Ze Cao

This paper aims to assess the nonlinear vibration of a radial gate induced by flood discharge; the measured acceleration response data of a spillway radial gate are analyzed using the chaos theory. The results show that the vibration responses of the gate at three opening heights present clear chaotic characteristics, and the chaotic characteristics of the lower main beam point are greater than other points. Moreover, the y-direction (vertical) correlation dimensions of the three measuring points on the supporting arm are larger than those of the x-direction (axial) and z-direction (lateral). The vertical vibration of the supporting arm is more complex and presents more uncertainties, which should be paid attention to in the literature. Under three different gate opening heights, the maximum Lyapunov exponent of each measuring point ranges from 0.0246 to 0.0681. In addition, the flow fluctuation load is the main excitation source of the gate vibration chaotic characteristics.

The cavity length, which is a vital index in aeration and corrosion reduction engineering, is affected by many factors and is challenging to calculate. In this study, 10-fold cross-validation was performed to select the optimal input configuration. Additionally, the hyperparameters of three ensemble learning models—random forest (RF), gradient boosting decision tree (GBDT), and extreme gradient boosting tree (XGBOOST)—were fine-tuned by the Bayesian optimization (BO) algorithm to improve the prediction accuracy and compare the five empirical methods. The XGBOOST method was observed to present the highest prediction accuracy. Further interpretability analysis carried out using the Sobol method demonstrated its ability to reasonably capture the varying relative significance of different input features under different flow conditions. The Sobol sensitivity analysis also observed two patterns of extracting information from the input features in ML models: (1) the main effect of individual features in ensemble learning and (2) the interactive effect between each feature in SVR. From the results, the models obtaining individual information both predict the cavity length more accurately than that using interactive information. Subsequently, the XGBOOST captures more correct information from features, which leads to the varied Sobol index in accordance with outside phenomena; meanwhile, the predicted results fit the experimental points best.

Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ, this effect is felt only at low Re, but as φ increases, the effect spreads to higher Re. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, “Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles,” Chem. Eng. Sci., 129, pp. 42–48) provides good estimates of the respective suspension mean Nusselt numbers.