-dimensional problem, the formulation of steady, rotational flows is presented. The boundary conditions for steady flows where the rotationality is introduced through entropy or total enthalpy gradients are introduced. A three-dimensional flow through a curved duct is analyzed as a sample problem, demonstrating the efficiency of the relaxation scheme. The accuracy of the numerical results is investigated by calculating the velocity and vorticity distributions at different sections of the channel, including the exit.