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.

Computational methods for investigation of surface curvature effects on airfoil boundary layer behavior

“…In this section, the CIRCLE method for the section side of an airfoil is summarized, and the design procedure for the pressure side of the airfoil is similar. 25 Curvature Curv and slope-of-curvature Curv' are defined as follows: where r denotes radius of curvature, (x,y) denotes Cartesian coordinates and y', y″, y″' are the first-, second-, and third-order derivative of y . The sign of the curvature is usually defined as the direction of the unit tangent vector moving along the curve.…”

“…In this section, the CIRCLE method for the section side of an airfoil is summarized, and the design procedure for the pressure side of the airfoil is similar. 25 Curvature Curv and slope-of-curvature Curv 0 are defined as follows:…”

“…The Bezier spline is iteratively manipulated until the slope and the y location of the airfoil surface are achieved at points P sk . 25 LE design. The CIRCLE method used a hybrid method to design the LE region.…”

“…In this study, the CIRCLE method 25 is used to redesign airfoils by removing their surface curvature and slope of surface curvature discontinuities from LE to TE. A symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 are judiciously selected for this investigation due to the existence of discontinuities of curvature and slope-of-curvature, their widespread use and the availability of detailed experimental measurements of airfoil performance.…”

An inverse design tool for two‐dimensional blade generation in aerospace engineering education

“…A special course “principle of aeronautical blades” is opened for undergraduate students in the major of aerospace engineering, where they learn the basic theory and methodology for designing blades. Normally, there are two dominant blade design approaches: direct design and inverse design . The first type is a straightforward method, that is, one designs the blade shape based on experience, validates the performance by simulation or experiment, modifies the blade geometry according to some optimization rules, and then repeats the above process until a satisfied performance is finally achieved.…”