Volume Fraction Advection Research Articles

A coupled level set/volume of fluid method for simulation of two-phase flow on unstructured grids

We present a fully coupled level set and volume of fluid method for free surface flow simulations on unstructured grids in two- and three-dimensions. The evolution of the level set function and the volume fraction are updated at each time step. The level set advection equation is solved by a least squares weighted residual method while the volume fraction advection is solved using an unsplit Eulerian-Lagrangian scheme. The reconstruction of the interface in the volume of fluid method is performed using the volume fraction information together with the normal vector obtained from the level set function. The reconstructed interface is then used to reinitialize the level set function. Thanks to the fully coupling of the two methods, the interface reconstruction is carried out efficiently and the mass conservation is preserved exactly. The proposed method is validated against several benchmarks and is coupled with the incompressible Navier-Stokes solver to solve two-phase flow problems. Numerical results show that the method is capable of resolving complex interface changes efficiently and accurately.

A modified switching technique for advection and capturing of surfaces

An interface capturing scheme called modified switching technique for advection and capturing of surfaces (MSTACS) has been proposed. The proposed interface capturing scheme utilizes a basic switching technique for advection and capturing of surfaces (STACS) for solution of the volume fraction advection equation. MSTACS has been compared against three interface capturing schemes with the help of various two and three dimensional test cases. It is proved that MSTACS is able to capture sharp interfaces with minimum numerical diffusion over a wide range of Courant numbers. Further, the interface capturing capability of MSTACS is demonstrated by coupling it with the Navier-Stokes equations (NSE) to simulate three dimensional flow problems such as Rayleigh-Taylor instability and dam break with an obstacle.

A-Priori Assessment of Interfacial Sub-grid Scale Closures in the Two-Phase Flow LES Context

Due to the continuous increase in available computing power, the Large Eddy Simulation (LES) of two-phase flows started to receive more attention in recent years. Well-established models from single-phase flows are often used to close the sub-grid scale convective momentum transport and recently some modifications have been suggested to account for the jump of density and viscosity at the interface of multi-phase flows. However, additional unclosed terms in multi-phase flows, which are absent in single-phase flows, often remain ignored. This paper focuses on the crucial gaps in literature, namely the modeling of volume fraction advection and surface tension effects on sub-grid level. An a-priori analysis has been conducted for this purpose, i.e. the Direct Numerical Simulation of an academic two-phase flow configuration (single wobbling bubble in a turbulent background flow) has been explicitly filtered (corresponding to implicit filtering in actual LES) for varying filter width and the corresponding sub-grid terms have been compared to potentially suitable model expressions. Besides other approaches, adequately formulated models based on the scale similarity principle emerged to be promising candidates for both sub-grid volume fraction advection as well as sub-grid surface tension effects. In this context, special attention has to be paid to the secondary filter. Owing to the nature of the quasi-singular surface tension term, surface-weighted filtering may be more appropriate and robust than standard volume filtering.

A coupled volume of fluid and level set method based on analytic PLIC for unstructured quadrilateral grids

We develop a coupled volume of fluid and level set (VOSET) method for unstructured quadrilateral grids to simulate incompressible two-phase interfacial flows in irregular domains. In the method, an analytic piecewise linear interface calculation (PLIC) is first proposed and its solution speed is much faster (about five times) than that of Brent's iterative method; then an iterative geometric operation by which the level set function near interfaces can be calculated, is extended to unstructured quadrilateral grids; moreover, the volume fraction advection is solved by a Lagrangian-Eulerian advection scheme. Finally, the present method is validated by the single vortex flow problem, bubble rising problem and falling droplet problem. Our simulation results show good agreement with those in previous studies.

Implementation and validation of an extended Schnerr-Sauer cavitation model for non-isothermal flows in OpenFOAM

In the present work cavitation in liquid hydrogen and nitrogen was investigated by using the open source toolbox OpenFOAM. Simulations were performed by means of a mass transfer model, based on the homogeneous mixture approach in combination with the Volume of Fluid (VOF) method for the reconstruction the liquid-vapor interface. Two additional transport equations were considered, i.e. the liquid volume fraction advection and the temperature equation. The implementation of an extended Schnerr- Sauer model allowed for the introduction of the thermal effects in terms of latent heat release/absorption and convective heat transfer inside the liquid-vapor interface. A set of Antoine-like equations relate the saturation conditions to the local conditions.

A coupled volume-of-fluid and level set (VOSET) method based on remapping algorithm for unstructured triangular grids

We propose a coupled volume-of-fluid and level set (VOSET) method for interfacial flow simulations on unstructured triangular grids. In this method, the volume fraction advection is performed using a Lagrangian–Eulerian remapping algorithm, and the level set function is calculated by a simple iterative geometric operation. The present VOSET method can not only satisfy mass conservation but also predict the surface tension with good accuracy, thus combining the advantages and overcoming the disadvantages of volume-of-fluid (VOF) and level set (LS) methods. Finally, the present method is verified by well known Zalesak's slotted-disk revolution, single vortex flow, dam break and single bubble rising problems. The results illustrate that the present method can accurately simulate incompressible two-phase flows for unstructured triangular grids.

Coupling a local adaptive grid refinement technique with an interface sharpening scheme for the simulation of two-phase flow and free-surface flows using VOF methodology

This study presents the implementation of an interface sharpening scheme on the basis of the Volume of Fluid (VOF) method, as well as its application in a number of theoretical and real cases usually modelled in literature. More specifically, the solution of an additional sharpening equation along with the standard VOF model equations is proposed, offering the advantage of “restraining” interface numerical diffusion, while also keeping a quite smooth induced velocity field around the interface. This sharpening equation is solved right after volume fraction advection; however a novel method for its coupling with the momentum equation has been applied in order to save computational time. The advantages of the proposed sharpening scheme lie on the facts that a) it is mass conservative thus its application does not have a negative impact on one of the most important benefits of VOF method and b) it can be used in coarser grids as now the suppression of the numerical diffusion is grid independent. The coupling of the solved equation with an adaptive local grid refinement technique is used for further decrease of computational time, while keeping high levels of accuracy at the area of maximum interest (interface). The numerical algorithm is initially tested against two theoretical benchmark cases for interface tracking methodologies followed by its validation for the case of a free-falling water droplet accelerated by gravity, as well as the normal liquid droplet impingement onto a flat substrate. Results indicate that the coupling of the interface sharpening equation with the HRIC discretization scheme used for volume fraction flux term, not only decreases the interface numerical diffusion, but also allows the induced velocity field to be less perturbed owed to spurious velocities across the liquid–gas interface. With the use of the proposed algorithmic flow path, coarser grids can replace finer ones at the slight expense of accuracy.

A dynamic interface compression method for VOF simulations of high-speed planing watercraft

A high speed surface craft is mostly supported by hydrodynamic lift force rather than by buoyancy force. The lift force directly influences the running attitude of the surface craft such as trim and sinkage. The pressure distribution is caused by a solution of free-surface flow around the surface craft. To deal with the free-surface flow, volume-of-fluid (VOF) method has been widely used even with its disadvantages including interface smearing. In the present study, a new dynamic interface compression method is introduced to reduce interface smearing and to avoid unphysical solutions. The method was validated by the volume fraction advection test and prismatic body problem. Finally, the method was applied to simulate the running attitude and resistance of several high speed planing vessels.

A compressible multiphase flow model for violent aerated wave impact problems

This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.

On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface

The process of free rise, collision on and bounce from a solid horizontal surface for a single isolated bubble is investigated by numerical simulations based on the Volume of Fluid method (VOF). The volume fraction advection equation is solved algebraically using the compressive scheme implemented in the CFD open source library (OpenFOAM®) using both axi-symmetrical and three dimensional domains. The solution sensitivity to the mesh refinement towards the solid boundary and the contact angle formulation (static and dynamic) are assessed with two different fluid mixtures for a range of Bond numbers [0.298–1.48] and two different surface hydrophilicities. Numerical results are assessed against published as well as new experiments to include both axi-symmetrical and three dimensional rise trajectories. The investigation addresses the liquid microfilm formation and drainage considering both flow and pressure fields and bubble dynamic characteristics over successive rebounds. Results highlight the importance of resolving the liquid microlayer at the interface between the gas and solid surface in particular in the case of superhydrophobic surfaces. A coarse mesh is shown to precipitate the liquid film drainage. This results in early formation of a triple phase contact line (TPCL) which can occur as soon as the first rebound whereas physical observations indicate that this typically happens much later at a stage when a significant part of the bubble kinetic energy has been dissipated following several rebounds. As a result numerical predictions are shown to be much more sensitive to the contact angle formulation than when a refined mesh allows a more accurate representation of the film drainage. In this case, static and dynamic contact angle models give broadly similar rebound characteristics. Following validation, the numerical simulations are used to provide some useful insight in the mechanisms driving the film drainage and the gas liquid interface as it interacts with the solid surface.

A multiphase DNS approach for handling solid particles motion with heat transfer

In the current work we propose a multiphase DNS method capable of resolving the motion of solid particles coupled with heat transfer effects. The method is based on solving a shared set of momentum and energy balance equations for the carrier phase and the particulate phase. Individual particles are tracked using a number of volume fraction advection equations. The proposed method is in very good agreement with the available data in the literature for the following cases: isothermal particle motion (in the presence of walls and other particles), natural convection around a stationary particle and solid particles motion accompanied with heat transfer effects. In addition, we show that the method is inherently capable of handling deformable particles (i.e. droplets and bubbles) co-existing with solid particles. The method is thus well suited to deal with challenging multiphase systems, such as diesel spray combustion with soot formation, spray drying with particle nucleation, and biological treatment of waste water.

A Hybrid Approach to Multiple Fluid Simulation using Volume Fractions

AbstractThis paper presents a hybrid approach to multiple fluid simulation that can handle miscible and immiscible fluids, simultaneously. We combine distance functions and volume fractions to capture not only the discontinuous interface between immiscible fluids but also the smooth transition between miscible fluids. Our approach consists of four steps: velocity field computation, volume fraction advection, miscible fluid diffusion, and visualization. By providing a combining scheme between volume fractions and level set functions, we are able to take advantages of both representation schemes of fluids. From the system point of view, our work is the first approach to Eulerian grid‐based multiple fluid simulation including both miscible and immiscible fluids. From the technical point of view, our approach addresses the issues arising from variable density and viscosity together with material diffusion. We show that the effectiveness of our approach to handle multiple miscible and immiscible fluids through experiments.

A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids

We present a new three-dimensional hybrid level set (LS) and volume of fluid (VOF) method for free surface flow simulations on tetrahedral grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a second-order characteristic based finite volume method. The volume fraction advection is performed using a bounded compressive normalized variable diagram (NVD) based scheme. The interface is reconstructed based on both the level set and the volume fraction information. The novelty of the method lies in that we use an analytic method for finding the intercepts on tetrahedral grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. Furthermore, the advection of volume fraction makes use of the NVD concept and switches between different high resolution differencing schemes to yield a bounded scalar field, and to preserve both smoothness and sharp definition of the interface. The method is coupled to a well validated finite volume based Navier-Stokes incompressible flow solver. The code validation shows that our method can be employed to resolve complex interface changes efficiently and accurately. In addition, the centroid and intercept data available as a by-product of the proposed interface reconstruction scheme can be used directly in near-interface sub-grid models in large eddy simulation.

An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids

We present an adaptive coupled level-set/volume-of-fluid (ACLSVOF) method for interfacial flow simulations on unstructured triangular grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a discontinuous Galerkin finite element method. The volume fraction advection is performed using a Lagrangian–Eulerian method. The interface is reconstructed based on both the level set and the volume fraction information. In particular, the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction. Different from previous works, we have developed an analytic method for finding the line constant on triangular grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. The level set function is finally reinitialized to the signed distance to the reconstructed interface. Since the level set function is continuous, the normal vector calculation is easy and accurate compared to a classic volume-of-fluid method, while tracking the volume fraction is essential for enforcing mass conservation. The method is also coupled to a finite element based Stokes flow solver. The code validation shows that our method is second order and mass is conserved very accurately. In addition, owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately.

Accurate computation of convective transport in transient two-phase flow

SUMMARY The Van Leer method for the computation of convective fluxes is extended to two-phase flow. By preventing spurious undershoots and overshoots, the scheme preserves physical realism while maintaining high-order accuracy. This is particularly important for two-phase flows, since phase exchange terms are typically a function of volume fraction products and numerical diffusion can incorrectly mix the two phases. The scheme described here is constructed to guarantee that the sum of the volume fractions is always unity and that the volume fiactions are always greater than or equal to zero. Various test problems are computed to demonstrate the accuracy of the method and to show how the scheme might be incorporated in existing computational methods. In addition to multiphase flow applications, setting equal phase velocities results in a volume marker scheme that is well suited to single-phase interface tracking problems. There are few known exact solutions of the governing equations of two-phase flow and those that are known represent simple physical systems that have limited practical application. Consequently, investigators of two-phase flow fall back on experimentally determined correlations and more recently solutions of the governing equations obtained by computer. This paper addresses the problem of minimizing numerical diffusion associated with numerical representation of the convective terms in the two-phase governing equations. It is well known that numerical schemes that discretize the convective terms with an upwind procedure suffer from excessive numerical diffusion; the use of a higher-order scheme can substantially reduce this problem but can also lead to oscillations causing non-physical undershoots or overshoots. The implication of these results for two-phase flow calculations is particularly significant for the computation of the convection of phase volume fraction (mass). If an upwind procedure is used for volume fraction advection, then numerical diffusion tends to smear gradients of volume fraction. Typical two-phase exchange terms involve the product of volume fractions, so smearing produces finite values in those exchange terms, leading to numerically induced source terms and consequent inaccuracies throughout the calculation. If a naive higher-order scheme is used for volume fraction advection, then non-physical oscillations might appear in the volume fraction profiles, as well as overshoots or undershoots, so that volume fractions may be less than zero or greater than unity, which again would produce unphysical phase exchange source terms. This paper describes the use of the Van Leer method' for the computation of convective fluxes as applied to the convective transport of phase volume fraction (mass) and phase momentum in two-phase flow. The Van Leer scheme prevents spurious oscillations while maintaining a high order of numerical