A New Method to Calculate the Coolant Requirements of a High-Temperature Gas Turbine Blade

Earlier papers by the first author have described a computational method of estimating the cooling flow requirements of blade rows in a high-temperature gas turbine, for convective cooling alone and for convective plus film cooling. This method of analysis and computation, when applied to the whole blade chord was compared to a well-known semi-empirical method. In the current paper, a more sophisticated method is developed from the earlier work and is used to calculate the cooling flow required for a nozzle guide vane (the first blade row) of a high-temperature gas turbine, with given inlet gas temperature and coolant inlet temperature. Now the heat flux through an elementary cross-sectional area of the blade, at given spanwise (y) and chordwise (s) locations, is considered, with a guessed value of the elementary coolant flow [as a fraction $dΨs$ of the external gas flow]. At the given s, integration along the blade length gives the blade metal temperatures at the outer and inner walls, $Tbgy$ and $Tbcly.$ If the value of $Tbg$ at the blade tip $y=H$ is assumed to be limited by material considerations to $Tbg,max$ then the elementary coolant flow rate may be obtained by iteration. Summation along the chord then gives the total coolant flow, for the whole blade. Results using the method are then compared to a simpler calculation applied to the whole blade, which assumes chordwise constant temperatures and constant selected values of cooling efficiency and film-cooling effectiveness.