Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.

Numerical Simulation of Separating Gas Mixtures via Hydrate Formation in Bubble Column

To develop a new technique for separating gas mixtures via hydrate formation,a set of medium-sized experimental bubble column reactor equipment was constructed.On the basis of the structure parameters of the ex- perimental bubble column reactor,assuming that the liquid phase was in the axial dispersion regime and the gas phase was in the plug flow regime,in the presence of hydrate promoter tetrahydrofuran(THF),the rate of hydrogen enrichment for CH4+H2 gas mixtures at different operational conditions(such as temperature,pressure,concentra- tion of gas components,gas flow rate,liquid flow rate)were simulated.The heat product of the hydrate reaction and its axial distribution under different operational conditions were also calculated.The results would be helpful not only to setting and optimizing operation conditions and design of multi-refrigeration equipment,but also to hydrate separation technique industrialization.

Numerical Simulation of Unsteady-State Flowsin Bubble Column Reactors

Unsteady-state operation has been widely applied in chemical engineering, such as optimizing a process, increasing yield and saving energy, etc. But the knowledge of the flow characteristics in bubble column reactors(BCRs) under unsteady state control is far from enough. In order to study the flow structures in this operation, the volume of fluid (VOF) model and the standard k-ε model to simulate the evolution of gas-liquid flow in BCRs under the start-up state are combined. For both the symmetry and asymmetry flow, the layout of the gas-inlets, the gas-in velocity, the liquid viscosity and the aspect ratio of the BCR all have effects on the liquid velocity distribution. The simulation results could provide some information for the design and scale-up of the BCRs.

Indoor experiment and numerical simulation study of ammonia-nitrogen migration rules in soil column

The riverbank soil is a natural purifying agent for the polluted river water(Riverbank filtration, RBF). This is of great importance to groundwater safety along the riverbank. This paper examines the migration and transformation rules of ammonia-nitrogen in three typical types of sand soil using the indoor leaching experiment of soil column, and then makes comparison with the indoor experiment results in combination with the numerical simulation method. The experiment process shows that the change in ammonia-nitrogen concentration goes through three stages including "removal-water saturation-saturation". As the contents of clay particles in soil sample increase, the removal of ammonia-nitrogen from soil sample will take more time and gain higher ratio. During the removal period, the removal ratio of Column 1, Column 2 and Column 3 averages 68.8%(1-12 d), 74.6%(1-22 d) and 91.1%(1-26 d). The ammonia-nitrogen removal ratio shows no noticeable change as the depth of soil columns varies. But it is found that the ammonia-nitrogen removal ratio is the least of the whole experiment when the soil columns are at the depth of 15 cm. It can be preliminary inferred that the natural purifying performance of soil along the river for ammonia-nitrogen in river water mainly depends on the proportion of fine particles in soil. HYDRUS-1D model is used to simulate this experiment process, analyze the change of the bottom observation holes by time and depth in three columns(the tenth day), and make comparison with the experiment result. The coefficients of determination for fitting curves of Column 1, Column 2 and Column 3 are 0.953, 0.909, 0.882 and 0.955, 0.740, 0.980 separately. Besides, this paper examines the contribution of absorption, mineralization and nitrification in the simulation process. In the early removal stage, mineralization plays a dominant role and the maximum contribution rate of mineralization is 99%. As time goes by, absorption starts to function and gradually assumes a dominant position. In the middle and late removal stage, nitrification in Column 1 and Column 2 makes more contribution than mineralization. So the experiment result of the ammonia-nitrogen concentration is 0.6% and 2.4% lower than that in effluent and the maximum contribution ratio of nitrification is -4.53% and -5.10% respectively when only the function of absorption is considered. The mineralization in Column 1 and Column 2 in the middle and late removal stage still plays a more important role than nitrification. So the experiment result is 1.4% higher than that in effluent and the maximum contribution ratio of nitrification is -2.51% when only the function of absorption is considered. Therefore, absorption, mineralization and nitrification make different contributions during different part of the stage. This means that the natural purifying performance of soil along the river for ammonia-nitrogen in river water not only depends on the proportion of fine particles in soil, but depends on the mineralization and nitrification environment. This can offer some insights into the protection and recovery of groundwater along the riverbank.

Modeling and optimization of industrial Fischer–Tropsch synthesis with the slurry bubble column reactor and iron-based catalyst

To optimize industrial Fischer-Tropsch （IT） synthesis with the slurry bubble column reactor （SBCR） and iron- based catalyst, a comprehensive process model for IT synthesis that includes a detailed SBCR model, gas liquid separation model, simplified CO2 removal model and tail gas cycle model was developed. An effective iteration algorithm was proposed to solve this process model, and the model was validated by industrial demonstration experiments data （SBCR with 5.8 m diameter and 30 m height）, with a maximum relative error 〈 10% for predicting the SBCR performances. Subsequently, the proposed model was adopted to optimize the industrial SBCR performances simultaneously considering process and reactor parameters variations. The results show that C5＋yield increases as catalyst loading increases within 10-70 ton and syngas H2/CO value decreases within 1.3-1.6, but it doesn＇t increase obviously when the catalyst loading exceeds 45 ton （about 15 wt% concentration）. Higher catalyst loading will result in higher difficulty for wax/catalyst separation and higher catalyst cost. There- fore, the catalyst loading （45 ton） is recommended for the industrial demonstration SBCR operation at syngas H2/ CO = 1.3, and the C5 ＋ yield is about 402 ton＂ per day, which has an about 16% increase than the industrial dem- onstration run result.

Centrifuge Model Tests and Numerical Simulations of the Impact of Underwater Explosion on an Air-Backed Steel Plate

Damage and threats to hydraulic and submarine structures by underwater explosions(UNDEXs)have raised much attention.The centrifuge model test,compared to prototype test,is a more promising way to examine the problem while reducing cost and satisfying the similitude requirements of both Mach and Froude numbers simultaneously.This study used a systematic approach employing centrifuge model tests and numerical simulations to investigate the effects of UNDEXs on an air-backed steel plate.Nineteen methodical centrifuge tests of UNDEXs were conducted.The shock wave pressure,bubble oscillation pressure,acceleration and the strain of the air-backed steel plate were recorded and compared with numerical studies using the finite element analysis(FEA)commercial software ABAQUS.By implementing empirically derived and physically measured pressures into the numerical models,the effects of the shock wave and bubble oscillation on the steel plate were investigated.Generally,the numerical results were in agreement with the experimental results.These results showed that the peak pressure of an UNDEX has a significant effect on the peak acceleration of the steel plate and that the impulse of the UNDEX pressure governs the peak strain of the steel plate.

Numerical simulation of a self-absorbing microbubble generator for a cyclonic-static microbubble flotation column

The Cyclonic-Static Microbubble Flotation Column (FCSMC) is currently a widely used, novel type of flotation device. The self-absorbing microbubble generator is the core component of this device. The structure of the microbubble generator directly influences flotation column performance by affecting bubble size and distribution as well as gas holdup in the column. However, the complicated flow inside the generator results in high R&D costs and difficulty in testing. Thus, the CFD software, FLUENT, was used to simulate the gas-liquid two-phase flow inside a self-absorbing microbubble generator. The effect of area ratio, a key structural parameter, was studied in detail. Critical flow-field parameters including velocity, turbulent kinetic energy, minimum static pressure and gas holdup were obtained. The simulation results demonstrate that the optimum area ratio is 3.

Numerical simulation and experimental verification of bubble size distribution in an air dense medium fluidized bed

Bubble size distribution is the basic apparent performance and obvious characteristics in the air dense medium fluidized bed (ADMFB). The approaches of numerical simulation and experimental verification were combined to conduct the further research on the bubble generation and movement behavior. The results show that ADMFB could display favorable expanded characteristics after steady fluidization. With different particle size distributions of magnetite powder as medium solids, we selected an appropriate prediction model for the mean bubble diameter in ADMFB. The comparison results indicate that the mean bubble diameters along the bed heights are 35 mm < D b < 66 mm and 40 mm < D b < 69 mm with the magnetite powder of 0.3 mm+0.15mm and 0.15mm+0.074mm, respectively. The prediction model provides good agreements with the experimental and simulation data. Based on the optimal operating gas velocity distribution, the mixture of magnetite powder and <1mm fine coal as medium solids were utilized to carry out the separation experiment on 6-50mm raw coal. The results show that an optimal separation density d P of 1.73g/cm 3 with a probable error E of 0.07g/cm 3 and a recovery efficiency of 99.97% is achieved, which indicates good separation performance by applying ADMFB.

DIRECT NUMERICAL SIMULATIONS OF TURBULENT CHANNEL FLOWS WITH CONSIDERATION OF THE BUOYANCY EFFECT OF THE BUBBLE PHASE

Turbulent channel flows with consideration of the buoyancy effect of the bubble phase is investigated by means of the Direct Numerical Simulation （DNS）. This two-phase system is solved by a two-way coupling Lagrangian-Eulerian approach. The Reynolds number based on the friction velocity and the half-width of the channel is 194, and the gravitational acceleration varies from -0.5 to 0.5, ranging from the upflow to the downflow cases. This study aims to reveal the influence of buoyancy on the turbulence behavior and the bubble motion. Some typical statistical quantities, including the averaged velocities and velocity fluctuations for the fluid and bubble phases, as well as the flow structures of the turbulence fluctuations, are analyzed.

Numerical simulation of single bubble rising in shear-thinning fluids by level set method

The behavior of single bubble rising in quiescent shear-thinning tlmds was lnvestlgateO numerically by level set metnoa. number of bubbles in a large range of Reynolds number and Eotvos number were investigated including spherical, oblate and spherical. The bubble shape and drag coefficient were compared with experimental results. It is observed that the simulated results show good conformity to experimental results over a wide range of Reynolds number. In addition, the detailed flow field based on the reference coordinate system moving with the bubble is obtained, and the relationship among flow field, bubble shape and velocity is discussed.

Numerical simulation of bubble chaotic motion in a cavitating water jet

A computational fluid dynamics (CFD) method is developed to investigate the radical motion of single cavitating bubble in the oscillating pressure field of a cavitating water jet. Regarding water as a compressible fluid, the simulation is performed at different oscillating frequencies. It is found that the bubble motion presents obvious nonlinear feature, and bifurcation and chaos appear on some conditions. The results manifest the indetermination of the cavitating bubble motion in the oscillating pressure field of the cavitating water jet.

Numerical simulation on dynamic behaviors of bubbles flowing through bifurcate T-junction in microfluidic device

Based on the volume of fluid(VOF) method, a numerical model of bubbles splitting in a microfluidic device with T-junction is developed and solved numerically. Various flow patterns are distinguished and the effects of bubble length,capillary number, and diameter ratio between the mother channel and branch are discussed. The break-up mechanism is explored in particular. The results indicate that the behaviors of the bubbles can be classified into two categories: break-up and non-break. Under the condition of slug flowing, the branches are obstructed by the bubbles that the pressure difference drives the bubbles into break-up state, while the bubbles that retain non-break state flow into an arbitrary branch under bubbling flow condition. The break-up of the short bubbles only occurs when the viscous force from the continuous phase overcomes the interfacial tension. The behavior of the bubbles transits from non-break to break-up with the increase of capillary number. In addition, the increasing of the diameter ratio is beneficial to the symmetrical break-up of the bubbles.

Numerical Simulation of Concentration Field on Liquid Side around Bubble during Rising and Coalescing Process in Non-Newtonian Fluid

On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian liquid were established. The formation of a single bubble from a submersed nozzle of 1.0 mm diameter and the mass transfer from an artificially fixed bubble into the ambient liquid were simulated by the volume-of-fluid （VOF） method. Good agreement between simulation results and experimental data confirmed the validity of the numerical method. Furthermore, the concentration distribution around rising bubbles in shear thinning non-Newtonian fluid was simulated. When the process of a single ellipsoidal bubble with the bubble deformation rate below 2.0 rises, the concentration distribution is a single-tail in the bubble＇s wake, but it is fractal when thebubble deformation rate is greater than 2.0. For the overtaking of two in-line rising bubbles, the concentration distribution area between two bubbles broadens gradually and then coalescence occurs. The bifurcation of concentration distribution appears in the rear of the resultant bubble.

Numerical simulation of gas-liquid two-phase jet flow in air-bubble generator

Air-bubble generator is the key part of the self-inspiration type swirl flotation machines,whose flow field structure has a great effect on flotation.The multiphase volume of fluid(VOF),standard k-ε turbulent model and the SIMPLE method were chosen to simulate the present model;the first order upwind difference scheme was utilized to perform a discrete solution for momentum equation.The distributing law of the velocity,pressure,turbulent kinetic energy of every section along the flow direction of air-bubble generator was analyzed.The results indicate that the bubbles are heavily broken up in the middle cross section of throat sect and the entrance of diffuser sect along the flow direction,and the turbulent kinetic energy of diffuser sect is larger than the entrance of throat sect and mixing chamber.

Numerical Simulation of Bubble Migration in Liquid Titanium Alloy Melt During Vertical Centrifugal Casting Process

The bubble migration in liquid titanium alloy melt during vertical centrifugal casting process has been predicted. The effects of different parameters, such as the initial bubble location, the mold rotational speed and the mold rotational direction on the bubble in the migration process are investigated. The results show that the bubble migration can be divided into the radial movement to the mould rotation axis and the circular movement to the mould wall opposite to rotational direction of the casting mould. The casting mould wall has an impeditive effect on the circular movement of the bubble during its migration process. And the bubble finally migrates like a straight line along the mould wall located at the opposite direction of the rotational casting mould whether it rotates clockwise or anti-clockwise. The bubbles at the position near the mould wall located at the opposite direction of the rotational casting mould are much easier to migrate in a straight line. The instantaneous speed of the gas bubble increases with the increment of the mould rotational speed. However the mould rotational speed is high or low, the moving speed of the gas bubble increases slightly at the primary stage, and then decreases gradually like a ladder.

Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.

Numerical simulation on the fluidized bed gasification and CaO dechlorination of refuse derived fuel

A three-dimensional numerical model verified by previous experimental data is developed to simulate the fluidized bed gasification of refuse derived fuel （RDF）. The CaO dechlorination model obtained by the thermal gravity analysis （TGA） is coupled to investigate the process of CaO dechlorination. An Eulerian-Eulerian method is adopted to simulate the gas-solid flow and self-developed chemical reaction modules are used to simulate chemical reactions. Flow patterns, gasification results and dechlorination efficiency are obtained by numerical simulation. Meanwhile, simulations are performed to evaluate the effects of Ca/Cl molar ratio and temperature on dechlorination efficiency. The simulation results show that the presence of bubbles in the gasifier lowers the CaO dechlorination efficiency. Increasing the Ca/Cl molar ratio can enhance the dechlorination efficiency. However, with the temperature increasing, the dechlorination efficiency increases initially and then decreases. The optimal Ca/Cl molar ratio is in the range of 3. 0 to 3. 5 and the optimal temperature is 923K.

Phase field simulation of single bubble behavior under an electric field

Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.

Numerical modeling of effect of slot on bubble motion in aluminum electrolytic process

A transient three-dimensional（3 D） model was established to understand the bubble motion in an industrial electrolytic process. An anode with a new design was tested. It incorporates two slots that allow an efficient removal of gas bubbles. The electromagnetic fields were described by solving Maxwell＇s equations. The bubble movement was studied with two-way coupling Euler-Lagrange approach. The interplay of current density and bubble nucleation rate was included. The collision and coalescence of bubbles were considered. Random walk module was invoked for involving the chaotic effect of the turbulence. The numerical results were validated by experimental measurements. The results indicate that the current distribution and the bubble nucleation periodically change. Due to the slot, the bubble elimination heavily increases. The contribution of the slot to the bubble removal exceeds 50% in the case of three currents, and the promotion of the slot decays with increasing the current.

Numerical Simulation on Ship Bubbly Wake

Based on a volume of fluid two-phase model imbedded in the general computational fluid dynamics code FLUENT6.3.26, the viscous flow with free surface around a model-scaled KRISO container ship （KCS） was first numerically simulated. Then with a rigid-lid-free-surface method, the underwater flow field was computed based on the mixture muitiphase model to simulate the bubbly wake around the KCS hull. The realizable k-e two-equation turbulence model and Reynolds stress model were used to analyze the effects of turbulence model on the ship bubbly wake. The air entrainment model, which is relative to the normal velocity gradient of the free surface, and the solving method were verified by the qualitatively reasonable computed results.