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The paper presents the setup and analysis of an experimental study on heat transfer of a jet cooled compressor rear cone with adjacent conical housing. The main goal of the paper is to describe the systematic derivation of empirical correlations for global Nusselt numbers to be used in the design process of a jet engine secondary air system. Based on the relevant similarity parameters obtained from literature, operating points are deduced leading to a full factorial design experiment to identify all effects and interactions. The varied similarity parameters are the circumferential Reynolds number, the non-dimensional mass flow, the non-dimensional spacing between rotor and stator, and the jet incidence angle. The range of the varied similarity parameters covers engine oriented operating conditions and is therefore suitable to predict Nusselt numbers in the actual engine component. In order to estimate measurement uncertainties, a simplified model of the test specimen, consisting of a convectively cooled flat plate, has been derived. Uncertainties of the measured quantities and derived properties are discussed by means of a linear propagation of uncertainties. A sensitivity study shows the effects of the input parameters and their interactions on the global Nusselt number. Subsequently, an empirical correlation for the global Nusselt numbers is derived using a multivariate non-linear regression. The quality of the empirical correlation is assessed by means of statistical hypotheses and by a comparison between measured and predicted data. The predicted values show excellent agreement with experimental data. In a wide range, accuracies of 15% can be reached when predicting global Nusselt numbers. Furthermore, the results of the sensitivity study show that pre-swirled cooling air does not have a positive effect on heat transfer.

Prediction of Heat Transfer in a Jet Cooled Aircraft Engine Compressor Cone Based on Statistical Methods