Reduced order, inviscid and fully simultaneous viscous-inviscid interaction models of flows in turbomachinery

The proper orthogonal decomposition technique is applied in the frequency domain to obtain reduced order models (ROM) of the unsteady flow in two-dimensional turbomachinery cascades. The method is applied to both subsonic and transonic flows. Both viscous and inviscid flows are investigated. The viscous flow is described by an inviscid-viscous interaction model. The inviscid part is described by the full potential equation. The viscous part is described by an integral boundary layer model. The fully nonlinear steady flow is computed and the unsteady flow is linearized about the steady solution. A frequency domain model is then constructed and validated. The model is shown to provide similar results when compared with previous computational and experimental data.; A cascade of airfoils forming a modified Tenth Standard Configuration is investigated. In the subsonic inviscid case, the ROM with only 15 modes is shown to capture accurately the dynamics of the full system with ∼7500 degrees of freedom (DOF). In the viscous subsonic case, the ROM with only 25 modes is shown to predict accurately the unsteady response of the full system with ∼10,000 DOF.; In a transonic inviscid approach, the ROM with only 25 modes is shown to predict accurately the response of the full system with ∼12500 DOF. In the transonic viscous case, for a fixed interblade phase angle, the ROM with only 15 modes is shown to predict accurately the unsteady response of the full system with ∼15,000 DOF, over a wide range of reduced frequencies. Conversely, for a fixed reduced frequency, only 15 modes are shown to model accurately the response of the system over a complete spectrum of interblade phase angles. A more complete model, with 75 modes, is also constructed, and shown to predict accurately the response of the system when both the frequency and the interblade phase angle are varied.