Modeling of annular reactors with surface reaction using computational fluid dynamics (CFD)

A CFD-based model for predicting the performance of annular reactors with surface reaction was developed. The capability of several hydrodynamic models to predict successfully the kinetic behavior of the reactor under diffusion limiting conditions was assessed against experimental data. The evaluation included five models: laminar, standard k–ε, realizable k–ε, Reynolds stress (RSM), and Abe–Kondoh–Nagano (AKN). The catalytic decomposition of hydrogen peroxide over a Mn/Al oxide catalyst coated on the reactor surface was used as a model reaction. The reactor was tested within a range of flow rates corresponding to 530<Re<11,000 and intrinsic reaction rate constants of 5×10^?5 to 1 m/s. The results demonstrated that the performance of the hydrodynamic models is associated with their capability to predict external mass transfer and ultimately, the level of mass transfer limitation present in the reacting system. For laminar flow conditions, the laminar model is capable of predicting the experimental behavior of the system. For transient and turbulent flow regimes, all the analyzed turbulence models provided good predictions of the system when the process was controlled by surface reaction. When the system presented some degree of mass transfer limitation, AKN and RSM exhibited better performance.     

Turbulence modelling of multiphase flow in high-pressure trickle-bed reactors

Computational fluid dynamics (CFD) has been used as a successful tool for single-phase reactors. However, fixed-bed reactors design depends overly in empirical correlations for the prediction of heat and mass transfer phenomena. Therefore, the aim of this work is to present the application of CFD to the simulation of three-dimensional interstitial flow in a multiphase reactor. A case study comprising a high-pressure trickle-bed reactor (30 bar) was modelled by means of an Euler-Euler CFD model. The numerical simulations were evaluated quantitatively by experimental data from the literature. During grid optimization and validation, the effects of mesh size, time step and convergence criteria were evaluated plotting the hydrodynamic predictions as a function of liquid flow rate. Among the discretization methods for the momentum equation, a monotonic upwind scheme for conservation laws was found to give better computed results for either liquid holdup or two-phase pressure drop since it reduces effectively the numerical dispersion in convective terms of transport equation.After the parametric optimization of numerical solution parameters, four RANS multiphase turbulence models were investigated in the whole range of simulated gas and liquid flow rates. During RANS turbulence modelling, standard k-ε dispersed turbulence model gave the better compromise between computer expense and numerical accuracy in comparison with both realizable, renormalization group and Reynolds stress based models. Finally, several computational runs were performed at different temperatures for the evaluation of either axial averaged velocity and turbulent kinetic energy profiles for gas and liquid phases. Flow disequilibrium and strong heterogeneities detected along the packed bed demonstrated liquid distribution issues with slighter impact at high temperatures.     

External and internal mass transfer effect on photocatalytic degradation

A rational approach is proposed in determining the effect of internal and external mass transfer, and catalyst layer thickness during photocatalytic degradation. The reaction occurs at the liquid–catalyst interface and therefore, when the catalyst is immobilized, both external and internal mass transfer plays significant roles in overall photocatalytic processes. Several model parameters, namely, external mass transfer coefficient, dynamic adsorption equilibrium constant, adsorption rate constant, internal mass transfer coefficient, and effective diffusivity were determined either experimentally or by fitting realistic models to experimental results using benzoic acid as a model component. The effect of the internal mass transfer on the photocatalytic degradation rate over different catalyst layer thickness under two different illuminating configurations was analyzed theoretically and later experimentally verified. It was observed that an optimal catalyst layer thickness exists for SC (substrate-to-catalyst) illumination.     

Hydrodynamics of upflow anaerobic sludge blanket reactors

The hydrodynamic characteristics of upflow anaerobic sludge blanket (UASB) reactors were investigated in this study. A UASB reactor was visualized as being set‐up of a number of continuously stirred tank reactors (CSTRs) in series. An increasing‐sized CSTRs (ISC) model was developed to describe the hydrodynamics of such a bioreactor. The gradually increasing tank size in the ISC model implies that the dispersion coefficient decreased along the axial of the UASB reactor and that its hydrodynamic behavior was basically dispersion‐controlled. Experimental results from both laboratory‐scale H₂‐producing and full‐scale CH₄‐producing UASB reactors were used to validate this model. Simulation results demonstrate that the ISC model was better than the other models in describing the hydrodynamics of the UASB reactors. Moreover, a three‐dimensional computational fluid dynamics (CFD) simulation was performed with an Eulerian‐Eulerian three‐phase‐fluid approach to visualize the phase holdup and to explore the flow patterns in UASB reactors. The results from the CFD simulation were comparable with those of the ISC model predictions in terms of the flow patterns and dead zone fractions. The simulation results about the flow field further confirm the discontinuity in the mixing behaviors throughout a UASB reactor. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Modeling of corrugated plate photocatalytic reactors and experimental validation

A mathematical model describing the performance of photocatalytic reactors was proposed, and fitted using data for 4-chlorophenol degradation collected with a flat plate reactor. It was used to predict the performance of corrugated plate photocatalytic reactors, and this was then compared with subsequent experimental results. With only three experimentally determined parameters, the new model incorporates reaction kinetics, mass transfer, and photon transfer. The model-predicted performance of the corrugated plate reactors, with different structural parameters and under different hydrodynamic and illumination conditions, was found to agree with the experimental data reasonably well.     

A review on computational fluid dynamic simulation for rotating packed beds

A rotating packed bed (RPB) is one of the cutting-edge process intensification technologies due to its high mass transfer and mixing efficiency. Nevertheless, owing to the complex structure and hydrodynamic characteristics of RPBs, valuable data inside the reactor is hard to obtain by conventional experimental methods. Computational fluid dynamics (CFD) owing to its unique advantages of low cost, completeness of data and ability to simulate real and ideal conditions, has been adopted by many researchers to carry out fundamental research and practical application of RPBs in recent years. This paper therefore elaborates on the research progress on CFD simulation of RPBs. The building of a physical model of these reactors as well as selection of mathematical models are described, then applicability and accuracy of these models are compared and discussed. Simulation results for gas and multiphase flow in reactors are also presented. Additionally, the application of CFD to mixing and mass transfer between phases and processes in rotating packed beds is introduced. Optimum designs of reactors by the CFD method are also described. Finally, problems remaining with CFD simulation of rotating packed beds and future development directions are discussed. © 2018 Society of Chemical Industry     

Flow and heat transfer in serpentine channels

Serpentine channels are often used in microchannel reactors and heat exchangers. These channels offer better mixing, higher heat and mass‐transfer coefficients than straight channels. In the present work, flow and heat transfer experiments were carried out with a serpentine channel plate comprising of 10 units (single unit dimensions: 1 × 1.5 mm² in cross section, length 46.28 mm, D_h 1.2 mm) in series. Pressure drop and heat‐transfer coefficients were experimentally measured. Flow and heat transfer in the experimental set‐up were simulated using computational fluid dynamics (CFD) models to understand the mechanisms responsible for performance enhancement. The CFD methodology, thus, developed was applied to understand the effect of various geometrical parameters on heat transfer enhancement. A criterion was defined for evaluation of heat transfer performance (heat transfer per unit pumping power), thus, ensuring due considerations to required pumping power. The effect of geometrical parameters and the corresponding mechanisms contributing for enhancement are discussed briefly. Based on the results, a design map comprising different serpentine channels showing heat transfer enhancement with pumping power was developed for Reynolds number of 200 which will be useful for further work on flow and heat transfer in serpentine channels. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1814–1827, 2013     

Modelling and design of thin-film slurry photocatalytic reactors for water purification

Photocatalytic oxidation processes are highly effective clean technologies for the degradation and mineralization of a wide variety of priority pollutants in water and wastewater. However, the application of heterogeneous photocatalysis for wastewater treatment on an industrial scale has been impeded by a lack of mathematical models that can be readily applied to reactor design and scale-up. As a results current photocatalytic reactors in research and development have been designed by empirical or semi-empirical methods only.In this paper, a simple and generic mathematical model for steady-state, continuous flow, thin-film, slurry (TFS) photocatalytic reactors for water purification using solar and UV lamps is presented. The model developed is applicable to TFS flat plate and annular photoreactors of (a) falling film design or (b) double-skin design, operating with three ideal flow conditions: (1) falling film laminar flow, (2) plug flow and (3) slit flow. The model is expressed in dimensionless form and scale-up of TFS photocatalytic reactors can be carried out by dimensional analysis. In addition, the model parameters can be estimated easily from real systems and model solutions can be obtained with little computational effort.Comparison of a number of ideal flow systems shows that both falling film laminar flow and plug flow operation modes give higher performance than the slit flow system. Slit flow operation mode results in lower conversions due to the non-correspondence of fluid-residence time and the transversal radiation field. The effect of optical thickness, on reactor performance and the evolution of radial profiles of a model pollutant with photoreactor length are presented for each of the operation modes. The falling film laminar flow system was found to be more efficient than the plug flow system when the reactor conversion is above 80%. For lower reactor conversion the plug flow system was found to be marginally more efficient than the falling film laminar flow system. A methodology for the optimal geometrical design of a highly efficient configuration of TFS photocatalytic reactors is also presented. The mathematical models presented may be used as a tool for the design, scale-up and optimization of these types of photocatalytic reactors.     

Modelling the liquid-phase adsorption in packed beds at low Reynolds numbers: An improved hydrodynamic model

A hydrodynamic model including only one parameter (λ_O) for the prediction of both axial dispersion and external mass transfer in fixed-bed adsorbers at low Reynolds numbers (creeping flow regime) has been developed. The theoretical analysis is based on the application of the (two-dimensional) uniform dispersion model originally proposed by Bischoff and Levenspiel [1962a. Fluid dispersion—generalization and comparison of mathematical models—I. Generalization of models. Chemical Engineering Science 17, 245-255] to the representative capillary of a tube bundle model for describing the flow and mixing behaviour in packed beds. The combination of this model with the relationship between longitudinal and radial dispersion leads to the definition of the sole hydrodynamic parameter λ_O (one-parameter hydrodynamic model). Furthermore, the detailed investigation reveals that the one-parameter concept may be utilized for the application of the (one-dimensional) axial dispersed plug flow model as well. The functional dependence of the parameter λ_O on the flow conditions is elaborated from axial dispersion measurements. Both the new (one-parameter) hydrodynamic model and the classical model including axial dispersion and external mass transfer coefficients (two-parameter model) are utilized to simulate the breakthrough curves for the adsorption of naphthalene onto silica gel. This simulation study reveals that only the one-parameter hydrodynamic model is able to predict the adsorber dynamics over a large range of flow rates.     

The influence of hydrodynamic and mass transfer entrance effects on the operation of a parallel plate electrolytic cell

Experimental measurements of mass transfer in an electrochemical flow cell of rectangular cross section with different hydrodynamic entrance and electrode lengths have been made. For fully developed flow, average Sherwood numbers under laminar conditions vary with Graetz number to a power 0·30. For turbulent flow, fully developed mass transfer conditions occur about twelve equivalent diameters along the electrode and are best represented by the Chilton-Colburn analogy which predicts Sherwood numbers varying with Reynolds number to a power of 0·8 and Schmidt number to a one-third power. For shorter electrodes Sherwood numbers can be adequately correlated by an expression with Reynolds number to a two-thirds power and dimensionless electrode length to a power of −0·2. For hydrodynamic entrance lengths of not less than eight equivalent diameters, data in the laminar region can be expressed by an emperical boundary layer type of equation which includes terms for the hydrodynamic entrance length and electrode length. In the turbulent regime substantially developed flow occurs after eight entrance lengths and correlations with fully developed flow equations are satisfactory     

Experimental and numerical analysis of the hydrodynamic behaviors of aerobic granules

Aerobic granular sludge has been recognized to be promising for wastewater treatment. Their hydrodynamic characteristics have a significant impact on the mass transfer process in reactors. In this study, the hydrodynamic characteristics of aerobic granules were studied using an experimental approach, and their fluid dynamic behaviors were analyzed using a numerical approach. Experimental results show that the aerobic granules are fractal‐like aggregates with porosity. Their porosity and permeability were found to increase with increasing granule size. The numerical model simulated the flow field surrounding a granule, which distinguished the flow behaviors of the granules with different permeability at different outflow Reynolds numbers. The velocity vectors colored by velocity magnitude in the granule internal depended significantly on the permeability of the granule and the Reynolds number. The results provided a helpful tool to investigate the hydrodynamic behavior of aerobic granules with a consideration of their porous structure characteristics. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Performance of stress-transport models in the prediction of particle-to-fluid heat transfer in packed beds

Computational fluid dynamics (CFD) as a simulation tool allows obtaining a more complete view of the fluid flow and heat transfer mechanisms in packed bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. This tool allows obtaining mean velocity and temperature values as well as their fluctuations at any point of the bed. An important problem when a CFD modeling is performed for turbulent flow in a packed bed reactor is to decide which turbulence model is the most accurate for this situation. Turbulence models based on the assumption of a scalar eddy viscosity for computing the turbulence stresses, so-called eddy viscosity models (EVM), seem insufficient in this case due to the big flow complexity. The use of models based on transport equations for the turbulence stresses, so-called second order closure modeling or Reynolds stress modeling (RSM), could be a better option in this case, because these models capture more of the involved physics in this kind of flow.To gain insight into this subject, a comparison between the performance in flow and heat transfer estimation of RSM and EVM turbulence models was conducted in a packed bed by solving the 3D Reynolds averaged momentum and energy equations. Several setups were defined and then computed. Thus, the numerical pressure drop, velocity, and thermal fields within the bed were obtained. In order to judge the capabilities of these turbulence models, the Nusselt number (Nu) was computed from numerical data as well as the pressure drop. Then, they were compared with commonly used correlations for parameter estimations in packed bed reactors. The numerical results obtained show that RSM give similar results as EVM for the cases checked, but with a considerably larger computational effort. This fact suggests that for this application, even though the RSM goes further into the flow physics, this does not lead to a relevant improvement in parameter estimation when compared to the performance of EVM models used.     

Electrochemical mass transfer measurements in a Y‐bifurcation model

A novel technique was used to fabricate nickel flow models of a straight pipe and a Y‐bifurcation. These were used to obtain integral mass transfer coefficients by the electrochemical technique. For the straight pipe, good agreement was obtained with previously reported mass transfer correlations. The use of an upstream anode in addition to the downstream anode led to higher mass transfer at the cathode with laminar flow because of the additional near‐wall ions produced by the upstream anode. With increasing Schmidt number, the effect of transition from laminar to turbulent flow on mass transfer was delayed to progressively higher Reynolds numbers because of the reduced mass transfer boundary layer thickness relative to the viscous sublayer. With the Y‐bifurcation, possible flow separation and the formation of a new mass transfer boundary layer in the daughter branches significantly influence the mass transfer behaviour.     

Mass transfer measurements and modeling in a microchannel photocatalytic reactor

The main objective of this paper was to evaluate the influence of mass transfer on the photocatalytic efficiency at a low flow rate in the order of several mL per hour. Several continuous flow microchannel reactors have been used to study the degradation of salicylic acid (SA) taken as a model pollutant. The photocatalytic degradation of salicylic acid, under UV illumination of 1.5 mW cm⁻², was assessed from the outlet concentration measured by liquid chromatography HPLC. It was shown that the degradation of SA by UV was limited by mass transfer. Numerical simulations have allowed establishing a relationship of the Sherwood number valuable for all the microchannel geometries. Computational fluid dynamics with Comsol Multiphysics is useful for predicting the degradation yield for a given geometry of the microreactor. The best representation of the experimental data is obtained by introducing a kinetic law taking into account mass transfer limitation.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Flow Pattern and Pressure Drop for Small Long‐Cylinder Cyclones Operating at High Flow Rates

To address the gas flow pattern and pressure drop characteristics for small long‐cylinder cyclones (SLCCs) in the high operating flow rate range, experimental investigation and computational fluid dynamics (CFD)‐based simulation were performed. The pressure drop coefficient depends insignificantly on the Reynolds number at high flow rates. The tangential and axial velocities present the Rankine vortex and the roughly inverted V‐shaped distribution, respectively, similar to those in typical cyclones. The CFD simulation approximated well the experimental data of pressure drop. The pressure drop caused by vortex loss, turbulent energy loss, and resistance loss accounted for 72.5 % of the total pressure drop. The Stairmand model was found to be relatively accurate among the classical pressure drop models for the proposed cyclone. The results may help in the design and applications of cyclone separators and reactors.     

CFD simulations of two stirred tank reactors with stationary catalytic basket

Among the different systems used for laboratory kinetic investigation, stationary catalytic basket stirred tank reactors (SCBSTRs) allow one to study triphasic reactions involving shaped catalyst with large size. The hydrodynamics of these complex reactors is not well known and has been studied experimentally in only a few cases. Despite the difference in the design of two commercial SCBSTRs reported in these works, the local measurements of the liquid-solid mass transfer coefficient inside the catalytic basket revealed the same velocity profile. The aim of the present work is therefore to investigate more accurately the hydrodynamics of the two reactors by means of CFD in order to compare the effect of the blade/baffle hydrodynamic interaction on the flow pattern. Owing to the geometrical complexity of the reactors, the hydrodynamic investigation is based on the k-ε model and the Brinkman-Forsheimer equations. The agreement at the local level with the experimental data (PIV and mass transfer measurements) validates this preliminary work performed with the standard values of the parameters present in the turbulent model and the Brinkman-Forsheimer equations. The simulations reveal in both reactors a ring-shaped vortex around the impeller in the agitation region. The high axial location of its centre induces a reverse flow at the tips of the basket. Owing to the fluid friction in the porous medium, the azimuthal flow in the core region is transformed into a radial flow in the basket where the flow decreases abruptly. Vertical vortices are located at the blade tips and at the downstream face of the baffles or they are located in the basket on both sides of the baffles, depending on the design and the location of the baffles. At the inner radius interface of the basket, the vertical blade impeller induces a rather homogeneous velocity profile, but the pitched blade impeller imposes a high velocity at the plane of symmetry. Therefore the simulations demonstrate that two different local velocity patterns and two different porous media may induce the same mass transfer properties.     

Model‐Based Optimization of a Photocatalytic Reactor with Light‐Emitting Diodes

The complicated interplay between mass and photon transfer within a photocatalytic reactor calls for an integrated design approach. A model‐based optimization approach for LED‐based photocatalytic reactors is presented. First, a model that describes the distribution of reactants and photons within a photocatalytic reactor is developed. Then, several design variables related to the reactor dimensions and light sources are optimized simultaneously using the photocatalytic degradation of toluene as a model system. The results demonstrate how different formulations of the problem can be used to either minimize the reactor cost or to obtain a specified concentration profile within the reactor.     

搅拌槽内假塑性流体洞穴研究进展

介绍了在假塑性流体层流搅拌中广泛存在的洞穴现象,表明其对物料的传质和传热极为不利;说明了假塑性流体剪切变稀的流变特性,阐述了预测洞穴大小的3种数学模型：球形模型、圆柱形模型和环形模型,同时综述了不同搅拌器洞穴形状及大小变化的最新研究成果,认为圆柱形模型（EN模型）能更好地描述假塑性流体洞穴的形状及其随雷诺数的变化,洞穴边界速度定义为 0.01U_tip;最后指出了利用 CFD 技术研究洞穴变化以及流场特征是必然趋势。