The present study deals with optimization of stage performance by the meanline analysis and it also carries out through-flow analysis by the streamline curvature method for an axial flow turbine.
First, an optimal design of an axial flow turbine stage based on the meanline analysis has been carried out for maximum-efficiency by using the gradient projection method. For the optimized design configuration, the radial equilibrium equation with entropy gradient due to viscosity is applied to consider the three dimensional effect. The secondary flow loss is assumed to be parabolically distributed along the blade in order to evaluate the pressure loss in connection with a quasi-three-dimensional analysis.
The stage efficiency is more sensitive to the design variables of mean diameter, relative exit flow angles and axial velocity compared with the stage chords and pitches for a subsonic turbine stage under a given blade loading coefficient. When the pressure ratio is fixed, the stage efficiency is found to be most dependent on the design constraints of degree of reaction at the root for low blade loading coefficient, whereas it depends on the flare angle of the annulus for high blade loading coefficient. However when the blade loading is fixed, the stage efficiency depends mostly on the blade height-to-mean diameter ratio for low total pressure ratio, and peripheral speed at the tip for high total pressure ratio. The optimum total pressure ratio obtained with the radial equilibrium equation is higher than that with the meanline analysis. Contrary to the total pressure ratio, the optimum blade height-to-mean diameter ratio with the radial equilibrium equation is lower than that with the meanline analysis.
Second, new models to distribute the deviation angle and the secondary loss coefficient have been proposed which can be used in association with the streamline curvature method as a through-flow analysis. The model of deviation angle due to passage vortex is approximately formulated by observing that the deviation is caused by the forced vortex in the region of the boundary layer whereas it is caused by the free vortex in the potential flow region. The loss by the secondary flow is assumed to consist of an endwall boundary layer loss and a secondary kinetic energy loss.
The spanwise variation of the exit flow angle for a nozzle blade is predicted very well. The peaky profile of loss coefficient and axial velocity due to the passage vortex near the edge of the boundary layer are in good agreement with corresponding experimental data. It has been proved that the present models of the deviation angle and the secondary flow loss are fairly satisfactory for use in the initial design phase of an axial flow turbine.