SOLUTION-ADAPTIVE STRUCTURED-UNSTRUCTURED GRID METHOD FOR UNSTEADY TURBOMACHINERY ANALYSIS .1. METHODOLOGY

A solution-adaptive method for the time-accurate analysis of two-dimen sional flows in multistage turbomachinery is presented. The method emp loys a hybrid structured-unstructured zonal grid topology in conjuncti on with appropriate modeling equations and solution techniques in each zone, thus combining the advantages of both structured and unstructur ed grid methods. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured 0-type grids, while the rest of the domain is discretized using an unstructured mesh of triangular ce lls. In the inner regions, the Navier-Stokes equations are solved usin g an implicit, third-order accurate, upwind-biased scheme. The use of both central difference and upwind schemes is explored for the solutio n of the Euler equations in the outer regions. An efficient and robust grid adaptation strategy, including both grid refinement and coarseni ng capabilities, is developed for the unstructured grid regions. Metho dologies for the accurate, conservative transfer of information at the interface between the structured and unstructured domains, as well as that between two unstructured grids in relative motion, are also deve loped. For generality, three-dimensional effects of stream-tube contra ction are modeled. The numerical methodology is presented in detail in the present article (Part 1). Results obtained using this method and comparisons of these results with experimental data and earlier struct ured-grid based methods are presented in a companion article (Part II) .