Free Surface Flow Model Research Articles

Decomposition model for naval hydrodynamic applications, Part I: Computational method

The present paper and its companion present a solution and domain decomposition model for general two-phase, incompressible and turbulent flows encountered in naval hydrodynamics. The mathematical and numerical model are derived within the framework of polyhedral finite volume method. Interface capturing is obtained with implicitly redistanced level set method derived from the phase field equation. This approach removes the need to redistance the level set field, thus saving CPU time and increasing numerical stability. A modified, Spectral Wave Explicit Navier–Stokes Equations method is introduced and used for wave modelling, where the solution is decomposed into incident and perturbation fields. The incident field is readily available from potential flow theories, and only the perturbation component is solved within the non-linear equation set of the free surface flow model. The domain is decomposed with implicit relaxation zones used to prevent wave reflection by forcing the perturbation fields to vanish in the far-field. A second-order, collocated finite volume method is used to discretise the equations. All equations are solved implicitly, which enables the use of higher Courant–Friedrichs–Lewy numbers compared to explicit scheme. The algorithm is implemented in foam-extend-3.1, a community driven fork of the OpenFOAM CFD software. Verification and validation of the model is presented in the accompanying paper.

Coupling 3D groundwater modeling with CFC-based age dating to classify local groundwater circulation in an unconfined crystalline aquifer

Nitrogen pollution of freshwater and estuarine environments is one of the most urgent environmental crises. Shallow aquifers with predominantly local flow circulation are particularly vulnerable to agricultural contaminants. Water transit time and flow path are key controls on catchment nitrogen retention and removal capacity, but the relative importance of hydrogeological and topographical factors in determining these parameters is still uncertain. We used groundwater dating and numerical modeling techniques to assess transit time and flow path in an unconfined aquifer in Brittany, France. The 35.5 km2 study catchment has a crystalline basement underneath a ∼60 m thick weathered and fractured layer, and is separated into a distinct upland and lowland area by an 80 m-high butte. We used groundwater discharge and groundwater ages derived from chlorofluorocarbon (CFC) concentration to calibrate a free-surface flow model simulating groundwater flow circulation. We found that groundwater flow was highly local (mean travel distance = 350 m), substantially smaller than the typical distance between neighboring streams (∼1 km), while CFC-based ages were quite old (mean = 40 years). Sensitivity analysis revealed that groundwater travel distances were not sensitive to geological parameters (i.e. arrangement of geological layers and permeability profile) within the constraints of the CFC age data. However, circulation was sensitive to topography in the lowland area where the water table was near the land surface, and to recharge rate in the upland area where water input modulated the free surface of the aquifer. We quantified these differences with a local groundwater ratio (rGW-LOCAL), defined as the mean groundwater travel distance divided by the mean of the reference surface distances (the distance water would have to travel across the surface of the digital elevation model). Lowland, rGW-LOCAL was near 1, indicating primarily topographical controls. Upland, rGW-LOCAL was 1.6, meaning the groundwater recharge area is almost twice as large as the topographically-defined catchment for any given point. The ratio rGW-LOCAL is sensitive to recharge conditions as well as topography and it could be used to compare controls on groundwater circulation within or between catchments.

3D CFD validation of invert trap efficiency for sewer solid management using VOF model

Earlier investigators have numerically carried out performance analysis of the invert trap fitted in an open channel using the stochastic discrete phase model (DPM) by assuming the open channel flow to be closed conduit flow under pressure and assuming zero shear stress at the top wall. This is known as the fixed lid model. By assuming the top wall to be a shear free wall, they have been able to show that the velocity distribution looks similar to that of an open channel flow with zero velocity at the bottom and maximum velocity at the top, representing the free water surface, but no information has been provided for the pressure at the free water surface. Because of this assumption, the validation of the model in predicting the trap efficiency has performed significantly poorly. In addition, the free water surface subject to zero gauge pressure cannot be modeled using the fixed lid model because there is no provision of extra space in the form of air space for the fluctuating part of the water surface profile. It can, however, be modeled using the volume of fluid (VOF) model because the VOF model is the appropriate model for open channel or free surface flow. Therefore, in the present study, three-dimensional (3D) computational fluid dynamics (CFD) modeling with the VOF model, which considers open channel flow with a free water surface, along with the stochastic DPM, was used to model the trap efficiency of an invert trap fitted in an open rectangular channel. The governing mathematical flow equations of the VOF model were solved using the ANSYS Fluent 14.0 software, reproducing the experimental conditions exactly. The results show that the 3D CFD predictions using the VOF model closely fit the experimental data for glass bead particles.

Phase-detection measurements in free-surface turbulent shear flows

High-velocity self-aerated flows are described as 'white waters' because of the entrained air bubbles. The air entrainment induces a drastic change in the multiphase flow structure of the water column and this leads to significant bubble-turbulence interactions, turbulence modulation and associated mixing processes impacting on the bulk flow properties. In these high-velocity free-surface turbulent flows, the phase-detection needle probe is a most reliable instrumentation. The signal processing of a phase-detection probe is re-visited herein. It is shown that the processing may be performed on the raw probe signal as well as the thresholded data. The latter yields the time-averaged void fraction, the bubble count rate, the particle chord time distributions and the particle clustering properties within the particulate flow regions. The raw probe signal analysis gives further the auto-correlation time scale and the power spectrum density function. Finally dimensional considerations are developed with a focus on the physical modelling of free-surface flows in hydraulic structures. It is argued that the notion of scale effects must be defined in terms of some specific set of air–water flow properties within well-defined testing conditions, while a number of free-surface flow characteristics are more prone to scale effects than others, even in large-size physical facilities.

Cavitation Inception in Crossflow Hydro Turbines

Cavitation is a common flow phenomena in most hydraulic turbines and has the potential to cause vibration, blade surface damage and performance loss. Despite the fact that crossflow turbines have been used in small-scale hydropower systems for a long time, cavitation has not been studied in these turbines. In this paper, we present the findings of a computational study on cavitation inception in crossflow turbines. Cavitation inception was assessed using three-dimensional (3D) Reynolds-Averaged Navier–Stokes (RANS) computations. A homogeneous, free-surface two-phase flow model was used. Pressure distributions on the blades were examined for different flow rates, heads and impeller speeds to assess cavitation inception. The results showed that cavitation occurs in the second stage of the turbine and was observed on the suction side near the inner edge of the blades. For the particular turbine studied, cavitation always occurred at shaft speeds greater than that, giving the maximum efficiency for each combination of flow rate and head. The implication is that the useful operating range of crossflow turbines is up to and including the maximum efficiency point.

SPH-DEM model for free-surface flows containing solids applied to river ice jams

ABSTRACTA meshless method is used to simulate free-surface fluid flows containing solid particles, motivated by the need to simulate river ice dynamics problems. A smoothed particle hydrodynamics model (SPH), with an arbitrary Lagrangian–Eulerian formulation for the fluid phase, is two-way coupled with the discrete element method (DEM) for the solid phase. Validation test cases include a bouncing sphere on a level surface, a collapse of a granular column, wedge entry into still water and solids of different densities falling into still water. The computed results using the SPH-DEM model agree quantitatively with the expected behaviour in the test cases. Numerical convergence is demonstrated for the wedge entry validation case. The SPH-DEM model is then used to simulate the stability of floating ice blocks approaching a stationary cover and ice accumulation upstream of an obstruction. The results show promise to serve as a useful quantitative engineering tool.

Свободное программное обеспечение для моделирования жидкости со свободной поверхностью

Problems of free-surface flow of viscous incompressible fluid are very useful in different practical cases. There are many specifies and limitations in these problems which are critically important for correct solving. The main goal is the review of existing numerical methods which can apply for modeling of free-surface flows and open-source programs where these methods are realized. Three methods for solving problems of free-surface flow were considered: Volume of Fluid, Smoothed Particle Hydrodynamics, Particle Finite Element Method v.2. They are realized in five open-source packages: OpenFOAM, Gerris, pySPH, DualSPHysics, Kratos. These packages were compared by modeling of two chosen cases: breaking of a dam and droplet impact to the liquid layer. Results of computations were compared with experimental results. There are good coincidence between them. The best results were obtained in OpenFOAM and Gerris. All main tools for modeling of free-surface flow are realized in these packages - the possibility of computations in 2D, 3D and axisymmetric model setup and also correct modeling of surface tension. Gerris can significantly accelerate computations in "big cases" due to dynamically adaptive remeshing. Further, DualSPHysics is the package for modeling of problems of coastal infrastructure where the most number of cases is 3D and the surface tension effect is negligible. The package pySPH was designed for clear demonstration of SPH working. The pySPH source code is on the Python language and not optimized. Kratos is the new package, which is in development now, therefore some tools are not developed in this moment.

An immersed boundary method for unstructured meshes in depth averaged shallow water models

SummaryThe representation of geometries as buildings, flood barriers or dikes in free surface flow models implies tedious and time‐consuming operations in order to define accurately the shape of these objects when using a body fitted numerical mesh. The immersed boundary method is an alternative way to define solid bodies inside the computational domain without the need of fitting the mesh boundaries to the shape of the object. In the direct forcing immersed boundary method, a solid body is represented by a grid of Lagrangian markers, which define its shape and which are independent from the fluid Eulerian mesh. This paper presents a new implementation of the immersed boundary method in an unstructured finite volume solver for the 2D shallow water equations. Moving least‐squares is used to transmit information between the grid of Lagrangian markers and the fluid Eulerian mesh. The performance of the proposed implementation is analysed in three test cases involving different flow conditions: the flow around a spur dike, a dam break flow with an isolated obstacle and the flow around an array of obstacles. A very good agreement between the classic body fitted approach and the immersed boundary method was found. The differences between the results obtained with both methods are less relevant than the errors because of the intrinsic shallow water assumptions. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical Modeling of Free Surface Dynamics of Melt in an Alternate Electromagnetic Field. Part II: Conventional Electromagnetic Levitation

By means of external coupling between electromagnetic (EM) problem in ANSYS and hydrodynamic problem in FLUENT, a numerical model for the liquid metal free surface flow in an alternate EM field has been developed and verified in the first part of the article. Volume of Fluid (VOF) algorithm has been used for tracking of free surface. In this work, improved performance of the model is presented. General validation of the VOF algorithm is performed by comparison of the calculated free oscillations of the liquid column to its analytical solution. The 3D/VOF calculation of coupled EM field and free surface flow with Large Eddy Simulation turbulence description for the first time is applied for modeling of conventional EM levitation. Calculation results are compared with 2D/VOF and 3D/VOF models that use less precise k–e and k–ω SST turbulence formulations. Obtained time-averaged droplet shapes are used for single-phase flow calculations with different turbulence models and free-slip/no-slip velocity conditions at the fixed free surface for validation of the flow. Meanwhile, series of levitation melting experiments are performed for verification of the simulated droplet shapes. In conclusion, parameter impact on the fully developed flow and the levitated droplet shape is discussed.

Multi-regime shallow free surface laminar flow models for quasi-Newtonian fluids

The mathematical modeling of thin free-surface laminar flows for quasi-Newtonian fluids (power-law rheology) is addressed with a particular attention to geophysical flows (e.g. ice or lava flows). Asymptotic thin-layer flow models (one-equation and two-equation models) consistent with various viscous regimes, corresponding to different basal boundary conditions (from adherence to pure slip), are derived. The challenge being to derive models consistent from slip to no-slip basal boundary condition, though at the price of balancing small friction by small mean slope. Starting from reference flows (the steady-state uniform ones) corresponding to different shear regimes, the exact expressions of all fields (σ,u,p) are calculated formally by a perturbation expansion method. The calculations are such that all field expressions remain valid for any laminar viscous regimes. The calculations are presented either in a mean slope coordinate system with local variations of the topography or in the Prandtl coordinate system, hence valid in presence of any non flat basal topography. Formal error estimates proving the consistency of the derivations are stated. An unified one-equation model (lubrication type in the depth variable h) is derived at order 1. Next, few unified two-equation models in variable (q,h) (shallow water type) are stated and discussed. The classical first order models from the literature are recovered if considering the corresponding particular cases (generally, flat bottom with a particular regime and/or specific basal boundary condition). Two one-dimensional numerical examples illustrate the robustness of these new multi-regime formulations (the change of flow regimes being due either to a sharp change of the mean-slope topography or to a sharp change of basal boundary condition).

Determining resistance coefficient for series 60 vessels using numerical and experimental modelling

In this paper, an experimental and computational approach is presented to determine the residual resistance of a 1.5-m ship-model in the series 60 category. The results are validated with the experimental works which have been confirmed by nine accredited institutes in Japan, including Yokohama and Hiroshima (using a 7-m ship-model established at the 17th International Towing Tank Conference). The 1.5-m model has been designed, manufactured and tested at Isfahan University of Technology (IUT) towing tank. Besides the experimental work, a computational free surface flow modelling is performed by using a finite volume method with the double phase and standard k-ϵ model. Comparison of the results indicates an accurate model design, the establishment of suitable similarity, and accurate computation of the residual resistance coefficients with a maximum deviation of 8%. Furthermore, a comparison of the total resistance coefficient obtained from the numerical analysis and from the experimental results of IUT laboratory, indicates a very low deviation of 1.3%. This verification not only shows the capability of the numerical computation method due to the boundary layer simulation around the body but it also indicates the compatibility of the results obtained in the IUT towing tank.

Modeling of Free Surface Flows Using Improved Material Point Method and Dynamic Adaptive Mesh Refinement

AbstractThe study uses the material point method (MPM) and dynamic adaptive mesh refinement (AMR) technique to simulate incompressible free surface flows. The MPM can be regarded as a quasi-meshless method in which the background grid acts like a scratch pad while the material point (hereafter referred to as particle) motion overlies it. The states of the particles are updated through the solutions on the background grid. The artificial compressibility coefficient is employed to treat incompressible flows as slightly compressible flows within the MPM framework. Boundary conditions, such as free surfaces and reflective walls (both slip and no-slip conditions), are implemented and tested using the ghost-cell method. A generalized far-field characteristic boundary for wave propagation simulation has been established. Typical water wave propagation and violent wave breaking involving discontinuous free surfaces are simulated as well as compared to the arbitrary Lagrangian-Eulerian (ALE) method. The results in...

Fully three-dimensional Reynolds-averaged Navier–Stokes modeling for solving free surface flows around coastal drainage gates

In this study we carry out numerical simulations of free surface flow through the drainage gates of the Saemangeum tidal barrier that is located in the west coast of South Korea and is also known as the world largest man-made tidal barrier. Instead of using depth-averaged numerical models, which have been widely used in hydraulic and coastal engineering, we employ the fully three-dimensional free surface flow model of Kang and Sotiropoulos (2012b) to simulate the flow around the gates. The numerical model is based on the two-phase level set method solving the air and water simultaneously and the curvilinear immersed boundary method that is able to handle arbitrarily complex geometries. In the simulations turbulent flows are also resolved by the shear stress transport k−ω model. The numerical model is applied to simulate fifteen different flow conditions with various gate opening scenarios, and for selected test cases laboratory experiments are also carried out. The computed flowfields at various flow conditions are compared with the laboratory measurements and the field observations and the comparisons showed satisfactory agreements both quantitatively and qualitatively. Using numerical simulation results, we elucidate the structures of turbulent flows associated with a high-speed jet-flow like structure and a hydraulic jump at the far downstream of the gates. The results presented in this paper demonstrate the predictive capabilities of the numerical model and its potential as a powerful engineering tool for estimating the discharge-water level relationship and the three-dimensional flowfield of real-life drainage gates.

A Smooth Particle Hydrodynamics discretization for the modelling of free surface flows and rigid body dynamics

SummaryThis work describes a unified discretization of rigid solids and fluids, allowing for spatially detailed and time‐resolved simulations of fluid–solid interaction. The model is based on a Smoothed Particle Hydrodynamics (SPH) discretization of the Navier–Stokes equations and Newton's equations for rigid body dynamics. A δ‐SPH term is added to the continuity equation, allowing for an effective interface description. The benchmark case of the buoyancy‐driven motion of an unrestricted rigid body allows for experimenting new computational approaches for the more general case of fluid–solid interactions, in the case of solid objects larger than the smallest flow scales. Numerical experiments and analytical solutions are recovered from the literature and compared with the numerical results from the proposed model. Experimental measurements were performed and numerical results are compared, resulting in a wide range study of the fundamental properties of fluid–solid systems. After an investigation on the influence of the stabilizing δ‐SPH terms, the model is shown to respect free stream consistency, the correct dynamics of a buoyant body, for a range of positive and negative relative densities and the correct recovery of equilibrium states. This work addresses these topics in an attempt to characterise the presented model with regard to the quality of its solutions and possible limitations. Copyright © 2015 John Wiley & Sons, Ltd.

Computational Modeling and Simulation of Nonisothermal Free-surface Flow of a Liquid Jet Impinging on a Heated Surface

The study is aimed at formulating and validating the computational model for the nonisothermal two-phase flow with free-surfaces. The testing flow configuration consists of the liquid jet impacting on a heated wall generating simultaneous heat transfer from the wall surface. The interface capturing methodology implemented in the open-source software OpenFOAM® based on the volume-of-fluid (VOF) model in the framework of Computational Fluid Dynamics (CFD) is extended to incorporate heat transfer. The potential of the model is evaluated by contrasting the results of numerical simulations to the existing experimental and numerical results. The computational procedure based on the numerical model demonstrates good qualitative and quantitative predictive capabilities by reproducing correctly the studied flow and heat transfer characteristics.

Finite Element Modeling of Free Surface Flow in Variable Porosity Media

The aim of the present work is to present an overview of some numerical procedures for the simulation of free surface flows within a porous structure. A particular algorithm developed by the authors for solving this type of problems is presented. A modified form of the classical Navier–Stokes equations is proposed, with the principal aim of simulating in a unified way the seepage flow inside rockfill-like porous material and the free surface flow in the clear fluid region. The problem is solved using a semi-explicit stabilized fractional step algorithm where velocity is calculated using a 4th order Runge–Kutta scheme. The numerical formulation is developed in an Eulerian framework using a level set technique to track the evolution of the free surface. An edge-based data structure is employed to allow an easy OpenMP parallelization of the resulting finite element code. The numerical model is validated against laboratory experiments on small scale rockfill dams and is compared with other existing methods for solving similar problems.

A Topology Based Discretization of PDAEs Describing Water Transportation Networks

AbstractWe consider partial differential algebraic systems (PDAEs) describing water transportation networks. Similar to the approach in [6], we follow the method of lines for the discretization. However, we do not consider free surface flow models but pressure flow models covering hydraulic shocks. Moreover, we include switching models reflecting the on/off state of pumpes and valves. Aiming at a stable numerical simulation of the PDAEs we present a topology based spatial discretization that results in a differential algebraic system (DAE) of index 1. Furthermore we show that the DAE index can be higher than 1 if the spatial discretization is not adapted to the position of reservoirs and demand nodes within the network. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

3D LBM NUMERICAL SIMULATION OF MIXED SAND SORTING UNDER OSCILLATORY FLOWS AND PROGRESSIVE WAVES

A 3D numerical model based on Lattice Boltzmann Method (LBM) has been developed to investigate the particle behavior of mixed-grain-size sediments under oscillatory flows and progressive waves. The model considers both particle-particle interaction and particle-fluid interaction with free surface flow and SGS turbulence model. By applying the present model, simulations of mixed-grain-size sediments with different influence factors (i.e., Shields parameters, periods, bottom layer thicknesses) under symmetric oscillatory flows as well as under progressive cnoidal wave are performed to understand the vertical sorting process of graded sands. The results of mixed sands under symmetric oscillatory flows show that the water particle semi-excursion is a key influence factor on the armoring effect. For the cnoidal wave, the vertical sorting proceeds until the wave crest passes by and it fully develops in a complete period. The concentration centroid of large particles becomes higher landward within 2 periods.

Operation of an irrigation canal by means of the passive canal control

Modern irrigation techniques involve large spatial and temporal demand variations in distribution networks. This makes the flow unsteady and generates perturbations that travel upstream along the network. Perturbations can also be generated by variable water inflows. This is the case when water is pumped into the network under variable energy rates, generating perturbations that travel downstream on the network. The passive canal control is a design criteria and a flow distribution method that make most of the storage capacity needed in any irrigation project, in order to mitigate the perturbations coming from both directions. In this paper, the passive canal control is applied to the design and operation of the Xerta-Senia Canal Irrigation Project considering an unsteady free-surface flow model. The key aspect of the project is the location of irrigation reservoirs in-line with the canals at the same level, allowing water flow from canals to reservoir and vice versa. Three performance scenarios are evaluated, and the results of a simulation model are presented.

Scale separation for multi-scale modeling of free-surface and two-phase flows with the conservative sharp interface method

In this paper we present a scale separation approach for multi-scale modeling of free-surface and two-phase flows with complex interface evolution. By performing a stimulus-response operation on the level-set function representing the interface, separation of resolvable and non-resolvable interface scales is achieved efficiently. Uniform positive and negative shifts of the level-set function are used to determine non-resolvable interface structures. Non-resolved interface structures are separated from the resolved ones and can be treated by a mixing model or a Lagrangian-particle model in order to preserve mass. Resolved interface structures are treated by the conservative sharp-interface model. Since the proposed scale separation approach does not rely on topological information, unlike in previous work, it can be implemented in a straightforward fashion into a given level set based interface model. A number of two- and three-dimensional numerical tests demonstrate that the proposed method is able to cope with complex interface variations accurately and significantly increases robustness against underresolved interface structures.