ABSTRACT Oil-jet lubrication and cooling of high-speed gears is frequently employed in aeronautical systems, such as novel high-bypass civil aero engines based on the geared turbofan technology. Using such oil-jet system, practitioners aim to achieve high cooling rates on the flanks of the highly thermally loaded gears with minimum oil usage. Thus, for an optimal design, detailed knowledge about the flow processes is desired. These involve the oil exiting the nozzle, the oil impacting on the gear teeth, the oil spreading on the flanks, the subsequent oil fling-off, as well as the effect of the design parameters on the oil flow. Better understanding of these processes will improve the nozzle design phase, e.g. regarding the nozzle positioning and orientation, as well as the nozzle sizing and operation. Most related studies focus on the impingement depth to characterize the two-phase flow. However, the level of information of this scalar value is rather low for a complete description of the highly dynamic three-dimensional flow. Motivated by the advancements in numerical methods and the computational resources available nowadays, the investigation of the oil-jet gear interaction by means of computational fluid dynamics (CFD) has come into focus lately. In this work, a numerical setup based on the volume-of-fluid method is presented and employed to investigate the two-phase flow phenomena occurring in the vicinity of the gear teeth. The setup consists of a single oil-jet impinging on a single rotating spur gear. By introducing new metrics for characterizing the flow phenomena, extensive use of the possibilities of modern CFD is made, allowing a detailed transient and spatially resolved flow analysis. Thus, not only the impingement depth, but also the temporal and spatial evolution of wetted areas on the gear flanks, as well as the evolution of the oil volume in contact with the gear flanks are extracted from the simulation data and compared in a CFD study. The study consists of 21 different simulation cases, whereby the effect of varying the jet velocity, the jet inclination angle, the jet diameter, and the gear speed are examined. Consistent results compared to a simplified analytical approach for the impinging depth are obtained and the results for the newly introduced metrics are presented.

The geared turbofan is a promising concept for civil aircraft jet engines. With the introduction of a gearbox between the low-pressure turbine and the fan, both components can rotate at their respective optimum speed. The geared turbofan enables a lower specific fuel consumption as well as jet engine noise reductions. A planetary gear train is usually chosen for the transmission with the sun gear connected to the low-pressure turbine. This high-speed reduction gear train needs to transmit high loads with a high efficiency in limited installation space. To ensure a safe operation of the gear train, the thermal behavior of the gears needs to be understood. The heat generated by the meshing processes is dissipated by oil impingement cooling. While the field of Elastohydrodynamic lubrication yields good results for the heat generation, no validated model for the impingement cooling process is available in literature. In this study, an analytical model is developed and validated against experimental data. First, the surface area of the oil film on the gear tooth flank formed by the impinging oil jet is calculated. Second, the heat transfer from the gear tooth flank to the oil film is determined. The fluid motion is modeled as an oil film that is flung off the gear tooth flank by centrifugal forces. In addition to the film flow, the presented model takes into account the temperature dependence of the viscosity of the oil and the initial oil film height. The effect of a lubrication oil film on the gear tooth flank before the oil jet impinges is included and its effect on the heat transfer is assessed. The analytical model agrees well with experimental results over the entire range of investigated operating conditions. Finally, a discussion on the effect of several assumptions in the derivation of the analytical model is presented. The validated analytical model can be used as an efficient tool for the design of gear trains with impingement cooled spur gears.

In this research paper, the cooling process of an impingement cooled spur gear is examined by means of an analytical model. The process is modeled as a coolant film, which is flung off a rotating gear tooth flank by centrifugal forces. During the process, heat is transferred from the isothermal gear tooth flank to the coolant film. With a numerical solution to the analytical model, a formulation for the transient local Nusselt number is derived. The evaluation of the numerical solution revealed that the heat transfer is dominated by heat conduction in the coolant film. The heat transfer process ends when the thermal capacity of the coolant film is reached. The transient Nusselt number is used to derive a time-averaged and a global heat transfer coefficient. Furthermore, the influence of the initial coolant film height is examined by using a modified version of the analytical model. The global heat transfer coefficient decreases toward smaller initial cooling film heights. The analytical model is then extended to include the temperature dependency of the viscosity of the coolant. A viscosity that decreases with increasing temperature yields a moderate decrease in heat transfer. A discussion is presented regarding the applicability of the analytical model toward impingement cooled spur gears. The effect of the simplifications made in the derivation of the analytical model is outlined and assessed with regard to the heat transfer mechanism.

Understanding the heat transfer characteristics of impingement cooling of high-speed high-power gears is essential to design a reliable gearbox for a new generation of jet engines. However, experimental data on the impingement cooling of gears is limited in the literature. The experimental setup at the Institute of Thermal Turbomachinery aims at closing this gap. It includes a rotating gear instrumented with thermocouples. The measured temperatures are used to determine a spatially resolved heat transfer coefficient distribution on the gear tooth. The iterative evaluation approach applied in the post-processing of the experimental data is validated with two reference cases. First, it is shown that the interpolation of temperature data between thermocouple locations leads to inaccurate results and would not be valid for the evaluation of the experiments, even if the number of thermocouples were increased. The iterative evaluation approach can reproduce the reference heat transfer coefficient distributions very accurately even with a low spatial resolution of temperature data. A new iterative method based on the Levenberg-Marquardt algorithm is implemented within this study. The new method generally converges faster than the existing method. The difference in required computational time is negligible in the easy to evaluate high heat transfer case, whereas a speed-up of up to three times is observed in the relatively cumbersome evaluation of the low heat transfer case.

Understanding the heat transfer characteristics of impingement cooling of high-speed high-power gears is essential to design a reliable gearbox for a new generation of jet engines. However, experimental data on the impingement cooling of gears is limited in the literature. The experimental setup at the Institute of Thermal Turbomachinery aims at closing this gap. It includes a rotating gear instrumented with thermocouples. The measured temperatures are used to determine a spatially resolved heat transfer coefficient distribution on the gear tooth. The iterative evaluation approach applied in the post-processing of the experimental data is validated with two reference cases. First, it is shown that the interpolation of temperature data between thermocouple locations leads to inaccurate results and would not be valid for the evaluation of the experiments, even if the number of thermocouples were increased. The iterative evaluation approach can reproduce the reference heat transfer coefficient distributions very accurately even with a low spatial resolution of temperature data. A new iterative method based on the Levenberg-Marquardt algorithm is implemented within this study. The new method generally converges faster than the existing method. The difference in required computational time is negligible in the easy to evaluate high heat transfer case, whereas a speed-up of up to three times is observed in the relatively cumbersome evaluation of the low heat transfer case.