This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier–Stokes (RANS) equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The state-of-the-art second-order accuracy of numerical methods for unsteady compressible flows with shocks is thus carried over, for the first time to the authors knowledge, to flutter computations. The dual time stepping technique is used to evaluate the nonlinear residual at each time step, thus extending to turbomachinery aeroelasticity the state-of-the-art efficiency of unsteady RANS solvers. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, the very severe 11th Aeroelastic Standard Configuration is computed, namely, the transonic flow through a turbine cascade at off-design conditions, where the turbulence model is found to be the critical feature of the method.
A numerical method for simulating fluid flow through 3-D fracture networks
