A three-dimensional viscous flow model of stator/rotor interaction in turbomachines

The current numerical model takes into account the full three-dimensionality and cyclic fluctuations of the flow variables in a turbomachinery stage. The cyclic fluctuations are the result of circumferential irregularities in the flow pattern generated by blade rows upstream of the airfoil cascade under consideration. The flow irregularities in the current model result from such flow zones as the viscous wakes produced by the preceding blade row. The model is based on the use of the finite element method to solve the time-dependent Navier-Stokes equations in a generally rotating blade-to-blade, hub-to-tip flow passage. Use of the finite element technique greatly simplifies the modeling of this highly complicated flow domain. The equations governing the relative flow through rotating blade rows are cast in cylindrical coordinates, enabling the model to be used for both rotor and stator blade rows. Real flow effects, such as separation and recirculation, are rigorously simulated as the flow ellipticity is retained throughout the flow domain. Retention of all the viscous terms is an upgrade of virtually all existing models which utilize such approximations as a totally or partially parabolic flow field. The resulting computer program yields velocity and pressure fields for selected radial locations in a single rotor or stator passage as a function of time. These, in turn, are used to identify regions of viscous losses in the flow domain and cyclic blade loadings which are highly important in predicting component efficiency and fatigue life.