Pressure drop measurements and modeling on SiC foams

Foam-structured beds are likely to be the next generation of catalyst supports due to their interesting specific properties (large exchange area, low pressure drop, easy control of external porosity, etc.). Nevertheless, chemical engineering parameters of this new catalyst support types are still not completely clear for the scientific community and many approaches are attempted to solve this problem. SiC foams offer the dual advantages of the interesting properties of structured beds and the intrinsic thermal and mechanical properties of silicon carbide as a catalytic support. In the present work, the problem of pressure drops along foam beds is studied with a new simplistic geometrical model as a first step in the understanding of the peculiar hydrodynamic behavior of SiC foams in chemical processes. The proposed model was successfully validated by experimental results on a relatively large range of parameters which fully confirm the validity of the model.     

Periodic open-cell foams: Pressure drop measurements and modeling of an ideal tetrakaidecahedra packing

Periodic open-cell foams of ideal tetrakaidecahedron geometry were manufactured by selective electron beam melting (SEBM) and characterized with respect to the morphological parameters, namely strut diameter, window diameter and porosity. The pressure drop over these periodic foam samples of different pore size and porosity was determined experimentally. The basic form of the Ergun equation (which contains no empirical coefficients) was modified to develop a new correlation for the prediction of the pressure drop in periodic open-cell foams of ideal tetrakaidecahedron geometry. The correlation was successfully validated by the experimental results of the pressure drop measured for the periodic open-cell foam samples. With the new correlation it is possible to predict the pressure drop in periodic open-cell foams by using only two geometrical parameters, namely the open porosity and the window diameter.The applicability of the new correlation for a large range of porosities was examined by comparing the experimental and simulated friction factors for the porous media with both high (foam structure) and low porosities (packed beds) for a large range of the Reynolds number. It was demonstrated that the correlation can successfully predict the pressure drop of foam structures as well as packed beds.     

Heat transfer performance of NETmix—A novel micro‐meso structured mixer and reactor

NETmix is a novel static mixing technology consisting on a network of unit cells, comprising chambers interconnected by channels. To assess the heat transfer capacity of NETmix, the NUB model was implemented to perform hydrodynamics and heat transfer simulations. Due to the periodic nature of the NETmix structure, two central chambers and six half‐chambers were found to be sufficient to be representative of the whole network. The Nusselt numbers were determined based on the CFD simulations, and when compared with theoretical results for laminar flow between parallel plates, 3–5 times higher Nusselt number values were obtained with NETmix. This observed heat transfer rate enhancement, makes it suitable for fast reactions where heat transfer is crucial. Finally, results obtained from this study show that NETmix presents a heat transfer capacity one order of magnitude greater than microreactors, and 2–5 orders of magnitude greater than the most commonly used devices in industry. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2496–2508, 2017     

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).     

Modeling of dry pressure drop for fully developed gas flow in structured packing using CFD simulations

Dry pressure drop in columns equipped with structured packings is considered to involve two components: drag force due to the direction changes near the column walls and in the transition region between two packing layers rotated to each other by 90°, and friction force between the different gas flows inside the crossing triangular channels and with the packing solid walls. It is believed that in a packed bed with compact sheet density and large packing surface area (above 250 m²/m³), the major contribution of the pressure drop is generated by the friction component.In this paper, a model is proposed to determine the dry pressure drop friction component. The gas is assumed to establish a fully developed turbulent flow inside the structured packing channels. The structured packing geometry consists of a combination of periodic elements. It is shown that the reproduction of one periodic element aerodynamics leads to determine the gas distribution and pressure drop inside the packed bed. Therefore, modeling the dry pressure drop through one periodic element is a meaningful representation of the dry pressure drop over the packing.CFD simulations are carried out on periodic elements using different turbulence models: RNG k−ε, realizable k−ε, and SST k−ω. The best results that agree with the experimental data in the literature are obtained with the SST k−ω model. The CFD model proposed is used to study the impact of packing geometry variations on the dry pressure drop and to bring up a correlation for the pressure drop with respect to changes of packing geometry: channel height dimension, channel opening angle, and corrugation angle.     

Pressure drop measurements of ceramic sponges—Determining the hydraulic diameter

This paper presents experimental results of pressure drop measurements for different solid ceramic sponges. In the experiments, the material, pore sizes and porosity were varied. Furthermore, this data is correlated using an Ergun-type equation. It was possible to obtain Ergun constants for sponges independently of the varied parameters. In the future, the presented pressure drop correlation will provide a simple method for determining hydraulic diameters for solid ceramic sponges with unknown geometric parameters (strut, window and pore diameter,…) based on pressure drop measurements. Furthermore a correlation is given to derive the hydraulic diameter from the ppi (pores per inch) number.     

Evaluation of global biomass devolatilization kinetics in a drop tube reactor with CFD aided experiments

A procedure coupling experimental characterization and computational fluid dynamics (CFD) is developed for providing valuable global kinetic parameters to large applications of biomass fuels (fast pyrolysis, co-combustion and gasification). This is based on an advanced lab-scale apparatus (drop tube reactor), reproducing high heating rates and low residence times at different nominal temperatures (400-800 °C) for particle size of practical interest. Although the relative simplicity of the operation, a detailed and accurate evaluation of the particle residence time and effective thermal history is needed to elaborate suitable global devolatilization kinetics, which differ significantly from low heating rate kinetics (for instance in thermogravimetric balance) and also from those obtained assuming strong hypotheses (e.g. constant particle temperature in the reactor). The developed procedure gives kinetic parameters which are not the intrinsic devolatilization kinetics but global kinetics at high heating rates. These global kinetic parameters are useful to simulate practical systems (characterised by high heating rate) with comprehensive codes (CFD), since detailed particle kinetics require additional sub-models (e.g. of external and internal heat transfer) which may be time consuming and need many data, often known only with uncertainty. In this work CFD is used as both diagnostic and predictive tool; its potentials and drawbacks in aiding advanced experimentation on biomass/coal pyrolysis are discussed.     

Pressure drop across vortex diodes: Experiments and design guidelines

Vortex diodes are used as leaky non-return valves in applications where it is desirable to avoid valves with moving parts. Despite their use in practice for several decades, no clear guidelines for design and optimization of vortex diodes are available. Detailed experimental study on flow and pressure drop characteristics of vortex diodes was therefore carried out to evolve such guidelines. The study covered a wide range of vortex diodes. The variation of diodicity (ratio of pressure drop for reverse and forward flow for the same flow rate) with respect to diode geometry, diode size (d_C), aspect ratio (d_C/h), nozzle configuration and Reynolds number (Re) was studied. The experimental results were critically analyzed to develop a design methodology. The methodology is shown to be useful for obtaining the diode dimensions that would yield the desired diodicity for the required operating flow rate.     

Pressure drop characteristics of flow in a symmetric channel with periodically expanded grooves

Pressure drop characteristics of flow in a periodically grooved channel are investigated experimentally. It is well known that a self-sustained oscillatory flow occurs from a steady-state flow at a certain critical Reynolds number in such grooved channels. The oscillatory flow enhances fluid mixing and leads to an increase in pressure drop. We measure the pressure drop with a pressure transducer. It is found that the pressure drop increases near the critical Reynolds numbers where the two- and three-dimensional oscillatory flows occur. In addition, the three-dimensional flow is confirmed by flow visualization.     

Scale-up in laminar and transient regimes of a multi-stage stirrer, a CFD approach

A multi-stage industrial agitator system adapted to the mixing of a mixture whose viscosity varies during the process has been characterized by using CFD. In the entire study the mixture is supposed to have a Newtonian behavior even though it is rarely the case. It is shown that the well-adapted propeller is able to efficiently blend high viscous media provided the Reynolds number is not too low. A scale-up study of the agitated system has also been carried out by respecting the classical scale-up rules such as the geometrical similarity and the conservation of the power per volume in the particular case of viscous media.Using an Eulerian approach, the hydrodynamics of three different scales with geometrical similarity have been numerically characterized by the energy curve (power number versus Reynolds number) and by the Metzner and Otto constant in which both are required for scale-up procedure. Experimental power measurements have been carried out at the smaller scale so that simulations have been partially validated. New hydrodynamic criteria have also been introduced in order to quantify the flows in the case of a multi-stage stirrer running at low Reynolds number. It has been shown how this hydrodynamic differs dramatically from one scale to another when scale-up at constant energy per volume is applied. From the CFD results, recommendations about the widely used scale-up rules have been suggested and modifications of stirring geometry have been proposed in order to reduce the flow pattern variations during scale-up.     

Pressure drop measurements and hydrodynamic model description of SiC foam composites decorated with SiC nanofiber

During the last decade there has been a growing interest in catalytic reactor engineering based on structured catalytic beds. Compared to traditional packed bed reactors, structured catalytic beds provide improved hydrodynamics and catalytic performance. In this context, silicon carbide (SiC) foam materials seems to be a good candidate for use as catalyst support due to their high geometrical surface area (m⁻¹) and open porosity leading to low pressure drop. However, foam structures have a relatively low specific surface area (m²/g) for performing good anchorage and dispersion of the active phase which is one of the crucial points in catalysis. This study proposes a new type of material which combined the advantage of foam (high porosity) with nanofiber of SiC (high specific surface (m²/g)). The knowledge of pressure drop characteristics of foam with nanofiber is necessary for the future process design. However, due to the complexity of the geometric shape of new foam materials, up to date, no general relationship exists for the calculation of the pressure drop through different foam matrix and generally, empirical equation with modified parameters of the Ergun's equation were needed to fit the data. This study show that a simple model can be used for the prediction of the pressure drop in the SiC foam with nanofiber through Ergun's equation without using any fitting in order to reconcile experimental data with theory.     

The ejector-driven monolith loop reactor — experiments and modeling

A novel catalytic gas–liquid reactor configuration, consisting of a monolithic reactor with a liquid-motive ejector as gas–liquid distributor is introduced as a retrofit or alternative to an agitated slurry reactor. The ejector distributes gas and liquid to the channels of a monolith reactor at velocities greater than those attainable with gravity-driven flow, intensifying mass transfer and reaction in a compact reactor. Pressure drops measured using this configuration do not conform to models from the literature. A strong effect of liquid coalescence properties was observed. Until fully predictive pressure drop and gas–liquid distribution models become available, successful scale-up will depend on pressure-drop data measured with industrial process conditions and fluids. Current literature models for mass transfer underpredict laboratory autoclave reaction results, indicating a need for further model development, and in the interim requiring pilot-scale testing for scale-up purposes.     

Experimental study of a cocurrent upflow packed bed bubble column reactor: pressure drop, holdup and interfacial area

Gas–liquid interfacial areas have been determined by means of chemically enhanced absorption of CO₂ into DEA in a packed bed bubble column reactor with an inner diameter of 156 mm. The influence of the gas velocity and particle diameter on the interfacial areas, pressure drops and liquid holdups has been investigated. For both packings the limiting values of the gas velocities have been determined above which the interfacial areas and liquid holdups stabilize. In particular gas channelling has been found, which is less pronounced in the bed of larger particles.     

CFD modeling of pilot-scale pump-mixer: Single-phase head and power characteristics

The present work involves single-phase computational fluid dynamics (CFD) simulations of continuous flow pump-mixer employing top-shrouded Rushton turbines with trapezoidal blades. Baffle—impeller interaction has been modeled using sliding mesh and multiple reference frame approaches. Standard k-ε model has been used for turbulence modeling. Several CFD runs representing different combinations of geometric and process parameters have been carried out. Results of CFD simulations have been used to find out two macroscopic performance parameters of pump-mixer—power consumption and head generated by the impeller. The simulation results have been compared with the experimental data obtained on a pilot-scale setup. Good agreement between CFD predictions and experimental results is observed. In most cases, sliding mesh approach is found to perform better than multiple reference frame approach. Details from CFD simulations have been used to have an insight into the pumping action of the impeller.     

Pressure drop in pulsed extraction columns with internals of discs and doughnuts

A study on the pressure drop in pulsed extraction columns with internals of immobile discs and rings, usually called Discs and Doughnuts Columns (DDC) is carried out. The local pressure at a desired level of the column is obtained by resolving of turbulent flow model based on Reynolds equations coupled with k–? model of turbulence. Consequently, the pressure drop for a column stage or for a unit of column length is determined. The results are used for development of correlations for determination of pressure drop as a function of plate free area, interplate distance and pulsation parameters – amplitude and frequency. Good correspondence to experimental data is observed. The developed quantitative relations are useful for non-experimental numerical optimization of stage geometry in view of lesser energy consumption.     

Pressure drop and mixing in single phase microreactors: Simplified designs of micromixers

Continuous flow microreactors can greatly improve the safety and product yields of processes in the pharmaceutical and fine chemical industry by overcoming many of the drawbacks of traditional batch and semi-batch stirred reactors. This study compares on a common scale the pressure drop and mixing performance of different size commercial microreactor plates composed of a tangential, SZ-shaped or caterpillar mixer followed by a rectangular serpentine main channel. The pressure drop was fitted to a friction factor model, which suggests that the mixing zone had significant chaotic secondary flow patterns, whereas the main channel did not. Moreover, the mixing zone was the main contributor to the overall pressure drop. Mixing performance was then characterized using competitive parallel reactions. Upon the formation of chaotic secondary flows, typically due to the interactions of artificially induced vortices, the mixer performance was found to be independent of geometry for a given energy dissipation rate. However, the mixer geometry will affect the critical Reynolds number that induces chaotic advection and changes the mixing time scale.     

Pressure drop and bubble-liquid interfacial shear stress in a modified gas non-Newtonian liquid downflow bubble column

A functional form of equation for predicting pressure drop in a modified non-Newtonian downflow bubble column has been formulated. The equation has been developed based on the bubble formation, drag at interface and the wettability effect of the liquid. Also the bubble-liquid interfacial shear stress in two-phase flow is analyzed and correlated with the dynamic, geometric and physical variables. The functional form of equation appears to predict the pressure drop satisfactorily for two-phase dispersed flow in the co-current modified downflow bubble column with carboxy methyl cellulose (CMC) solution in water with different concentrations.     

Prediction of pressure drop and liquid holdup in trickle bed reactor using relative permeability concept in CFD

A Computational Fluid Dynamics (CFD) model based on porous media concept is presented to model the hydrodynamics of two-phase flow in trickle-bed reactors (TBRs). The aim of this study is to develop a comprehensive CFD based model for predicting hydrodynamic parameters in trickle-bed reactors under cold-flow conditions. The two-phase Eulerian model describing the flow domain as a porous region has been used to simulate the macroscale multiphase flow in trickle beds operating under trickle flow regime using FLUENT 6.2 software. The closure terms for phase interactions have been addressed by adopting the relative permeability concept [Sàez, A.E., Carbonell, R.G., 1985. Hydrodynamic parameters for gas-liquid cocurrent flow in packed beds. A.I.Ch.E. Journal 31, 52-62]. The model has been evaluated by comparing predictions with the data (collected under a varied set of laboratory conditions) available in the open literature. It is shown that while being relatively simple in structure, this CFD model is flexible and predictive for a large body of experimental data presented in the open literature.     

Hydrodynamics in a jet bubbling reactor: Experimental research and mathematical modeling

The radial distribution of liquid velocity in the axial direction of a jet bubbling reactor has been measured by experimentation. Three different typical flow structures controlled by liquid jet, gas bubbling, and liquid jet coupled with bubbling are observed. A tank in series model is established on this basis. Calculated values in each region are in good agreement with measured values in jet, bubbling, and wall effect controlled areas. Axial flow rate, radial exchange rate, and jet controlled volume η are analyzed from energy input aspect under different u_g and u_j. Simulation results indicate that under the synergetic action of the liquid jet and gas bubbling effect, jet controlled area exhibits a “spindle” structure, and its size decreases with the increase of u_g. When gas input power occupies about 67% of total energy consumption, the best synergy of liquid jet and gas bubbling is obtained. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1814–1827, 2018