Abstract A computationally efficient mathematical model is developed to analyze the unsteady flow through an harmonically oscillating cascade of airfoils, including inviscid-viscous interactions. 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. Fourier series unsteady periodic boundary conditions are implemented in the flow solver to reduce computational requirements. 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. A isolated airfoil is used to validate the steady interaction model with experimental data. Then a flat plate cascade is used to verify the unsteady flow solver with linear theory predictions. The code is then utilized to predict the unsteady aerodynamics and flutter characteristics of a loaded cascade executing torsional oscillations.
Wolff et al. (Sun,) studied this question.