The objective of this study was to acquire improved understanding of viscous interanl flows related to turbomachinery compents by analyzing appropriate model flow problems. Significant effort was directed towards developing basic computational methods which were made available to interested researchers involved in computational fluid dynamics (CFD) research and to users involved in the designof turbomachinery components. Several analyses were developed and include an asymptotic analysis for the fully developed three-dimensional flow in curved ducts, a parabolilzed navier-Strokes analysis for developing flow in curved ducts, an unsteady Navier-Strokes analysis for internal and externall flows, adaptive grid generation for one and two dimensional vilscous flows, analysis of the Neumann problem in generalized orthogonal coordinates, efficient semi-implicit solution techniques consisting of the alternating direction implicit multi grid and strongly implicit multi grid methods, the direct block Gaussian elimination(GBE) method for solution of the Poisson equation for the unsteady Navier Strokes analysis of incompressible flows. For the flow inside a shear driven cavity, the asymptotic flow in curved ducts and clarity for interpretation of the available corresponding experimental results and have now become benchmark solutions for these problems.

This report describes the technical progress achieved in research sponsored by the Air Force Office of Scientific Research during the period between March 1981 and February 1982. Three areas of research were pursued; two of these consist of analysis of laminar and turbulent duct flows, and study of laminar and turbulent separated flows. Both of these studies were aimed at acquiring a better understanding of isolated physical phenomena significant to turbomachinery applications via the use of appropriate model problems. The third area of research pursued consisted of the analysis of numerical methods with the goal of improving the efficiency and accuracy of the various methods developed and implemented. In the first area of research, fine-grid asymptotic solutions were obtained for laminar flow through curved ducts of simple cross sections; also marching solutions have been obtained for further flow in the entrance region of curved ducts of simple cross sections. The subject of streamwise separation is examined using the laminar flow through a constructed asymmetric channel and the laminar and turbulent flows past a thick blunt plate as the model problems. In the third category, high-Re very fine-grid solutions have been provided for the shear-driven cavity problem using a multi-grid strongly implicit method.

This research is motivated by the need for accurate prediction of three-dimensional viscous flow in a turbine or compressor passage. As a major step towards the investigation of these problems, the three-dimensional entrance flow through ducts of various regular cross-sections, with longitudinal and transverse curvature effects, have been studied. The mathematical model has been formulated using time-averaged three-dimensional parabolized Navier-Stokes equations. The analysis has been developed using an existing two-equation turbulence model and is checked by obtaining satisfactory comparison of the present results for straight and curved circular pipes. The effects of the problem parameters on the flow fields are accurately evaluated and the limitations of the turbulence model have been briefly stated. Four related areas were identified and studied separately. These consist of the law of the wall, coordinate transformations and efficiency and accuracy of the numerical algorithm. The last three of these areas have been studied with some success already, and the additional analysis developed will be implemented in the basic turbulent-flow program to make the latter a truly predictive tool.

Viscous flow is treated usually in the frame of boundary-layer theory and as two-dimensional flow. Books on boundary layers give at most the describing equations for three-dimensional boundary layers, and solutions often only for some special cases. This book provides basic principles and theoretical foundations regarding three-dimensional attached viscous flow. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers. This wider scope is necessary in view of the theoretical and practical problems to be mastered in practice. The topics are weak, strong, and global interaction, the locality principle, properties of three-dimensional viscous flow, thermal surface effects, characteristic properties, wall compatibility conditions, connections between inviscid and viscous flow, flow topology, quasi-one- and two-dimensional flows, laminar-turbulent transition and turbulence. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice. The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility conditions; connections between inviscid and viscous flows; flow topology; quasi-one- and two-dimensional flows; laminar-turbulent transition; and turbulence. Detailed discussions of examples illustrate these topics and the relevant phenomena encountered in three-dimensional viscous flows. The full governing equations, reference-temperature relations for qualitative considerations and estimations of flow properties, and coordinates for fuselages and wings are also provided. Sample problems with solutions allow readers to test their understanding.

Provides an account of internal, external and unsteady slow viscous flows, including the advances. This book shows how the method of eigenfunctions, in conjunction with least squares, can be used to solve problems of low Reynolds number flows, including three-dimensional internal and unsteady flows.

A numerical study of the effects of viscous-inviscid interactions in three-dimensional duct flows is presented. In particular interacting flows for which the oncoming flow is not fully-developed were considered. In this case there is a thin boundary layer still present upstream of the surface distortion, as opposed to the fully-developed pipe flow situation wherein the flow is viscous across the cross section. Bodonyi, R. J. Unspecified Center NASA-CR-181336, NAS 1.26:181336 NAG3-528