Numerical study of turbulent flows over vibrating blades with positive interblade phase angle

In this paper, a locally implicit scheme on unstructured dynamic meshes is presented to study transonic turbulent flows over vibrating blades with positive interblade phase angle. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low- Reynolds-number k-epsilon turbulence model are solved in the Cartesian coordinate system. To treat the viscous flux on quadrilateral-triangular meshes, the first-order derivatives of velocity components and temperature are calculated by constructing auxiliary cells and Green's theorem for surface integration is applied. The assessment of accuracy of the present scheme on quadrilateral-triangular meshes is conducted through the calculation of the turbulent flow around an NACA 0012 airfoil. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which include the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady pressure wave, shock wave and vortex-shedding phenomena are demonstrated and discussed.