Complex Free Surface Flows Research Articles

OVERSET-RANS COMPUTATIONS OF TWO SURFACE SHIPS MOVING IN VISCOUS FLUIDS

A structured overset grid approach coupled with Reynolds-Averaged Navier-Stokes (overset-RANS) method is presented to provide an accurate resolution of two surface ships moving with opposite velocity in viscous fluids. The RANS equations with shear stress transport (SST) k - ω model are employed to treat the viscous turbulent flows. The fully nonlinear boundary condition at the free surface is satisfied at each time step and the evolution of the free surface is achieved by using the level set method. A structured overset grid approach is used to allow flexibility in grid generation, local mesh refinement, as well as the simulation of moving objects while maintaining good grid quality. The presented overset-RANS method is demonstrated by two surface Wigley ship hulls moving with opposite velocity in still water. The simulating results illustrate the feasibility of the presented method to compute the complex viscous free surface flows interacting with many moving ships in still water or in waves.

GPUs, a New Tool of Acceleration in CFD: Efficiency and Reliability on Smoothed Particle Hydrodynamics Methods

Smoothed Particle Hydrodynamics (SPH) is a numerical method commonly used in Computational Fluid Dynamics (CFD) to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs) or Graphics Processor Units (GPUs), a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA) of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability.

A simple two-phase method for the simulation of complex free surface flows

In this article we propose a simple and efficient diffuse interface (interface- capturing) two-phase algorithm for the simulation of complex non-hydrostatic free surface flows in general geometries. The physical model is given by a special case of the more general Baer–Nunziato model for compressible multi-phase flows. In the applications considered here, the relative pressure of the gas phase with respect to atmospheric reference conditions is assumed to be zero everywhere and the momentum of the gas phase can be neglected compared to the one of the liquid. The reduced system is closed by the Tait equation of state, which is a widespread model for water. The resulting PDE system is solved by a high order path-conservative WENO finite volume scheme on unstructured triangular meshes, to be applicable also in complex geometries. To assure low numerical dissipation at the free surface, which actually is crucial for the applications under consideration here, we use the new generalized Osher-type scheme of Dumbser and Toro [29], which resolves steady shear and contact waves exactly, in contrast to the simpler centered path-conservative FORCE schemes presented in [26]. The model derives directly from first principles, namely the conservation of mass and momentum, hence it does not make any of the classical simplifications inherent in the commonly used shallow water models, which are based on depth-averaging, neglecting accelerations in gravity directions and on the resulting hydrostatic pressure distribution. We validate the new two-phase model against available analytical, numerical and experimental reference solutions and we also show some comparisons with the classical shallow water model for typical dambreak-type problems.

3D simulation of flow around a single spur dike with free-surface flow

In the present study, flow patterns around a single spur dike (also termed a groyne) with free-surface flow was simulated using a numerical model known as Fluent. The model solved the fully three-dimensional, Reynolds-averaged Navier–Stokes equation to predict flow near the structure where three-dimensional flow is dominant. To treat the complex free-surface flow, the volume of fluid method with geometric reconstruction scheme was applied and turbulence was simulated using standard equations. In this research work, both a structured and an unstructured mesh were used and the density of the mesh spacing was selected the highest near the walls and also free surface to obtain more accurate results. Comparison of free surface and velocities of 3D model showed good agreement with three experimental flume data obtained by other researchers. The reattachment length for various conditions was computed using the numerical results and flow pattern was presented for repelling, attracting and vertical spur dikes together. Also, bed-shear stress distribution was presented and the effects of flow discharge and the length and angle of the spur dike upon the bed shear-stress distribution were evaluated.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien–Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the PTT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters ɛ and ξ on the extrudate swell and jet buckling problems is reported.

경계면 포착법에 의한 밀도차이에 따른 물질경계면을 갖는 다상유동 수치해석

The Rayleigh-Taylor instability, the bubble rising in both partially and fully filled containers and the droplet splash are simulated by an in-house solution code(PowerCFD), which are typical benchmark problems among multiphase flows with material interface due to density difference. The present method(code) employs an unstructured cell-centered method based on a conservative pressure-based finite-volume method with interface capturing method(CICSAM) in a volume of fluid(VOF) scheme for phase interface capturing. The present results are compared with other numerical solutions found in the literature. It is found that the present method simulates efficiently and accurately complex free surface flows such as multiphase flows with material interface due to both density difference and instability.

A new 3D parallel SPH scheme for free surface flows

We propose a new robust and accurate SPH scheme, able to track correctly complex three-dimensional non-hydrostatic free surface flows and, even more important, also able to compute an accurate and little oscillatory pressure field. It uses the explicit third order TVD Runge–Kutta scheme in time, following Shu and Osher [Shu C-W, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys 1988;89:439–71], together with the new key idea of introducing a monotone upwind flux for the density equation, thus removing any artificial viscosity term. For the discretization of the velocity equation, the non-diffusive central flux has been used. A new flexible approach to impose the boundary conditions at solid walls is also proposed. It can handle any moving rigid body with arbitrarily irregular geometry. It does neither produce oscillations in the fluid pressure in proximity of the interfaces, nor does it have a restrictive impact on the stability condition of the explicit time stepping method, unlike the repellent boundary forces of Monaghan [Monaghan JJ. Simulating free surface flows with SPH. J Comput Phys 1994;110:399–406]. To asses the accuracy of the new SPH scheme, a 3D mesh-convergence study is performed for the strongly deforming free surface in a 3D dam-break and impact-wave test problem providing very good results. Moreover, the parallelization of the new 3D SPH scheme has been carried out using the message passing interface (MPI) standard, together with a dynamic load balancing strategy to improve the computational efficiency of the scheme. Thus, simulations involving millions of particles can be run on modern massively parallel supercomputers, obtaining a very good performance, as confirmed by a speed-up analysis. The 3D applications consist of environmental flow problems, such as dam-break flows and impact flows against a wall. The numerical solutions obtained with our new 3D SPH code have been compared with either experimental results or with other numerical reference solutions, obtaining in all cases a very satisfactory agreement.

HyPAM: A hybrid continuum-particle model for incompressible free-surface flows

Three major issues associated with numerical simulations of complex free-surface flows, viz. interface tracking, fragmentation and large physical jumps, are addressed by a new hybrid continuum-particle model (HyPAM). The new model consists of three parts: (1) the Polygonal Area Mapping method [Q. Zhang, P.L.-F. Liu, A new interface tracking method: the polygonal area mapping method, J. Comput. Phys. 227(8) (2008) 4063-4088]; (2) a new algorithm that decomposes the interested (water) phase into a continuum zone, a buffer zone and a particle zone, based on material topology and graph theory; (3) a ‘passive-response’ assumption, in which the air phase is assumed to respond passively to the continuum part of the water phase. The incompressible inviscid Euler equations and the equations describing the free fall of rigid bodies are used as the governing equations for the continuum-buffer zone and the particle zone, respectively, and separately. A number of examples, including water droplet impact, solitary wave propagation, and dam-break problems, are simulated for the illustration and validation of HyPAM. It is shown that HyPAM is more accurate and versatile than a continuum-based Volume-of-Fluid model. One major contribution of this work is the single-phase decomposition algorithm, useful for many other hybrid formulations. Neglecting surface tension, viscosity and particle interactions, HyPAM is currently limited to mildly-fragmented free-surface flows with high Reynolds and Weber numbers.

Free surface flow in the mixing zone of an annular centrifugal contactor

AbstractThe annular centrifugal contactor has been developed as the central piece of equipment for advanced liquid–liquid extraction processes for use in recycling spent nuclear fuel. While a sufficient base of experience exists to support successful operation of current contactor technology, a more complete understanding of the fluid flow within the contactor would enable further advancements in design and operation of future units. In particular, an important characteristic of the flow that is not well understood and which significantly complicates computational modeling of the contactor is the complex free surface flow in the annular mixing zone. This study presents the results of time‐dependent, multiphase computational fluid dynamics (CFD) modeling using the volume‐of‐fluid (VOF) interface tracking method to characterize the mixing zone in a model centrifugal contactor. Laser doppler velocimetry (LDV) measurements of the actual flow velocities within the contactor were also performed. The experimental results were compared with simulations using various turbulence modeling schemes. The CFD model predictions using a coarse grid large eddy simulation (LES) method are in good agreement with the experimental measurements and observations. © 2007 American Institute of Chemical Engineers AIChE J, 2008

Numerical solution of 3D free surface flows using implicit methods

AbstractThis work presents an implicit technique for simulating three‐dimensional unsteady low Reynolds number free surface flows of non‐Newtonian fluids. It is based on the Marker‐and‐Cell technique and it employs finite differences on a staggered grid. Validation results and the numerical simulation of complex free surface flows are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A marker-and-cell approach to viscoelastic free surface flows using the PTT model

This work is concerned with the development of a numerical method capable of simulating two-dimensional viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien–Tanner). In particular, we are interested in flows possessing moving free surfaces. The fluid is modelled by a marker-and-cell type method and employs an accurate representation of the fluid surface. Boundary conditions are described in detail and the full free surface stress conditions are considered. The PTT equation is solved by a high order method which requires the calculation of the extra-stress tensor on the mesh contour. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. In order to validate the numerical method fully developed flow in a two-dimensional channel was simulated and the numerical solutions were compared with known analytic solutions. Convergence results were obtained throughout by using mesh refinement. To demonstrate that complex free surface flows using the PTT model can be computed, extrudate swell and a jet flowing onto a rigid plate were simulated.

The Application of Numerical Methods for the Solution of Some Problems in Free-Surface Hydrodynamics

The aim of this contribution is to present some of the recent developments achieved at INSEAN in the context of accurate and robust algorithms for the solutions of the system of partial differential equations governing complex free-surface flows. The paper addresses several problems of relevant interest in naval hydrodynamics, for example, sloshing, water on deck, microscale breaking waves, bow-stern flows, ship waves, steady and unsteady ship flows. Each problem is solved through the most appropriate numerical method, which is selected on the basis of the approximations that can be done for the particular problem and of the kind of result that the analysis has to provide. Numerical methods adopted involve classical boundary element approaches, smoothed particle hydrodynamics, heterogeneous domain decomposition techniques, level-set methods, steady and unsteady Reynolds averaged Navier-Stokes equations. Validation versus experimental data are presented. Comparisons among different numerical approaches are also established in a few cases with the aim of highlighting their limits and/or capabilities.

Simulation of viscous water column collapse using adapting hierarchical grids

AbstractAn adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.

Numerical simulation of gas–liquid–solid flows using a combined front tracking and discrete particle method

In this paper a hybrid model is presented for the numerical simulation of gas–liquid–solid flows using a combined front tracking (FT) and discrete particle (DP) approach applied for, respectively, dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP model, originally developed by Hoomans et al. [1996. Chemical Engineering Science 51, 99–108] for dense gas–solid systems, has been extended to account for all additional forces acting on particles suspended in a viscous liquid and has been combined with the FT model presented recently by Deen et al. [2004a. CD-ROM Proceedings of Fifth International Conference on Multiphase Flow, ICMF’04, Yokohama, Japan, May 30–June 4, 2004; 2004b. Chemical Engineering Science 59, 1853–1861] for complex free surface flows. In this paper, the physical foundation of the combined FT-DP model will be presented together with illustrative computational results highlighting the capabilities of this hybrid model. The effect of bubble-induced particle mixing has been studied focusing on the effect of the volumetric particle concentration. In addition the retarding effect (drag modification) on the bubble rise velocity due to the presence of the suspended solid particles has been quantified.

Three-Dimensional Modelling of Density Variation Due to Phase Change in Complex Free Surface Flows

A three-dimensional model of droplet impact and solidification has been modified to include the effects of density variation during phase change. The governing equations for conservation of mass, momentum, and energy, and a volume-of-fluid (VOF) equation are derived by assuming different but constant solid and liquid densities. The equations are solved numerically using a control-volume approach. The model is validated against the Stefan and planar solidification problems. It is then applied to simulate the effects of density variation during solidification of molten tin in a mold and also of an impacting tin droplet on a substrate.

An Effective Implementation of Surface Tension Using the Marker and Cell Method for Axisymmetric and Planar Flows

This work presents a method for simulating axisymmetric and planar free-surface flows dominated by surface tension forces. The surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is evaluated by fitting a least squares curve to the free surface using the tracking markers in the cell and in its close neighbors. To avoid short wavelength perturbations on the free surface, a mass-conserving local four-point stencil filter is employed. This filter is an extension of the trapezoidal subgrid undulations removal (TSUR) method. The TSUR technique consists of modifying the positions of two ``internal' markers of the four-point stencil in such a way that the surface length and the curvature are minimized, while still preserving the volume. The computation of the curvature is modified at cells adjacent to solid boundaries in order to apply contact angle boundary conditions. To identify neighboring cells efficiently, an implementation is effected through a dual representation of the cell data: in addition to a matrix representation, a list structure is also employed which permits the representation of specific groups of cells and associated data. This technique was implemented in the GENSMAC code, and it has been proved to be robust. The code is shown to produce accurate results when compared with exact solutions of selected fluid dynamical problems involving surface tension. Additionally, it is demonstrated that the method is applicable to complex free-surface flows, such as containers filling, splashing drops, and bursting bubbles.

Strongly Coupled Analysis of Fluid‐Structure Interaction with Free Surface Flow

AbstractFor the numerical analysis of interactions of immiscible two‐fluid flows and lightweight elastic structures a discretization method based on stabilized space‐time finite elements is applied. The use of the level set method provides an implicitly given description of the evolving flow domains and useful geometrical information of the moving and topological changing fluid‐fluid interface. Due to the choice of a proper enriched basis within the partition of unity concept, the method is able to capture strong discontinuous solutions in space and time introduced by interfacial jump conditions and different material properties on each side of the moving interface. A numerical example demonstrates the ability of the method to handle complex free surface flow situations and their interplay with elastic bodies. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of cast systems using smoothed-particle hydrodynamics

To understand and control the filling process for metals in high-pressure die casting and ingot casting, researchers have used new flow-simulation software for the modeling of mold filling. Smoothed-particle hydrodynamics (SPH) is a non-conventional computational fluid dynamics method that has been successfully applied to these problems. Due to its mesh-free nature, it can handle complex splashing free surface flows and the differential motion of multiple solid-casting equipment components relatively easily. The ability of SPH to predict the detailed filling patterns of real large-scale automotive die castings is demonstrated in this study, and the use of SPH simulation for wheel shape optimization in ingot casting based on minimizing oxide generation while increasing the throughput is also presented.

Simulation of the effect of defence structures on granular flows using SPH

Abstract. This paper presents the SPH (Smoothed Particles Hydrodynamics) numerical method adapted to complex rheology and free surface flow. It has been developed to simulate the local effect of a simple obstacle on a granular flow. We have introduced this specific rheology to the classical formalism of the method and thanks to experimental devices, we were able to validate the results. Two viscosity values have been simultaneously computed to simulate "plugs" and "dead zone" with the same code. First, some experiments have been done on a simple inclined slope to show the accuracy of the numerical results. We have fixed the mass flow rate to see the variations of the flow depth according to the channel slope. Then we put a weir to block the flow and we analysed the dependence between the obstacle height and the length of influence upstream from the obstacle. After having shown that numerical results were consistent, we have studied speed profiles and pressure impact on the structure. Also results with any topography will be presented. This will have a great interest to study real flow over natural topography while using the model for decision help.

Algebraic factorizations for 3D non-hydrostatic free surface flows

The high amount of computer resources required to simulate complex free surface flows has prompted for developing fractional step schemes capable of reducing the computational effort. These schemes are borrowed from a wider family of methods originally devised for the incompressible Navier–Stokes equations. An alternative approach is to perform an algebraic splitting on the coefficient matrix of the linear system resulting from the discretized problem, ending up with the successive solution of sub-problems of smaller size. The resulting schemes are shown in different cases to be the algebraic counterpart of the standard fractional step formulations. This algebraic procedure was again originally devised in the context of incompressible Navier–Stokes system, but we believe it is far more general: in this paper it is indeed extended to the more involved 3D free surface flow model. The inexact block factorization technique is applied to the coefficient matrix arising from the problem at hand and two significant choices for the approximation are discussed and numerically tested.