Simulation and machine learning-based modeling of oil flow behavior in hydrostatic bearings of vertical Francis turbines

In this thesis, the effects of fundamental geometric parameters determining the fluid flow and tribological performance of hydrostatic bearings used in vertical Francis turbines were investigated in detail through comprehensive Computational Fluid Dynamics (CFD) analyses and an Artificial Neural Network (ANN) based prediction optimization approach. Critical design variables, including oil pocket depth, oil pocket height, oil film thickness, angular wrap angle of the oil pocket, and shaft diameter, were systematically varied within literature-accepted limits to establish an extensive variation set. As a result of the CFD analyses performed for various geometric combinations, load-carrying capacity, power loss coefficient, support force orientation angle, and pressure and velocity distribution indices for the oil pocket and film regions were obtained. These analyses elucidated the effects of geometric parameters on hydrodynamic behavior within a multi-dimensional design space and established a comprehensive database regarding the physical trends of hydrostatic bearing performance. Using this dataset, a multi-output ANN structure was developed to model the relationships between performance outputs and geometric parameters. The model was evaluated using k-fold cross-validation and exhibited high accuracy across critical performance indicators. During the training process, the generalization capability of the model was enhanced by using normalized inputs, rescaled distribution index parameters, and averaged predictions from seven independent networks specifically structured for each output. Model performance was validated using Pearson correlation coefficient (R), coefficient of determination (R2), root mean square error (RMSE) and mean absolute percentage error (MAPE) metrics, achieving high consistency for all target outputs. Optimization functions were developed to enable the ANN model to be utilized not only for prediction but also within the optimization process. These functions rapidly scan different geometric combinations while considering physical constraints and standard tolerance intervals, determining the optimum bearing. Consequently, the reliance on high-cost CFD-based optimization loops is reduced, significantly improving the design process in terms of both speed and accuracy. To rationalize the model outputs, an original sensitivity analysis was conducted, defining the Improvement Success Coefficient (Cpi) to measure performance gain and the Solution Sensitivity Coefficient (Spi) to test stability against manufacturing tolerances. These analyses facilitated the isolation of critical variables contributing most to performance and allowed for the determination of the impact of potential manufacturing errors. Thus, it was demonstrated that the optimum solutions obtained meet the reliability and sustainability criteria required for industrial applications. This study presents a hybrid engineering approach that integrates numerical analyses with data-driven prediction methods in hydrostatic bearing design, providing a robust foundation for future design, improvement, and automated optimization studies.