Improved turbine-blade design techniques using 4th-order parametric-spline segments

Abstract

The paper presents a method for generating blade shapes to be used as inputs to direct- or inverse-blade-design sequences. Isolated airfoils and gas-turbine-blade cascades are designed by a mixture of iterative and direct- and inverse-blade-design methods. In the direct-design method, the designer inputs the geometry of the airfoils, and flow solvers are used to study the resulting performance in terms of Mach numbers or pressure distributions along the airfoil surfaces. In the inverse-design method, the designer specifies as input the desirable performance along the airfoil surfaces, and flow solvers are used to compute the airfoil geometry that will provide the performance. The design iterations are enormously reduced if the initial blade shape has performance characteristics that are near the desirable ones. The method can be used to generate airfoils for compressors and turbines, or isolated airfoils, but the discussion in the paper is limited to subsonic-exit axial-turbine blade rows. The desirable performance characteristics are presented, and ways to specify the input aiming for such characteristics (minimizing design iterations) are discussed. It is shown that continuous curvature and continuous slope of curvature are necessary conditions for improved blade designs. A set of parametric curves that satisfy the above conditions is developed, and used to specify the geometry of turbine cascades. Thickness distributions satisfying the same conditions are used near the leading edge of the cascades. The performance characteristics of two turbine cascades generated by this method are included. The shape and distribution of curvature of the suction and pressure surfaces of the airfoil are particularly important for the aerodynamic and heat-trasfer performance. The 4th-order (continuous-slope-of-curvature) parametric splines should be used wherever separation in fluid streams at the walls would be detrimental to performance, and they have additional applications in smooth-surface-generation activities such as automobile-surface design.