One of the most important factors to improve the performance and thrust generation of a jet engine is to increase the turbine inlet temperature. With ongoing researches in this field, the temperature in the main gas path of a high-pressure turbine exceeds the maximum tolerable material temperature.

Therefore, efficient cooling of turbine blades and vanes is required. However, the extraction of cooling mass flow from the compressor means a penalty to the overall thermal efficiency of the jet engine. Therefore, it is crucial to use as few cooling air as possible. A better understanding of the complex interaction between the design parameters and the system behavior, helps designing more efficient cooling systems. The present study investigates two stochastic methods, the Elementary-Effects Method by Morris and the Coefficient-of-Importance, for quantifying the sensitivity of the cooling flow to geometric variations using a one-dimensional flow network of a high-pressure-turbine blade.

The Elementary-Effects Method is a One-at-Time screening method for the quantification of the overall importance of a design variable as well the interactive effect in combination with another variable on the system behavior. The Coefficient-of-Importance is based on polynomial regression models and quantifies the variance in the system response evoked by a design variable.

As testcase for the comparison of the two methods a multipass cooling system with rib-roughened walls is investigated in which the geometry parametrization is based on cubic splines. Since cubic splines can deform extremely even with small displacement of the distribution points, using the point coordinates directly for the geometric variation can lead to implausible design variants. Therefore, the Analytical-Coupling parametric for the variation of splines is developed, which consists of seven independent parameters.

The parametric proves to be universally applicable regardless of the shape of the underlying spline. Furthermore, the new developed parametric facilitates the interpretation of the physical relationships between the variable parameters and the resulting system behavior.

 

With the Analytical-Coupling approach the sensitivity of the cooling mass flow and total pressure change to geometric variations of the webs, ribs, bends, entry and exit of the turbine blade cooling system is considered which leads in total to 49 variable design parameters. The influence of the sampling size as well as different variable ranges on the importance quantification of variables is investigated. It is shown that the Coefficient-of-Importance and the Elementary-Effects Method lead in general to the same importance ranking of the design variables.

However both methods have their own advantages and drawbacks that are highlighted  in the present study.


Comparison of Two Methods for the Sensitivity Analysis of a One-Dimensional Cooling Flow Network of a High-Pressure-Turbine Blade

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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