Moment Of Fluid Research Articles

A Lagrangian-Eulerian advection scheme with moment-of-fluid interface reconstruction

ABSTRACTA Lagrangian–Eulerian advection scheme (LEAS) with Moment-of-Fluid (MoF) interface reconstruction is presented for interfacial flows. In MoF method, in addition to the volume fraction field, material centroid is used for interface reconstruction. Physically material centroid indicates the material location inside a mixed cell. Therefore, MoF method reconstructs linear interfaces exactly and is second order accurate for curved interfaces. Despite being second order accurate for static interface reconstruction, MoF reconstruction is inaccurate when centroid is not properly advected. An accurate centroid advection method based on Barycenter of centroid is discussed here. A comparison of this centroid advection with the pure Lagrangian advection based on Runge–Kutta integrator is demonstrated for two different advection tests. The superiority of MoF is established by comparing the volume error norm with other interface reconstructions. Significant improvement in accuracy is observed when LEAS material advection is used in conjuction with accurate centroid advection for MoF reconstruction.

Heat transfer analysis of a non-Newtonian fluid flowing through a Plate Heat Exchanger using CFD

In this work, the moment and heat transfers of a non-Newtonian fluid flowing in steady laminar regime through a plate heat exchanger at constant wall temperature is studied using CFD. Single-pass U-type plate heat exchangers with multiple flat plates with and without baffles are used. The effect of plates' number and distance between plates on the heat transfer and the pressure drop are investigated. An empirical correlation for the friction factor as a function of the generalized Reynolds number and the ratio between the friction characteristic length and the flow trajectory length is developed. It is found that the dependence of the Nusselt number on the Peclet number can be described by the modified Sieder–Tate equation. Although the flow pattern is highly complex, under an adequate definition of the characteristics parameters, it is possible to establish simple correlations between the dimensionless numbers that characterize the thermal-hydraulic behavior of plate heat exchangers.

Heat transfer analysis of a non-Newtonian fluid flowing through a circular tube with twisted tape inserts

In this paper, the moment and heat transfers of a non-Newtonian fluid flowing in steady laminar regime through a circular tube with a twisted tape at constant wall temperature is studied using CFD. The effect of different twist ratios of the tape on the convective heat transfer and the pressure drop are investigated over the Reynolds number range of 0.2–600. It was found that a twisted tape induces a swirling flow, which increases the velocity gradient at the tube wall and consequently generates an enhancement in heat transfer. Data reduction is applied to CFD data; and it is found a good agreement between the calculated Reynolds and Fanning friction numbers and the theoretical relationship (f = 16/Re). A novel formulation for evaluating the thermo-hydraulic performance was developed. The results indicate that the thermo-hydraulic performance increases when the twist ratio decreases and the Reynolds number increases.

MMALE numerical simulation for multi-material large deformation fluid flows

Multi-material arbitrary Lagrangian Eulerian (MMALE) method, coupled with moment of fluid (MOF) interface reconstruction, was studied and applied to multi-material large deformation flow problems. In MMALE method, the mesh lines are allowed to cross the material interfaces and mixed cells are introduced. In mixed cells, the MOF method is used to reconstruct the interfaces. The numerical examples show the high accuracy and resolution of MOF-MMALE, it is validated that MOF-MMALE method is an effective way to simulate flow problems of multi-material large deformation.

Oxygen Bubble Nucleation Modeling in a PEM Electrolyzer Electrode

The polymer electrolyte membrane (PEM) electrolyzer is a promising technology that reduces water into hydrogen and oxygen, from which the hydrogen is captured and stored for use in fuel cells. One of the challenging issues in PEM electrolyzers is flow inhibition of liquid water within the porous gas diffusion layer (GDL), due to the formation of oxygen bubbles (1). The bubbles block pores within the GDL, limiting the transport of liquid water to the catalyst layer, which in turn negatively affects the electrolyzer performance (2). Moreover, the presence of the oxygen bubbles can increase the solution resistance, inhibit electron transfer, and consequently increase ohmic losses, leading to efficiency reduction (1).Investigation of the oxygen bubbles behavior generated at the anode side of the PEM electrolyzer in operational pressure and temperature can give us a more accurate insight for predicting its influence on the performance. A number of promising studies on bubble nucleation and detachment have been done over the past few years. Various numerical techniques were introduced and improved to increase the accuracy of the bubble interface tracking such as volume-of-fluid (VOF) (3), moment-of-fluid (MOF) (4), and level-set (LS) methods (5).In this study, a numerical simulation has been performed to mimic the nucleation, growth and detachment of the oxygen bubbles in electrolyzers. Utilizing a state-of-the-art multiphase algorithm (6), a three-dimensional, two-phase computational algorithm was developed using the LS method to track the oxygen bubble interface expansion. To simulate the multiphase system more precisely, the thermodynamic free energy of the system has been taken into account by employing the Gibbs free energy function. The behavior of the oxygen bubble through the GDL as a function of the geometrical properties of the GDL was then studied and compared to the experimental results presented by Arbabi et al. (7). Acknowledgements The authors would like to gratefully acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).

A Multi-Material CCALE-MOF Approach in Cylindrical Geometry

AbstractIn this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multi-material compressible fluid flows on unstructured grids in cylindrical geometries. Especially, our attention is focused here on the following points. First, we propose a new formulation of the scheme used during the Lagrangian phase in the particular case of axisymmetric geometries. Then, the MOF method is considered for multi-interface reconstruction in cylindrical geometry. Subsequently, a method devoted to the rezoning of polar meshes is detailed. Finally, a generalization of the hybrid remapping to cylindrical geometries is presented. These explorations are validated by mean of several test cases using unstructured grid that clearly illustrate the robustness and accuracy of the new method.

The Symmetric Moment-of-Fluid interface reconstruction algorithm

The Symmetric Moment-of-Fluid (MoF) interface reconstruction algorithm is proposed. This new scheme modifies the existing MoF scheme to operate in a pairwise manner, utilising both the moment of the material being extracted, and the moment of the materials remaining. The Symmetric MoF scheme is shown, via a number of two- and three-material test cases, to deal with errors in the reference moment data with greater accuracy and robustness. Furthermore, due to the symmetric nature of the scheme, gains in computational efficiency over the existing MoF scheme are seen.

An effective integration of methods for second-order three-dimensional multi-material ALE method on unstructured hexahedral meshes using MOF interface reconstruction

This paper presents an effective second-order three-dimensional unstructured multi-material arbitrary Lagrangian–Eulerian (MMALE) method for compressible fluid dynamics. This is an integration work. The MMALE method utilizes Moment of Fluid (MOF) capability with interface reconstruction for multi-material modeling of immiscible fluids. It is of the explicit time-marching Lagrange plus remap type. In the Lagrangian phase, the staggered compatible discretization for Lagrangian gas dynamics is used also with Tipton’s pressure relaxation model for the closure of mixed cells. For the remapping phase, an improved second-order cell-intersection-based method for three-dimensional unstructured mesh is presented. It is conservative for remapping cell-centered variables such as density and internal energy. It is suitable for remapping between two meshes with different topology. By using this remapping method, the new material centroid position in the rezoned cells can be geometrically computed. This enables it to be combined with the MOF algorithm for constructing a second-order MMALE method. The MMALE method can be implemented on three-dimensional unstructured hexahedral meshes. Numerical results have proved the accuracy and robustness of the MMALE method.

A multi-material ReALE method with MOF interface reconstruction

We present a comparison of a classical arbitrary Lagrangian–Eulerian (ALE) method with a new multi-material reconnection-based arbitrary-Lagrangian–Eulerian (Re-ALE) strategy devoted to the computation of multi-material compressible fluid flows using the Moment Of Fluid (MOF) interface reconstruction. In ReALE we replace the rezoning phase of classical ALE method by a rezone where we allow the connectivity between cells of the mesh to change where rezoned grid is a polygonal mesh. Nevertheless, the ability of pure Lagrangian method to deal with multi-material problem, where mesh is aligned with material interfaces, is lost. In this work we have implemented MOF interface reconstruction on polygonal mesh in ReALE framework. This leads to a formulation that recover the Lagrangian features of following material and material interface that we lose using standard ALE methods with fixed connectivity. Some numerical examples, are used to clearly illustrate the robustness and accuracy of the new method.

‘Moment of fluid’ interface reconstruction method in axisymmetric coordinates

In this paper the ‘Moment of Fluid’ interface reconstruction method is extended to axisymmetric coordinate. In order to perform this extension, two modifications are applied to the original method. First, a new fluid moment is defined in the axisymmetric coordinate. Second, the remap phase is altered to incorporate the effect of symmetry. The capability of the extended method is assessed by testing its potential to track interfaces through large topology change. Also, the accuracy of the method is compared against widely used Young's method. Copyright © 2011 John Wiley & Sons, Ltd.

A 2D unstructured multi-material Cell-Centered Arbitrary Lagrangian–Eulerian (CCALE) scheme using MOF interface reconstruction

We present an original Cell-Centered Arbitrary Lagrangian–Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction devoted to the numerical simulation of two-dimensional multi-material compressible fluid flows on general unstructured grids. Our methodology is assessed through several demanding two-dimensional tests and comparison with Volume Of Fluid (VOF) interface reconstruction. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.

Some applications of generalized moments of the density in an inviscid compressible flow

A generalized moment of an inviscid compressible fluid contained in a domain Ω is a function of the form I = ∫ Ω ρ Φ d V , where ρ is the density and Φ is an arbitrary, time-independent function. The moment I satisfies an evolution equation which relates the energy of the flow, the distribution of matter and the pressure at the boundary. By considering convex domains and choosing appropriately Φ we show that any flow which does not blow-up must satisfy a balance between these magnitudes which preclude e.g. a vacuum at the boundary. Another possibility is to take Φ = r α , where r is the distance to the center of a ball or to an axis; the classical moment of inertia corresponds to α = 2 . For this case we find estimates on the evolution of the growth of I which show that in general this growth rate decreases with α .

Moment of fluid interface reconstruction method in multi-material arbitrary Lagrangian Eulerian (MMALE) algorithms

A new Lagrangian interface evolution method to use in a multi-material ALE (MMALE) algorithm is proposed. The input data set for the method consists of the volume fractions after the Lagrangian step and the orientation-position of the interfaces before this step. In the present work, the moment of fluid (MoF) method is used at the end of the ALE cycle to provide required interface information for this method. Compared to traditional reconstruction methods, in addition to the volume fractions, the proposed method incorporates the configuration of the interfaces in the calculations. The effect of compressibility is also considered in prioritizing the materials. The capability of the method is assessed by testing its potential to track interfaces through large topology change, in the domains which contain two or more materials. Numerical results for these tough test problems provide enough evidence for the accuracy and robustness of the proposed method.

Multi‐material incompressible flow simulation using the moment‐of‐fluid method

AbstractThis paper compares the numerical performance of the moment‐of‐fluid (MOF) interface reconstruction technique with Youngs, LVIRA, power diagram (PD), and Swartz interface reconstruction techniques in the context of a volume‐of‐fluid (VOF) based finite element projection method for the numerical simulation of variable‐density incompressible viscous flows. In pure advection tests with multiple materials MOF shows dramatic improvements in accuracy compared with the other methods. In incompressible flows where density differences determine the flow evolution, all the methods perform similarly for two material flows on structured grids. On unstructured grids, the second‐order MOF, LVIRA, and Swartz methods perform similarly and show improvement over the first‐order Youngs' and PD methods. For flow simulations with more than two materials, MOF shows increased accuracy in interface positions on coarse meshes. In most cases, the convergence and accuracy of the computed flow solution was not strongly affected by interface reconstruction method. Published in 2009 by John Wiley & Sons, Ltd.

Adaptive moment-of-fluid method

A novel adaptive mesh refinement (AMR) strategy based on the moment-of-fluid (MOF) method for volume-tracking of evolving interfaces is presented. Moment-of-fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids. The mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process. The centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments. A new Lagrange + remap scheme is presented for advecting moments, which includes Lagrangian backtracking, polygon intersection-based remapping and forward tracking to define the material centroid. The effectiveness and efficiency of AMR-MOF method is demonstrated with classical test problems, such as Zalesak’s disk and reversible vortex problem. The comparison with previously published results for these problems shows the superior accuracy of the AMR-MOF method over other methods. In addition, two new test cases with severe deformation rates are introduced, namely droplet deformation and S -shape deformation problems, for further demonstration of the capabilities of the AMR-MOF method.

The moment‐of‐fluid method in action

AbstractThe moment‐of‐fluid (MOF) method is a new volume‐tracking method that accurately treats evolving material interfaces. The MOF method uses moment data, namely the material volume fraction, as well as the centroid, for a more accurate representation of the material configuration, interfaces and concomitant volume advection. In contrast, the volume‐of‐fluid method uses only volume fraction data for interface reconstruction and advection. Based on the moment data for each material, the material interfaces are reconstructed with second‐order spatial accuracy in a strictly conservative manner. The MOF method is coupled with a stabilized finite element incompressible Navier–Stokes solver for two materials. The effectiveness of the MOF method is demonstrated with a free‐surface dam‐break and a two‐material Rayleigh–Taylor problem. Copyright © 2008 John Wiley & Sons, Ltd.

Reconstruction of multi-material interfaces from moment data

The moment-of-fluid (MoF) method is an extension of popular volume-of-fluid (VoF) technique for tracking material interface in multi-material fluid flows. VoF methods track the cell-wise material volumes and use these data for reconstructing the interfaces in mixed cell. The MoF method goes one step further and, in additional to the volumes, keeps track of the cell-wise material centroids; this approach provides sufficiently more information for the interface reconstruction algorithm. The MoF algorithm reconstructs interfaces in volume-conservative manner, by minimizing the defect of the 1st moment in each mixed cell. In case of two materials, this strategy allows to construct the linear interface in a mixed cell using no material volume data from the neighboring cells. Compared to the VoF interface reconstruction techniques, the MoF algorithm shows higher accuracy and better resolution, allows uniform processing of internal and boundary cells. In this paper we show how the same governing principle (minimization of the 1st-moment defect) can be used to reconstruct the interfaces in case of multiple materials.

Multi-material interface reconstruction on generalized polyhedral meshes

We describe multi-material (more than two materials) interface reconstruction methods for 3D meshes of generalized polyhedra. The basic information used in interface reconstruction is the volume fraction of each material in mixed cells, that is, those containing multiple materials. All methods subdivide a mixed cell into a set of pure non-overlapping sub-cells, each containing just one material that have the reference volume fraction. We describe three methods. The first two methods represent an extension of standard piece-wise linear interface construction (PLIC) methods to 3D and use information only about volume fractions. The first method is first-order accurate and is based on the discrete gradient of the volume fraction as an estimate of the normal to the interface. The second method is planarity-preserving (second-order accurate) and is an extension to 3D of the least squares volume-of-fluid interface reconstruction algorithm (LVIRA, see [E. Puckett, A volume-of-fluid interface tracking algorithm with applications to computing shock wave refraction, in: H. Dwyer (Ed.), Proceedings of the Fourth International Symposium on Computational Fluid Dynamics, 1991, pp. 933–938; J.E. Pilliod, E.G. Puckett, Second-order accurate volume-of-fluid algorithms for tracking material interfaces, Journal of Computational Physics 199 (2004) 465–502] for the 2D case). The third method is an extension to 3D of the so-called moment-of-fluid (MoF) method [V. Dyadechko, M. Shashkov, Moment-of-fluid interface reconstruction, Tech. Rep. LA-UR-05-7571, Los Alamos National Laboratory, 2005. Also available as http://cnls.lanl.gov/~shashkov/; V. Dyadechko, M. Shashkov, Multi-material interface reconstruction from the moment data, Tech. Rep. LA-UR-06-5846, Los Alamos National Laboratory, 2006. Also available as http://cnls.lanl.gov/~shashkov/]. The MoF method is also second-order accurate. This method uses information not only about volume fractions but also about the position of the centroids of each material. In contrast to standard PLIC methods, the MoF method uses only information from the cell where reconstruction is performed; no information from neighboring cells is needed. Also, the MoF method provides automatic ordering of the materials during interface reconstruction. Optimal ordering is based on comparing the positions of the reference centroids and actual centroids of the reconstructed pure sub-cells. The performance of the methods is demonstrated with numerical examples.

Numerical simulation of biomagnetic fluid downstream an eccentric stenotic orifice

Biomagnetic fluid dynamics is the study of the interaction of biological fluids with an applied steady magnetic field. The composition of the biological fluid is considered nonconducting; however, it has magnetic moment. The magnetic moment of the biological fluid can be enhanced by tagging superparamagnetic particles. Several biomedical applications recently developed utilize the magnetic labeling of cellular components. In this paper, the biomagnetic fluid downstream an eccentric stenotic orifice is considered. An external magnetic field is applied at different locations down stream the stenotic orifice. It is found that based on the location of the magnetic field, the reattachment point downstream the stenotic orifice changes; it is also found that the shear stress will be affected based on the magnetic field location. Major changes in the flow pattern have been also observed based on the magnetic field strength.

How to build a better pair potential for water

With the objective of improving the effective pair potentials for water, we develop a potential model that employs diffuse charges, in addition to the usual point charges, on the oxygen and hydrogen atoms, to account for charge penetration effects. The potential has better transferability from the liquid to gaseous phases since, unlike many existing models, it does not require an enhanced dipole moment. As a result it accurately reproduces the structural and thermodynamic properties of water over a wide range of conditions. Moreover, by allowing for electronic polarization when evaluating the total dipole moment of the simulated fluid, the model leads to the correct value of the dielectric constant for virtually any state point. At room temperature the calculation produces an average dipole moment of 3.09 D, in accord with recent theoretical and experimental evaluations. This supports the idea that induction effects in water are more important than previously expected.