An analytical method for the preliminary assessment of blade cooling flow rates in gas turbine blades

It is well known that -for a given compressor technology- the gas turbine efficiency increases with the turbine inlet temperature (TIT): modern 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 current material limitations make it necessary to adopt internal air cooling to reduce blade creep and improve operational life. The cooling medium is generally 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 properly model the cooling system for a given turbine blade geometry under engine operating conditions: basically, what we are after is the minimum amount of coolant to attain a prescribed maximum material temperature in the blade with the maximum possible uniformity (lower thermal stresses). Therefore, it is essential for designers to rely on simple models in the preliminary design of the first statoric and rotoric blading. Such models neglect the small scales effects on the external flows and also adopt a much simplified treatment of the internal ones. The degree of approximation attainable with such models must though be sufficient to lead to 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 paper also presents a preliminary validation against some published data.