Study of Inclined Dense Jet Behavior on Sloped Bottom in Stagnant Water through Numerical and Experimental Approaches

Abstract

Desalination plants have contributed significantly to relieving global freshwater scarcity. However, the highly concentrated byproduct brine from the desalination process is usually discharged back into the ocean, making the design of the outfall system a critical concern to prevent further pollution and damage to the oceanic ecosystem. Inclined dense jet is a common method for discharging highly concentrated brine. Numerous studies of inclined dense jet have been done, and the discharge performance is influenced by several factors. However, research on the receiving bottom remains limited, especially considering the long-term effects of continuous discharge. Investigating the behavior of inclined dense jet on sloped bottoms is therefore essential. This study focuses on the characteristics of single-port inclined jets on sloped bottoms and their impact on the jet development process. We investigate the behavior of inclined dense jet over sloped bottoms using experimental measurements and computational fluid dynamics (CFD) simulations. Laboratory experiments were conducted with laser-induced fluorescence (LIF) to analyze concentration distributions of inclined dense jet with three common discharge angles (30°,45°,60°) on four different sloped bottoms (0°,1°,3°,5°) discharged into a stationary environment. Large Eddy Simulation (LES) was employed to simulate jet dynamics and assess its reliability by comparing experimental results with one practical discharge angle (60°) on two different bottom conditions (0° and 5°). In addition, four different common Reynolds-Averaged Navier-Stokes (RANS) models were compared as a supplementary study to evaluate their performance for predicting the single-port inclined dense jet with three discharge angles (30°,45°,60°) on a horizontal bottom. Moreover, gene expression programming (GEP) was explored as an extended tool to develop predictive models based on part of experimental and numerical data to simply and easily access the geometrical and mixing properties of the inclined dense jet on different sloped bottoms. The experimental results show that geometrical characteristics prior to the impact point are not affected by the bottom slope. However, both the impact point nondimensional location and the dilution value on different bottom surfaces can be described by linear equations. Increased turbulence intensity, higher dilution along the bottom, an extended mixing zone, and a thicker bottom layer jointly suggested that a sloped bottom could enhance mixing efficiency. In addition, the Froude number (Fr) was found to significantly influence brine mixing along the sloped bottom, which suggested a potential direction for future studies. In the numerical simulation, a multilayer mesh is used for LES, and the results are in good agreement with LIF experimental data. The concentration distribution at the impact point area can be described by a Gaussian surface-fitting formula. The comparison with the RANS models also verifies that LES has better performance than the RANS model in simulating larger discharge angles and dilution characteristics. Although RANS models have been adopted in many studies of inclined dense jet or other engineering practices due to their low computational cost and reasonable results, the selection of different turbulence models will also affect the accuracy of the simulation results. As an extension of this research, a comparative study of different RANS models confirmed that they generally underestimate brine mixing. The results showed that when the jet angle exceeds 45°, RANS models tend to underpredict the jet trajectory and dilution, whereas their results remain reasonable when the discharge angle is below 45º. In addition to traditional experimental and CFD approaches—which can be time-consuming for analyzing key characteristics of inclined dense jets over sloped bottoms—Gene Expression Programming (GEP), an evolutionary algorithm-based modeling approach, offers a user-friendly and efficient alternative. GEP could generate regression equations and provide a mathematical relationship between input and output variables. Based on experimental and LES data, it enables direct estimation of key geometric and concentration characteristics of the inclined dense jet with different discharge angles, including information along different bottom angles after the impact point. These findings enhance the understanding of inclined dense jet behavior under different receiving bottom conditions and provide a practical approach for predicting important geometric and concentration characteristics. Future studies could explore a wider range of receiving bottom conditions and investigate the influence of Froude number on dilution results. Advanced experimental techniques such as PIV, 3D LIF, or other high-resolution methods are recommended to capture the velocity field and detailed turbulence characteristics along different bottom conditions. For numerical simulations, further investigations into alternative meshing strategies (such as dynamic mesh) or different CFD methods, such as SPH (Smoothed Particle Hydrodynamics), could help improve computational efficiency while reducing costs. The expansion of datasets from experiments, numerical simulations, and field studies of inclined dense jets under various conditions could enhance the training of GEP models as a potential predictive tool for estimating key jet parameters efficiently for rapid and early-stage design.