Computation of unsteady viscous flows with aeroelastic applications

Calculation of unsteady flows is of great importance in engineering applications, such as the prediction and prevention of buffeting of aircraft wings, dynamic distortion in aircraft inlets, flutter of turbomachinery blades. In this research, a multigrid Navier-Stokes method with a two-equation k-{dollar}omega{dollar} turbulence model is developed for calculating unsteady viscous flows. The method uses a staggered finite-volume scheme to discretize the Navier-Stokes and the turbulence model equations in space. A fully implicit time-accurate scheme is reformulated so that an efficient explicit multistage method with local time stepping, residual smoothing, and multigrid is used to accelerate convergence within each unsteady time step. The method combines the advantages of implicit and explicit schemes for unsteady flow calculations. Solutions for the forced oscillation of an airfoil are obtained with the Euler and the Navier-Stokes equations. Results agree well with experimental data. The Navier-Stokes solutions show better agreement than the Euler solutions.; It is well known that transonic flow often exhibits self-excited unsteady oscillations due to shock-boundary layer interactions. Viscous effects play a very important role in such circumstances. Turbulence modeling is very important for accurate prediction of the onset of such self-excited unsteadiness. Therefore, self-excited oscillation of transonic flow around a biconvex airfoil in a channel is studied using the developed unsteady Navier-Stokes solver. The amplitude and unsteady range of shock movement are predicted with Baldwin-Lomax algebraic turbulence model. Flows with the same conditions are also calculated with the two-equation k-{dollar}omega{dollar} turbulence model. Results are compared with experimental data to assess the validity of the computation and turbulence models.; The aim of the rest of the work is to study flutter of turbomachinery blades which may be influenced by non-linear effects. The efficient 2-D time-marching Navier-Stokes solver is extended to cover quasi-three-dimensional cases. Then a parallel version Unsteady flows around oscillating turbomachinery blades are computed on single and multiple passage domains. The so-called phase-shifted periodic boundary condition is applied by a conventional 'Direct Store' method over a single blade passage. A parallel program for calculating flows through multiple passages is also developed by using the Message Passing Interface (MPI) standard. This code is tested on a specialized high end parallel machine as well as on a PC cluster connected by the common ethernet. Almost linear parallel speed-up is obtained on both systems due to the small amount of message passing needed in the parallel algorithm. In the parallel multiple passage computation, the phase-shifted periodic boundary condition is converted to a simple in-phase periodic condition. This greatly accelerates the convergence of the computation to a periodic solution. The aeroelastic flutter boundaries are predicted by an uncoupled energy method. Results are compared with linear theory and experimental data.