Characterization and modeling of diglycidyl ether of bisphenol‐a epoxy cured with aliphatic liquid amines

The characterization by DMA and compressive stress‐strain behavior of an epoxy resin cured with a number of liquid amines is studied in this work along with predictions of the associated properties using Group Interaction Modeling (GIM). A number of different methods are used to assign two of the input parameters for GIM, and the effect on the predictions is investigated. Excellent predictions are made for the glass transition temperature, along with good predictions for the beta transition temperature and modulus for the majority of resins tested. Predictions for the compressive yield stress and strain are less accurate, due to a number of factors, but still show reasonable correlation with the experimental data. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3130–3141, 2013     

Quantitative structure-property relationships for composites: prediction of glass transition temperatures for epoxy resins

The glass transition temperatures of nine stoichiometric resin systems of tetraglycidyl-4,4′-diamino-diphenylmethane (TGDDM), triglycidyl p-amino phenol and diglycidyl ether of bisphenol A with 4,4′-diaminodiphenylsulphone (DDS), diethyl-toluenediamine and dimethylthiotoluenediamine were calculated using group interaction modelling (GIM) and atomic additivity (AA) methods. The input parameters were generated from kinetics simulation, which outputs the structure information for the cured systems. The modelling parameters were also applied to four non-stoichiometric systems of TGDDM and DDS. The predicted values from GIM were in good quantitative agreement with measured results from temperature modulated differential scanning calorimetry for all systems studied. Compared to GIM, the AA method gave inferior predictions for the highly crosslinked systems, especially for those, where epoxy was in excess.     

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.     

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR=2.4, 4, 8 and 12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streak line photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at De≈200, 300, 70 and 450 for CR=2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments.     

Numerical simulation and validation of dilute turbulent gas-particle flow with inelastic collisions and turbulence modulation

This work describes a theoretical and numerical study of turbulent gas-particle flows in the Eulerian framework. The equations describing the flow are derived employing Favre averaging. The closures required for the equations describing the particulate phase are derived from the kinetic theory of granular flow. The kinetic theory proposed originally is extended to incorporate the effects of the continuous fluid on the particulate phase behavior. Models describing the coupling between the continuous phase kinetic energy and particulate phase granular temperature are derived, discussed, and their effect on the flow predictions is shown.The derived models are validated with benchmark experimental results of a fully developed turbulent gas-solid flow in a vertical pipe. The effect of the models describing the influence of turbulence on the particle motion as well as the turbulence modulation due to the presence of particles is analyzed and discussed.     

Model validation for low and high superficial gas velocity bubble column flows

In the present work, gas-liquid flow dynamics in a bubble column are simulated with CFDLib using an Eulerian-Eulerian ensemble-averaging method in a two-dimensional Cartesian system. The two-phase flow simulations are compared to experimental measurements of a rectangular bubble column performed by Mudde et al. [1997. Role of coherent structures on Reynolds stresses in a 2-D bubble column. A.I.Ch.E. Journal 43, 913-926] and a cylindrical bubble column performed by Rampure et al. [2003. Modeling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. The Canadian Journal of Chemical Engineering 81, 692-706] for low and high superficial gas velocities, respectively. The objectives are to obtain grid-independent numerical solutions using CFDLib to reconcile unphysical results observed using FLUENT with increasing grid resolutions [Law, D., Battaglia, F., Heindel, T.J., 2006. Numerical simulations of gas-liquid flow dynamics in bubble columns. In: Proceedings of the ASME Fluids Engineering Division, IMECE2006-13544, Chicago, IL], and to validate computational fluid dynamics (CFD) simulations with experimental data to demonstrate the use of numerical simulations as a viable design tool for gas-liquid bubble column flows. Numerical predictions are presented for the local time-averaged liquid velocity and gas fraction at various axial heights as a function of horizontal or radial position. The effects of grid resolution, bubble pressure (BP) model, and drag coefficient models on the numerical predictions are examined. The BP model is hypothesized to account for bubble stability, thus providing physical solutions.     

非对称型外凸式波节管内的传热和流动特性

针对一种新型的非对称外凸式波节管(ACT)换热元件,基于三维RST模型对其进行了数值模拟研究。通过与传统的对称型外凸式波节管(SCT)分析比较,考察了两者流动及传热特性的区别。为了验证雷诺应力模型(RST)在研究波节管结构时的可靠性,比较了现有波纹壁面中直接数值模拟(DNS)与RST模型在同一条件下的计算结果。通过对比发现,RST模型得出的包括速度场、压力系数等计算结果与DNS所得出的结果基本吻合。随后对外凸型的流动及传热机理进行了深入探讨。结果表明,与传统的SCT相比,ACT提高综合传热性能最多能够提高32.3%。     

Continuous‐Flow Surface Aeration Systems

An aeration process in an activated sludge plant is a continuous‐flow system. In this system, there is a steady input flow (flow from the primary clarifier or settling tank with some part from the secondary clarifier or secondary settling tank) and output flow connection to the secondary clarifier or settling tank. The experimental and numerical results obtained through batch systems can not be relied on and applied for the designing of a continuous aeration tank. In order to scale up laboratory results for field application, it is imperative to know the geometric parameters of a continuous system. Geometric parameters have a greater influence on the mass transfer process of surface aeration systems. The present work establishes the optimal geometric configuration of a continuous‐flow surface aeration system. It is found that the maintenance of these optimal geometric parameters systems result in maximum aeration efficiency. By maintaining the obtained optimal geometric parameters, further experiments are conducted in continuous‐flow surface aerators with three different sizes in order to develop design curves correlating the oxygen transfer coefficient and power number with the rotor speed. The design methodology to implement the presently developed optimal geometric parameters and correlation equations for field application is discussed.     

纳米流体圆管内的湍流流动特性

采用Eulerian-Eulerian模型和Eulerian-Lagrange模型研究了TiO₂-水纳米流体在水平管内的湍流流动特性,并与实验结果进行对比分析,探讨了不同模型中各种相间作用力的影响。从微流动角度探索纳米流体的流动本质,从而进一步揭示其传热强化机理。结果表明：在壁面附近,纳米颗粒与水存在着明显的速度差异,相间的动量交换十分明显,从而强化了局部微流动,导致边界层变薄。纳米颗粒在整个流场内部是不均匀分布的,使得边界层内部换热能力得到大幅度增强。纳米流体流动特性的改变是影响其强化换热的主要因素。     

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

This work systematically simulates the external mass transfer from/to a spherical drop and solid par-ticle suspended in a nonlinear uniaxial extensional creeping flow.The mass transfer problem is gov-erned by three dimensionless parameters:the viscosity ratio (2),the Peclet number (Pe),and the nonlinear intensity of the flow (E).The existing mass transfer theory,valid for very large Peclet num-bers only,is expanded,by numerical simulations,to include a much larger range of Peclet numbers(1 ≤ Pe ≤ 105).The simulation results show that the dimensionless mass transfer rate,expressed as the Sherwood number (Sh),agrees well with the theoretical results at the convection-dominated regime (Pe ＞ 103).Only when E ＞ 5/4,the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer.Empirical correlations are proposed to pre-dict the influence of the dimensionless governing parameters (λ,Pe,E) on the Sherwood number (Sh).The maximum deviations of all empirical correlations are less than 15％ when compared to the numerical simulated results.     

Transient analysis of gas flow in a straight pipe

In the present work, numerical simulation has been done to analyze transients in gas flow and pressure in a horizontal straight pipe. For a single gas pipeline, eight representative cases corresponding to different causes of transient behaviour are simulated to predict unsteady state flow and the evolution of pressure profiles. The numerical results show that depending upon the pipe dimensions and operating variables such as pressure and gas flow rate, transient effects in the pipeline may last for a long time and/or over significant length of pipe. The simulations predict an initial surge in gas flow rate greater than the final steady‐state value if the pressure drop across the pipe is increased. Similarly, initial flow rate may decrease below the final steady‐state value if the pressure drop is decreased. In case of complete closure of a valve, oscillations in both pressure and mass flow rate are observed, which gradually decay and the steady state conditions of no flow are ultimately achieved. The present results are compared with a published work from the literature. A reasonably good agreement is found between these two predictions. The present study is of practical significance in safe design and operation of a gas delivery system.     

Numerical simulation and validation of gas-particle rectangular jets in crossflow

This paper presents a numerical study of a gas-particle flow in three inclined rectangular jets in crossflow. The predicted gas phase velocities and particle phase velocities are validated against previously reported experimental data. Two turbulence models, the standard k-? model and Shear Stress Transfer (SST) model, are used to model the gas phase turbulence. This work shows that both models provide acceptable predictions of the gas flow and mixing generated by the three jets. Neither model could accurately reproduce the jet core and the flow near bottom wall. The particle phase in this flow comprises a large number of small particles. Thus particles follow the gas phase flow closely and any errors in the turbulence model and gas flow predictions are passed on to the particle phase simulation. This paper also includes a literature review on rectangular jets in crossflow and gas-particle laden jets in crossflow.     

Numerical simulation and experimental study of emulsification in a narrow-gap homogenizer

The present experimental and theoretical study investigates the fragmentation of the oil phase in an emulsion on its passage through a high-pressure, axial-flow homogenizer. The considered homogenizer contains narrow annular gap(s), whereupon the initially coarse oil drops break into fine droplets. The experiments were carried out using either a facility with one or two successive gaps, varying the flow rate and the material properties of the dispersed phase. The measured drop size distributions in the final emulsion clearly illustrated that the flow rate, as well as the dispersed-phase viscosity, and the interfacial tension can significantly affect the drop size after emulsification. The larger mean and maximum drop diameters obtained for the homogenizer with one gap in comparison to those obtained with two gaps (at the same Reynolds number and material parameters of the emulsion phases), highlighted the strong relevance of the flow geometry to the emulsification process. The numerical simulation of the carrier phase flow fields evolving in the investigated homogenizer was proven to be a very reliable method for providing appropriate input to theoretical models for the maximum drop size. The predictions of the applied droplet breakup model using input values from the numerical simulations showed very good agreement with the experimental data. In particular, the effect of the flow geometry—one-gap versus two-gaps design—was captured very well. This effect associated with the geometry is missed completely when using instead the frequently adopted concept of estimating input values from very gross correlations. It was shown that applying such a mainly bulk flow dependent estimate correlation makes the drop size predictions insensitive to the observed difference between the one-gap and the two-gaps cases. This obvious deficit, as well the higher accuracy, strongly favors the present method relying on the numerical simulation of the carrier phase flow.     

Simulation of the consolidation of paper coating structures: probabilistic versus deterministic models

Two categories of mathematical models were compared for the simulation of consolidation of paper coating structures, that is for the packing of pigments on a paper substrate under dewatering conditions. The first category uses probabilistic methods, relying on a random number generator to either determine the initial position of the pigments or their motion. The second category uses deterministic methods based on force balances. In this work, two probabilistic models and two deterministic models are described and their respective advantages and drawbacks are critically reviewed. Simulation results obtained using three of these methods are compared for the case of monodisperse and bidisperse spherical suspensions. Porosity calculations of the numerical packings obtained with the (deterministic) discrete element method (DEM) and two probabilistic methods, the Monte-Carlo (MCD) and the steepest descent (SDD) deposition methods, are compared with experimental data from the literature. These calculations reveal significant differences in the pore volume obtained with these three models. An analysis based on the bridging and relaxation phenomena that prevail in the flow of such particulate systems provide an explanation for these differences and show the strong potential of the discrete element method.

The choice of the simulation method depends on the objective of the simulations. DEM will provide more accurate predictions of macroscopic quantities such as the porosity or the roughness, but requires very long computational times. MCD or SDD will only provide qualitative trends, but is computationally far less intense. A combination of strategies might be appropriate, using MCD (or SDD) to provide guidelines and DEM to enhance the results predicted by MCD.     

Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

In this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non-Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in-house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.     

Coiled flow inverter as an inline mixer

Helical coils are widely used in the process industries to improve the mixing efficiency under laminar flow conditions. It was further observed that in the regular helical coils, there exists a confined region in the tube cross-section where fluids are entrapped and can escape only by diffusion. In the present work, an attempt has been made to further enhance the mixing in the coiled tube at low Dean number using the phenomenon of flow inversion. The study is performed in coiled flow inverter (CFI) [Saxena, A.K., Nigam, K.D.P., 1984. Coiled configuration for flow inversion and its effect on residence time distribution. A.I.Ch.E. Journal 30, 363-368] which was developed using the concept of inverting the direction of fluid by 90^°. It comprises coils with equidistant 90^° bends. The scalar mixing of two miscible fluids has been quantified for different process conditions (Dean number, Schmidt number and number of bends) by using scalar transport technique. There was a significant increase in mixing performance of CFI as compared to regular helical coils at low Dean number. The mixing efficiency increased with the increase in Dean number and number of bends. It was also observed that the mixing performance was enhanced with increase in Schmidt number. A new correlation has been proposed for unmixedness coefficient of CFI as a function of Dean number, Schmidt number and number of bends. The proposed correlation has maximum error of ±20% with the numerical predictions.     

Measurements and modelling of free-surface turbulent flows induced by a magnetic stirrer in an unbaffled stirred tank reactor

Measurements and numerical simulations of turbulent flows with free-surface vortex in an unbaffled reactor agitated by a cylindrical magnetic stirrer are presented. Measurements of the three mean and fluctuating components of the velocity vector are made using a laser Doppler velocimetry in order to characterise the flow field at different speeds of the stirrer. A homogeneous Eulerian-Eulerian multiphase flow model coupled with a volume-of-fluid method for interface capturing is applied to determine the vortex shape and to compute the turbulent flow field in the reactor. Turbulence is modelled using a second-moment differential Reynolds-stress transport (RST) model, but for some cases the k-ε/k-ω based shear-stress transport (SST) model is also used. The predictions obtained using the ANSYS CFX-5.7 computational fluid dynamics code are compared with the images of the vortex and the measured distributions of mean axial, radial and tangential velocities and turbulent kinetic energy. The predicted general shape of the liquid free-surface is in good agreement with measurements, but the vortex depth is underpredicted. The overall agreement between the measured and the predicted axial and tangential velocities obtained with the RST model is good. However, the radial velocity is significantly underpredicted. Predictions of the turbulent kinetic energy yield reasonably good agreement with measurements in the bulk flow region, but discrepancy exists near the reactor wall where this quantity is underpredicted. The SST model predictions are generally of the same quality as those of the RST model, with the latter model providing better predictions of the tangential velocity distribution.     

Investigating liquid-fronts during spontaneous imbibition of liquids in industrial wicks. Part II: Validation by DNS

To validate the experimental results of Part-1, we conducted a two-phase flow simulation of imbibition of a wetting liquid through 2D microstructures made of ellipses of varying aspect ratios. The flow simulation in the particulate microstructures, characterized by low (ellipse) aspect ratio, produced somewhat even micro-fronts, thus replicating the sharp fronts at the visual (macroscopic) scale observed in Part-1. Whereas simulations in the fibrous microstructures produced highly uneven micro-fronts, suggesting the formation of semi-sharp or diffuse visual fronts. Increasing the porosity from 50% to 70% resulted in solid-phase clustering and led to further increase in the unevenness of micro-fronts, pointing to purely diffuse visual fronts. The evolution of the saturation plots along the flow direction, obtained from area-averaging of fluid-distribution plots, pointed to diffusing of sharp fronts with time. The predictions matched our previous experimental and numerical observations, that is, the particulate media create sharp fronts while the fibrous media create semi-sharp/diffuse fronts.     

Void fraction in vertical gas-liquid slug flow: Influence of liquid slug content

In this study we develop a model for computing the mean void fraction and the liquid slug void fraction in vertical upward gas-liquid intermittent flow. A new model for the rate of gas entrained from the Taylor bubble to the liquid slug is formulated. It uses the work done by the pressure force at the rear of the Taylor bubble. Then an iterative approach is employed for equating the gas entrainment flux and the gas flux obtained via conservation equations. Model predictions are compared with experimental data. The developed iterative method is found to provide reasonable quantitative predictions of the entrainment flux and of the void fraction at low and moderate liquid slug void fraction conditions. However, with an increased liquid slug void fraction experimental data indicate that the flow in the liquid slug transits to churn-heterogeneous bubbly flow thus gas entrainment flux tends to zero. Considering this effect in the iterative model significantly improved the predictions for large liquid slug void fraction conditions.