The prescribed surface curvature distribution blade design (CIRCLE) method is presented for the design of two-dimensional (2D) and three-dimensional (3D) blades for axial compressors and turbines, and isolated blades or airfoils. The original axial turbine blade design method is improved, allowing it to use any leading-edge (LE) and trailing-edge (TE) shapes, such as circles and ellipses. The method to connect these LE and TE shapes to the remaining blade surfaces with curvature and slope of curvature continuity everywhere along the streamwise blade length, while concurrently overcoming the “wiggle” problems of higher-order polynomials is presented. This allows smooth surface pressure distributions, and easy integration of the CIRCLE method in heuristic blade-optimization methods. The method is further extended to 2D and 3D compressor blades and isolated airfoil geometries providing smooth variation of key blade parameters such as inlet and outlet flow angles, stagger angle, throat diameter, LE and TE radii, etc. from hub to tip. One sample 3D turbine blade geometry is presented. The efficacy of the method is examined by redesigning select blade geometries and numerically evaluating pressure-loss reduction at design and off-design conditions from the original blades: two typical 2D turbine blades; two typical 2D compressor blades; and one typical 2D isolated airfoil blade geometries are redesigned and evaluated with this method. Further extension of the method for centrifugal or mixed-flow impeller geometries is a coordinate transformation. It is concluded that the CIRCLE method is a robust tool for the design of high-efficiency turbomachinery blades.

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