GENSMAC3D: a numerical method for solving unsteady three‐dimensional free surface flows

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

An adaptive multi-resolution SPH approach for three-dimensional free-surface flow with fluid impacting

Unsteady viscoelastic free surface flows are common in many industrial processes and a variety of numerical techniques have been employed to simulate these flows. The majority of constitutive models employed are based on differential equations to define the extra stress tensor. However, for some complex fluids, for instance, Boger fluids, integral models are more adequate to approximate the nonlinear behaviour of these fluids. This work deals with the numerical solution of the integral constitutive model KBKZ-PSM for two-dimensional unsteady free surface flows. The proposed numerical method is a numerical technique that employs finite differences to simulate moving free surface flows that interact with solid walls. The main features of the method are: numerical solution of the momentum and mass equations by an implicit method; the pressure condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by the modified Euler method. This new technique is verified by solving shear and uniaxial elongational flows. Moreover, an analytic solution for channel flows is obtained that is used in the verification and convergence analysis of the proposed methodology. For free surface flows, the assessment of convergence lies on the mesh refinement on the simulation of a jet impinging on a flat surface and the extrudade swell problem. Finally, the new method is applied to investigate the jet buckling phenomenon and extrudate swell of KBKZ-PSM fluids.

Towards non-intrusive reduced order 3D free surface flow modelling

A diffuse interface method for complex three-dimensional free surface flows

Advances of the in-house developed SWLBM framework in simulating large-scale three-dimensional violent free surface flow with intense splashing

A mathematical model of three-dimensional (3D) free surface flows has been applied to simulate the curved channel flows and mass transport. In the horizontal plane, a channel-fitted curvilinear coordinate system is used, whereas in the vertical plane, the σ-transformation is adopted to track the free surface and variable bed topography. To reduce the numerical diffusion, the second-order upwind scheme of Roe is incorporated to discretize the convection terms. The standard k-ε model has been modified to take account of some anisotropic effects appearing in shallow curved channels, i.e., streamline curvature and the damping effects of free surface and solid walls. The governing equations are solved in a collocated grid system by a fractional three-step implicit algorithm. Two test cases from curved flumes have been studied: (1) A 270° channel bend with a sloped outer bank; and (2) a meandering channel with mass transport. The results are compared with the available data, which shows generally good agreement.

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

Wave impact load occurring in a liquid storage tank during a sloshing motion is numerically simulated. Due to a violent sloshing, an excessive impact load can cause a critical damage to the tank structure. Recently this type of the accidents are reported and the problem becomes an important research topic in LNG (Liquefied Natural Gas) Tanker and FPSO (Floating Production Storage Offloading) design. To predict the sloshing impact load, Morison’s formula could be used for a practical reason. But using the Morison formula may provide directly an inaccurate estimation for the impact load because this formula is based on the linear model in the present nonlinear dominating phenomena. In this study, the wave impact load on the structure is obtained by imposing the exact nonlinear free surface conditions numerically and compared with that predicted by Morison’s formula. As a numerical method, a three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory with the nonlinear free-surface conditions. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The nonlinear problem is numerically solved through an iterative method at each time step.

Three-dimensional numerical simulations of strongly nonlinear free surface flows are performed by lattice Boltzmann method (LBM), which features a number of performance-related advantages, particularly concerning data locality and parallel computing. A Multi-Passage-Interface (MPI) multicore processors parallelized free surface LBM solver is applied for the present three-dimensional numerical simulations. A Smagorinsky LES turbulent model serves to capture the small-scale turbulent structures of the flow. Experiments on dam breaking from previous articles are used to compare and verify two-dimensional (2D) and three-dimensional (3D) LBM model. A new experimental setup is also developed in order to observe the three-dimensionality effect. The findings demonstrated that the free surface LBM simulation agrees well with the experiments.

Arbitrary Lagrangian–Eulerian finite element analysis of free surface flow using a velocity–vorticity formulation

A three-dimensional non-hydrostatic coupled model for free surface – Subsurface variable – Density flows

Up to now, no a real liquid metal (LM) free surface flow have been successfully used in magnetic fusion devices as MHD instability and unavoidable rivulet flow. Recently, after we carried out a guidable free curve-surface flow on theoretically and experimentally, seeking for other way to get a full-cover free surface flow is also in implementing. The superficial layer MHD effect in free surface flow is experimentally observed. After compared and analyzed the characteristic parameters of the free surface flow, the new two parameters of surface cover ratio and rivulet flow index are introduced to characterize the flowing characteristic of the full-cover free surface flow under magnetic field. According to the analysis rule, for different liquid metal, there are the different unique conditions to meet full-cover free surface flow under magnetic field.

The steady and unsteady free-surface flow of hyperconcentrated water-kaolinite clay mixtures is analysed experimentally. These mixtures exhibit non-Newtonian behaviour if volumetric concentrations of solid particles exceed about 10%. The viscosity-concentration correlations, determined by rotary viscometer, indicate that the Bingham model can be used to describe such fluids. Using the rheological parameters of this model, the water-clay laminar flow friction factors can be determined either by calculating the Reynolds and Hedstróm numbers, or by applying the concept of the extended Reynolds number. A quantitative analysis of the unsteady dam-break type of the free-surface flow is presented, giving a comparison of flow depth profiles and propagation rates between the investigated mixtures and water.

While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipments or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented fur the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm.