Systematic mesh development for 3D CFD simulation of fixed beds: Contact points study

In the development of meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds of spheres, particle–particle and wall–particle contact points often present difficulties. We give results for drag coefficient (C_D) and heat flow (Q) for flow past sphere–sphere and wall–sphere contact points, focusing on higher flow rates typical of industrial steam reformers (500 < Re < 10,000). Global methods, in which all particles in a bed are either shrunk or enlarged uniformly, change bed voidage giving erroneous results for C_D. Local methods, in which bridges are inserted or spherical caps are removed only at the points of contact, give much better results for C_D. The bridges approach is preferable for heat transfer, as fluid gaps reduce heat transfer too much, and particle overlaps increase it. A set of graphs is presented to allow estimation of the error introduced by the various methods of dealing with contact points.     

CFD modeling of pressure drop and drag coefficient in fixed and expanded beds

The aim of this study is computational fluid dynamic (CFD) simulation of the single-phase pressure drop in fixed and expanded beds. A fixed bed with a column to particle diameter ratio (D/d_p) of 5 and having 151 particles arranged in 8 layers was taken as a computational geometrical model. In the case of expanded beds, 0.605 voidage bed consisted of 105 particles and 0.783 voidage bed consisted of 55 particles. Simulations were performed in the creeping, transition and turbulent flow regimes, where Reynolds number (d_pV_Lρ_L/μ_L) was varied from 0.1 to 10,000. The deviations from Ergun's equation due to the wall effects, which are important in D/d_p < 10 beds, were well explained by the CFD simulations. Thus, an increase in the pressure drop was observed due to the wall friction in the creeping flow, whereas, in turbulent regime a decrease in the pressure drop was observed due to the channeling near the wall. Energy balance has been established through the CFD predicted values of energy dissipation rates (viscous as well as turbulent).     

CFD study on particle-to-fluid heat transfer in fixed bed reactors: Convective heat transfer at low and high pressure

Computational fluid dynamics (CFD) has proven to be a reliable tool for fixed bed reactor design, through the resolution of 3D transport equations for mass, momentum and energy balances. Solution of these equations allow to obtain velocity and temperature profiles within the reactor. The numerical results obtained allow estimating useful parameters applicable to equipment design. Particle-to-fluid heat transfer coefficient is of primal importance when analyzing the performance of a fixed bed reactor. To gain insight in this subject, numerical results using a modified commercial CFD solver are presented and particle-to-fluid heat transfer in fixed beds is analyzed. Two different configurations are studied: forced convection at low pressure (with air as circulating fluid) and mixed (i.e., free+forced) convection at high pressure (with supercritical CO₂ as circulating fluid). In order to impose supercritical fluid properties to the model, modifications into the CFD code were introduced by means of user defined functions (UDF) and user defined equations (UDE). The obtained numerical data is compared to previously published data and a novel CFD-based correlation (for free, forced and mixed convection at high pressure) is presented.     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

A CFD model for predicting the heat transfer in the industrial scale packed bed

Compared to the traditional lumped-parameter model,computational fluid dynamics (CFD) attracted more attentions due to facilitating more accurate reactor design and optimization methods when analyzing the heat transfer in the industrial packed bed.Here,a model was developed based on the CFD theory,in which the heterogeneous fluid flow was resolved by considering the oscillatory behavior of voidage and the effective fluid viscosity.The energy transports in packed bed were calculated by the convection and diffusion incorporated with gaseous dispersion in fluid and the contacting thermal conductivity of packed particles in solids.The heat transfer coefficient between fluid and wall was evaluated by considering the turbulence due to the packed particles adjacent to the wall.Thus,the heat transfer in packed bed can be predicted without using any adjustable semi-empirical effective thermal conductivity coefficient.The experimental results from the literature were employed to validate this model.     

Wall-to-particle heat transfer in steam reformer tubes: CFD comparison of catalyst particles

Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tube-to-particle diameter ratio (N) equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185-5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order: solid cylinders>one-hole particles>multi-hole particles. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study.     

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.     

Computational Fluid Dynamics Study of Heat Transfer in Turbulent Fluidized Beds

The fluidization and heat transfer behaviors of a turbulent fluidized bed were investigated using computational fluid dynamics (CFD). The effects of inlet superficial velocity on heat transfer behaviors in a turbulent fluidized bed were analyzed and compared with those operated in other fluidization regimes. The effects of using particles belonging to different Geldart groups in a turbulent fluidized bed on fluidization and heat transfer behaviors were evaluated. For both fluidization regimes investigated, the solids temperature distribution during the heat transfer process became less uniform when the particle size was reduced.     

CFD simulation of laser enhanced modified chemical vapor deposition process

The modified chemical vapor deposition (MCVD) process is one of the most widely used processes to manufacture the optical fiber preforms. There have been several experimental and numerical studies to establish that thermophoresis is the dominant mechanism for the transport of silica particles to the preform wall. There also exists several modification of this process to increase the deposition efficiency in the MCVD process. In this work we have carried out computational fluid dynamics simulation of the coupled equations of mass, momentum, energy and species transport in the laser enhanced thermophoretic deposition process using the conservative finite volume scheme. The effect of laser heating on different parameters such as thermophoresis, conversion rate and deposition efficiency is examined in this study. The presence of laser heating alters the velocity and temperature profile that leads to increase in the conversion and deposition efficiency due to high thermophoresis. The results of numerical simulations are in support of experimental and analytical studies. Our numerical simulations using the conservative finite volume scheme show that deposition efficiency increases with increasing power of the laser.     

Fluid dynamic simulation in a chemical looping combustion with two interconnected fluidized beds

Flow behavior of gas and particles is simulated in a 2-D chemical-looping combustion (CLC) process with two interconnected fluidized beds. A Eulerian continuum two-fluid model is applied for both the gas phase and the solid phase. Gas turbulence is modeled by using a k-ε turbulent model. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. Instantaneous and local velocity, concentration of particles and granular temperature are obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in the air reactor. Flow behavior of bubbles is predicted in the fuel reactor and pot-seal. Computed leakage qualitatively agrees with experimental data in the fuel reactor and pot-seal.     

Verification and validation of CFD models and dynamic similarity for fluidized beds

Claims and suggestions in the literature that verification or validation of CFD numerical models has been achieved for fluidized beds are shown to be inconsistent with objective criteria and accepted usage of terminology. Verification involves confirming the accuracy of the computational aspect of the model, for example by comparing results against known solutions, something that is virtually impossible in dense multiphase systems, except for trivial cases. Validation requires objective consideration of computational and numerical error, as well as comparison of model predictions and experimental data over broad ranges of conditions. More care is required in applying these terms, and in planning and conducting experiments to test the validity of fluidized bed numerical codes. Similar considerations apply to experimental attempts to confirm the completeness of sets of matched dimensionless groups used for dynamic scaling of multiphase systems.     

Uncertainties in the simulation of catalytic distillation process: A systematic grid refinement study

Computational fluid dynamics (CFD) methods are gradually finding applications in the simulation of distillation processes. In the discretization of the governing differential equations for the mass- and the energy-balance, finite volume method (FVM) is commonly employed. Upwind differencing scheme (UDS) and central differencing scheme (CDS) are most commonly employed in FVM to approximate the values of the variables on the control volume faces. The problems that arise while using these approximation methods are discussed here. These may be overcome by using a bounded linear deferred correction scheme (LDC). When solutions on more than one grid sizes are available, and the order of the numerical scheme is known, the exact solution may be predicted by using Richardson extrapolation technique. If the order is unknown, then the order of the scheme may be determined from grid refinement studies. However, for the determined order of the scheme to be meaningful, sufficiently fine grids must be used for these studies.     

CFD simulation of gas-liquid contacting in tubular reactors

Gas-liquid contacting in tubular reactors was simulated using an Eulerian-Eulerian CFD approach in which accurate interphase momentum closure relations are incorporated, bubble-induced turbulence is accounted for, and population balance equations are used to describe bubble breakage and coalescence. The ability of two breakup kernels (Luo, H., Svendsen, H.F., 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225-1233; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) and three coalescence kernels (Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and breakup in air sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499; Luo, H., 1993. Coalescence, breakup and liquid recirculation in bubble column reactors. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) to accurately predict several flow parameters in pipe flow was tested.Good agreement between simulation and experimental results (radial profiles of gas holdup, turbulence intensity, and local Sauter bubble diameter) was achieved without the use of empirically derived relationships (such as Drift flux) by adjusting a single parameter which accounts for the deviation in the coalescence behaviour of tap water from that of pure water. The approach adopted in this investigation may thus be applicable to more complex hydrodynamic situations such as those encountered in mechanically agitated tanks and the need for extensive experimental testing may be replaced by single measurement of the effect interfacial properties have on coalescence rates.     

A Reynolds mass flux model for gas separation process simulation:I. Modeling and validation

Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The aniso-tropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux (RMF) model. With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerical y. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation, while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and mo-mentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To val-idate the presented RMF model, simulation is carried out for CO2 absorption into aqueous NaOH solutions in a packed column (0.1 m id, packed with 12.7 mm Berl saddles up to a height of 6.55 m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temper-ature distributions. The sequel Part II extends the model application to the simulation of an unsteady state ad-sorption process in a packed column.     

CFD simulation study of the effect of baffles on the fluidized bed for hydrogenation of silicon tetrachloride

In this study, the effect of channel baffles and louver baffles on the flow pattern in the large-scale industrial fluidized beds was studied by computational fluid dynamics (CFD) methods. Then, the effect of flow pattern on the chemical reaction performance was studied for the first time. Simulation results showed that the gas velocity distributed more uniformly, solid particles dispersed more homogeneously and aggregation scarcely occurred in the fluidized bed with louver baffles than that with channel baffles. The residence time distribution indicated that louver baffles remarkably suppressed gas back-mixing in comparison with channel baffles. The reasonable agreements of pressure distribution and reaction results between the simulation in the bed with channel baffles and the data on a large-scale industrial apparatus demonstrated the accuracy of the CFD model. The predicted conversion of SiCl₄ in the bed with louver baffles (27.44%) was higher than that with channel baffles (22.69%), indicating that louver baffles markedly improved the performance of the fluidized bed. This study could provide useful information for future structural improvements of baffles in large-scale fluidized beds.     

Evaluation of pseudohomogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow

Several pseudohomogeneous models are used by researchers in the study of heat transfer in packed beds. In this work, five of the most used pseudohomogeneous models (to one, two and three parameters) are analyzed, for gas and gas-liquid flow configurations. The models were evaluated concerning the following aspects: (a) the fitting between calculated and measured temperatures, (b) the values of thermal parameters, (c) their confidence intervals, (d) the quality of the estimation of the thermal parameters by analysis of their Box biases, and (e) the nonlinear dependence of the calculated temperatures on the thermal parameters (using the curvature measures of Bates and Watts). It was observed, particularly in gas-liquid flow, that the fittings between calculated and measured temperature profiles are better for models in which a wall heat transfer coefficient is incorporated to consider the convective resistance at the bed wall. It was also noted that the values of the thermal parameters fitted from the pseudohomogeneous models may be very different at identical operational conditions. The effective axial thermal conductivity may be neglected in the modeling because its estimation does not affect the residual functions. Besides, the estimation of k_a is tricky because it depends on the initial guess and also because the parameter is extremely sensitive to changes in the operational conditions. The confidence intervals for the parameters depend on the model and are also affected by the experimental conditions. The estimation of the parameters was adequate for the k_r-h_W and k_r-k_a models and the curvatures measures were satisfactory only for models in which h_W was not incorporated.     

Parametric optimization of packed bed for activated coal fly ash waste heat recovery using CFD techniques

Coal fly ash is an industrial solid waste generated from coal preparation during the processing and cleaning of coal for electric power generation. Comprehensive investigation on the reutilization of waste heat of activated coal fly ash is of great economic significance. The method of recovering the waste heat, proposed in this study,is the transfer of heat from activated coal fly ash to gas with the movement of air using the packed bed, providing valuable energy sources for preheating the raw coal fly ash to reduce the overall energy consumption. The investigation is carried on the heat transfer characteristics of gas–solid(activated coal fly ash) phases and air temperature fields of the packed bed under some key conditions via computational fluid dynamics. A two dimensional geometry is utilized to represent key parts of packed bed. The distribution mechanism of the temperature field for gas phase is analyzed based on the transient temperature contours at different times. The results show that the obtained rule of gas–solid heat transfer can effectively evaluate the influences of operating parameters on the air temperature in the packed bed. Simultaneously, it is found that no temperature differences exist in the hot air at the outlet of the packed bed. The investigation provides guidance for the design and optimization of other similar energy recovery apparatuses in industries.     

Effect of a Draft Tube on the Fluid Dynamics of a Spouted Bed: Experimental and CFD Studies

Knowledge about the gas and particle dynamics in spouted beds is important in the evaluation of particle circulation rates and the efficiency of gas-solid contacts. In this work, the mechanism of transition from a static bed to a spouted bed was numerically simulated using a Eulerian multiphase model. This model was applied to two distinct spouted bed geometries: a conventional device and a spouted bed with draft tube. The radial voidage and particle velocity profiles along the longitudinal position in the annular and spout regions were simulated for the geometries under study. The characteristic simulated curves were congruous with the experimental data.     

Effect of a Draft Tube on the Fluid Dynamics of a Spouted Bed: Experimental and CFD Studies

Knowledge about the gas and particle dynamics in spouted beds is important in the evaluation of particle circulation rates and the efficiency of gas-solid contacts. In this work, the mechanism of transition from a static bed to a spouted bed was numerically simulated using a Eulerian multiphase model. This model was applied to two distinct spouted bed geometries: a conventional device and a spouted bed with draft tube. The radial voidage and particle velocity profiles along the longitudinal position in the annular and spout regions were simulated for the geometries under study. The characteristic simulated curves were congruous with the experimental data.     

Computation of system turbulences and dispersion coefficients in circulating fluidized bed downer using CFD simulation

In this study, the Eulerian computational fluid dynamics model with the kinetic theory of granular flow model was effectively used to compute the system turbulences and dispersion coefficients in a circulating fluidized bed (CFB) downer. In addition, the obtained model was used to simulate all the system velocities.