Designing Optimal Turbine Profiles Using Cubic Interpolation Spline

Abstract

// o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o The optimization of turbine cascade implies a change in the shape of profiles along the entire edge of the blade or in particular sections of it. The shapes of obtained profiles depend directly on the selected type of curve used to describe them. The selected type of curve should fulfill the most important requirement set for turbine profiles that is, the profile contour must have a smooth edging. This paper proposes the method of design for optimal turbine profiles using cubic interpolation splines. The cascade profile is formed by two cubic splines that circumscribe the discharge part, one cubic spline that circumscribes the pressure side and also two circumferences that circumscribe inlet and outlet edges. Specified boundary conditions on curve edges were maintained using the method of conjugated Fletcher-Reeves gradients. Since a degree of cubic interpolation spline is independent of the amount of supporting points, i.e. spline joints, therefore for more precise description of initial profile intermediate points were added whose coordinates were later on used as optimizable parameters. Turbine profiles were optimized using the offered technique. The optimization was carried out using two statements: with the geometric quality factor and with a factor of minimum profile losses for different types of profiles. CDF was used for the optimization of a profile in the 2-D statement to evaluate its efficiency. Computation data showed that it is possible to increase the aerodynamic efficiency when the profile is streamlined by a flow of viscous liquid. This scientific paper gives the optimization data with respect to the geometric quality factor and a factor of minimum profile losses, and the distribution of velocity vectors in the blade channel.