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Three-Dimensional Design Method for Long Blades of Steam Turbines Using Fourth-Degree NURBS Surface

[+] Author Affiliations
Shigeki Senoo, Koji Ogata, Tateki Nakamura, Naoaki Shibashita

Hitachi, Ltd., Hitachi, Ibaraki, Japan

Paper No. GT2010-22312, pp. 2149-2158; 10 pages
  • ASME Turbo Expo 2010: Power for Land, Sea, and Air
  • Volume 7: Turbomachinery, Parts A, B, and C
  • Glasgow, UK, June 14–18, 2010
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4402-1 | eISBN: 978-0-7918-3872-3
  • Copyright © 2010 by ASME


A new blade design method for steam turbines using the fourth-degree NURBS surface was developed. The method enables engineers to easily generate three-dimensional complex blade shapes that have inherently good aerodynamic performance and constraint satisfaction. The developed design method has three steps. First, 2D aerofoils are independently generated at each design height. The convergent or convergent-divergent aerofoils are selected on the basis of the outlet Mach number. The convergent flow path is defined by a fourth-degree NURBS curve to preserve the continuity of the slope of the curvature. The divergent flow path for supersonic flow is generated by the method of characteristic curves to avoid strong shock waves. The inlet and outlet angles are constrained to coincide with the flow angle of the velocity triangle. The design parameters, such as chord length, stagger angle and control points of NURBS are automatically decided using an evolutionary optimization technique NSGA-II to minimize the loss by computational fluid dynamics. Therefore, fewer man-hours are needed for design work and better proficiency is not a significant requirement. Second, the number of control points and knot vectors are equalized for all aerofoils by inserting or removing knots and fitting the divergent part by the fourth-degree NURBS curve. Finally, all aerofoils are stacked radially, for example, along the centroid axis, and the fourth-degree NURBS surface is generated by interpolating the control points of the NURBS curves of all the aerofoils. This design method can easily generate long blades of the last stage for steam turbines. The blade has a surface with continuity of the slope of curvature in all directions and good aerodynamic performance under constraints.

Copyright © 2010 by ASME



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