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In the urban water cycle, adsorption facilitated by engineered granular media increasingly is deployed for solute separation in potable water, stormwater, and wastewater systems. Of these systems, stormwater treatment is inordinately complex. Stormwater systems are passive, decentralized, and subject to highly unsteady and uncontrolled fluxes with multiphase interactions. This study proposes a multiphase and multiphysics computational fluid dynamics (CFD) model, interAdsFoam, to simulate turbulence mixing and adsorption with dynamic water–air interface and reaction zones. An original CFD model is proposed, benchmarked, and validated with data sets across a range of scales: (1) bench-scale columns for model parameter estimation, (2) physical modeling of a radial flow adsorption reactor (RFR) subject to controlled fluxes, and (3) field monitoring of a commercial volumetric radial flow adsorption reactor (VRFR) system subject to uncontrolled event-based fluxes. The results illustrate (1) the nonuniqueness of numerical solutions for parameter estimation in adsorption modeling; (2) that regulating the parameter estimation process with isotherms improves model generalizability; (3) inverse modeling of the RFR hydraulic resistance with the quadratic Thiem model can provide a more accurate representation than the Ergun model; and (4) that turbulence transport and chemical adsorption are dynamically coupled with the air–water momentum balance. The proposed CFD model predicts total dissolved phosphorus (TDP) transport and fate based on field monitoring of the VRFR. System dynamics and treatment functionality are elucidated, and implications for practical reactor design are discussed. The proposed open-source CFD model provides a novel framework for higher-fidelity urban water adsorption reactor simulation, design, and optimization than current methods for adsorption. [ABSTRACT FROM AUTHOR]

Eulerian–Lagrangian methods are common for computational fluid dynamics (CFD) modeling of particle fate. Near-wall turbulence flow profiles are frequently modeled with wall function (WF) for computational efficiency and stability. However, WF does not provide the viscous and buffer sublayers solution for Lagrangian particle tracking (LPT). This study examines Reynolds-averaged Navier-Stokes (RANS)-LPT model combinations with near-wall models (two-layer, low-Reynolds number, WF), common LPT boundary conditions (trap, reflect), near-wall grids resolution (Δy+), and LPT solver configurations. Near-wall LPT in an open channel clarifier illuminates embedded numerical errors/artifacts generated by widely-used RANS-WF-LPT model combinations as benchmarked to direct numerical simulations (DNS). Near-wall LPT can be subject to grid resolution irrespective of particle-boundary interactions and LPT boundary conditions applied. Clarifier simulations illustrate LPT solver configurations influence particulate matter (PM) separation. RANS-LPT solutions are a function of particle diameter, maximum particle integration steps, and to a lesser degree on tracked particle number. Low-Reynolds number and two-layer models improve per particle size separation predictions compared to the WF model by up to 50% for 25–100 μm particles based on physical model benchmarking. [ABSTRACT FROM AUTHOR]

Stormwater basins, which are subject to highly unsteady flows and loads, function as clarifiers for particulate matter (PM) and PM-bound constituents. Quasi-steady flow hydrodynamics in water and wastewater treatment plant units, from grit to contact chambers, are known to impact treatment. In contrast, there is sparse basin design guidance for unsteady hydrodynamics and clarification interactions. Basins can become impaired with needed retrofits. Lumped models, such as surface overflow rate (SOR), are less suitable for complex geometries, hydrodynamics, and loadings. A computational fluid dynamics (CFD) and evolutionary optimization framework as higher-fidelity tools is proposed for relatively shallow basins with permeable baffle retrofits. This study extends previous research and optimizes baffle configuration by further considering routing effects and unsteady loading on clarification. For an influent heterodisperse particle size distribution (PSD), baffles improve PM clarification by 58.8% based on baffle number. Strategically altering the baffle position, length, and angle yields an optimal configuration with improved clarification of 32% in comparison to conventional baffle configurations. Baffle optimization leads to construction costs that are one-third to one-fifth those of conventional baffle configurations. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) can be a powerful tool for higher-fidelity water infrastructure planning and design. Despite decades of development and demonstration over a wide range of water systems such as clarification basins, activated sludge processes, ozone contactors, etc., CFD remains primarily used in academic research, with limited application in civil and environmental engineering practice. This limitation is contributed by its higher computational cost and demand for specialized user skills. This, however, need not be the case, if a robust and efficient surrogate model can be developed from CFD simulations and independently deployed for engineering purposes. Leveraging the emerging scientific machine learning (ML) techniques of physics-informed ML and operator learning, this study develops a composite neural network (CPNN) for learning the flow hydrodynamics and particulate matter (PM) transport and fate in clarification systems. The CPNN consists of a deep operator network (DeepONet) as an encoder and a physics-informed neural network (PINN) as a decoder. In contrast to common "black box" and lumped ML approaches, the developed CPNN directly incorporates physics principles into its architecture. Furthermore, the CPNN is designed for process-resolved and operator learning, enabling it to predict spatial hydrodynamics and PM concentration distribution (i.e., contours) across different basin geometrics and loading conditions. Compared to CFD simulation, the developed CPNN model has significantly higher computational efficiency (∼ milliseconds) while demonstrating robust predictive capability. For predicting basin hydrodynamics across 10,000 test cases, the trained CPNN model achieves an R 2 above 0.8 for 66.4% of cases and an R 2 above 0.4 for 89.2% of cases. A similar performance is also demonstrated by the CPNN in predicting basin PM concentration. Further investigation reveals that basin geometrics that trigger bi-modal flow solutions can be particularly challenging for ML. Additionally, this study visualizes the dependency of basin hydrodynamics and PM concentration on basin geometrics and loading conditions, providing valuable insights for optimizing basin configuration. Lastly, the potentials and benefits of web-based applications, e.g., DeepXtorm , as a user-friendly interface for the developed CPNN model is discussed. This study represents the initial step toward achieving real-time higher-fidelity water infrastructure planning, design, optimization, and regulation. [Display omitted] • Formulate basin flow and particulate matter fate prediction as an operator learning. • Composite neural network (CPNN) model was developed by hybridizing DeepONet and PINN. • CPNN predicts basin PM transport and fate for a range of geometrics and loadings. • Basin flow bifurcation can "confuse" machine learning models. • Potential of real-time higher-fidelity water infrastructure design is discussed. [ABSTRACT FROM AUTHOR]

Prediction of turbulent flow is required for design and assessment of clarifier systems that have been implemented throughout history to treat water in the urban water cycle through physical clarification. Yet, turbulent flow modeling is a relatively new tool that has not existed until the last half-century and can be, and often is, a tenuous component in a computational fluid dynamics simulation of unit operations and processes. Common Reynolds-averaged Navier–Stokes equation (RANS) approaches can be inadequate to obtain consistent and accurate flow solutions. In contrast, this study presents an application of large-eddy simulations (LES) for a clarification system with a high-order spectral element method employing 48 million degrees of freedom. Turbulent and unsteady flow characteristics are investigated, and statistics are examined for such a system. Simulation results are compared with laser Doppler anemometry measurements for mean flow velocity, turbulence kinetic energy, and Reynolds shear stress. LES results agree well with measurements, and the differences between LES and measurements are generally less than the reported measurement error. LES results capture the transition behavior from a jet-like flow at the near-inlet region to an open-channel flow at the downstream end of the system. Furthermore, LES results reveal that the widely adopted log-law of a classical turbulent boundary layer is not established in the system even at the most downstream location. Preliminary examination of commonly used RANS models identifies the challenges in application of RANS to such systems. The results from this study provide a benchmark for turbulence modeling of common water clarification systems. [ABSTRACT FROM AUTHOR]

• Generalization of clarifier design as a non-linear constrained optimization problem. • Machine learning (ML)-based water clarifier cost-benefit optimization was developed. • Integrate OpenFOAM, PyTorch, and Dakota for water clarifier design and retrofit. • Clarifier cost is reduced by 5.6X to 83.5X, varying with particle size distributions. • ML-based design optimization is computationally efficient and can be used on a laptop. [Display omitted] Clarification basins are ubiquitous water treatment units applied across urban water systems. Diverse applications include stormwater systems, stabilization lagoons, equalization, storage and green infrastructure. Residence time (RT), surface overflow rate (SOR) and the Storm Water Management Model (SWMM) are readily implemented but are not formulated to optimize basin geometrics because transport dynamics remain unresolved. As a result, basin design yields high costs from hundreds of thousands to tens of million USD. Basin optimization and retrofits can benefit from more robust and efficient tools. More advanced methods such as computational fluid dynamics (CFD), while demonstrating benefits for resolving transport, can be complex and computationally expensive for routine applications. To provide stakeholders with an efficient and robust tool, this study develops a novel optimization framework for basin geometrics with machine learning (ML). This framework (1) leverages high-performance computing (HPC) and the predictive capability of CFD to provide artificial neural network (ANN) development and (2) integrates a trained ANN model with a hybrid evolutionary-gradient-based optimization algorithm through the ANN automatic differentiation (AD) functionality. ANN model results for particulate matter (PM) clarification demonstrate high predictive capability with a coefficient of determination (R 2) of 0.998 on the test dataset. The ANN model for total PM clarification of three (3) heterodisperse particle size distributions (PSDs) also illustrates good performance (R 2 > 0.986). The proposed framework was implemented for a basin and watershed loading conditions in Florida (USA), the ML basin designs yield substantially improved cost-effectiveness compared to common designs (square and circular basins) and RT-based design for all PSDs tested. To meet a presumptive regulatory criteria of 80% PM separation (widely adopted in the USA), the ML framework yields 4.7X to 8X lower cost than the common basin designs tested. Compared to the RT-based design, the ML design yields 5.6X to 83.5X cost reduction as a function of the finer, medium, and coarser PSDs. Furthermore, the proposed framework benefits from ANN's high computational efficiency. Optimization of basin geometrics is performed in minutes on a laptop using the framework. The framework is a promising adjuvant tool for cost-effective and sustainable basin implementation across urban water systems. [ABSTRACT FROM AUTHOR]

[Display omitted] Particulate matter (PM), while not an emerging contaminant, remains the primary labile substrate for partitioning and transport of emerging and known chemicals and pathogens. As a common unit operation and also green infrastructure, clarification basins are widely implemented to sequester PM as well as PM-partitioned chemicals and pathogens. Despite ubiquitous application for urban drainage, stormwater clarification basin design and optimization lacks robust and efficient design guidance and tools. Current basin design and regulation primarily adopt residence time (RT) as presumptive guidance. This study examines the accuracy and generalizability of RT and nondimensional groups of basin geometric and dynamic similarity (Hazen, Reynolds, Schmidt numbers) to scale clarification basin performance (measured as PM separation and total PM separation). Published data and 160,000 computational fluid dynamics (CFD) simulations of basin PM separation over a wide range of basin configurations, loading conditions, and PM granulometry (particle size distribution [PSD], density) are examined. Based on the CFD database, a novel implementation of machine learning (ML) models: decision tree (DT), random forest (RF), artificial neural networks (ANN), and symbolic regression (SR) are developed and trained as surrogate models for basin PM separation predictions. Study results indicate that: (1) Models based solely on RT are not accurate or generalizable for basin PM separation, with significant differences between CFD and RT models primarily for RT < 200 hr, (2) RT models are agnostic to basin configurations and PM granulometrics and therefore do not reproduce total PM separation, (3) Trained ML models provide high predictive capability, with (R 2) above 0.99 and prediction for total PM separation within ± 15 %. In particular, the SR model distilled from CFD simulations is entirely defined by only two compact algebraic equations (allowing use in a spreadsheet tool). The SR model has a physical basis and indicates PM separation is primarily a function of the Hazen number and basin horizontal and vertical aspect ratios, (4) With common presumptive guidance of 80% for PM separation, a Pareto frontier analysis indicates that the CFD-ML augmented SR model generates significant economic benefit for basin planning/design, and (5) CFD-ML models show that enlarging basin dimensions (increasing RT) to address impaired behavior can result in exponential cost increases, irrespective of land/infrastructure adjacency conflicts. CFD-ML applications can extend to intra-basin retrofits (permeable baffles) to upgrade impaired basins. [ABSTRACT FROM AUTHOR]

[Display omitted] • A large clarifier basin retrofit is monitored and modeled for unsteady tracer fate. • The retrofit consisted of permeable baffles to modify basin hydrodynamics. • Results indicate basin volume and mean flow metric not representative guidance. • Retrofit improved short-circuiting and volume utilization of same bathymetry. • Proposed CFD model extended for basin forensics and to retrofit alternatives. Clarification basins have been implemented for millennia as a unit operation (UO). Modern basins are intended to manage hydrologic/hydraulic phenomena while sequestering particulate matter (PM) and PM-bound constituent loads. Water treatment systems, subject to steady flows, have used baffles to modulate dead zones, residence time and hydrodynamics. Yet, permeable baffling impacts to larger-scale basin hydrodynamics subject to highly unsteady continuous time domain flows is a novel investigation. In this study, in situ monitoring and numerical simulations are conducted for a full-scale prototype urban drainage basin, while geometrically oversized with respect to the relatively coarse particle size distribution and hydraulic loading, retrofitted with gabion baffles composed of crushed carbonated recycled concrete. A 40-day tracer monitoring of hydrodynamics within the retrofit basin is tested against a novel application of a depth-averaged unsteady Reynolds-averaged Navier-Stokes equations (URANS) as a computational fluid dynamics (CFD) model in the OpenFOAM framework. A dual-peak elution pattern is observed in response to tracer injections in the physical and simulated (fully transient and quasi-steady) results. Short-circuiting around the baffles in the as-built retrofit is elucidated with monitoring and modeling. Simulations of retrofit configurations (pre-retrofit, as-designed, as-built and impervious baffles) indicate, in comparison to the pre-retrofit, a well-baffled system reduces short-circuiting, delays elution, and improves PM separation. Permeable baffles provide hydrodynamic benefits as compared to impervious baffles. The novel application of this depth-averaged URANS CFD model accommodates complex geometry and physics; and elucidates contrasting Reynolds number distributions of inter- and intra-baffle flows. The CFD model with continuous time domain flows is a viable tool for design, analysis, permitting and management of basins with or without baffle retrofits. The model extends insights beyond analytical tools and complements tools such as the SWMM (Stormwater Management Model). [ABSTRACT FROM AUTHOR]

Neural network-based approaches have emerged as alternatives to conventional computational fluid dynamics (CFD) in solving multiphase flow problems. However, most of these approaches are based on data-driven machine learning methods that require training datasets prepared beforehand through CFD simulations or experiments and cannot be used independently. This study presents an unsupervised parameterized physics-informed neural networks (P-PINNs) approach for obtaining the full flow field information over a multi-dimensional parametric space. This approach is then applied to solve the three-dimensional flow around an arbitrarily rotating sphere subjected to a cross-flow. This solution is obtained for a continuous range of three parameters: the Reynolds number based on cross-flow (Re ∈ [ 1 , 400 ]), non-dimensional streamwise and spanwise angular velocity components ( Ω x ∗ , Ω y ∗ ∈ [ − 3 , 3 ]). The predictions from the P-PINNs model are compared against particle-resolved direct numerical simulation (PR-DNS) results, demonstrating that the neural network model predicts all flow variables (velocity, pressure, and their spatial derivatives) accurately with R 2 ≳ 0. 9. The force and torque on the particle obtained from the P-PINNs model are also compared well against the corresponding PR-DNS results with R 2 > 0. 94. The key observation is that the computational cost of the unsupervised parameterized neural network model training and deployment is substantially lower than performing numerous conventional CFD simulations to systematically vary the parameters. Furthermore, once trained, the resultant neural network model is substantially more compact than the huge database of discretized numerical solutions. The P-PINNs model is then used to reveal several interesting flow features and phenomena about the rotating sphere, including flow symmetry, secondary drag and lift, critical Reynolds number, flow bifurcation, and flow separation. This study presents P-PINNs as an efficient alternative for solving parameterized flow problems, demonstrating its practical usage in flow physics discovery with the example of flow past an arbitrarily rotating sphere. [Display omitted] • Proposed an unsupervised parameterized PINNs method that requires no training data. • Developed neural network to infer flow fields, drag, and lift of spinning spheres. • Validated flow fields, force, and torque against simulation and experiment results. • Discovered new phenomena, such as secondary lift force, in 3D spinning conditions. [ABSTRACT FROM AUTHOR]