Piecewise Linear Interface Calculation Method Research Articles

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.

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.

Algorithms of three-dimensional concrete ablation front tracking (CAFT) and crust growth

A 3D MCCI code, CORCAAB, has been developed to account for uncertainty factors in the long-term molten corium–concrete interaction including changes in the three-dimensional cavity contour, which affect the convective heat transfer of the molten debris and late ablation behaviors. In this work, a 3D concrete ablation front tracking algorithm was formulated using the piecewise linear interface calculation method. The ablation and crust growth rates are governed by the local heat transfer across the 1D boundary layer that consists of molten debris, crust, slag, and concrete. This combination of the 3D and 1D methods led to the energy mismatch that was shown to be small enough even under a significantly large change of the cavity contour shape; thus, the proposed algorithm is compatible with the energy conservation law of the entire MCCI code. In order to test the efficacy and restriction of the proposed ablation algorithm, a simple rectangular cavity connected with a double sump on the cavity floor was adopted. Ablation surface formations including saddle points with multiple curvatures were confirmed to be adequate. A moderate dependence on the cell size was observed in predicting the disappearance of the thin walls separating the two partitions.

A numerical model of superspreading surfactants on hydrophobic surface

Many contributions significantly on experimental and mathematical studies are made to understand the mechanism of superspreading. Only few numerical methods have been proposed which solve the system of equations with soluble and insoluble surfactants. Among them, we propose a computational fluid dynamics model, based on the volume of fluid technique, with the piecewise linear interface calculation method. Interface reconstruction is applied to simulate the time evolution of the dynamics of drop spreading of surfactants on a thin water layer. We have allowed the occurrence of both the regimes relating to a series of trisiloxane (M(D′EnOH)M), sodium dodecyl sulphate, and Tergitol NP10 surfactants drop on a thin water layer with the influence of Marangoni stress. The numerical data seem consistent with those experimental for both regimes. It validates predictions for the spreading exponent in which the law of the radius of the circular area covered by the surfactant grows as tα, where 0 < α < 1. The comparison of the numerical and experimental predictions by Lee et al. [“Spreading of trisiloxanes over thin aqueous layers,” Colloid J. 71, 365–369 (2009)] is well represented in both regimes. The numerical study confirms that the spreading rates during the first stage increase as the solubility increases. This finding suggests that the model is adequate for describing the spreading of surfactants on thin fluid layers.

A comparison between the surface compression method and an interface reconstruction method for the VOF approach

In direct numerical simulations of multiphase flows, based on the Volume of Fluid (VOF) approach, the advection of the volume fraction field is a crucial point. The choice of the discretisation scheme for the transport of the volume fraction is decisive for an accurate description of surface dynamics. In this paper we assess two numerical methods: a high order discretisation scheme, namely the surface compression scheme, and an interface reconstruction scheme based on a piecewise linear interface calculation (PLIC). We compare accuracy, convergence rate and computational cost of these methods with results from literature. The comparative study includes reference 2D and 3D advection test cases. Moreover, the advection algorithm is tested coupled to an incompressible Navier–Stokes solver and used to simulate a rising bubble in a liquid for different Eötvös and Reynolds numbers. We establish via the advection tests and through the study of rising bubbles that the PLIC method converges to second order while the compression method fails to converge systematically. The computational overhead of both methods is negligible compared to an incompressible flow solver to which it might be coupled.

A simple volume-of-fluid reconstruction method for three-dimensional two-phase flows

A new PLIC (piecewise linear interface calculation)-type VOF (volume of fluid) method, called APPLIC (approximated PLIC) method, is presented. Although the PLIC method is one of the most accurate VOF methods, the three-dimensional algorithm is complex. Accordingly, it is hard to develop and maintain the computational code. The APPLIC method reduces the complexity using simple approximation formulae. Three numerical tests were performed to compare the accuracy of the SVOF (simplified volume of fluid), VOF/WLIC (weighed line interface calculation), THINC/SW (tangent of hyperbola for interface capturing/slope weighting), THINC/WLIC, PLIC, and APPLIC methods. The results of the tests show that the APPLIC results are as accurate as the PLIC results and are more accurate than the SVOF, VOF/WLIC, THINC/SW, and THINC/WLIC results. It was demonstrated that the APPLIC method is more computationally efficient than the PLIC method.

Adaptive subdivision piecewise linear interface calculation (ASPLIC) for 2D multi‐material hydrodynamic simulation codes

SummaryIn this work, we propose an adaptive subdivision piecewise linear interface calculation (PLIC) for 2D multimaterial hydrodynamic simulation codes. Classical volume‐of‐fluid PLIC technique uses one line segment and one given normal to separate two materials. Unfortunately, these paradigms are not sufficient when filaments occur, leading to the creation of flotsam and jetsam. We propose to detect such situations and to split the computational mixed cell into reconstruction subzones. Within these subzones, one computes a so‐called subgradient using an incomplete stencil of neighbors, and the material is distributed in these subzones. Given subzone volume fraction and the subgradient, one computes one line segment using classical PLIC method, leading to a modified PLIC method for subscale material entity. The subdivision procedure relies on a splitting point, which is chosen as a specific information about the relative location of the filament in the cell, leading to an adaptive subdivision for PLIC reconstructions. Numerical tests are carried out in a 2D Lagrange + Remap multimaterial hydrodynamics Eulerian code. Static and dynamic filaments and fragments are simulated in advection or stretched in vortex‐like motion. The full hydrodynamics equations are solved on a more realistic test (shock‐bubble impact). Results show that our approach supplements classical PLIC method for situations when filaments and fragments occur. Copyright © 2014 John Wiley & Sons, Ltd.

A Piecewise Linear Interface-Capturing Volume-of-Fluid Method Based on Unstructured Grids

A piecewise linear interface calculation (PLIC) technique on triangular unstructured grids is proposed for the volume-of-fluid (VOF) method. For an interface cell, a straight line segment is set to approximate the actual interface by the gradient of the volume fraction function. Three gradient models are discussed, and the results show that the gradient model introduced from the moving particle semi-implicit method is of the highest accuracy. Mass flux is calculated in a Eulerian scheme depending on the relationship between the line segment and each boundary of the cell. It is proved that the combination of geometric and algebraic methods is most precise, because both geometric interface position and algebraic mass conservation are considered. Numerical experiments are conducted on unstructured grids generated by the traditional Delaunay triangulation method and the bubble packing method (BPM), which can produce much more regular triangular cells than the Delaunay method (see Wu and Chen, Numerical Heat Transfer B, vol. 58; pp. 343–369, 2010). Compared with Young's PLIC-VOF, our method is of satisfactory accuracy and sharpness. The deformation errors on the BPM grid are even smaller than those by the PLIC method on a structured grid. In addition, it is observed that the accuracy is higher on the unstructured grid, with better quality.

주조유동 시뮬레이션에서 자유경계면 추적 기법 비교 연구

We applied two numerical schemes to improve accuracy of the solution in the flow simulation of molten metal. One method is Piecewise Linear Interface Calculation (PLIC) method and the other is Donor-Acceptor (D-A) method. In the present work, we have tested simple problems to verify the module of the interface reconstruction algorithms. After validations, accuracy and efficiency of these two methods have compared by simulating various real products. On the numerical simulation of free surface flow, it is possible for PLIC method to track very accurately the interface between phases. PLIC method, however, has the weak point where a lot of computational time hangs, though it shows the more accurate interface reconstruction. Donor-Acceptor method has enough effectiveness in the macro observation of mold filling sequence though it shows the inferior accuracy.

Large deformation analysis of adhesive by Eulerian method with new material model

The material model to describe large deformation of a pressure sensitive adhesive (PSA) is presented. A relationship between stress and strain of PSA includes viscoelasticity and rubber-elasticity. Therefore, we propose the material model for describing viscoelasticity and rubber-elasticity, and extend the presented material model to the rate form for three dimensional finite element analysis. After proposing the material model for PSA, we formulate the Eulerian method to simulate large deformation behavior. In the Eulerian calculation, the Piecewise Linear Interface Calculation (PLIC) method for capturing material surface is employed. By using PLIC method, we can impose dynamic and kinematic boundary conditions on captured material surface. The representative two computational examples are calculated to check validity of the present methods.