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Effort has been devoted to extending a pressure correction based incompressible flow algorithm developed earlier to calculate compressible flows. The resulting algorithm represents a substantial generalization of the original algorithm, retaining the same basic structure (curvilinear coordinates, staggered grid, pressure correction method, no artificial smoothing terms) and capabilities of the original scheme while adding the new capabilities. With the inclusion of the density variation effects, the pressure correction equation now becomes a convection-diffusion type of transport equation, instead of being a difision type of equation as it is for incompressible cases. The convection effects are dominant for high Mach number flow, and can affect the stability of the low Mach number flow computation. Appropriate numerical treatments are necessary to account for this change of characteristics of the pressure correction equation. The modified pressure correction equation also requires a change of the boundary conditions for pressure between subsonic and supersonic flows. By combining the revised algorithm and an adaptive grid procedure developed earlier, accurate inviscid flow solutions over a wide range of Mach numbers can now be successfully obtained. Several different flow problems, ranging from subsonic and transonic to hypersonic, have been computed to demonstrate the performance of the new algorithm.

The three-dimensional turbulent flow in a curved hydraulic turbine draft tube is studied numerically. The analysis is based on the steady Reynolds-averaged Navier-Stokes equations closed with the k--E model. The governing equations are discretized by a conservative finite volume formulation on a non-orthogonal bodyfitted co-ordinate system. Two grid systems, one with 34 x 16 x 12 nodes and another with 50 x 30 x 22 nodes, have been used and the results from them are compared. In terms of computing effort, the number of iterations needed to yield the same degree of convergence is found to be proportional to the square root of the total number of nodes employed, which is consistent with an earlier study made for two-dimensional flows using the same algorithm. Calculations have been performed over a wide range of inlet swirl, using both the hybrid and second-order upwind schemes on coarse and fine grids. The addition of inlet swirl is found to eliminate the stalling characteristics in the downstream region and modify the behaviour of the flow markedly in the elbow region, thereby affecting the overall pressure recovery noticeably. The recovery factor increases up to a swirl ratio of about 0.75, and then drops off. Although the general trends obtained with both finite difference operators are in agreement, the quantitative values as well as some of the fine flow structures can differ. Many of the detailed features observed on the fine grid system are smeared out on the coarse grid system, pointing out the necessity of both a good finite difference operator and a good grid distribution for an accurate result.

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