1. Tlic boundary conditions rcquirrd to transfcr iiilorrnation from patch to patch in the patched-grid approach (Fig. la) are developed in detail in Refs. 8 - 10. In Ref. 8, a conservative patch boundary-condition is developed for first-order-accurate explicit schemes. Results demonstrating the conservativeproperty of the new boundary condition and the quality of solutions possible with patched-grids are presented. In Refs. 9 and 10, this boundary condition is extended to work with implicit second-order-accurate schemes. The modifications to the boundary scheme that are required in order to transfer information between two patches that a m moving relative to each other are also dcveloped in Ilfs.0 and 10. Preliminary results for a rotor-stator configuration are presented in Ref. 10.
2. The patched-grid t,echniqueas developed in Refs. 8-10 is used in Ref. 11 to simulate the flow past thr rotorstator configuration of an axial turbine. The airfoil geometry and flow conditions used are the same as those in Ref. 6. The unsteady, thin-layer Navier-Stokes equations are solved in a time-accurate manner to obtain the unsteady flow field associated with this configuration. The numerically obtained results are compared with the experimental results of Ref. 6. A good comparison of theory and experiment is obtained in the case of timeaveraged pressures on the rotor and stator. Pressure amplitudes (corresponding to the pressure variation in time) were also found to compare well with experiment, thus indicating the validity of the computed unst,eady cornponent of the flow.
3. Grid System for the Rotor-Stator Configuration
4. , I I hc rnultizone grid used to disrrrtiae the rrgion conrids of five zones. The three-dimensional grid consis 1.s of a sequence of two-dimensional grids that are stacked togrther in t,heradial direct,ion (from huh to tip). Since the two-dimensional grids at each radial location aresimilar (except in the tip clearance area), only the grid at midspan isconsidered. It consists affour two-dimensional zones. Figure 3 shows the first two zones. The first zone contains thc stator and is discretized with an 0-grid. Thc second zonecontains the rotor and is also discrrtizcd with an 0-grid. The grids in these two zones were gcnwated using an elliptir grid grnerator of the t,ypc drvrlopcd in Rel. 15. Hotti thr zonrs lie on a cylindrr 01 constant radius, t . h adius bring mcasurrd from tht. c m t w of t h hub. Thc radial locat,ionsof thr stackcd two-dimensional grids are thr samc for thr rotor and stator zones. This leads to two-dimrnsional interface boundaries and thus reduces interfarv logic: by almost an order of magnitude. Although the actual grids used for the calrulation are very dcnsc nrar t.he airfoil surfaces (toresolve the viscous effects),for the purpose of clarity Fig. 3 shows grids in which the points art. pquispared in the direction normal to the airfoil surfarcs.