Prescribed-Curvature-Distribution Airfoils for the Preliminary Geometric Design of Axial-Turbomachinery Cascades

Blade surfaces with continuous curvature and continuous slope of curvature minimize the possibility of flow separation, lead to improved blade designs, and reduce the direct and inverse blade-design iterations for the selection of isolated airfoils and gas-turbine-blade cascades. A method for generating two-dimensional blade shapes is presented. The geometry near the trailing edge is specified by an analytic polynomial, the main portion of the blade surface is mapped using as input a prescribed surface-curvature distribution, and the leading edge is specified as a thickness distribution added to a construction line. This procedure is similar for the suction and pressure surfaces, and by specification it constructs continuous slope-of-curvature surfaces that result in smooth surface-Mach-number and surface-pressure distributions. The method can be used to generate subsonic or supersonic airfoils for compressors and turbines, or isolated airfoils. The resulting geometric shapes can be used as inputs to various blade-design sequences. It is shown that, with other cascade-design parameters being equal, increasing the stagger angle of turbine blades results in more front-loaded and thinner blades, and that there is an optimum stagger angle resulting in minimum wake thickness. The subsonic axial-turbine blade rows included for discussion in this paper have been designed by iterative modifications of the blade geometry to obtain a desirable velocity distribution. The blade-design method can be used to improve the aerodynamic and heat transfer performance of turbine cascades, and it can result in high-performance airfoils, even if using the direct method exclusively, in very few iterations.