58838 - Experimental Determination of Heat Transfer Coefficient on Impingement Cooled Gear Flanks: Validation of the Evaluation Method 

The gearbox has proven itself as an instrumental component for a more efficient jet engine design. Sitting between the low-pressure spool and the fan, the planetary gearbox enables these components to operate at their respective optimal speeds. Even though the transmission technology has been established for a long time, its implementation in jet engines poses new challenges.

Jet engines and, therefore, all of its components have to be efficient and reliable. Ensuring the reliability of a high-speed high-power gearbox requires comprehensive knowledge about its thermal state. Part of the transmitted power over the gears is dissipated as heat through various loss mechanisms such as friction and churning. An optimal cooling design is needed to transfer a substantial part of the dissipated heat out of the gearbox while minimizing the additional losses caused by the coolant flow. Oil jet impingement cooling is the industrial standard for gearbox cooling in the aviation industry. Nevertheless, its design and implementation are heavily based on experience, since the complex heat transfer mechanism has not been thoroughly understood.

Oil jet impingement cooling is investigated experimentally at the Institute of Thermal Turbomachinery to acquire a better understanding of the heat transfer mechanism and its dependence on various operating parameters. An evaluation based on a finite element analysis (FEA) is required to determine the heat transfer coefficient (HTC) distribution using the measured temperatures. Implementing a boundary condition with an interpolated temperature distribution results in an underestimation of the mean HTC and can not reproduce the sharp gradients in the reference results.

Two iterative approaches for determining the HTC distribution accurately, the von Plehwe and the Levenberg-Marquardt methods, are implemented and validated. In both methods, an initial HTC distribution is applied as the boundary condition in the FEA to calculate a simulated temperature field. Simulated and reference temperatures on thermocouple locations are used to update the HTC distribution for the next iteration until the mean absolute difference between the two temperatures fall beyond a given threshold of 0.01 K. The von Plehwe method is implemented as described by von Plehwe et al. (2020). Implementation of the Levenberg-Marquardt method including the simplified heat transfer model for sensitivity matrix calculation is presented in this paper. Two reference cases are evaluated with the aforementioned methods to ensure their validity. The effect of the spatial resolution of the experimental setup is also investigated.

Both methods are found to converge at accurate solutions, validating their use in the experiments for HTC determination. The Levenberg-Marquardt method can reach the convergence up to three times faster than the von Plehwe method in the low heat transfer case. The performance difference is less significant in the high heat transfer case. Increasing the spatial resolution of the experimental setup would lead to an increase in the accuracy of the HTC determination. Both methods can recreate local extrema in the HTC distribution if the resolution is high enough. However, the spatial resolution of the existing experimental setup is also found to be sufficiently high for an accurate determination of the mean HTC and a qualitative representation of its distribution.