Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Visualization of vortical flows in computational fluid dynamics

The concepts and methods of the visual representation of fluid dynamics computations of vortical flows are studied. Approaches to the visualization of vortical flows based on the use of various definitions of a vortex and various tests for its identification are discussed. Examples of the visual representation of solutions to some fluid dynamics problems related to the computation of vortical flows in jets, channels, and cavities and of the computation of separated flows occurring in flows around bodies of various shapes are discussed.     

Determination of open boundary conditions for computational fluid dynamics (CFD) from interior observations

An optimization approach for the determination of open boundary conditions for Computational Fluid Dynamics is introduced, whereas the error between the solution σ and interior observations ω is minimized. The numerical weather prediction (NWP) model ALADIN–Austria provides data of wind speed and wind direction at virtual weather stations within the area of interest. Also, data from real weather stations and other sources can be incorporated into the model, respectively. In this work, the optimization method is applied to the constant density Navier–Stokes Equations. Thereby, for stabilizing the ill-posed pseudo inverse problem several regularization methods are reviewed. Further, numerical studies are carried out to identify the supreme regularization method for the presented application. Finally, the algorithm is applied to the micro- and meso-scale flow over the Grimming mountain, Austria. The results are compared with real weather station data and show suitable correlation with the measurements.     

Incipient sediment transport for non-cohesive landforms by the discrete element method (DEM)

We introduce a numerical method for incipient sediment transport past bedforms. The approach is based on the discrete element method (DEM) [1], simulating the micro-mechanics of the landform as an aggregate of rigid spheres interacting by contact and friction. A continuous finite element approximation [2] predicts the boundary shear stress field due to the fluid flow, resulting in drag and lift forces acting over the particles. Numerical experiments verify the method by reproducing results by Shields [3] and other authors for the initiation of motion of a single grain. A series of experiments for sediments with varying compacity and constituting piles yields enhanced relationships between threshold shear stress and friction Reynolds number, to define incipient sediment transport criterion for flows over small-scale bed morphologies.     

Numerical simulation of (nearly) incompressible material,using adaptive mixed finite element method

In this paper we present a way to numerically simulate large deformations of incompressible material and the corresponding hydrostatic pressure by using a mixed, adaptive finite element method (FEM). Starting from the system of differential equations we will derive the weak nonlinear formulation, which can be solved with a Newton's method. In every iteration step this will lead to a saddle point problem. By using Taylor Hood finite elements we will obtain a discrete, indefinite problem, which can be handled with the Bramble Pasciak conjugate gradient method. Finally we give a numerical example. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of powder mixed electric discharge machining (PMEDM) using finite element method

In the present paper, an axisymmetric two-dimensional model for powder mixed electric discharge machining (PMEDM) has been developed using the finite element method (FEM). The model utilizes the several important aspects such as temperature-sensitive material properties, shape and size of heat source (Gaussian heat distribution), percentage distribution of heat among tool, workpiece and dielectric fluid, pulse on/off time, material ejection efficiency and phase change (enthalpy) etc. to predict the thermal behaviour and material removal mechanism in PMEDM process. The developed model first calculates the temperature distribution in the workpiece material using ANSYS (version 5.4) software and then material removal rate (MRR) is estimated from the temperature profiles. The effect of various process parameters on temperature distributions along the radius and depth of the workpiece has been reported. Finally, the model has been validated by comparing the theoretical MRR with the experimental one obtained from a newly designed experimental setup developed in the laboratory.     

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.     

Inter-comparison and validation of computational fluid dynamics codes in two-stage meandering channel flows

This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–ε turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y⁺, are satisfied. A rigorous inter-comparison of the codes is performed using large-scale experimental data from the UK Flood Channel Facility for a two-stage meandering channel. This example data set shows complex hydraulic behaviour without the additional complications found in natural rivers. Standardised methods are used to compare each model with the available experimental data. Results are shown for the streamwise and transverse velocities, secondary flow, turbulent kinetic energy, bed shear stress and free surface elevation. They demonstrate that the models produce similar results overall, although there are some differences in the predicted flow field and greater differences in turbulent kinetic energy and bed shear stress. This study is seen as an essential first step in the inter-comparison of some of the computational fluid dynamics codes used in the field of river engineering.     

Numerical simulation of stationary fluid flows in rivers with islands

The algorithm is presented for numerical solution of problems on stationary fluid flows with surface gravitational waves in multiply-connected domains with complicated geometry using adaptive grids in the framework of plane shallow water model taking into account bottom irregularities, frictional force and Coriolis force. The stream function - vorticity function statement in curvilinear coordinates is used. The alternating triangular iterative method is developed for solving the system of difference equations for the vorticity function. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach

A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier–Stokes equations for the liquid phase supplemented with an additional vapor transport equation for the vapor phase. The novel cavitation-induced-momentum-defect (CIMD) correction methodology developed in this study accounts for cavitation inception and collapse events as relevant momentum-source terms in the liquid phase momentum equations. The model tracks cavitation zones and applies compressibility effects, employing homogeneous equilibrium model (HEM) assumptions, in constructing the source term of the vapor transport model. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG k–ε model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Numerical simulations are carried out using a finite volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in good qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the CIMD approach. Our results indicate the profound influence of re-entrant jet motion and adverse pressure gradients on the cavitation dynamics.     

Numerical simulation two phase flows of casting filling process using SOLA particle level set method

Mould filling process is a typical gas–liquid metal two phase flow phenomenon. Numerical simulation of the two phase flows of mould filling process can be used to properly predicate the back pressure effect, the gas entrapment defects, and better understand the complex motions of the gas phase and the liquid phase. In this paper, a novel sharp interface incompressible two phase numerical model for mould filling process is presented. A simple ghost fluid method like discretization method and a density evaluation method at face centers of finite difference staggered grid are proposed to overcome the difficulties when solving two phase Navier–Stokes equations with large-density ratio and large-viscosity ratio. A new mass conservation particle level set method is developed to capture the gas–liquid metal phase interface. The classical pressure-correction based SOLA algorithm is modified to solve the two phase Navier–Stokes equations. Two numerical tests including the Zalesak disk problem and the broken dam problem are used to demonstrate the accuracy of the present method. The numerical method is then adopted to simulate three mould filling examples including two high speed CCD camera imaging water filling experiments and an in situ X-ray imaging experiment of pure aluminum filling. The simulation results are in good agreement with the experiments.     

Analysis of performance of an iron-bath reactor using computational fluid dynamics

The performance of an iron-bath reactor has been studied using a comprehensive numerical model that combines a computational fluid dynamics approach for the gas phase and a heat and mass balance model for the bath. The model calculates:

• •coal, ore, flux and oxygen consumption;
• •post-combustion ratio (PCR);
• •heat-transfer efficiency (HTE);
• •off-gas temperature and composition;
• •heat transfer and chemical reactions between gas and iron and slag droplets; and
• •heat transfer between gas and bath, refractories and lance.

The model was validated with data reported by the Nippon Steel Corporation for a 100 t pilot plant, and the calculated and measured data are in good agreement. Modelling results showed that the dominant mechanisms of heat transfer from the gas to the bath are radiation to the slag surface and convection heat transfer to droplets.     

Numerical solution of bed load transport equations using discrete least squares meshless (DLSM) method

The discrete least squares meshless (DLSM) method is extended in this paper for solving coupled bedload sediment transport equations. The mathematical formulation of this model consists of shallow water equations for the hydrodynamical component and an Exner equation expressing sediment continuity for the bedload transport. This method uses the moving least squares (MLS) function approximation to construct the shape functions and the minimizing least squares functional method to discretize the system of equations. The method can be viewed as a truly meshless method as it does not need any mesh for both field variable approximation and the construction of system matrices; it also provides the symmetric coefficient matrix. In the present work, several benchmark problems are studied and compared with the work of other researchers; the proposed method shows good accuracy, high convergence rate, and high efficiency, even for irregularly distributed nodes. At the end, a real test problem is performed to show and verify the main benefit and applicability of the proposed method to cope with complex geometry in practical problems.     

Numerical simulation of electromagnetically influenced plasma flows using discontinuous Galerkin methods

We study several model cases to find possibilities to control the plasma flow by alternating magnetic fields, in particular travelling and high frequency (HF) fields, using numerical simulations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detailed computational and experimental fluid dynamics of fluidized beds

To describe the hydrodynamic phenomena prevailing in large industrial scale fluidized beds continuum models are required. The flow in these systems depends strongly on particle–particle interaction and gas–particle interaction. For this reason, proper closure relations for these two interactions are vital for reliable predictions on the basis of continuum models. Gas–particle interaction can be studied with the use of the lattice Boltzmann model (LBM), while the particle–particle interaction can suitably be studied with a discrete particle model. In this work it is shown that the discrete particle model, utilizing a LBM based drag model, has the capability to generate insight and eventually closure relations in processes such as mixing, segregation and homogeneous fluidization.     

On the definition of a computational fluid dynamic solver using cellular discrete-event simulation

The Discrete Event System Specification (DEVS) has rarely been applied to the physics of motion. To explore the formalism's potential contribution to these applications, we need to investigate the definition of moving gases, liquids, rigid bodies, and deformable solids. Here, we show how to use Cell-DEVS to analyze the movement and interactions of fluids using computational fluid dynamics (CFD). We describe a set of rules that produce the same patterns as traditional CFD implementations. We present the inner workings of the CFD algorithm, the incorporation of solid barriers, and the adoption of variable time steps within the context of biomechanical simulations.     

Analysis of a stabilized finite element method for fluid flows through a porous interface

This work is devoted to the numerical simulation of an incompressible fluid through a porous interface, modeled as a macroscopic resistive interface term in the Stokes equations. We improve the results reported in [M.A. Fernández, J.-F. Gerbeau, V. Martin, Numerical simulation of blood flows through a porous interface, Math. Model. Num. Anal. (M2AN) 42 (6) (2008) 961–990], by showing that the standard Pressure Stabilized Petrov–Galerkin (PSPG) finite element method is stable, and optimally convergent, without the need for controlling the pressure jump across the interface.