Volume Of Fluid Method Research Articles

Influence of wettability and surface tension on bubble formation from a needle

AbstractThe multiphase flow accompanied by contact line motion is a common flow phenomenon in nature and industry. When investigating the bubble formation from a needle, it is generally assumed that the contact line is fixed at the inner diameter of a needle. Namely, the influence of contact line motion on bubble formation is ignored. In this paper, the effects of wettability and surface tension on the characteristics of bubble formation were studied using volume of fluid method. The changes of bubble volume, instantaneous contact angle, contact line radius, and the motion mechanism of contact line were analyzed in detail. It is found that when surface wettability and/or surface tension are different, the motion type of contact line during bubble formation is different, and the stage of bubble formation shows a great difference too. The motion of contact line is mainly affected by the pressure inside a bubble, the adhesion force, and the hydrostatic pressure of liquid outside a bubble. The sum of all forces driving contact line to move inward or outward controls the motion type of contact line.

Effects of Homogeneous and Inhomogeneous Roughness on the Ship Resistance

Ship hull roughness can significantly increase the ship resistance. The roughness caused by biofouling attached to the ship hull is not uniform but has a random distribution. The purpose of this study is to investigate how the inhomogeneous surface roughness distribution affects the ship resistance and the various resistance components. The KRISO container ship (KCS) is considered as a case study. To model the inhomogeneous surface roughness, the ship hull is divided into three segments with equal wetted surface area. Combinations of three roughness heights, denoted as P, Q, and R with ks values of 125 μm, 269 μm, and 425 μm, respectively, are considered to obtain homogeneous and inhomogeneous roughness arrangements (PPP, QQQ, RRR, PQR, PRQ, QPR, QRP, RPQ, and RQP). CFD method is utilized in this study, utilizing RANS equations and k-ω SST turbulence model. A VoF method is used to model the free surface. CFD simulation results show that for the homogeneous roughness, the total resistance coefficient CT increases with increasing ks (PPP < QQQ < RRR), as expected. For the inhomogeneous roughness, the friction resistance coefficient CF increases in the order PQR < PRQ < QPR < QRP < RPQ < RQP, consistent with results from earlier studies. In all the cases, the friction resistance (CF) is the dominant component of the total resistance. As Re increases from 2.2 x 109 to 2.7 x 109, the percentage of the friction resistance decreases, while the percentage of the wave resistance increases. The viscous-pressure resistance decreases slightly as Re increases from 2.2 x 109 to 2.7 x 109.

CFD Analysis of Takeoff from a Water Surface for an Insect-Scale Aerial/Aquatic Robot

To develop an insect-scale aerial/aquatic robot, we analyzed takeoff mechanisms to counteract surface tension, such as paddling, slapping, and clap-and-fling. Because a diving beetle, Eretes griseus, takes off directly from the water surface, a flapping-wing robot is promising as an alternative to a drone with multiple rotary wings. In this study, we first investigated diving beetle flight with a three-dimensional high-speed camera system and analyzed the motion characteristics. Subsequently, we developed a computational fluid dynamics method that tracked the water surface using a volume of fluid method, reproduced the motion with a multibody model, treated the deformation of the elastic membrane wing with the phase delay of the joint angle functions, and simulated takeoff, that is, the transition from water to air, and hovering near the water surface. The simulation result showed that during the transition, the slapping motion exerted the maximum and average lift per unit of body weight of 18 and 9.2, respectively, while those of paddling produced 0.46 and 0.23, respectively. The water surface effect improved the lift by 25% at the normalized height of less than 0.44 and disappeared at a height greater than 0.7. During hovering, while the clap-and-fling motion improved lift by 2.6% and the water surface effect was 9.8%, the synergy effect was 22%. In addition, the former enhanced it significantly after the fling, while the latter was remarkable during the wing acceleration phase. In contrast to ground effects, flapping reduced the water level and caused the ripples, dynamically changing the water surface effect.

A Study on the Breakthrough Pressure of Porous Rock Formations in Gas Storage Reservoirs

Breakthrough pressure of natural gas in rock is an important evaluation parameter in gas reservoir development. In this study, experimental measurements of porosity and permeability of the caprock core were carried out. A digital core model was obtained by body rendering of rock CT (Computed Tomography) slices using Avizo software. Then, the grid model was imported into Fluent software for a numerical simulation of natural gas breakthrough pressure in the core. The innovations of this paper include (1) an accurate calculation method of cap breakthrough pressure based on the VOF method; (2) the method performs a perceptual analysis of average pore radius, wettability, roughness height, and viscosity ratio.

Free surface simulation over broad crested weirs using VOF and SPH methods

Free surface simulation over broad crested weirs using VOF and SPH methods

Pore-scale numerical investigation on spontaneous imbibition in natural fracture with heterogeneous wettability using the volume of fluid method

Understanding the spontaneous imbibition in the natural fracture with heterogeneous wettability is crucial for predicting and mitigating the impacts of unstable displacement on unconventional recovery. In this paper, the fracture structured mesh model is reconstructed based on the micro-computed tomography (micro-CT) image of naturally fractured tight sandstone. The mineralogy map-based modeling method for heterogeneous-wetting fracture is developed by combining the thin section images, X-ray diffraction (XRD) analysis, and multiple point statistics method. The simulation of the single-phase flow is performed to test the mesh independence. The effects of gravity and wettability on spontaneous imbibition in natural fracture and corresponding imbibition front dynamics are analyzed and discussed using the volume of fluid (VOF) method. The results show that (1) The structured mesh reconstruction method proposed in this paper can more effectively preserve the fracture structure compared to the unstructured mesh reconstruction method. (2) Gravity has a negligible impact on the pore-scale spontaneous imbibition in natural fracture. Under homogeneous-wetting conditions, spontaneous imbibition in natural fracture consistently exhibits stable displacement without significant residual gas formation. However, under the heterogeneous-wetting condition, the spontaneous imbibition displays typical capillary fingering, resulting in approximately 24.04% of the gas being trapped after spontaneous imbibition. The residual gas trapping mechanisms mainly include adhered, isolated, and connected gas. (3) Under both homogeneous- and heterogeneous-wetting conditions, the imbibing water saturation and the length of the imbibition front are proportional to the power of imbibition time during spontaneous imbibition in the natural fracture.

Investigation of Aerodynamic Performance of Multi-element Airfoil in Free Surface Effect

Abstract This study examines the aerodynamic performance of the 30P30N multi-element airfoil flying on a free surface, a numerical computational model is established, the governing equations are addressed through the application of the finite volume method, while the volume of fluid method is utilized for the simulation of two-phase flow. Different mesh strategies and turbulence models are compared, with the numerical methods validated against experimental data. The aerodynamic properties of the 30P30N multi-element airfoil on the free surface at different wavelengths and wave heights are given by numerical computations, which show that the ground effect of the 30P30N multi-element airfoil differ from those on a clean airfoil, the aerodynamic coefficients of the 30P30N multi-element airfoil decrease as flight altitude lowers, with the pitching and drag moment of the slat is opposite to that of the main airfoil and the flap. Additionally, when the 30P30N multi-element airfoil flies over a regular wave surface, the aerodynamic coefficients of each component exhibit periodic behavior.

Experimental and numerical analysis of the fluid flow behavior of a tank corner impacting a water surface

The interaction of a tank impacting a water surface is an extremely complex nonlinear multiphase flow phenomenon. In this study, experiments and numerical simulations are used to systematically investigate the flow physics and load characteristics of a tank corner impacting a water surface. Free surface flow at different fall heights (200–800 mm) and inclination angles (0°–15°) was obtained through free fall experiments. The volume of fluids method and overset grid technology were used to simulate the water impact process of a three-dimensional structure accurately. For typical bubble flows, the numerical and experimental results agree well. On the basis of the three-dimensional flow characteristics and pressure distribution, flow behaviors, such as fluid climbing, corrugation disturbances, and air cavity effects, are analyzed. Bubble flow has a significant effect on the behavior mode of the impact load. In particular, the bubbles at the upper wall play a key role in the load characteristics at different locations. In addition, the influences of corrugations inside the tank's corner and the impact velocity on fluid flow were investigated. These results provide beneficial references for an in-depth understanding of the fluid flow and load characteristics between a tank and fluid.

Heat transfer research on the cooling process of waxy crude oil storage in the vault tank based on VOF model

This paper focuses on the static cooling process for waxy crude oil stored in dome roof tanks. For the three phases of gas on top, liquid crude oil, and bottom water in storage tank, the VOF method is used to describe the evolution of physical quantities at the “oil–water”/“oil–gas” interface. The porous medium method is used to quantitatively characterize the sol–gel conversion process for waxy crude oil. A physical and mathematical models are established to describe the flow-heat transfer coupling behavior of the three-phase medium of crude oil, gas on top, and water at the bottom of the dome roof tank. In terms of the overall cooling process,The gas at the top of the tank has the simplest and fastest physical field evolution. It has the most uneven distribution (average temperature variance of 4 °C2), the strongest flow (average flow velocity of 0.4 m/s), the highest cooling rate (0.632 °C/h), and the lowest temperature (14.84 °C at the end). Its physical field is influenced by both the atmosphere and crude oil. The evolution of the physical field of crude oil is the most complex. It lags behind the gas at the top of tank and is directly effectted by it. Based on the evolution characteristics of the flow field of crude oil, the cooling process is divided into three stages: Stage I (0–––10 h) is the stage of convection generation and evolution in the crude oil region; Stage II (10 h − 34 h) is the stage of convection stability in the crude oil region; Stage III (after 35 h) is the stage of flow field transformation of crude oil. In stages I and II, the flow and momentum exchange at the oil–gas interface are significant. Crude oil is jointly influenced by the natural convection of the gas at the top of the tank and its own natural convection, forming a counterclockwise large vortex structure. The low-temperature area is near the central axis boundary of storage tank, oil–gas interface, and tank wall. The high-temperature area is within a range of 0.1 m − 3.3 m from the tank wall. After entering stage III, the flow and momentum exchange at the oil–gas interface weaken. The flow field of crude oil is only controlled by its own natural convection and transforms into a clockwise large vortex dominated. The low-temperature area is concentrated in the enclosed area of “oil–gas interface − tank wall” and “oil–water interface − tank wall”. The temperature field changes accordingly. Eventually, the high-temperature area is concentrated in the area slightly above the center of the tank. The physical field evolution of bottom water lags behind crude oil and is most unstable. Its cooling rate is 0.164 °C/h, slightly higher than crude oil’s 0.157 °C/h. The temperature is always slightly lower (33.47 °C at the end), and the physical field is the most uniform (average temperature variance of 0.0003 °C2), affected by the tank bottom environment and liquid crude oil.

Analysis and numerical simulation of different flowmeters based on an open channel in an irrigation area

ABSTRACT This study establishes an ultrasonic open channel flow measurement test and numerical simulation model and systematically compares the performance and reliability of the ultrasonic method and the traditional flowmeter in flow measurement in the irrigation area by observing and analysing the test data and combining it with the numerical simulation. In the indoor ultrasonic flowmeter flow measurement experiments in the trapezoidal nullah section, the flow rate measurement was carried out by using a high-precision variable slope flume and a variety of flow measurement tools. A numerical study was carried out using the VOF method to calculate the flow in the open channel flume under two-phase flow conditions. Combining experimental measurements and numerical simulations, this study aims to quantify the magnitude of flow measurement errors and water surface fluctuations in open channel flumes and to address the discrepancies between different flow measurement methods in open channels in irrigation areas.

A quasi-three-phase flow simulation of the interactions between solitary waves and a vertical seawall installed on a sandy beach

Local scour and wave loading are two key factors that affect the safety of seawalls under tsunami attacks. In this study, the scouring process at the toe of and wave impact force on a vertical seawall under consecutive solitary wave attacks are simulated using a quasi-three-phase (air, water, and sediment) flow model, which models the air and water as a fluid mixture phase and sediment as a solid phase. The air and water interface is modeled by a VOF method and the sediment–fluid interaction is modeled using the Eulerian two-phase flow method. A comparison between the beach profiles with and without the seawall shows that, with a seawall, a deeper scour hole is generated at the toe of the seawall. Besides, the presence of the seawall causes the eroded sediment to be deposited further offshore. The numerical results are then analyzed in detail regarding the flow field and sediment transport process to reveal the mechanisms of the above eroding/depositing patterns. The wave impact force on the seawall is also analyzed to understand the effect of scouring on the wave loading. It is shown that the wave impact force, despite being stochastic for a specific wave, increases in general with the deepening of the scour hole because the latter increases the exposure of the seawall to wave slamming.

Annular two-phase flow in a small diameter tube: OpenFOAM simulations with turbulence damping vs optical measurements

In this work, numerical simulations are performed to predict two-phase annular flow of refrigerant R245fa inside a 3.4 mm diameter vertical channel. The VOF (Volume of Fluid) method implemented in an OpenFOAM solver is used to accurately track the vapor-liquid interface. A 2D axisymmetric domain is considered and the Adaptive Mesh Refinement (AMR) method is applied to the cells near the liquid/vapor interface. The Reynolds-Averaged Navier Stokes (RANS) equations are solved and the k-ω SST model is adopted for turbulence modelling in both the liquid and vapor phase. Simulations are used to calculate instantaneous and mean values of the liquid film thickness at mass flux G = 100 kg m-2 s-1 and vapor quality ranging between 0.2 and 0.85. Numerical results are compared against measurements of the liquid film thickness taken during vertical annular downflow. Previous works from the literature and the deviations observed between present numerical and experimental results suggest the need for turbulence damping at the vapor-liquid interface by adding a source term in the ω equation. The simulations show that a low value of the turbulence damping parameter (e.g. 1) causes the average liquid film thickness to increase by 25 %–52 % compared to the non-damped scenario. The interface presents large amplitude disturbance waves in the non-damped case, whereas small ripple waves are predicted when turbulence damping is introduced. Furthermore, the difference between the application of a symmetric and asymmetric treatment for the source term is analysed. From the comparison between experimental data and numerical simulations, it emerges that the value of the correct damping source term to be applied is strictly dependent on the vapor quality.

Analysis of Flow Field Characteristics in the Three-Phase Jet Fire Monitor Head

To enhance the jet performance of the three-phase jet fire monitor (TPJFM), an analysis was conducted on the internal flow field (IFF) characteristics of the monitor head. Using the volume of fluid method, the impact of key structural parameters, such as the powder-pipe bending angle and the supporting blade length, on the turbulent kinetic energy (TKE) of the IFF, the velocity distribution uniformity at the nozzle outlet, and the pressure drop (PD) between the inlet and outlet of the internal flow field, was analyzed. The study revealed that increasing the bending angle of the powder pipe will lead to a significant improvement in the uniformity of velocity distribution in the IFF. Extending the supporting blade length helps reduce the average TKE at the nozzle outlet but has a minimal impact on the velocity distribution uniformity and the PD between the inlet and outlet. Reasonable design of the distance between the supporting blades and the bending section of the powder pipe can improve the IFF characteristics, reducing local pressure losses and peak TKE. The research results can effectively improve the IFF characteristics, enhance jet performance, and provide theoretical basis and technical support for the design and optimization of the TPJFM.

Collision dynamics of binary equal-size droplets at high pressures: a focus on stretching separation and reflexive separation

ABSTRACT Stretching separation and reflexive separation are two collision regimes that give rise to satellite droplets, significantly impacting the droplet size distribution. However, the influence of high pressure on these regimes remains unclear. This paper investigates the collision dynamics of binary equal-size droplets under varying ambient pressures using the volume of fluid method and adaptive mesh refinement. The results show that vortices, generated during droplet motion changes or ligament ruptures, facilitate mass transport within the droplet–droplet deformation. Additionally, this paper summarizes four phases of droplet deformation in the separation regimes, which are delayed in stretching separation and advanced in reflexive separation with increasing ambient pressure. Elevated ambient pressure restricts droplet movement, resulting in tougher ligament fractures, smaller satellite droplets, and an expanded coalescence regime boundary. Unlike previous works, this paper incorporates gas kinetic and dissipation energies during droplet collisions at high pressures, revealing that at 7 MPa, the gas dissipation energy is comparable to the liquid dissipation energy and cannot be neglected. To account for these effects, a pressure-dependent formula is integrated into the composite collision model under the Lagrangian framework, offering enhanced predictions of droplet size within the stretching separation regime.

Numerical study on the motion characteristics of free fall lifeboats entering calm water and rough sea

As ocean engineering operations extend into deeper seas, the working environment becomes increasingly complex, making free fall lifeboats (FFLBs) more vital for maritime disaster rescues. Unlike traditional davit-launched lifeboats, FFLBs are propelled into the water at a specific velocity and angle, engaging in a complex motion process of launch, impact, submersion, and resurfacing. Therefore, to assess the safety of FFLBs, this paper regarding the lifeboat as a rigid body aims to investigate the six-degree-of-freedom motion characteristics of lifeboat entering the water with different entry angles θ and wave environment, with a specific focus on analyzing the primary causes of capsizing. The numerical simulations of water entry with various θ, wave heights H, and relative entry positions are carried out by combining large eddy simulation and overset mesh technology. The free surface is captured by the volume of fluid method, and the attitude change, acceleration change, motion trajectory, and free surface evolution law of lifeboats are analyzed. The findings suggest that lifeboats can enter calm water safely at θ of 20°–50° and maintain a stable posture. Moreover, in extreme conditions where θ is either 0° or 90°, there is a high risk of entry failure due to excessive vertical acceleration and poor motion attitude, respectively. Furthermore, when facing waves, lifeboats experience reduced horizontal displacement when entering at peak and downward zero point compared to calm water conditions, which poses challenges for avoiding potential dangers.

Formation of sodium-alginate droplets in an X-microdevice: Characterization of the pinching efficiency

Experiments and simulations are used jointly to gain a comprehensive insight into the pinching mechanism that generates alginate droplets in an X-microdevice operating in a hydrodynamic flow-focusing configuration. The X-microdevice is fed with an aqueous alginate solution into one inlet channel, while sunflower oil and Span80 are fed into the other two inlet channels. The use of the adaptive mesh refinement and volume of fluid method allows accurate tracking of the interface in numerical simulations. The sensitivities of numerical predictions to the contact angle and the surface tension are estimated through dedicated sets of simulations. Subsequently, numerical simulations and experiments are compared for different flow rates with a satisfactory agreement. We observe that the pinch-off mechanism may lead to the formation of several satellite drops in addition to the main droplet. A pinching performance indicator is suggested based on the amount of alginate that is encapsulated in the main droplet. The effect of operating conditions on the pinching efficiency, frequency, and droplet diameter is discussed to provide valuable information to optimize the droplets production. The pinching efficiency is closely related to the length and diameter of the liquid thread. At low flow rates, a short liquid thread is observed. This leads to the formation of few satellites and, thus, to high pinching efficiency but low droplet production. Increasing the dispersed-phase flow rate slightly reduces the efficiency but significantly increases the production.

Splashing impact of a falling liquid drop

The splashing phenomenon associated with the impact of a liquid drop on a liquid pool is investigated in this study using the volume of fluid method. The different outcomes of this phenomena largely depend on the height (/depth) of a liquid pool and the impinging drop velocity. The impingement angle, drop shape, fluid properties, and other non-isothermal effects also play a role, but we have eliminated those dependencies by considering no variation in these parameters. The different phenomena that are observed when a drop impacts a liquid pool are controlled by (i) crater depth and wave-swell (rim of the crater) expansion, (ii) wave-swell retraction followed by crater side retraction, and (iii) crater base retraction. During splashing, a deep crater is produced in the receiving liquid after the drop impact. At its rim, a crown-like cylindrical liquid film is ejected out of the crater. Small droplets are normally shed from this rim. It is seen that the depth of the pool has dramatic effects on the dynamics of the crown formed during splashing. When observed even more comprehensively, the physical attributes of the crown, such as crown height and crown radius, are found to strongly relate to the velocity of the falling drop. Finally, we try to demarcate the regions of splashing with and without the formation of secondary droplets on the regime map of Weber number–dimensionless pool depth.

Numerical investigation on the ventilated supercavitating model with propeller

To achieve stable and continuous supercavitating flow over underwater vehicles, artificial ventilation is implemented, particularly effective at lower speeds. Previous research on supercavitation primarily focused on analyzing ventilated supercavitating flow with various cavitator types and/or ventilation rates. In this investigation, we examine the behavior of ventilated supercavitating flow over an axisymmetric model featuring both a disk cavitator and a Postdam propeller placed at the bow. Utilizing the Large Eddy Simulation turbulence model, Volume of Fluid method, and Kunz cavitation model, our simulation aims to capture the cavitating flow around the propeller and the ventilated supercavitating flow over the model. Validation of our numerical methods is achieved by comparing our results with experimental data of a ventilated model by Chung and Cho [“Ventilated supercavitation around a moving body in a still fluid: Observation and drag measurement,” J. Fluid Mech. 854, 367–419 (2018)] and the cavitating Postdam propeller by SVA Postdam [S. Potsdam, “PPTC smp'11 Workshop,” in Proceedings of the Workshop on Cavitation and Propeller Performance (2011)]. The results show that with a rotating propeller at the bow of the supercavitating model, the cavitating flow extends and stabilizes compared to configurations utilizing a traditional disk cavitator. The presence of the propeller accelerates the formation of supercavitating flow at a consistent incoming flow speed. Additionally, coupling the propeller with the disk cavitator results in significant increases in propeller thrust, torque, and efficiency. While there is an observed rise in model drag, the impact is not substantial.

Characterization on the impact load of a local corner region of a liquid tank entering water

This study conducts a detailed examination of the characteristics of impact loads in complex triangular areas within liquid tanks via the volume of fluids (VOF) method, with a general understanding of impact loads. By comparing the numerical results with previous experimental data of oblique wedge impacts on water surfaces, the effectiveness of the VOF method was confirmed. Complex dynamic phenomena such as fluid climbing, jet impact, and air cavity effects in corner areas were analyzed through 3D flow characteristics. By examining two types of impacts (a structure impacting fluid and a fluid impacting structure), the equivalence between them is verified. An in-depth exploration of the load characteristics in different areas is conducted by combining the free surface evolution. The multipeak characteristics of the load and synchronicity of the peak loads at different parts are closely related to the phenomenon of the climbing fluid being obstructed. Bubble flow also plays a crucial role in affecting the load characteristics. Further exploration of the effects of structural motion on load characteristics reveals complex load variability. These findings provide a valuable reference for understanding the impact loads in complex corner areas of liquid tanks.

Physical modeling of conjugate heat transfer for multiregion and multiphase systems with the Volume-of-Fluid method

AbstractThe Volume-of-Fluid (VOF) method is commonly used for numerical simulations of phase change phenomena, such as nucleate boiling or droplet evaporation. A key issue with the standard VOF method is the averaging of the liquid and vapor properties in interface cells, which causes non-physical conjugate heat transfer with a solid wall. Therefore, we aim at a physical model for conjugate heat transfer between a solid and a multiphase fluid. The first measure for higher quality simulations is the splitting of the single temperature field in the fluid region into separate liquid and vapor temperature fields. The second measure is the development of a new, more physical temperature boundary condition for conjugate heat transfer between a solid region and a multiphase fluid, based on experimental results, theoretical models and theoretical considerations. In interface cells, the vapor phase is excluded from the conjugate heat transfer because only heat transfer to the liquid phase occurs resp. dominates. Additionally, the conjugate heat transfer between solid and liquid in the interface cells is performed with virtual subcells, depending on the respective volume fraction of the liquid phase. This new approach (we name it distinctive approach) is successfully validated for energy conservation, and stability issues are discussed for the first time. Significant differences to simulations with averaged properties are observed due to the (now) physically correct modeling of conjugate heat transfer. In our boiling cases, the more accurate numerical simulations lead to considerably larger bubble growth rates. Higher quality simulations are also expected for nearly all applications, where there is a three-phase contact line, be it vapor bubbles in nucleate boiling or droplets impacting on a heated surface.