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Multiphase and Granular Flows

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Fluid Science and Technology".

Deadline for manuscript submissions: closed (20 June 2023) | Viewed by 26676

Special Issue Editor


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Guest Editor
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Interests: spray cooling; gas–liquid flow; heat transfer; droplet
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

This Special Issue is devoted to the mechanisms and applications of Multiphase and Granular Flows in various fields. Multiphase and Granular Flows are the simultaneous flows of materials with two or more thermodynamic phases. They are central to many industries such as processing, energy production, spray cooling, pharmaceuticals, and agriculture, and are also prevalent in many natural phenomena.

The scope of this Special Issue includes all aspects of mass, momentum, and energy exchange phenomena among different phases that occur in disperse flows, including gas–liquid and liquid–liquid flows, flows in porous media, boiling, granular flows, etc. In particular, topics related to atmospheric governance and the spread of respiratory viruses are also welcome.

In this Special Issue, we invite submissions exploring cutting-edge research and recent advances in the fields of Multiphase and Granular Flows. Both theoretical and experimental studies are welcome, as well as comprehensive review and survey papers.

Prof. Dr. Zhifu Zhou
Guest Editor

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Keywords

  • multiphase flow
  • granular flow
  • biofluid
  • micro-nano fluid
  • flow induced vibration
  • respiratory virus transmission
  • aerosol transmission
  • optimization and control of flow
  • phase change
  • heat transfer

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Published Papers (13 papers)

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Research

19 pages, 4331 KiB  
Article
Numerical Investigation of the Water-Drop Impact on Low-Drag Airfoil Using the Euler–Euler Approach and Eulerian Wall Film Model
by Lingjie Long, Xiaogang Liu, Chenxi Zhao, Zhongyi Wang and Haifeng Sun
Appl. Sci. 2023, 13(13), 7743; https://doi.org/10.3390/app13137743 - 30 Jun 2023
Cited by 2 | Viewed by 1333
Abstract
The Eulerian Wall Film (EWF) model is a mathematical model employed to analyze the behavior of fluid films on a surface. The model has been widely adopted in various engineering applications due to its accuracy and efficiency. However, it is rarely applied in [...] Read more.
The Eulerian Wall Film (EWF) model is a mathematical model employed to analyze the behavior of fluid films on a surface. The model has been widely adopted in various engineering applications due to its accuracy and efficiency. However, it is rarely applied in the aerospace field. The solution of the water-drop impact constitutes an indispensable prerequisite for the computation of ice accretion on the exterior of aircraft wings. In this study, we propose a novel approach for the estimation of water-drop impact on wing surfaces by integrating the Euler–Euler approach and EWF model. This approach is capable of furnishing a point of reference and a theoretical foundation for prospective water-drop impact experiments. Through comparison with pertinent experimental findings, the precision of the numerical simulation approach utilized in this paper is substantiated. Specifically, the research object is the NACA653-218 airfoil of the C-919 transport aircraft, for which the aerodynamic properties, water-drop collision, and liquid film flow characteristics during steady flight were simulated. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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33 pages, 6639 KiB  
Article
An AMR-Based Liquid Film Simulation with Surfactant Transport Using PLIC-HF Method
by Tongda Lian, Shintaro Matsushita and Takayuki Aoki
Appl. Sci. 2023, 13(3), 1955; https://doi.org/10.3390/app13031955 - 2 Feb 2023
Cited by 4 | Viewed by 1729
Abstract
In this study, an AMR-PLIC-HF method is proposed and implemented by GPU parallel computing based on CUDA programming language and NVIDIA GPU. The present method improves the computation efficiency without compromising the accuracy and conservation of the volume. To satisfy the requirements of [...] Read more.
In this study, an AMR-PLIC-HF method is proposed and implemented by GPU parallel computing based on CUDA programming language and NVIDIA GPU. The present method improves the computation efficiency without compromising the accuracy and conservation of the volume. To satisfy the requirements of stencil points of the PLIC-HF method, an extended stencil computation method based on the tree-based AMR method is proposed and implemented. The Weakly Compressible Scheme (WCS) is used in the present work as a fluid solver. An evolving pressure projection method is adopted to suppress the oscillation induced by the reflection of acoustic waves. The Langmuir model is introduced into the solver to calculate surfactant transport and the Marangoni effect caused by the gradient of the interface concentration of the surfactant. The single vortex flow results verify the accuracy of the AMR-PLIC method. A single bubble rising problem with two different physical property settings is simulated. The results show good agreement with the results given by incompressible solvers. This verifies the accuracy of the two-phase flow solver including the AMR-PLIC-HF method and the WCS. The generation and rupture of liquid film by a single bubble freely rising to an interface is simulated by the present solver with a 1024×2048 AMR grid as the finest resolution. This simulation successfully calculates surfactant transport and the Marangoni effect. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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17 pages, 4891 KiB  
Article
Numerical Gas–Liquid Two-Phase Flow Regime Identification in a Horizontal Pipe Using Dynamic Pressure Data
by Umair Khan, William Pao and Nabihah Sallih
Appl. Sci. 2023, 13(2), 1225; https://doi.org/10.3390/app13021225 - 16 Jan 2023
Cited by 6 | Viewed by 3108
Abstract
Gas–liquid two-phase flow is very common in industrial pipelines. Flow regime identification is the first step to design, analyze, and operate the gas–liquid system successfully. The purpose of this study is to develop a methodology for identification of a two-phase flow regime using [...] Read more.
Gas–liquid two-phase flow is very common in industrial pipelines. Flow regime identification is the first step to design, analyze, and operate the gas–liquid system successfully. The purpose of this study is to develop a methodology for identification of a two-phase flow regime using post signal processing techniques, namely Fast Fourier Transform (FFT) and Probabilistic Density Function (PDF). Three different flow regimes were simulated in a 6 m horizontal pipe with a 0.050 m inner diameter. A Level-Set (LS) method coupled with Volume of Fluid (VOF) method is used to model the air–water interface. After validation of the numerical method, dynamic pressure readings were collected with the intent to identify the associated flow regimes by post-processing of these signals. It was concluded that dynamic pressure signals of different flow regimes show different characteristics (like dominant frequency, FFT amplitude, PDF location and PDF magnitude) in the time and frequency domains. These characteristics can be potentially used as differentiating factors to distinguish different flow regimes. This research is limited to stratified, slug, and annular flow in the horizontal pipe. This paper uses a new approach to identify the flow regime in a horizontal pipe by Fast Fourier Transform and Probability Density Function of dynamic pressure readings obtained by using numerical simulation. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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20 pages, 5223 KiB  
Article
Thermal Performance Estimation of Nanofluid-Filled Finned Absorber Tube Using Deep Convolutional Neural Network
by Yue Hua, Chang-Hao Yu, Jiang-Zhou Peng, Wei-Tao Wu, Yong He and Zhi-Fu Zhou
Appl. Sci. 2022, 12(21), 10883; https://doi.org/10.3390/app122110883 - 27 Oct 2022
Cited by 4 | Viewed by 1399
Abstract
Numerical simulations are usually used to analyze and optimize the performance of the nanofluid-filled absorber tube with fins. However, solving partial differential equations (PDEs) repeatedly requires considerable computational cost. This study develops two deep neural network-based reduced-order models to accurately and rapidly predict [...] Read more.
Numerical simulations are usually used to analyze and optimize the performance of the nanofluid-filled absorber tube with fins. However, solving partial differential equations (PDEs) repeatedly requires considerable computational cost. This study develops two deep neural network-based reduced-order models to accurately and rapidly predict the temperature field and heat flux of nanofluid-filled absorber tubes with rectangular fins, respectively. Both network models contain a convolutional path, receiving and extracting cross-sectional geometry information of the absorber tube presented by signed distance function (SDF); then, the following deconvolutional blocks or fully connected layers decode the temperature field or heat flux out from the highly encoded feature map. According to the results, the average accuracy of the temperature field prediction is higher than 99.9% and the computational speed is four orders faster than numerical simulation. For heat flux estimation, the R2 of 81 samples reaches 0.9995 and the average accuracy is higher than 99.7%. The same as the field prediction, the heat flux prediction also takes much less computational time than numerical simulation, with 0.004 s versus 393 s. In addition, the changeable learning rate strategy is applied, and the influence of learning rate and dataset size on the evolution of accuracy are investigated. According to our literature review, this is the first study to estimate the temperature field and heat flux of the outlet cross section in 3D nanofluid-filled fined absorber tubes using a deep convolutional neural network. The results of the current work verify both the high accuracy and efficiency of the proposed network model, which shows its huge potential for the fin-shape design and optimization of nanofluid-filled absorber tubes. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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16 pages, 14099 KiB  
Article
Real-Time Prediction of Transarterial Drug Delivery Based on a Deep Convolutional Neural Network
by Xin-Yi Yuan, Yue Hua, Nadine Aubry, Mansur Zhussupbekov, James F. Antaki, Zhi-Fu Zhou and Jiang-Zhou Peng
Appl. Sci. 2022, 12(20), 10554; https://doi.org/10.3390/app122010554 - 19 Oct 2022
Cited by 4 | Viewed by 1523
Abstract
This study develops a data-driven reduced-order model based on a deep convolutional neural network (CNN) for real-time and accurate prediction of the drug trajectory and concentration field in transarterial chemoembolization therapy to assist in directing the drug to the tumor site. The convolutional [...] Read more.
This study develops a data-driven reduced-order model based on a deep convolutional neural network (CNN) for real-time and accurate prediction of the drug trajectory and concentration field in transarterial chemoembolization therapy to assist in directing the drug to the tumor site. The convolutional and deconvoluational layers are used as the encoder and the decoder, respectively. The input of the network model is designed to contain the information of drug injection location and the blood vessel geometry and the output consists of the drug trajectory and the concentration field. We studied drug delivery in two-dimensional straight, bifurcated blood vessels and the human hepatic artery system and showed that the proposed model can quickly and accurately predict the spatial–temporal drug concentration field. For the human hepatic artery system, the most complex case, the average prediction accuracy was 99.9% compared with the CFD prediction. Further, the prediction time for each concentration field was less than 0.07 s, which is four orders faster than the corresponding CFD simulation. The high performance, accuracy and speed of the CNN model shows the potential for effectively assisting physicians in directing chemoembolization drugs to tumor-bearing segments, thus improving its efficacy in real-time. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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14 pages, 3987 KiB  
Article
Droplet Formation and Impingement Dynamics of Low-Boiling Refrigerant on Solid Surfaces with Different Roughness under Atmospheric Pressure
by Shu-Yan Chen, Dong-Qing Zhu, Hong-Jie Xing, Qin Zhao, Zhi-Fu Zhou and Bin Chen
Appl. Sci. 2022, 12(17), 8549; https://doi.org/10.3390/app12178549 - 26 Aug 2022
Cited by 4 | Viewed by 1561
Abstract
The dynamic behavior of droplet impingement is one of the most important processes of spray cooling. Although refrigerants with a low boiling point have been widely used in spray cooling, their high volatility makes it difficult to generate a stable droplet under atmospheric [...] Read more.
The dynamic behavior of droplet impingement is one of the most important processes of spray cooling. Although refrigerants with a low boiling point have been widely used in spray cooling, their high volatility makes it difficult to generate a stable droplet under atmospheric pressure, and thus the dynamic behavior of droplet impingement is rarely reported. Therefore, it is of great significance to study the behavior of refrigerant droplet impingement to fill the relevant research gaps. In this paper, an experimental system for single refrigerant droplet generation and impingement at atmospheric pressure has been established. By means of high-speed photography technology, the morphology and dynamics of R1336mzz(Z) droplet impingement on grooved carbon steel walls have been studied. Phenomena such as a truncated sphere, boiling, and finger-shaped disturbance were observed, and the reasons responsible for them were analyzed. The effects of Weber number (We) and surface roughness (Ra) on droplet spreading factor (β) were investigated quantitatively. Higher We always causes a larger βmax, while Ra has a different influence on βmax. The Cassie–Wenzel transition occurs when Ra increases from 1.6 μm to 3.2 μm, leading to a rapid decrease in βmax. An empirical formula has been proposed to predict βmax under different conditions. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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17 pages, 2477 KiB  
Article
An Experimental Analysis of Gas Reduction in Multiphase Flow with a KMS Helical Static Mixer
by Jose Alejandro Vasquez-Santacruz, Rogelio de Jesus Portillo-Velez, Pedro Javier Garcia-Ramirez, Luis Felipe Marín-Urías, Diego Sánchez-Montero and Luis Hector Porrágas-Beltrán
Appl. Sci. 2022, 12(16), 7988; https://doi.org/10.3390/app12167988 - 10 Aug 2022
Cited by 1 | Viewed by 1456
Abstract
The separation dynamics of a multiphase fluid mixture is studied with the aim to validate the gas reduction from the mixture by means of a KMS helical static mixer device through a laboratory prototype based on the jet-pump artificial lift system for oil [...] Read more.
The separation dynamics of a multiphase fluid mixture is studied with the aim to validate the gas reduction from the mixture by means of a KMS helical static mixer device through a laboratory prototype based on the jet-pump artificial lift system for oil extraction. The study is focused on the cyclone phenomenon, produced by the KMS, to experimentally verify the reduction of foaming in a reservoir behaving as a horizontal gravity separator of an oil–gas–water mixture under specific dynamics conditions of velocity and pressure of an incoming streamline, as well as some physical mounting configurations of the device. The results were numerical and experimentally validated, projecting the real performance in three-phase separators in an oil extraction field to improve efficiency in pumping machines regarding the negative effects of the gas. Concerning the gas reduction, a KMS of two elements located at 100 mm from the entrance of the horizontal reservoir and 20 mm from a gas casing tube successfully improves the gas isolation from the mixture, from 29.2% to practically 0% over 200 min in the reservoir, to let oil and water become separated by sedimentation. This gas reduction is indirectly assessed by the emulsion that is generated, which affects the time of oil separation in the counterbalance. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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16 pages, 6137 KiB  
Article
Hole Cleaning Performance of V-Shaped Hole Cleaning Device in Horizontal Well Drilling: Numerical Modeling and Experiments
by Yunjian Zhou, Yufa He, Zijian Li and Guoshuai Ju
Appl. Sci. 2022, 12(10), 5141; https://doi.org/10.3390/app12105141 - 19 May 2022
Cited by 5 | Viewed by 1977
Abstract
The application of hole cleaning devices can effectively solve the hole cleaning problem during the drilling of horizontal wells. Improving the hole cleaning performance is directly related to subsequent drilling time and cost. In this paper, the solid–liquid two-phase hydrodynamic characteristics under the [...] Read more.
The application of hole cleaning devices can effectively solve the hole cleaning problem during the drilling of horizontal wells. Improving the hole cleaning performance is directly related to subsequent drilling time and cost. In this paper, the solid–liquid two-phase hydrodynamic characteristics under the action of the V-shaped hole cleaning device for drilling horizontal wells were studied experimentally and numerically. The decay law of spiral flow induced by the V-shaped hole cleaning device was obtained numerically using the commercial CFD code “Fluent” by changing the blade rotational speed, blade helix angle, and consistency coefficient of drilling fluid. The helix angle will cause the flow direction of local fluid to deflect. The swirl intensity of spiral flow increases significantly with an increase in rotational speed. The hole cleaning performance was better when the helix angle was from about 10 to 20 degrees. Increasing the fluid consistency coefficient will rapidly make the spiral flow decay, resulting in a shorter effective action distance and a worse hole cleaning effect. The simulation results were validated against the experimental results of the flow loop. Both experimental and simulation results showed that the hole cleaning performance was improved by using the V-shaped hole cleaning device. The very good agreement achieved between the results has presented an opportunity to study the hole cleaning effect of a hole cleaning device in unsteady state conditions. The results will provide theoretical guidance for efficient hole cleaning using V-shaped hole cleaning devices for horizontal well drilling. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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23 pages, 3958 KiB  
Article
CFD-DEM Simulation of the Transport of Manganese Nodules in a Vertical Pipe
by Shuang Teng, Can Kang, Kejin Ding, Changjiang Li and Sheng Zhang
Appl. Sci. 2022, 12(9), 4383; https://doi.org/10.3390/app12094383 - 26 Apr 2022
Cited by 11 | Viewed by 2572
Abstract
The present study aims to describe the characteristics of the hydraulic transport of manganese nodules in a vertical pipe. The solid–liquid two-phase flows were simulated using a numerical technique that combines the computational fluid dynamics (CFD) method and the discrete element method (DEM). [...] Read more.
The present study aims to describe the characteristics of the hydraulic transport of manganese nodules in a vertical pipe. The solid–liquid two-phase flows were simulated using a numerical technique that combines the computational fluid dynamics (CFD) method and the discrete element method (DEM). Manganese nodules with diameters of 5.0 mm, 15.0 mm, and 30.0 mm were selected. The effects of the initial solid volume fraction and the initial mixture velocity were investigated. The results show that with increasing initial solid volume fraction, the liquid and solid velocities decrease but the total pressure drop over the pipe increases. Small particles are responsible for high particle collision frequency, which causes decreases in both the liquid velocity and the total pressure drop. Energy loss is aggravated by increasing the initial mixture velocity, manifesting in the increase of the total pressure drop. The retention ratio of manganese nodules varies inversely with the initial mixture velocity. A formula is proposed to describe the pressure drop due to the presence of solid particles and collisions. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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10 pages, 3421 KiB  
Article
Breakup Dynamics of Droplets in Symmetric Y-Junction Microchannels
by Li Lei, Yuting Zhao, Jun An, Bo Zhang and Jingzhi Zhang
Appl. Sci. 2022, 12(8), 4011; https://doi.org/10.3390/app12084011 - 15 Apr 2022
Cited by 3 | Viewed by 1941
Abstract
The experimental method is used to study the droplet breaking characteristics of an immiscible liquid–liquid t8wo-phase fluid in symmetric Y-junction microchannels. Silicone oil is used as the dispersed phase and distilled water containing 0.5% SDS is used as the continuous phase. Three breakup [...] Read more.
The experimental method is used to study the droplet breaking characteristics of an immiscible liquid–liquid t8wo-phase fluid in symmetric Y-junction microchannels. Silicone oil is used as the dispersed phase and distilled water containing 0.5% SDS is used as the continuous phase. Three breakup behaviors were observed: breakup with permanent obstruction, breakup with gaps, and no breakup. Two stages of the change of the neck width of the sub-droplet during the breakup process were discovered: a rapid breakup stage and a thread breakup stage. The effect of the breakup behavior on the flow pattern was investigated and it was found that the breakup behavior of the droplets made the slug flow area smaller; further, a new flow pattern was observed, being droplet flow. The length of the sub-droplet increases with an increase of the volume flow rate of the dispersed phase and the ratio of the volume flow rate of the dispersed phase to the continuous phase, while decreasing with an increase of the volume flow rate and the capillary number of the continuous phase. Based on the influence of the two-phase flow parameters on the length of the sub-droplet, a correlation formula for the length of the sub-droplet with good predictive performance is proposed. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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15 pages, 4472 KiB  
Article
Study on Thermal Performance of Single-Tank Thermal Energy Storage System with Thermocline in Solar Thermal Utilization
by Chao Zhu, Jian Zhang, Yueshe Wang, Zehong Deng, Peng Shi, Jian Wu and Zihao Wu
Appl. Sci. 2022, 12(8), 3908; https://doi.org/10.3390/app12083908 - 13 Apr 2022
Cited by 11 | Viewed by 2663
Abstract
For the intermittence and instability of solar energy, energy storage can be a good solution in many civil and industrial thermal scenarios. With the advantages of low cost, simple structure, and high efficiency, a single-tank thermal energy storage system is a competitive way [...] Read more.
For the intermittence and instability of solar energy, energy storage can be a good solution in many civil and industrial thermal scenarios. With the advantages of low cost, simple structure, and high efficiency, a single-tank thermal energy storage system is a competitive way of thermal energy storage (TES). In this study, a two-dimensional flow and heat transfer model of a cylindrical storage tank with water as heat transfer fluid (HTF) is developed, in which the effects of time, flow velocity, and height-to-diameter ratio of the tank on the thermocline thickness have been highlighted. The results show that the thermocline thickness in the storage tank is increasing during the charging and discharging processes, and it increases with the increase of the inlet flow velocity and the height to diameter ratio. It is emphasized that in our cases when the time period of t is 14,400 s, the fluid inlet velocity of uin is 4.577 × 10−4 m/s, and the height-to-diameter ratio of H/D is 1.2, the performance evaluation index reaches the maximum 0.9575, and the efficiency of the system is the highest. It is expected that all of the findings herein can provide a fundamental understanding of the design and operation of the single-tank thermal energy storage system in water heating for civil and industrial applications. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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13 pages, 3553 KiB  
Article
Interactions between Two Deformable Droplets in Tandem Fixed in a Gas Flow Field of a Gas Well
by Zhibin Wang, Tianli Sun, Zhongwei Yang, Guo Zhu and Hongyan Shi
Appl. Sci. 2021, 11(23), 11220; https://doi.org/10.3390/app112311220 - 25 Nov 2021
Cited by 3 | Viewed by 1882
Abstract
Knowing the droplet-deformation conditions, the droplet-breakup conditions, and the drag force in the interaction between two droplets with a high Reynolds number is of importance for tracking droplet movement in the annular flow field of a gas well. The interactions between two droplets [...] Read more.
Knowing the droplet-deformation conditions, the droplet-breakup conditions, and the drag force in the interaction between two droplets with a high Reynolds number is of importance for tracking droplet movement in the annular flow field of a gas well. The interactions between two droplets with a high Reynolds number in a tandem arrangement fixed in flowing gas was investigated. The volume of fluid (VOF) method was used to model the droplets’ surface structure. Two different body forces were exerted on both droplets to hold them suspended at a fixed location, which eliminated the effect of droplet acceleration or deceleration on the drag and decreased the amount of computation required. The exerted body forces were calculated using the Newton iteration procedure. The interactions between the two droplets were analyzed by comparison with the simulation results of a single isolated droplet. The effect of the separation distance on the drag force was investigated by changing the separation spacing. The simulation results showed that for droplets with a small separating space between them, the dynamics of the downstream droplet were influenced significantly by the upstream droplet. The drag coefficient of the downstream droplet decreased considerably to a small, even negative, value, especially for droplets with higher Weber numbers and smaller initial separating spaces between them, while the drag force of the upstream droplet was influenced only slightly. In addition, a formula for predicting the final drag coefficient of the downstream droplet was devised. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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17 pages, 4554 KiB  
Article
Air-Water Bubbly Flow by Multiple Vents on a Hydrofoil in a Steady Free-Stream
by Kiseong Kim, David Nagarathinam, Byoung-Kwon Ahn, Cheolsoo Park, Gun-Do Kim and Il-Sung Moon
Appl. Sci. 2021, 11(21), 9890; https://doi.org/10.3390/app11219890 - 22 Oct 2021
Cited by 6 | Viewed by 2018
Abstract
Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, c, is oriented at the [...] Read more.
Flow features, due to air injection through multiple vents on the surface of a hydrofoil inclined at an angle with respect to the free-stream in a cavitation tunnel, are presented here. The hydrofoil, with a chord length, c, is oriented at the angle of inclination, α = 3.5°. The Froude number, Fn, based on the free-stream velocity, V, and air injection vent diameter, dh, is 30.30, 50.51 and 70.71. Air is injected through multiple vents on the hydrofoil at the non-dimensional air injection coefficient, Cq168917. The air bubble packing per unit area is quantified using spatial density, SD, at various combinations of Fn,Cq based on a high-speed video from the side view. The time-averaged spatial density, <SD>, is observed to increase in a logarithmic manner with an increase in the air injection rate, Q, at various Froude numbers. There is an increase in the mean spatial density of the bubbles with the increase in Cq at all Fn. A power–law relation is shown to exist between the time-averaged spatial density, <SD>, and the non-dimensional flow variables, Reynolds number, Reair, Fn and Cq based on a regression analysis. By tracking individual finite volume bubbles flowing with the free-stream, the bubble dimensions in pixels are quantified using quantities such as the deformation rate, ϵ, and standardization, ϵS, from the side-view videos. It is observed that ϵ and ϵS change with time, even as they become advected with the free-stream. Through high-speed imaging from the top view, we characterize the bubbly flow features’ time-averaged thickness, t, at various combinations of Fn,Cq at α = 3.5°. We obtain a power-law relation between the non-dimensional time-averaged jet thickness, t/c, and the non-dimensional flow parameters such as, Reair, Fn,Cq and the non-dimensional streamwise distance, x/xref, based on a regression analysis, where xref is a reference distance. The results are relevant to engineering applications where the air–water bubbly flow in a free-stream is important. Full article
(This article belongs to the Special Issue Multiphase and Granular Flows)
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