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The unsteady flow around an airfoil NACA0012 (National Advisory Committee for Aeronautics) is simulated using Computational Fluid Dynamics approach and the behavior of flow stabilityis analyzed using the energy gradient method.In the numerical model,the Reynolds averaged Navier-Stokes equations and the Spalart-Allmaras turbulent model or k-ε model are employed.The main work is concerning the aerodynamic behavior of the flow around the airfoil and the flow stability under the influence of various parameters.The simulation results are analyzed using the energy gradient theory.The numerical method is first validated using experimental data in literature.The study is carried out at a quite low Reynolds number of 5000 with a Spalart-Allmaras model,then a Reynolds number of 3.5*106with a k-ε model.It is found that the flow instability varies with the attack angle,the position of Kmax occurrences the place of instability first occurrence.Therefore,the energy gradient function Kmax reflects the behavior of the flow instability.