Computation Of Free Surface Flows Research Articles

Computation of Free-Surface Flows Including Particles through Porous Media Structure

Computation of Free-Surface Flows Including Particles through Porous Media Structure

Cost-effective CFD simulation to predict the performance of a hydrokinetic turbine farm

After the performance assessment of a new hydrokinetic turbine prototype in the tailrace channel of a run-of-river power plant (Lavey, CH), the possibility to install a farm of such hydrokinetic turbines on this pilot site is investigated. In order to identify the optimal number and size of the machines as well as their location on this site, numerical simulations are carried out. Such a process requires to simulate a set of several free surface flow computations including different configurations of the farm in order to maximize the energy tapped by the machines. However, free surface flow computations are time and resources consuming. To allow such flow investigations, a different approach has been selected. In the present study, the turbines were replaced by a model mimicking the resistance effect of the machines. This model consists in a pressure drop applied at the turbine location to emulate the disturbance effect on the flow, especially the wake effect that will modify the available kinetic energy for the neighboring machines. Finally, it results that such a low CPU approach allows us to estimate the best location of the hydrokinetic turbines maximizing the energy harvested.

Large-scale GPU Computation of Free-surface Flow using AMR Method Following Interface

Large-scale GPU Computation of Free-surface Flow using AMR Method Following Interface

Boundary-conforming free-surface flow computations: Interface tracking for linear, higher-order and isogeometric finite elements

The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options, be dealt with using an interface-tracking approach with the Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A difficult issue that is connected with this type of approach is the determination of a suitable coupling mechanism between the fluid velocity at the boundary and the displacement of the boundary mesh nodes. In order to avoid large mesh distortions, one goal is to keep the nodal movements as small as possible; but of course still compliant with the no-penetration boundary condition. Standard displacement techniques are full velocity, velocity in a specific coordinate direction, and velocity in normal direction. In this work, we investigate how the interface-tracking approach can be combined with isogeometric analysis for the spatial discretization. If NURBS basis functions of sufficient order are used for both the geometry and the solution, both a continuous normal vector as well as the velocity are available on the entire boundary. This circumstance allows the weak imposition of the no-penetration boundary condition. We compare this option with an alternative that relies on strong imposition at discrete points. Furthermore, we examine several coupling methods between the fluid equations, boundary conditions, and equations for the adjustment of interior control point positions.

A new two-step projection method in an ISPH model for free surface flow computations

In this study, we propose a new two-step projection method in connection with an ISPH model. Compared to the traditional ISPH model that uses the future time step pressure to calculate the intermediate velocity, in the present study the pressure at both current time step and future time step is employed. In addition, the velocity and pressure obtained at the end step of the projection method are re-projected onto the updated particle locations using an interpolation method. While the use of current time step pressure provides a better energy conserving property of the numerical scheme, the interpolation smooths the velocity field and ensures a more stringent constraint for incompressibility condition. The accuracy of the model is further enhanced by implementing C2 consistency kernel approximation for variable and derivative calculation. The model is first calibrated by using the still water and liquid sloshing tests. It is then validated against a series of benchmark tests of linear wave and solitary wave propagation in constant water depth, followed by the case of nonlinear wave transformation over a submerged breakwater. The numerical results are compared to available theories, experimental data, and previously published simulation results. It is shown that the present model can achieve a much better energy conservation than the traditional ISPH model, even with the use of a much larger time step.

Minimum Specific Energy and Transcritical Flow in Unsteady Open-Channel Flow

AbstractThe study and computation of free surface flows is of paramount importance in hydraulic and irrigation engineering. These flows are computed using mass and momentum conservation equations, ...

Recent advances in EdgeCFD on wave-structure interaction and turbulence modeling

The computation of free surface flows is challenging since waves are highly nonlinear and commonly present merging, frag mentation and cusps, leading to the use of interface capturing ALE approaches. Turbulence is also important on several offshore applications. In this work we report recent advances of EdgeCFD to simulate these problems. EdgeCFD is a fully implicit 3D incompressible stabilized parallel edge-based finite element flow solver associated to the Volume-of-Fluid (VoF) method. The VoF marking function is also solved by a fully implicit parallel edge-based finite element formulation. Turbulence in EdgeCFD is treated within the Large Eddy Simulation (LES) framework. The performance and accuracy of EdgeCFD is tested in the simulation waves and in the interaction between waves and a semisubmersible structure. We also access the performance of several LES models on the simulation of the flow around a cylinder at Reynolds 3,900.

Computation of Free Surface Flows around Box-Shaped Ships by an Unstructured Navier-Stokes Solver

A novel ship concept which is called ultra large block coefficient ship (ULBS) to enable efficient environmentconscious sea transportation is under investigation at Yokohama National University. Since ULBS is supposed to have a very blunt hull, flow field analysis around a ship is crucial for a design of hull forms with better hydrodynamic performance. Computational Fluid Dynamics (CFD) is expected to be an efficient design tool for unconventional hull forms such as ULBS. However, it is desirable to examine applicability of the CFD method before the actual design application. Thus, free-surface flow computations of two box-shaped ships which can be considered as the extreme cases of ULBS are carried out. Grid convergence study is performed with respect to resistance for the verification of the results. Total resistance coefficients are compared with each other and also with available experimental data. The pressure and velocity distributions of the two ships are compared with each other. The flow structures with large separations are observed and the influences of the box geometry to the flow fields are discussed.

Improved efficiency of a non-hydrostatic, unstructured grid, finite volume model

An efficient depth-integrated non-hydrostatic unstructured grid finite volume model is presented and applied to several test cases, which involve the computation of free surface flows. The model solves the non-linear shallow water equations, with extra non-hydrostatic pressure terms to describe dispersion effects. The efficiency of the model is a major issue when it involves large spatial domains with high resolution meshes. Lumping of the pressure gradient of the horizontal velocities is employed, which reduces the number of non-zero elements in the sparse matrix of the Poisson equation by half. This greatly reduces both the memory requirements and the number of floating point operations required to solve the Poisson equations. In addition, for a model using a collocated grid, both the water surface and the non-hydrostatic pressure need to be defined at the incoming wave boundary. A non-hydrostatic pressure boundary, has been derived based on linear wave theory, that is accompanied with the regular incoming short wave for depth-integrated models. It can serve as a simple way to introduce short incoming waves in models with collocated grids. The model has been validated through several test problems including an oscillating basin, propagation of a solitary wave, wave propagation over a submerged bar, wave refraction and diffraction over an elliptical shoal, as well as solitary wave run-up on a conical island. The model gives good results for all test cases. We show that the lumping of the pressure gradient generates identical results to simulations without lumping, while the execution CPU time is reduced by around 30%, demonstrating a good computational efficiency of the model.

A coupled arbitrary Lagrangian–Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE approach, the surface tension, which may be a linear or nonlinear function of surfactant concentration (equation of state), and the Marangoni forces can be incorporated directly into the numerical scheme. Further, the Laplace–Beltrami operator technique, which reduces one order of differentiation associated with the curvature, is used to handle the curvature approximation. A number of 3D-axisymmetric computations are performed to validate the proposed numerical scheme. An excellent surfactant mass conservation without any additional mass correction scheme is obtained. The differences in using a linear and a nonlinear equation of state, respectively, on the flow dynamics of a freely oscillating droplet are demonstrated.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier–Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems.

Computation of free-surface flows and fluid–object interactions with the CIP method based on adaptive meshless soroban grids

The CIP Method [J comput phys 61:261–268 1985; J comput phys 70:355–372, 1987; Comput phys commun 66:219–232 1991; J comput phys 169:556–593, 2001] and adaptive Soroban grid [J comput phys 194:57–77, 2004] are combined for computation of three- dimensional fluid–object and fluid–structure interactions, while maintaining high-order accuracy. For the robust computation of free-surface and multi-fluid flows, we adopt the CCUP method [Phys Soc Japan J 60:2105–2108 1991]. In most of the earlier computations, the CCUP method was used with a staggered-grid approach. Here, because of the meshless nature of the Soroban grid, we use the CCUP method with a collocated-grid approach. We propose an algorithm that is stable, robust and accurate even with such collocated grids. By adopting the CIP interpolation, the accuracy is largely enhanced compared to linear interpolation. Although this grid system is unstructured, it still has a very simple data structure.

The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions

The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection–diffusion, Comput Struct 2004;83:1459–75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput Struct 2003;81:655–71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964–84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian–Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme.

A second-order boundary-fitted projection method for free-surface flow computations

This paper describes a new approach to the high-fidelity simulation of axisymmetric free-surface flows. A boundary-fitted grid is coupled with a new projection method for the solution of the Navier–Stokes equations with second-order accuracy in space and time. Two variants of this new method are developed by adapting two existing algorithms, suitable for prescribed velocity boundary conditions, to the case of prescribed normal and tangential stresses at the free boundary. A normal-mode analysis for a fixed-boundary problem confirms the second-order accuracy of the algorithms. The approach is validated by comparison with a Rayleigh–Plesset solution for an oscillating spherical bubble, with an analysis of shape oscillations, and with existing results for the buoyant rise of a deforming bubble for Reynolds numbers up to 200 and Weber numbers up to 12. In addition to the simulation of axisymmetric free-surface flows of intrinsic interest, the present approach is suitable for the validation of genuinely three-dimensional calculations.

Computation of free-surface flows with local mesh adaptation

This paper describes a modern free-surface capturing strategy implemented in an unstructured finite-volume viscous flow solver that can handle moving grids composed of arbitrary-shaped control volumes. An adaptive mesh strategy is fully integrated in the code making it a single tool for dynamically maintaining a prescribed density of grid points around the steady or unsteady interface between air and water. The whole adaptive procedure is described in detail. The efficiency of the overall approach is examined on two- and three-dimensional hydrodynamic applications. The adaptive strategy achieves interesting gains in terms of computational and human efforts compared to single-mesh computations. Copyright © 2005 John Wiley & Sons, Ltd.

Computation of free surface flows with a projection FEM in a moving mesh framework

A numerical model for the simulation of incompressible viscous free surface flows is presented. The equations governing the fluid flow are solved with the finite element fractional-step projection method. A moving mesh approach, similar to the arbitrary Lagrangian–Eulerian method is introduced to deal with the presence of a free surface. Validations are carried out with a two-dimensional sloshing problem with small deformations. Thus, results concerning, respectively, the damped oscillations of a gravity and a capillary wave are compared with the initial-value linear theory. Then, a three-dimensional computation concerning the behavior of a uniform flow field subjected on its free surface to an external applied traction is presented.

An Arbitrary Lagrangian-Eulerian finite difference method for computations of free surface flows

A numerical model based on a finite-difference scheme is presented for simulation of two-dimensional transient flow in open channels. The Arbitrary Lagrangian-Eulerian (ALE) kinematic description, and the techniques of moving grids and boundary-fitted coordinate system are adopted for the computation of free surface flows. An iterative flow field solver using an algorithm of velocity divergence with an adjusted pressure is employed to ensure mass conservation. The proposed model is demonstrated on three well-known problems, which include wave propagation caused by dam-break, viscous damping of a solitary wave, and reflection of a wave running against a vertical wall. The simulated results show good agreement with available experimental data or theoretical solutions.

Computation of ship transom stern flow using a multiblock grid method

The incompressible Reynolds Averaged Navier-Stokes (RANS) code using the multiblock grid method has been developed for simulating the steady free surface flows over ship having complex geometries. “Horizontal Mode”, “Vertical Mode” and “BJ-SGS” which are methods of updating boundary conditions on block interfaces are incorporated in the present code and investigated in the computation of free surface flows about Wigley hull. The new code is applied to computation of transom stern flow about a container ship and a high speed vessel and those numerical results are compared with the experimental results.

Computation of free surface flows with a Taylor–Galerkin/pressure–correction algorithm

Computation of free surface flows with a Taylor–Galerkin/pressure–correction algorithm

Computation of free surface flows with a Taylor-Galerkin/pressure-correction algorithm

A semi-implicit Taylor–Galerkin/pressure–correction finite element scheme (STGFEM) is developed for problems that manifest free surfaces associated with the incompressible creeping flow of Newtonian fluids. Such problems include stick–slip and die-swell flows, both with and without a superimposed drag flow, and for plane, axisymmetric and annular systems. The numerical solutions are compared with available analytical and numerical solutions, both in the neighbourhood of singularities and elsewhere. Close correspondence in accuracy is extracted from the literature for both stick–slip and die-swell flows. Stick–slip flow is used as a precursor study to the more complex free surface calculations involved for die-swell in extrudate flow. Two different free surface techniques are reported and results are analysed with mesh refinement and varying structure. Copyright © 2000 John Wiley & Sons, Ltd.