Effective Radial Thermal Conductivity Research Articles

On the Role of Radial Dispersion in the Behavior of a Cooled Fixed‐Bed Reactor: Numerical Investigation of Fischer–Tropsch Synthesis with a Cobalt‐Based Catalyst

AbstractThe impact of radial dispersion of both heat and mass on the behavior of cooled fixed‐bed reactors was explored using a two‐dimensional reactor model. This study accounted for dispersion through an effective radial thermal conductivity (λrad) and a radial dispersion coefficient of mass (Drad), with Fischer–Tropsch synthesis serving as an illustrative process example. Under moderate reaction conditions and hence still rather gentle radial temperature profiles, the effect of mass dispersion on reactor performance was found to be minimal, even if disregarded (Drad = 0), whereas dispersion of heat (λrad) always significantly impacts reactor behavior. Nevertheless, for precise thermal runaway predictions by a reactor model, incorporating mass dispersion by a realistic Drad value is essential.

Radial Thermoelectric Model for Stranded Transmission Line Conductors.

Bare-stranded conductors play a critical role in the efficiency and safe operation of transmission lines. The heat generated in the interior of the conductor is conducted radially to the outer surface, creating a radial thermal gradient. The radial temperature gradient between the core and the surface depends on multiple factors, such as stranding, number of layers, current level, electrical resistance and the effective radial thermal conductivity. Therefore, the radial temperature model must be considered when developing accurate conductor models. Such models are particularly important in the development of dynamic line rating (DLR) approaches to allow the full current carrying capacity of the conductor to be utilized while ensuring safe operation. This paper develops a radial one-dimensional thermoelectric model for bare-stranded conductors used in transmission lines. The accuracy of the proposed model is determined by experimental tests performed on three conductors.

Improved multiphysics model of the High Temperature Engineering Test Reactor for the simulation of loss-of-forced-cooling experiments

We present a multiphysics model of the High Temperature Engineering Test Reactor for comparison with past and predict future loss-of-forced-cooling (LOFC) experiments. The approach selected combines (1) 3-D full-core superhomogenization-corrected neutronics, (2) 3-D full-core homogenized or semi-heterogeneous heat transfer (macroscale), (3) 2-D axisymmetric fuel rod heat transfer (pin-scale), and (4) 1-D thermal-hydraulics channels. Although large uncertainties remain, the time and magnitude of the first power peak after re-criticality is predicted within 1.5 h and 175 kW, respectively. The novelty of our work includes (1) a new macroscale/pin-scale heat transfer coupling approach relying on gap conductance to drastically speed up numerical convergence by two orders of magnitude, (2) determination of a radial effective thermal conductivity, reproducing the semi-heterogeneous re-criticality time within one hour using a homogenized macroscale model, and (3) a preliminary study of the reactor’s early behavior following a LOFC event, enabling further assessment of numerical models against fission power measurements.

A pseudo-local heat transfer approach in a low tube to particle diameter ratio packed bed catalytic reactor: Oxidative dehydrogenation of ethane as a case study

A generalized approach to model heat transfer in an industrial-scale wall-cooled packed bed reactor with a low tube-to-particle diameter ratio (<8) is proposed and assessed in this work. The modeling approach rests on the realization of experiments carried out in absence of reaction in bench-scale as well as in industrial-scale packed beds. The approximation overcomes historical limitations identified when modeling radial heat transfer mechanisms by applying conventional approaches. The methodology leads to the reliable determination of the external wall heat transfer coefficient and pseudo-local radial effective thermal conductivity. The approach allows the quantification of heat transfer resistances through the core, the internal and the external wall of the bed indicating that approximately 30 % of the resistances are located along the internal side of the packed bed when it was operated at Particle Reynolds numbers ranging from 700 to 1400. Because of its complex impact on heat transfer, fluid dynamics is accounted for by implementing a methodology that uses pressure drop data and the mass conservation criterion to describe velocity profiles, including the determination of the viscous and inertial resistances caused by solid surfaces at the core and near the wall. Finally, the heat transfer information is transferred to a pseudo-heterogenous model to simulate the performance of an industrial-scale wall-cooled packed bed reactor for the highly exothermic oxidative dehydrogenation of ethane. Simulations demonstrate both the reliability of the proposed heat transfer approach and the limitations of the conventional approximations when describing temperature profiles in a packed bed reactor.

Radial heat transport in a fixed-bed reactor made of metallic foam pellets: Experiment and particle-resolved computational fluid dynamics

Open-cell metallic foams in the shape of pelletized catalysts are regarded as potential catalyst substrates for the application in fixed-bed reactors. This work reports an experimental study and a detailed Computational Fluid Dynamics (CFD) model to investigate the heat transfer performance of a fixed-bed reactor made of open-cell metallic foam pellets. The steady-state heat transfer behavior of a hot gas flowing through such a packed bed under wall-cooled conditions was examined. The proposed CFD model is in line with the particle-resolved CFD (PRCFD) approach that accounts explicitly for the random packing structure, so that the transport processes in the interstitial regions are fully resolved. The momentum and energy transports inside the highly porous foam particles are considered by closure equations based on the porous-media model. The Rigid Body Dynamics (RBD) method is adopted to create the packing geometry. The axial temperature and the pressure drop obtained by the CFD simulations show good agreement with experimental data. To evaluate the thermal performance, effective heat transport parameters in a packed bed such as the effective radial thermal conductivity and the apparent wall-fluid heat transfer coefficient are determined, with the aid of a 2D pseudo-homogenous plug-flow reactor model. The correlations for heat transport characteristics as a function of particle Reynolds number for the metallic foam packed bed are also presented.

Thermal radiation effects on heat transfer in slender packed-bed reactors: Particle-resolved CFD simulations and 2D modeling

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 1000 spheres and rings with N = 5.1 over 300 < Rep< 2000 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.

Simulation and Experimental Methodology for Virtual Prototyping of Annealed Industrial Coils

The finite element three-dimensional transient model of the annealing process, including conductive and convective heat transfer in an aluminum (Al) coil was developed, implemented, and validated. It combines winding force dependent effective radial thermal conductivity model and the novel convective heat transfer modeling methodology. Experimental validation of the finite element model was performed for two industrial coils having different dimensions, strip thickness and crowning depth. The general agreement between the predicted and measured temperatures for most of the probes was better than 10% at the target material temperature. A series of measurements were configured and performed to supply both the input and validation data for the simulations. The effect of the additional wetted area on the convective heat transfer at the coil base was quantified. The guidelines on the virtual prototyping of the Al coil annealing process were provided, which can be of interest for the process designers.

Enhancing the Thermal Performance of Slender Packed Beds through Internal Heat Fins

Slender packed beds are widely used in the chemical and process industry for heterogeneous catalytic reactions in tube-bundle reactors. Under safety and reaction engineering aspects, good radial heat transfer is of outstanding importance. However, because of local wall effects, the radial heat transport in the vicinity of the reactor wall is hindered. Particle-resolved computational fluid dynamics (CFD) is used to investigate the impact of internal heat fins on the near wall radial heat transport in slender packed beds filled with spherical particles. The simulation results are validated against experimental measurements in terms of particle count and pressure drop. The simulation results show that internal heat fins increase the conductive portion of the radial heat transport close to the reactor wall, leading to an overall increased thermal performance of the system. In a wide flow range (100&lt;Rep&lt;1000), an increase of up to 35% in wall heat transfer coefficient and almost 90% in effective radial thermal conductivity is observed, respectively.

Wall heat transfer coefficient and effective radial conductivity of ceramic foam catalyst supports

In this work, different tubular solid-foam packed-beds were experimentally investigated under air flow in order to determine the effective conductivity and wall-to-bed heat transfer coefficient. Several foam types with different material, namely silicon carbide and alumina, and cell density were tested. Foam samples were experimentally studied using different air flow rates and wall temperatures ranging between 200 and 500°C. Axial and radial steady-state temperatures in the bed were experimentally measured and analysed with a two-dimensional, one-equation model. A Chilton–Colburn-type correlation based on the reactor diameter as characteristic dimension was proposed for the wall-to-bed heat transfer coefficient, which proved good to describe the behaviour of all tested foams. Effective radial thermal conductivity and pressure drop in the foams were also characterized.

Adoption of 3D printed highly conductive periodic open cellular structures as an effective solution to enhance the heat transfer performances of compact Fischer-Tropsch fixed-bed reactors

Heat transfer is universally recognized as a key challenge for the intensification of the Fischer-Tropsch (FT) process in compact fixed-bed reactors. For the first time in the scientific literature we demonstrate experimentally that the adoption of a highly conductive periodic open cellular structure (POCS, 3D-printed in AlSi7Mg0.6 by Selective Laser Melting) packed with catalysts pellets is a promising solution to boost heat exchange in fixed-bed FT reactors. This reactor configuration enabled us to assess the performances of a highly active Co/Pt/Al2O3 catalyst packed into the POCS at process conditions relevant to industrial Fischer-Tropsch operation. Unprecedented performances (CO conversion ≈ 80%) could be thus achieved thanks to an outstanding heat management. In fact, almost flat axial and radial temperature profiles were measured along the catalytic bed even under the most severe process conditions (i.e. high CO conversions corresponding to high volumetric heat duties), demonstrating the effective potential of this reactor concept to manage the strong exothermicity of the FT reaction.The heat transfer of the packed-POCS reactor outperformed both packed-bed and packed-foam reactors, granting smaller radial temperature gradients in the catalytic bed, as well as smaller temperature differences at the reactor wall, with larger volumetric power releases. The strengths of the packed-POCS reactor configuration are its regular geometry, which enhances the effective radial thermal conductivity, and the improved contact between the structure and the reactor wall, which governs the limiting wall heat transfer coefficient.

Effective Radial Thermal Conductivity of a Parallel Channel Corrugated Metal Structured Adsorbent

The effective radial thermal conductivity (keff) of a 2-D analog of a 3-D, parallel channel, corrugated metal, structured adsorbent bed was studied using COMSOL Multiphysics. This 2-D structure con...

Facile preparation of highly thermal conductive ZnAl2O4@Al composites as efficient supports for cobalt-based Fischer-Tropsch synthesis

The development of alternative to silicon carbide (SiC) holds great promise in energy and environmental related catalysis because the harsh preparation process and high cost limit its large-scale application. In this work, the core-shell structured ZnAl2O4@Al ceramic-metal composites (Zn-Al-T) are prepared from low cost metallic Al powder by a facile and environment-friendly approach to replace silicon carbide for Co-based Fischer-Tropsch synthesis (FTS, a typical strong exothermic heterogeneous catalytic reaction). The composition, thermal conductivity, surface chemical properties and pore configuration of the ZnAl2O4@Al composites can be easily modulated by controlling the calcination condition. Among Zn-Al-T composites, the Zn-Al-650 and Zn-Al-750 samples demonstrate optimum coupling of physicochemical properties, i.e., robust chemical stability, meso-macropore structure (wide mesopore and high macroporosity) and high thermal conductivity. Thus, the excellent FT performance (low CH4 selectivity and high selectivity to C5+) was obtained on the Co/Zn-Al-650 and Co/Zn-Al-750 catalysts. The heat transfer experiments were conducted on a special tubular fixed-bed reactor (I.D. = 22 mm) under near-industrial conditions. At similar reaction rates, the effective radial thermal conductivity coefficient (keaff) in the Co/Zn-Al-650 catalyst bed is 3–4 times and 1–2 times that in the Co/Al2O3 and Co/SiC catalyst beds respectively, resulting in a more uniform temperature distribution in Co/Zn-Al-650 catalyst bed. In addition, the ZnAl2O4@Al composite has wide application prospect in strong exothermic/endothermic catalytic system owing to its high thermal conductivity, adjustable physico-chemical properties, facile preparation method and low cost.

Two-dimensional thermal analysis of radial heat transfer of monoliths in small-scale steam methane reforming

Monolithic catalysts have received increasing attention for application in the small-scale steam methane reforming process. The radial heat transfer behaviors of monolith reformers were analyzed by two-dimensional computational fluid dynamic (CFD) modeling. A parameter study was conducted by a large number of simulations focusing on the thermal conductivity of the monolith substrate, washcoat layer, wall gap, radiation heat transfer and the geometric parameters (cell density, porosity and diameter of monolith). The effective radial thermal conductivity of the monolith structure, kr,eff, showed good agreement with predictions made by the pseudo-continuous symmetric model. This influence of the radiation heat transfer is low for highly conductive monoliths. A simplified model has been developed to evaluate the importance of radiation for monolithic reformers under different conditions. A wall gap as thin as 0.05 mm significantly decreased kr,eff, while the radiation heat transfer showed limited improvement. A pseudo-homogenous two-dimensional model combined with the symmetric model has been developed for a quick evaluation of geometric parameters for a monolith reformers. Monolithic reformers based on highly conductive substrates e.g., Ni and SiC showed great potential for small-scale hydrogen production.

Heat transfer in packed-beds of agricultural waste with low rates of air flow applicable to solid-state fermentation

Heat transfer studies were carried out in packed-beds (PBs) heated by the wall and percolated by low air flow rates. Porous media were composed by particles of sugarcane bagasse (SCB) and by a mixture of particles of SCB, orange pulp and peel (OPP) and wheat bran (WB) at proportion SCB:OPP:WB 1:2:2 w/w (composed medium), agricultural waste used as substrates in bioreactors of solid-state fermentation (SSF), an interesting biotechnological application of PBs. Once metabolic heat generated has to be dissipated, heat transfer studies and thermal parameters are required. Tube-to-particle diameter ratio was D/dp = 260, bed height ranged from L = 60 to 180 mm, while air flow rate ranged from 400 to 1200 L/h. Air temperature was 40 °C and wall temperature 65 °C. The outlet bed temperatures (TL) were measured by ring-shaped sensors and by aligned thermocouples. Average temperatures (Tavg) and global heat transfer coefficients (U) were calculated separately for central region of the beds and for wall-vicinity. Radial effective thermal conductivity (Λr) and wall-to-fluid convective heat transfer coefficient (αwall) have been estimated by means of the traditional two-parameters model. Radial temperature profiles at bed outlet were flattened in the central region and convergent at the edge of the packs. The two-regions approximation for U calculations showed to be appropriate for both packs. Global coefficient U, thermal conductivity Λr and convective coefficient αwall increased with increasing air flow rate and decreased with bed height. Λr tended to the stagnant value of the thermal conductivity and αwall were lower than 50 W/m2/°C, addressing the difficulty on removing metabolic heat from PBs of SSF.

Fiber‐Optic Temperature Measurements in Fixed‐Bed Reactors for Model‐Based Evaluation of Effective Radial Thermal Conductivity

AbstractEin vielversprechender Ansatz für die Modellierung von Festbettreaktoren ist das quasihomogene, zweidimensionale Λr(r)‐Modell nach Winterberg. Dieses hat sich bislang nur teilweise bewährt, weil eine zuverlässige Datenbasis zur Validierung fehlte. In diesem Beitrag erfolgt eine Evaluierung des Modells anhand faseroptischer Temperaturprofilmessungen (Messauflösung: 2,56 mm) in einem Rohrreaktor mit technisch relevantem Durchmesser. Die Schüttung im Innern des Rohrreaktors besteht aus sphärischen, porösen Partikeln. Deren physikalische Eigenschaften entsprechen keinem exakten Wert, so dass repräsentative Mittelwerte für die Modellierung ermittelt werden.

Local transport and reaction rates in a fixed bed reactor tube: Endothermic steam methane reforming

Resolved-particle 3-D computational fluid dynamics (CFD) simulations are presented of endothermic steam methane reforming in a random packed bed of 807 spherical catalyst particles at a tube-to-particle diameter ratio of N=5.96 with constant wall heat flux. The fluid flow field is fully coupled to the temperature and species distributions inside the particles. This enables simulation of diffusion, conduction and reaction inside the catalyst particles, as opposed to only surface reactions.The results illustrate 3-D distributions of flow, temperature, species and reaction rates inside a 0.7m length of packed tube. These show large variations on near-wall particle external surfaces, and non-symmetric distributions inside the catalyst particles on cross-sections through the bed. The detailed CFD approach allows statistical analysis of the particle-to-particle reaction rate variations, the correlation of rate with location in the bed, and the intrinsic variability of radial temperature and species mass fraction profiles. Comparisons to a 1-D reactor tube heterogeneous effective medium model showed that axial profiles of cross-sectional average temperature, species and velocity could not be reproduced using particle-fluid heat and mass transfer coefficients estimated from non-reacting simulations in the same tube. Comparisons to a 2-D reactor tube heterogeneous effective medium model showed good agreement with axial profiles if radial local void fractions and axial velocities were included in the model. Improved agreement with radial temperature profiles resulted from the model with a radially-varying effective radial thermal conductivity.

Prediction of thermal behavior of trickle bed reactors: The effect of the pellet shape and size

Heat transfer plays an important role in several applications of packed bed reactors with cocurrent downflow of liquid and gas (widely known as trickle-bed reactor – TBR).A literature survey shows that the amount of articles dealing with the prediction of heat transfer rates between a TBR and an external heating or cooling source is limited for spherical catalyst pellets and definitively scarce for other pellet shapes as cylinders and multilobes.Results from an experimental program devoted to study heat transfer between a TBR and an external jacket, employing spherical and cylindrical particles and a commercial trilobe pellet, are presented. A wide range of gas (air) and liquid (water) flow rates were covered corresponding to low and high interaction regime. A two dimensional pseudohomogeneous model was employed to represent the thermal behavior of the packed bed. Values of the effective radial thermal conductivity and the wall heat transfer coefficient were obtained by regression of radial temperature profiles for three different bed lengths. Finally, expressions to estimate both parameters for the different particle shapes were developed, thus providing a useful predictive tool, not available in the literature up to the best of our knowledge.

Heat transport in catalytic sponge packings in the presence of an exothermal reaction: Characterization by 2D modeling of experiments

Heat transfer in catalytically coated sponge packings (open-cell foams) was investigated by experiments in a tubular cooled-wall reactor while conducting an exothermal reaction. A two-dimensional (2D) reactor model was developed to analyze quantitatively the steady-state temperature distributions, which were measured at 108 different positions in the reaction zone at well-defined reaction conditions of varied severity. The heat transport inside the packings was described by correlations for the effective axial and radial two-phase thermal conductivities. The key model parameters are the effective static two-phase thermal conductivities and the axial and radial dispersion coefficients, which have been assessed for sponge supports made of mullite and of α-Al2O3 with different porosities. The resulting simulations of conversions and spatial temperature distributions were in very good agreement with the experimental data. The reactor model was also used as a predictive tool to evaluate other sponge types. The simulations indicate that packings made of well-conducting solids like SiC or Al-alloys are useful supports for reactions with high enthalpy change, when hot spot or catalyst bed temperatures need to be controlled.

A critical review on heat transfer in trickle bed reactors

AbstractA critical review of the available information about heat transfer between a packed bed with cocurrent downflow of gas and liquid and an external medium was undertaken. Several aspects such as experimental set-ups and methods employed to study heat transfer in trickle bed reactors, models used to interpret experimental data, and literature correlations of heat transfer parameters are addressed. From the analysis of the available experimental information, a refined database has been built, which allows comparing the performance of the existing correlations for the parameters of the extensively employed two-dimensional pseudohomogeneous plug flow model (i.e., effective radial thermal conductivity and wall heat transfer coefficient). In addition, new correlations for effective thermal conductivity have been developed. Identification of gaps in the current knowledge and recommendations for future works are summarized.

Study on Effective Radial Thermal Conductivity of Gas Flow through a Methanol Reactor

Abstract The heat conduction performance of the methanol synthesis reactor is significant for the development of large-scale methanol production. The present work has measured the temperature distribution in the fixed bed at air volumetric flow rate 2.4–7 m3 · h−1, inlet air temperature 160–200°C and heating tube temperature 210–270°C. The effective radial thermal conductivity and effective wall heat transfer coefficient were derived based on the steady-state measurements and the two-dimensional heat transfer model. A correlation was proposed based on the experimental data, which related well the Nusselt number and the effective radial thermal conductivity to the particle Reynolds number ranging from 59.2 to 175.8. The heat transfer model combined with the correlation was used to calculate the temperature profiles. A comparison with the predicated temperature and the measurements was illustrated and the results showed that the predication agreed very well with the experimental results. All the absolute values of the relative errors were less than 10%, and the model was verified by experiments. Comparing the correlations of both this work with previously published showed that there are considerable discrepancies among them due to different experimental conditions. The influence of the particle Reynolds number on the temperature distribution inside the bed was also discussed and it was shown that improving particle Reynolds number contributed to enhance heat transfer in the fixed bed.