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A Dynamic Convergence Control Algorithm for the Solution of Two-Dimensional Streamline Curvature Methods

[+] Author Affiliations
Vassilios Pachidis, Pericles Pilidis

Cranfield University, Cranfield, Bedfordshire, UK

Ioannis Templalexis

Hellenic Air Force Academy, Dekelia Air Base, Greece

Paper No. GT2009-59758, pp. 287-296; 10 pages
doi:10.1115/GT2009-59758
From:
  • ASME Turbo Expo 2009: Power for Land, Sea, and Air
  • Volume 4: Cycle Innovations; Industrial and Cogeneration; Manufacturing Materials and Metallurgy; Marine
  • Orlando, Florida, USA, June 8–12, 2009
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4885-2 | eISBN: 978-0-7918-3849-5
  • Copyright © 2009 by ASME

abstract

Frequently, the analysis of complex phenomena falls beyond the range of applicability of the numerical methods available in the public domain, and demands the design of dedicated algorithms that will approximate, to a specified precision, the mathematical solution of specific problems. These algorithms can be developed from scratch or through the amalgamation of existing techniques. In any case, they need to execute efficiently and robustly. The accurate solution of the full Radial Equilibrium Equation (REE) in Streamline Curvature (SLC) through-flow analyses presents such a case. This manuscript discusses the development, validation and application of an ‘intelligent’ Dynamic Convergence Control (DCC) algorithm for the fast, accurate and robust numerical solution of the non-linear equations of motion for two-dimensional flow fields. The algorithm was developed to eliminate the large user intervention, usually required by standard numerical methods. Although this hybrid DCC algorithm was specifically developed around a conventional Newton-Raphson scheme, to address the computational challenges presented by SLC-type of analyses, it can also be used in many other applications. The DCC algorithm was integrated into a compressor SLC software and was tested rigorously, particularly at compressor operating regimes traditionally exhibiting convergence difficulties (i.e. far off-design conditions). Typical error histories and comparisons of simulated results against experimental are presented in this manuscript for a particular case-study. For all case-studies examined, it was found that the algorithm could successfully ‘guide’ the solution down to the specified error tolerance, at the expense of a slightly slower iteration process (compared to a conventional Newton-Raphson scheme).

Copyright © 2009 by ASME

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