Interface Tracking Simulations Research Articles

Pressure drop and bubble velocity in Taylor flow through square microchannel

Interface tracking simulations of gas–liquid Taylor flow in horizontal square microchannels were carried out to understand the relation between the pressure drop in the bubble part and the curvatures at the nose and tail of a bubble. Numerical conditions ranged for 0.00159 ≤ CaT ≤ 0.0989, 0.0817 ≤ WeT ≤ 25.4, and 8.33 ≤ ReT ≤ 791, where CaT, WeT, and ReT are the capillary, Weber, and Reynolds numbers based on the total volumetric flux. The dimensionless pressure drop in the bubble part increased with increasing the capillary number and the Weber number. The curvature at the nose of a bubble increased and that at the tail of a bubble decreased as the capillary number increased. The variation of the curvature at the tail of a bubble was more remarkable than that at the nose of a bubble due to the increase in the Weber number, which was the main cause of large pressure drop in the bubble part at the same capillary number. The relation between the bubble velocity and the total volumetric flux was also discussed. The distribution parameter of the drift-flux model without inertial effects showed a simple relation with the capillary number. A correlation of the distribution parameter, which is expressed in terms of the capillary number and the Weber number, was developed and was confirmed to give good predictions of the bubble velocity.

Pore‐Scale Modeling of Reactive Transport with Coupled Mineral Dissolution and Precipitation

AbstractWe present a new pore‐scale model for multicomponent advective‐diffusive transport with coupled mineral dissolution and precipitation. Both dissolution and precipitation are captured simultaneously by introducing a phase transformation vector field representing the direction and magnitude of the overall phase change. An effective viscosity model is adopted in simulating fluid flow during mineral dissolution‐precipitation that can accurately capture the velocity field without introducing any empirical parameters. The proposed approach is validated against analytical solutions and interface tracking simulations in simplified structures. After validation, the proposed approach is employed in modeling realistic rocks where mineral dissolution and precipitation are dominant at different locations. We have identified three regimes for mineral dissolution‐precipitation coupling: (a) compact dissolution‐precipitation where dissolution is dominant near the inlet and precipitation is dominant near the outlet, (b) wormhole dissolution with clustered precipitation where dissolution generates wormholes in the main flow paths and precipitation clogs the secondary flow paths, and (c) dissolution dominant where all solid grains are gradually dissolved. In the three regimes, the proposed approach provides reliable porosity‐permeability relationships that cannot be described well by traditional macroscale models. We find that the permeability can increase while the overall porosity decreases when the main flow paths are expanded by dissolution and adjacent pore spaces are clogged by precipitation.

A novel ANN-CFD model for simulating flow in a vortex mixer

The study presents a novel ANN-CFD model for simulating flow in a vortex mixer (an unbaffled vessel stirred by a magnetic stirrer). Large eddy simulations (LES) are performed to simulate flow and turbulence considering presence of both air and liquid phases. The flow fields in air and liquid phases are coupled by applying suitable boundary conditions at the air–liquid interface represented by the vortex. The shape of the vortex is built-in in the computational domain and obtained by using an artificial neural network (ANN) model trained and validated with the data obtained from experiments carried out to capture the vortex shape under different parametric conditions. ANN-CFD model is validated with PIV data reported in literature. The ANN-CFD model reduces the computational time significantly by obviating the need of performing computationally very intensive interface tracking simulations. The model is used to understand hydrodynamics and turbulence characteristics of flow in the vortex mixer.

Microlayer formation and depletion beneath growing steam bubbles

Microlayers, the few-microns-thick layers of liquid that sometimes remain beneath bubbles growing on a heated substrate, are widely observed in experiments, but theoretical understanding of their formation, behaviour and role in bubble growth is limited.In this paper we present detailed interface-tracking simulations of the formation and depletion of such microlayers. Validation of our results is presented to the degree that available measurements of such a rapid and microscopic phenomenon allow.The work extends previous mechanistic hydrodynamic-only CFD simulations of early microlayer formation up to typical bubble departure times. These calculations confirm the understanding that the bubble growth rate and the resulting bubble shape determine the presence and overall extent of microlayers underneath steam bubbles. Their thickness is strongly influenced by viscous effects and surface tension.We then present coupled, physically self-consistent CFD simulations of the formation and evaporative depletion of such microlayers. This modelling suggests strongly that the evaporation process itself constitutes a significant fraction of the small resistance to heat and mass transfer presented by the very thin liquid layer. Inclusion of representations of evaporative thermal resistance, consistent with those suggested in the literature, is seen to promote the prediction of microlayer formation. Identification of the classes of conditions under which microlayers seem likely to be formed is presented, along with an assessment of their relative contributions to bubble growth. Comparisons of the predictions with recent detailed microlayer measurements indicate good agreement.

Bubble tracking analysis of PWR two-phase flow simulations based on the level set method

Bubbly flow is a common natural phenomenon and a challenging engineering problem yet to be fully understood. More insights from either experiments or numerical simulations are desired to better model and predict the bubbly flow behavior. Direct numerical simulation (DNS) has been gaining renewed interests as an attractive approach towards the accurate modeling of two-phase turbulent flows. Though DNS is computationally expensive, it can provide highly reliable data for model development along with experiments. The ever-growing computing power is also allowing us to study flows of increasingly high Reynolds numbers. However, the conventional simulation and analysis methods are becoming inadequate when dealing with such ‘big data’ generated from large-scale DNS. This paper presents our recent effort in developing the advanced analysis framework for two-phase bubbly flow DNS. It will show how one can take advantage of the ‘big data’ and translate it into in-depth insights. Specifically, a novel bubble tracking method has been developed, which can collect detailed two-phase flow information at the individual bubble level. Due to the importance of subcooled boiling phenomenon in pressurized water reactors (PWR), the bubbly flow is simulated within a PWR subchannel geometry with the bubble tracking capability. It has been demonstrated that bubble tracking method significantly improves the data extraction efficiency for level-set based interface tracking simulations. Statistical analysis was introduced to post-process the recorded data to study the dependencies of bubble behavior with local flow dynamics.

A conservative interface-interaction model with insoluble surfactant

In this paper we extend the conservative interface-interaction method of Hu et al. (2006) [34], adapted for weakly-compressible flows by Luo et al. (2015) [37], to include the effects of viscous, capillary, and Marangoni stresses consistently as momentum-exchange terms at the sharp interface. The interface-interaction method is coupled with insoluble surfactant transport which employs the underlying sharp-interface representation. Unlike previous methods, we thus achieve discrete global conservation in terms of interface interactions and a consistently sharp interface representation. The interface is reconstructed locally, and a sub-cell correction of the interface curvature improves the evaluation of capillary stresses and surfactant diffusion in particular for marginal mesh resolutions. For a range of numerical test cases we demonstrate accuracy and robustness of the method. In particular, we show that the method is at least as accurate as previous diffuse-interface models while exhibiting throughout the considered test cases improved computational efficiency. We believe that the method is attractive for high-resolution level-set interface-tracking simulations as it straightforwardly incorporates the effects of variable surface tension into the underlying conservative interface-interaction approach.

Interface tracking simulations of bubbly flows in PWR relevant geometries

The advances in high performance computing (HPC) have allowed direct numerical simulation (DNS) approach coupled with interface tracking methods (ITM) to perform high fidelity simulations of turbulent bubbly flows in various complex geometries. In this work, we have chosen the geometry of the pressurized water reactor (PWR) core subchannel to perform a set of interface tracking simulations (ITS) with fully resolved liquid turbulence.The presented research utilizes a massively parallel finite-element based code, PHASTA, for the subchannel geometry simulations of bubbly flow turbulence. The main objective for this research is to demonstrate the ITS capabilities in gaining new insight into bubble/turbulence interactions and assisting the development of improved closure laws for multiphase computational fluid dynamics (M-CFD).Both single- and two-phase turbulent flows were studied within a single PWR subchannel. The analysis of numerical results includes the mean gas and liquid velocity profiles, void fraction distribution and turbulent kinetic energy profiles. Two sets of flow rates and bubble sizes were used in the simulations. The chosen flow rates corresponded to the Reynolds numbers of 29,079 and 80,775 based on channel hydraulic diameter (Dh) and mean velocity. The finite element unstructured grids utilized for these simulations include 53.8million and 1.11billion elements, respectively. This has allowed to fully resolve all the turbulence scales and the deformable interfaces of individual bubbles. For the two-phase flow simulations, a 1% bubble volume fraction was used which resulted in 17 bubbles in the smaller case and 262 bubbles in the larger case. In the larger simulation case the size of the resolved bubbles is 0.65mm in diameter, and the bulk mesh cell size is about 30microns.Those large-scale simulations provide new level of details previously unavailable and were enabled by the excellent scaling performance of our two-phase flow solver and access to the state-of-the-art supercomputing resources. The presented simulations used up to 256 thousand processing threads on the IBM BG/Q supercomputer “Mira” (Argonne National Laboratory).

Mass transfer from single carbon dioxide bubbles in contaminated water in a vertical pipe

Mass transfer from single carbon dioxide bubbles rising through contaminated water in a vertical pipe of 12.5mm diameter was measured to investigate effects of surfactant. The bubble diameter was widely varied to cover various bubble shapes such as spheroidal, wobbling, cap and Taylor bubbles. The gas and liquid phases were 99.9% purity carbon dioxide and a surfactant solution made of purified water and Triton X-100. Comparison of mass transfer rates between contaminated and clean bubbles made clear that the surfactant decreases the mass transfer rates of small bubbles. The Sherwood numbers of small bubbles in the extreme cases, i.e. zero and the highest surfactant concentrations, are well correlated in terms of the bubble Reynolds number, Schmidt number and the ratio, λ, of the bubble diameter to pipe diameter. The Sherwood numbers at intermediate surfactant concentrations, however, are not well correlated using available correlations. The mass transfer rates of Taylor bubbles also decrease with increasing the surfactant concentration. They however increase with the diameter ratio and approach those of clean Taylor bubbles as λ increases. The main cause of this tendency was revealed by interface tracking simulations, i.e. the surfactant adsorbs only in the bubble tail region and the nose-to-side region is almost clean at high λ.

Effects of shape oscillation on mass transfer from a Taylor bubble

Interface tracking simulations of mass transfer from Taylor bubbles were carried out to investigate effects of shape oscillation on the mass transfer. Mass transfer from carbon dioxide Taylor bubbles in a glycerol-water solution was also measured to obtain experimental data for the validation of the numerical method. A high spatial resolution was used to resolve thin concentration boundary layers on the bubble interface, which enabled us to capture the agitation of boundary layer due to interfacial waves. The predicted mass transfer coefficients were in good agreements with the experimental data, provided that the spatial resolution was high enough to capture thin concentration boundary layers of high Schmidt number Taylor bubbles. The simulations have made it clear that the effect of agitation of concentration boundary layer due to interfacial waves on the total mass transfer rate is small and a fluctuation of the Sherwood number is caused by a fluctuation of the bubble surface area. This result implies that interface tracking methods using boundary layer approximations can give accurate predictions for mass transfer from bubbles even when the flow field is not fully resolved when the wave effect on the net mass transfer is negligible.

Terminal velocities of clean and fully-contaminated drops in vertical pipes

Terminal velocities and shapes of drops rising through vertical pipes in clean and fully-contaminated systems are measured by using a high-speed video camera and an image processing method. Silicon oils and glycerol water solutions are used for the dispersed and continuous phases, respectively. Triton X-100 is used for surfactant. Clean and contaminated drops take either spherical, spheroidal or deformed spheroidal shapes when the diameter ratio λ is less than a critical value, λC, whereas they take bullet shapes for λ>λC (Taylor drops). The applicability of available drag and Froude number correlations is examined through comparisons with the measured data. Effects of surfactant on the shape and terminal velocity of a Taylor drop are also discussed based on the experimental data and interface tracking simulations. The conclusions obtained are as follows: (1) drag and Froude number correlations proposed so far give reasonable estimations of the terminal velocities of clean drops at any λ, (2) the terminal velocities of contaminated drops are well evaluated by making the viscosity ratio μ* infinity in the drag correlation for clean drops in the viscous force dominant regime, (3) the effects of surfactant on the shape and terminal velocity of a Taylor drop become significant as the Eötvös number, EoD, decreases and μ* increases, and (4) the reduction in surface tension due to the addition of surfactant would be the cause of the increase in the terminal velocity and elongation of a contaminated Taylor drop.

916 フェーズフィールドモデルアプローチによる二相・三相流界面追跡シミュレーション(OS9.フェーズフィールド法とその多様な展開(4),OS・一般セッション講演)

916 フェーズフィールドモデルアプローチによる二相・三相流界面追跡シミュレーション(OS9.フェーズフィールド法とその多様な展開(4),OS・一般セッション講演)

Terminal velocity of a Taylor drop in a vertical pipe

A scaling analysis based on the field equations for two phases and the jump conditions at the interface is carried out to deduce a balance of forces acting on a Taylor drop rising through stagnant liquid in a vertical pipe. The force balance is utilized to deduce a functional form of an empirical correlation of terminal velocity of the Taylor drop. Undetermined coefficients in the correlation are evaluated by making use of available correlations for two limiting cases, i.e. extremely high and low Reynolds number Taylor bubbles in large pipes. Terminal velocity data obtained by interface tracking simulations are also used to determine the coefficients. The proposed correlation expresses the Froude number Fr as a function of the drop Reynolds number Re D , the Eötvös number Eo D and the viscosity ratio μ *. Comparisons between the correlation, simulations and experimental data confirm that the proposed correlation is applicable to Taylor drops under various conditions, i.e., 0.002 < Re D < 4960, 4.8 < Eo D < 228, 0 ⩽ μ * ⩽ 70, 1 < N < 14700, −12 < log M < 4, and d/ D < 1.6, where N is the inverse viscosity number, M the Morton number, d the sphere-volume equivalent drop diameter and D the pipe diameter.

Numerical verification of a simplified model for vapor bubble lift-off from a hydrophilic heated flat-wall

Three-dimensional interface tracking simulations were carried out to investigate the role of surface tension force in the process of vapor bubble lift-off from a hydrophilic heated surface in nucleate boiling. Since bubbles are frequently flattened along the heated surface in photographic experiments reported in literature, a bubble was assumed to be spheroidal in shape in the initial condition. The effect of phase change at the bubble interface was not taken into consideration for the sake of simplicity. In the present numerical simulations, the initially spheroidal bubble approached the spherical shape due to the surface tension force and was eventually lifted off the surface. The change in bubble shape induced local liquid flow directing toward the bubble base, that was the direct cause of the occurrence of the bubble lift-off. The dependence of the bubble migration velocity on several important parameters including the bubble size, surface tension coefficient and the density of surrounding liquid was also investigated. The change in bubble shape from flattened to more rounded causes the reduction of the surface energy, while the formation of local liquid flow leads to an increase in the kinetic energy. It was demonstrated that the bubble migration velocity after the lift-off can successfully be interpreted from the standpoint of energy conservation during the lift-off process.

Interface Tracking Simulation of Drops Rising through Liquids in a Vertical Pipe Using Three Coordinate Systems

Interface tracking simulations of single drops rising through a vertical pipe are carried out using three coordinate systems, i.e. cylindrical, general curvilinear and Cartesian coordinates, to investigate the effects of coordinate system and spatial resolution on the accuracy of predictions. Experiments of single drops in a vertical pipe are also conducted to obtain experimental data for comparisons with simulations. The drop shape observed are spheroidal and deformed spheroidal at low values of the diameter ratio, Λ, of the sphere-volume equivalent diameter of a drop to the pipe diameter, whereas they take bullet-shapes at large Λ. The conclusions obtained are as follows: (1) the effects of coordinate system on drop shape are small at low Λ. At large Λ, the effects are also small for drops in a low viscosity system, whereas non-physical shape distortion takes place when the Cartesian coordinates are used with low spatial resolution for drops in a high viscosity system, and (2) the drop terminal velocity and the velocity profile in the liquid film between a bullet-shaped drop and a pipe wall are well predicted using all the coordinate systems tested even at low spatial resolution.

A drag correlation of fluid particles rising through stagnant liquids in vertical pipes at intermediate Reynolds numbers

A drag correlation for a fluid particle rising along the axis of a vertical pipe at low and intermediate Reynolds numbers, Re, is proposed by making use of available correlations and a numerical database accumulated by interface tracking simulations. The accuracy of the interface tracking method has been verified through comparisons between measured and predicted velocities of single drops in vertical pipes. Being similar to drag model for solid spheres proposed by Michaelides, the developed drag correlation takes into account inertial and wall effects as their linear combination. The correlation gives good estimation of the drag coefficient for fluid particles rising through stagnant liquids in vertical pipes under the conditions of 0.13⩽ Eo⩽30, −10.0⩽log M⩽2.0, 0.083⩽ Re<200, 0⩽ κ⩽10.0 and λ⩽0.6, where Eo is the Eötvös number, M the Morton number, κ the viscosity ratio and λ the ratio of particle diameter to pipe diameter.

混相流研究の進展 ４ 液滴・液膜衝突に及ぼす液膜厚さおよび衝突角度の影響

Two-dimensional interface tracking simulations and photographic experiments were carried out to investigate the effects of film thickness and impingement angle on the splashing event during single-drop impact onto a plane liquid surface. For sufficiently small values of liquid film depth, liquid originally included in the inner region of liquid crown was not transported to the outer region. As a result, the pressure rise at the impact neck became significant, a thin liquid crown was formed, and the crown wall was broken into many secondary drops. Numerical results showed that the pressure rise induced on the bottom wall by drop impact is significantly mitigated if the impacted wall is covered with the liquid film whose thickness is comparable to the primary drop size. With respect to the effect of impingement angle, pressure rise in liquid was equally dependent on the normal and tangential components of impact velocity for slightly and moderately oblique impacts; however, the pressure rise was mitigated for very oblique impacts.

Adherence and bouncing of liquid droplets impacting on dry surfaces

The paper explores liquid drop dynamics over a solid surface, focusing on adherence and bouncing phenomena. The study relies on detailed interface tracking simulations using the Level Set approach incorporated within a Navier–Stokes solver. The investigation deals with moderate Reynolds number droplet flows, for which two-dimensional axisymmetric simulations can be performed. The modelling approach has been validated against experiments for axisymmetric and full three-dimensional impact upon dry surfaces. A drop-impact regime map is generated for axisymmetric conditions, in which the impact dynamics is characterized as a function of Weber number and equilibrium contact angle, based on about 60 simulations. The detailed simulations also helped validate a new mechanistic model based on energy-balance analysis, delimiting the boundary between adherence and bouncing zones at low Weber numbers. The mechanistic model is only valid for moderate droplet Reynolds numbers and it complements existing models for higher Reynolds numbers.

A Hybrid Method for Predicting Dispersed Gas-Liquid and Liquid-Liquid Multi-Phase Flows

A hybrid CMFD (computational multi-fluid dynamics) method is proposed for the prediction of gas-liquid and/or liquid-liquid dispersed two-phase flows including large-scale interface, poly-dispersed bubbles and drops. The method is the hybrid integration of an interface tracking method (ITM), three kinds of particle tracking methods (PTM) and an averaging method based on a multi-fluid model (MFM). The integration enables us to cover a wide range of d*=d/Δx, where d is the particle diameter and Δx the grid size, and to perform various kinds of multiphase CFD such as standard interface tracking, particle tracking and multi-fluid simulations, and hybrid simulations by making an arbitrary combination of ITM, PTM and MFM. The field equations and numerical solution procedure of the proposed method are described in detail. To demonstrate its potential, a poly-dispersed air-water bubbly flow in a vertical square duct and an air-water bubble plume in an open vessel are computed using the combination of ITM, PTM and MFM.

表面張力評価へのＣａｈｎ‐Ｈｉｌｌｉａｒｄ方程式の応用

An accurate method for evaluating surface tension force was proposed. The method utilizes a solution of the Cahn-Hilliard equation for the color function of the Continuum Surface Force model. Curvature vectors on three surfaces of revolution, i.e., sphere, distorted spheroid and spherical-cap were accurately evaluated by the method. Interface tracking simulations of a flow around a neutrally buoyant fluid sphere and of a drop rising through a stagnant liquid demonstrated that the proposed method could significantly reduce pseudo parasitic currents caused by numerical errors in surface tension force.

Interface Slip on Gas-Liquid Stratified Interface.

Most of interface tracking simulations conducted so far have been based on the assumption that the gas velocity is equal to the liquid velocity on gas-liquid interfaces. To the contrary, the theory of jump conditions presented by Ishii and Delhaye implies that an interfacial slip would exist when interfacial entropy generation takes place. In the present study, we therefore measured velocity distributions in the vicinity of a flat gas-liquid interface using an LDV system with a high spatial resolution of about 10 μm to examine whether or not the interface slip exist. To accurately measure the interface position, we utilized a secondary measurement volume formed by beams reflected by the interface. As a result, we could confirm that the interface slip does exist and its magnitude is large where the interfacial shear stress is large, i.e. where a large interfacial momentum transfer takes place.