Volume Of Fluid Simulations Research Articles

Atomizing industrial gas-liquid flows – Development of an efficient hybrid VOF-LPT numerical framework

Atomizing gas-liquid flows are used in industrial applications where high interphase heat and mass transfer rates and good mixing are of primary importance. Today, there is no single mathematical framework available to predict the entire liquid breakup process at an acceptable computational cost for a typical problem of industrial size.In this work, we develop a volume-of-fluid (VOF) framework that is combined with Lagrangian particle tracking (LPT) to take advantage of the respective strengths of these two approaches. The two frameworks are coupled via a statistical model that enables a transition from the VOF to the LPT formulation using input data about the primary breakup process obtained from detailed VOF simulations in dedicated switching zones. LPT-to-VOF transitions are handled directly by analyzing the proximity of LPT parcels to larger VOF structures.The combined framework is specifically designed to accommodate situations where atomization occurs in several locations simultaneously and when separated and dispersed turbulent gas-liquid flows co-exist in the same industrial unit. The procedure in which the statistical model is derived is presented and discussed, its performance is verified and the computational efficiency of the combined VOF-LPT model is assessed. Finally, the application of the coupled framework to the simulation of an industrial gas-liquid mixer with four separate atomization regions is presented.

피에조 잉크젯 헤드의 액적 토출 형상 전산해석

피에조 DOD(drop-on-demand) 잉크젯 프린팅 방식은 다양한 종류의 잉크를 사용할 수 있기 때문에 최근에 첨단 산업에 적용이 활발히 연구되고 있다. 피에조 잉크젯 헤드에서 토출되는 액적의 형성 과정을 VOF(Volume-of-Fluid) 기법을 이용한 전산해석으로 예측하고 이를 측정결과와 비교하였다. 작동유체는 에틸렌 글리콜 50%와 IPA(Isopropil alchol) 50%의 혼합액을 사용하였다. 노즐 출구에서 메니스커스 변위의 시간에 따른 변화를 직접 측정하여 노즐 입구의 속도분포를 예측하고 이를 해석의 초기조건 입력자료로 사용하였다. 측정치와 해석치를 비교한 결과 전산해석이 측정치의 액적 형성 과정을 잘 예측함을 알 수 있었다. 주액적 형성과정보다 위성액적 형성과정 예측에 오차가 약간 컸는데, 이는 정지중의 공기에 큰 질량의 주액적이 날아가는 것을 예측할 때는 해석오차가 적지만 주액적에 의해서 주변 공기 유동이 활발해진 상태에서 적은 질량의 위성액적이 날아가는 것을 예측할 때는 해석오차가 상대적으로 커지기 때문이다. 또한 에틸렌 글리콜과 IPA의 혼합 비율을 달리하여 물성치를 변화시킨 다른 잉크에 대해서도 잉크 액적 형상을 예측한 결과 실험 결과를 비교적 정확히 예측할 수 있었다. A drop-on-demand inkjet is used widely for various applications. Therefore, it is important to understand the jetting behavior of the drop from the piezo inkjet. In this study, to predict the jetting behavior, VOF (Volume-of-Fluid) simulation techniques were used and compared with the experimental results. The experimentally measured meniscus movement was used as the input data for the simulation. To verify the simulation, the measured jetting behavior of the mixture fluids of ethylene glycol and IPA (isopropyl alcohol), which has a mixing ratio of 50:50, was used. The numerical simulation of the drop formation using various mixture ratios and its comparison with the measured drop formation confirmed that the proposed method can predict the actual jetting. On the other hand, the satellite drop behavior showed slight differences because the small sized droplet is subject to a more aerodynamic effect during flight because the kinetic energy of the satellite droplet is far smaller than that of the main droplet.

Angular Color Uniformity Enhancement of White LEDs by Lens Wetting Phosphor Coating

In this letter, we proposed a remote phosphor coating method by lens wetting for enhancing the angular color uniformity of phosphor-converted white light-emitting diodes. Simulations based on the volume of fluid (VOF) method were applied to investigate the geometry evolution of a phosphor gel droplet after being dropped onto the lens, and the stable geometry of the phosphor gel was obtained. Monte Carlo ray tracing was used to study the optical performance of LED samples with the stable phosphor geometries. Besides, experiments were conducted to verify the fabrication flexibility of the proposed method. The VOF simulation and experimental results show that the proposed method can realize the hemispherical remote phosphor layers with uniform or non-uniform thickness by adjusting the coating volume. The optical simulations and the experimental measurements show that the LED samples with non-uniform thickness remote phosphor geometry achieves smaller correlated color temperature deviation (<;200 K at 5000 K) than the uniform thickness remote phosphor geometry.

An algorithm to calculate interfacial area for multiphase mass transfer through the volume-of-fluid method

Mass transfer occurs in many simple and complex processes. As mass transfer persists across the interface separating immiscible fluids, the proper determination of the interfacial area is critical in accurately capturing the mass transfer process. In this paper, an algorithm is proposed and developed whereby the interfacial area is ascertained within the framework of the volume-of-fluid (VOF) multiphase model. The algorithm is based on a concept similar to the Piecewise-Linear Interface Calculation (PLIC) method where a plane cutting an orthogonal mesh cell is considered. Through this algorithm, the interfacial area can be approximated as the area of the resulting polygon from the plane cut. A series of test cases are conducted to verify the accuracy of the algorithm. The results indicate that the algorithm is able to correctly calculate the interfacial area of multiphase systems including for complex cases such as droplets in microchannels. The algorithm is also shown to simulate mass transfer accurately and is demonstrated to be superior to the standard |∇α| function, which is used widely in literature to approximate the interfacial area in VOF simulations.

Conditions for peak pressure stability in VOF simulations of dam break flow impact

This work addresses the problem of numerical simulation of the dynamic loads generated during a dry dam break flow impact on a wall. The numerical model used is the multi-fluid Navier–Stokes Volume Of Fluid (VOF) model THETIS. The results are compared with two experiments allowing pressure evolution validation at two relative positions on the wall. A first analysis of the results shows the large spatial and temporal variability of the pressure field after impact, highlighting the need for extreme care when performing measurements. When using first a free-slip boundary conditions on the bottom, the computed pressure peaks are found to behave differently depending on the distance to the stagnation point. Above a certain position, which is determined in the paper, computed peak pressures are stable with resolution while under this position, a divergent behavior is observed. This divergence is attributed to the shape of the bore tip which is poorly resolved with our model when a free-slip condition is used. This is confirmed by showing that starting from an identical free surface profile right before impact, the pressure peaks are convergent. The pressure peak instability problem can be solved by resolving the boundary layer structure with a suitable model (in our paper a v2−f RANS model) but this requires much more CPU resources.

Numerical Simulation of Dam-Break Problem Using an Adaptive Meshing Approach

The numerical simulation of free-surface flows is a vast topic, with applications to various fields of engineering such as aerospace, automotive, nuclear, etc. The Volume of Fluid (VOF) method represents a suitable technique to simulate free surface flows, tracking the air-liquid interface within the calculation domain. However this method requires a very fine mesh to successfully reconstruct the liquid surface, leading to very high computational costs. In this paper, VOF simulations of three-dimensional dam-break problem have been carried out using an adaptive meshing approach. Unsteady calculations have been performed exploiting the adaptive mesh feature implemented in ANSYS Fluent. In particular, a grid adaptation strategy has been defined as a way of significantly reducing the numerical effort. The main idea is to keep high resolution only locally at the air-liquid interface, minimizing numerical diffusion, and to maintain a coarse mesh size elsewhere. The dam-break problem was analyzed because it has been widely studied experimentally and numerically, representing a benchmark problem for verifying numerical models involving free-surface flows. The accuracy of the method has been assessed comparing simulation results with experimental data.

A dynamic interface compression method for VOF simulations of high-speed planing watercraft

A high speed surface craft is mostly supported by hydrodynamic lift force rather than by buoyancy force. The lift force directly influences the running attitude of the surface craft such as trim and sinkage. The pressure distribution is caused by a solution of free-surface flow around the surface craft. To deal with the free-surface flow, volume-of-fluid (VOF) method has been widely used even with its disadvantages including interface smearing. In the present study, a new dynamic interface compression method is introduced to reduce interface smearing and to avoid unphysical solutions. The method was validated by the volume fraction advection test and prismatic body problem. Finally, the method was applied to simulate the running attitude and resistance of several high speed planing vessels.

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.

CFD Model Study of a New Four-Port Submerged Entry Nozzle for Decreasing the Turbulence in Slab Casting Mold

In recent years, the continuous casting process in which molten metal is constantly cast into semifinished shapes has been widely adopted in the steel and nonferrous metal producing industry, mainly due to its economic advantages associated with increased yields and the elimination of intermediate processing steps. Turbulent flow in submerged entrance nozzle and mold of continuous casting is associated with costly failure such as the entrainment of slag inclusions and the formation of surface defects. A number of previously studies have analyzed the flow. A CFD model study has done to decrease the turbulence within the mold by developing a 4-port submerged entry nozzle in comparison with conventional 2-port submerged entry nozzle. VOF (volume of fluid) simulation study has been done to find out the effect of turbulence within mold on slag metal interaction, level fluctuation, and risk of breakout. In all the cases the performance of new 4-port SEN over 2-port SEN has been compared by plotting graph.

Investigation on Dynamic Water Transport of PEFCs Combining Neutron Radiography and CFD Simulation

The dynamic water transport of a polymer electrolyte fuel cell was investigated using neutron radiography and CFD simulation. Different operating conditions with dry and humidified gas supply were analyzed at 0.2 and 0.8 A cm-2. The regions with liquid water occurrence were identified using CFD simulations and were verified by neutron radiography. Water accumulation at anode was identified, while at cathode side condensate was sufficiently removed. Thus, the experimentally determined specific pressure drop criterion of 20 mbar m-1 was confirmed for the investigated type of meander-shaped flow field. The observed maximum water thickness was 0.4 mm inside the channel and served as an input for a closer investigation of dynamic water transport using the Volume of Fluid (VOF) model. The water removal capability at anode and cathode were verified with the VOF simulations. The droplet velocity was approximately 44 % / 50 % of gas velocity at anode / cathode for the investigated droplet shapes.

VOF modeling and experimental validation of ozonation reactive flow under high ozone concentration in three-phase reactors for environment protection

In the realm of multiphase reaction engineering, the dynamic behavior of an ozonation bubble column reactor was comprehensively investigated under high ozone concentration (30–90g/Nm3) by means of a volume-of-fluid (VOF) model embedding the transport phenomena and the detoxification parameters. First, the CFD framework was validated in terms of hydrodynamic data to gather novel insights on the bubbly flow in three-phase reactors for environment protection. The numerical computations highlighted that both profiles for the bubble velocity, detachment time and diameter of ozone bubbles handled agreeably well with the experimental data. Second, the evolvement of bubble diameter when increasing the superficial gas/liquid velocity under different surface tension/viscosity conditions was investigated throughout various hydrodynamic flow regimes. According to the VOF simulation results, the detachment of ozone bubbles was more prominent at high interaction regimes when the bubble column was operated under high superficial liquid velocities, which correspondingly controlled the time-averaged bubble diameter. Afterwards, the VOF model was experimentally validated for the ozonation of phenol-like compounds under low and high interaction regimes reinforcing how the bubbly phenomena dictate the overall bubble column reactor performance. A heterogeneous distribution of ozone concentration has been found at the gas–liquid interface enlightening the competition between mass transfer and chemical reaction during the initial reaction time, which was most likely due to the unsteady phase holdup distributions and pollutant removal efficiencies.

VOF Simulations of Countercurrent Gas-Liquid Flow in a PWR Hot Leg

In order to evaluate flow patterns and CCFL (countercurrent flow limitation) characteristics in a PWR hot leg under reflux condensation, numerical simulations have been done using a two-fluid model and a VOF (volume of fluid) method implemented in the CFD software, FLUENT6.3.26. The two-fluid model gave good agreement with CCFL data under low pressure conditions but did not give good results under high pressure steam-water conditions. On the other hand, the VOF method gave good agreement with CCFL data for tests with a rectangular channel but did not give good results for calculations in a circular channel. Therefore, in this paper, the computational grid and schemes were improved in the VOF method, numerical simulations were done for steam-water flows at 1.5 MPa under PWR full-scale conditions with the diameter of 0.75 m, and the calculated results were compared with the UPTF data at 1.5 MPa. As a result, the calculated flow pattern was found to be similar to the flow pattern observed in small-scale air-water tests, and the calculated CCFL characteristics agreed well with the UPTF data at 1.5 MPa except in the region of a large steam volumetric flux.

Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel

Abstract In this study, the behavior of condensing single vapor bubble in subcooled boiling flow within two different vertical rectangular channels has been numerically investigated by using the VOF (Volume Of Fluid) multiphase flow model. The mass and energy transfer model of bubble condensing process induced by the interfacial heat transfer was proposed to describe the interfacial transportation between the two phases. The results of VOF simulations show a good agreements with previous experimental data in the bubble size variation and lifetime. The bubble lifetime is almost proportional to bubble initial size and be prolonged at increasing system pressure. With the increasing of the subcooling, the bubble lifetime reduces significantly, and the effect of mass flux could be negligible. When the bubble size increased, the bubble shape tends to be changed in a large channel. The VOF simulation results of deformation have good agreement with those of Kamei’ experiment and the results of MPS (Moving Particle Semi-implicit) simulation in a larger channel. Furthermore, the initial bubble size, subcooling of liquid and system pressure play an important role to influence the bubble deformation behaviors significantly. The bubble could be deformed sharper with the increasing subcooling and initial diameter, or could breakup when the subcooling and the initial diameter reach a certain value at the last bubble stage. Nevertheless, the trends of bubble deformation will be weakening with the increasing system pressure.

Influence of surface tension models on the hydrodynamics of wavy laminar falling films in Volume of Fluid-simulations

Three surface tension models are investigated within the Volume-of-Fluid code Free Surface 3D: unbalanced Continuum Surface Force, Continuum Surface Stress, and balanced Continuum Surface Force with height functions, where the latter was adapted to the simulation of laminar falling films. Unbalanced Continuum Surface Force exhibits large distortions when the grid is refined and is discarded for producing unphysical results. The remaining two models are thoroughly evaluated by comparison to recent experimental data of Dietze, and to an analytical solution for an oscillating free surface. Furthermore, grid dependence is examined. The most apparent hydrodynamical difference between Continuum Surface Stress and balanced Continuum Surface Force is the number of vortices inside the solitary wave in the reference frame of the moving wave. The first model shows three vortices, whereas the latter model displays only one vortex. It is demonstrated that Continuum Surface Stress gives inadequate results, whereas balanced Continuum Surface Force yields a considerable improvement. Thus it is shown that the choice of the surface tension model and its discretization heavily influence the resulting hydrodynamics in simulations of falling films. Although all models work in three dimensions, the numerical experiments are performed in 2D.

Numerical simulations for steam–water CCFL tests using the 1/3 scale rectangular channel simulating a PWR hot leg

Abstract In reflux condensation, steam generated in the reactor core and water condensed in a steam generator (SG) form countercurrent flow in a hot leg, which consists of a horizontal pipe, an elbow and an inclined pipe. Both countercurrent air–water and steam–water tests were previously carried out at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) using the 1/3 scale rectangular channel simulating a PWR hot leg installed in the pressure chamber of the TOPFLOW facility. In this paper, in order to evaluate the effects of fluid properties, the steam–water CCFL (countercurrent flow limitation) tests at HZDR were simulated using the CFD software, FLUENT 6.3.26. The computational domain included the reactor vessel simulator, hot leg and SG inlet chamber in order to avoid uncertainties of boundary conditions at both ends of the hot leg. The VOF (volume of fluid) method and two-fluid (2F) model were used. In the 2F model, the combination of three correlations on the interfacial friction coefficients, which had been validated for the 1/15 and 1/5 scale tests at Kobe University, was used as a function of local void fractions. The CCFL characteristics predicted by the 2F and VOF agreed relatively well with the steam–water CCFL data at HZDR but overestimated the effects of fluid properties on CCFL. The VOF simulations were better able to reproduce the fluid properties than the 2F simulations.

Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

Diffuse interface (DI) tracking methods frequently adopt the double-well energy density function to describe the free energy variation across an interface, leading to phase interpenetration and spontaneous drop shrinkage when applied to immiscible two-phase systems. While the observed continuity losses can be limited by constraints placed on the interfacial width and mobility parameter, the associated increase in computational cost and mesh requirements has limited DI methods to 2D planar and axi-symmetric flow. Using the proposed temperature-variant simplified energy density function (TVSED), the effect of the metastable thermodynamic region on phase continuity is examined using a reduced temperature parameter, T R . The solutions obtained by the proposed DI implementation and a volume-of-fluid (VOF) based solver are discussed for two common benchmark simulations (collapse of a column of water, and droplet deformation/relaxation in simple shear). While comparable solutions are obtained from the T R = 0 and VOF simulations; the large metastable region of the more commonly used double-well function ( T R = 1) promoted inter-mixing in the bulk phases, diluting the inertia transferred between impacting fluids and under-predicting deformation in shear. The fundamental mechanisms responsible for spontaneous drop shrinkage are eliminated at T R = 0, allowing for constraints on the interfacial width and mobility to be relaxed. The comparable performance of T R = 0 and VOF simulations is a promising indication of the potential for application to complex 3D flows at reduced mesh resolution relative to existing DI methods.

VOF Simulations of Gas Bubbles Motion in a Reciprocally Stirred Flow

This paper reports progress in the numerical simulations of movement and the coalescence of two neighbor bubbles (leading and trailing bubble) in a reciprocally stirred liquid flow field. The full Navier-Stokes equations are solved by the volume-of fluid (VOF) method for tracking the interface between the bubble and the liquid flow. A dynamic mesh method was used to predict the gas-liquid flow in a two-dimensional foaming tank. Results indicate that the motion and merge behavior of the bubbles is dominantly influenced by the initial locations and the sizes of the bubbles as well as by the surface tension, while the reciprocating effect is insignificant.

VOF simulation of marangoni flow of gas bubbles in 2D-axisymmetric column

Abstract The migration of gas bubbles immersed in a liquid under the action of temperature gradient and surface tension (Marangoni flow) in zero gravity environment is numerically investigated for different Ma, Re, and Pr (Marangoni, Reynolds, and Prandtl numbers). The full Navier–Stokes equations as well as the energy equation for temperature gradient are solved by a volume of fluid (VOF) method/Finite Volume method, and the surface tension force is modeled by a continuum surface force (CSF) model. The behavior of bubble migrating toward the hotter side by the action of surface tension using the flow relations between two bubbles (leading and trailing bubble), and the trajectories and the velocities of the different bubbles diameters, in microgravity environment have been investigated numerically. It has been verified that the calculated results are in good agreement with available experimental and numerical results. It is also concluded that the VOF is able to simulate two-phase flow under zero gravity conditions.

Parasitic current generation in Combined Level Set and Volume of Fluid immiscible fluid simulations

The Continuum Surface Force technique is a popular tool used to implement surface tension forces in Eulerian based Computational Fluid Dynamics codes. Under this technique, inaccuracies present in calculating the surface tension force can manifest themselves as `parasitic' currents. We detail a new Combined Level Set and Volume of Fluid implementation of the Continuum Surface Force method. We then develop a correlation for the magnitude of parasitic currents that are generated under this new method, as a function of both the numerical and physical parameters employed in a simulation. A set of numerical experiments validate this correlation and show that, importantly, the magnitude of currents produced by the method decreases as the computational cell size reduced. References J. U. Brackbill, D. B. Kothe, and C. Zemach. A continuum method for modelling surface tension. Journal of Computational Physics, 100:335--354, 1992. Dalton J. E. Harvie, M. R. Davidson, and Murray Rudman. An analysis of parasitic current generation in volume of fluid simulations. Appl. Math Mod., 30(10):1056--1066, 2006. doi:10.1016/j.apm.2005.08.015 D. B. Kothe and R. C. Mjolsness. RIPPLE: A new model for incompressible flows with free surfaces. American Institue of Aeronautics and Astronautics, 30 (11):2694--2700, 1992. Bruno Lafaurie, Carlo Nardone, Ruben Scardovelli, Stephane Zaleski, and Gianluigi Zanetti. Modelling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics, 113:134--147, 1994. Murray Rudman. A volume-tracking method for incompressible multifluid flows with large density variations. International Journal for Numerical Methods in Fluids, 28:357--378, 1998. Ruben Scardovelli and Stepahe Zaleski. direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 31:567--603, 1999. J. A. Sethian and Peter Smereka. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics, 35:341--372, 2003. doi:10.1146/annurev.fluid.35.101101.161105 Mark Sussman. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics, 187:110--136, 2003. doi:10.1016/S0021-9991(03)00087-1 Mark Sussman and Elbridge Gerry Puckett. A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 162:301--337, 2000. doi:10.1006/jcph.2000.6537 Mark Sussman, Peter Smereka, and Stanley Osher. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 114:146--159, 1994. S. P. van der Pijl, A. Segal, C. Vuik, and P. Wesseling. A mass-conserving level-set method for modelling of multi-phase flows. International Journal for Numerical Methods in Fluids, 47:339--361, 2005. doi:10.1002/fld.817

Modern Trends in CFD Simulations: Application to GTL Technology

Multiphase flow processes are frequently observed in several important reactor technologies. These technologies are found in diverse applications such as in manufacture of petroleum-based fuels and products, conversion of synthesis gas into liquid hydrocarbons (Gas-to-liquid technology), production of commodity chemicals, pharmaceuticals, herbicides, pesticides, polymers etc. Due to the inherent complexity of these processes, the knowledge of fluid dynamic and transport parameters is necessary for development of appropriate reactor models and scale-up rules. It is, therefore, of paramount importance to develop understanding and predictive tools to simulate multiphase flow processes for better and economically viable reactor technologies. In the past, knowledge of hydrodynamics and transport characteristics of multiphase reactors has been interpreted in the form of empirical correlations, which have numerous restrictions in terms of their validity for different operating conditions. Computational fluid dynamics (CFD) simulation, on the other hand, deals with the solution of fluid dynamic equations on digital computers, requiring relatively few restrictive assumptions and thus giving a complete description of the hydrodynamics of these reactors. This detailed predicted flow field gives an accurate insight to the fluid behaviour and can sometimes give information, which cannot be obtained from experiments. These days, due to cheaper computational resources, CFD simulations are becoming economically reliable for modeling of multiphase processes including GTL (Gas-to-liquid) processes. In this paper, a comprehensive review of different multiphase flow simulation approaches has been presented. The recent progress made in hydrodynamic modeling of multiphase reactors, their capabilities and limitations (with special focus on GTL processes) are discussed in detail. Finally, case studies with different simulation approaches (Eulerian-Eulerian and VOF (Volume of fluid) simulations of bubble column reactors operating in different flow regimes) are discussed to demonstrate the power of this emerging research tool.