International Journal of Multiphase Flow最新文献

{"title":"Investigation of the dynamic characteristics of compound droplet impacting on microcolumn arrays","authors":"Li Dai,&nbsp;Yuying Du,&nbsp;Lijuan Qian","doi":"10.1016/j.ijmultiphaseflow.2025.105193","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105193","url":null,"abstract":"<div><div>An experimental study on the impact behavior of compound droplet on microcolumn arrays was performed. The deforming, spreading and retraction were investigated by varying Weber number (<em>We</em> = 25–250), inner liquid viscosity (<em>μ</em> = 5.92–21.1 mPa·s) and ratios of inner to outer radii (<em>α</em> = 0.35–0.72). The results show that droplets with larger α exhibits jet spreading in the early stage and slower retraction in the later stage. The increasing <em>We</em> yields larger inertia force, contributing to that the spreading pattern gradually changes from a rhombus shape to a circular shape. The spreading factor increases with the increasing inner liquid viscosity. In the retracting stage, the spreading factor increases with the decreasing <em>α</em> due to the additional surface tension force causing by the presence of inner interface in the rim. When the viscosity of inner liquid is considerably large, the microstructure inhibits the spreading process. The retraction maximum height on the microstructure increases with the increasing <em>α</em>. Furthermore, the energy dissipation equation was analyzed. It can be concluded that the increasing friction coefficient, contact area and viscosity lead to greater energy dissipation, significantly affecting spreading dynamics. This study provides vital information for fundamental understanding of the dynamic characteristics when the compound droplet impacts on the microcolumn arrays.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105193"},"PeriodicalIF":3.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comprehensive lift force model for deformable bubbles rising in moderate shear flows","authors":"Niklas Hidman,&nbsp;Henrik Ström,&nbsp;Gaetano Sardina,&nbsp;Srdjan Sasic","doi":"10.1016/j.ijmultiphaseflow.2025.105166","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105166","url":null,"abstract":"<div><div>We provide comprehensive regression models for the lift force coefficient <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>L</mi></mrow></msub></math></span> and the terminal relative velocity for clean deformable bubbles in moderate shear flows. The models are expressed as functions of the a priori known Galilei (<span><math><mi>Ga</mi></math></span>) and Eötvös (<span><math><mi>Eo</mi></math></span>) numbers, eliminating the need for additional sub-models to predict, for example, the bubble shape. The proposed models are developed for a wide range of governing parameters (approximately <span><math><mrow><mo>(</mo><mn>3</mn><mo>&lt;</mo><mi>Ga</mi><mo>&lt;</mo><mn>10000</mn><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mi>Eo</mi><mo>&lt;</mo><mn>20</mn><mo>)</mo></mrow></math></span>) and show good agreement with the existing numerical and experimental data. This robustness makes the models highly applicable to most practical gas–liquid systems. The <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>L</mi></mrow></msub></math></span>-model is particularly suited for moderate-to-high non-dimensional shear rates <span><math><mrow><mi>Sr</mi><mo>=</mo><mi>O</mi><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>−</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, where the lift force is significant compared to other hydrodynamic forces.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105166"},"PeriodicalIF":3.6,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A high-fidelity methodology for particle-resolved direct numerical simulations","authors":"M. Houssem Kasbaoui,&nbsp;Marcus Herrmann","doi":"10.1016/j.ijmultiphaseflow.2025.105175","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105175","url":null,"abstract":"<div><div>We present a novel computational method for direct numerical simulations of particle-laden flows with fully-resolved particles (PR-DNS). The method is based on the recently developed Volume-Filtering Immersed Boundary method [Dave et al, <em>Journal of Computational Physics</em>, 487:112136, 2023] derived by volume-filtering the transport equations. This approach is mathematically and physically rigorous, in contrast to other PR-DNS methods which rely on ad-hoc numerical schemes to impose no-slip boundary conditions on the surface of particles. With the present PR-DNS strategy, we show that the ratio of filter size to particle diameter acts as a parameter that controls the level of fidelity. In the limit where this ratio is very small, a well-resolved PR-DNS is obtained. Conversely, when the ratio of filter size to particle diameter is large, a classic point-particle method is obtained. The discretization of the filtered equations is discussed and compared to other PR-DNS strategies based on direct-forcing immersed boundary methods. Numerical examples with sedimenting resolved particles are discussed.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105175"},"PeriodicalIF":3.6,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Machine learning uncertainty framework applied to gas-liquid horizontal pipe flow","authors":"André Mendes Quintino,&nbsp;Milan Stanko","doi":"10.1016/j.ijmultiphaseflow.2025.105184","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105184","url":null,"abstract":"<div><div>Accurate multiphase pipe flow modeling (e.g. prediction of pressure drop and volume fraction) is important for several disciplines and industries. It is possible to develop pipe multiphase flow models using laboratory data or simulator output and machine learning techniques but their application is limited due to their black-box nature and subpar generalization performance. The effectiveness of these models can be improved by “teaching the models to know what they know” and outputting the prediction uncertainty together with a mean value. By giving a stochastic prediction, the model can inform the user about the uncertainty of its prediction, facilitating informed decision-making. In this work, we evaluate 3 machine learning frameworks and 3 parametrization strategies for the development of a stochastic data-driven gas-liquid pipe flow (pressure and holdup) model. This to ultimately determine which machine learning framework and parametrization strategy produces stochastic models that best fit the data set, capture its associated uncertainty and where the predicted uncertainty grows considerably in extrapolation scenarios, rendering the model useless. For this purpose, a steady-state two-phase horizontal flow synthetic dataset was created using a commercial multiphase flow simulator to train and validate three deep learning frameworks: deep ensembles, hyper-deep ensembles, and Monte Carlo dropout. The effect of the performance using different groups of input features to predict the pressure gradient and holdup is also evaluated, and the performance metrics are assessed based on in-domain (validation) and out-of-domain (extrapolation) cases, the latter consisting of a scale-up scenario (bigger diameter). Results indicate that all three frameworks accurately predicted the mean values. However, deep ensembles outperformed the other in predicting the uncertainty range. Additionally, the results show the feature importance of different dimensional and dimensionless inputs for the model training and prediction.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105184"},"PeriodicalIF":3.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ML-based semantic segmentation for quantitative spray atomization description","authors":"Basil Jose ,&nbsp;Oliver Lammel ,&nbsp;Fabian Hampp","doi":"10.1016/j.ijmultiphaseflow.2025.105179","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105179","url":null,"abstract":"<div><div>Fuel spray atomization in gas turbine systems significantly impacts the combustion process and thereby emission formation. Considering the necessity for quantitative description of the influence of operating conditions on the spray breakup mechanisms, a machine learning (ML) based methodology is introduced to accurately segment the dispersed liquid from the continuous gaseous phase in shadowgraphy images. The segmented images subsequently facilitate a high-level statistical analysis of gas-liquid-interface contours and ultimately instability dynamics. For this purpose, multiple ML models varying in architecture (Semantic FPN and DeepLabV3+), datasets and augmentations are benchmarked to achieve the best performance. Subsequently, the best model is validated and used to obtain conditional statistics on the detected spray contours of three different spray types (jet-in-crossflow, pressure swirl spray and prefilming airblast spray). The model showcases high robustness, transferability across spray configurations and accuracy along multiple never-seen sprays thereby illustrating the superiority of deep learning methods for scientific image segmentation tasks. Moreover, the inferred high-level statistical analysis provides novel quantitative insights into the involved turbulence-spray interactions aiding the understanding of jet, sheet and film atomization under highly turbulent flow conditions.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105179"},"PeriodicalIF":3.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The influence of drag, lift and torque modelling on the dynamics of ellipsoidal particles in a turbulent channel flow","authors":"A. Michel,&nbsp;B. Arcen","doi":"10.1016/j.ijmultiphaseflow.2025.105176","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105176","url":null,"abstract":"<div><div>Direct numerical simulation is coupled with a Lagrangian point-particle tracking to study the dynamics of inertial prolate ellipsoids in a turbulent channel flow. Two models are employed to compute the hydrodynamic force and torque acting on the ellipsoids in order to assess the influence of the fluid inertia. The first one is an analytical model derived under the assumption of a creeping flow motion at the particle scale while the second model relies on semi-empirical correlations to account for the effect of the fluid inertia on the hydrodynamic actions. For spherical and ellipsoidal particles alike, the hydrodynamic actions model has a weak influence on the probability density function of the particle Reynolds number and on their translational velocity statistics. The hydrodynamic actions modelling however strongly affects the near-wall rotation of weakly and moderately inertial ellipsoids, owing to the different rotation orbits favoured by the ellipsoids. This causes significant variations of the mean orientation and of the ellipsoids angular velocity statistics. In contrast, the rotational dynamics of highly inertial ellipsoids weakly depends on the hydrodynamic actions modelling in the near-wall region, but significantly varies in the buffer region. This effect is associated with the torque generated by the particle motion relative to the surrounding fluid, which results in a strong enhancement of the particle angular velocity fluctuations. Preferential alignment of the ellipsoids normal to the relative translational velocity vector is observed when the inertial effects are accounted for, corresponding to recent experimental observations and theoretical developments.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"188 ","pages":"Article 105176"},"PeriodicalIF":3.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Viscoplastic drops impacting a free-slip surface","authors":"Kindness Isukwem,&nbsp;Elie Hachem,&nbsp;Anselmo Pereira","doi":"10.1016/j.ijmultiphaseflow.2025.105177","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105177","url":null,"abstract":"<div><div>This theoretical and numerical study investigates the physical mechanisms that drive the spreading of viscoplastic drops of millimetric to centimetric size after they collide with a solid surface under free-slip conditions and negligible capillary effects. These impacting drops are modeled as Bingham fluids. The numerical simulations are conducted using a variational multi-scale method tailored to multiphase non-Newtonian fluid flows. The results are analyzed by examining the dynamics of spreading, energy balance, and scaling laws. The findings indicate that the kinetic energy from the impact of the drops is dissipated through viscoplastic effects during the spreading process, leading to the emergence of three distinct flow regimes: inertio-viscous, inertio-plastic, and mixed inertio-visco-plastic. These regimes are heavily influenced by the initial aspect ratio of the impacting drops, suggesting that morphology can be used to control spreading behavior. The study concludes with a diagram that correlates the drop’s maximum spreading and spreading time with various spreading regimes using a single dimensionless quantity termed the <em>impact parameter</em>.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105177"},"PeriodicalIF":3.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Drag and interfacial vorticity of spherical bubble contaminated with soluble surfactant","authors":"Kosuke Hayashi ,&nbsp;Yuya Motoki ,&nbsp;Dominique Legendre ,&nbsp;Akio Tomiyama","doi":"10.1016/j.ijmultiphaseflow.2025.105173","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105173","url":null,"abstract":"<div><div>Numerical simulations of spherical bubbles contaminated with soluble surfactant were carried out to investigate the surfactant effects on the drag coefficient, <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span>, and the interfacial vorticity, <span><math><mi>ω</mi></math></span>, produced at the bubble interface. The different surface contamination regimes are considered in both the diffusion-dominant case and advection-dominant case, for different ambient contamination conditions controlled by varying the Marangoni, Langmuir and Hatta numbers, <span><math><mrow><mi>M</mi><mi>a</mi></mrow></math></span>, <span><math><mrow><mi>L</mi><mi>a</mi></mrow></math></span> and <span><math><mrow><mi>H</mi><mi>a</mi></mrow></math></span>. The combinations, <span><math><mrow><msub><mrow><mi>Π</mi></mrow><mrow><mi>M</mi></mrow></msub><mo>=</mo><mi>L</mi><mi>a</mi><mi>M</mi><mi>a</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>Π</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>=</mo><mi>H</mi><mi>a</mi><mo>/</mo><mi>L</mi><mi>a</mi></mrow></math></span>, of the dimensionless groups were found to play dominant roles in the surfactant effects on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> and <span><math><mi>ω</mi></math></span> in both cases. Four different regimes for the dependence of the drag force and vorticity distribution as a function of the above dimensionless group were identified. In the diffusion-dominant case the vorticity is well correlated with a weighting average for those of clean and fully-contaminated bubbles, and a linear relation between <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> and the maximum vorticity holds as in the case with clean bubbles. The characteristics of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> in the advection-dominant case are more complicated, but they have been classified into four regimes in terms of <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span>. A simple correlation of the stagnant-cap angle expressed in terms of <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>M</mi></mrow></msub></math></span> was also obtained. This study thus revealed the surfactant effects on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> and <span><math><mi>ω</mi></math></span> and the drag-vorticity relations in detail at the first time for the different regimes of surface contamination.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105173"},"PeriodicalIF":3.6,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lattice Boltzmann flux solver for immiscible three-phase fluids boiling with large density ratio and spontaneous nucleation","authors":"Da Zhang ,&nbsp;Yan Li","doi":"10.1016/j.ijmultiphaseflow.2025.105174","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105174","url":null,"abstract":"<div><div>In this study, we propose a three-phase boiling lattice Boltzmann flux solver (TB-LBFS) based on phase field theory. The TB-LBFS is capable of achieving spontaneous nucleation in nucleate boiling and handling multiphase flow calculations with large density ratios, such as 1:1000. The source terms in the control equations of TB-LBFS can be freely added and solved, offering high flexibility for secondary development. Additionally, TB-LBFS addresses the limitation of previous phase field boiling models that could not achieve spontaneous nucleation. The model's excellent capability in simulating three-phase flow phase transitions has been tested through multiple classic 2D and 3D cases, including 2D composite droplet evaporation, the 2D Leidenfrost phenomenon, and 3D nucleate boiling in both two-phase and three-phase systems.</div></div>","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"187 ","pages":"Article 105174"},"PeriodicalIF":3.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large eddy simulations of free-falling perforated disks with small inertias","authors":"Wenhui Zhang,&nbsp;Yingjie Wei","doi":"10.1016/j.ijmultiphaseflow.2025.105154","DOIUrl":"10.1016/j.ijmultiphaseflow.2025.105154","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The dynamics of free-falling perforated disks of porosity &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; are numerically investigated by the large eddy simulation (LES) within the range &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1000&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Three falling styles are identified, namely spiral motion, spiral irregular motion and Hula-Hoop motion. A linear relationship of the Archimedes number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and the Reynolds number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is observed within the intermediate Reynolds number regime. The mean values of crucial kinematic and dynamic variables are also given, and some scaling laws related to the perforated disk thickness &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and diameter &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are determined. For the mean descent velocity &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;, the gravitational velocity &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a suitable characteristic velocity scale; this is not the case for the terminal velocity &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, which is proportional to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The characteristic timescale &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; for vortex shedding is proportional to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, which indicates thin perforated disks facilitate vortex shedding. The mean normal force &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt; is proportional to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and irrespective of falling styles. It indicates different falling styles are","PeriodicalId":339,"journal":{"name":"International Journal of Multiphase Flow","volume":"186 ","pages":"Article 105154"},"PeriodicalIF":3.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}