Special Issue "Advances in Numerical Methods for Multiphase Flows"

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Flow of Multi-Phase Fluids and Granular Materials".

Deadline for manuscript submissions: closed (15 January 2021).

Special Issue Editor

Prof. Stéphane Vincent
E-Mail Website
Guest Editor
Laboratoire MSME, UMR CNRS 8208, Université Paris-Est Marne-La-Vallée, 77420 Marne-la-Vallée, France
Interests: finite volume method; non-isothermal multiphase flow; penalty and augmented Lagrangian methods; interface tracking; real flows; turbulence in heterogeneous environments; multiscale modeling of two-phase flows
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Special Issue Information

Dear Colleagues,

The main goal of this Special Issue is to bring together developers and users of different numerical approaches and codes to share their experience in the development and validation of specific algorithms for multiphase flows. Both resolved scale interfaces and Eulerian–Eulerian or Eulerian–Lagrangian approaches are of interest. The participants will be encouraged to discuss the difficulties and limitations of the different methods and their pros and cons.

Prof. Stéphane Vincent
Guest Editor

Manuscript Submission Information

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Keywords

  • non-isothermal multiphase flow
  • Eulerian–Eulerian approach
  • numerical methods
  • Eulerian–Lagrangian approach
  • multiscale modeling of multiphase flow

Published Papers (10 papers)

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Research

Article
Numerical Study on an Interface Compression Method for the Volume of Fluid Approach
Fluids 2021, 6(2), 80; https://doi.org/10.3390/fluids6020080 - 10 Feb 2021
Viewed by 703
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios
Fluids 2021, 6(1), 23; https://doi.org/10.3390/fluids6010023 - 05 Jan 2021
Cited by 1 | Viewed by 690
Abstract
In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such [...] Read more.
In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Assessment and Prediction of Air Entrainment and Geyser Formation in a Bottom Outlet: Field Observations and CFD Simulation
Fluids 2020, 5(4), 203; https://doi.org/10.3390/fluids5040203 - 09 Nov 2020
Viewed by 714
Abstract
Air entrainment at the intake of a bottom outlet often gives rise to air pockets in its conduit and formation of geysers. The outlet in question comprises a bulkhead gate, gate shaft, horizontal conduit, and exit. Operations show that it suffers from appreciable [...] Read more.
Air entrainment at the intake of a bottom outlet often gives rise to air pockets in its conduit and formation of geysers. The outlet in question comprises a bulkhead gate, gate shaft, horizontal conduit, and exit. Operations show that it suffers from appreciable flow fluctuations and blowouts in the tailwater, which leads to gate operation restrictions. For the purpose of understanding the hydraulic phenomenon, both prototype discharge tests and three-dimensional computational fluid dynamics (CFD) modeling of two-phase flows are performed. The operational focus of the facility are small and large gate openings. The CFD results reveal that, with air entrained in the gate shaft, continual breakup and coalescence of air bubbles in the conduit typify the flow. At small openings below 1 meter, the air–water flow is characterized by either distinct blowouts of regular frequency or continuous air release. In terms of geyser behaviors inclusive of frequency, the agreement is good between field and numerical studies. At large openings, the gate becomes fully submerged, and the flow is discharged without air entrainment and blowouts. The paper showcases the air–water flow features in a typical bottom outlet layout in Sweden, which is intended to serve as an illustration of the study procedure for other similar outlets. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques
Fluids 2020, 5(3), 156; https://doi.org/10.3390/fluids5030156 - 10 Sep 2020
Viewed by 722
Abstract
The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems [...] Read more.
The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems with tracking-type functionals is proposed. Continuous (differentiate-then-discretize) and discrete (discretize-then-differentiate) adjoint-based gradient computations are formulated and compared in a one-dimensional configuration, the latter being ultimately used to perform optimisation in two dimensions. The gradient is used in truncated Newton and steepest descent optimisers, and the algorithms are shown to recover optimal solutions. These validations raise a number of open questions, which are finally discussed with directions for future work. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Numerical Study on the Flow and Heat Transfer Coupled in a Rectangular Mini-Channel by Finite Element Method for Industrial Micro-Cooling Technologies
Fluids 2020, 5(3), 151; https://doi.org/10.3390/fluids5030151 - 03 Sep 2020
Viewed by 817
Abstract
Nowadays, cooling high thermal flows in compact volumes continues to be one of the crucial problems in the industry. With the advent of advanced technologies, much more attention has been paid to how to improve the performance of cooling systems in the area [...] Read more.
Nowadays, cooling high thermal flows in compact volumes continues to be one of the crucial problems in the industry. With the advent of advanced technologies, much more attention has been paid to how to improve the performance of cooling systems in the area of micro-technologies. Rectangular mini-channels are typical representatives which commonly used for cooling applications. However, micro-technologies still face the problem of low performance due to the low productivity of cooling related to unbefitting physical parameter values. Here, this work studies the applicability of the heat transfer scheme of convective flow and flow boiling in a rectangular mini-channel for satisfying the cooling requirement of industrial micro-technologies, through a simulation model governed by the coupled mechanism from Navier-Stokes (N-S) equation and heat transfer equations with phase change effect. In this work, various hydraulic diameters and different inlet fluid speed are used to calculate the different velocity profiles, pressure drops, coefficients of friction and finally, the distribution of the temperatures and dissipated heat flux. The simulation results show the applicability of the rectangular mini-channel in diverse applications such as engine cooling, electronic components, automotive on-board electronics and aerospace engineering. Flow boiling simulation results reveal that the obtained patterns were smooth mixture flow and discrete flow. The dissipated heat flux can reach 1.02–5.34 MW/m2 for a hydraulic diameter of 0.5 mm. We show that the system with the gradient temperature that evolves increasingly along the top and bottom walls of the channels presents the highest heat flux dissipated in flow boiling. Additionally, the fin efficiency of the system is 0.88 and the coefficient value of convective heat transfer is in the range between 5000 < h < 100,000, which indicates the flow boiling heat transfer is effective in the mini-channel when the Reynolds number is less than 400. It provides a significant heat exchange for cooling in these application areas. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Computational Modeling of Bubbles Growth Using the Coupled Level Set—Volume of Fluid Method
Fluids 2020, 5(3), 120; https://doi.org/10.3390/fluids5030120 - 23 Jul 2020
Cited by 1 | Viewed by 1310
Abstract
Understanding the generation, growth, and dynamics of bubbles as they absorb or release dissolved gas in reactive flows is crucial for optimizing the efficiency of electrochemically gas-evolving systems like alkaline water electrolysis or hydrogen production. To better model these bubbly flow systems, we [...] Read more.
Understanding the generation, growth, and dynamics of bubbles as they absorb or release dissolved gas in reactive flows is crucial for optimizing the efficiency of electrochemically gas-evolving systems like alkaline water electrolysis or hydrogen production. To better model these bubbly flow systems, we use a coupled level set and volume of fluid approach integrated with a one-fluid transport of species model to study the dynamics of stationary and rising bubbles in reactive two-phase flows. To accomplish this, source terms are incorporated into the continuity and phase conservation equations to allow the bubble to grow or shrink as the species moves through the interface. Verification of the hydrodynamics of the solver for non-reactive systems demonstrates the requisite high fidelity interface capturing and mass conservation necessary to incorporate transport of species. In reactive systems where the species impacts the bubble volume, the model reproduces the theoretically predicted and experimentally measured diffusion-controlled growth rate (i.e., R(t)t0.5). The model is then applied to rising bubbles to demonstrate the impact of transport of species on both the bubble velocity and shape as well as the concentration field in its wake. This improved model enables the incorporation of electric fields and chemical reactions that are essential for studying the physicochemical hydrodynamics in multiphysics systems. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
CFD Modeling of Hydrocyclones—A Study of Efficiency of Hydrodynamic Reservoirs
Fluids 2020, 5(3), 118; https://doi.org/10.3390/fluids5030118 - 21 Jul 2020
Cited by 7 | Viewed by 1310
Abstract
The dynamics of hydrocyclones is complex, because it is a multiphase flow problem that involves interaction between a discrete phase and multiple continuum phases. The performance of hydrocyclones is evaluated by using Computational Fluid Dynamics (CFD), and it is characterized by the pressure [...] Read more.
The dynamics of hydrocyclones is complex, because it is a multiphase flow problem that involves interaction between a discrete phase and multiple continuum phases. The performance of hydrocyclones is evaluated by using Computational Fluid Dynamics (CFD), and it is characterized by the pressure drop, split water ratio, and particle collection efficiency. In this paper, a computational model to improve and evaluate hydrocyclone performance is proposed. Four known computational turbulence models (renormalization group (RNG) k- ε , Reynolds stress model (RSM), and large-eddy simulation (LES)) are implemented, and the accuracy of each for predicting the hydrocyclone behavior is assessed. Four hydrocyclone configurations were analyzed using the RSM model. By analyzing the streamlines resulting from those simulations, it was found that the formation of some vortices and saddle points affect the separation efficiency. Furthermore, the effects of inlet width, cone length, and vortex finder diameter were found to be significant. The cut-size diameter was decreased by 33% compared to the Hsieh experimental hydrocyclone. An increase in the pressure drop leads to high values of cut-size and classification sharpness. If the pressure drop increases to twice its original value, the cut-size and the sharpness of classification are reduced to less than 63% and 55% of their initial values, respectively. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Assessment of CFD Solvers and Turbulent Models for Water Free Jets in Spillways
Fluids 2020, 5(3), 104; https://doi.org/10.3390/fluids5030104 - 30 Jun 2020
Cited by 2 | Viewed by 808
Abstract
The capability of two different OpenFOAM® solvers, namely interFoam and twoPhaseEulerFoam, in reproducing the behavior of a free water jet was investigated. Numerical simulations were performed in order to obtain the velocity and air concentration profiles along the jet. The turbulence intensity [...] Read more.
The capability of two different OpenFOAM® solvers, namely interFoam and twoPhaseEulerFoam, in reproducing the behavior of a free water jet was investigated. Numerical simulations were performed in order to obtain the velocity and air concentration profiles along the jet. The turbulence intensity was also analyzed. The obtained results were compared with published experimental data and, in general, similar velocity and air concentration profiles were found. InterFoam solver is able to reproduce the velocity field of the free jet but has limitations in the simulation of the air concentration. TwoPhaseEulerFoam performs better in reproducing the air concentration along the jet, the results being in agreement with the experimental data, although the computational runs are less stable and more time consuming. The sensitivity analysis of the inlet turbulent intensity showed that it has no influence in the characteristics of the jet core. With this research it is possible to conclude that: interFoam with k-Epsilon (k-ε) turbulence model is the best choice if the goal of the numerical simulations is the simulation of the velocity field of the jet. Meanwhile, twoPhaseEulerFoam with mixturek-Epsilon (mk-ε) shall be considered if the objective is the simulation of the velocity field and the air concentration. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Numerical Simulation of Breathing Mode Oscillation on Bubble Detachment
Fluids 2020, 5(2), 96; https://doi.org/10.3390/fluids5020096 - 16 Jun 2020
Viewed by 906
Abstract
When a bubble detaches from a nozzle immersed in water, a sound is emitted owing to the detachment. The bubble deformation and sound emission generated after detachment has been investigated in many studies, in which the breathing mode with a natural frequency was [...] Read more.
When a bubble detaches from a nozzle immersed in water, a sound is emitted owing to the detachment. The bubble deformation and sound emission generated after detachment has been investigated in many studies, in which the breathing mode with a natural frequency was discussed based on the dynamics of the interface between the air and water. In this study, the deformation of a bubble was observed, and the sound emitted upon detachment was measured experimentally. To analyze the bubble deformation process, a computational fluid dynamics (CFD) simulation was conducted using the volume of fluid (VOF) method to predict the sound emission. In the analysis, the deformation behavior, the oscillation frequencies, sound pressure, and radius variation were discussed by comparing the numerical and experimental data. Furthermore, the natural frequency and low frequency vibrations were discussed based on the interference between the detached bubbles and the air column vibrations. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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Article
Consistent Velocity–Pressure Coupling for Second-Order L2-Penalty and Direct-Forcing Methods
Fluids 2020, 5(2), 92; https://doi.org/10.3390/fluids5020092 - 10 Jun 2020
Cited by 1 | Viewed by 672
Abstract
The present work studies the interactions between fictitious-domain methods on structured grids and velocity–pressure coupling for the resolution of the Navier–Stokes equations. The pressure-correction approaches are widely used in this context but the corrector step is generally not modified consistently to take into [...] Read more.
The present work studies the interactions between fictitious-domain methods on structured grids and velocity–pressure coupling for the resolution of the Navier–Stokes equations. The pressure-correction approaches are widely used in this context but the corrector step is generally not modified consistently to take into account the fictitious domain. A consistent modification of the pressure-projection for a high-order penalty (or penalization) method close to the Ikeno–Kajishima modification for the Immersed Boundary Method is presented here. Compared to the first-order correction required for the L 2 -penalty methods, the small values of the penalty parameters do not lead to numerical instabilities in solving the Poisson equation. A comparison of the corrected rotational pressure-correction method with the augmented Lagrangian approach which does not require a correction is carried out. Full article
(This article belongs to the Special Issue Advances in Numerical Methods for Multiphase Flows)
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