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Amongst the multitude of approaches available in literature to reduce spurious velocities in Volume of Fluid approach, the Sharp Surface Force (SSF) model is increasingly being used due to its relative ease to implement. The SSF approach relies on a user-defined parameter, the sharpening coefficient, which determines the extent of the smeared natur...
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... the iterative procedure used to solve rgh , p i.e., the PISO algorithm, converges based on a user defined tolerance (Deshpande et al., 2012). This tolerance, required to calculate rgh p , introduces a force imbalance between surface tension, gravitational force, and pressure gradient which can be reduced by setting a very low convergence criterion, like 10 20 -used in Table 1, as recommended by Deshpande et al. (2012). ...Context 2
... governing equations are discretized using first and second order methods in time and space respectively, see Vachaparambil and Einarsrud (2019a), and solved based on methods described in Table 1. Other numerical settings like the sub-cycling of volume fraction equation and momentum predictor, which are relevant in solving the governing equations, are set based on OpenFOAM default settings/recommendations for simulating multiphase flows which has also been used in Vachaparambil and Einarsrud (2019a). ...Context 3
... use of larger sharpening coefficients seems to reduce the error in calculating Laplace pressure as well as spurious velocities in the simulations, see Table 4. Decreasing the mesh size does not always exacerbate spurious velocities which is contrast to the increasing sc U observed with CSF model in the work by Deshpande et al. (2012) and Vachaparambil and Einarsrud (2019a). The variation between sc U reported in Table 4 and the work by Vachaparambil and Einarsrud (2019a) is due to the difference in the sh C and solver setting, in Table 1, used for the simulations. ...Citations
... Within the two-phase flow community, a common procedure for addressing this error is the use of a level set function, φ(x, t), which is much smoother than α and can subsequently provide more accurate curvature predictions. This combination of φ with α has been in existence for quite some time [12] and has also been adopted within OpenFOAM, for instance in the work of Ferrari et al. [7], Bilger et al. [9], Albadawi et al. [13], Menon et al. [14], Kassar et al. [15], Elsayed et al. [16], Vachaparambil and Einarsrud [17]. More explicitly in Ferrari et al. [7], Albadawi et al. [13], Menon et al. [14], the level set is initially constructed from the α field, namely by an equation of the form φ o = (2α − 1)ζ, where ζ is related to the local grid spacing, ∆x. ...
... Subsequently, this initial φ o is reinitialized through the solution of a Hamilton-Jacobi equation, resulting in a signed distance function, which is then used to compute curvature. In other work [9,17], the α field is smoothed out before calculating curvature. Other alternatives include the construction of a uniform voxel mesh followed by isosurface triangulation [16] or the representation of the interface by a cloud of points [15], both of which are used to generate more accurate predictions of κ. ...
... This problem has been documented previously [18,19] and it results from the propagation of information from the wrong side of the interface for some interfacial nodes. For the sake of providing an additional comparison, the common smoothing of the α field [9,17] is also implemented. ...
Improvements to the interfacial curvature of interFoam based on (i) the smoothing of the liquid fraction field and (ii) the creation of a signed distance function (ϕ-based) are implemented. While previous work in this area has focused on evaluating spurious currents and similar configurations, the tests implemented in this work are more applicable to sprays and hydrodynamic breakup problems. For the ϕ-based method, a dual approach is developed based on a geometric reconstruction of the interface at interfacial cells and the solution of the Hamilton-Jacobi equation away from these cells. The more promising results are from this method, where the lack of convergence of Laplace pressure predictions existing in the standard version of interFoam is fixed, resulting in second-order convergence. Similar but less drastic improvements are observed for other exercises consisting of the oscillation of a droplet, a 2-phase Orr–Sommerfeld problem, the Rayleigh–Plateau instability, and the retraction of a liquid column. It is only when the dynamics are either entirely governed by surface tension or are heavily influenced by it that we see the need to substitute the standard interFoam curvature approach with a more accurate scheme. For more realistic problems, which naturally include more complicated dynamics, the difference between the standard approach and the ϕ-based approach is minimal.
Inspired by the hydrodynamic perception abilities based on lateral lines on fish surfaces, the artificial lateral lines (ALLs) based on pressure and flow sensors were proposed by the researchers. As the ALLs are widely used in underwater robots, the mechanisms of lateral line perception are urgently needed to be studied. Based on the lattice Boltzmann method, immersion boundary method, and large eddy simulation, a three-dimensional numerical model of underwater robot motion is established and verified. The distribution and variation of velocity and surface pressure on robots with different shapes under different flow fields are studied in detail. It is found that the robots with the upstream surface curvature aspect ratio of 1:1 are more suitable for placing ALLs. Then, similarly, the hydrodynamic perception abilities of robots with different sizes are further investigated. It was observed that the smaller the robot size, the better the perception ability. In addition, sensing devices are more suitable for placement on the upstream surface of the robots. These conclusions can also explain the physiological characteristics of cavefish with well-developed lateral lines in nature. Finally, based on the above analysis, to guide the shape design and sensor layout of the robots, an evaluation index for the perception ability of the robot is proposed. The reliability of the evaluation index is verified by using a machine learning method based on polynomial regression to predict the flow field. The R-square of machine learning can reach 0.99 at the upstream surface of the robot.
The analysis of catalytic processes and the development of innovative technologies require a deep comprehension of the complex interplay between the intrinsic functionality of the heterogeneous material and the surrounding environment in the reactor. This is particularly important for multiphase catalytic reactors where complex interactions among the phases distribution, the inter- and intra-phase transport and the catalytic material occur. In this work, a computational framework has been developed to couple the solution of the hydrodynamics of multiphase flow using Computational Fluid Dynamics (CFD) with the detailed description of the surface reactivity through first-principles microkinetic models. In particular, the methodology employs an algebraic Volume-Of-Fluid (VOF) approach for the advection of the phases and takes advantage of the Compressive-Continuous Species Transfer (CST) for the modeling of the species mass interfacial transfer. The heterogeneous chemistry is included as source terms to the mass and energy equations acting at the catalytic surface, while the solution of the mass balance equation employs an operator splitting approach. The numerical framework has been assessed with respect to simple geometries by direct comparison with analytical and fully coupled solutions followed by examples of application in the context of the nitrobenzene hydrogenation to aniline. The envisioned approach is the first step toward the first-principles-based multiscale analysis of multiphase catalytic processes paving the way toward the detailed understanding and development of innovative and intensified technologies.
One of the important aspects in improving the efficiency of electrochemical processes, such as water electrolysis, is the efficient removal of bubbles which evolve from the electrodes. Numerical modelling based on Computational Fluid Dynamics (CFD) can describe the process, provide insights into its complexity, elucidate the underlying mechanisms of how bubbles evolve and their effect as well as aid in developing strategies to reduce the impact of the bubble.
In this paper, a Volume of Fluid (VOF) based simulation framework to study the evolution of hydrogen bubbles in the order of few hundred micrometers, refered to as continuum scale bubbles, is proposed. The framework accounts for the multiphase nature of the process, electrochemical reactions, dissolved gas transport, charge transport, interfacial mass transfer and associated bubble growth. The proposed solver is verified, for two-dimensional cases, by comparison to analytical solution of bubble growth in supersaturated solutions, stationary bubble, rising bubbles and qualitative analysis based on experimental observations of the variations in current based on static simulations. The proposed solver is used to simulate the evolution of a single bubble under various wetting conditions of the electrode as well as the coalescence driven evolution of two bubbles. The results show that as the bubbles detach, its surface oscillates and the shape of the rising bubble is determined by the balance between drag force and surface tension. These surface oscillations, which causes the bubble to get flattened and elongated, results in temporal variation of the electrical current. The reduction of current due to bubble growth is visible only when these surface oscillations have reduced. The simulations also show the current as a function of the position of the bubble in the interelectrode gap. The framework also predicts the increase in current as a result of bubbles leaving the surface which is larger when the process is coalescence driven. The simulations indicate that bubble coalescence is the underlying mechanism for continuum scale bubble detachment.
A commonly encountered phenomenon in chemical processes is bubble evolution driven by supersaturation. On the continuum scale, this essentially involves interfacial mass transfer resulting in the growth of bubbles and their subsequent detachment from a surface. Analytical approaches to study this phenomenon typically involve estimating the driving force for interfacial mass transfer based on Sherwood number (Sh) correlations and the bulk concentration of dissolved gas. This is often not practical since the bulk concentration is often unknown and Sh correlations are sometimes not available to provide an accurate description of the associated flow fields. With the use of interface-resolved simulations to model these processes, the local distribution of dissolved gas can be obtained by solving for the concentration field. The driving force for interfacial mass transfer can be computed based on Sh correlations (which can be adopted for specific flows and are typically used in “engineering” applications) or the universally applicable Fick’s first law. This paper compares the predictions of these approaches for the well-studied case of a two-dimensional bubble growing in an unbounded supersaturated solution for three different levels of supersaturation. The equivalent two-dimensional simulations are run in a previously developed volume of fluid framework on OpenFOAM® [K. J. Vachaparambil and K. E. Einarsrud, Appl. Math. Model. 81, 690–710 (2020)]. The results show that the choice of an appropriate Sh correlation can provide a reasonable estimate of bubble growth. In a more universal approach, which is relevant when the flow being simulated cannot be captured by a single Sh correlation (e.g., bubble growth/coalescence and detachment) or when existing Sh correlations are not applicable, Fick’s first law can be used to compute the driving force for bubble growth, provided that the concentration boundary layer can be resolved.
