Numerical Simulation of Absorbing CO2 with Ionic Liquids

Although separating CO₂ from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of CO₂ absorption in these solvents have not been researched. In this paper, a coupled computational fluid dynamic (CFD) model and population balance model (PBM) was applied to study the mass transfer properties for capturing CO₂ with ionic liquids solvents. The numerical simulation was performed using the Fluent code. Considering the unique properties of ionic liquids, the Eulerian‐Eulerian two‐flow model with a new drag coefficient correlation was employed for the gas‐liquid fluid dynamic simulation. The gas holdup, interfacial area, and bubble size distribution in the bubble column reactor were predicted. The mass transfer coefficients were estimated with Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor were also predicted in this paper.     

Dynamics of foam growth: Bubble growth in a limited amount of liquid

A mathematical model for the growth of a spherical gas bubble in a limited amount of a viscous liquid is presented. The growth of the bubble is assumed to be controlled by both momentum and mass transfer. The simplified approach suggested, by assuming a parabolic concentration profile for the volatile component in the liquid, results in approximated analytical expressions for the final parameters of the process. The numerical results of the model can be used to predict the increase in the bubble size as well as the decrease of the solute concentration in the liquid and the decrease of the cell density with time. The model is able to deal with real processes, such as polymer melt devolatilization and the production of polymeric foams, where many bubbles grow simultaneously. Polym. Eng. Sci. 44:1900–1906, 2004. © 2004 Society of Plastics Engineers.     

Experimental and numerical studies on bubble dynamics in nonpressurized foaming systems

This work explores the influence of rheological properties on polymer foam development in nonpressurized systems. To understand the complex contributions of rheology on the mechanism of bubble growth during different stages of foam processing, visualization studies were conducted by using a polymer‐foaming microscopy setup. The evolving cellular structure during foaming was analyzed for its bubble surface density, bubble size, total bubble projected area, and bubble size distribution. Morphological analysis was used to determine the rheological processing window in terms of shear viscosity, elastic modulus, melt strength and strain‐hardening, intended for the production of foams with greater foam expansion, increased bubble density and reduced bubble size. A bubble growth model and simulation scheme was also developed to describe the bubble growth phenomena that occurred in nonpressurized foaming systems. Using thermophysical and rheological properties of polymer/gas mixtures, the growth profiles for bubbles were predicted and compared to experimentally observed data. It was verified that the viscous bubble growth model was capable of depicting the growth behaviors of bubbles under various processing conditions. Furthermore, the effects of thermophysical and rheological parameters on the bubble growth dynamics were demonstrated by a series of sensitivity studies. POLYM. ENG. SCI., 54:1947–1959, 2014. © 2013 Society of Plastics Engineers     

Numerical simulation of bubble growth in viscoelastic fluid with diffusion of dissolved foaming agent

Viscoelastic simulations of bubble growth in polypropylene (PP) physical foaming were performed. A multimode Phan‐Thien Tanner (PTT) model was used to analyze the dynamic growth behavior of spherically symmetric bubbles with the diffusion of a foaming agent (CO₂). Changes in the dissolved foaming agent concentration in the polymer and in the strain of the polymer melt surrounding the bubbles were simulated with the Lagrangian FEM method. The simulation technique was validated by comparison with the bubble growth data, which were experimentally obtained from visual observations of the PP/CO₂ batch foaming system. The simulation results demonstrated that the strain‐hardening characteristic of polymer does not strongly affect the bubble growth rate. The linear viscoelastic characteristic is more influential, and the relaxation mode around 0.01 s is the most important factor in determining the bubble growth rate during the early stage of foaming. A multivariate analysis for the simulation results was also carried out. This clarified that bubble nucleus population density, surrounding pressure, initial dissolved foaming agent concentration, and diffusion coefficient are more important factors than the viscoelastic characteristics. POLYM. ENG. SCI., 45:1277–1287, 2005. © 2005 Society of Plastics Engineers     

Bubble growth model and its influencing factors in a polymer melt under nonisothermal conditions

Traditionally, in order to simplify the bubble growth process in a polymer melt, an isothermal model is typically used. In fact, the temperature of the polymer melt is changing during the foaming process. In order to accurately study the growth mechanism of bubbles in polymer melts, we build a physical and mathematical model of bubble growth in a polymer melt under nonisothermal conditions. The parameters of pressure, zero-shear viscosity, relaxation time, Henry's constant, diffusion coefficient, and surface tension were determined. The fourth-order Runge–Kutta method was used to solve the nonisothermal bubble model in the polymer melt. A computational program is developed to find the dimensional change during the bubble growth process, and the correctness of the model is verified. The nonisothermal growth mechanism of and factors influencing bubbles in the polymer melt are analyzed. Combined with the design of experiment (DOE) analysis method, the transfer function of the bubble radius and the maximum growth rate of bubbles with the process parameters were obtained, such as cooling rate, system pressure, and gas concentration. The results show that system pressure has the most significant effect on bubble growth. At the same time, a bubble growth prediction model is built, which can be used to predict the growth of bubbles. Through optimization analysis, it can be used to control the growth of bubbles. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47210.     

矩形薄腔中聚合物熔体非等温注气充填的数值模拟

采用五参数Cross粘度模型,利用有限元和控制体积法对矩形薄腔中聚合物熔体非等温注气充填过程中不同时刻的气泡边界、熔体前沿、熔体压力场、温度场和速度场等进行了数值模拟,结果表明:气泡主体边界平行于模壁方向生长,其前沿总是先向中心线附近移动,再向中心线两边移动;熔体压力在气泡周围某一区域内保持不变且等于气压;对于充模时间很短的情况,除气泡附近外,温度在各处相差不大。     

Numerical and experimental studies for gas assisted extrusion forming of molten polypropylene

In this study, the experiments of gas‐assisted extrusion (GAE) for molten polypropylene were carried out under different gas pressures, the different extrudate deformations and sharkskin defects of melt were observed. To ascertain the effects of gas on melt extrusion, non‐isothermal numerical simulation of GAE based on gas/melt two‐phase fluid model was proposed and studied. In the simulations, the melt extruded profile, physical field distributions (velocities, pressure drop, and first normal stress difference) were obtained. Numerical results showed that the deformation degree of melt increased with increasing gas pressure, which was in good agreement with experimental results. It was demonstrated that the influence of gas pressure on the melt extrusion could be well reflected by GAE simulation based on gas/melt two‐phase fluid model rather than simplified‐GAE (SGAE) based on full‐slip wall boundary condition used in the past time. Experimental and numerical results demonstrate that the gas pressure induced first normal stress difference is the main reason of triggering flow behavior changes, extrudate deformations, and sharkskin defects of melt. Therefore, the reasonable controlling of gas pressure is a key in practice of GAE, and the gas layer and its influence should be considered in GAE numerical simulation. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42682.     

Viscous co‐current downward Taylor flow in a square mini‐channel

This article presents a computational study of the co‐current downward Taylor flow of gas bubbles in a viscous liquid within a square channel of 1 mm hydraulic diameter. The three‐dimensional numerical simulations are performed with an in‐house computer code, which is based on the volume‐of‐fluid method with interface reconstruction. The computed (always axi‐symmetric) bubble shapes are validated by experimental flow visualizations for varying capillary number. The evaluation of the numerical results for a series of simulations reveals the dependence of the bubble diameter and the interfacial area per unit volume on the capillary number. Correlations between bubble velocity and total superficial velocity are also provided. The present results are useful to estimate the values of the bubble diameter, the liquid film thickness and the interfacial area per unit volume from given values of the gas and liquid superficial velocities. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Study on Dynamic Burning Rate Equation of Propellant

Aiming at the difficulty that the actual burning law of propellant in the gun bore couldn't be described exactly by static burning rate equation in the closed‐bomb, propellant dynamic burning rate equation and its acquisition method were established in the paper, which are based on static burning rate equation and considering burning gas flow and loading density influence factors in bore. A numerical code for interior ballistic two‐phase flow was successfully developed. And corresponding firing tests were also carried out. The comparison of simulations with interior ballistic code and firing test results show that the propellant dynamic burning rate equation makes the maximum errors of muzzle velocity and pressure in breech decreased from 2.97 % to 0.75 % and from 6.68 % to 0.38 %, respectively. This method not only improves simulation precision of gun muzzle velocity and pressure significantly, but also provides a means to improve the design accuracy for interior ballistic performance.     

Bubble growth in the microcellular foaming of CO2/polypropylene solutions

This article is concerned with bubble growth dynamics in the CO₂/polypropylene microcellular foaming process. The effect of the melt strength on the bubble growth was thoroughly investigated in theory for the first time. The theoretical results indicate that enhanced melt strength effectively restrains the bubble growth and stabilizes the bubble oscillation. Higher melt strength leads to lower bubble growth rate, shorter growth time, and smaller ultimate bubble size. Compared to the melt strength, the viscoelasticity and the gas pressure have less effect on the microcellular foaming process. The bubble growth varies a little as the viscoelasticity is varied. The bubble oscillation and growth rate are enhanced with increasing gas pressure, which leads to the augmentation of the bubble size. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Prediction of cellular structure in free expansion of viscoelastic media

A systematic model is presented for a free expansion polymer foaming process that includes simultaneous nucleation and bubble growth. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. The melt rheology is described using the Larson viscoelastic model. The initial conditions are obtained at the upper bound of critical cluster size under conditions of elastic deformation. The resulting set of equations are solved using a combination of numerical techniques. A parametric study is conducted to examine the effects of key process variables on bubble growth, nucleation, and final bubble size distribution. It shows that the factors influencing nucleation and growth affect the ultimate bubble sizes and their distribution. The Gibbs number, a dimensionless measure of the barrier to overcome for nucleation, has the strongest impact on the cellular structure of the foam. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:1353–1368, 1998     

Blown film extrusion of poly(lactic acid) without melt strength enhancers

Processing strategies were developed to manufacture poly(lactic acid) (PLA) blown films without melt strength enhancers (MSEs). The effects of processing temperature on PLA's melt properties (shear and elongational viscosities), PLA grades, and other processing conditions [ratio of take‐up roller to extruder's rotational screw speeds or processing speed ratio (PSR) and internal air pressures] on film's blow‐up ratio were examined. Experimental results indicate that extrusion‐blown amorphous and semicrystalline PLA films can be successfully manufactured without MSEs by controlling melt rheology through processing temperature and other extrusion processing conditions. PLA processed at lower extrusion temperature had higher melt viscosities, which favored the formation of stable films depending on the PSR and internal air pressure used. Inappropriate control of PSR and internal air pressure led to unstable films with various processing defects such as melt sag, bubble dancing, or draw resonance, irrespective of the lower extrusion processing temperature. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45212.     

液体蒸汽向单气泡中传质过程的数值分析

<正>当气体通过液相介质时,由于气液界面和气相主体间存在液体蒸汽的浓度差,使液体迅速蒸发,可以大大强化对流传热及沸腾传热.此外,在鼓泡设备中,这种溶剂汽化现象亦可能对气含率及传质带来很大影响.因此,定量地分析液体蒸汽向气泡中传质的过程是很有意义的.此过程为具人体积变化的自由边界问题.对于核状沸腾过程的自由边界问题已有很多研究,其气泡长大的控制步骤为兴高采烈相可能提供的气化潜热速率,而由于气泡中质量传递控制的移动边界问题尚未见有研究.本文提出了液体溶剂向单气泡中传质的数学模型,获得了数值解.并且对各种影响因素进行了讨论.     

气液两相流摆动特性实验的数值模拟

为了给鼓泡塔反应器设计提供依据,运用计算流体力学(CFD)软件模拟了鼓泡塔气液两相流动态行为。采用双欧拉法对鼓泡塔矩形反应器内不同曝气量下气液两相流的摆动特性进行了模拟考察,液相采用标准κ-ε紊流模型,气相采用分散相零方程模型,分析了网格尺寸、时间步长以及相间作用力对模拟结果的影响,模拟的曝气量为42.5~237 m L/s。结果表明,当相间作用力仅考虑阻力时,气液两相流呈现周期性摆动规律;随着气流量的增加,气泡羽流的摆动幅度和频率增大,同时液体的气含率也在增加;模拟的气液两相流摆动频率数据与实验值吻合较好,两者的相对误差为7.2%~12.9%。     

Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models

This work compares numerical simulations of fluid dynamics in fluidized beds using different closure models and air feed system models. The numerical results are compared to experiments by means of power spectral density distributions of fluctuating pressure signals and bubble statistics obtained from capacitance probe measurements. Two different particle rheology models are tested in combination with two different values of the maximum particle volume fraction. The first particle model predicts the particle pressure by an exponential power law and assumes a constant particle viscosity (CPV), and the second model predicts the stresses using the kinetic theory of granular flow (KTGF). Furthermore, two model approaches for the air inflow are evaluated. The first inflow model includes the coupling between the air-feed system and the fluidized bed in the simulation, and the second model assumes a constant mass flow of gas into the fluidized bed. Finally, the influence of the compressibility of the gas phase on the numerical predictions is investigated. The numerical simulations are made using the CFX-4.4 commercial flow solver.The simulations show that the KTGF model gives a more evenly distributed bubble flow profile over the bed cross-section, while the CPV model gives a more parabolic bubble flow profile, with a higher bubble flow in the central part of the bed. This work shows that the KTGF model results are in significantly better agreement with the experiments. It is furthermore shown that the modelling of the air-feed system is crucial to for predicting the overall bed dynamic behaviour.     

Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns

Experiments and simulations were conducted for bubble columns with diameter of 0.2 m(180 mm i.d.), 0.5 m(476 mm i.d.) and 0.8 m(760 mm i.d.) at high superficial gas velocities(0.12–0.62 m·s-1) and high solid concentrations(0–30 vol%). Radial profiles of time-averaged gas holdup, axial liquid velocity, and turbulent kinetic energy were measured by using in-house developed conductivity probes and Pavlov tubes. Effects of column diameter, superficial gas velocity, and solid concentration were investigated in a wide range of operating conditions. Experimental results indicated that the average gas holdup remarkably increases with superficial gas velocity, and the radial profiles of investigated flow properties become steeper at high superficial gas velocities. The axial liquid velocities significantly increase with the growth of the column size, whereas the gas holdup was slightly affected. The presence of solid in bubble columns would inhibit the breakage of bubbles, which results in an increase in bubble rise velocity and a decrease in gas holdup, but time-averaged axial liquid velocities remain almost the same as that of the hollow column. Furthermore, a 2-D axisymmetric k–ε model was used to simulate heterogeneous bubbly flow using commercial code FLUENT 6.2. The lateral lift force and the turbulent diffusion force were introduced for the determination of gas holdup profiles and the effects of solid concentration were considered as the variation of average bubble diameter in the model. Results predicted by the CFD simulation showed good agreement with experimental data.     

On the growth of a non‐ideal gas bubble in a solvent‐polymer solution

A model for the growth of an ideal and a non‐ideal spherical gas bubble in a quiescent viscous liquid is presented. The growth of the bubble is assumed to be controlled by both mass transfer and viscous forces. Using the integral method, the differential momentum and binary mass balances were transformed into ordinary differential equations, which were numerically solved. Some analytical solutions for simple cases are also presented. The relevance of this work to the process of polymer melt devolatilization is discussed.     

Primary and secondary gas penetration during gas‐assisted injection molding. Part II: Simulation and experiment

Simulation and experimental studies have been carried out on the transient gas‐liquid interface development and gas penetration behavior during the cavity filling and gas packing stage in the gas‐assisted injection molding of a spiral tube cavity. The evolution of the gas/melt interface and the distribution of the residual wall thickness of skin melt along with the advancement of gas/melt front were investigated. Numerical simulations were implemented on a fixed mesh covering the entire cavity. The residual thickness of a polymer layer and the length of gas penetration in the moldings were calculated using both the simulation and model developed in Part I of this study and commercial software (C‐Mold). Extensive molding experiments were performed on polystyrene at different processing conditions. The obtained results on the gas bubble dynamics and penetration behaviors were compared with those predicted by the present simulation and C‐Mold, indicating the good predictive capability of the proposed model. Polym. Eng. Sci. 44:992–1002, 2004. © 2004 Society of Plastics Engineers.     

新型洗涤冷却室内气液两相的分布特性

采用双头电导探针法对新型洗涤冷却室环隙鼓泡床内气液两相的局部气含率、气泡直径等分布规律进行了实验研究,并用Fluent商业软件对床层内气含率分布进行了模拟计算,模拟结果与实验结果吻合较好。研究结果表明：新型洗涤冷却室内部构件对环隙鼓泡床内气液两相的分布特性影响显著,气相分布更加均匀,液面波动更趋平稳,有效地减少了气体带水问题,相比国外技术具有更好的操作弹性。     

CFD-PBM耦合模型模拟气液鼓泡床的通用性研究

通过对不同操作压力和不同液体性质气液鼓泡床的模拟值与实验数据进行对比，从而验证CFD-PBM耦合模型的通用性。结果表明，CFD-PBM耦合模型在加入了气泡破碎修正因子后，可以很好地预测压力对鼓泡床流体力学行为的影响趋势，当压力升高时，气含率显著升高。不同液体黏度和表面张力条件下CFD-PBM耦合模型的模拟结果与实验结果均吻合较好。随液体黏度增大，气泡破碎速率减小，气泡尺寸分布变宽，曳力显著下降，气含率随之降低。随表面张力减小，气泡破碎速率增大，气泡变小，气含率升高。CFD-PBM耦合模型具有很好的通用性，原因在于考虑了压力、液体黏度和表面张力对气泡聚并、破碎和气液相间作用力的影响。