Complex Free Surface Flows Research Articles

Assessment of interfacial turbulence treatment models for free surface flows

The modelling of complex free surface flows is challenging due to the mobility and deformability of the interface and air entrainment characteristics, which are highly affected by turbulence. With the framework of Reynolds averaged Navier–Stokes (RANS) models and the volume of fluid (VOF) method, turbulence quantities at the air–water interface tend to be over-estimated. In this study, interfacial turbulence treatment methods including the buoyancy modification model based on the simple gradient diffusion hypothesis (SGDH) and Egorov’s turbulence damping model are investigated. Furthermore, due to the unconditionally unstable characteristics of the standard k-ε turbulence model, the stabilized k-ε turbulence model is applied as a comparison. The turbulence attenuation performance using different interfacial turbulence treatment methods in the vicinity of the interface is compared and discussed for stratified flows and free overflow weirs for aerated and non-aerated nappe scenarios. The turbulence quantities and free surface profile under different flow conditions are validated against experimental data and an analytical model. The results show that for free surface waves, both the SGDH model and the turbulence damping model give strong improvements in turbulence production compared with the standard k-ε model. The SGDH model augments the turbulence kinetic energy (TKE) in the unstable stratification, leading to unphysical behaviour for the partially dispersed and separated flow.

Compact moving particle semi-implicit method for incompressible free-surface flow

Recently, consistent meshfree particle methods have been intensively studied. It has been pointed out that numerical inaccuracy or instability could easily occur with incomplete or biased neighbor support. This study proposes a new meshfree particle method called the compact moving particle semi-implicit (CMPS) method to decrease the condition number. In the proposed CMPS, the first-order and second-order derivatives are discretized separately, enhancing the numerical stability significantly. By adopting a small dilation parameter of the compact support, the CMPS can remarkably improve accuracy and reduce computational costs. Formulations for zeroth-order, first-order, and second-order derivatives are derived, and various boundary conditions, e.g., Dirichlet and Neumann, are discussed. In order to better deal with complex free-surface flows using the CMPS, some new numerical techniques, i.e., optimized regularization and reconstructed particle shifting schemes, are also developed. Furthermore, the surface fitting method is extended to address the surface tension. A convergence study is conducted in complex geometry to verify the stability, accuracy, and efficiency of the CMPS. Then, second-order accuracy is confirmed using the Taylor–Green vortex problem. After that, numerical examples concerning various free-surface flows, including square patch, hydrostatic pressure, dam break, droplet oscillation, and droplet coalescence, are calculated to demonstrate the potential of the CMPS.

An Improved Neural Particle Method for Complex Free Surface Flow Simulation Using Physics-Informed Neural Networks

The research on free surface flow is of great interest in fluid mechanics, with the primary task being the tracking and description of the motion of free surfaces. The development of numerical simulation techniques has led to the application of new methods in the study of free surface flow problems. One such method is the Neural Particle Method (NPM), a meshless approach for solving incompressible free surface flow. This method is built on a Physics-Informed Neural Network (PINN), which allows for training and solving based solely on initial and boundary conditions. Although the NPM is effective in dealing with free surface flow problems, it faces challenges in simulating more complex scenarios due to the lack of additional surface recognition algorithms. In this paper, we propose an improved Neural Particle Method (INPM) to better simulate complex free surface flow. Our approach involves incorporating alpha-shape technology to track and recognize the fluid boundary, with boundary conditions updated constantly during operation. We demonstrate the effectiveness of our proposed method through three numerical examples with different boundary conditions. The result shows that: (1) the addition of a surface recognition module allows for the accurate tracking and recognition of the fluid boundary, enabling more precise imposition of boundary conditions in complex situations; (2) INPM can accurately identify the surface and calculate even when particles are unevenly distributed. Compared with traditional meshless methods, INPM offers a better solution for dealing with complex free surface flow problems that involve random particle distribution. Our proposed method can improve the accuracy and stability of numerical simulations for free surface flow problems.

Enhanced Dirichlet boundary condition in MPS method for free-surface flow with negative pressure

To enhance the computational accuracy and stability of the moving particle semi-implicit (MPS) method in simulating complex free-surface flow with negative pressure, an enhanced Dirichlet boundary condition (EDBC) for meshless particle methods is proposed. The method is based on the establishment of a virtual boundary using second-order linear fitting, and the Dirichlet boundary assignment is corrected according to the deviation vector from the virtual boundary to the free-surface particle. Some methods to reduce the fitting error are proposed to avoid surface destruction caused by introducing errors. The method is numerically verified using the hydrostatic pressure problem, Torricelli's experiment, and rotating square patch simulation. Furthermore, an inverted tank flow experiment is conducted to verify the accuracy and stability of the method. The results show that the proposed method exhibits significant stability in dealing with complex free-surface flow under negative pressure.

A free surface flow solver based on an efficient improvement to a coupling method for interface computations

In this paper, a free surface flow solver based on an improved coupling method for practical, highly nonlinear, complex free-surface flows is presented. The coupling method which is based on taking the advantages of the continuity and boundedness properties of the conservative level-set (LS) function and the mass conservation property of the VOF approach is integrated into a Navier-Stokes solution to build a new free surface solver. The developed solver is then validated with several practical free surface flows of engineering applications. The test cases are selected so that the developed solver is challenged in simulations of flows with a large scale of density ratio, high-nonlinear, and complicated free surface in a wide range of engineering applications to explore its capability. The simulated flow fields are presented and compared with the available experimental data and of other numerical simulations. Good agreement is achieved implying the capability of the developed solver, and also exhibiting the ability to extend to other applications.

Analysis of high Reynolds free surface flows

ABSTRACT In this paper, we will combine an upwind radial basis function-finite element with direct velocity–pressure formulation to study the two-dimensional Navier-Stokes equations with free surface flows. We will examine this formulation in an improved mixed-order finite element and localized radial basis function method. A particle tracking method and the arbitrary Lagrangian-Eulerian scheme will then be applied to simulate the two-dimensional high Reynolds free surface flows. An upwind improved finite element formulation based on a localized radial basis function differential quadrature (LRBFDQ) method is used to deal with high Reynolds number convection dominated flows. This study successfully obtained very high Reynolds number free surface flows, up to Re = 500 000. Finally, we will demonstrate and discuss the capability and feasibility of the proposed model by simulating two complex free surface flow problems: (1) a highly nonlinear free oscillation flow and (2) a large amplitude sloshing problem. Using even very coarse grids in all computing scenarios, we have achieved good results in accuracy and efficiency.

Stabilized LSMPS method for complex free-surface flow simulation

In this study, a new quasi-Lagrangian particle method is developed aiming at accurate and stable numerical simulation of complex free-surface flows. The main novelties of this development are the free-surface treatment using surface fitting and the new discretization schemes. By using linear surface fitting, the normal vector and the signed distance to the free surface are accurately and stably obtained. The existing consistent spatial discretization scheme, namely, the LSMPS scheme, is extended by adopting regularized least squares, diffuse derivative constraints, and constrained least squares. Based on this scheme, new formulations are proposed particularly for the pressure Poisson equation and the pressure gradient operator. By using a Taylor–Green vortex problem, 2nd-order accuracy in space is confirmed for the 2nd-order discretization scheme. Furthermore, highly accurate solutions are obtained for various test cases, including free-surface deformations of moderate to high complexity. Thus, the proposed method is indicated to have high accuracy and stability for complex free-surface flow simulations.

Numerical investigation of non-Newtonian power law flows using B-spline material point method

• A weakly compressible BSMPM method for simulating non-Newtonian flow is proposed. • Complex free surface flow and fluid structure interaction problems for power law fluid are studied. • Shear thickening/thinning, jet buckling/splashing, and vortex whirling are well represented. • Results demonstrate the efficacy of the proposed method for non-Newtonian power law flow problems. Simulating the complex flow with free surface and large deformation of non-Newtonian fluid is a challenging problem and plays a significant role in many industrial areas. In this paper, a weakly compressible B-spline material point method (WC-BSMPM) is presented and extended to solve the complex free surface flow of non-Newtonian fluid with a power law rheology model. Numerical examples including two-dimensional problems of plane Poiseuille, dam break, and container filling flow as well as three-dimensional sphere water entry problems are adopted to demonstrate the effectiveness and capabilities of the proposed method. The simulated results show good agreements with analytical solutions or published experimental data. Moreover, significant flow features for non-Newtonian power law fluid, including shear thickening, shear thinning, jet buckling, jet splashing, vortex whirling, and fluid-structure interactions can be well captured. Meanwhile, the numerical noise of the traditional MPM can be eliminated by the proposed method, which confirms that the WC-BSMPM method is a promising alternative to simulate the complex free surface flow and fluid-structure interactions for the non-Newtonian power law fluid.

A machine learning strategy for computing interface curvature in Front-Tracking methods

In this work we have described the application of a machine learning strategy to compute the interface curvature in the context of a Front-Tracking framework. Based on angular information of normal and tangential vectors between marker points, the interface curvature is predicted using a neural network. The Front-Tracking-Machine-Learning method is validated using a sine wave and then applied in combination with a Marker-And-Cell method for solving a complex free surface flow. Our results indicate that it is feasible to employ machine learning concepts as an alternative approach for computing curvatures in Front-Tracking schemes.

SPH modeling of caisson stability on rubble-mound foundation under wave action

<p indent="0mm">The caisson breakwater is the representative protective structure in coastal and offshore zones, which is mainly composed of the reinforced concrete caisson and the rubble-mound foundation. The displacement and inclination of caisson structures are generally considered to be the typical features of the failure of the composite breakwaters. Therefore, understanding the motion response characteristics of caisson structures under wave action is of great importance for the design and the safe operation of caisson breakwaters. The dynamic response of caisson breakwaters under wave action is very complex, due to the interaction between wave-porous media-solid structures. In order to predict the stability of caisson breakwaters numerically, the complex free surface flow and the porous flow in the permeable foundation, as well as the contact interaction between the permeable foundation and the caisson structure should be accurately described. The existing numerical research for wave interaction with caisson breakwaters is usually assumed that the caisson structure is fixed in space, and the main interests focus on the wave deformation, the wave load acting on the caisson structure as well as the velocity and pressure fields in the vicinity of the composite breakwater. Few studies pay attention to the motion response and the instability of caisson structures. In addition, the traditional grid-based numerical models are commonly introduced to model wave interaction with the composite caisson breakwaters. These models, although powerful, may have difficulty dealing with extremely large deformation problems and usually also require an explicit surface capturing scheme. In comparison, the mesh-free smoothed particle hydrodynamics(SPH) method does not require the explicit surface capturing scheme in treating strong nonlinear flows with large free surface deformation and enables the easy modeling of coastal structures with complex geometrical boundaries. In this paper, based on the previously established SPH porous flow model, a contact interface boundary condition is developed between the permeable foundation and the upper caisson structure by modeling the supporting force and the sliding friction force at the interface boundary, and a new SPH model is established to study the caisson stability on the permeable foundation under wave action. Compared with the corresponding experimental data, it is found that the developed SPH model can reasonably predict the horizontal wave load, the vertical lift force acting on the caisson structure, and the motion response of the caisson structure. Compared with the other numerical model, it is found that the motion responses of the caisson structure predicted by the present SPH model have a better agreement with the experimental data. All the results indicate that the developed SPH model can be used as a robust tool to predict the stability of caisson breakwaters. However, it is undeniable that the predicted motion response of the caisson structure still deviates from the corresponding experimental data slightly. The main reason is that the contact interface boundary condition between the caisson structure and the permeable foundation ignores the deformation of the contact surface and the adjustment of the stress distribution, which is caused by the embedded effect of the caisson toe and the stone dislocation of the rubble-mound foundation.

Simulation of flow around a permeable dike using physical and 3D-CFD models

ABSTRACT In this research, complementary numerical and experimental physical models were conducted to investigate flow parameters around an isolated permeable spur dike using ANSYS FLUENT ver. 16.1 software. The volume of fluid method VOF with the help of CFD technique and the turbulence model was used to simulate the complex free-surface flow by applying a geometric reconstruction scheme. Two different mediums with different porosities were used, namely, gravel and glass beads. It was found that, for low flow rate values, there are no significant changes in the water profiles in both longitudinal and lateral directions for both media. Although for high flow rate values, the differences tend to be clearer. Results showed that there is a slight effect of the medium's properties if the dike width is less than 1/3 of width of the channel, in particular with low flow rate values. Good agreement was observed between the computational and the measured results for the water surface profiles. Also, there is an exact match between the lateral velocity distribution of gravels and glass beads. Downstream the dike, the lateral velocity profiles exhibit an S shape curve due to high velocity in the free flow and small flow velocity behind the porous dike. The results show good agreement between the CFD results and the experimental observations of the water surface profiles and velocity distribution according to the statistical analysis using some standard indexes error.

Application of Three-Dimensional CFD VOF to Characterize Free-Surface Flow over Trapezoidal Labyrinth Weir and Spillway

AbstractThe current literature for labyrinth weirs suggests that little attention has been paid to the complex free-surface flows generated downstream of these structures. In particular, there is n...

Simulation of complex free surface flows

We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].

Investigation of Free Surface Turbulence Damping in RANS Simulations for Complex Free Surface Flows

The modelling of complex free surface flows over weirs and in the vicinity of bridge piers is presented in a numerical model emulating open channel flow based on the Reynolds Averaged Navier-Stokes (RANS) equations. The importance of handling the turbulence at the free surface in the case of different flow regimes using an immiscible two-phase RANS Computational Fluid Dynamics (CFD) model is demonstrated. The free surface restricts the length scales of turbulence and this is generally not accounted for in standard two-equation turbulence modelling approaches. With the two-phase flow approach, large-velocity gradients across the free surface due to the large difference in the density of the fluids can lead to over-production of turbulence. In this paper, turbulence at the free surface is restricted with an additional boundary condition for the turbulent dissipation. The resulting difference in the free surface features and the consequences for the solution of the flow problem is discussed for different flow conditions. The numerical results for the free surface and stream-wise velocity gradients are compared to experimental data to show that turbulence damping at the free surface provides a better representation of the flow features in all the flow regimes and especially in cases with rapidly varying flow conditions.

Three-dimensional flow prediction in mould filling processes using a GFDM

The aim of this work is to achieve a meshfree implementation for the numerical prediction of 3D flows during mould filling processes in metal casting using a generalized finite difference method. The free surface incompressible flow problem is numerically solved using a semi-implicit Chorin–Uzawa’s projection scheme where the normal vectors needed for the free surface computations are computed with a simple and efficient idea. Further, the boundary conditions incorporation involved in this industrial problem is done in a simple and direct manner. The main characteristics in this meshfree formulation together with details of its computational implementation are given. The numerical results of a benchmark example using this formulation are reported and compared with published numerical and experimental results, and finally, the numerical solution of some three-dimensional test problems is reported which show that this formulation is promising for predicting three-dimensional complex free surface flows in mould filling processes in casting.

CFD-modelling of free surface flows in closed conduits

Computational fluid dynamics (CFD) is gaining an increasing importance in the field of hydraulic engineering. This publication presents different application examples of a two-phase approach as implemented in the open source software OpenFOAM. The chosen approach is based on the volume of fluid method focusing on the simulation of flow in closed conduits. Three examples are presented: single-phase flow over a ground sill and free surface flow over a hill as well as complex free surface flow in a sewer model. The first example compares the results of different RANS turbulence models with experimental results. The results of the second example are compared with an analytical solution. In the last example the behaviour of the free surface flow is compared with the results of a model test and existing simulations using a simplified, open channel geometry for the closed conduit. For the examples analysed, the two-phase approach provides stable and reliable results.

CFD-modelling of free surface flows in closed conduits

Computational fluid dynamics (CFD) is gaining an increasing importance in the field of hydraulic engineering. This publication presents different application examples of a two-phase approach as implemented in the open source software OpenFOAM. The chosen approach is based on the volume of fluid method focusing on the simulation of flow in closed conduits. Three examples are presented: single-phase flow over a ground sill and free surface flow over a hill as well as complex free surface flow in a sewer model. The first example compares the results of different RANS turbulence models with experimental results. The results of the second example are compared with an analytical solution. In the last example the behaviour of the free surface flow is compared with the results of a model test and existing simulations using a simplified, open channel geometry for the closed conduit. For the examples analysed, the two-phase approach provides stable and reliable results.

Numerical solution of the Giesekus model for incompressible free surface flows without solvent viscosity

We present a numerical method for solving the Giesekus model without solvent viscosity. This paper is concerned with incompressible two-dimensional free surface flows and employs the finite difference method to solve the governing equations. The methodology involves solving the momentum equation using the implicit Euler scheme and an implicit technique for computing the pressure condition on the free surface. The nonlinear Giesekus constitutive equation is computed by a second order Runge–Kutta method. A novel analytic solution for channel flow is developed and is used to verify the numerical technique presented herein. Mesh refinement studies establish the convergence of the method for complex free surface flows. To demonstrate that the technique can deal with complicated free surface flows, the time-dependent flow produced by a fluid jet flowing onto a rigid surface is simulated and the influence of the parameter α on the jet buckling phenomenon is investigated. In addition, the simulation of the extrudate swell of a Giesekus fluid was carried out and the effect of the parameter α on the flow was similarly examined.

A well balanced diffuse interface method for complex nonhydrostatic free surface flows

In this paper we propose an efficient second order accurate well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model directly derived from the Baer–Nunziato system for compressible multi-phase flows. In particular, as proposed for the first time in [1], the number of equations is reduced from seven to three by assuming that the relative pressure of the gas with respect to the atmospheric reference pressure is zero, and that the gas momentum is negligible compared to the one of the liquid. The two-phase model does not make any of the classical assumptions of shallow water type systems, hence it does not neglect vertical accelerations and the free surface is not constraint to be a single-valued function, so even complex shapes as those of breaking waves can be properly captured.The resulting PDE system is solved by a novel well balanced second order accurate path-conservative finite volume method on structured Cartesian grids, which is able to preserve exactly the equilibrium states even in the presence of obstacles. It furthermore automatically computes the location of the water-air interfaces, and assures low numerical dissipation at the free surface thanks to a novel Osher-Romberg-type approximate Riemann solver. Finally, high computational performance is guaranteed by an efficient parallel implementation on a GPU-based platform that reaches the efficiency of twenty million of volumes processed per seconds and makes it possible to employ even very fine meshes. The validation of our new well balanced scheme is carried out by comparing the obtained numerical results against existing analytical, numerical and experimental reference solutions for a large number of test cases, among which oscillating elliptical drops, dambreak problems, breaking waves, over topping weir flows, and wave impact problems.

A fully hydrodynamic urban flood modelling system representing buildings, green space and interventions

City Catchment Analysis Tool – CityCAT-is a novel software system for rapid assessment of combined pluvial and fluvial flood risk using a unique combination of: efficient software architecture throughout and especially in the numerical part; use of standard, readily available data sets; efficient algorithms for grid generation; and robust and accurate solutions of the flow equations. It is based on advanced software architecture and accurate solutions for complex free-surface flow over the terrain distinguishing between permeable and impermeable surfaces and taking into account effects of man-made features such as buildings as obstacles to flow. The software is firstly rigorously validated with demanding test cases based on analytical solutions and laboratory studies. Then the unique capability for assessment of the effectiveness of specific flood alleviation interventions across large urban domains, such as roof storage on buildings or introduction of permeable surfaces, is demonstrated.