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Axial-Flow Compressors
Ronald H. Aungier
Ronald H. Aungier
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ASME Press
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The flow in the end-wall regions has a substantial influence on the aerodynamic performance of axial-flow compressors. As noted in Chapter 6, a significant portion of the losses in axial-flow compressors is directly associated with the end-wall flow. The through-flow analysis of Chapter 7 requires some external specification of the viscous end-wall blockage factor for solution of Eq. (7-5). In addition, individual stage loading limits and the compressor surge flow limit are often associated with end-wall stall. Unfortunately, there is no available theoretical aerodynamic model capable of predicting the detailed behavior of these highly complex end-wall flows. Indeed, even modern computational fluid dynamics (CFD) viscous flow solvers are found to be incapable of resolving many of the important flow patterns that are observed in the end-wall regions of axial-flow compressors. When fundamental analysis techniques are not sufficient to treat a problem of interest, engineers commonly resort to a combination of theoretical and empirical models. That approach is always used when formulating an aerodynamic performance analysis for axial-flow compressors. The role of end-wall boundary layer models used within specific performance analyses varies considerably. It is always necessary to address the problem of end-wall blockage effects to effectively apply an inviscid through-flow analysis to the problem. Attempts to model end-wall work and loss effects from boundary layer analysis results will be briefly discussed in this chapter. But, in this writer's experience, none of the available end-wall boundary layer models is sufficiently accurate and reliable for that purpose. Chapter 6 has already described empirical models used to extend cascade loss models to account for clearance and end-wall loss effects.

This chapter presents an end-wall boundary layer analysis used to account for end-wall boundary layer blockage effects. The blade row performance models of Chapter 6, the through-flow analysis of Chapter 7 and this end-wall boundary layer analysis are the basic components of an aerodynamic performance analysis. Chapter 9 describes the performance analysis and qualifies it by comparing performance predictions with experimental data. In keeping with the stated objective of this book, Chapters 6 through 9 provide a detailed description of the aerodynamic performance analysis. But it should be emphasized that qualification of the performance analysis evaluates its basic components in combination. That type of qualification does not separate the parts from the whole. In Chapters 6 and 7, it was possible to discuss the assumptions, approximations and limitations of the models. That is not the case in the present chapter. The merits of the present end-wall boundary layer analysis cannot be established beyond demonstrating its effectiveness in supporting the methods of Chapters 6 and 7 to predict the overall performance of axial-flow compressors.

8.1 Historical Development of End-Wall Boundary Layer Theory
8.2 The End-Wall Boundary Layer Equations
8.3 The Boundary Layer Velocity Profile Assumptions
8.4 Empirical Models for Entrainment and Wall Shear Stress
8.5 The Blade Force Defect Thicknesses
8.6 Seal Leakage Effects for Shrouded Blades
8.7 Boundary Layer Jump Conditions
8.8 Solution Procedure
8.9 Typical Results
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