Two- and Three-Dimensional Prescribed Surface Curvature Distribution Blade Design (CIRCLE) Method for the Design of High Efficiency Turbines, Compressors, and Isolated Airfoils

Abstract

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.

Numerical and Theoretical Investigations Concerning the Continuous-Surface-Curvature Effect in Compressor Blades

“…Unlike the optimization methods in [11][12][13][14][15][16], which aim at building a blade surface with the best aerodynamic performance and result in much alteration of the shape of blade surface, the method suggested in this paper is to get an optimized continuous curvature blade without major modification to the datum blade geometry, which helps to exclude the influence of blade shape alteration when analyzing the effect of curvature continuity. The method for the leading edge and the main surface, respectively, is detailed as follows.…”

“…[17][18][19][20], and it is considered to be the state of the art [21]. More specifically, Langtry [17] validated CFX with the γ-Reθ model on computing the flowfield around a double-circular airfoil, and Korakianitis [14] used the software FLUENT with the γ-Reθ model in his curvature-based blade optimization system. Marciniak [21] validated the ability of γ-Reθ model on predicting the performance of a CDA profile.…”

“…Blade A, just like the datum blade, has discontinuous curvature or gradient of curvature in the main surface. (It should be noted that the datum curvature distribution is calculated by using 3-point difference method as in [14], so the discontinuities in curvature cannot be accurately captured.) But Blade B is represented by the B-spline curvature distribution, so the continuity of the curvature as well as the gradient of curvature is satisfied implicitly.…”

“…Korakianitis [11][12][13] found that the aerodynamic and heat transfer performances of turbine cascades are affected significantly by the curvature distributions and proposed a design method for turbine blades, in which a curvature distribution of the blade is prescribed to construct a blade surface with both a continuous curvature and gradient of curvature. The method has been further extended to compressor blades and reduction of losses inside the boundary layer on the suction surface as well as improvement of blade performance is observed numerically for the optimized compressor blades [14]. Sommer [15] and Fathi [16] also presented surface curvature optimizations for compressor blades.…”

A 3D Parameterization for Transonic Fan Blade Multidisciplinary Design

“…Pierret et al [4] proposed using mean camber line distribution as a design variable. However, as discussed by various authors [10][11][12], flow properties also depend strongly on blade curvature; thus a direct control on the variation of the blade angles along the blade chord is also important to control diffusion.…”