A Comprehensive Study of Buoyant Rosette Jets Using Laboratory Experiments, CFD, and Machine Learning

Abstract

Rosette diffusers are increasingly used in modern outfall designs due to their unique structure and efficient initial dilution performance. However, the complex mixing behavior of the resulting buoyant jets poses a challenge for accurate modeling, requiring more advanced mixing methods. This study integrates laboratory laser-induced fluorescence (LIF) experiments, computational fluid dynamics (CFD) simulations, and machine learning (ML) modeling to conduct a comprehensive analysis of buoyant rosette multiport jets. The main goal is to improve the accuracy, efficiency, and interpretability of trajectory and normalized concentration field predictions in wastewater discharge systems. Experiments were conducted using LIF techniques to obtain high-resolution scalar concentration fields, and visual jet trajectory data under different operating conditions were obtained. These experimental results can be used as a benchmark dataset for validating CFD simulations and training ML models. CFD simulations were performed using a modified version of the OpenFOAM benchmark solver pimpleFoam, which incorporates temperature-driven buoyancy effects while ignoring salinity transport to reduce computational costs. The prediction performance of three RANS turbulence models - standard k-ε, RNG k-ε, and SST k-ω - was evaluated for two different Fr number cases (high Fr number 5.81 and low Fr number 2.23). The RNG k-ε model performs well in predicting centerline trajectories and concentration fields under momentum-dominated conditions, thanks to its enhanced formulation, including an improved turbulent transport model and an additional ε equation term. Importantly, the model achieves higher accuracy than the standard k-ε model without significantly increasing computational time. To address the limitations of CFD and experimental coverage near the nozzle region, three machine learning models—extreme learning machine (ELM), adaptive neuro-fuzzy inference system (ANFIS), and multivariate adaptive regression splines (MARS)—are trained on 870 data points from 34 different Fr number cases obtained experimentally. Input features included Fr number, x/D, and y/D, while the target variable was normalized concentration. ANFIS outperforms the other models on the test dataset with an R² of 0.9088 and an RMSE of 0.0551. ELM exhibits high accuracy and fast training speed, while MARS provides an interpretable piecewise linear representation but has limited generalization capabilities. The results show that combining LIF experiments with ML algorithms can effectively reduce the reliance on resource-intensive CFD while maintaining prediction accuracy. This comprehensive hybrid experiment-CFD and experiment-ML integrated framework provides a reliable solution for rosette jet dynamics modeling, diffuser design optimization, and environmental impact assessment under different hydraulic conditions. Future work suggestions include improving the experimental density control, integrating optimization algorithms with ML models, and extending the application to real-time scenarios.