Nonlinear separated inviscid-viscous analysis of oscillating cascade aerodynamics using an inverse integral method

A mathematical model is developed to analyze the unsteady flow through an h armonically oscillating cascade of airfoils, including separated flow. The model incorporates an inverse integral boundary layer solution with the tim e-marching Euler analysis NPHASE. An embedded composite grid formulation is incorporated, specifically a deforming C-grid embedded in a Cartesian H-Qr id thereby simplifying grid generation. To reduce computational requirement s, Fourier series unsteady periodic boundary conditions are implemented. Th e integral turbulent boundary layer model is closed with steady correlation s adopted in a quasi-steady manner. To couple the inviscid and viscous solu tions, the viscous effect is modeled in the unsteady Euler solution in a qu asi-steady manner by a transpiration boundary condition. An isolated airfoi l is used to compare the steady interaction model with experimental data. T hen a flat plate cascade is used to verify the unsteady flow solver with li near theory predictions. An experimental unsteady aerodynamics data set of a loaded cascade with separated meanflow executing torsional oscillations c ompared favorably with the analysis. The code is then utilized to study the effect of flow separation on the unsteady aerodynamics.