Chapter 12
Quasi-Three-Dimensional Blade Passage Flow Field Analysis


The aerodynamic design and analysis of multistage axial-flow compressors is usually based on empirical cascade performance models as described in Chapters 6 through 11. Although that approach is sufficient for most applications, designers occasionally require the support offered by more fundamental internal flow analyses. When a specific application requires operating a blade row at conditions more extreme than justified by experience, supplemental analysis can greatly increase the designer's confidence or perhaps prevent a poor decision. In the case of industrial axial-flow compressors, this usually relates to the blade row inlet Mach number level. The industrial compressor designer usually has a number of discrete geometrical scales or frame sizes available. If a specific application slightly exceeds the upper limit of flow capacity for a frame size, the designer must either accept somewhat higher Mach number levels or choose a larger frame size with a substantial increase in cost. Alternatively, transonic blade sections such as double-circular-arc blades might be considered. Usually that also involves increased cost and may be unattractive with respect to structural integrity. Even when the application is well within the normal flow capacity limits of a frame size, an unusual working fluid or a required rotation speed can result in Mach number levels beyond the designer's experience. In those cases, designers need a more fundamental internal flow analysis to better evaluate probable impact of the higher Mach number levels.

Chapter 5 presented several useful techniques for the analysis of the internal flow on stream surfaces within blade passages. Those blade-to-blade flow analyses can provide the desired detailed evaluation, but all of them require that the stream surface geometry and stream sheet thickness be specified in some fashion. An approximate analysis can be conducted using the stream sheet geometry before and after the blade row from the meridional through-flow analysis of Chapter 7, while assuming a linear variation between those stations. That is certainly the fastest and simplest approach and often may be considered sufficient.

Alternatively, a more accurate analysis can be conducted using the quasi-three-dimensional flow analysis technique mentioned in Chapters 3 and 5. That is a very efficient analysis technique that provides a reasonable approximation to the three-dimensional flow field through a blade row. Originally suggested by Wu (1952), this technique relies on solving for the two-dimensional flow on the blade-to-blade stream surfaces and on the hub-to-shroud stream surface, with interaction between them until they are consistent with each other. This chapter describes a quasi-three-dimensional flow analysis suitable for that purpose. This analysis was originally developed for centrifugal compressors (Aungier, 2000), where it plays an essential role in the aerodynamic design of impellers. It was subsequently extended to treat arbitrary three-dimensional blade geometry for additional flexibility in centrifugal impeller design. That extension made it possible to use the analysis directly for axial-flow compressor blade rows.

  • 12.1 Quasi-Three-Dimensional Flow
  • 12.2 Hub-to-Shroud Flow Governing Equations
  • 12.3 Numerical Integration of the Governing Equations
  • 12.4 Repositioning Stream Surfaces
  • 12.5 The Hub-to-Shroud Flow Analysis
  • 12.6 Coupling the Two Basic Flow Analyses
  • 12.7 Boundary Layer Analysis

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