Computer simulation of the filling process in gas‐assisted injection molding based on gas‐penetration modeling

Gas‐assisted injection molding can effectively produce parts free of sink marks in thick sections and free of warpage in long plates. This article concerns the numerical simulation of melt flow and gas penetration during the filling stage in gas‐assisted injection molding. By taking the influence of gas penetration on the melt flow as boundary conditions of the melt‐filling region, a hybrid finite‐element/finite‐difference method similar to conventional‐injection molding simulation was used in the gas‐assisted injection molding‐filling simulation. For gas penetration within the gas channel, an analytical formulation of the gas‐penetration thickness ratio was deduced based on the matching asymptotic expansion method. Finally, an experiment was employed to verify this proposed simulation scheme and gas‐penetration model, by comparing the results of the experiment with the simulation. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 2377–2384, 2003     

Progress in membrane gas–liquid reactors

Gas–liquid reactions are crucially important in chemical synthesis and industries. In recent years, membrane gas–liquid reactors have attracted great attentions due to their high selectivity, productivity and efficiency, and easy process control and scale‐up. Membrane gas–liquid reactors can be divided into three categories: dispersive membrane reactor, non‐dispersive membrane reactor and pore flowthrough reactor. The progress in membrane gas–liquid reactors, including features, applications, advantages and limits, is briefly reviewed. © 2012 Society of Chemical Industry     

Modeling heterogeneous downward dense gas‐particle flows

A novel approach is proposed to model heterogeneous downward dense gas‐particle flows. The homogeneous behavior of the flow is described by the mass and momentum transport equations of the gas and particulate phases solved using a mono‐dimension finite volume method on staggered grids. The heterogeneous features of the flow are predicted simultaneously using the bubble‐emulsion formalism. The gas compressibility is taken into consideration. The model is supplemented with a new correlation to account for the wall‐particle frictional effects. The predictions are compared with the vertical profiles of pressure and the amount of gas that flows up and down two standpipes and a cyclone dipleg of an industrial fluid catalytic cracking unit and of a cold small‐scale circulating fluidized bed. The trends are well predicted. The model gives further information and is thus an innovative starting point for downward dense gas‐particle flow hydrodynamics investigation. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Mathematical modeling of gas‐phase biofilter performance

In the present paper, a new mathematical model describing the physical, chemical and biological phenomena involved in the process of contaminant removal in biofilters is developed. In addition to the contaminant, the key components of the present theoretical model are carbon dioxide and oxygen. The model predicts the concentration profile of the key components in the gas phase, the biofilm and the sorption liquid retained in the solid particles composing the filter bed at both steady and transient regimes. The model equations were solved numerically and comparison between theory and experiment showed that the model results for styrene and carbon dioxide concentration profiles were in very good agreement with experimental data for the biofiltration of styrene vapors at steady state. The analysis of oxygen concentration profile in the biofilm predicted by the theoretical model revealed that oxygen limitation does not occur under the operating styrene biodegradation rate in the biofilter. Copyright © 2003 Society of Chemical Industry     

Borescopy in pressurized gas‐solid fluidized beds

A borescopic technique was used for finding the effect of pressure on the hydrodynamics of gas‐solid fluidized beds. The results showed that solids radial distribution may become more or less uniform with increasing pressure depending on the superficial gas velocity. Moreover, it is found that the solids volume fraction of the emulsion phase may decrease at relatively high pressures, only in the central region of the bed. Additionally, it is observed that with increasing pressure the bubble size generally decreased in the central regions and increased near the wall regions. This trend was more complicated at low excess gas velocities. The number of bubbles increased for the central regions and near the walls for all the performed experiments. However, this parameter showed a different trend at other radial positions. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 3303–3311, 2018     

Local hydrodynamics of gas–liquid-nanoparticles three-phase fluidization

The laser Doppler anemometer (LDA) and conductivity probes were used for measuring the local hydrodynamic performances such as gas holdup and liquid velocity in a lab-scale gas–liquid–TiO₂ nanoparticles three-phase bubble column. Effects of operating parameters on the local gas holdup and liquid velocity were investigated systematically. Experimental results showed that local averaged axial liquid velocity and local averaged gas holdup increased with increasing superficial gas velocity but decreased with increasing TiO₂ nanoparticles loading and the axial distance from the bottom of the bubble column. A three-dimensional computational fluid dynamic (CFD) model was developed in this paper to simulate the structure of gas–liquid–TiO₂ nanoparticles three-phase flow in the bubble column. The time-averaged and time-dependent predictions were compared with experimental data for model validation. A successful prediction of instantaneous local gas holdup, gas velocity, and liquid velocity were also presented.     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

A new mechanistic model to predict gas–liquid interface shape of gas–liquid flow through pipes with low liquid loading

Devising a new mechanistic method to predict gas–liquid interface shape in horizontal pipes is concerned in this article. An experiment was conducted to find the pressure gradients of air–water flow through a 1‐in. pipe diameter. Comparing results of model with some experimental data available in the literature demonstrates that the model provides quite better predictions than existed models do. This model also predicts flow regime transition from stratified to annular flow better than Apparent Rough Surface and Modified Apparent Rough Surface models for both 1‐ and 2‐in. pipe diameters. The model also leads to reliable predictions of wetted wall fraction experimental data. Although one parameter of new model was evaluated based on air–water flow pressure loss experimental data for 1 in. pipe, it was considerably successful to predict pressure drop, liquid holdup, stratified‐annular transition and wetted wall fraction for other gas–liquid systems and pipe diameters. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1043–1053, 2015     

Towards monitoring electrostatics in gas–solid fluidized beds

The electrostatic charge distribution in a lab‐scale 2‐D fluidized bed of 900 µm glass beads was determined using arrays of induction probes, and the influence of relative humidity and superficial gas velocity was examined. The bubble presence, relative humidity, and superficial gas velocity were found to influence charge separation. Bipolar charging was observed; the net charge build‐up was found to be negligible. Moreover, the system was monitored by applying the attractor comparison method to the electrostatic charge signals from an induction probe. It was concluded that this approach can indeed be used to monitor changes in the electrostatic behaviour.     

Mathematical modeling and simulation for gas–liquid reactors

Gas–liquid reactors are widely used in many industrial processes such as oxidation, hydroformylation, chlorination, etc. The paper develops comprehensive model for reactors using the mixing cell approach. It incorporates heat and mass transfer effects in the film and uses a boundary element method to solve the film model equations. The fluxes obtained at the interface are then directly used as the link to the reactor model. Simple isothermal and non-isothermal reactions were numerically tested. Application to two industrially important case studies, chlorination of butanoic acid and oxidation of cyclohexane are briefly illustrated. For the autocatalytic chlorination of butanoic acid, the yield of desired product, monochlorobutanoic acid, is favored by the high degree of mixing in the liquid phase. Therefore, this reaction should be carried out in a CSTR. A series of five bubble tanks with parallel gas reactant feed for cyclohexane oxidation was also simulated. It was found that the cyclohexane conversion is low while the oxygen conversion is relatively high and almost constant in each tank. Due to the complex multistep nature of this reaction scheme, oxygen is consumed in many steps of oxidation and selectivity of main products (which are intermediate products in the reaction scheme) depends on the critical control of over-oxidation in the kinetic mechanism.     

Friction on a solid sphere exposed to gas–liquid and gas–liquid–solid flow in bubble column and fluidized bed reactors

Local velocity gradients on a solid spherical surface have been studied in a bubble column and in two- and three-phase fluidized beds, in order to clarify the influence of gas flow. The electrochemical method, measuring apparent local mass transfer coefficients, was verified and used to obtain the local velocity gradients, shear stresses and total frictional forces. The observed mass transfer rate was independent of liquid velocity, owing to a non-changing flow structure around the particles and not to averaging opposing effects. The identity in flow structure also held for three-phase fluidized beds up to a superficial gas velocity of 5 cm s^?1. The dramatic increase in velocity gradient on gas introduction was not a result of decreased homogenous density, but was caused by a change in the turbulent structure around a particle, leaving a larger portion of the total drag as frictional drag, thus improving the mass transfer characteristics of the bed. Use of velocity gradient measurements, including span of fluctuations and exposure time, to predict biomass growth and mechanical degradation in a reactor is also discussed.     

Hydrodynamics of gas–solid fluidization in tapered beds

Gas–solid fluidization has a wide range of industrial applications like catalytic reactions, combustion, gasification, etc. In a number of these applications, there is particle size reduction during the operation leading to severe entrainment and limitation of operating velocity. The various problems associated with particles of different sizes or changing particles sizes could be overcome by adopting tapered beds in fluidization operation. In the present investigation, the fluidization phenomenon in tapered beds has been critically assessed through experimental investigations using particles of different sizes and materials and wide range of apex angles of the vessels. The effect of particle size and apex angle on the fluidization behaviour is clearly brought out which has not been reported so far in literature. The importance of compressive force existing in tapered beds is highlighted. In addition, correlations for all hydrodynamic characteristics, viz. critical fluidization velocity, minimum velocity for full fluidization, maximum velocity for defluidization, peak pressure drop, fluctuation ratio, compressive force, and hysteresis have been developed some of which are proposed for the first time.     

Three-dimensional numerical simulation method for gas–solid injector

A three-dimensional turbulent gas–solid two-phase flow model for a gas–solid injector is developed in the present study. Time-averaged conservation equation for mass and momentum and a two-equation k– closure are used to model the carried fluid phase. The solid phase is simulated by using a Lagrangian approach. In this model, the drag and lift forces on particles, the multi-body collisions among particles and the mutual interaction between gas and particles were taken into account. Interparticle interactions and particle–wall collisions are emulated by using the three-dimensional distinct element method (DEM). A new correlation, which represents the transfer of kinetic energy of the particle motion to kinetic energy of the carrier fluid, is introduced in the additional source term S_d of the transport equation of turbulence kinetic energy, K. The calculated pressure distributions along the axis in the different parts of gas–solid injectors using pressured pneumatic conveying system under different driving jet velocities, pressures and values of angle of convergent section () are found to be in agreement with the experimental results. The axial mean velocity of particles and the behavior of gas and particles in the gas–solid injector are calculated, their results reasonably explaining actual phenomenon observed in experiment.     

Minimum fluidization velocity in gas‐liquid‐solid minifluidized beds

The initial fluidization characteristics of gas‐liquid‐solid minifluidized beds (MFBs) were experimentally investigated based on the analyses of bed pressure drop and visual observations. The results show that U_Lmf in 3–5 mm MFBs can not be determined due to the extensive pressure drop fluctuations resulting from complex bubble behavior. For 8–10 mm MFBs, U_Lmf can be confirmed from both datum analyses of pressure drop and Hurst exponent at low superficial gas velocity. But at high superficial gas velocity, U_Lmf was not obtained because the turning point at which the flow regime changes from the packed bed to the fluidized bed disappeared, and the bed was in a half fluidization state. Complex bubble growth behavior resulting from the effect of properties of gas‐liquid mixture and bed walls plays an important role in the fluidization of solid particles and leads to the reduction of U_Lmf. An empirical correlation was suggested to predict U_Lmf in MFBs. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1940–1957, 2016     

Controlled gas‐phase sulfonation of low‐density polyethylene films

In the current research, a highly controllable system operating at low temperatures and for short reaction times is employed for the surface sulfonation of low‐density polyethylene. This system provides the advantages of short reaction times and low reaction temperatures, as compared with previous methods of surface sulfonation. Low‐density polyethylene films were sulfonated at 40°C for time periods ranging from 5 to 30 min. Subsequently, all films were analyzed by SEM, EDX, horizontal ATR–FTIR, surface roughness, and dynamic contact‐angle measurements. Sulfonation was effected at all reaction times. The degree of surface sulfonation increased through 10 min and reached a maximum between 10‐ and 30‐min reaction times with concomitant changes in the physicochemical properties of the material. At 30 min, the film topography changed substantially, indicating that sulfonation was no longer limited to a strictly surface reaction. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1865–1869, 2000     

Minimum fluidization velocities for gas—liquid—solid three-phase systems

Cocurrent upward gas—liquid fluidization of coarse solids is actuated primarily by the motion of the liquid at relatively low gas velocities and by the momentum of the gas at zero or low liquid velocities. Our gas-perturbed liquid model, which has previously been shown to give good predictions of the minimum liquid fluidization velocity, U_lmf, at a fixed low gas velocity, is shown here also to give reasonable agreement with U_lmf measurements for inverse three-phase fluidization at a given upward gas velocity, using the coefficient in the gas hold-up equation of Yang et al. [X.L. Yang, G. Wild, J.P. Euzen, Int. Chem. Eng. 33 (1993) 72] as an adjustable parameter. It is further shown that a liquid-buoyed solids/liquid-perturbed gas model can predict with moderate success the minimum gas fluidization velocity, U_gmf, for three-phase cocurrent upward fluidization of coarse solids at zero or low liquid velocities.     

Fluid‐particle drag in inertial polydisperse gas–solid suspensions

In this article, we extend the low Reynolds number fluid‐particle drag relation proposed by Yin and Sundaresan for polydisperse systems to include the effect of moderate fluid inertia. The proposed model captures the fluid‐particle drag results obtained from lattice‐Boltzmann simulations of bidisperse and ternary suspensions at particle mixture Reynolds numbers ranging from 0 ≤ Re_mix ≤ 40, over a particle volume fraction range of 0.2 ≤ ? ≤ 0.4, volume fraction ratios of 1 ≤ ?_i/?_j ≤ 3, and particle diameter ratios of 1 ≤ d_i/d_j ≤ 2.5. © 2009 American Institute of Chemical Engineers AIChE J, 2010