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.     

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).     

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.     

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.     

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.     

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.     

环形分布器内变质量流动的CFD模拟研究

环形分布器是实现导热介质在列管式固定床反应器壳程均匀流动的关键部件,文中采用计算流体力学方法(CFD)对环形分布器内的变质量流动进行了模拟研究。首先计算了环形通道内的速度和静压力分布,在此基础上研究了穿孔阻力系数随开孔几何结构以及入口流体流速的变化规律。模拟结果表明:环形通道内存在较明显的速度梯度和压力梯度;随着流体不断分流,在流道内的流动速度不断减小,静压力逐渐增大。因此,需要沿流动方向将开孔直径逐渐减小,以增大穿孔阻力,从而实现流体的均布。对穿孔阻力系数变化规律的研究结果表明:穿孔阻力系数ξ与出口和主流道的流速比ui/u、厚径比δ/di和入口雷诺数Re0有关。在模拟范围内,ξ先随ui/u的增大而减小,到达一个临界值后,ξ不再随ui/u的增大而变化;δ/di对ξ影响不太明显;当Re0属于湍流范围时,ξ随Re0的变化不太明显,但是总体随Re0的增大而减小。     

CFD simulation and PIV measurement of the flow field generated by modified pitched blade turbine impellers

The hydrodynamics generated by modified pitched blade turbine (m-PBT) impellers with down-pumping mode were systematically investigated through particle image velocimetry (PIV) measurements and computational fluid dynamics simulations. The simulated mean axial velocity, mean radial velocity, and turbulent kinetic energy by the standard k–? turbulent model were validated against the measured PIV data. This shows that the standard k–? turbulent model predicts mean velocity well, but underestimates turbulent kinetic energy near the blade. The flow field and power consumption as well as pumping number for the m-PBT and the standard PBT impeller were predicted. The simulation results demonstrate that a few simple changes of the blade shape influence the velocity distribution, i.e., increasing the magnitude of mean velocity in the vicinity of impeller, and that the m-PBT impeller has a higher pumping efficiency than the standard one.     

Hydrodynamic and transport properties of packed beds in small tube-to-sphere diameter ratio: pore scale simulation using an Eulerian and a Lagrangian approach

In fixed bed catalytic reactors radial heterogeneities of the granular structure are present owing to topologic constraints imposed by the reactor wall. In order to analyse the influence of this structure on the fluid flow and the radial mass transfer properties, the study of sphere packings in cylindrical container and flow simulations at the pore scale are carried out. A collocated finite volume is used to solve the 3D Navier-Stokes equations. The Reynolds number ranges from 7 to 200 allowing to use the direct numerical simulation method in stationary flow regime combined to the no-slip condition at the interface solid/fluid. Therefore no correlation are used in this study. Furthermore, representative fixed beds, composed of several hundreds of spheres, are used for a diameter ratio of 5.96 and 7.8. Radial profile of the longitudinal velocity and the probability density function of the velocity components agree with the experimental data found in the literature. At low Reynolds number, the computation of current lines reveals the presence, at the reactor wall, of a layer whose width is around one-fourth of the sphere diameter. In this layer, the fluid flow is longitudinal and tangential. Particle tracking reveals also the existence of a second layer all along the spheres in contact with the reactor wall. Mass transfer in these two regions is controlled by the diffusive mechanism at low Reynolds number. The flow structure at high Reynolds number contains lots of eddies distributed homogeneously in the fixed beds. These structures are not recirculating zones (particle traps). On contrary, they accelerate the radial mass transfer so that the layers found at low Reynolds number tend to disappear at high Reynolds.     

Effect of the wall Nusselt number on the simulation of catalytic fixed bed reactors

Literature correlations for the apparent wall heat transfer coefficient (h_w) in fixed bed catalytic reactors are compared. At low to moderate values of the Reynolds number (Re), different correlations can produce estimates of the dimensionless wall Nusselt number (Nu_w = h_wd_p/k_f) that differ by an order of magnitude or more. Some correlations give Nu_w as a function of Re only, others allow for the effects of tube-to-particle diameter ratio and particle and fluid thermal conductivities. The value of Nu_w that is used in a simulation of a fixed bed catalytic reactor can have a strong effect on the predicted behavior. Two examples of fixed bed reactors are simulated and show that the more general correlations for Nu_w are to be preferred.