Interface-capturing Scheme Research Articles

Performance analysis and reconstruction of interface capturing schemes for multiphase flows

This article aims to provide a roadmap for analysis of the interface capturing schemes and their possible modification with recommended design principles. Blending the suitable high resolution (HR) scheme with a bounded downwind (BD) scheme is the core of the development of any interface capturing scheme. However, the concrete guidelines for choice of HR and BD schemes are not clear. For this purpose, the HR and BD constituents of a popular scheme known as “Switching Technique for Advection and Capturing of Surfaces (STACS)” are analyzed. Subsequently, it is observed that the scheme fails to satisfy some critical design principles. This leads to a reconstruction of the scheme by introducing a newly compliant bounded downwind scheme. The novel re-constructed scheme is then accessed through typical advection problems, including the shear flow on structured and unstructured meshes. The scheme convincingly outperforms its parent scheme in all test cases irrespective of the Courant number. Moreover, it generates superior or at least at par results while compared with a few well-established schemes like Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) and Cubic Upwind Interpolation based Blending Scheme (CUIBS).

Multiscale multiphase flow simulations using interface capturing and Lagrangian particle tracking

Numerical simulations of multiphase flows with both interfaces and discrete particles are challenging because they possess a wide range of length and time scales. Meanwhile, the volume of fluid (VOF) method is suitable for resolving the interface, while the discrete particle model (DPM) under the Lagrangian frame better simulates unresolvable particles; a multiscale VOF–DPM combined model is urgently needed for multiscale multiphase flows. The present work implements a VOF–DPM solver that includes a two-way transition algorithm to model the transformation between discrete and continuous phases for bubbles or droplets using OpenFOAM. The interface-capturing scheme in the solver is based on the interIsoFoam solver, which supports the geometric reconstruction of the interface and adaptive mesh refinement. A connected component labeling approach is used for particle detection and VOF-to-DPM transition for discrete bubbles or droplets produced by interface breakup. Conversely, a DPM-to-VOF transition algorithm for particles touching the interface is incorporated to achieve a two-way transition. In addition, phase change modeling between continuous phases and bubble dynamic modeling for cavitating flow cases are also implemented in the solver. Test simulations are performed for validation, including the gas–liquid two-phase dam break and cavitating flow in a convergent–divergent test section. The results demonstrate that the solver is reasonably accurate and can adequately represent the complex phase structure, including the interface and discrete particles.

Onset and evolution of counter-rotating baroclinic vortex pair in shock induced aerobreakup of droplets

The interactions between shock and a droplet result in counter-rotating baroclinic vortex pairs. In this work, to better understand the initiation of the stripping droplet breakup regime, the onset and evolution of the counter-rotating baroclinic vortex pair produced via the interaction between a shock wave and a spherical water droplet was numerically studied. The water droplet and surrounding air were simulated using a shock- and interface-capturing scheme for compressible multi-component Euler equations. The sequence of the droplet interaction events and the evolution of the counter-rotating baroclinic vortex pair were analyzed. The time variation of circulation was computed as a function of the shock Mach number; it was decomposed into positive and negative components. Moreover, the circulation of the counter-rotating baroclinic vortex pair was extracted using spatial filtering. The counter-rotating baroclinic vortex pair was initiated as a result of the baroclinic effect caused by two different shock–droplet interactions: the interaction between the incident shock and the droplet and the interaction between the droplet and the diffracted shock moving radially outward. Lastly, circulations of the counter-rotating baroclinic vortex pair were computed for various shock Mach numbers. These results provide a better understanding of the stripping droplet breakup regime in the interactions between shock and a droplet.

Numerical analysis of ventilated cavitating flow around an axisymmetric object with different discharged temperature conditions

Nowadays, with the widespread use of modern technology in underwater vehicles, particularly in naval applications, the artificial gas ejected from ventilated holes is normally heated because of engine operations. However, the dynamics of ventilated hot gas have not yet been fully studied. In this study, the cavitating flow around an axisymmetric body with different ventilated temperatures was numerically investigated. A fully compressible mixture model based on a homogeneous multiphase approach was employed. A high-order accuracy flow solver based on the numerical models of a dual-time preconditioning technique, a sharp interface-capturing scheme, and an enhanced cavitation model was used to examine the effects of temperature on the cavitating flow. First, the numerical results were validated by comparison with available experimental data of cavitating flow around a conical cavitator. Reasonable agreements on the cavity shape, cavity length, and cavity thickness were achieved. The solver was then applied in simulations to analyze the development of the ventilated cavity, including the cavity formation at the early stage, the re-entrant jet phenomenon, and the cavity shedding mechanism. In addition, the effects of ventilated temperatures on the cavity length and cavity thickness were studied. Further insight into the distributions of the flow field inside the cavity, and the instability of the gas-water interface when temperature increases were also provided.

An efficient operator-split CICSAM scheme for three-dimensional multiphase-flow problems on Cartesian grids

Conventional algebraic Volume of Fluid (VOF) schemes utilize a Crank-Nicholson-based unsplit advection framework which is necessary for maintaining second-order accuracy in time as well as to allow extension to arbitrary meshes. However, the unsplit advection approach proves to be a bottleneck to computational performance for CFD solvers opting for non-body-conforming Cartesian grids for treating complex domains and immersed boundaries. To this effect, we propose a general operator-splitting framework for algebraic VOF schemes and develop a direction-split version of the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The resulting operator-split CICSAM (OS-CICSAM) scheme is compared against unsplit CICSAM as well as two recent algebraic VOF schemes for standard advection tests. In terms of volume tracking performance as well as interfacial shape preservation, it is demonstrated that OS-CICSAM attains comparable or lower L1 error norm, has rates of convergence intermediate to first and second order and is at least 600% faster in comparison to unsplit algebraic VOF schemes. The OS-CICSAM scheme is then coupled with the in-house CFD solver IITM-RANS3D. The robustness of the proposed scheme is established by applying to benchmark problems such as Rayleigh-Taylor instability and free surface wave interactions with a structure.

Adjoint complement to the volume-of-fluid method for immiscible flows

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular challenge of the primal and the corresponding adjoint VoF-approach refers to the sharp interface treatment featuring discontinuous physical properties. Both the continuous adjoint two-phase system (integration-by-parts) and the corresponding dual compressive convection schemes (summation-by-parts) are derived for two prominent compressive convection schemes, namely the High Resolution Interface Capturing Scheme (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The dual scheme rigorously mirrors the primal Normalized-Variable-Diagram (NVD) stencils. Attention is restricted to steady state applications. Thus both the primal and the dual procedures are performed in pseudo-time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field. Therefore, the adjoint system experiences the same time step size restrictions as the primal system, is independent of the primal time horizon and forms a robust as well as an a priori stable adjoint solution process.The paper analyses the primal and adjoint equations for an engineering model problem. An analytical solution to the model problem is initially presented, which displays that the adjoint part does not offer a unique, non-trivial solution. As a remedy, an additional diffusive concentration term is introduced to the adjoint concentration equation. The imposed heuristic modification violates the dual consistency but strongly regularizes the solution of the adjoint system. The modification can be justified by reference to phase-separating diffuse-interface models and inheres a free mobility-parameter. Numerical results obtained from the modified approach are benchmarked against the analytical solution for the model problem. Supplementary, the influence of the modification on the sensitivities obtained from simulations for the two-dimensional flow around a submerged hydrofoil at Froude and Reynolds numbers of practical interest are discussed for a range of mobility-parameters. The final application refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter, even for an objective functional that directly depends on the manipulated (dual) field quantity.

THINC scaling method that bridges VOF and level set schemes

We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two different approaches widely used in various applications. The key to success is to maintain a high-quality THINC reconstruction function using the level set field to accurately retrieve geometrical information and the VOF field to fulfill numerical conservativeness. The interface is well defined as a surface in form of a high-order polynomial, so-called the polynomial surface of interface (PSI). The THINC reconstruction function is then used to update the VOF field via a finite volume method, and the level set field via a semi-Lagrangian method. Seeing the VOF field and the level set field as two different aspects of the THINC reconstruction function, the THINC-scaling scheme preserves at the same time the advantages of both VOF and level set methods, i.e. the mass/volume conservation of the VOF method and the geometrical faithfulness of the level set method, through a straightforward solution procedure. The THINC-scaling scheme allows to represent an interface with high-order polynomials and has algorithmic simplicity which largely eases its implementation in unstructured grids. Two and three dimensional algorithms in both structured and unstructured grids have been developed and verified. The numerical results reveal that the THINC-scaling scheme, as an interface capturing method, is able to provide high-fidelity solution comparable to other most advanced methods, and more profoundly it can resolve sub-grid filament structures if the interface is represented by a polynomial higher than second order.

Unsteady 2D and 3D Navier-Stokes Solver with Application of Multigrid Scheme to Pressure Poisson Fractional Step on Arbitrary Unstructured Grids in Various Applications with Emphasis on Ship Motion

A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various applications, especially around a marine vessel. The Navier-Stokes solver is based on the fractional steps method coupled with a finite volume scheme and collocated grids by which velocity components and pressure fields are defined at the center of the control volume. However, the fluxes are defined at the midpoint on their corresponding cell faces. On the other hand, the CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) scheme is applied to capture the free surface. In the presented fractional step method, the pressure Poisson equation suffers from poor convergence rate by simple iterative methods like Successive Overrelaxation (SOR), especially in simulating complex geometrics like a ship with appendages. Therefore, to accelerate the convergence rate, an agglomeration multigrid method is applied on arbitrary moving mesh for solving pressure Poisson equation with two well-known cycles, V and W. In order to maintain accuracy, the geometry details should not change in grid coarsening procedure. Therefore, the boundary faces are assumed to be fixed in all grids level. This assumption requires nonstandard cells in coarsening procedures. To investigate the performance of the applied algorithm, various flows including one and two-phase flows are studied in two and three dimensions. It is found that the multigrid method can speed up the convergence rate of fractional step twofold. In most cases (not all), W cycle displays better performance. It is also concluded that the efficiency of the cycle depends on the number of meshes and complexity of the problem and this is mainly due to the data transferring between grids. Therefore, the type of cycle should be selected judiciously and carefully, while considering the mesh size and flow properties.

Numerical analysis of an unsteady natural cavitating flow around an axisymmetric projectile under various free-stream temperature conditions

Here, an unsteady natural cavitating flow around an axisymmetric projectile is computationally studied using a homogeneous multiphase approach. The numerical models used are based on a dual-time preconditioning method, an interface-capturing scheme, and a modified cavitation model, to capture unsteady cavitation structure behaviors. Full compressibility of two phases and an energy equation are used to determine the effects of temperature on a cavitating flow. First, the experimental data were validated at a cavitation number of σ = 0.435. Both quantitatively and qualitatively good agreements were achieved, including the evolution of the cavity shape, cavity length, and cavity thickness. Then, the key characteristics of an unsteady cavitation structure regarding the cavity growth, re-entrant jet, cavity shedding, and collapse were analyzed. In particular, the mechanism of the re-entrant jet inside the cavity, causing the periodic cavity shedding, was explored. Furthermore, detailed mechanisms of cavity shedding with periodic cavity–vortex–pressure interaction behaviors were analyzed. Finally, the influences of free-stream temperature on the cavitation structure behaviors were carefully investigated. It was found that both the cavity length and thickness increased with the free-stream temperature under the atmospheric pressure condition. The most sensitive effects occurred when the free-stream temperature approached its boiling point. In case of the same reference cavitation number and Reynolds number, the cavity shape tended to be mushier with increasing water temperature.

Numerical simulation of bubble collapse between two parallel walls and saturated film boiling on a sphere

The present study aims at validating a computer simulation code for compressible interface flows with and without mass transfers. The numerical method was based on a dual-time fully compressible multiphase homogeneous mixture flow model. The interfaces with a large jump in density, pressure, velocity, and temperature were captured using a compressive high-resolution interface-capturing scheme. Lee’s boiling model was adopted for implementing the mass and energy transfers via interfaces. The bubble collapse between two parallel walls was first examined. The bubble profile during the collapse process was predicted and compared with experimental images. The numerical results showed good agreement. To evaluate the present model for multiphase flows, including the effects of heat and mass transfers, computations were performed for saturated film boiling on a sphere at atmospheric pressure. The evolution of the wavy liquid–vapor interface around the sphere during the film boiling process was observed. The time-averaged heat fluxes obtained from the numerical simulation were compared with those predicted from numerical data and analytical correlations. The effects of the superheated wall on heat fluxes were also investigated.

Design, analysis and verification of a volume-of-fluid model with interface-capturing scheme

The Volume-of-Fluid (VoF) model with interface-capturing scheme, available in many commercial and open-source CFD packages, may be widely used for simulations of free-surface hydrodynamics but is certainly not used without difficulties. While practitioners have come to expect conservation of mass and momentum, unconditional stability, second-order of accuracy and good iterative convergence, none of these qualities are evident when a free surface gets involved. In this paper, we investigate how these qualities are affected by the discontinuous nature of the volume fraction, which requires specialized numerical techniques for advection, for the interpolation of material properties, for the hydrostatic balance and for the pressure-weighted interpolation used in finite-volume methods with co-located variables. We find that conservation properties and good iterative convergence can still be attained, but not second-order of accuracy and unconditional stability. Code verification is presented to substantiate these findings, with cases ranging from one to three dimensions, from uniform to locally refined grids and from the stand-alone volume fraction equation to the complete set of mass, momentum and volume fraction equations. For the latter, a novel manufactured solution based on a sinusoidal wave in deep water is introduced. These tests permit not only to quantitatively assess the results for comparison with theoretical predictions but also ensure that our findings are characteristic of the VoF method and not of a particular implementation.

Numerical simulation of a water droplet splash: Effects of density interpolation schemes

Flows of two immiscible fluids are widely found in many industrial and natural applications, such as: refrigeration, combustion, irrigation, rain and cavitation. The comprehension/prediction of these kind of flows, simply termed henceforward as two-phase flows, is very important. In this work, water droplet splash cases were studied numerically. This problem is a very interesting two-phase flow, since it occurs in film formation problems, and reliable experimental measures are easily obtained (which is rare in two-phase flow problems), being found in the literature. The VoF model was employed to simulate the impact of a water droplet on a water pool. Although the geometrical schemes, such as PLIC (Piecewise-Linear Interface Calculation) has been demonstrated to yield good results for this problem, it is a rather complex, computationally expensive method, especially when applied to unstructured meshes in many practical problems. Instead, the CICSAM scheme (Compressive Interface Capturing Scheme for Arbitrary Meshes) was used in this work because of its low computational cost and accuracy. The effect of four different schemes for the density interpolation was investigated: central difference, first-order upwind, the second-order and volume fraction weighted. All simulations were compared with experimental data for both the crater depth and ascending jet resulting from the droplet impact. In general, good agreement for the crater depth was found for all the density interpolation schemes, although the volume fraction weighted scheme produced the best results for the ascending jet height. Thus, the VoF/CICSAM method, mainly using the volume fraction weighted scheme for density, proved to be computationally cheaper and reliable to analyze the water droplet splash cases. The methodology presented in this work can be extended to other two-phase flows applications.

Numerical study of advection schemes for interface-capturing using gradient smoothing method

Based on the newly developed gradient smoothing method (GSM), three interface-capturing schemes have been implementing using unstructured mesh. The volume of fluid (VOF) model is solved without explicitly interface reconstructing in the framework of GSM. The variables on upwind points are successfully approximated using centroid GSM (cGSM) scheme, which generally cannot be clearly defined on unstructured mesh. Compressive interface-capturing scheme for arbitrary meshes (CICSAM), flux-blending interface-capturing scheme (FBICS), and cubic upwind interpolation-based blending scheme (CUIBS) have been employed through three benchmark cases. The results indicate that FBICS and CUIBS can produce more accurate predictions using unstructured meshes.

A compressive interface-capturing scheme for computation of compressible multi-fluid flows

Abstract In this paper, a compressive high-resolution interface-capturing scheme is presented for the computation of compressible multi-fluid flows with high-density ratios and strong shocks. The proposed scheme is coupled with a preconditioned dual-time compressible mixture solver for robust and accurate computations over a wide range of Mach numbers. The scheme is simple and relatively easy to implement. It does not require any calculations for the interface curvature and the normal vector. The numerical approximations were implemented on general, structured grids using an implicit MUSCL upwind approach. Validation tests were conducted for a single reversible vortex, advection of an air-water interface, dam-break flow, and air shock-helium bubble interaction. Finally, a three-dimensional gas-lift flow is presented to demonstrate the capability of the present scheme for handling an interface with large jumps in pressure, temperature, and density.

Wave transformation over submerged breakwaters by the constrained interpolation profile method

A multiphase flow model based on the Navier–Stokes equations using a constrained interpolation profile based Cartesian grid method is applied to estimate the wave interaction with a submerged breakwater. The free surface is captured by the Tangent of Hyperbola for Interface Capturing scheme. Wave transformations around submerged breakwaters are simulated with this model. Two kinds of waves (regular wave and solitary wave) and two shapes of submerged structures (rectangle and trapezoid) are investigated to verify the ability of the presented wave model to simulate the flow characteristics in these wave-structure interaction problems. Comparisons with experimental results show good agreements. It is demonstrated that the numerical wave model with the constrained interpolation profile method can reproduce the nonlinear flow phenomena and capture the complex free surface of wave transformation around submerged breakwaters accurately.

A sharpness preserving scheme for interfacial flows

Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) [1] is a numerical scheme which is extensively used in commercial computational fluid dynamics solvers. However it generates significant numerical diffusion at higher Courant number. In order to improve its performance a modification is proposed in the existing algorithm to improve its interface capturing capability at high Courant number. The ULTIMATE QUICKEST scheme for interpolation of face value of volume fraction in the existing CICSAM algorithm is replaced by Fromm scheme [2] in the modified CISCAM algorithm. The Fromm scheme [2] imbibes better dispersion properties than conventional ULTIMATE QUICKEST. The modified algorithm is tested extensively for known two and three dimensional velocity fields. Also the scheme is coupled with Navier–Stokes’ solver and its performance is tested for collapse of water-column and bubble-rise with high surface tension coefficient. The modified scheme results in significant reduction of numerical diffusion and improves the interface capturing abilities.

Investigation of Different Droplet Formation Regimes in a T-junction Microchannel Using the VOF Technique in OpenFOAM

Here we aimed to investigate various droplet formation regimes in a two-dimensional T-junction microchannel geometry using the open source software OpenFOAM. Two incompressible fluids, continuous phase in the main channel and dispersed phase in the lateral channel, have been considered. The interFoam solver was used to simulate laminar flow with two incompressible and isothermal phases. We evaluated the capability of “Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM)” volume of fluid (VOF) technique of the OpenFOAM for modeling of the droplet formation and movement in different regimes. The flow behavior in the T-junction microchannel over a wide range of capillary numbers (0.006 to 0.12), volume flow rate ratio (0.125, 0.25, 0.5), and contact angle (130° to 180°) in the squeezing, dripping and jetting regimes were examined.The importance of parameters such as contact angle, capillary number, flow rate ratio, and Reynolds number at the time of separation, as well as the formation of droplets, was investigated in different regimes. We found that droplet detachment time increases by increasing the contact angle in the squeezing regime while increasing the contact angle in the dripping regime results in a decrease in the droplet detachment time. We compare the role of pressure gradient and shear stress forces in the droplet formation process in both dripping and squeezing regimes in details. We also provide a classification of two-phase flow regimes in the investigated T-junction microchannel in terms of three main parameters of, e.g., flow rate ratio, contact angle, and capillary number.

Numerical simulation of mold-filling capability for a thin- walled aluminum die casting

Mold-filling capability is an important property of casting materials. Especially in thin-walled die casting, fast cooling of the melt by contact to the die makes complete filling difficult to ensure. Simulation is an important tool enabling investigation of filling problems, even before the die is manufactured. However, the prediction of misruns is challenging. Flow and solidification have to be computed as closely coupled. The effects of surface tension, the wetting angle and reduced melt flow due to solidification must be modeled with high precision. To meet these requirements, a finite-volume method using arbitrary polyhedral control volumes is used to solve flow and solidification as closely coupled. The Volume-of-Fluid approach is used to capture the phase separation between gas, melt and solid in connection with a High-Resolution Interface-Capturing scheme to obtain sharp interfaces between phases. To model the resistance of the dendrite network to the melt flow, an additional source term in the momentum equation was implemented. The Bolt test was performed for A356 alloys at a range of different casting temperatures. Numerical prediction of incomplete filling in the bottleneck regions agreed well with experimental findings using 3D camera scanning. The simulation enables derivation of the dependence of critical wall-thickness, i.e. the thickness which is fillable, on casting temperature and metallostatic pressure. This could prove useful in predicting filling problems ahead of casting.

Numerical Modelling of Melt Behaviour in the Lower Vessel Head of a Nuclear Reactor

This paper describes progress on a consistent approach for multi-phase flow modelling with phase-change. Although, the de- veloped methods are general purpose the applications presented here cover the LIVE experiments involving core melt phenomena at the lower vessel head of a nuclear reactor. These include corium pool formation, coolability and solidification. A new method for solving the compositional multi-phase flow equations to calculate material indicator fields is adopted. An interface-capturing scheme based on high-order accurate compressive advection methods including a Petrov-Galerkin approach is employed to main- tain sharpness of the interfaces between materials. A novel control volume-finite element mixed formulation based on the P1DG-P2 (linear discontinuous in velocity and quadratic continuous in pressure) element pair which can uniquely ensure that key balances are maintained in the equations is developed to discretise the governing equations in space. Anisotropic mesh adaptivity is used to focus the numerical resolution around the interfaces and other areas of important dynamics.

Phase-field-based Finite Volume Method for Simulating Thermocapillary Flows

Based on the phase-field interface-capturing scheme, a novel and common simulation strategy is put forward with the finite volume method to study the thermocapillary flows, which avoids the fourth-order derivative efficaciously and adopts the mean parameter method to preserve the convergence in the large density ratio flows. Through simulating the thermocapillary migration of bubble, the results show that the new strategy can successfully describe the performance of bubble with different density ratios, i.e. 0.1 and 0.01, and dimensionless parameters Re=1.5×10-2 and 1.5×102. When Re is 1.5×102, the bubble has an apparent deformation, and a larger migration velocity of the bubble is observed with a larger temperature gradient along the surface.