Air-cooled gas turbine cycles – Part 1: An analytical method for the preliminary assessment of blade cooling flow rates

Abstract

It is well known that, for a given compressor technology, gas turbine efficiency increases with the turbine inlet temperature (TIT): both modern aeronautical and land-based gas turbines operate at very high temperatures (1500–2000K) –and correspondingly high pressure ratios. As the TIT increases, the heat transferred from the expanding gas to the turbine blade also increases, and the need to extend the operational life make it necessary to adopt internal air cooling to reduce blade creep, oxidation and low-cycle fatigue. The cooling medium is usually air extracted from the high-pressure compressor stages, and since this extraction decreases the thermal efficiency and power output of the engine, it is important to bleed the minimum amount of coolant to attain a prescribed maximum material temperature in the blade with the maximum possible uniformity (lower thermal stresses): thence the need to properly model the cooling system for a given turbine blade geometry under realistic engine operating conditions. In the preliminary design of the first statoric and rotoric blading, it is essential for designers to rely on simple models that often neglect the small scales effects on the external flows and also by force adopt a much simplified treatment of the internal ones, and as a result attain a substantially lower degree of approximation than that offered by more complex and expensive numerical simulations. The goal in the design of a lumped model is therefore to make it both sufficiently general and accurate to analyze blade shapes and cooling channels structures that can be further refined by means of more accurate, but also more computationally intensive, models.This paper presents a simple, globally lumped thermodynamic model of blade cooling whose most important feature is its being analytical, so that the solution is devoid of numerical approximations and leads to closed-form expressions that can be easily manipulated to accommodate for different process parameters, blade arrangements, cooling channel structure and fluid properties. The model predicts the mass-averaged gas temperature along the channel and the required cooling air flowrate, under the assumption of a constant metal temperature along and inside of the blade: therefore, thermo-mechanical effects are completely neglected.The results are validated against some published data, and the agreement is found to be quite satisfactory: when discrepancies arise, a phenomenological explanation is offered.