Boundary Conditions

Two classes of boundary conditions must be enforced on the grid bound­aries: (1) natural boundary conditions, and (2) zonal boundary conditions. The natural boundaries include inlet, outlet, periodic and the airfoil surfaces. The zonal boundaries include the patched and overlaid boundaries.

The inlet boundary conditions include the specification of the flow angle, average total pressure and downstream propagating Riemann invariant. The upstream propagating Riemann invariant is extrapolated from the interior of the domain. At the outlet, the average static pressure is specified, while the downstream propagating Riemann invariant, circumferential velocity, and en­tropy are extrapolated from the interior of the domain. Periodicity is enforced by matching ft>w conditions between the lower surface of the lowest H-grid of a row and the upper surface of the top most H-grid of the same row. At the airfoil surface, the following boundary conditions are enforced: the "no slip”
condition, the adiabatic wall condition, and the zero normal pressure gradient condition.

For the zonal boundary conditions of the overlaid boundaries, data are trans­ferred from the H-grid to the O-grid along the O-grid’s outermost grid line. Data are then transferred back to the H-grid along its inner boundary. At the end of each iteration, an explicit, corrective, interpolation procedure is per­formed. The patch boundaries are treated similarly, using linear interpolation to update data between adjoining grids [Rai, 1985].

2. Results

This section presents selected the results of the numerical simulation of un­steady transport phenomena inside a four-stage turbine-combustor. The sec­tion begins with a description of the geometry and ft>w conditions, followed by a brief discussion of the accuracy of numerical results. The last part of this section presents the effects of in situ reheat on the unsteady flow and blade loading.