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Fluids
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Numerical Modeling and Experimental Studies of Two-Phase Flows
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Numerical Modeling and Experimental Studies of Two-Phase Flows

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (12 July 2024) | Viewed by 21659

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Van-Tu Nguyen

E-Mail Website
Guest Editor
School of Mechanical Engineering, Pusan National University, Busan 46241, Republic of Korea
Interests: computational fluid dynamics; numerical methods; numerical algorithms; numerical programming; fluid mechanics; multiphase flows, shock capturing; free surface flows; water entry/water exit; cavitation; bubble dynamics; cavitation erosion; heat and mass transfer; gas dynamics and industrial gas flows; supercavitation; high-speed subsonic-supersonic flows
Special Issues, Collections and Topics in MDPI journals
Dr. Hemant J. Sagar

E-Mail Website
Guest Editor
Faculty of Mechanical Engineering, University of Duisburg-Essen, 47057 Duisburg, Germany
Interests: computational fluid dynamics; multiphase flow; experimental fluid dynamics; cavitation; erosion; bubble dynamics; hydrodynamics; flow measurement; fluid–structure interaction; image processing

Special Issue Information

Dear Colleagues,

Two-phase flows (e.g., gas–gas, gas–liquid, liquid–liquid) are found in many natural phenomena, engineering, and industrial applications. The nonlinear motions of the interface between two phases (two fluids) and its deformations and breaks, phase change, heat transfer, turbulence, shockwaves, and violent interaction with devices/systems become very complicated, both in terms of developing experimental techniques for their measurement and for numerical modeling for the analysis of these two-phase flows. However, the significance of these topics has motivated the recent advances in thermodynamics, experimental measurements, and numerical modeling; these advances have demonstrated and provided a solid understanding of fundamental and physical insights into the two-phase flows in many fields of engineering and industry. These advances are in parallel with highly advanced technologies of high-speed cameras and lighting as well as high-speed computing sources, and therefore resolve the underlying physical processes satisfactorily and support the development of new technologies/treatment protocols.

This Special Issue aims to provide researchers and scientists with the opportunity to present and discuss their original works on new numerical modeling, simulations, and experimental representation of engineering and industrial systems or any other two-phase systems from microscale to larger-scale problems. Papers related to two-phase flows are highly welcome which not only address fundamental science, but also engineering applications.

Dr. Van-Tu Nguyen
Dr. Hemant J. Sagar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Methodologies:
    • Two-phase flow measurement; visualization techniques
    • Numerical modeling; simulation of two-phase flows
    • Modeling phase change/boiling
    • Treatments of interface discontinuity and shockwave
  • Basic research:
    • Bubble/droplet dynamics
    • Surface tension/Capillary effects
    • Natural and ventilated Cavitation/ Supercavitation
    • Sheet, cloud, and/or tip vortex cavitation
    • Boiling and condensation in benchmark problems
    • Free surface flows
    • Water entry and exit flows
    • Fluid-Structure-Interaction
    • Slamming and Sloshing
  • Advances in Applications:
    • The potential risks of failure of levees, dams, and reservoirs
    • Breaking waves; overtop- ping of coastal structures
    • Moving ships; interaction of extreme waves; and green water on decks
    • Spray cooling and two-phase heat transfer
    • Hydrodynamic cavitation and dynamic bubble processes
    • Enhancement of critical heat flux

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Related Special Issue

Published Papers (13 papers)

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Editorial

Jump to: Research, Review

4 pages, 161 KiB  
Editorial
Computational Fluid Dynamics Modeling and Experiments of Two-Phase Flows
by Van-Tu Nguyen and Hemant J. Sagar
Fluids 2024, 9(9), 207; https://doi.org/10.3390/fluids9090207 - 3 Sep 2024
Viewed by 1221
Abstract
Two-phase flows are prevalent in natural phenomena, as well as a wide range of marine engineering and industrial applications [...] Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)

Research

Jump to: Editorial, Review

21 pages, 1166 KiB  
Article
Pressure Drop Estimation of Two-Phase Adiabatic Flows in Smooth Tubes: Development of Machine Learning-Based Pipelines
by Farshad Bolourchifard, Keivan Ardam, Farzad Dadras Javan, Behzad Najafi, Paloma Vega Penichet Domecq, Fabio Rinaldi and Luigi Pietro Maria Colombo
Fluids 2024, 9(8), 181; https://doi.org/10.3390/fluids9080181 - 11 Aug 2024
Cited by 1 | Viewed by 1054
Abstract
The current study begins with an experimental investigation focused on measuring the pressure drop of a water–air mixture under different flow conditions in a setup consisting of horizontal smooth tubes. Machine learning (ML)-based pipelines are then implemented to provide estimations of the pressure [...] Read more.
The current study begins with an experimental investigation focused on measuring the pressure drop of a water–air mixture under different flow conditions in a setup consisting of horizontal smooth tubes. Machine learning (ML)-based pipelines are then implemented to provide estimations of the pressure drop values employing obtained dimensionless features. Subsequently, a feature selection methodology is employed to identify the key features, facilitating the interpretation of the underlying physical phenomena and enhancing model accuracy. In the next step, utilizing a genetic algorithm-based optimization approach, the preeminent machine learning algorithm, along with its associated optimal tuning parameters, is determined. Ultimately, the results of the optimal pipeline provide a Mean Absolute Percentage Error (MAPE) of 5.99% on the validation set and 7.03% on the test. As the employed dataset and the obtained optimal models will be opened to public access, the present approach provides superior reproducibility and user-friendliness in contrast to existing physical models reported in the literature, while achieving significantly higher accuracy. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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14 pages, 2736 KiB  
Article
Air Flow Monitoring in a Bubble Column Using Ultrasonic Spectrometry
by Ediguer Enrique Franco, Sebastián Henao Santa, John Jairo Cabrera and Santiago Laín
Fluids 2024, 9(7), 163; https://doi.org/10.3390/fluids9070163 - 18 Jul 2024
Cited by 1 | Viewed by 912
Abstract
This work demonstrates the use of an ultrasonic methodology to monitor bubble density in a water column. A flow regime with droplet size distribution between 0.2 and 2 mm was studied. This range is of particular interest because it frequently appears in industrial [...] Read more.
This work demonstrates the use of an ultrasonic methodology to monitor bubble density in a water column. A flow regime with droplet size distribution between 0.2 and 2 mm was studied. This range is of particular interest because it frequently appears in industrial flows. Ultrasound is typically used when the size of the bubbles is much larger than the wavelength (low frequency limit). In this study, the radius of the bubbles ranges between 0.6 and 6.8 times the wavelength, where wave propagation becomes a complex phenomenon, making existing analytical methods difficult to apply. Measurements in transmission–reception mode with ultrasonic transducers operating at frequencies of 2.25 and 5.0 MHz were carried out for different superficial velocities. The results showed that a time-averaging scheme is necessary and that wave parameters such as propagation velocity and the slope of the phase spectrum are related to the number of bubbles in the column. The proposed methodology has the potential for application in industrial environments. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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11 pages, 3666 KiB  
Article
Shedding of Cavitation Clouds in an Orifice Nozzle
by Taihei Onishi, Kaizheng Li, Hong Ji and Guoyi Peng
Fluids 2024, 9(7), 156; https://doi.org/10.3390/fluids9070156 - 5 Jul 2024
Cited by 1 | Viewed by 759
Abstract
Focused on the unsteady property of a cavitating water jet issuing from an orifice nozzle in a submerged condition, this paper presents a fundamental investigation of the periodicity of cloud shedding and the mechanism of cavitation cloud formation and release by combining the [...] Read more.
Focused on the unsteady property of a cavitating water jet issuing from an orifice nozzle in a submerged condition, this paper presents a fundamental investigation of the periodicity of cloud shedding and the mechanism of cavitation cloud formation and release by combining the use of high-speed camera observation and flow simulation methods. The pattern of cavitation cloud shedding is evaluated by analyzing sequence images from a high-speed camera, and the mechanism of cloud formation and release is further examined by comparing the results of flow visualization and numerical simulation. It is revealed that one pair of ring-like clouds consisting of a leading cloud and a subsequent cloud is successively shed downstream, and this process is periodically repeated. The leading cloud is principally split by a shear vortex flow along the nozzle exit wall, and the subsequent cloud is detached by a re-entrant jet generated while a fully extended cavity breaks off. The subsequent cavitation cloud catches the leading one, and they coalesce over the range of x/d≈1.8~2.5. Cavitation clouds shed downstream from the nozzle at two dominant frequencies. The Strouhal number of the leading cavitation cloud shedding varies from 0.21 to 0.29, corresponding to the injection pressure. The mass flow rate coefficient fluctuates within the range of 0.59~0.66 at the same frequency as the leading cloud shedding under the effect of cavitation. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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29 pages, 8011 KiB  
Article
Hartmann Flow of Two-Layered Fluids in Horizontal and Inclined Channels
by Arseniy Parfenov, Alexander Gelfgat, Amos Ullmann and Neima Brauner
Fluids 2024, 9(6), 129; https://doi.org/10.3390/fluids9060129 - 30 May 2024
Cited by 1 | Viewed by 981
Abstract
The effect of a transverse magnetic field on two-phase stratified flow in horizontal and inclined channels is studied. The lower heavier phase is assumed to be an electrical conductor (e.g., liquid metal), while the upper lighter phase is fully dielectric (e.g., gas). The [...] Read more.
The effect of a transverse magnetic field on two-phase stratified flow in horizontal and inclined channels is studied. The lower heavier phase is assumed to be an electrical conductor (e.g., liquid metal), while the upper lighter phase is fully dielectric (e.g., gas). The flow is defined by prescribed flow rates in each phase, so the unknown frictional pressure gradient and location of the interface separating the phases (holdup) are found as part of the whole solution. It is shown that the solution of such a two-phase Hartmann flow is determined by four dimensionless parameters: the phases’ viscosity and flow-rate ratios, the inclination parameter, and the Hartmann number. The changes in velocity profiles, holdups, and pressure gradients with variations in the magnetic field and the phases’ flow-rate ratio are reported. The potential lubrication effect of the gas layer and pumping power reduction are found to be limited to low magnetic field strength. The effect of the magnetic field strength on the possibility of obtaining countercurrent flow and multiple flow states in concurrent upward and downward flows, and the associated flow characteristics, such as velocity profiles, back-flow phenomena, and pressure gradient, are explored. It is shown that increasing the magnetic field strength reduces the flow-rate range for which multiple solutions are obtained in concurrent flows and the flow-rate range where countercurrent flow is feasible. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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16 pages, 4393 KiB  
Article
Prediction of Critical Heat Flux during Downflow in Fully Heated Vertical Channels
by Mirza M. Shah
Fluids 2024, 9(3), 79; https://doi.org/10.3390/fluids9030079 - 20 Mar 2024
Cited by 1 | Viewed by 1300
Abstract
Boiling with downflow in vertical channels is involved in many applications such as boilers, nuclear reactors, chemical processing, etc. Accurate prediction of CHF (Critical Heat Flux) is important to ensure their safe design. While numerous experimental studies have been done on CHF during [...] Read more.
Boiling with downflow in vertical channels is involved in many applications such as boilers, nuclear reactors, chemical processing, etc. Accurate prediction of CHF (Critical Heat Flux) is important to ensure their safe design. While numerous experimental studies have been done on CHF during upflow and reliable methods for predicting it have been developed, there have been only a few experimental studies on CHF during downflow. Some researchers have reported no difference in CHF between up- and downflow, while some have reported that CHF in downflow is lower or higher than that in upflow. Only a few correlations have been published that are stated to be applicable to CHF during downflow. No comprehensive comparison of correlations with test data has been published. In the present research, literature on CHF during downflow in fully heated channels was reviewed. A database for CHF in downflow was compiled. The data included round tubes and rectangular channels, hydraulic diameters 2.4 mm to 15.9 mm, reduced pressure 0.0045 to 0.6251, flow rates from 15 to 21,761 kg/m2s, and several fluids with diverse properties (water, nitrogen, refrigerants). This database was compared to a number of correlations for upflow and downflow CHF. The results of this comparison are presented and discussed. Design recommendations are provided. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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14 pages, 2821 KiB  
Article
Application of Deep Learning in Predicting Particle Concentration of Gas–Solid Two-Phase Flow
by Zhiyong Wang, Bing Yan and Haoquan Wang
Fluids 2024, 9(3), 59; https://doi.org/10.3390/fluids9030059 - 27 Feb 2024
Cited by 3 | Viewed by 1676
Abstract
Particle concentration is an important parameter for describing the state of gas–solid two-phase flow. This study compares the performance of three methods, namely, Back-Propagation Neural Networks (BPNNs), Recurrent Neural Networks (RNNs), and Long Short-Term Memory (LSTM), in handling gas–solid two-phase flow data. The [...] Read more.
Particle concentration is an important parameter for describing the state of gas–solid two-phase flow. This study compares the performance of three methods, namely, Back-Propagation Neural Networks (BPNNs), Recurrent Neural Networks (RNNs), and Long Short-Term Memory (LSTM), in handling gas–solid two-phase flow data. The experiment utilized seven parameters, including temperature, humidity, upstream and downstream sensor signals, delay, pressure difference, and particle concentration, as the dataset. The evaluation metrics, such as prediction accuracy, were used for comparative analysis by the experimenters. The experiment results indicate that the prediction accuracies of the RNN, LSTM, and BPNN experiments were 92.4%, 92.7%, and 92.5%, respectively. Future research can focus on further optimizing the performance of the BPNN, RNN, and LSTM to enhance the accuracy and efficiency of gas–solid two-phase flow data processing. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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21 pages, 8709 KiB  
Article
Dynamics of a Laser-Induced Cavitation Bubble near a Cone: An Experimental and Numerical Study
by Jianyong Yin, Yongxue Zhang, Dehong Gong, Lei Tian and Xianrong Du
Fluids 2023, 8(8), 220; https://doi.org/10.3390/fluids8080220 - 29 Jul 2023
Cited by 3 | Viewed by 1894
Abstract
A bubble’s motion is strongly influenced by the boundaries of tip structures, which correspond to the bubble’s size. In the present study, the dynamic behaviors of a cavitation bubble near a conical tip structure are investigated experimentally and numerically. A series of experiments [...] Read more.
A bubble’s motion is strongly influenced by the boundaries of tip structures, which correspond to the bubble’s size. In the present study, the dynamic behaviors of a cavitation bubble near a conical tip structure are investigated experimentally and numerically. A series of experiments were carried out to analyze the bubble’s shape at different relative cone distances quantitatively. Due to the crucial influence of the phase change on the cavitation bubble’s dynamics over multiple cycles, a compressible two-phase model taking into account the phase change and heat transfer implemented in OpenFOAM was employed in this study. The simulation results regarding the bubble’s radius and shape were validated with corresponding experimental photos, and a good agreement was achieved. The bubble’s primary physical features (e.g., shock waves, liquid jets, high-pressure zones) were well reproduced, which helps us understand the underlying mechanisms. Meanwhile, the latent damage was quantified by the pressure load at the cone apex. The effects of the relative distance γ and cone angle θ on the maximum temperature, pressure peaks, and bubble position are discussed and summarized. The results show that the pressure peaks during the bubble’s collapse increase with the decrease in γ. For a larger γ, the first minimum bubble radius increases while the maximum temperature decreases as θ increases; the pressure peak at the second final collapse is first less than that at the first final collapse and then much greater than that one. For a smaller γ, the pressure peaks at different θ values do not vary very much. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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24 pages, 11341 KiB  
Article
Bulk Cavitation in Model Gasoline Injectors and Their Correlation with the Instantaneous Liquid Flow Field
by Dimitrios Kolokotronis, Srikrishna Sahu, Yannis Hardalupas, Alex M. K. P. Taylor and Akira Arioka
Fluids 2023, 8(7), 214; https://doi.org/10.3390/fluids8070214 - 22 Jul 2023
Cited by 2 | Viewed by 1223
Abstract
It is well established that spray characteristics from automotive injectors depend on, among other factors, whether cavitation arises in the injector nozzle. Bulk cavitation, which refers to the cavitation development distant from walls and thus far from the streamline curvature associated with salient [...] Read more.
It is well established that spray characteristics from automotive injectors depend on, among other factors, whether cavitation arises in the injector nozzle. Bulk cavitation, which refers to the cavitation development distant from walls and thus far from the streamline curvature associated with salient points on a wall, has not been thoroughly investigated experimentally in injector nozzles. Consequently, it is not clear what is causing this phenomenon. The research objective of this study was to visualize cavitation in three different injector models (designated as Type A, Type B, and Type C) and quantify the liquid flow field in relation to the bulk cavitation phenomenon. In all models, bulk cavitation was present. We expected this bulk cavitation to be associated with a swirling flow with its axis parallel to that of the nozzle. However, liquid velocity measurements obtained through particle image velocimetry (PIV) demonstrated the absence of a swirling flow structure in the mean flow field just upstream of the nozzle exit, at a plane normal to the hypothetical axis of the injector. Consequently, we applied proper orthogonal decomposition (POD) to analyze the instantaneous liquid velocity data records in order to capture the dominant coherent structures potentially related to cavitation. It was found that the most energetic mode of the liquid flow field corresponded to the expected instantaneous swirling flow structure when bulk cavitation was present in the flow. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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21 pages, 13275 KiB  
Article
Vapor Bubble Deformation and Collapse near Free Surface
by Yue Chen, Qichao Wang, Hongbing Xiong and Lijuan Qian
Fluids 2023, 8(7), 187; https://doi.org/10.3390/fluids8070187 - 22 Jun 2023
Cited by 1 | Viewed by 1735
Abstract
Vapor bubbles are widely concerned in many industrial applications. The deformation and collapse of a vapor bubble near a free surface after being heated and raised from the bottom wall are investigated in this paper. On the basis of smoothed particle hydrodynamics (SPH) [...] Read more.
Vapor bubbles are widely concerned in many industrial applications. The deformation and collapse of a vapor bubble near a free surface after being heated and raised from the bottom wall are investigated in this paper. On the basis of smoothed particle hydrodynamics (SPH) and the van der Waals (VDW) equation of state, a numerical model of fluid dynamics and phase change was developed. The effects of fluid dynamics were considered, and the phase change of evaporation and condensation between liquid and vapor were discussed. Quantitative and qualitative comparisons between our numerical model and the experimental results were made. After verification, the numerical simulation of bubbles with the effects of the shear viscosity ηs and the heating distance L were taken into account. The regularity of the effect of the local Reynolds number (Re) and the Ohnesorge number (Oh) on the deformation of vapor bubbles is summarized through a further analysis of several cases, which can be summarized into four major patterns as follows: umbrella, semi-crescent, spheroid, and jet. The results show that the Re number has a great influence on the bubble deformation of near-wall bubbles. For Re > 1.5 × 102 and Oh < 3 × 10−4, the shape of the bubble is umbrella; for Re < 5 × 100 and Oh > 10−3, the bubble is spheroidal; and for 5 × 100 < Re < 1.5 × 102, 3 × 10−4 < Oh < 10−3, the bubble is semi-crescent. For liquid-surface bubbles, the Re number effect is small, and when Oh > 5 × 10−3, the shape of the bubble is jet all the time; there is no obvious difference in the bubble deformation, but the jet state is more obvious as the Re decreases. Finally, the dynamic and energy mechanisms behind each mode are discussed. The bubble diameter, bubble symmetry coefficient, and rising velocity were analyzed during their whole processes of bubble growth and collapse. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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15 pages, 7639 KiB  
Article
Experimental Study of the Cavitation Effects on Hydrodynamic Behavior of a Circular Cylinder at Different Cavitation Regimes
by Yuxing Lin, Ebrahim Kadivar and Ould el Moctar
Fluids 2023, 8(6), 162; https://doi.org/10.3390/fluids8060162 - 23 May 2023
Cited by 4 | Viewed by 1613
Abstract
In this work, we experimentally investigated the cavitation effects on the hydrodynamic behavior of a circular cylinder at different cavitating flows. We analyzed the cavitation dynamics behind the circular cylinder using a high-speed camera and also measured the associated hydrodynamic forces on the [...] Read more.
In this work, we experimentally investigated the cavitation effects on the hydrodynamic behavior of a circular cylinder at different cavitating flows. We analyzed the cavitation dynamics behind the circular cylinder using a high-speed camera and also measured the associated hydrodynamic forces on the circular cylinder using a load cell. We studied the cavitation dynamics around the cylinder at various types of the cavitating regimes such as cloud cavitation, partial cavitation and cavitation inception. In addition, we analyzed the cavitation dynamics at three different Reynolds numbers: 1 × 105, 1.25 × 105 and 1.5 × 105. The results showed that the hydrodynamics force on the circular cylinder can be increased with the formation of the cavitation behind the cylinder compared with the cylinder at cavitation inception regime. The three-dimensional flow caused complex cavitation behavior behind the cylinder and a strong interaction between vortex structures and cavity shedding mechanism. In addition, the results revealed that the effects of the Reynolds number on the cavitation dynamics and amplitude of the shedding frequency is significant. However the effects of the cavitation number on the enhancement of the amplitude of the shedding frequency in the cavitating flow with a constant velocity is slightly higher than the effects of Reynolds number on the enhancement of the amplitude of the shedding frequency at a constant cavitation number. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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13 pages, 1016 KiB  
Article
Comparison of Vortex Cut and Vortex Ring Models for Toroidal Bubble Dynamics in Underwater Explosions
by Lingxi Han, Tianyuan Zhang, Di Yang, Rui Han and Shuai Li
Fluids 2023, 8(4), 131; https://doi.org/10.3390/fluids8040131 - 13 Apr 2023
Cited by 5 | Viewed by 2187
Abstract
The jet impact from a collapsing bubble is an important mechanism of structural damage in underwater explosions and cavitation erosion. The Boundary Integral Method (BIM) is widely used to simulate nonspherical bubble dynamic behaviors due to its high accuracy and efficiency. However, conventional [...] Read more.
The jet impact from a collapsing bubble is an important mechanism of structural damage in underwater explosions and cavitation erosion. The Boundary Integral Method (BIM) is widely used to simulate nonspherical bubble dynamic behaviors due to its high accuracy and efficiency. However, conventional BIM cannot simulate toroidal bubble dynamics, as the flow field transforms from single-connected into double-connected. To overcome this problem, vortex cut and vortex ring models can be used to handle the discontinuous potential on the toroidal bubble surface. In this work, we compare these two models applied to toroidal bubble dynamics in a free field and near a rigid wall in terms of bubble profile, bubble gas pressure, and dynamic pressure induced by the bubble, etc. Our results show that the two models produce comparable outcomes with a sufficient number of nodes in each. In the axisymmetric case, the vortex cut model is more efficient than the vortex ring model. Moreover, we found that both models improve in self-consistency as the number of bubble surface elements (N) increases, with N=300 representing an optimal value. Our findings provide insights into the numerical study of toroidal bubble dynamics, which can enhance the selection and application of numerical models in research and engineering applications. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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Review

Jump to: Editorial, Research

23 pages, 6128 KiB  
Review
A Review of Preconditioning and Artificial Compressibility Dual-Time Navier–Stokes Solvers for Multiphase Flows
by Van-Tu Nguyen and Warn-Gyu Park
Fluids 2023, 8(3), 100; https://doi.org/10.3390/fluids8030100 - 16 Mar 2023
Cited by 5 | Viewed by 2657
Abstract
This review paper aims to summarize recent advancements in time-marching schemes for solving Navier–Stokes (NS) equations in multiphase flow simulations. The focus is on dual-time stepping, local preconditioning, and artificial compressibility methods. These methods have proven to be effective in achieving high time [...] Read more.
This review paper aims to summarize recent advancements in time-marching schemes for solving Navier–Stokes (NS) equations in multiphase flow simulations. The focus is on dual-time stepping, local preconditioning, and artificial compressibility methods. These methods have proven to be effective in achieving high time accuracy in simulations, as well as converting the incompressible NS equations into a hyperbolic form that can be solved using compact schemes, thereby accelerating the solution convergence and allowing for the simulation of compressible flows at all Mach numbers. The literature on these methods continues to grow, providing a deeper understanding of the underlying physical processes and supporting technological advancements. This paper also highlights the imposition of dual-time stepping on both incompressible and compressible NS equations. This paper provides an updated overview of advanced methods for the CFD community to continue developing methods and select the most suitable two-phase flow solver for their respective applications. Full article
(This article belongs to the Special Issue Numerical Modeling and Experimental Studies of Two-Phase Flows)
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