Unsteady turbulent flow simulations on moving Cartesian grids using immersed boundary method and high-order scheme

To simulate the unsteady compressible turbulent flow around moving bodies, a new moving grid method that uses the immersed boundary method on Cartesian grids is proposed. Here, the immersed boundary method is combined with the wall function to impose the wall boundary conditions for turbulent flow simulation around moving bodies. In addition, the high-order scheme for stationary Cartesian grids is extended to that for moving Cartesian grids. The proposed method is validated through two- and three-dimensional flow simulations on moving grids. First, steady flow simulations around NACA0012 airfoil on stationary and moving grids are conducted, with identical results obtained using the proposed method when the relative velocity of the airflow to the grid is the same. Second, flow simulations around the pitching airfoil are conducted. The conservation laws are not strictly satisfied when immersed boundary methods are used. Therefore, the results are compared with the simulation on a body-fitted grid that satisfies the conservation laws as well as with the experimental results. When the proposed method is used, the hysteresis loop of the aerodynamic coefficients is consistent with that on the body-fitted grid. Finally, flow simulations of specific rotor blades in the hover condition are conducted to explore the capacity of the proposed method to predict the aerodynamic coefficients and unsteady flow phenomena. The surface pressure coefficient distributions and the vortex trajectories of the simulations show good agreement with the experimental data. Moreover, fine vortex structures are observed when the high-order scheme is used.