Piecewise Linear Interface Calculation Research Articles

On polytope intersection by half-spaces and hyperplanes for unsplit geometric volume of fluid methods on arbitrary grids

Several tools with improved accuracy and computational efficiency, along with added capabilities, are presented for performing analytic and geometric operations involving intersections between half-spaces or hyperplanes and 2- or 3-polytopes (polygons or polyhedra, either convex or non-convex) that typically arise in advanced volume of fluid (VOF) methods on arbitrary grids. In particular, tools for the intersection between a polyhedron and a half-space, and for the computation of the interface position to cut off a given area/volume fraction from an arbitrary polygonal/polyhedral grid cell in PLIC (piecewise linear interface calculation) reconstruction have been improved in terms of accuracy and computational efficiency. In addition, specific tools are also proposed for (1) the intersection in 3D between a planar polygon and a half-space, and the computation of the resulting intersected area, which can be useful for unsplit methods based on wetted-area time-integration advection (WATIA) schemes, and for (2) the efficient computation of the geometric center of the set of clipped vertices and volume resulting from the intersection between an arbitrary polyhedron and a half-space, which can be useful for, respectively, several PLIC reconstruction methods and unsplit methods based on fluid-volume intersection advection (FVIA) schemes. Finally, a convenient strategy to perform the recursive intersections required during the advection step in advanced geometric VOF methods based on FVIA schemes is also proposed. To assess the performance and accuracy of the proposed tools, different tests were carried out for several convex and non-convex polytopes. Speedups of ×5 and improvements in accuracy of up to 5 orders of magnitude over previous tools have been achieved for certain geometries and operations. The proposed tools have been included in two advection methods (an FVIA method and a new WATIA method proposed in this work) and in a PLIC reconstruction method to demonstrate their improved performance and capabilities on structured and unstructured grids.

Development of a modified thermal phase change model based on the interfacial area concentration determined by an interface reconstruction algorithm

In order to enhance the physical basis of the mass transfer model in numerical simulation of gas-liquid direct contact condensation and improve the fidelity, a set of methods and models are developed. Based on the concept of the piecewise-linear interface calculation (PLIC), an interface reconstruction algorithm is proposed to calculate the interfacial area concentration in three-dimensional non-orthogonal structured grids. The actual interface in the cell is replaced by a plane, whose position is determined iteratively to satisfy the local volume fraction and orientation of the actual interface. The area of the polygonal cut by the plane is taken as the interfacial area in the cell. The proposed algorithm is validated by calculating the surface area of a series of basic geometries. Obvious superiority of the proposed algorithm over the traditional models (gradient model and algebraic model) is seen. Then, the reconstructed area is used to determine the interfacial area concentration in the thermal phase change model. The process is implemented by ANSYS Fluent user-defined functions. The Stefan problem and steam bubble condensation experiment are used to test the performance of the developed methods and models. The simulation results agree well with the theoretical and experimental results with the quantitative relative errors no more than 4.3 % and 15 %, respectively. The oxygen jets condensation experiments are also used as test cases. The primary dominant frequencies predicted by the simulations are 163.01 Hz and 131.65 Hz, which agree well with the 139.72 Hz and 125.75 Hz in the experiments. The relative errors are only 17 % and 4.7 %. The unstable flow pattern of oxygen jet in liquid oxygen crossflow is explained based on the dynamic characteristics of turbulence, heat and mass transfer. The periodic variation of mass transfer rate is considered as the cause of condensation oscillation. The method for calculating the interfacial area proposed in this paper can serve as an optional and practical improvement to the numerical simulation of direct contact condensation.

A circle-based interface reconstruction algorithm based on the coupled volume-of-fluid and level set method

The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method.

An efficient bilinear interface reconstruction algorithm and consistent multidimensional unsplit advection scheme for accurate capturing of highly-curved interfacial shapes on structured grids

A new bilinear interface reconstruction algorithm (BLIC) is presented to capture highly-curved interfaces more accurately on structured grids without a significant increase in computational costs compared to the standard piecewise linear interface calculation (PLIC) methods. The new reconstruction algorithm uses the initial PLIC segment and improves continuity of the interface using an averaging method. A curvature-weighted method improves the repositioning of the linear segments.A new unsplit donating quadrant advection (DQA) scheme is introduced that is conservative and can create consistency with the momentum flux for two-phase flow models with a staggered MAC arrangement of variables within a grid cell. The consistent discretization of the fluxes prevents spurious interface velocities, negative densities, and instabilities. Standard 2D test cases and benchmarks demonstrate the performance of the BLIC and the DQA scheme, showing high accuracy and low costs compared to other available methods.

A volume of fluid method for three dimensional direct numerical simulations of immiscible droplet collisions

This paper presents an advanced Volume of Fluid (VOF) method that enables performant three dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g., binary droplet collisions. One of the challenges associated with the introduction of a third immiscible phase into the VOF method is the reconstruction of the phase boundaries near the triple line in arbitrary arrangements. For this purpose, an efficient method based on a Piecewise Linear Interface Calculation (PLIC) is shown. Moreover, the surface force modeling with the robust Continuous Surface Stress (CSS) model was enhanced to treat such three-phase situations with large topology changes and thin films. A consistent scaling of the fluid properties at the interfaces ensures energy conservation.The implementation of these methods in the multi-phase flow solver Free Surface 3D (FS3D) allowed a successful validation. A qualitative comparison of the morphology in binary collisions of immiscible droplets as well as a quantitative comparison regarding the threshold velocities that distinguish different collision regimes shows excellent agreement with experimental results.These simulations enable the evaluation of experimentally inaccessible data like the contributions of kinetic, surface and dissipative energy of both immiscible liquids during the collision process. Furthermore, the comparison against binary collisions of the same liquids highlights similarities and differences between immiscible and equal droplet collisions. Both can support the modeling of the immiscible liquid interaction in the future.

Validation of HiG-Flow Software for Simulating Two-Phase Flows with a 3D Geometric Volume of Fluid Algorithm

This study reports the development of a numerical method to simulate two-phase flows of Newtonian fluids that are incompressible, immiscible, and isothermal. The interface in the simulation is located and reconstructed using the geometric volume of fluid (VOF) method. The implementation of the piecewise-linear interface calculation (PLIC) scheme of the VOF method is performed to solve the three-dimensional (3D) interface transport during the dynamics of two-phase flows. In this method, the interface is approximated by a line segment in each interfacial cell. The balance of forces at the interface is accounted for using the continuum interfacial force (CSF) model. To solve the Navier–Stokes equations, meshless finite difference schemes from the HiG-Flow computational fluid dynamics software are employed. The 3D PLIC-VOF HiG-Flow algorithm is used to simulate several benchmark two-phase flows for the purpose of validating the numerical implementation. First, the performance of the PLIC implementation is evaluated by conducting two standard advection numerical tests: the 3D shearing flow test and the 3D deforming field test. Good agreement is obtained for the 3D interface shape using both the 3D PLIC-VOF HiG-Flow algorithm and those found in the scientific literature, specifically, the piecewise-constant flux surface calculation, the volume of fluid method implemented in OpenFOAM, and the high-order finite-element software FEEL. In addition, the absolute error of the volume tracking advection calculation obtained by our 3D PLIC-VOF HiG-Flow algorithm is found to be smaller than the one found in the scientific literature for both the 3D shearing and 3D deforming flow tests. The volume fraction conservation absolute errors obtained using our algorithm are 4.48×10−5 and 9.41×10−6 for both shearing and deforming flow tests, respectively, being two orders lower than the results presented in the scientific literature at the same level of mesh refinement. Lastly, the 3D bubble rising problem is simulated for different fluid densities (ρ1/ρ2=10 and ρ1/ρ2=1000) and viscosity ratios (μ1/μ2=10 and μ1/μ2=100). Again, good agreement is obtained for the 3D interface shape using both the newly implemented algorithm and OpenFOAM, DROPS, and NaSt3D software. The 3D PLIC-VOF HiG-Flow algorithm predicted a stable ellipsoidal droplet shape for ρ1/ρ2=10 and μ1/μ2=10, and a stable cap shape for ρ1/ρ2=1000 and μ1/μ2=100. The bubble’s rise velocity and evolution of the bubble’s center of mass are also computed with the 3D PLIC-VOF HiG-Flow algorithm and found to be in agreement with those software. The rise velocity of the droplet for both the ellipsoidal and cap flow regime’s is found, in the initial stages of the simulation, to gradually increase from its initial value of zero to a maximum magnitude; then, the steady-state velocity of the droplet decreases, being more accentuated for the cap regime.

Efficient sequential PLIC interface positioning for enhanced performance of the three-phase VoF method

This paper presents an efficient algorithm for the sequential positioning, also called nested dissection, of two planes in an arbitrary polyhedron. Two planar interfaces are positioned such that the first plane truncates a given volume from this arbitrary polyhedron and the next plane truncates a second given volume from the residual polyhedron. This is a relevant task in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid (VoF) method (Hirt and Nichols, 1981) with a Piecewise Linear Interface Calculation (PLIC) (Youngs, 1982). An efficient algorithm for this task significantly speeds up the three-phase PLIC algorithm. The present study describes a method based on a recursive application of the Gaussian divergence theorem, where the fact that the truncated polyhedron shares multiple faces with the original polyhedron can be exploited to reduce the computational effort. A careful choice of the coordinate system origin for the volume computation allows for successive positioning of two planes without reestablishing polyhedron connectivity. Combined with a highly efficient root finding, this results in a significant performance gain in the reconstruction of the three-phase interface configurations.The performance of the new method is assessed in a series of carefully designed numerical experiments. Compared to a conventional decomposition-based approach, the number of iterations and, thus, of the required truncations was reduced by up to an order of magnitude. The PLIC positioning run-time was reduced by about 90% in our reference implementation. Integrated into the multi-phase flow solver Free Surface 3D (FS3D), an overall performance gain of about 20% was achieved. The reference implementation of the efficient sequential PLIC positioning is available as a Fortran module at https://doi.org/10.18419/darus-2488. Allowing for simple integration into existing numerical schemes, the proposed algorithm is self-contained, requiring no external decomposition libraries.

Numerical Investigation on Effect of Bubbles Arrangement and Volume Fraction on Apparent Viscosity of Bubbly Suspensions

Background:: Bubbly suspensions can be often run into in natural and industrial processes. The addition of bubbles with different sizes can lead to a significant change in the rheological properties of a matrix liquid. It is extremely significant to fully understand the rheological properties of bubbly suspensions for improving process efficiencies and optimizing productive processes. background: Bubbly suspensions can be often run into in natural and industrial processes. The addition of bubbles of different sizes can greatly change the rheological properties of matrix liquid. It is extremely significant to fully understand the rheological properties of bubbly suspensions for improving process efficiencies and optimizing productive processes. Objective:: The objective of this study is to explore qualitatively the physical law and internal mechanism of the apparent viscosity of suspensions formed by a Newtonian liquid containing different bubbles. Methods:: Based on the parallel plate model of shear flow, the volume of fluid method (VOF) was used to investigate the effect of bubble arrangement and volume fraction on the apparent viscosity of bubbly suspensions at low volume fractions. The piecewise linear interface calculation (PLIC) method was applied to reconstruct the interface based on the phase function. Results:: The present results show that the relative viscosity (ηr) of bubbly suspensions shows a nonlinear change with an increase in bubble volume fraction (ϕ). When the capillary number (Ca) is less than 0.6, ηr shows a nonlinear increase with an increase in ϕ (ηr increases from 1 to 1.03 with an increase in ϕ from 0 to 2.94% at Ca=0.1). However, Ca is greater than or equal to 0.6, ηr shows a nonlinear decrease with an increase in ϕ (ηr decreases from 1 to 0.92 with an increase in ϕ from 0 to 2.94% at Ca=2.5). Even if ϕ is the same, different arrangements of bubbles can lead to different magnitudes of apparent viscosity of bubbly suspensions Conclusion:: As ϕ increases, the region of low shear rate increases, which leads to a non−linear decrease in the relative viscosity. When ϕ is the same, the different arrangements of bubbles can lead to different effects on bubble dynamics and flow fields. This results in different viscous dissipation in bubbly suspensions. Thus, the apparent viscosity of bubbly suspensions is different. other: Nothing

Numerical investigation on the water entry of curved wedge-shaped sections into waves

The water entry of structures with curved boundaries into waves can be frequently observed in actual operations as they are often exposed to harsh wave conditions. To investigate the problem, a numerical model which can simulate the water entry of complex objects into waves is developed in this paper. Under the framework of Cartesian grid, Volume of Fluid method combined with Piecewise Linear Interface Calculation (VOF-PLIC) are used to capture free surface. In addition, Volume of Solid Based Immersed Boundary Method (VOS-IB) is adopted to treat the body condition. Relaxation zones are applied to generate and absorb waves. After a careful validation, five curvatures and three entry locations are selected to investigate the influences of curvature and entry locations on slamming characteristics. Discoveries can be generally summarized as follows: 1) The arriving moment of force peak is not sensitive to the entry location, but is sensitive to the shape of curvatures because of its significant influence on flow separation. 2) The magnitude of force peak is always the smallest at wave peak, followed by calm water and wave trough, regardless of the shape of curvature. 3) The relative magnitude of the pressure on the left and right sides of body surface is influenced not only by the curvature but also by the entry location, and it changes during the water entry process. 4) Sequence of flow separation on the left and right sides of the body is determined by entry location, not by the curvature.

A mesoscopic model of mechanical erosion for the characterization of ablation behavior of C/C woven composites

Carbon/carbon (C/C) composites suffer from the thermochemical ablation and mechanical erosion in the thermal protection system. A mathematical model describing the reaction/diffusion problem for the thermochemical ablation of C/C composites is established and numerically solved on the basis of the finite volume method and piecewise linear interface calculation. Then, a mesoscopic model including a failure criterion for the simulation of mechanical erosion of C/C woven composites is proposed. In the mesoscopic model of mechanical erosion, the mechanical erosion mechanism of C/C woven composites on the microscale is analyzed, and the mechanical erosion criterion of C/C woven composites from 2D plain woven structure is extended to 2.5D woven structure. The ablation performances of woven structures under thermochemical ablation with and without mechanical erosion criterion are compared, and the effects of weaving structure features on the ablation performances of 2.5D woven structure under simulated mechanical erosion are investigated. It shows that the mesoscopic model of mechanical erosion can well characterize the ablation behavior of C/C woven composites with different weaving forms. Some suggestions are provided for the design of C/C woven composites in the thermal protection system.

Influence of the free surface reconstruction on the spatial laser energy distribution in high power laser beam welding modeling

An accurate and efficient description of the spatial distribution of laser energy is a crucial factor for the modeling of laser material processing, e.g., laser welding, laser cutting, or laser-based additive manufacturing. In this study, a 3D heat transfer and fluid flow model coupled with the volume-of-fluid algorithm for free surface tracking is developed for the simulation of molten pool dynamics in high-power laser beam welding. The underlying laser-material interactions, i.e., the multiple reflections and Fresnel absorption, are considered by a ray-tracing method. Two strategies of free surface reconstruction used in the ray-tracing method are investigated: a typical piecewise linear interface calculation (PLIC)-based method and a novel localized level-set method. The PLIC-based method is discrete, resulting in non-continuous free surface reconstruction. In the localized level-set method, a continuous free surface is reconstructed, and, thus, the exact reflection points can be determined. The calculated spatial laser energy distribution and the corresponding molten pool dynamics from the two methods are analyzed and compared. The obtained numerical results are evaluated with experimental measurements to assure the validity of the proposed model. It is found that distinct patterns of the beam multiple reflections are obtained with the different free surface reconstructions, which shows significant influence not only on the molten pool behaviors but also on the localized keyhole dynamics.

Investigation of droplet grouping in monodisperse streams by direct numerical simulations

Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by direct numerical simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code framework is based on the volume-of-fluid method and uses the piecewise linear interface calculation method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that, on the one hand, large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. On the other hand, higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500, affecting the next pair of droplets, even for larger separation distances.

Estimation radius regression in PLIC-VOF method for droplet evaporation

Heat & fluid flow conservation equations of carburant liquid droplet are solved by a semi-implicit method of the Volume Of Fluid ( VOF ) scheme. A new technique of the droplet radius regression estimation based on the Piece-wise Linear Interface Calculation ( PLIC ) is developed. Numerical computation is performed for stagnant carburant droplets in evaporation in natural convection (which takes into consideration the buoyancy forces) and in an air atmosphere at a pressure of 1 bar. The results are presented in the form of radius, area and mass regressions, volumetric mass flow, liquid temperature, surface temperature, and vapor temperature evolutions by taking into account the influence of the ambient temperature, the initial radius, and the component variations. Using the time evolution of the color function, our radius regression estimation technique is related to the instant detection of the liquid volume fraction. This regression is not affected by the changing of the droplet’s shape nor the temperature collecting and synchronization with the method for the evaporation analysis.

Air injection in vertical water column: Experimental test and numerical simulation using volume of fluid and two-fluid methods

• VOF model was used to reproduce the interaction of two fluids in an experiment. • Eulerian model was used to reproduce the interaction of two fluids in an experiment. • Comparisons of numerical results using VOF and Eulerian model were made. • Results of different models based on VOF were compared with the traditional VOF. • The effect of turbulence was studied with different RANS turbulence models. A novel test consisting on fast air injection into a vertical water column was experimentally and numerically studied. Measurements were focused on capturing the air–water interface as well as the volume of water evicted by the air, for a wide range of air flow rates. The numerical simulations, were performed with the Eulerian Two-Fluid (TF) and the Volume of Fluid (VOF) methods.For the TF method three topologies were considered: bubbly flow, dropUNR Universidad Nacional de Rosario flow, and blending. The last is a more smart methodology to automatically handle with the different flow regimes. For the VOF method, the standar VOF (SVOF), the Adaptive Mesh Refinement (AMR), and the high order Piecewise Linear Interface Calculation (PLIC) methods were assessed. SVOF and TF blending methods were choice to study the mesh convergence and turbulence modeling. Two-dimensional (2D) meshes of 2, 1 and 0.5 mm, and three-dimensional (3D) meshes of 2, 1 and 0.75 mm were considered. In all cases the standard VOF (SVOF) formulation showed mesh convergence and good agreement with experiments. The error for the finest 3D mesh was around 1 % , but increased up to 20% for the finest 2D mesh. On the other hand, for the TF method mesh convergence was only evidenced for the 2D meshes. Regard the TF method, the bubbly and drop topology cases led to unacceptable solutions both in terms of inteface capturing as well as liquid evicted. On the other hand, the blending methodology clearly improved the estimations, although the interface was only partially captured because of the numerical diffusion. On the other hand, all the VOF methods were in relative good agreement both in terms of the liquid evicted as well as interface capturing. Errors were were reduced by refining the mesh. The initial swelling, with small bubbles and large slugs around the air injector was well captured, and the ligaments and drops spilled for high air flow rates were quite well estimated. The SVOF method showed low computational cost for coarse grids, but the computing time increased more than linearly with the mesh size. The AMR method showed accurate solutions, but the computing cost was largely increased with the refining level. Finally, the use of PLIC method for the coarser mesh reduced the error from 15% (SVOF) to 3.5% keeping low the computing cost.

GVOF: An open-source package for unsplit geometric volume of fluid methods on arbitrary grids

The gVOF package implements several accurate and efficient geometric volume of fluid (VOF) methods on arbitrary grids, either structured or unstructured with convex or non-convex cells, based on multidimensional unsplit advection and piecewise linear interface calculation (PLIC) schemes, with the purpose of facilitating and extending the use of advanced unsplit geometric VOF methods in new or existing computational fluid dynamics codes. The package includes a complete and self-contained set of routines for VOF initialization, interface reconstruction and fluid advection, and uses as external libraries a set of publicly available in-house tools to perform several analytical and geometrical operations. These operations may involve handling of high-complex non-convex flux polyhedra, even with self-intersecting faces, which are robustly and efficiently treated in this work without the need of costly techniques based on convex decomposition. Results for the accuracy, computational efficiency, and volume (local and global) conservation properties of different combinations of the implemented advection and reconstruction methods are presented for several numerical tests on structured and unstructured grids. An extensive comparison with results obtained by other authors using advanced geometric VOF methods shows the outstanding performance of the gVOF package in terms of efficiency and accuracy. To demonstrate the performance of the package in solving complex two-phase flow problems, the implemented methods are combined with an existing in-house code to simulate the impact of a water drop on a free surface. Program summaryProgram Title:gVOFCPC Library link to program files:https://doi.org/10.17632/9gmn6gsb6p.1Licensing provisions: GPLv3Programming language:FORTRAN and C, with C interfacesExternal routines/libraries:VOFTools (https://doi.org/10.17632/brrgt645bh.3) and isoap (https://doi.org/10.17632/4rcf98s74c.1) librariesNature of problem: The software package includes efficient and accurate routines for volume of fluid initialization, reconstruction of interfaces and fluid advection on arbitrary grids, either structured or unstructured with convex or non-convex cells, which are used to implement advanced unsplit geometric VOF methods. In particular, the package includes a fluid volume fraction initialization method, six PLIC reconstruction methods and three multidimensional unsplit advection methods. Routines to visualize interfaces and compute reconstruction errors; tests to assess the accuracy, computational efficiency, and volume conservation of the implemented methods for the reconstruction and advection of complex interfaces on arbitrary grids; and a user manual have also been included in the supplied package.Solution method: Basically, the implemented methods, which can be used on grids with polyhedral cells of arbitrary geometry, have the following general characteristics. The methods implemented for fluid volume fraction initialization and reconstruction error calculation are based on a recursive grid refinement procedure to compute the fluid volume bounded by cell edges and an implicitly-defined fluid interface. The six implemented interface reconstruction methods are the following: a least-squares gradient interface reconstruction method; three isosurface-based interface reconstruction methods; an extension to 3D of the iterative Swartz interface reconstruction; and a least-squares fit interface reconstruction method. Three unsplit advection methods, which are based on edge-matched, face-matched and non-matched flux polyhedra and are valid for 3D arbitrary grids, are implemented. All the implemented methods can be combined by the user to solve different tests on arbitrary grids. The implemented routines can be used in FORTRAN or C. The OpenMP application programming interface is used to improve the computational efficiency.

Modeling of the bubble collapse with water jets and pressure loads using a geometrical volume of fluid based simulation method

The dynamic behavior of bubble collapses, water jets, and pressure loads during the collapse of the bubble near walls and a free surface were numerically investigated via a geometrical volume of fluid (VOF)-based simulation method. The numerical method is based on the compressible Navier–Stokes equations in a conservative form that describe the flow of compressible viscous fluids. The equations are discretized on a general curvilinear grid using an associated Godunov-type numerical scheme, and a reconstruction of a computational finite-volume Riemann solver is introduced for suppression of oscillation near the interface between fluids. The interface was tracked using the VOF reconstruction method. The VOF method is based on a geometrical tool and Lagrangian propagation of the interface reconstructed by a piecewise linear interface calculation (PLIC), resulting in strictly mass-conserving and sharp interface solutions. The numerical procedure was validated for capturing sharp interface and strong shock waves. For the simulation of bubble collapse, grid dependence studies of a spark-generated bubble were studies of both spherical and non-spherical bubbles were conducted. The results showed good agreement between the simulation and experiment of the bubble dynamics during the collapse process. Subsequently, an investigation of a single bubble near a wall with different standoff distances was performed. The pressure loads induced by the jets impacting the walls were calculated and analyzed. Furthermore, a more complex case of bubble collapse near an oblique wall and free surface was simulated. The resulting bubble dynamics with the jets and free surface shape were compared via photographs of the experiments.

Eulerian and Lagrangian transport by shallow-water breaking waves

This study examines the mass and Lagrangian transport, kinematic and dynamic characteristics of shallow-water breaking waves, focusing on the wave breaking, and jet impingement processes. A multiphase Navier–Stokes flow model has been developed to track the origin and trajectory for the jet and the splash-up using both a geometric piece-wise linear interface calculation volume-of-fluid (PLIC-VOF) and the Lagrangian particle tracking approaches. The model is first validated both quantitatively and qualitatively against the experimental data for the plunging jet and the splash-up during wave breaking, in which a good agreement is obtained. The mass transport and the origin of the jet and splash-up are studied using the new multi-component PLIC-VOF approach, and the different regions in the interior of the wave are tracked in an Eulerian way. Both horizontal and vertical drifts for the interior and surface particles are shown using the Lagrangian particles. The location and origin of the plunging jet can be clearly seen from the simulations. Various wave steepness and beach slopes have been investigated for different types of breakers. Furthermore, the detailed jet impingement, velocity, pressure, vorticity, and turbulence fields during wave breaking are discussed and presented, providing more detailed flow fields to gain further insight into the plunging jet and splash-up in shallow-water breaking waves.

On estimating the interface normal and curvature in piecewise linear interface calculation‐volume of fluid approach for three‐dimensional arbitrary meshes

AbstractVolume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC‐generated planes in comparison with the exact interface, a point‐cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3‐dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.

Numerical simulation of merging of two rising bubbles with different densities and diameters using an enhanced Volume-Of-Fluid (VOF) model

In this study, the transient evolution of two rising bubbles with different densities is investigated numerically using an enhanced version of the VOF model, aiming to establish an state-of-the-art benchmark solutions and up-to-date data set for CFD validations. The simulations are performed on the staggered grid system where a novel third‐order accurate monotone convection scheme is applied for the discretization of the convection terms in Navier-Stokes and volume fraction equations while the semi-iterative PISOC algorithm (a combined version of the classical PISO and Chorin's model) are used to solve the pressure-velocity coupling. To reduce the false diffusion errors and mitigate smearing of interface thickness in the regions of physical discontinuities, the interface compression technique is also incorporated into the transport equation. To further enhance the accuracy of the numerical solutions, the idea of Piecewise Linear Interface Calculation (PLIC) based on the ELVIRA technique (Efficient Least-square Volume-of-fluid Interface Reconstruction Algorithm) is also utilized for the interface reconstruction and accurate implementation of surface tension force. The validity and accuracy of the enhanced VOF model is further demonstrated against a series of challenging benchmark cases including draining of liquids from the storage tank (tank draining), single rising bubble, three-phase Rayleigh-Taylor Instability and dam-break flows over dry and wet beds. The comparison of the obtained results with previously published data vividly demonstrates the superiority of the proposed method over the standard VOF/Level-Set models in handling multiphase/multi-fluid flow problems with large topological changes. In the last stage, the morphology and hydrodynamic characteristics of merging of two rising bubbles with different densities and diameters are examined and analyzed in details. The results show that, the initial/final deformations and the subsequent steady-state rise of two bubbles are remarkably influenced by the diameters of leading (upper) and trailing (lower) bubbles.

A computational study of thermally induced secondary atomization in multicomponent droplets

This study presents computational simulations of multicomponent and multiphase flows to reproduce the physical phenomena in the secondary atomization of a droplet induced by a hot temperature environment. The computational fluid dynamics model is based on the geometric volume of fluid method, with piecewise linear interface calculation reconstruction for accurate determination of the curvature and evaporation fluxes at the interface. The purpose of the model was to faithfully reproduce complex physical processes, such as internal gas cavity formation, liquid–vapour interface instability, cavity collapse and liquid jet ejection, and the pinch-off of a secondary droplet, leading to the microexplosion phenomenon that greatly enhances the evaporation rate of non-volatile liquid droplets. The solver was validated against the analytical solution in benchmark cases, and experimental data with bicomponent droplets reported in the literature. The developed model was used to predict the atomization of heavy fuel oil exposed at high temperatures under microgravity conditions. Different atomization regimes were identified, depending on the initial size of the internal bubbles. While small bubbles led to simple gas ejections, cavity collapse caused the larger bubbles to produce a jet formation. When the ratio between the bubble and droplet volumes was bigger than 0.7, microexplosions occurred. The results were found to be consistent with cases of bubble burst on flat surfaces, showing a strong dependence on the Ohnesorge number ( $Oh$ ). Key observable quantities, particularly jet velocity and bubble cap drainage velocity, were found to agree with correlations reported in other studies. The similarities were also supported by studies extending over a wide range of simulations (4000 cases) at different $Oh$ . An inversion in the dependence of the jet velocity on $Oh$ (above a critical value $Oh_c$ ) was observed.