Nonlinear Separated Inviscid-Viscous Analysis of Oscillating Cascade Aerodynamics Using an Inverse Integral Method

Abstract

A mathematical model is developed to analyze the unsteady flow through an harmonically oscillating cascade of airfoils, including separated flow. The model incorporates an inverse integral boundary layer solution with the time-marching Euler analysis NPHASE. An embedded composite grid formulation is incorporated, specifically a deforming C-grid embedded in a Cartesian H-grid, thereby simplifying grid generation. To reduce computational requirements, Fourier series unsteady periodic boundary conditions are implemented. The integral turbulent boundary layer model is closed with steady correlations adopted in a quasi-steady manner. To couple the inviscid and viscous solutions, the viscous effect is modeled in the unsteady Euler solution in a quasi-steady manner by a transpiration boundary condition. An isolated airfoil is used to compare the steady interaction model with experimental data. Then a flat plate cascade is used to verify the unsteady flow solver with linear theory predictions. An experimental unsteady aerodynamics data set of a loaded cascade with separated meanflow executing torsional oscillations compared favorably with the analysis. The code is then utilized to study the effect of flow separation on the unsteady aerodynamics.