Calculation of temperature distribution in various turbine blades using a boundary-fitted coordinate transformation method

Gas turbine engines operating at high temperature and high pressure ratio have been developed to increase power output and efficiency. However, due to the limitations of material properties, internal convective cooling is needed in many turbine blades. Knowledge of the temperature distribution in the cooled blade is necessary for its thermal stress analysis. Improvements in prediction capability in this area can benefit turbine life, reduce development and maintenance costs, and improve engine performance.; Numerical solutions of partial differential equations in regions with arbitrarily shaped boundaries are relatively difficult. Finite-difference solutions in irregular domains have been hindered in the past by the problem of fitting curved boundaries into the computational grid. In this study the physical region where the heat transport occurs is mapped onto a rectangular computational domain by means of a boundary-fitted coordinate transformation method. The finite-difference approach is then used to give solutions that do not lack continuity of derivatives. A general convection-diffusion equation is derived for the transformed computational domain and a computer program is developed to solve the heat transfer in any blade shape. The program has five main subroutines. The first subroutine transforms the physical domain to the computational domain and generates the grid. The second calculates the "scale factors" for use in the solution of the partial differential equation transformed to the computational domain. The third subroutine solves the governing equations. The fourth makes contour line data from randomly located temperature distribution data. The last shows the grid generation and the final contour lines by two graphs.; Only one outer blade shape, the Allison/NASA C3X vane, is studied with various inner hole geometries and boundary conditions. The study shows that by developing a multi-part technique the problem of complicated geometry can be solved. Regardless of the temperature distribution on the outer boundary, the best cooling effect is obtained when the inner cooling holes have a similar shape to the outer blade surface. It is shown that the cooling of the tail region is important especially at the tail end.