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A Nonbody Fitted Cut-Cell Meshing Strategy with Locally Refined Hexahedral Mesh for Particle-Resolved Computational Fluid Dynamics Study
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The present study focuses on the assessment of the performance of a finite volume method based, particle-resolved simulation approach to predict the flow through a model packed-bed consisting of 21 layers of spheres arranged in the body centered cubic packing. The unsteady flow developing in the freeboard is also considered. Two highly resolved large eddy simulation were preformed, for two Reynolds numbers, 300 and 500, based on the particle diameter, employing a polyhedral, boundary-conforming mesh. The geometry and the flow conditions are set to reproduce the flow conditions investigated in the experiment carried out by Velten and Zähringer [“Flow field characterisation of gaseous flow in a packed bed by particle image velocimetry,” Transp. Porous Media 150, 307 (2023)] using particle image velocimetry. The numerical results compare favorably with the measurements both inside and above the bed. The effect of differences arising between the physical and numerical configurations is thoroughly discussed alongside the impact of meshing strategy on the accuracy of the predictions.
For packed beds of low tube‐to‐particle diameter ratio (N<10), pressure drop has been found to increase at low Re <100 and decrease at high Re >1000, compared to that in unbounded beds. Particle‐resolved CFD (PRCFD) in the low Re viscous region shows that widely accepted corrections overestimate the wall effect, and an improved correction formula is given. In the inertial region at high Re it is important to use accurate and consistent values for void fraction, which strongly affects pressure drop. Literature data show reasonable agreement with a correlation developed for unbounded beds (Dixon AG., AIChE J. 2023;69(6):e18035), when the void fractions for the bounded beds are used. PRCFD simulations also confirm this agreement, and only a small further correction is suggested for the remaining wall effects on fixed bed pressure drop in the inertial range, since the correlation uses the correct limit for fk as Re increases.
A method based on particle‐resolved CFD is built and validated, to calculate the fluid‐to‐particle mass and heat transfer coefficients in packed beds of spheres with different tube‐to‐particle diameter ratios (N) and of various particle shapes with N = 5.23. This method is characterized by considering axial dispersion. The mass and heat transfer coefficients increase by 5%–57% and 9%–63% after considering axial dispersion, indicating axial dispersion should be included in the method. The mass and heat transfer coefficients are reduced as N decreases. The catalyst particles without inner holes show higher mass and heat transfer coefficients than the ones with inner holes, because of unfavorable fluid flow in inner holes. The bed of trilobes has the highest mass and heat transfer coefficients, being 85% and 95% higher than the one of spheres. This work provides a versatile method and some useful guidance for the design of packed bed reactors.
Packed bed reactors are widely used to perform solid‐catalyzed gas‐phase reactions and local turbulence is known to influence heat and mass transfer characteristics. We have investigated turbulence characteristics in a packed bed of 113 spherical particles by performing particle‐resolved Reynolds‐averaged Navier–Stokes (RANS) simulations, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). The predictions of the RANS and LES simulations are validated with the lattice Boltzmann method (LBM)–based DNS at particle Reynolds number (Rep) of 600. The RANS and LES simulations can predict the velocity, strain rate, and vorticity with a reasonable accuracy. Due to the dominance of enhanced wall‐function treatment, the turbulence characteristics predicted by the ε‐based models are found to be in a good agreement with the DNS. The ω‐based models under‐predicted the turbulence quantities by several orders of magnitude due to their inadequacy in handling strongly wall‐dominated flows at low Rep. Using the DNS performed at different Rep, we also show that the onset of turbulence occurs between 200≤Rep≤250.
Liquid mixing is studied in a helical pipe numerically and experimentally to investigate the influence of computational domain discretization and gradient limiters on the unwanted numerical diffusion. Five mesh types with multiple resolutions are examined, including hexahedral, automated polyhedral, extruded polyhedral, automated tetrahedral, and extruded tetrahedral meshes. The mixing efficiency is calculated using the scalar transport technique and compared with data obtained by Laser-Induced Fluorescence measurements. Two gradient limiters are considered in the analysis, i.e., Venkatakrishnan and Min-Mod limiters, which are typically used to stabilize the simulation while limiting the numerical diffusion. The results reveal that all extruded meshes show generally a very good agreement with the experiments, while automated meshes involve unavoidable numerical diffusion, even for resolutions up to 90 million cells. The reason for this is that the cells of the automated meshes are hardly aligned with the flow direction, resulting in higher truncation errors. Furthermore, the use of MinMod limiter with extruded meshes effectively minimized the numerical diffusion in most cases. Compared to all other types, the hexahedral mesh is found the least diffusive and most accurate. Comparing the pressure drop, an acceptable accuracy on all meshes was found already at low mesh resolutions with slightly increased errors when using the automatic tetrahedral mesh. Finally, the computational cost is compared among all the considered cases. All extruded meshes are found very cost-efficient since they are mostly aligned with the flow, consuming only about 50% CPU time compared to automated unstructured meshes. Therefore, using the extruded meshes, and in particular the hexahedral mesh as far as possible, with the MinMod limiter is strongly recommended for an accurate prediction of the mixing performance at low cost.
Thermal mixing behavior of shear-thinning fluids with the specified heat flux boundary condition at mixing zone walls is studied numerically to investigate the effect of Reynolds number (10 to 50), power-law index (0.6161 to 1), Nusselt number (10⁴ to 10⁶) for external air flows and dimensionless ambient temperature (−2.7 to 1.3). The temperature is a passive tracer that quantifies the degree of mixing in this study. Detailed kinematics shows the formation of recirculation zones at the mixing channel walls. Length required to achieve the well mixed condition (i.e., a flat temperature profile across the channel height) is shorter at low Reynolds number, convective heat transfer coefficient and ambient temperature, and high power-law index values. In the impingement zone, a faster reduction in mixing index has been observed with respect to mixing length at high power-law index and low Reynolds numbers, while Nusselt number and ambient temperature exert only a weak influence. Under appropriate conditions, significant energy exchange between the system and surroundings can occur and has been analyzed in detail in this work. This work finds its applications in the improved mixing as practiced in the processing and production of food-stuffs, fine chemicals, personal care products, etc.
CFD modeling of fixed bed reactors is indispensable for understanding and optimization of its internal heat and mass dispersion. Those CFD models were earlier developed with continuum approach for high tube-to-particle diameter ratio (Np) beds. Particle-resolved CFD models followed, in spite of much higher computational cost, for investigating low Np bed with high heat flux, in which transport phenomena at near wall region with high porosity significantly affects the entire bed performance. Although segmented-continuum approaches were recently paid attention again, the validity and applicability regarding the extent of near-wall region and simplification of porosity distribution have not been carefully discussed yet. In this study, two of segmented-continuum approaches, namely, (Approach 1) two lumped segments and (Approach 2) near-wall-detailed and bulk-lumped segments approaches, were proposed and examined for CFD modelling of sphere fixed bed. The numerical results of those approaches were validated using experimental and particle-resolved CFD simulation data in the literature. In terms of heat dispersion, both approaches were in good agreement with the experimental data. However, the model accuracy in terms of mass dispersion was sensitive to the near-wall treatments because mass diffusion in fluid phase was much higher than that in solid phase of particles.
In this work, 3D particle-resolved CFD simulations have been performed to investigate the thermal effects of natural gas production from coke oven gas. The catalyst packing structures with uniform, gradient rise and gradient descent distribution and the operating conditions of pressure, wall temperature, inlet temperature and feed velocity are optimized for reduced hot spot temperature. The simulation results show that compared with packing structures with uniform distribution and gradient descent distribution, the gradient rise distribution could effectively reduce the hot spot temperature without affecting the reactor performance in the reactor with upflow reactants feeding, of which the reactor bed temperature rise is 37 K. Under the conditions with the pressure of 20 bar, wall temperature of 500 K, inlet temperature of 593 K, inlet flow rate of 0.04 m/s, the packing structure with gradient rise distribution exhibits the minimum reactor bed temperature rise of 19 K. By optimizing the catalyst distribution and operation conditions, the hot spot temperature of CO methanation process could be dramatically reduced by 49 K at the sacrifice of slightly reduced CO conversion.
In this work, the hydrodynamics and heat transfer characteristics within a gas-solid spout fluidized bed were investigated from a multiple-zone view by employing the coupled computational fluid dynamic and discrete element method. Results show that both the axial and radial particle mixing rates are accelerated with the axial particle mixing rate much faster than the radial one when increasing the spouting gas velocity. Besides, the particle-scale and the multiple-zone heat transfer analyses show that the annulus zone makes the major contribution to inter-particle conduction with the particle-particle conduction and the particle-fluid-particle conduction heat fluxes taking up about 64% and 73%, followed by the fountain zone taking up about 28% and 22%, respectively. As for the particle-fluid convective heat transfer, the spouting and annulus zones make almost the comparative contributions being about 38%, followed by the fountain zone being less than 24%. Moreover, the full-bed time-averaged heat transfer analysis shows that the particle-fluid convective heat transfer plays a dominant role in the heat transfer process in the spout fluidized bed with the particle-particle conductive and the particle-fluid-particle conductive heat fluxes being about 0.1% and 1% of the particle-fluid convective heat flux. The results of this study can provide an efficient theoretical reference for the gas-solid flow-mixing-heat transfer processes optimization and intensification of spout fluidized beds.
Radial heat management is crucial for a safe and stable operation of fixed-bed reactors with small tube-to-particle diameter ratios (N). Under high temperature conditions, thermal radiation can contribute substantially to the overall heat transfer. In the present work, the influence of radiation is studied with particle resolved computational fluid dynamics (PRCFD) in a fixed-bed reactor consisting of 1,000 spheres and rings with N = 5.1 over 300 < Rep < 2, 000 and for three different temperature levels (300-800 ∘ C). Two heat transfer parameters, i.e., the wall Nusselt number Nuw and the effective radial thermal conductivity of the bed keff, r, are derived directly from PRCFD. While the radiation effect is minor in keff, r, it is substantial for Nuw, which is not captured adequately in the current correlations presented in literature. Depending on the temperature level and flow conditions, thermal radiation between the hot wall and the packed bed intensifies the radial heat transfer represented by an increase of up to 170% in Nuw and 65% in keff, r. A 2D axisymmetric pseudo-homogeneous model including the derived heat transfer parameters can predict the radial temperature profile of the PRCFD with reasonable accuracy also with radiation except for the near-wall region.
In this work, the hydraulic tortuosity (Th) specific for the binary-sized elliptical particle packings is studied using the Lattice Boltzmann method (LBM) and discrete element method (DEM). The model is validated by comparing with experimental and simulation data with an average deviation of 6% (Max 10%). Then the model is used to develop a reliable Th correlation to describe the fluid streamlines in elliptical particle packings. Firstly, a generalized Th correlation format is proposed, containing porosity (ε) and two empirical coefficients (a, b). Then the effects of ε and size ratio (r) on the Th are studied, and by curve-fitting the simulation results, the empirical coefficients (a, b) are formulated as a function of r. Meanwhile, the generalized Th correlation format is applicable for predicting the Th in porous media with different microstructures. The Th correlations provide a theoretical basis for macroscopic modelling of fluid flow through porous media of elliptical particles.
Superheated steam (SHS) was capable of fast and uniformly torrefying heavily loaded biomass. This work detailedly investigated the torrefied biomass in terms of fuel property and combustion behavior. The reactor chamber (300mL) was fully loaded with pinewood pellets (160g). Overall residence times were 20, 40 and 60min (including preheating and holding periods) under 225, 275 and 325°C. Biomass was estimated by elements, TG, FTIR, HHV, fuel property, combustion and pyrolysis behaviors, combustion kinetics and moisture reabsorption. Holding period as short as 2min at 325°C with a heating rate of 15°C‧min⁻¹ was found to enhance energy density by 45% and generated homogeneous coal-like products with HHV of 26.76MJ‧kg⁻¹. Fixed carbon content increased to 64.84wt%. The combustion activation energy increased to 79.66kJ‧mol⁻¹. Combustion indices and behaviors indicated that torrefied biomass had benign characteristics either for co-firing or as fuel. All suggests good potential of SHS torrefaction to obtain fuel alternatives.
Packed-bed reactors are one of the simplest and most widely used reactors in chemical processes. Although simple, the random packing of solid particles can lead to inadequate heat and mass transfer, high pressure drop caused by suboptimal fluid pathways. A combination of a structure with random packing provides simplicity with designed fluid paths to alleviate mass transfer problems. In this paper, we introduce a simplified approach to developing structure-directed random packing (a 3D printed structure surround by randomly packed spherical particles), to improve the interfacial gas-liquid area and reduce pressure drop.
The random filling of particles was simulated to minimise the void fraction differences between the near-wall and away-from-wall regions. Conventional structures based on sheets made the void distribution less uniform and also created vertical channels. We developed an alternative set of structures based on short vertical pillars suspended by horizontal supports. The pillars were discontinuous and did not create consistent vertical channels, while the horizontal supports created horizontal channels to enhance radial mass and heat transfer. These structure-directed random packing enhanced void uniformity and modestly (3%) increased gas-liquid interfacial area compared to the randomly packed reactors. Importantly, the pressure drop was reduced by up to 30%. The structure-directed random packings present an opportunity for more efficient scrubbing applications with 20% lower pumping energy consumption compared to randomly packed beds.
In this work we developed an open-source work-flow for the construction of data-driven models from a wide Computational Fluid Dynamics (CFD) simulations campaign. We focused on the prediction of the permeability of bidimensional porous media models, and their effectiveness in filtration of a transported colloidal species. CFD simulations are performed with OpenFOAM, where the colloid transport is solved by the advection–diffusion equation. A campaign of two thousands simulations was performed on a HPC cluster, the permeability is calculated from the simulations with Darcy’s law and the filtration (i.e. deposition) rate is evaluated by an appropriate upscaled parameter. Finally a dataset connecting the input features of the simulations with their results is constructed for the training of neural networks, executed on the open-source machine learning platform Tensorflow (integrated with Python library Keras). The predictive performance of the data-driven model is then compared with the CFD simulations results and with traditional analytical correlations.
Particle-resolved computational fluid dynamics simulations of flow and pressure drop in fixed beds of spheres give poor accuracy at higher Reynolds number (Re) under turbulent conditions. The influence of meshing is investigated for two cases, a face centered cubic packing with no wall effects, and a narrow bed of tube-to-particle diameter ratio three with strong wall effects. Local approaches to meshing at contact points were compared, using both surface flattening (caps) and bridging between spheres. Accurate results for pressure drop at moderate to high Re > 1000 required computationally expensive fine uniform meshes, however at highest Re pressure drop appeared to be low. The use of boundary adaption improved results with less expensive meshes. The aspect ratio of surface prisms and the sizes of the bridges used at contact points had strong effects. Velocity profiles were much less sensitive to the mesh refinement and could be obtained at reasonable cost.
In recent years, computational fluid dynamic (CFD) simulation of fully resolved fixed beds has become a popular tool for getting deeper insight in local phenomena in packed beds. To get correct simulation results, special care has to be taken on how to treat particle/particle and particle/wall contact points.
In this work a local contact point modification, the local bridges method is investigated to study its effect on the heat transfer in packed beds. Packings were created using the Discrete Element Method (DEM) software discrete Flow, and were modified to implement the bridges. Using Design of Simulation Experiments (DoSE) the influence of different parameters on the heat transfer was studied. The simulated heat transfer in packed beds, considering conduction as well as natural convection, is compared to measurements and well-established correlations. Based on the Design of Simulation Experiments, a model for the correction of the effective thermal conductivity of bridges, to reduce the simulation error as a function of particle diameter D, is suggested. The suggested correction was tested on spheres of different material and sizes to check its validity. Using this correction, the simulation error for the beds surface temperature could be reduced by 75 % in a representative example case.
The modeling of Viscous Fingering (VF) is of interest to the study of multiphase flow in porous media, especially in the O&G industry, where this phenomenon is one of the root causes of high-water production and low sweep efficiency. In this study, 3D coreflood experiments found in the literature were simulated with CFD, and nine different structured and unstructured meshes were compared to determine which one gives the best description of this phenomenon. The meshes included the structured orthogonal mesh, commonly used in reservoir simulation, up to unstructured hexahedral, polyhedral, and tetrahedral meshes, among others. On the other hand, the CFD model, which was based on the Volume of Fluid (VOF) model and the porous media model, was validated against experimental data for the oil recovery profile with an absolute error below 7% for the best cases. It was found that VF is severely affected by the type of mesh and the Courant–Friedrichs–Lewy (CFL) number used. It was concluded that the unstructured polyhedral and structured hexahedral meshes gave the most reliable description of the finger growth dynamics and oil recovery compared to experimental data. Finally, a mesh independence test using the Grid Convergence Index (GCI) methodology, along with a CFL number analysis, allowed to determine that the modeling of this phenomenon should be made using an average CFL number of 0.25.
Single and multi-component adsorption fixed bed breakthrough experiments of carbon dioxide (CO2), methane (CH4) and nitrogen (N2) on commercial binder-free beads of 4A zeolite have been studied at 313, 373, and 423 K and total pressure up to 5 bar. The ternary experiments (CO2/CH4/N2) show a practically complete separation of CO2 from CH4/N2 at all the temperatures studied, with selectivity at 313 K of CO2 over CH4 around 24 and 50 over N2. The adsorption equilibrium data measured from the breakthrough experiments were modelled by the dual-site Langmuir (DSL) isotherm, and the breakthrough results simulated with a fixed bed adsorption model taking into account axial dispersion, mass transfer resistances, and heat effects. The mathematical model predicts with a good accuracy the systematic behavior of the single and multi-component breakthrough results, based on independent parameters calculated from well-established correlations, and intracrystalline diffusivities for zeolite 4A available on literature. The results showed in the present work, evidence that binder-free beads of zeolite 4A can be employed to efficiently separate CO2 from CO2/CH4/N2 mixtures by fixed bed adsorption.
Sand filtration is widely used in drinking water treatment processes, yet the hydraulic fundamentals at particle-scale are not well defined, especially the fluid velocity profile near the sand particles surface. In this study, a numerical model is developed by combining the Lattice Boltzmann (LBM) and the Discrete Element Method (DEM), used to describe the fluid flow over the sand particles surface and the micro-structure details of the sand packed bed respectively. The model is validated by comparing the simulation results with the experimental measurements using two systems, showing that the model can describe the fluid velocity distribution around the particles surface. Critical flow velocity is introduced as the balance between hydrodynamic and adhesive torques acting on sand particle surface. Furthermore, a new concept - effective filter surface (EFS), is defined as the area where the velocity near sand particles surface is less than the critical flow velocity, aiming for indirectly evaluating the performance of sand filtration. It is quantitatively demonstrated that increasing the sand particle size or feed flow velocity results in the decrease of both critical flow velocity and EFS under the given tested conditions. The LBM-DEM model provides a useful tool for understanding the fundamentals of liquid flow distribution and also estimating sand filtration performance under different operation conditions.
A comparison of the particle-scale PIV measurements with the corresponding particle-resolved CFD simulations in the turbulent flow regime using SST k-ω model is performed. A cylindrical packed bed containing spherical particles with the tube-to-particle diameter ratio of ∼4.3 operating at Rebed in the range of 1100–6600 was considered. The measured and predicted distribution of the first-order (Vx and Vy) and second-order (vorticity and strain rate) mean velocity quantities showed a reasonable agreement, which improved with the increase in the Rebed. The observed deviations were caused by the differences in the geometry (particle position and upstream packing condition) used in the CFD model compared to the measurements. On the other hand, the turbulent quantities (k and ε) were under-predicted in the simulations. However, for the ε, the agreement with the measurements was found to be better at higher Rebed compared to that of the k illustrating the influence of the turbulence model on the predictions. From the results, it can be inferred that the SST k-ω turbulence model appears to be more suitable for the high-Re flows. The present work helps to establish a methodology to validate the particle-resolved CFD simulations in the turbulent flow regime.
Particle-resolved CFD simulations are widely used for the predictions of particle-scale flow, transport processes and chemical reactions. However, the effect of turbulence models used in such simulations is not quantitatively established. In the present work, particle-resolved simulations are performed to understand the influence of different turbulence models (standard k − ε (KE), SST k − ω (SST), SSG Reynolds-stress (SSG), BSL Reynolds-stress (BSL) and LES WALE (LES)) on the particle-scale predictions of the flow, heat transfer and reactions. A comparison of the PIV measurements and particle-resolved simulations of a square column containing 72 spherical particles with a tube-to-particle diameter ratio (TPDR) of ∼3.6 and Rebed of 9765 was performed. The ε−based models (KE and SSG) under-predicted the velocity (Vx and Vy) profiles due to the over-estimation of the turbulence parameters (k and ε) and an opposite behaviour was observed for the ω−based models (SST and BSL). The LES model showed a better agreement with the measurements. In addition, numerical investigations of methane steam reforming reactions were performed in a packed bed containing 30 randomly packed 7-hole cylindrical particles with a TPDR of 5, and Ret of 50,000. The ε−based models predicted lower values of velocities, temperature and species concentration in the bulk region (and higher values on the particle surfaces) resulting into higher CH4 conversion compared to the ω−based models, whereas the LES model showed the highest ΔP and CH4 conversion. Overall, the predictions of the LES model were found to be closer to the experiments. The predictions of the RSM (SSG and BSL) models did not show any improvements over the eddy-viscosity (KE and SST) models.
Fixed bed reactor is widely used in the petrochemical industry. The most rigorous description of it is particle-resolved simulation. In this study, a particle-resolved CFD model coupling reaction-diffusion was developed. The gas and porous particle phase were solved separately and the data of heat and mass is exchanged across the phase interface. Detailed flow and reaction process for synthesis of vinyl acetate were investigated by this model. The results showed that the local flow was not uniform under different flow patterns, which leads to the non-uniform distributions of temperature and concentration. In addition, the intra-particle pore diffusion influenced the reactor performance. The increase of particle pore size can obviously promote average reaction rate and decrease product concentration inside particles. The proposed modeling provided deep insight for local flow and reaction-diffusion process and can be extended to entire fixed bed reactor.
The traditional fixed-bed reactor design is usually not suitable for the low tube-to-particle diameter ratios (N = D/d < 8) where the local phenomena of channeling near the wall and backflow in the bed are dominant. The recent “solid particle” meshing method is too complicated for mesh generation, especially for non-spherical particles in large random packed beds, which seriously hinders its development. In this work, a novel high-fidelity mesh model is proposed for simulation of fixed bed reactors by combining the immersed boundary and adaptive meshing methods. This method is suitable for different shapes of particles, which ingeniously avoids handling the complex “contact point” problem. Several packed beds with two different shapes of particles are investigated with this model, and the local flow in the bed is simulated without geometrical simplification. The predicted pressure drop across the fixed bed and heat transfer of the single particle are in good agreement with the corresponding empirical relations. Compared with spherical particles, the packed bed packing with pentaphyllous particles has lower pressure drop and better heat/mass transfer performance, and it shows that this method can be used for the screening of particle shapes in a fixed bed.
A method has been demonstrated using particle-resolved CFD simulations to simulate the transient catalyst deactivation due to carbon formation process and its impact on the particle properties. Preliminary simulations with cylindrical particles and propane dehydrogenation reactions showed higher carbon accumulation for the near-wall particles due to the presence of wall heat flux. Significant gradients of carbon concentration within the particle pointed to the presence of diffusion limitations. The accumulated carbon decreased the rate of the reactions thereby decreased the propene formation with time. Later, the effect of particle shape on the catalyst deactivation was investigated using five different particle shapes with constant particle volume, but varying in particle surface area. Considerable variations in the accumulated carbon were observed both with respect to the particle position and the particle shapes. The initial reaction rate increased with the particle surface area due to reduced diffusion limitation, but after a certain time, it decreased with particle surface area due to faster catalyst deactivation. As a result, the propane conversion and propene yield decreased with particle surface area. Also, the propene yield to ΔP ratio decreased with particle surface area due to smaller ΔP offered by particles with the lower surface area. Therefore, the present work showed that the particles with the lower surface area are favorable for propane dehydrogenation process due to slower catalyst deactivation leading to higher conversion and longer operating time. The trilobe particle shape gave the highest propane conversion and highest propene yield to ΔP ratio.
Industrial catalytic reactors are made of steel, operate at high temperatures and pressures and contain hazardous chemicals. What happens inside remains hidden. Reactor optimization requires costly trial and error or is based on simplified mathematical models employing more or less accurate transport correlations and reaction kinetics. In the present work a pilot-scale fixed-bed reactor was developed for measuring concentration and temperature profiles for n-butane oxidation to maleic anhydride on vanadyl pyrophosphate catalyst pellets under industrially-relevant conditions. The reactor was equipped with five heating zones. The reactor was modeled by particle-resolved computational fluid dynamics. The catalyst bed was created by discrete element simulation and the result was validated by comparison with experimental radial porosity profiles. Catalytic chemistry was included by a kinetic model of intrinsic reaction rates. Transport resistances and packing deviations were lumped in reaction rate multipliers determined by fitting the model to profiles measured at a uniform reactor wall temperature. Simulation results reveal strong inhomogeneities inside the bed. A hot-spot develops at uniform wall temperature. At this hot-spot temperature differences of 40 K exist on one and the same pellet with negative impact on maleic anhydride selectivity and catalyst lifetime. An optimized wall temperature profile was derived by combining knowledge from the experimental profiles at uniform wall temperature and the CFD results. A gradual increasing temperature was predicted by the model to eliminate the hot-spot and increase integral maleic anhydride selectivity at constant n-butane conversion. This prediction was confirmed by experiment. At 80% n-butane conversion the maleic anhydride selectivity could be improved by 2%. Facing the scale of the process, this improvement translates into significant n-butane savings, reduced COx emissions and increased revenue.
In this work an industrial Biomass-To-Liquid (BTL) plant simulation and optimization are presented. Biomass is first gasified with oxygen and steam, and the produced syngas is fed to a multi-tubular fixed bed reactor for Fischer-Tropsch (FT) synthesis, obtaining a distribution of hydrocarbons with different molecular weight. A simplified model for the biomass gasification section is implemented in HYSYS® V8.4, while the Fischer-Tropsch reactor is simulated using MATLAB® R2013a. The kinetic parameters of the FT reaction have been determined by using a non-liner regression performed with the experimenta data obtained with a bench-scale FT-rig. The model developed for the Fischer-Tropsch reactor takes into account the catalytic pellet's effectiveness factor and the eventual formation of a liquid phase in each point along reactor's axial coordinate. The whole BTL plant is simulated connecting MATLAB and HYSYS. Moreover, the staging of the Fischer-Tropsch reactor is studied performing a techno-economic analysis of three different plant configurations and evaluating the corresponding pay-back time.
Maleic Anhydride (MA) production by selective oxidation of n-butane in a Multi-Tubular Fixed Bed reactor is constrained by the flammability limits. The use of Fluidized Bed circumvents this constraint but suffers from high back mixing. The Circulating Fluidized Bed (CFB) reduces the back mixing of the catalyst and enhances the catalyst activity by reactivating the catalyst. A simple reactor model with suitable hydrodynamic and kinetic models at the operating conditions of both the pilot and commercial MA CFB reactors is proposed. A dispersion model with variable gas density is used for modeling the hydrodynamics of these reactors. The reactors' configurational complexities are also accounted for in the model. The data fitting exercise of the proposed reactor model is performed. The proposed method simultaneously minimizes the total bias based on the individual biases for each component of the multi component reactor system and the total error in a multi-objective framework.
A two-dimensional transient numerical study of the adsorption of CO2/N2 and CO2/H2 mixtures on activated carbon and MOF-177 in a fixed bed is presented. Because most of the commercial CFD codes are not capable of simulating adsorption processes in a straightforward fashion, we developed an additional code to solve for the different species transport including adsorption and diffusion and used Fluent to simulate the adsorption process, fluid flow, heat and, mass transfer.
We simulated the adsorption process at high temperature-low pressure and low temperature-high pressure conditions as well as the pressure swing adsorption. For adsorption of CO2/N2 and CO2/H2 mixtures, Toth and Viral models are used calculate equilibrium isotherms. The breakthrough curves obtained from the simulations compare well with the experimental data. Moreover, the effects of aspect ratio and geometric shapes were studied. The results show that varying the bed aspect ratio from 7.77 to 2 has an insignificant effect on the adsorption capacity and performance.
One of the major issues for particle-resolved CFD simulations of fixed beds are particle-particle and particle-wall contacts. A fixed bed of cylinders is studied with different local contact modifications, i.e., caps and bridges method for line and area contacts, and caps and united method for overlaps resulting from composite DEM-particles. Effects are analyzed regarding pressure drop, local velocity, and local heat transfer for 191 < Rep < 763. Modeling particle-wall contacts is becoming more important with increasing Rep. Contact modifications inside the bed are becoming less important, since convective heat transfer is dominant. The stable caps method shows promising results in comparison with heat-transfer predictions. However, it overestimates convective heat transfer in the contact regions for high flow rates. The bridges method shows good results for pressure drop and heat-transfer predictions. A difficulty remains the choice of the thermal conductivity of these bridges.
We propose the application of a Cell Agglomeration (CA) algorithm for coupling detailed microkinetic models with multi-region steady-state Computational Fluid Dynamics (CFD) simulations of catalytic reactors. This numerical methodology − originally developed for dynamic CFD simulation with detailed gas-phase kinetics − is herein applied in the context of steady-state microkinetic CFD simulations of catalytic reactors by exploiting the particular structure of the governing equations of the adsorbed species, which are characterized by the absence of the transport term. The potentialities of the method are assessed by the analysis of different reactor geometries and microkinetic mechanisms in a wide range of operating conditions. Our tests show this method to allow for a reduction of the computational time up to an order of magnitude. Thus, the CA algorithm turns out to be a useful tool to enable the detailed and fundamental simulation of catalytic devices in steady-state conditions.
Dry reforming of methane (DRM) over nickel in a fixed-bed reactor of spheres was studied experimentally and with CFD simulations. Temperature and mole fraction profiles were measured in a dedicated profile reactor as function of axial coordinate. Particle-resolved CFD simulations took into account conjugate heat transfer, surface-to-surface radiation, and surface reactions described by microkinetics. Energy transport of CFD simulations were verified by studying heat transfer without chemical reactions. DRM experiments could not be reproduced with the original microkinetics formulation, even with the axial temperature profile applied. A detailed analysis of the microkinetics showed that thermodynamic inconsistencies are present, which are amplified by high surface coverage of CO*. After modifying the mechanism the experiments could be reproduced. This study shows how complex interactions between local transport phenomena and local kinetics can be quantified without relying on transport correlations.
Fixed-bed reactors with a small tube-to-particle diameter ratio are typically used for highly exothermic or endothermic reactions. Flow, temperature and species distribution as well as the reaction rates are affected by the effect of the confining wall. In this study we have investigated numerically a spatially resolved fixed-bed including a detailed reaction mechanism for dry reforming of methane (DRM). Operating conditions in terms of feed composition, feed and heating temperature and feed mass flow could be identified, where the deactivation of the catalyst due to coking is prevented but still a reasonable conversion of methane and carbon dioxide as well as a high hydrogen selectivity can be achieved. Finally the need of a spatially resolved simulation is shown. While a pseudo-homogeneous 2D simulation needs significantly less computation time, it over predicts the conversion by approx. 20% due to an overestimated heat transfer.
In this work we implement the log-conformation reformulation for viscoelastic constitutive equations as proposed by Fattal and Kupferman (2004) in the open-source CFD-software OpenFOAM(R), which is based on the collocated finite-volume method (FVM). The implementation includes an efficient eigenvalue and eigenvector routine and the algorithm finally is second-order accurate both in time and space, when using it in conjunction with an adequate convection scheme such as the CUBISTA scheme (Alves et al., 2003). The newly developed solver is first validated with the analytical solution for a startup Poiseuille flow of a viscoelastic fluid and subsequently applied to the three-dimensional and transient simulation of a lid-driven cavity flow, in which the viscoelastic fluid is modeled by the Oldroyd-B constitutive equation. The results are presented for both the first-order upwind scheme and the CUBISTA scheme on four hexahedral meshes of different size in order to check for mesh convergence of the results and a tetrahedral mesh to show the applicability to unstructured meshes. The results obtained for various values of the Weissenberg number are presented and discussed with respect to the location of the primary vortex center, streamline patterns and velocity and stress profiles besides others. We are able to obtain sufficiently mesh converged results for Weissenberg numbers, which would have been impossible to obtain without use of the log-conformation reformulation. An upper limit for the Weissenberg number in terms of stability could not be found.
The simulation of flow and transport in packed-bed (catalytic and non-catalytic) reactors is of paramount importance in the chemical industry. Different tools have been developed in the last decades for generating particle packings, such as the Discrete Element Method (DEM), whereas Computational Fluid Dynamics (CFD) is generally employed for simulating fluid flow and scalar dispersion. This work-flow presents the main drawbacks of being computationally expensive, as most packing generation algorithms deal with non-convex objects, such as trilobes, with cumbersome strategies, and of making use of in-house or commercial codes, that are either difficult to access or costly. In this paper a novel open-source and easily accessible work-flow based on Blender, a rigid-body simulation tool developed for computer graphics applications, and OpenFOAM a very well-known CFD code, is presented. The approach, which presents the main advantage of being computationally fast, is validated by comparison with experimental data for global bulk porosity, particle orientation, local porosity and velocity distributions, and pressure drop. To our knowledge this is the very first application of Blender for the simulation of packed-bed reactors.
The influence of the container walls on the pressure drop of packed beds is investigated. A detailed analysis of more than 2300 experimental data points reveals the Reynolds number dependence of this effect. Physical evidence is given that the observed behavior is caused by the counteracting effects of the wall friction and the increased porosity near external boundaries. A comparison of the predictions of 24 published pressure drop correlations with available experimental data shows that Reichelt's approach (Chem. Ing. Tech. 44 (1972) 1068) of correcting the Ergun equation for the wall effect is the most promising one. Improved correlations are obtained for different types of packings by fitting the coefficients of that equation to the database.
Abstract Highly endothermic (or exothermic) heterogeneous catalytic reactions are performed commonly in fixed-bed reactors with small tube-to-particle-diameter ratios N both in industrial and lab-scale applications. For these reactor configurations conventional plug flow models and pseudo-homogeneous kinetic models fail. An adequate modeling can be carried out with full computational fluid dynamics (CFD) in combination with detailed reaction mechanisms. In this study, a full three-dimensional fixed-bed reactor for the catalytic dry reforming of methane (DRM) over rhodium was simulated with a detailed reaction mechanism. The bed consists of 113 spherical solid particles in which thermal conductivity was considered. Two different Reynolds numbers were investigated, i.e., 35 and 700. The simulated DRM fixed-bed reactor demonstrates the strong interaction between chemical kinetics and transport of momentum, heat and mass. The observed velocity, temperature and species fields are characterized by their three-dimensional behavior and interactions highlighting their complexity and discrepancy from lumped model predictions. In addition, the reaction mechanism determines regions with catalyst deactivation by carbon deposition. This study demonstrates the advantages of modeling heterogeneous catalytic fixed-bed reactors with small N fully in three-dimensional in combination with detailed reaction mechanisms. Finally, this modeling approach reduces dependencies on empiricism for the calculation of multiscale reaction devices.
A new velocity-based approach to fixed bed radial heat transfer is presented. Axial and radial velocity components were averaged from detailed 3D computational fluid dynamics (CFD) fixed bed simulations of computer-generated beds of spheres and used to model radial thermal convection. The convection terms were coupled with a radially varying stagnant bed thermal conductivity in a 2D pseudocontinuum fixed-bed heat transfer model. The usual effective radial thermal conductivity kr and apparent wall heat transfer coefficient hw were not used, and there were no adjustable parameters. The radial and axial temperature variation predicted by the velocity-based model agreed well with the angular-averaged temperatures from the detailed 3D CFD simulations over the range 80 ≤ Re ≤ 1900 and for N = 3.96, 5.96, and 7.99.
The present paper systematically investigated the appropriateness of different contact point modification approaches for forced convective heat transfer analysis in structured packed beds of spheres. The three-dimensional Navier–Stokes equations and RNG k–ɛ turbulence model with scalable wall function are adopted to model the turbulent flow inside the pores. Both macroscopic and local flow and heat transfer characteristics for different packing forms (simple cubic, body center cubic and face center cubic packing forms) and contact treatments (gaps, overlaps, bridges and caps modifications) are carefully examined. In particular, the effects caused by the bridge size for the bridges treatment are discussed, and the numerical results are compared with available experiments in literature. It is found that the effects of contact treatments on the pressure drops are remarkable for different structured packing forms, especially when the porosity is relatively low, while such effects on the Nusselt numbers are relatively small. Among the four different contact modifications, the bridges method would give the most reasonable pressure drops for all the structured packing forms studied and this method is also proved to be suitable for predicting the Nusselt numbers. The local flow and heat transfer characteristics in the structured packed bed are sensitive to the methodology of contact modifications. The gaps and caps treatments would distort the local flow and temperature distributions in the packed bed, especially near the contact zones. While the local flow and temperature distributions from the overlaps and bridges treatments would be more reasonable and close to those in the original packing with points contact. Based on both the macroscopic and local flow and heat transfer analyses, the bridges treatment is recommended. The effects caused by the bridge size in the bridges treatment are also remarkable. It is noted that too small or too large bridge size would lead to unreasonable results for both the macroscopic and local flow and heat transfer analyses. A reasonable range of bridge diameter is found to be from 16% dp to 20% dp.
A resource and time saving method is introduced for optimizing fixed bed reactors by the combination of Response Surface Methodology (RSM) and CFD simulation. This is demonstrated for the oxidative coupling of methane (OCM) based on the reaction kinetics by Stansch1997. Firstly, a parameter screening is performed to identify the power factors modified reaction time, heating temperature and CH4 to O2 ratio. Secondly, utilizing central composite design, meta models for the most interesting responses are developed, i.e. C2 selectivity and yield as well as CH4 conversion. The statistical models describe the characteristics of the responses over a wide range. Thirdly, an optimization of C2 yield is carried out using RSM. The maximum is detected to be approx. 14 % and validated by three dimensional CFD simulations. In the investigated parameter space the optimized parameter conditions are found for a feed composition of 20 % nitrogen, 26.7 % oxygen, 53.3 % methane (CH4 to O2 ratio of 2), a modified reaction time of 61 kg s/m3 and a heating temperature of 801.5 °C.
CFD simulations of heat transfer in fixed beds of spheres were validated by comparison to experimental measurements in a pilot-scale rig. The comparisons were made for particle Reynolds numbers in the range 2200 < Re < 27000 for tube-to-particle diameter ratio N = 5.45, and in the range 1600 < Re < 5600 for N = 7.44. Radial temperature profiles were obtained at four axial positions in the heated bed spaced 0.16 m apart.CFD models of a 0.72 m long tube containing 1000 spheres (N = 5.45) and a 0.35 m long tube of 1250 spheres (N = 7.44) were solved to obtain well-developed flow fields. These provided inlet velocity profiles to reduced models of 0.20 m heated packed length, consisting of 304 spheres for N = 5.45 and 722 spheres for N = 7.44. The measured temperature profiles were used as inlet boundary conditions and profiles 0.16 m downstream were computed. A mesh verification study showed negligible difference between the profiles from a medium and a fine mesh.Contact points were treated by one of three methods: global reduction of sphere size resulting in gaps, or local insertion of bridges at particle–wall contact points with either surface flattening or bridges at the particle–particle contact points. The gaps method gave slightly poorer results; the two bridges methods were better and indistinguishable from each other. CFD simulations compared well to the experimental data: trends with Re, N and bed depth were captured, and quantitative agreement of temperature profiles was reasonable.
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 (CD) 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 CD. Local methods, in which bridges are inserted or spherical caps are removed only at the points of contact, give much better results for CD. 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.