Computation of Turbomachinery Boundary Layers

Abstract

In this chapter, the term "boundary layer" is applied very loosely in the generic sense of a shear layer that is not necessarily thin, rather than the quite precise terminology usually implied in classical external aerodynamics. Excluded from this very broad category of flows are shear layers whose behavior can be adequately described by assuming that the transport of momentum or energy across the streamlines of the mean flow is quite negligible. The present chapter is devoted to describing the concepts and procedures available to allow the prediction of the behavior of these "boundary layers" in the diverse and special circumstances found in turbomachinery.In view of the crucial role of boundary layers in setting loss levels, heat-transfer rates, and operating limits, there can be no doubting the desire of the turbomachinery designer to understand and predict the behavior of these boundary layers as they are influenced by flow and geometric changes. Despite this desire, boundary-layer prediction schemes are not, with minor exceptions, at present in extensive use in practical design systems. Real engines have been found to introduce complexities that cannot be allowed for in the prediction schemes and that subsequently dominate the flow behavior. Fortunately, it appears that in the near future this rather sad state of affairs will be changed, due to the combined development of efficient methods for solving multidimensional nonlinear systems of partial differential equations, together with recent advances in the modeling of turbulent transport processes. In the subsequent sections, a hierarchy of techniques will be evolved, all based on using modern computers to effect the solution. The particular turbomachinery application of the various techniques will be introduced, together with their current status and shortcomings and, since many of the techniques are still being evolved, a prognosis for their eventual success will be given.In developing the solution hierarchy, it is first convenient to divide the problem into its two major constituents: (1) the problem of developing and then solving the set of equations purporting to describe the problem at hand, and (2) the problem of describing the turbulent transport of momentum and energy to some reasonable degree of accuracy for that problem. The first part of the problem can be broken down further on the basis that certain physical approximations greatly simplify the numerical process of 331 Purchased from American Institute of Aeronautics and Astronautics Downloaded by PURDUE UNIVERSITY on June 20, 2016 | http://arc.aiaa.org | 332 AIRCRAFT ENGINE COMPONENTSsolving the set of equations. In particular, the neglect of streamwise diffusion in the equations is usually a very good approximation. When this is followed by the assumption that the pressure forces can be approximated either locally by mass conservation (i.e., a blockage correction) and/or without an a priori knowledge of the boundary-layer behavior, the governing equations for time-averaged steady flow are grea...