Nonlinear separated unsteady flow modeling
Abstract
A computationally efficient mathematical model is developed to analyze the unsteady flow through a harmonically oscillating cascade of airfoils, including strong inviscid-viscous interaction effects, such as boundary layer separation, shock/boundary layer interaction, and trailing edge/wake interaction. The flow solver incorporates an inverse integral boundary layer solution with the time-marching Euler analysis NPHASE in a quasi-steady manner. An embedded composite grid formulation was incorporated, specifically a deforming C-grid embedded in a Cartesian H-grid, thereby simplifying grid generation. Fourier series unsteady periodic boundary conditions were implemented in the flow solver to reduce computational requirements. A flat plate cascade is analyzed to verify the flow solver with linear theory predictions. Compressor rotor configurations are then analyzed to investigate nonlinear effects. The effects of the Fourier series periodic boundary conditions, bi-linear interpolation from the composite grid formulation, and the inviscid-viscous interaction model are analyzed to determine their effectiveness for unsteady aerodynamic calculations. The analysis of oscillating cascades over a range of steady operating conditions clearly demonstrated the importance of considering viscous interactions. The nonlinearities of the unsteady cascade aerodynamics are increased by viscous effects. The inverse integral boundary layer model incorporated in a quasi-steady manner with a time marching Euler solution is an effective way to analyze the viscous unsteady aerodynamics of a cascade of oscillating airfoils. Furthermore, applying a Fourier periodic boundary condition was demonstrated to model the nonlinear behavior of the flow field while greatly reducing the computer resources in both time and memory requirements. Finally, the unsteady flow solver implemented on embedded composite grids with bi-linear interpolation accurately predicts the unsteady aerodynamics of an oscillating cascade of airfoils, except for situations where a shock wave extends across the interpolation region.
Degree
Ph.D.
Advisors
Fleeter, Purdue University.
Subject Area
Mechanical engineering|Aerospace materials
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