Volume Of Fluid Method Research Articles

Application of Motion Interface Tracking CVOFLS Method to Zalesak Disk Problem

The interface curvature calculation is not accurate in VOF method and the interface mass is not conserved in Level Set method, A new interface tracking method CVOFLS is proposed (Coupled Volume of Fluid and Level Set method). This method combines the advantages of VOF and Level Set, The VOF and Level Set functions are simultaneously solved according to the fluid velocity, The interface obtained by the VOF function is used to correct the fluid quality, The Level Set function is used to calculate the interface norma, The Level Set function reinitialization process is omitted, Thus, the deficiencies of the two methods are overcome effectively. An example of interface tracking numerical simulation shows that, this method can guarantee high precision of free interface tracking and good mass conservation, and it can improve the calculation efficiency.

Laser coupling in waterjets subject to jet instabilities, laser parameters, and alignment errors.

High coupling accuracy and efficiency attract wide attention in waterjet-guided laser technology due to the requirements for high processing performance in hard-to-cut material and diamond industries. The behaviors of axisymmetric waterjets injected into the atmosphere through different types of orifices are investigated by adopting a two-phase flow k-epsilon algorithm. The water-gas interface is tracked with Coupled Level Set and Volume of Fluid method. The electric field distributions of laser radiation inside the coupling unit are modeled by wave equations and numerically solved with the full-wave Finite Element Method. The coupling efficiency of the laser beam affected by waterjet hydrodynamics is studied by considering the profiles of the waterjet shaped at transient stages, namely vena contracta, cavitation, and hydraulic flip. The growth of the cavity leads to a larger water-air interface and increases the coupling efficiency. Eventually, two types of fully developed laminar waterjets, i.e. constricted waterjets and non-constricted waterjets, are formed. Constricted waterjets that are detached from the wall throughout the nozzle are preferable to guide laser beams since they significantly increase the coupling efficiency compared to non-constricted waterjets. Furthermore, the trends of coupling efficiency affected by Numerical Aperture (NA), wavelengths, and alignments errors are analyzed to optimize the physical design of the coupling unit and develop the alignment strategies.

Computational and experimental studies of wave–structure interaction: Wave attenuation by a floating breakwater

Interactions between surface gravity waves and a floating rigid body are complex, as waves may reflect from, break on, and be transmitted behind the body. Studies of these phenomena are critically important in improving the safety and functional efficiency of offshore structures. Here, the wave attenuation performance and motions of a type of floating breakwater (FB) are studied through numerical and experimental approaches. A numerical wave tank (NWT) is developed based on the software OpenFOAM and properties of wave channel from a laboratory. In the NWT, the air–water interface is captured by the volume of fluid method. The motions of FB are tracked by the six degrees of freedom model. A mooring system model is developed to simulate the constraints of the FB. Large eddy simulation turbulence modeling is implemented for the wave breaking processes. A model FB with a scale of 1:20 is tested in both the experimental and numerical wave channel. Wave heights at the back/front of the FB and the constraint forces of the mooring wires are measured. The numerical models are validated by comparing the results with experimental measurements. The variations of transmission/reflection coefficients, energy dissipation rate, and maximum mooring force are calculated. Changes of the response amplitude operators with the ratio of FB width to wavelength ( B / L w) and wave steepness are analyzed. The wave transmission coefficient will drop below 0.8 if the value of B / L w is larger than 0.3, but will go over 0.95 if B / L w is less than 0.1. Wave steepness has a large influence on FB motions and the mooring system. The effect of Stokes drift is observed by the shift of position of the FB.

CFD Simulation of a container ship in random waves using a coupled level-set and volume of fluid method

CFD Simulation of a container ship in random waves using a coupled level-set and volume of fluid method

Morphology and kinematics of a train of power-law droplets in a corrugated microchannel

We numerically investigate the deformation of a train of power-law droplets in a highly viscous suspending medium in nonlinear microfluidic geometry. We examine how viscous stresses conspire against surface tension in two-dimensional incompressible liquid–liquid flow in a corrugated microchannel using the finite volume technique with the volume of fluid method. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.7-1.3. We validate our numerical model with the available literature data in good agreement. Interestingly, the corrugated cavities are found to have an elongating effect on the non-Newtonian droplets, whereas literature delineates a compressive effect of the nonlinear geometry on bubbles. Specific orbital trajectories are found in the (droplet length A, spacing B) space with dispersed and synchronized orbitals at low and high capillary number for all power-law droplets, respectively. Furthermore, the hysteresis in the droplet shape is found to increase with the capillary number. Consequently, the hysteretic area Ap revealed that the slope increases with (n). An interesting finding is elucidated where the hysteresis loops are found to rotate from low capillary to high capillary number for all power-law droplets. A new finding is reported where the evolution of the droplet perimeter revealed the development of secondary peaks as the capillary number increases. The power-law droplets are found to pack themselves up in the corrugated section in two distinct regimes: smaller droplets obey the linear deformation regime. In contrast, large droplets lie in the flow-induced deformation regime. The instantaneous cap velocities produce a nonmonotonic behavior for the front velocity as the capillary number increases for all power-law droplets. We develop functional relationships between flow parameters of segmented flows at the pore scale for every non-Newtonian droplet. Given the implications of this setup with industrial and biomedical applications, the illustrations shown herein could be beneficial in tackling problems at the pore scale with nonlinear fluids.

Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study

Using direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. For this purpose, homogeneous isotropic turbulence (HIT) is generated using a linear forcing method, enhanced by a proportional–integral–derivative (PID) controller, ensuring a constant turbulent kinetic energy (TKE) for two-phase flows, where the TKE balance equation contains an additional term due to surface tension. Then, the forcing is stopped, and gravitational acceleration is activated. The proposed computational setup represents a unique and well-controlled configuration to study emulsification and segregation. We consider four different density ratios, which are applied in industrial processes, to investigate the influence of the density ratio on the statistically steady state of the emulsions, and their segregation under decaying turbulence and constant gravitational acceleration. At the statistically steady state, we hold the turbulence constant and study the effects of the density ratio ρd/ρc, on the interface area, the Sauter mean diameter (SMD), and the statistical droplet size distribution. We find that all are affected by the density ratio, and we observe a relation between the SMD and ρd/ρc. Furthermore, we assume a dependence of the critical Weber number on the density ratio. In the second part of our work, we study the segregation process. To this end, we consider the change in the center of mass of the disperse phase and the energy release, to analyze the dependence of segregation on the density difference Δρ/ρd. We show that segregation scales with the density difference and the droplet size, and a segregation time scale has been suggested that collapses the height of the center of mass for different density ratios.

Capillary-driven horseshoe vortex forming around a micro-pillar

Hypothesis: Horseshoe vortices are known to emerge around large-scale obstacles, such as bridge pillars, due to an inertia-driven adverse pressure gradient forming on the upstream-side of the obstacle. We contend that a similar flow structure can arise in thin-film Stokes flow around micro-obstacles, such as used in textured surfaces to improve wettability. This could be exploited to enhance mixing in microfluidic devices, typically limited to creeping-flow regimes.Experiments: Numerical simulations based on the Navier–Stokes equations are carried out to elucidate the flow structure associated with the wetting dynamics of a liquid film spreading around a 50 μm diameter micro-pillar. The employed multiphase solver, which is based on the volume of fluid method, accurately reproduces the wetting dynamics observed in current and previous (Mu et al., Langmuir, 2019) experiments.Findings: The flow structure within the liquid meniscus forming at the foot of the micro-pillar evinces a horseshoe vortex wrapping around the obstacle, notwithstanding that the Reynolds number in our system is extremely low. Here, the adverse pressure gradient driving flow reversal near the bounding wall is caused by capillarity instead of inertia. The horseshoe vortex is entangled with other vortical structures, leading to an intricate flow system with high-potential mixing capabilities.

Numerical study of the impact and aggregation characteristics of alumina droplets on a wall in the solid rocket motor

The impact and aggregation of multiple alumina droplets on the inner wall of the solid rocket motor may generate a larger rebound aggregated droplet or adhere to the wall to form a liquid film. The rebound and adhesion characteristics of the aggregated droplet are of great significance for slag deposition and two-phase flow prediction in the motor. In this paper, the VOF (Volume of fluid) method is used to study the impact and aggregation process of multiple alumina droplets on the wall. Detailed numerical verifications are carried out, including the impact and aggregation of moving droplets, the aggregation and rebound of stationary droplets and the impact process of a single alumina droplet on the wall. It is found that the aggregated droplet will rotate when two droplets aggregate under small droplet diameter ratio, which is caused by the asymmetry aggregation process. The oscillation process intensifies when three droplets impact and aggregate on the wall, as a result, the aggregated droplet is easier to adhere to the wall. The viscous dissipation in the aggregation of droplets is huge, and the total viscous dissipation energy accounts for about 50% of the total energy when the aggregated droplets rebound. The influence of droplet diameter on the V⁎ (rebound recovery coefficient) of the aggregated droplet and the rebound/adhesion results are dominated by the viscosity effect. While the influence of the parameters involving the initial spatial arrangement of droplets is dominated by the oscillation process, which will reduce the effective rebound kinetic energy, making a lower V⁎ and the aggregated droplet easier to adhere.

Numerical Simulation of Impinging Jet Drying Multiphase Flow in Gravure Printing Water-Based Ink Based on the Volume of Fluid Method

Gravure printing is widely used in food, pharmaceutical, and other packaging industries. As a green printing material, water-based ink has problems such as non-volatile and poor drying on non-absorbent packaging substrates, which has a great impact on its application. To solve these difficulties, this study adopts the volume of fluid (VOF) method and user-defined function (UDF) to establish a multiphase flow impinging air jets drying model of water-based ink in the gravure printing process, taking a water-based ink droplet as an example. The model was used to simulate the ink drying state in the impinging air jets region and analyze the effects of impinging air jets’ temperature and velocity, as well as ink viscosity and thickness, on the ink drying efficiency. Meanwhile, the heat and mass transfer mechanism between impinging air jets and water-based ink was investigated. The results show that the higher impinging air jet temperature and velocity, the faster the drying rate of the ink; a lower viscosity and thinner thickness of ink can also enhance the drying efficiency of the ink. The multiphase impinging air jets drying model based on the computational fluid dynamics (CFD) method provides a new research idea for the analysis of drying characteristics of water-based ink on non-absorbent substrates, and the research results provide theoretical support to promote its application.

Analysis of fluid dynamic behavior and impact load on oblique water entry of a two-dimensional seaplane based on VOF method

Seaplane landing is a typical water entry impact phenomenon. However, our understanding on the development of jet flow and air cavity, and corresponding load characteristic is still limited. In this paper, the impact problem of oblique water entry of a two-dimensional seaplane is studied to clarify the relationship between theses complex flows and loads. A gas-liquid two-phase model is established to model these complex fluid flows, where the air-water interface is captured based on a VOF algorithm. The accuracy is validated by the published experimental data. Some hydrodynamic impact characteristics related to seaplane model under different oblique water entry postures, including air-water free surface and local impact pressure are discussed. Complicated flows (air cavity and jet flow impact) are the internal cause to some unusual load characteristics such as multiple pressure peaks, negative pressure, simultaneity of impact load on the airfoil, and great difference of load at different positions on the cabin. The evolution of jet flow and air cavity is further discussed through combing free surface and pressure distribution. Results clarified the mechanism of complex flows under the influence of bottom cabin and inclined postures, which will be helpful to further understand the impact phenomenon of seaplane landing.

When does an impacting drop stop bouncing?

Non-wetting substrates allow impacting liquid drops to spread, recoil and take-off, provided they are not too heavy (Bianceet al.,J. Fluid Mech., vol. 554, 2006, pp. 47–66) or too viscous (Jhaet al.,Soft Matt., vol. 16, no. 31, 2020, pp. 7270–7273). In this article, using direct numerical simulations with the volume of fluid method, we investigate how viscous stresses and gravity oppose capillarity to inhibit drop rebound. Close to the bouncing to non-bouncing transition, we evidence that the initial spreading stage can be decoupled from the later retraction and take-off, allowing us to understand the rebound as a process converting the surface energy of the spread liquid into kinetic energy. Drawing an analogy with coalescence-induced jumping, we propose a criterion for the transition from the bouncing to the non-bouncing regime, namely by the condition${Oh}_{c} + {Bo}_{c} \sim 1$, where${Oh}_{c}$and${Bo}_{c}$are the Ohnesorge number and Bond number at the transition, respectively. This criterion is in excellent agreement with the numerical results. We also elucidate the mechanisms of bouncing inhibition in the heavy and viscous drop limiting regimes by calculating the energy budgets and relating them to the drop's shape and internal flow.

Effect of incident direction and droplet position on dynamic and heat transfer behaviors of droplet impacting on super-hydrophilic cylindrical surface

Abnormal impact of droplet with different incident directions and positions can be found in evaporator, desalinator and nuclear engineering etc. The researches devoted to droplet abnormal impingement on a super-hydrophilic cylindrical surface are limited. In this paper, a numerical study of individual droplet impacting on super-hydrophilic cylindrical heated surface was conducted by applying VOF method. The incident direction and position of droplet were characterized by the impact angle φ and horizontal offset δx, the effect of which on dynamic and heat transfer behaviors was analyzed. Results show that there is an anisotropic spread during droplet impingement. Compared to no-offset vertical impact, the peaks of liquid film thickness for impact with an impact angle or horizontal offset are not the same at two edges of liquid film along circumferential direction. Impact angle or horizontal offset leads to a reduced contact area, a lower average temperature of liquid film and smaller total droplet input heat flow. For φ from 0° to 75° and δx from 0 mm to 5 mm, the maximum total droplet input heat flow decreases by 42.1% and 27.6% respectively. The local heat flux shows apparent fluctuations along the circumferential direction, and the high heat flux region is concentrated at a lower position in the circumferential direction of the cylinder for a larger φ or δx due to the auxiliary effect of gravity.

A numerical study on the levitation system for droplet preparation in a fuel-coolant interaction experiment

The MISTEE facility at KTH was designed to investigate the process and phenomena of a molten droplet falling into a water pool that may be encountered in fuel-coolant interactions (FCI) during a severe accident of light water reactors. An aerodynamic levitation mechanism is proposed to hold the molten droplet during its preparation (melting and heating up to a prescribed temperature) in an induction furnace. The crucible is flushed with argon through an injection nozzle at the bottom to prevent the droplet from falling out of the crucible. A numerical simulation of the aerodynamic levitation system is performed in the present study with the objective of determining and optimizing the design. The problem was simplified as an isothermal two-phase flow in an axisymmetric geometry. The simulation is realized through ANSYS Fluent v17 platform, which employs the VOF method to track interfaces between two phases and the SST k-omega model to describe turbulence flow of argon gas. The numerical model is validated against tests performed in the MISTEE facility after mesh sensitivity study. It is then applied to investigate the impacts of various parameters on the facility levitation capability and the droplet stability. According to the simulation results, stable molten droplets can be obtained in the designed experimental setup. The simulation also provides the appropriate values of argon inlet velocity and sample mass at which a stable droplet can be obtained inside the crucible before its discharge. Either higher or lower inlet velocity will destabilize the formation of the droplet. Considering the temperature-dependent melt properties, both surface tension and viscosity affect the movement and deformation of the molten droplet. The wettability of melt on the crucible wall is critical to droplet formation, and it is found that a poor wettability can ensure the levitation of droplet.

Analysis of Water-Lifting Aerator Performance Based on the Volume of Fluid Method

Water quality deterioration is a major problem faced by reservoirs globally, owing to the inflow of pollution from industrial and municipal activities. Water-lifting aeration is an in situ water quality improvement technology that mixes and oxygenates deep water bodies in reservoirs to improve pollution control efficiency and water quality. While previous studies have mainly focused on the mixing process in the reservoir outside the water-lifting aerator (WLA), knowledge of the internal flow remains limited. In this study, a two-phase flow within a WLA system was numerically studied using the volume of fluid (VOF) method to comprehensively analyze the internal two-phase flow characteristics and the influence on the water-lifting and oxygenation performance of the system. The statistical analysis results showed that increasing the aeration chamber volume enhanced the bottom oxygenation performance by 27% because of the prolonged time of the deflector plate outlet outflow. Additionally, increasing the air release rate enhanced the water-lifting performance by 47%, which was induced by the shortened air piston release period. This study demonstrates the internal flow mechanism of the WLA and provides technical support for parameter optimization design, which has significant scientific research and engineering application value.

Numerical simulation of the interaction and coalescence of inline hydrogen bubbles in biohydrogen production by photofermentation with corncob

The escape rate of hydrogen in photobiological hydrogen production plays an important role in the biochemical reaction process, and the interaction of hydrogen bubbles in bio-hydrogen production material liquid affects the escape rate of hydrogen. In this paper, the Eulerian-Eulerian-Multifluid VOF method is used to simulate the interactions of three types of hydrogen bubbles: coalescence of equal-sized inline hydrogen bubbles, a small leading hydrogen bubble is chased by a large trailing hydrogen bubble and a large leading hydrogen bubble is chased by a small trailing hydrogen bubble. The results show that the interaction strength between hydrogen bubbles is influenced by the initial interval and initial diameter of the hydrogen bubbles and the flow index of the hydrogen-producing material liquid. The hydrogen bubbles exhibit three types of aggregation. In the pre-merger period, the velocity of the trailing hydrogen bubble also shows four stage changes, which are acceleration to the maximum velocity - deceleration - small increase in velocity - deceleration to the merging velocity. There is also a brief acceleration of the leading hydrogen bubble. For the interaction between Type II and Type III hydrogen bubbles of the same size, there is no significant difference in the rise rate of large hydrogen bubbles after the coalescence.

Modeling the impingement deformation and solidification of a hollow zirconia droplet onto a dry substrate and solidified layer

Despite the numerous research studies involving the solidification of continuous molten metal droplet impingement on dry substrates during the process of plasma spraying, the impingement between a hollow molten metal droplet and a solidified layer has, to date, not yet been thoroughly explored. A liquid shell enclosing the air cavity forms a hollow droplet. The coupled level set and volume of fluid method is used to track the air–liquid interface, and the enthalpy–porosity method is used to track the liquid–solid interface. A two-dimensional axis symmetric model is adopted to describe the impingement and solidification process. This study includes a detailed investigation of transient impact deformation and solidification. The heat transfer characteristics of the solidification of a continuous dense and hollow molten droplet impacting on a dry substrate and solidified layer are studied and compared. A thin solidified layer appears and develops between the droplet and the substrate, and the impacting droplet finally pins to the surface with mainly the liquid solidified. For a hollow droplet impact on the solidified layer, a splashed crown liquid sheet forms from the drop-solidified layer neck area. Various temperatures of the solidified layer induce a different development of the crown, spreading, and rebound counter-jet. The deterioration of local heat transfer is attributed to a strong fluctuation of the rebound counter-jet and the existence of an annular cavity (formed by the crown sheet falling back). Attention should be paid to this phenomenon in industrial applications involving droplet impact.

Application of CVOFLS method in multi vortex shear flow field

Coupled Volume of Fluid and Level Set method inherits the advantages of VOF and Level Set methods, takes VOF function as the main body to simulate the fluid motion interface, and corrects the normal direction of the interface through Level Set function, so as to effectively overcome the shortcomings of the two methods. The numerical simulation example of multi vortex shear flow field shows that this method can ensure better simulation accuracy of moving interface and higher calculation efficiency.

Analysis of wave added resistance and motion response of fishing boat sailing against waves

In order to accurately predict the on-wave resistance and responses to hull motions of ships in actual sea conditions, the k-ε method of the RNG model is adopted on the basis of the unsteady RANS method. The twoformula turbulence model deals with the viscous flow, the VOF method captures the free surface, the velocity boundary method makes waves, the artificial damping method is used to eliminate waves, and the nested grid technology is used to deal with the motion response of ships on waves. Combined with the 6-DOF motion formula, a three-dimensional numerical wave cell for regular waves is established. For one example, taking a KCS Container ship and fishing boat sailing at a mid-high-speed, the increase of wave resistance and motion response at different wavelengths are analyzed, and the simulation results are compared with the experimental value, the content of strip theory in potential flow theory and the panel method to prove the reliability of CFD method in predicting ship motion.

DO DAILY ACTIVITIES AFFECT GAS TAMPONADE‒RETINA CONTACT AFTER PARS PLANA VITRECTOMY?: A Computational Fluid Dynamics Study.

To calculate the retinal surface alternatively in contact with gas and aqueous because of fluid sloshing during daily activities such as ocular saccade, turning the head, standing up, and being a passenger of a braking car. Fluid dynamics of aqueous and gas tamponade was reproduced using computational methods using the OpenFOAM open-source library. The double-fluid dynamics was simulated by the volume of fluid method and setting the contact angle at the aqueous-gas-retina interface. Sloshing increased the retinal surface in contact with aqueous by 13% to 16% regardless of fill rate and standing up determined the largest area of wet retina, followed by car braking, head rotation, and ocular saccade ( P < 0.001). All activities except the ocular saccade determined a significant increase in the surface of retina in contact with the aqueous ( P < 0.005). Car braking induced the highest shear stress (6.06 Pa); standing up determined the highest specific impulse and saccade the lowest. Daily activities instantaneously reduce the amount of retina consistently in contact with gas tamponade and increase shear stress giving aqueous a potential access to the subretinal space regardless of patients' compliance.

Numerical method for gas-liquid two-phase flow with phase change heat transfer considering compressibility using OpenFOAM

The numerical simulation of phase change heat transfer is important for predicting the gas-liquid two-phase flow and heat transfer characteristics and optimizing the phase change heat dissipation system. For the isovolumetric phase change heat transfer process, the compressibility of the gas phase has a significant impact on the simulation accuracy. A numerical simulation method of flow and phase change heat transfer considering gas-liquid two-phase compressibility is established based on VOF method using OpenFOAM in this paper. This method introduces a generalized phase change source term and a compressible source term to improve the isoAdvector geometric reconstruction algorithm and establishes a method for capturing the phase interface of a compressible two-phase flow. The phase change flux based on the phase interface is converted into a phase change source term based on the unit volume by calculating the phase interface density. The compressible term of the governing equation is constructed and its implicit discrete method is proposed. The coupling between velocity and pressure is realized based on the PISO algorithm. A numerical calculation method for phase change heat transfer of compressible two-phase flow is established. The effectiveness and accuracy of the proposed numerical method for predicting the heat transfer characteristics of phase change flows are verified by the simulation of vertical flat film condensation and film boiling. The numerical simulation results are in good agreement with the experiment. Compared with the other numerical simulation methods, the proposed method considering the influence of the compressibility of the gas phase on the flow and heat transfer characteristics in the heat pipe has high accuracy in predicting the gas-liquid two-phase flow, capturing the evolution characteristics of the phase interface and predicting the phase change heat transfer. The numerical simulation method can provide algorithm support for the numerical simulation of compressible two-phase flow phase change heat transfer and the design of a phase change heat dissipation system.