A Novel Mixing Plane Method Using Nonreflecting Boundary Conditions for Multirow Analysis in Turbomachines

Abstract

A new formulation of the mixing plane boundary condition to analyze the steady-state interaction between adjacent rows of a turbomachine, used in conjunction with steady two-dimensional nonreflecting boundary conditions, is presented. Existing mixing plane formulations rely on the differences between some variables at the interface of adjacent rows to determine the boundary condition. These differences are driven to zero as the case is converged to the steady state. By contrast, the proposed approach determines the differences that result in the conservation of mass, momentum, and energy after the boundary condition is enforced, ensuring conservation at any instant during the iterative process. The reverse flow within the mixing plane boundary is naturally treated, but both inlet and outlet boundary conditions fail when the mixing plane normal velocity tends to zero, giving rise to sharp variations of the fluid variables that must be properly limited to prevent convergence problems. Some examples will be given to demonstrate the ability of the new method to resolve these cases while preserving the boundary condition robustness.