A Mechanism-Informed Gaussian Process Surrogate Model for Solid-Particle Erosion Prediction in Gas–Solid Bent Pipe Flows

In cold hydrogenation processes, bent pipes are highly susceptible to severe localized erosion under hydrogen–silica powder gas–solid two-phase flow. However, high-fidelity numerical simulations are computationally expensive and thus inadequate for rapid assessment under multiple operating conditions. To overcome this limitation, an MI-UK-GPR-based method is proposed for predicting the erosion rate of cold hydrogenation bent pipes. Based on a validated CFD model, six input variables, namely pipe inner diameter, curvature ratio, bend angle, particle mass flow rate, particle size, and particle velocity, were selected. Latin hypercube sampling was employed to generate parameter combinations, and the corresponding maximum erosion rates were obtained through high-fidelity CFD simulations to construct an LHS-CFD sample database. The input variables were then normalized, and the maximum erosion rates were log-transformed. On this basis, an MI-UK-GPR model integrating a mechanistic trend term with a Gaussian process residual term was developed to capture both the global trend of erosion peaks and local nonlinear deviations. Model performance was assessed using leave-one-out cross-validation with MAE, RMSE, MAPE, R2, and PICP as evaluation metrics. The results show that, under leave-one-out cross-validation, the proposed MI-UK-GPR model achieved an MAE of 7.10 × 10−5, an RMSE of 1.29 × 10−4, a MAPE of 14.53%, an R2 of 0.9573, and a PICP of 88.33%, outperforming RSM, SVR, and ordinary GPR in terms of overall prediction performance. In addition, for 50 independent operating conditions, the total computational time of parameterized CFD batch simulations was 5083.51 s, whereas the trained MI-UK-GPR model required only 0.004860 s, corresponding to a speedup of approximately 1.05 × 106. Overall, the proposed method provides a physically consistent, uncertainty-aware, and computationally efficient framework for rapid erosion assessment of cold hydrogenation elbows under multiple operating conditions.