Free Surface Flow Research Articles

Performances of constructed wetland system to treat whey and dairy wastewater during a macrophytes life cycle

Constructed wetlands system (CWs) have been proposed as an economical, efficient and sustainable wastewater treatment technology. The aim of this paper was to provide the first published data on the efficiency of CWs for dairy wastewater treatment in Tunisia. In most CWs, good organic, total suspended solids (TSS) and nutrient removal was measured. In order to evaluate the efficiency of this process, hybrid small-scale wetland system was designed containing three horizontal subsurface flow (HSSF) and one free water surface flow (FWS). A mixture of Reeds (Phragmites australis), Cattails (Typha latifolia), and Papyrus (Cyperus papyrus) was planted. Several water quality parameters in both raw and treated wastewaters were monitored during the macrophytes life cycle. The average influent properties for 20 % of whey are: TSS (3040 mg/L), COD (5060 mg O2/L), BOD5 (3020 mg O2/L), TKN (79 mg N/L) and TP (32,2 mg P/L). Removal efficiencies of 99.6 % for TSS, 80 % for COD, 97 % for BOD5, 90.4 % for TKN and 99.6 % for TP were observed. The results reveal temporal variations in system performance according to macrophyte growth rates. Reeds, Cattails and Papyrus start their life cycle at the beginning of the winter and continue growing in summer. The effluent pH, TSS, COD,BOD5, TKN and TP concentrations were in compliance with both irrigation reuse and discharge regulations.

Wave run-up characteristic on armour layer breakwater using the smoothed particle hydrodynamics (SPH) method

Coastal structures, such as breakwater, play a critical role in protecting shorelines from the erosive forces of waves and currents. Understanding the wave run-up phenomenon on these structures is essential for designing effective coastal defense systems. This research aims to investigate the wave run-up characteristics on an armour layer breakwater using the Smoothed Particle Hydrodynamics (SPH) method (Meshless particle method based on the Lagrangian formulation), a numerical method that captures complex fluid-structure interactions. The SPH method’s inherent ability to handle free-surface flows and dynamic interactions makes it particularly suited for simulating wave run-up. The research employs numerical testing and modelling of a non-overtopping breakwater using the smoothed particle hydrodynamics method simulated with the DualSPHysics program. The wave characteristic data used in this research are the waves on the south coast of Java. The results of this research indicate that the correlation between wave run-up characteristics (Ru/H) and the Iribarren number, both using the numerical SPH method and theory, tends to exhibit a similar pattern. Remarkably, the results from both approaches exhibit a striking similarity, revealing that as the Iribarren number increases, the incremental growth of Ru/H diminishes, eventually stabilizing at a critical threshold. The Coefficient of Determination (R2) between wave run-up characteristics (Ru/H) obtained from numerical simulations using the SPH method and Günbak’s theory is 0.8824.

Depth from defocus technique: a simple calibration-free approach for dispersion size measurement

Particle size measurement is crucial in various applications, be it sizing droplets in inkjet printing or respiratory events, tracking particulate ejection in hypersonic impacts or detecting floating target markers in free-surface flows. Such systems are characterised by extracting quantitative information like size, position, velocity and number density of the dispersed particles, which is typically non-trivial. The existing methods like phase Doppler or digital holography offer precise estimates at the expense of complicated systems, demanding significant expertise. We present a novel volumetric measurement approach for estimating the size and position of dispersed spherical particles that utilises a unique ‘Depth from Defocus’ (DFD) technique with a single camera. The calibration-free sizing enables in situ examination of hard to measure systems, including naturally occurring phenomena like pathogenic aerosols, pollen dispersion or raindrops. The efficacy of the technique is demonstrated for diverse sparse dispersions, including dots, glass beads and spray droplets. The simple optical configuration and semi-autonomous calibration procedure make the method readily deployable and accessible, with a scope of applicability across vast research horizons.

Numerical simulation and experimental study of fluid–structure interactions in elastic structures based on the SPH method

The study of fluid–structure interactions in elastic structures is highly important in hydraulic structural engineering. This paper adopts the smooth particle hydrodynamics (SPH) coupling method to simulate dam failure water impact elastic plate flow and solid coupling problems. In addition, a numerical simulation is performed on the study of the free surface flow impact of the elastic plate structure on the main dynamic characteristics, including the impact force distribution and the change process. Additionally, the elastic structure of the vibration amplitude and frequency change rule, as well as the drastic changes in free surface flow, are also carried out. In this paper, the synchronous finite element algorithm is used to analyze the problem to obtain FEM results Additionally, two-dimensional benchmark physical tests are designed for dam-break water flow impacting an elastic plate are conducted, focusing on a comparative analysis of the numerical results of the SPH method with the results of physical tests and verifying the validity, accuracy, and superiority of the SPH coupling method for solving the problem of fluid‒solid coupling in elastic structures. On this basis, to explore the relevant physical quantities that cannot be measured or described during the test process, the flow–solid coupling characteristics of the elastic plate impacted by water flow are further understood by analyzing the nature of the flow field, the change in the flow–solid force of the elastic plate and the change rule of the frequency spectrum. The results show the following: (i) The jumps in velocity between the streams and the strong curvature of the free liquid surface lead to the creation of vortices at the cavities. (ii) The flow solid force under the impact of water flow increases and then decreases, and the smaller the deformation of the elastic structure is, the greater the force is. (iii) The vibration frequency of the fixed end of the elastic structure gradually decreases along the free end frequency, and the larger the deformation of the free end of the elastic plate is, the weaker its vibration response is. In addition, the natural frequency of the elastic plate under water flow impact is slightly lower than that under free vibration of the elastic plate. The related research results provide reference and guidance for the fluid–structure interaction problem.

Slot coating of viscoplastic materials: A computational study of the effects of viscoplasticity on the flow dynamics and low-flow limit

Yield-stress materials such as structurally complex formulations of paints, slurries, and waxes have been long ubiquitous in the coating industry, though the practice of coating engineering remains largely empirical as the fundamental role of viscoplasticity due to the yield stress of the coating material in most coating applications is still unclear. Here, we couple a recent harmonic mean viscosity regularization for the Bingham model with a well-established finite element/elliptic mesh generation method for free surface flows to present a detailed computational study of slot coating applications of viscoplastic materials. By neglecting inertia and focusing on the downstream section of a slot coater, we introduce suitable dimensionless parameters to discuss a comprehensive set of results that unravels a striking impact of viscoplasticity on the flow dynamics and low-flow limit. We show that viscoplastic effects have major implications to the velocity field and recirculation pattern in the coating bead as well as to the development length and free surface in the film formation region. Most importantly, we find that viscoplastic effects markedly widen the operating window of the process, delaying the onset of the low-flow limit and thereby suggesting that structurally complex yield-stress materials may be used to coat thinner films and/or at higher speeds than predicted by the standards far established for simple Newtonian liquids.

Simulation of viscoelastic free-surface flows with the Particle Finite Element Method

Viscoelastic fluids are central in numerous applications from polymer manufacturing to the pharmaceutical industry and biological research. However, since analytical solutions are generally not available or too complex, it is common practice to study free-surface viscoelastic flows through numerical simulation techniques. This work proposes the use of the so-called particle finite element method (PFEM), a Lagrangian approach combining standard FEM techniques with a remeshing strategy. The PFEM is able to efficiently handle mesh distortion and to accurately track the free-surface evolution. Therefore, it is exploited in this work to deal with large displacements problems in the context of nonlinear viscoelasticity. An implementation of the Oldroyd-B constitutive model in the PFEM framework is here presented including details regarding how to deal with the transfer of the internal variables during remeshing events. Additionally, an innovative approach to impose unilateral Dirichlet boundary conditions ensuring optimal mass conservation is presented. The implementation is verified with two free-surface highly viscous benchmark flows: the impacting drop and the jet buckling problems. The results show perfect agreement with those obtained with other numerical techniques. The proposed framework opens the way for using PFEM in various applications, ranging from polymer extrusion to more sophisticated scenarios involving viscoelastic and viscoelasto-plastic constitutive laws.

Numerical simulation of wedges slamming non-Newtonian fluids based on SPH method

Current research on non-Newtonian fluids using Smoothed Particle Hydrodynamics (SPH) has primarily focused on dynamic behavior, with limited exploration into interactions between rigid bodies and non-Newtonian fluids. Leveraging the SPH method's effectiveness in addressing free surface flow challenges, a two-dimensional numerical model of a rigid body impacting non-Newtonian fluids based on the Herschel-Bulkley-Papanastasiou (HBP) constitutive model is developed within the SPH framework. The study integrates experimental and numerical findings from non-Newtonian dam break scenarios, comparing particle distribution and the evolution of the waterfront over time to ensure accurate representation of non-Newtonian fluid behavior. While ensuring the convergence of SPH results, the research simulates the impact of a wedge on the surface of non-Newtonian fluids. This comparison of the slamming load exerted by non-Newtonian fluids on the wedge serves to validate the accuracy of the numerical method. Furthermore, the study explores the effects of varying initial velocities and roll angles of wedges slamming into specific non-Newtonian fluids. It analyzes fluid jet phenomena and changes in slamming loads.

An immersed boundary method coupled non-hydrostatic model for free surface flow

An efficient numerical model has been developed for the study of three-dimensional free surface flow, which combines a non-hydrostatic model with the immersed boundary method (IBM). The model utilizes the transformed σ coordinate in the vertical direction, which has been found to be highly effective in accurately capturing the free surface and uneven bottom. In addition, IBM is implemented by introducing a virtual boundary force into the momentum equations to emulate the natural boundary conditions. This implementation enhances the ability of the model in simulating the interactions of wave and solid structures. A robust boundary recognition method is used to identify the location of IB cells neighboring the virtual boundary. Furthermore, a water elevation correction method has been proposed to handle the integral discontinuity in the vertical direction caused by the submerged solid bodies. By adding the virtual boundary forces to the IB cells, the no-slip velocity condition at the solid boundary is effectively enforced. To validate the performance of the model, the numerical results have been compared with experimental data. The benchmark tests focused on the free surface evolution, velocity distributions and the dynamic pressures verified the performance of the numerical model and the robust strategy of the IBM.

A holistic model for microplastic dispersion in a free-surface wetland flow

The holistic model for microplastic dispersion is essential to conserving natural wetlands and enhancing the sewage treatment efficiency of constructed wetlands. A holistic mode is presented to analyze the microplastic transport caused by a continuous point-source discharge of substances into a wetland with an exposed water surface. The microplastic cloud's total quantity and centroid movement over each streamline are rigorously derived using the method of separation of variables and integral transform, and its longitudinal dispersion, skewness, and kurtosis are numerically analyzed using the finite difference method. Three dimensionless groups for the microplastic movement in wetland are presented. The relative importance of autonomous movement to the vertical diffusion coefficient can noticeably influence the mass center velocity and the longitudinal spread of the microplastic cloud, and its augments can enhance the amplitude of skewness and kurtosis in the initial transport stage. For the transient stage of transport during which microplastic cloud develops, the pulsating term of emission intensity shows little effect on skewness and kurtosis. The oscillation of skewness and kurtosis show less obvious for the long term evolution of microplastic cloud when the time scale across the water depth by diffusion is much larger than the oscillatory period.

Investigation of applicability of long-distance LP system for Li target diagnostics in Fusion Neutron Source

The beam target for generating a fusion neutron field in the Advanced-Fusion Neutron Source (A-FNS) is currently designed as a one-side free-surface liquid lithium (Li) jet flowing along a vertical concave wall. Characteristics of its thickness fluctuation were diagnosed in the EVEDA (Engineering Validation and Engineering Design Activity) Lithium Test Loop (ELTL), which has almost the same scale as the actual target excepting its channel width. In the diagnostics, the Laser Probe (LP) system was used. However, in an actual fusion neutron source, the diagnostics need to be operated from over 10 m away with no condenser lens at a downstream point from the final mirror for directing the incident laser to the Li surface from the perspective of Li vapor and radio activation. Whereat, the long-distance LP system for the actual Li target was conceptually designed for the IFMIF, and its precision error was also verified using a specular-reflection object and a water loop. In this previous study, the precision of measurement was evaluated as sufficiently high compared with the required limitation of surface variation (±1 mm). Then, in this study, we aim to verify the possibility of long-distance measurement of thickness variation for the free-surface Li flow. In the measurement, the incident laser head was set at a distance of about 10 m from the Li surface. And, while the previous measurement setup employed the focusing lens system with a focal length of 300 mm, some focusing lenses with longer focal length were used in this study. As a consequence, the Li surface variation was successfully detected and measured though the signal intensity of the reflected laser became low. Furthermore, it was confirmed that the impact of focal lengths on the detected signal was small.

Numerical analysis of 3D hydrodynamics and performance of an array of oscillating water column wave energy converters integrated into a vertical breakwater

Performance and hydrodynamics of an array of Oscillating Water Column (OWC) Wave Energy Converter (WEC) integrated into a vertical breakwater is studied. The FLUENT® software, in which the numerical model is based on the Reynolds-Averaged Navier-Stokes equations and the Volume of Fluid method for free surface flow modeling, is used in a 3D numerical wave tank. Three vertical breakwater configurations subject to the action of incident regular waves with periods from 6 to 12 s are studied: normal breakwater, with vertical walls parallel to the direction along the breakwater length; and two novel breakwater geometries, partially and fully convergent breakwaters, whose converging vertical walls are inclined θ in relation to this direction. Different spacing S from 0 to 20 m between the array of OWC devices and two converging wall angles θ, 30 and 45°, are investigated. Firstly, analysis of the influence of S for the normal breakwater shows that the vertical wall concentrates naturally a higher quantity of the incident wave energy inside OWC chamber devices and, consequently, increases their efficiencies. This effect is intensified as the spacing S increases. Secondly, analyses of the partially and fully convergent breakwaters allow concluding that these novel geometries, which direct an amount of incident wave energy into the OWC chamber, increase significantly the efficiency of the array of the OWC devices at the range of the wave periods. The highest performance of OWC device is obtained by the fully convergent breakwater with S = 20 m and θ = 45°, once 10 OWC devices inserted in a breakwater 300 m long have the same efficiency of 20 OWC devices inserted into the normal breakwater.

Steady free-surface flow in vegetation debris pad clogging trash racks

ABSTRACT We consider a steady water flow in a channel where a vertical grid is clogged by a rectangular patch of aquatic vegetation. Laboratory experiments are conducted to observe the decrease in the water table within the patch, as well as the subsequent head loss, as a function of the patch length, the flowrate and the upstream water height. Various models of porous media are used to produce theoretical formulae describing the water surface profile within the patch, among which the Barree–Conway model proves to perform reasonably well. However, for large enough Froude numbers a seepage face or water chute appears past the vegetation patch while non-hydrostatic effects become important. Under the latter condition, the accuracy of our analytic solution is less satisfactory, while remaining accurate enough for practical purposes. As confirmed by numerical simulations, with the specific aquatic plants used in our experiments the porous flow is not Darcian, so that the seepage and head loss could not be explained by the exact Polubarinova–Kochina theory.

Numerical modeling of structural body deformation under free surface flow based on volume of fluid–discrete element method coupling

In this work, we proposed a numerical model based on the coupling of the volume of fluid–discrete element method and bond particle method (BPM). The simulation of particle bonding and the structural body formation process had been presented, and the inter-particle bonding mechanism was introduced. We also tested dam-busting impact elastic and wedge plates at high Reynolds numbers (1.26 × 107 and 2.16 × 106) and compared the results with numerical simulations. The results show that the model has mean errors of 3.9% and 6.5% for the large and the micro-deformations, respectively. It is in perfect agreement with the curve trends of the test and keeps good convergence for different particle sizes. In addition, we also used the model used to study the hydrodynamic changes in underwater box net structures in offshore aquaculture, and the deformation kinematic properties of box nets under different material strengths were evaluated. This numerical model of this study provides the effective theoretical support and engineering guidance for the further study of the behavior of structural bodies under hydrodynamic action.

A consistent second order ISPH for free surface flow

The Incompressible Smoothed Particle Hydrodynamics (ISPH) is now a popular numerical method for modelling free surface flows, in particular the breaking waves and violent wave-structures interaction. The ISPH requires the projection approach, leading to solving a pressure Poisson's equation (PPE). Although the accuracy and convergence of the numerical scheme to discretise the Laplacian operator involved in PPE is critical for securing a satisfactory solution of the PPE, the overall performance of the ISPH is also influenced by other key numerical implementations, including (1) estimation of the viscous terms; (2) calculation of the velocity divergence; (3) discretisation of the boundary conditions for the PPE; and (4) evaluation of the pressure gradient. In our previous paper [29], the quadratic semi-analytical finite difference interpolation scheme (QSFDI), which has a leading truncation error at third order derivatives, has been adopted to discretise the Laplacian operator. In this paper, the QSFDI will be adopted, not only for discretising the Laplacian operator, but also for approximating viscous terms, velocity divergence, boundary conditions and pressure gradient. The performance of the newly formulated consistent second order ISPH is assessed by various cases including the oscillating liquid drop, the wave propagation, and the liquid sloshing. The results do not only demonstrate a second order convergence over a limited range of conditions and a higher computational efficiency, i.e., requiring less computational time to achieve the same accuracy, but also show a better mass/energy conservation property and capacity of reproducing a smooth pressure field, than other ISPH models considered in this study.

Vertically averaged and moment equations: New derivation, efficient numerical solution and comparison with other physical approximations for modeling non-hydrostatic free surface flows

Efficient modeling of flow physics is a prerequisite for a reliable computation of free-surface environmental flows. Non-hydrostatic flows are often present in shallow water environments, making the task challenging. In this work, we use the method of weighted residuals for modeling non-hydrostatic free surface flows in a depth-averaged framework. In particular, we focus on the Vertically Averaged and Moment (VAM) equations model. First, a new derivation of the model is presented using expansions of the field variables in sigma-coordinates with Legendre polynomials basis. Second, an efficient two-step numerical scheme is proposed: the first step corresponds to solving the hyperbolic part with a second-order path-conservative PVM scheme. Then, in a second step, non-hydrostatic terms are corrected by solving a linear Poisson-like system using an iterative method, thereby resulting in an accurate and efficient algorithm. The computational effort is similar to the one required for the well-known Serre-Green-Naghdi (SGN) system, while the results are largely improved. Finally, the physical aspects of the model are compared to the SGN system and a multilayer model, demonstrating that VAM is comparable in physical accuracy to a two-layer model.

Laboratory and non-hydrostatic modelling of focused wave group evolution over fringing reef

This paper presents physical experiments and numerical simulations to study the propagation of focused waves group across hypothetical fringing reef profiles. A wave flume is 69 m long and 1.0 m deep, and the reef cross section is made up of a reef face, a reef flat and a vertical wall. A reef crest of 0.085 m is optionally constructed on the outside to replicate the reef crown. By focusing wave trains of the JONSWAP or constant wave amplitude spectrum, the transient wave group is generated on the reef slope. Free surface elevations and flow velocity are measured over time along the flume's centreline. The focused wave process and the development of higher harmonics as a result of the nonlinear interaction over the reef face are clearly visible in the wavelet and FFT analyses of the observed free surface elevation. Low frequency wave is increasing on the reef flat while these short-period wave motions are primarily absorbed by rapid breaking on reef edge and crest. On the flat, it is discovered that reef crest has the effect of reducing short-period wave motion and increasing long-period wave motion. A numerical multi-layer non-hydrostatic wave model is employed and its ability to describe the propagation of focused wave groups over fringing reef profiles is assessed.

An Efficient Explicit Moving Particle Simulation Solver for Simulating Free Surface Flow on Multicore CPU/GPUs

The moving particle simulation (MPS) method is a simulation technique capable of calculating free surface and incompressible flows. As a particle-based method, MPS requires significant computational resources when simulating flow in a large-scale domain with a huge number of particles. Therefore, improving computational speed is a crucial aspect of current research in particle methods. In recent decades, many-core CPUs and GPUs have been widely utilized in scientific simulations to significantly enhance computational efficiency. However, the implementation of MPS on different types of hardware is not a trivial task. In this study, we present an implementation method for the explicit MPS that utilizes the Taichi parallel programming language. When it comes to CPU computing, Taichi’s computational efficiency is comparable to that of OpenMP. Nevertheless, when GPU computing is utilized, the acceleration of Taichi in parallel computing is not as fast as the CUDA implementation. Our developed explicit MPS solver demonstrates significant performance improvements in simulating dam-break flow dynamics.

Conceptual analogy between the water hammer phenomenon in free-surface and pressurized-pipe flows

ABSTRACT The water hammer phenomenon, commonly acknowledged in pressurized pipe-flows is relevant to various water distribution systems. This phenomenon constitutes a major concern for hydraulic researchers and designer, given the dramatic consequences of this phenomenon on hydraulic structures and human life. This study aimed at expanding research on the water hammer waves in the free-surface flow framework. The main objective was to address a comprehensive simulation of the free-surface wave behavior caused by the abrupt closure of sluice-gate in prismatic open channel. The one-dimensional Saint-Venant equations embedding the Boussinesq add-on was used to predict the free-surface wave behavior; which was discretized using the (2–4)-dissipative scheme. Results evidenced the analogy between the water hammer wave behavior in free-surface and pressurized pipe flows. Furthermore, results illustrated that the water hammer maneuver produced a sudden depth rise, about three times of the normal depth value in the cross section adjacent to the gate. From a computational point of view, the proposed solver provided simplicity and accuracy attributes in simulating shock-waves in free-surface-flow. This solver also consumed low computational time compared with the conventional or multiple grid technique – based Finite Element Algorithm.

Numerical Study of a Model and Full-Scale Container Ship Sailing in Regular Head Waves

In the present study, the added resistance, heave, and pitch of the KRISO Container Ship (KCS) in waves, at both model scale and full scale, are predicted numerically in regular head waves, for four wavelengths and three wave heights. The ISIS-CFD viscous flow solver, implemented in the Fidelity Fine Marine software provided by CADENCE, was employed for the numerical simulations. The spatial discretization was based on the finite volume method using an unstructured grid. The unsteady Reynolds-averaged Navier–Stokes (RANS) equations were solved numerically, with the turbulence modeled by shear stress transport (k-ω) (SST). The free-surface capturing was based on the volume-of-fluid method. The computed solutions were validated through comparisons with towing test data available in the public domain. To predict the uncertainties in the numerical solution, a systematic grid convergence study based on the Richardson extrapolation method was performed for a single wave case on three different grid resolutions. Specific attention was given to the free-surface and wake flow in the propeller plane. The purpose was to compare the numerical results from the model- and full-scale tests to examine the scale’s effect on the ship’s performance in regular head waves. The comparison between the model scale and full scale showed obvious differences, less accentuated for the free-surface topology and clearly observed in terms of boundary layer formation in the propeller’s vicinity.

Computational Fluid Dynamics Numerical Simulation on Flow Behavior of Molten Slag–Metal Mixture over a Spinning Cup

Centrifugal granulation technology using a spinning cup opens a potential way to recycle steel slag that is currently difficult to reuse. The objective of this research was to study the flow characteristics of a molten slag–metal mixture that was produced during smelting reduction in molten steel slag, passing over a spinning cup, so as to explore the feasibility of using centrifugal granulation technology to treat the steel slag. This was achieved by developing and implementing a computational fluid dynamics (CFD) model that incorporated free-surface multiphase flow to predict the thickness of the liquid slag film at the edge of the spinning cup (slag film thickness for short), which was an important parameter for estimating the size of the slag particles resulting from centrifugal granulation of the molten slag–metal mixture. The influences of various relevant parameters, including spinning cup diameter, slag feeding rate, cup spinning speed, etc., on the slag film thickness were analyzed. Additionally, hot experiments on centrifugal granulation of a molten slag–metal mixture were conducted to verify the results of the numerical simulations. The experimental results indicated a progressive reduction in the Sauter mean diameter of the slag particles as the metallic iron content in the slag increased. Specifically, when the iron content rose from 5% to 15% at a cup spinning speed of 2500 RPM, the Sauter mean diameter decreased by 13.77%. The numerical simulation results showed that the slag film thickness had a positive relationship to the slag feeding rate but a negative relationship to the spinning cup diameter and the cup spinning speed. Furthermore, the ratio between the mean slag particle diameter and the slag film thickness decreased nearly linearly with the increase in the metallic iron content in slag, with the average ratio being approximately 4.25, and this relationship was useful for estimating the slag particle size from the slag film thickness. Therefore, the present research results can provide theoretical guidance for the industrial application of spinning cup centrifugal granulation technology to effectively treat and recycle steel slags.