Numerical Model

The numerical model used herein is based on an existing algorithm devel­oped for unsteady fbws in turbomachinery [Cizmas and Subramanya, 1997]. The Reynolds-averaged Navier-Stokes equations and the species equations are written in the strong conservation form. The fully implicit, finite-difference approximation is solved iteratively at each time level, using an approximate factorization method. Three Newton-Raphson sub-iterations are used to re­duce the linearization and factorization errors at each time step. The con­vective terms are evaluated using a third-order accurate upwind-biased Roe scheme. The viscous terms are evaluated using second-order accurate central differences. The scheme is second-order accurate in time.

Grid Generation

The computational domain used to simulate the flow inside the turbine – combustor is reduced by taking into account flow periodicity. Two types of grids are used to discretize the flow field surrounding the rotating and station­ary airfoils, as shown in Fig. 1. An O-grid is used to resolve the governing equations near the airfoil, where the viscous effects are important. An H-grid is used to discretize the governing equations away from the airfoil. The O-grid is generated using an elliptical method. The H-grid is algebraically gener­ated. The O – and H-grids are overlaid. The fbw variables are communicated between the O – and H-grids through bilinear interpolation. The H-grids corre­sponding to consecutive rotor and stator airfoils are allowed to slip past each other to simulate the relative motion.