Numerical Simulations Of Bubbly Flows Research Articles

Numerical simulations of bubbly flows in a vertical periodic channel

In this study, numerical simulations of bubbly flows in an infinitely long vertical channel were performed. Generally, the upper and lower boundaries of such channels are simplified as periodic boundary conditions. Unlike horizontal channel flows, the presence of gravity in the streamwise direction complicates the establishment of periodic boundary conditions. Therefore, a specialized treatment is required to prevent fluid acceleration. Here, we developed a novel treatment for the imposition of periodic boundaries and proposed a new microbubble model to consider the surface tension effect of microbubbles. To detect each bubble in the flow field, we implemented a bubble identification algorithm, which facilitates a thorough statistical analysis of bubble number, size, and spatial distribution. Validation tests were conducted, and good agreement was achieved between our results and reference data. We also confirmed that the results obtained with periodic boundaries are consistent with those achieved without them. Finally, we simulated the evolution of rising bubble swarms in a quiescent liquid. The method presented here contributes to the numerical simulations of bubbly flows in industrial systems, including oil-gas transportation, bubble columns, and nuclear reactors.

Numerical simulation of bubbly flows by the improved lattice Boltzmann method for incompressible two-phase flows

Bubbly flow problems are simulated to verify the effectiveness of the improved lattice Boltzmann method for incompressible two-phase flows. In this method, it is possible to compute two-phase fluid flows with high density ratios accurately and efficiently compared with the previous method. Firstly, we simulate a stationary bubble to investigate the accuracy of the interfacial tension. As a result, the calculated pressure differences are in good agreement with the theoretical predictions, and the relative errors of the pressure difference are less than 5%. Secondly, we simulate a single bubble rising in a liquid under gravity. It is found that the terminal bubble shapes and Reynolds numbers are in good agreement with available numerical and experimental data. Thirdly, we simulate two bubbles rising in a liquid under gravity for different initial arrangements. It is found that the bubble shapes and transient Reynolds numbers during the coalescence process are generally in agreement with the available numerical results. Finally, we simulate typical slug and churn flows in a square duct. It is found that transition from slug flow to churn flow occurs when the pressure difference between inlet and outlet of the duct is increased. In addition, it is found that square ducts with larger width tend to generate churn flows. These results demonstrate that the present method is applicable to complicated bubbly flow problems.

A multiphase MPS method for bubbly flows with complex interfaces

The bubbly flows have always been a key research object in the field of multiphase simulations. However, when the bubbly flows become violent to cause the large deformations of bubbles, complex interfaces may be generated and bring great challenges to the traditional mesh-based methods. To overcome this challenge, one of the most commonly used mesh-free particle methods - moving particles semi-implicit (MPS) method, is adopted in this paper for the numerical simulations of bubbly flows with complex interfaces. Firstly, a multiphase MPS method is developed by combining the single-phase improved MPS (IMPS) method proposed in our previous study with different multiphase models, including the improved density smoothing scheme, interparticle viscosity model, continuous acceleration model, surface tension model, incompressible-compressible model and multiphase collision model. Then, the deformations of 2D/3D square droplets are simulated to validate the surface tension model, and the multiphase MPS method is verified through the benchmark cases of 2D/3D single bubble rising with large density and viscosity ratios (up to 1000 and 100, respectively). Finally, a series of bubbly flows with increasing complexity are performed, including the bubble rising and breaking at a high Reynolds number, the co-axial coalescence of two bubbles with different radiuses, and the violent interactions between a set of bubbles. The MPS results keep fair agreements with other numerical and experimental results, through which the advantages of the present multiphase MPS method in bubbly flows with complex interfaces can be well demonstrated.

Numerical Simulation of Bubbly Flow Using Partially Averaged Navier–Stokes Simulation and a Path Oscillation Model in the Euler–Lagrange Approach

Large bubbles always undergo asymmetric paths due to the wake instability, which was rarely considered in the simulation of bubbly flow in complex flow systems such as bubble columns. Here, we prop...

Estimation of the spatial discretization error in numerical simulations of bubbly flows

Accurate spatial discretization error estimates are essential for some CFD applications. Notwithstanding, this subject has been systematically disregarded in the literature on bubbly flow simulation. This work evaluated the suitability of three error estimators (EEMs) in simulations of a benchmark bubble column. The employed EEMs were: Direct Taylor series (DTS), Richardson Extrapolation (RExt), and Eça-Hoekstra Least-Squares (EH-LS). The modeling approaches for the bubbly flow were: standard two-fluid model (TFM), hyperbolic TFM (hTFM), and mixture model (MixtM). Geometric means of the estimated error and of the difference between the solution obtained with the considered mesh and a nearly mesh-independent solution were used as comparison metrics. DTS resulted in inaccurate estimates for coarse meshes. Both EH-LS and RExt generated accurate results for MixtM, the latter presenting lower computational cost. RExt could not deal adequately with the oscillatory convergence pattern of hTFM. EH-LS was the only method suitable for both MixtM and hTFM.

Numerical simulation of bubbly flow around a cylinder by semi-Lagrangian–Lagrangian method

Purpose The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle. Design/methodology/approach The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field. Findings The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well. Originality/value A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

Bubble induced turbulence model improved by direct numerical simulation of bubbly flow

Direct numerical simulations (DNS) provide a description of turbulent flow fields at every point in space and time. Since every statistical quantity can be computed, this data should be useful for the development of closure models. In this paper, models for bubbly turbulent flows, in a two-fluid framework, are investigated using DNS data. A front tracking method is employed to simulate turbulent flow with deformable bubbles in a vertical channel. Quantities such as void fraction, average velocities, velocity fluctuations, and turbulence statistics are computed and presented. After processing the DNS data, the turbulence kinetic energy and dissipation equations, based on the k-ε model and explicit algebraic stress model (EASM), are analyzed. The model for bubble-induced turbulence, represented by source terms in the k and ε equations, is re-evaluated using coefficients derived from the DNS results. This work is a first step to show what can be done by using the DNS data to evaluate turbulence closure models. More simulations should be conducted in future works to further improve such models.

An SPH modeling of bubble rising and coalescing in three dimensions

Abstract The numerical simulation of bubbly flows is challenging due to the unstable multiphase interfaces with large density ratios and viscous ratios. The multiphase Smoothed Particle Hydrodynamics (SPH) method is applied in this paper to simulate the phenomena of bubbles rising and coalescing in three dimensions. Firstly, the multiphase SPH model is introduced in detail, including the derivation of the discretized governing equations based on the principle of virtual work, the viscous force, the multiphase interface treatment, the time-stepping scheme, the boundary implementation, etc. Considering the expensive computational cost in three-dimensional (3-D) SPH simulations, the effects of the scale of the computational domain and the density ratio on the multiphase interface are numerically investigated in order to decrease the amount of calculation. Afterwards, several cases of single bubbles rising through viscous fluids are tested and the SPH results are validated by both the experimental data and other numerical results in the literature. Furthermore, the phenomena of bubbles coalescing in both vertical and horizontal directions are simulated and the results agree well with the experimental data. It is found that the background pressure in the equation of state is essential to keep the multiphase interface smooth and stable when the Bond number is relatively small. The fair agreements between the results of SPH and other reference results demonstrate that the present multiphase SPH model is robust and stable enough to accurately simulate the dynamic phenomena of rising bubbles in different conditions, which can give a reference for engineering applications.

Numerical Simulation of Bubbly Flow by Vortex in Cell Method

A vortex in cell (VIC) method for bubbly flow is proposed. It computes the time evolution of the flow by calculating the behavior of the vortex element as well as the bubble motion with the Lagrangian approach. The proposed method is also applied to simulate a bubble plume to demonstrate the validity. In a tank containing water, small air bubbles are released from the base of the tank. The bubbles rise due to the buoyant force, inducing the water flow around them. The simulation for the plume at the starting period highlights that the rising bubbles induce vortex rings at their top and that a bubble cluster appears owing to the entrainment of the bubbles into the vortex rings. The rising velocity for the top of the bubbles is proportional to the square root for the flow rate of the released bubbles, being consistent with an existing theoretical investigation. The simulation also demonstrates that the developed bubble plume having jet characteristics is successfully captured.

F232 二相流解析コードTPFITの垂直矩形管における空気と水二相流に対する検証(OS9 熱・流動(6))

In Japan Atomic Energy Agency, the detailed two-phase flow analysis code TPFIT has been developed to simulate and evaluate two-phase flow characteristics in nuclear systems. In this study, a numerical simulation of bubbly flow in a vertical square channel was performed to validate the applicability of TPFIT code on bubbly flow simulation. By checking bubble distribution development in the flow direction, the calculation of the forces acting on bubbles was validated through comparing simulation results and experimental results from Matos et al. (2004). Comparisons between the experimental and numerical data revealed, in general, good agreement except serious bubble coalescence appeared in numerical simulation.

Direct numerical simulations of bubbly flows

Direct numerical simulations (DNS) of multi-fluid and multiphase flows have progressed enormously over the last decade or two. It is, in particular, now possible to simulate the evolution of hundreds of bubbles in laminar and turbulent flows for a long enough time so that meaningful statistical quantities can be collected. For bubbly flow in vertical channels DNS have provided considerable new insight into the structure of the flow and how it can be modeled. The flow structure depends sensitively on the sign of the lift force on the bubbles. For nearly spherical bubbles in both upflow and downflow the lateral migration of bubbles results in a core region where the weight of the mixture exactly balances the imposed pressure gradient. For upflow bubbles accumulate at the wall but for downflow the region next to the wall is free of bubbles. The results lead to a very simple model of the void fraction distribution and, for downflow the velocity and the flow rate can be predicted relatively accurately. Deformable bubbles result in a very different flow structure, with no bubbles accumulating at the wall. Simulations of the transient motion show that it takes a long time for the flow to reach a steady state and that the evolution is complex, with bubbles moving in and out of the wall-layer. The availability of DNS results calls for more intense efforts to use the data for developing closure terms for models of the average and large-scale flows, as well as the development of efficient and accurate methods for more complex flows, such as those undergoing topology changes and involving additional physical effects like surfactants and heat and mass transfer.

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part II: numerical simulation

Numerical simulations of bubbly flows in a four by four rod bundle are carried out using a multi-fluid model to examine effects of the numerical treatment of phase distribution and drag model. The transport equations of bubble number density and void fraction are used as the continuity equation of the gas phase. Two drag models are tested: one of them accounts for the bubble deformation (aspect ratio), whereas the other does not. The rod diameter, the rod pitch and the hydraulic diameter of the rod bundle are 10, 12.5 and 9.1 mm, respectively. The gas and liquid volume fluxes are JG = 0.06 m/s and JL = 0.9 and 1.5 m/s, respectively. The bubble diameter ranges from 1 to 5 mm. Comparisons between the numerical and measured data show that (1) the restriction on bubble lateral motion due to the presence of rods can be taken into account by using the transport equation of bubble number density, whereas that of the void fraction cannot deal with the restriction and causes large errors in the distribution of void fraction and (2) the reduction in the bubble-relative velocity near the wall is predictable by using the drag model accounting for the bubble deformation effect.

Direct Numerical Simulations of the drag force of bi-disperse bubble swarms

Numerical simulations of bubbly flows in industrial process equipment rely for an important part on accurate modeling of the drag force. The drag acting on bubbles determines the rise velocity to a very large extent and hence the inter-phase mass transfer characteristics. Recently, we have proposed a correlation (Roghair et al., 2011a) to describe the drag on bubbles in a mono-disperse bubble swarm up to high gas fractions, and in this work we have extended this work to simulations of dense bi-disperse bubble swarms.The influence of the gas hold-up is determined by simulating a bi-disperse swarm of 8 relatively small bubbles (3.5mm) and 8 relatively large bubbles (4.4mm) in a periodic domain. The resulting drag coefficient acting on the bubbles agrees very well with the earlier proposed correlation.The composition of the swarm has first been varied in different ways; first, the ratio of the number of large to small bubbles was varied. In this case, the resulting drag coefficient remained constant indicating that no influence of the number of large and small bubbles is expected, with a typical deviation from the mono-disperse correlation up to 15%. Second, the composition of the bi-disperse swarm has been changed by altering the diameter ratio. These simulations showed a good agreement with the mentioned correlation as well. In general, it can be said that the mono-disperse correlation describes the drag coefficient of the bubbles in a bi-disperse swarm well if an error margin in the order of 15% is allowed for.

303 界面追跡法による垂直管内上昇気泡流の数値解析(OS9 オーガナイズドセッション《熱・流体・エネルギー変換工学の進展》)

In Japan Atomic Energy Agency, the detailed two-phase flow analysis code TPFIT has been developed to simulate and evaluate two-phase flow characteristics in nuclear systems [1]. In this study, a numerical simulation of bubbly flow in a vertical circular pipe was performed to validate the applicability of TPFIT code on bubbly flow simulation. By checking bubble distribution development in the flow direction, the calculation of the forces acting on bubbles was validated through comparing simulation results and experimental results from Lucas et al. (2005), who used wire-mesh sensor to obtain a high resolution of the gas fraction data in space as well as in time.

Simulation of bubbly flow in a vertical turbulent channel

AbstractThe paper presents results of Direct Numerical Simulation of bubbly flow to analyse the interaction between the turbulent fluid and the bubbles. The simulations aim to investigate the effect of the bubble Reynolds number, related to the bubble size, and the void fraction. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical Simulation of Bubbly Flow by Vortex in Cell Method

The Vortex in Cell (VIC) method for bubbly flow, proposed in the authors' prior study, is improved to promote the numerical accuracy and efficiency. The improvements are concerned with a discretization method using staggered grids, a correction method for vorticity and a single-stage calculation method for the convection of vortex element. To enlarge the applicability of the VIC method, vortex elements without core structure are employed. The improved VIC method is applied to simulate a bubble plume. In a tank containing water, small air bubbles are released from the base of the tank. The bubbles rise due to the buoyant force, inducing the water flow around them. The simulation for the plume at the starting period highlights that the rising bubbles induce vortex rings at their top and that a bubble cluster appears owing to the entrainment of the bubbles into the vortex rings. The rising velocity for the top of the bubbles is proportional to the square-root for the flowrate of the released bubbles, being consistent with existing theoretical and numerical investigations. The simulation also demonstrates that the developed bubble plume having some characteristics of a jet is successfully captured.

Numerical simulation of drop impact on a liquid–liquid interface with a multiple marker front-capturing method

The gravity-driven motion of a droplet impacting on a liquid–liquid interface is studied. The full Navier–Stokes equations are solved on a fixed, uniform grid using a finite difference/front-capturing method. For the representation of fluid–fluid interfaces, a coupled Level-Set/Volume-Of-Fluid method [M. Sussman, E.G. Puckett, A coupled Level-Set and Volume-of-Fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comp. Phys. 162 (2000) 301–337] is used, in which we introduce the novel approach of describing separate interfaces with different marker functions. As a consequence, we prevent numerical coalescence of the droplet and the liquid–liquid interface without excessive (local) grid refinement. To validate our method, numerical simulations of the drop impact event are compared with experiments [Z. Mohamed-Kassim, E.K. Longmire, Drop impact on a liquid–liquid interface, Phys. Fluids 15 (2003) 3263–3273]. Furthermore, a comparison is made with the numerical results of [A. Esmaeeli, G. Tryggvason, Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays, J. Fluid Mech. 385 (1999) 325–358] for an array of rising bubbles. The investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension.

Numerical simulation of bubbly flow around two tandem square-section cylinders by vortex method

The air—water bubbly flow around two tandem square-section cylinders is simulated with the vortex method proposed by the authors in a prior study. The flow was experimentally investigated by Shakouchi et al. The side length of cylinder s is 30 mm, and the distance between the cylinders is 2s. The water Reynolds number is 10 000, and the air volumetric flow ratio to whole fluid is 0.03. A pair of Karman vortices appear behind the first cylinder. The strength of the Karman vortex downstream of the second cylinder is larger than that for the single-cylinder. The strength of the Karman vortex reduces due to the bubble entrainment. The pressure reduction on the rear surface of the first cylinder is relaxed when compared with that on the single-cylinder. Therefore, the present simulation can predict the reduction of the drag force acting on the first cylinder, which was clarified by the corresponding experimental study.

Direct numerical simulation of bubbly flow in the turbulent boundary layer of a horizontal parallel plate electrochemical reactor

We perform direct numerical simulation (DNS) of a turbulent bubble-laden channel flow of shear Reynolds number Re τ = 131 to analyse mass transfer in a parallel plate electrochemical reactor. We set aside the electrochemical part of the problem and focus on the simulation of a turbulent channel flow of a liquid electrolyte with gas bubbles evolving from an electrode located at the bottom wall of the channel. We use an Eulerian–Lagrangian representation to simulate dispersed two-phase flow, where two-way momentum coupling between the bubbles and the electrolyte is taken into account. Three-dimensional simulations are obtained using a distributed memory parallel computer architecture. Investigations on the bubble motion due to advection and gravitational rise are carried out and the interaction of bubbles with turbulent flow structures is analysed. Furthermore, the role of the lift force acting on the bubbles is investigated. Mean volume fraction statistics are shown for validation purposes. An analysis of instantaneous flow fields and bubble distributions as well as order-of-magnitude analyses are used to determine which forces are mostly influencing the bubble dynamics and dispersion.

Diameters of Bubbles Released from Single Holes

Evaluation of the mean diameter of bubbles released from a hole is indispensable in designing gas distributors and for numerical simulation of bubbly flows in a Fischer-Tropsch reactor in a GTL plant, which is now being developed by JOGMEC. The objective of the present study is to develop a correlation for evaluating the mean diameter of bubbles released into a column through a hole. A simple correlation for the bubble diameter is deduced by modifying the Davidson & Schuler model based on the fact that a coalescence of two or three bubbles takes place just after the detachment. The proposed correlation is applicable to the evaluation of the mean diameter of bubbles discharged from two holes when the ratio of a pitch between holes to a bubble diameter is larger than 1.7.