Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes

2011 ◽  
Author(s):  
Hua Shan ◽  
Sung-Eun Kim
Keyword(s):  
Free Surface ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Unstructured Meshes ◽  
Higher Order ◽  
Numerical Dispersion ◽  
Numerical Dissipation ◽  
Interface Capturing ◽  
Advection Schemes

In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fraction. In this case, the numerical dissipation of the advection scheme smears the sharp interface and the numerical dispersion causes unphysical oscillations near the interface. Utilizing the guidance of boundedness criteria, many limited higher-order non-liner advection schemes have been developed in an attempt to balance numerical dissipation and dispersion. Though it is well-known that these non-linear advection schemes can lead to solutions combining boundednesss and accuracy, users are often overwhelmed by the wide variety of available schemes. Also, these schemes are developed with the assumption of a uniform Cartesian-type mesh. Thus, a thorough investigation and comparison of the performance of these interface-capturing advection schemes are necessary, especially for naval hydrodynamics problems solved on unstructured meshes. In this study, a systematic comparison and evaluation of several existing and new bounded, higher-order advection schemes has been conducted within the framework of NavyFOAM, which is developed based on OpenFOAM — an object orientated C++ toolbox for the customization and extension of numerical solvers for continuum mechanics problems, including CFD, where the governing equations are discretized using the cell-centered finite volume method on unstructured mesh. The flexible infrastructure of the code enables us to implement and test the selected advection schemes very quickly. The test cases include advection of hollow cylinders, Zalesak’s rotating slotted disk, traveling solitary wave, dam breaking problem.

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

An Improved High-Resolution Discretization Scheme for Volume-of-Fluid CFD Simulations

2007 ◽  
Author(s):  
D. Keith Walters ◽  
Nicole M. Wolgemuth
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Volume Fraction ◽  
Phase Interface ◽  
Volume Of Fluid ◽  
Volume Control ◽  
Test Cases ◽  
Discretization Scheme ◽  
Spatial Discretization ◽  
Interface Capturing

A new high-resolution spatial discretization scheme for use with the interface capturing volume-of-fluid (VOF) method is presented and applied to several test cases. The new scheme is shown to preserve the volume fraction discontinuity within a single computational control volume (CV), without the need to explicitly reconstruct the interface within CVs near the interface. The method is based on maximization of the volume fraction gradient in the region of the interface, while stability is preserved by maintaining net upwind biasing of the face flux prescription in each CV. In addition, the scheme employs face limiting to satisfy physical boundedness criteria at finite-volume control surfaces (faces) and prevent variable overshoot. The method has been developed for use with unstructured, anisotropic, and/or inhomogeneous meshes that are often used for simulation of geometrically complex flowfields. This paper presents the implementation of the new discretization scheme into a steady-state solver in order to isolate the spatial discretization from the time integration technique. The new scheme is validated for steady-state two-phase flow using several demonstration test cases, and is shown to preserve the phase interface almost exactly, with essentially zero dissipative or dispersive error in the volume fraction solution. Results are compared to existing 2nd order and high-resolution interface capturing (HRIC) schemes, and shown to be superior in all cases.

An Improved Anti-Diffusive VOF Method to Predict Two-Fluid Free Surface Flows

2011 ◽  
Author(s):  
Y. G. Chen ◽  
W. G. Price ◽  
P. Temarel
Keyword(s):  
Free Surface ◽  
Diffusion Processes ◽  
Volume Fraction ◽  
Volume Of Fluid ◽  
Free Surface Flows ◽  
Vof Method ◽  
Advection Equation ◽  
Diffusion Term ◽  
Surface Flows ◽  
Two Fluid

This investigation continues the development of an anti-diffusive volume of fluid method [1] by improving accuracy through the addition of an artificial diffusion term, with a negative diffusion coefficient, to the original advection equation describing the evolution of the fluid volume fraction. The advection and diffusion processes are split into a set of two partial differential equations (PDEs). The improved anti-diffusive Volume of Fluid (VOF) method is coupled with a two-fluid flow solver to predict free surface flows and illustrated by examples given in two-dimensional flows. The first numerical example is a solitary wave travelling in a tank. The second example is a plunging wave generated by flow over a submerged obstacle of prescribed shape on a horizontal floor. The computational results are validated against available experimental data.

Application of High-Resolution Spatial Discretization Schemes to Volume-of-Fluid Simulations on Three-Dimensional Unstructured Meshes

2007 ◽  
Author(s):  
D. Keith Walters
Keyword(s):  
High Resolution ◽  
Volume Fraction ◽  
Phase Interface ◽  
Three Dimensional ◽  
Volume Of Fluid ◽  
Unstructured Meshes ◽  
Spatial Discretization ◽  
Upwind Schemes ◽  
Discretization Schemes ◽  
Control Volumes

The interface capturing approach to volume-of-fluid (VOF) simulation relies on high-resolution spatial discretization of the volume fraction equation, without explicit reconstruction of the phase interface within computational control volumes. One advantage of this approach is that it may be applied on general topology meshes in a straightforward manner. This paper investigates the performance of two different high-resolution discretization schemes used for the solution of the volume fraction equation on three-dimensional unstructured meshes. The schemes are used to obtain results for several simple test problems, including convection of a round and a square phase profile in a uniform fluid stream, two-phase oil and water flow in an inclined channel, and convection of a round jet-in-crossflow. The performance of the two schemes is compared in terms of their ability to minimize the effects of numerical dissipation, which tends to “smear” the phase interface over several computational control volumes. It is shown that a recently proposed scheme that relies on maximization of the volume fraction gradient in the region of the interface yields substantially better results than a more commonly used NVD (normalized variable diagram) based scheme, as well as traditional first and second-order upwind schemes.

Numerical Study of Surface Tension Effect on the Hydrodynamic Modeling of the Partially Submerged Propeller's Blade Section

2016 ◽  
Vol 32 (5) ◽  
pp. 653-664 ◽  
Author(s):  
E. Yari ◽  
H. Ghassemi
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Volume Fraction ◽  
Numerical Study ◽  
Suction Side ◽  
Navier Stokes ◽  
Surface Tension Effect ◽  
Pressure Distributions ◽  
Blade Section ◽  
The Impact

AbstractThis article is presented the surface tension effect on the two-dimensional blade section of the partially submerged propeller (PSP). In this regard, blade is entered to the water that causes to splash the water due to the impact and free surface. Also, because of the blade's angle of attack suction side is vented by air and pressure side is wetted and gripped the water to generate thrust. The Reynolds-Averaged Navier-Stokes (RANS) method is used in order to predict the hydrodynamic flow from entering to the exit. Present paper is numerically investigated the effect of free surface and surface tension i.e. related to the Weber number. So, many numerical results are presented and discussed that are included volume fraction, ventilation zones, pressure distributions, vertical and horizontal forces at various Weber numbers.

The Direct Numerical Simulation of the Rising Gas Bubble With the Volume of Fluid (VOF) Method

2011 ◽  
Author(s):  
Shuji Hironaka ◽  
Saki Manabe ◽  
Yuki Fujisawa ◽  
Gen Inoue ◽  
Yosuke Matsukuma ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Volume Fraction ◽  
Fluid Model ◽  
Volume Of Fluid ◽  
Vof Method ◽  
Phase Flow ◽  
Actual Behavior ◽  
Simulation Code ◽  
Advantages And Disadvantages

A gas-liquid two phase flow is complicated and it has not been understood well thus far, in spite of extensive investigation. Numerical simulation is a potential approach to understand this phenomenon. Although a number of studies have been conducted to understand the behavior of bubbles on the basis of computational fluid dynamics (CFD), it is difficult to completely simulate a complicated three-phase flow, including coalescence and breakup of bubbles. Although the two-fluid model based on the semi-empirical model can well estimate the actual behavior of the system in which the equations are derived, the estimation over the applicable region of equations does not always agree with the actual result. Since the 1960s, various procedures have been proposed to directly track the free surface between two phases, for example, the adaptive mesh method and the particle method. Although each of these methods has certain advantages and disadvantages, the volume of fluid (VOF) method is the most acceptable method for capturing the free surface accurately and clearly. However, a concern related to this method is the maintenance of a constant volume of the fluid. In this study, a simulation code using the VOF method is developed in order to estimate the behavior of bubbles in a vertical pipe. Further, an offset of the volume fraction is introduced to stably calculate and minimize the volume fluctuation. The effect of the surface tension is also built into the program in order to estimate the behavior of the bubbles rising through the liquid medium. The simulations of the collapsed water column and a single rising bubble are conducted with the proposed simulation code. Consequently, we confirm that these results fairly agree with the experimental ones.

A Parametric Numerical Study of Radiative Transfer in Thermotropic Materials

2013 ◽  
Author(s):  
Adam C. Gladen ◽  
Susan C. Mantell ◽  
Jane H. Davidson
Keyword(s):  
Particle Size ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Parametric Study ◽  
Volume Fraction ◽  
Numerical Study ◽  
Anisotropic Scattering ◽  
Index Of Refraction ◽  
Spherical Particles ◽  
Size Parameter

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

Evaluation of Scalar Advection Schemes in the Advanced Research WRF Model Using Large-Eddy Simulations of Aerosol–Cloud Interactions

2009 ◽  
Vol 137 (8) ◽  
pp. 2547-2558 ◽  
Author(s):  
Hailong Wang ◽  
William C. Skamarock ◽  
Graham Feingold
Keyword(s):  
Large Eddy Simulations ◽  
Numerical Dispersion ◽  
Integration Scheme ◽  
Cloud Albedo ◽  
Flux Limiter ◽  
Aerosol Cloud ◽  
Advection Schemes ◽  
Large Eddy ◽  
Runge Kutta ◽  
Aerosol Cloud Interactions

Abstract In the Advanced Research Weather Research and Forecasting Model (ARW), versions 3.0 and earlier, advection of scalars was performed using the Runge–Kutta time-integration scheme with an option of using a positive-definite (PD) flux limiter. Large-eddy simulations of aerosol–cloud interactions using the ARW model are performed to evaluate the advection schemes. The basic Runge–Kutta scheme alone produces spurious oscillations and negative values in scalar mixing ratios because of numerical dispersion errors. The PD flux limiter assures positive definiteness but retains the oscillations with an amplification of local maxima by up to 20% in the tests. These numerical dispersion errors contaminate active scalars directly through the advection process and indirectly through physical and dynamical feedbacks, leading to a misrepresentation of cloud physical and dynamical processes. A monotonic flux limiter is introduced to correct the generally accurate but dispersive solutions given by high-order Runge–Kutta scheme. The monotonic limiter effectively minimizes the dispersion errors with little significant enhancement of numerical diffusion errors. The improvement in scalar advection using the monotonic limiter is discussed in the context of how the different advection schemes impact the quantification of aerosol–cloud interactions. The PD limiter results in 20% (10%) fewer cloud droplets and 22% (5%) smaller cloud albedo than the monotonic limiter under clean (polluted) conditions. Underprediction of cloud droplet number concentration by the PD limiter tends to trigger the early formation of precipitation in the clean case, leading to a potentially large impact on cloud albedo change.

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