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Chapter 4
Empirical Performance Models for Axial-Flow Turbine Blade Rows

Excerpt

This chapter presents empirical models used by this writer for predicting the fluid turning and the total pressure losses in axial-flow turbine blade rows. This is the logical starting point for the discussion of this class of turbines, since all aerodynamic design and analysis procedures are governed by these basic performance characteristics. Ainley and Mathieson [41] published a design and off-design performance system for axial-flow turbines in 1951. Dunham and Came [42] published a series of improvements to the Ainley-Mathieson system in 1970. This modified system is commonly referred to as the AMDC performance system. Kacker and Okapuu [43] suggested further refinements to the AMDC system in 1981. The performance system described in this chapter is derived from these three references, but with several modifications.

The original performance systems were all developed for use in one-dimensional or mean-line performance analyses. The present performance system is intended for use in the more general hub-to-shroud or multiple-streamline performance analysis of chapter 5. A hub-to-shroud performance analysis provides the benefit of more detailed fluid dynamic data that mean-line methods must seek to estimate from the mean-line flow data. But it also requires addressing the more severe off-design operating conditions that are often encountered near the end- walls. A number of practical modifications were necessary to generalize the original methods to the intended application and to achieve a performance system that is reliable under severe off-design operating conditions. Several extensions to the original methods were found necessary to treat modern high-pressure steam turbines. The methods for including Reynolds number effects required extension to consider the effects of surface finish, which has become essential for the high-Reynolds-number applications encountered today. It was also necessary to consider cases where the flow is diffusing through the blade row. This condition can be encountered near the hub stream surface under off-design operating conditions. It can result in a total breakdown of some of the original mean-line models. Many of the original performance models are provided in graphical form. In keeping with the objective of this book to provide complete descriptions, the empirical equations developed to apply the graphical models are provided and compared with the original models.

While derivatives of the AMDC performance system are probably the most widely used methods, a number of alternative methods have been published. Among the best-documented alternatives are those of Craig and Cox [44], Traupel [45] and Stewart [46]. The method of Craig and Cox is particularly significant and unique in regard to its thorough treatment of Reynolds number effects, including the effect of surface finish. In that context, it influenced the development of the present performance system by providing independent confirmation of the approach used.

  • 4.1 Blade Row Geometry
  • 4.2 Fluid Deviation Angle
  • 4.3 Overview of the Loss System
  • 4.4 Profile Loss Coefficient
  • 4.5 Secondary Flow Loss Coefficient
  • 4.6 Trailing-Edge Loss Coefficient
  • 4.7 Shock Loss Coefficient
  • 4.8 Supersonic Expansion Loss Coefficient
  • 4.9 Blade Clearance Loss Coefficient
  • 4.10 Lashing Wire Loss Coefficient
  • 4.11 Leakage Bypass Loss
  • 4.12 Partial Admission Loss
  • 4.13 Disk Friction Loss
  • 4.14 Clearance Gap Windage Loss
  • 4.15 Moisture Loss

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