In this paper, a new method is developed to solve the N-S equations with vorticity-velocity variables, which is suitable for describing the flow-field of turbomachinery in non-inertia coordinates. It is derived that the expansions of the vorficity-velocity equations (VVE)have the same form in arbitrary non-orthogonal curvilinear coordinates, because the non-inertia effect is only related to the initial and the boundary conditions. This method greatly simplifies the solution for the flowfield of turbomachinery with complicated geometrical domain and reduces the calculation cost.
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