Calculation of three-dimensional boundary layers on turbomachinery blades

The aerodynamic behaviour of turbomachinery is dominated by viscous effects. In the design of a component for the machine, inviscid methods are normally employed. However, it is useful to cover the viscosity in the calculation to achieve a better understanding of the fluid behaviour. This feature can be analysed by using Navier-Stokes calculations or simpler and more approximate techniques such as boundary-layer calculation. In recent years there have been a considerable number of Navier-Stokes solvers as well as boundary-layer solvers. However, Navier-Stokes methods require a large amount of computer storage and CPU time, which limits the number of grid points that can be used inside the boundary-layer. Hence, boundary-layer techniques become very attractive. The purpose of this study is to develop a boundary-layer calculation that is efficient, accurate and simple to implement, and can be applied to flow over complex geometry such as turbomachinery blades. To account for the surface curvature and rotation, the three-dimensional unsteady boundary layer equations are expressed in generalised curvilinear co-ordinate system on the body surface with respect to a rotating frame of reference. The equations are solved numerically by using Finite Difference Approximation without employing the similarity transformation. The steady state solutions are obtained by integrating the equations in time. Two methods, an interactive scheme and FLARE approximation scheme, are described for calculating separated flow. The concept of the interactive approach is general but its application, in this study, is limited to two-dimensional flow. The viscous losses, expressed in term of entropy generation, is also calculated from the computed flowfield. Computational results on a wide variety of flow situations and configurations are validated and show good agreement with analytical results and experimental measurements. Results reveal, in general, that the method holds a practical advantage, in both speed and accuracy of computation, for solving the boundary-layer problems to which it is best suited