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.     

Determining the specific surface area of ceramic foams: The tetrakaidecahedra model revisited

Silicon carbide foams were characterized with respect to their specific surface area as well as their morphological parameters including strut diameter, window diameter and open porosities. Image analysis, computed tomography, He-pycnometry and mercury intrusion were used for characterization purposes. State-of-the-art correlations (based on different geometrical models for foam structures) for the estimation of the specific surface area were applied and evaluated. Based on the tetrakaidecahedron geometry and different strut morphologies of the foams, new correlations for the specific surface area were developed and successfully validated by comparison with both, own and external experimental data. With the new correlations it is possible to estimate the specific surface area of ceramic foams by using only two measured parameters, namely the window diameter and the open porosity.     

The NETmix reactor: Pressure drop measurements and 3D CFD modeling

NETmix is a new static mixing technology based on a network of mixing chambers interconnected by channels. Three NETmix reactors with different geometries were used to obtain experimental data for pressure drop and a generalized model for pressure drop in NETmix reactors has been developed. This model features a single adjustable parameter and it is only dependent on the geometric configuration of the NETmix design. The Z factor and the power number were also determined to compare the performance of different NETmix configurations with other existing mixers. The dynamic measurement of pressure drop was used to evaluate the mixing dynamics in the NETmix chambers and, above the critical Reynolds number, the natural oscillation frequency was quantified. Furthermore, a three-dimensional computational fluid dynamic transport model was also developed and validated. The energy performance of the three NETmix prototypes was quantified and shown to be very competitive with the compared existing static mixers. The developed 3D CFD transport model, validated by the reported experimental data, enables the computation of transport properties for any geometrical design and fluid properties, and avoids the need for experimental data each time a new NETmix configuration is designed.     

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.     

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.     

CO oxidation over structured carriers: A comparison of ceramic foams, honeycombs and beads

This work aims an experimental comparison of different packings on the basis of their pressure drop, mass and heat transfer properties. Ceramic foams, beads and a honeycomb monolith were used as carriers in the oxidation of carbon monoxide. The carriers were coated with active Pt/SnO₂. The CO oxidation rate was measured in the regime of external diffusion control at superficial gas velocities between 1 and 10 m/s. The volumetric rate coefficients and the pressure drop of packings with similar geometric surface area decreased in the sequence particles > foams > honeycomb. The magnitude of the temperature gradient along the catalytic bed decreased as going from honeycomb over larger particles to foams and small particles. Foams were superior over particle beds from the viewpoint of combined high mass transfer and low-pressure drop. The main advantage of foams as compared to honeycomb resided in the radial mixing enabling a better heat transfer to the reactor walls.     

A predictive model based on tortuosity for pressure drop estimation in ‘slim’ and ‘fat’ foams

The use of porous structures with high external surface area represents an important breakthrough in several industrial applications. Foam structures have received an increasing scientific and industrial interest since the last decade. Knowledge of pressure drop induced by these foam structures is thus essential for successful design and operation of high performance industrial systems. In this context, an analytical investigation was conducted for the determination of the permeability and the inertial coefficient in foams. The theoretical model is based on modified cubic lattice, which allows to take into account the presence of matter at the junction of struts. The existing model developed in the literature is then modified to incorporate this geometrical approach for determining the tortuosity of the foam. Finally, the permeability and inertial coefficient analysis are performed in order to derive the pressure drop on foams. The modeling procedure is based only on physical principles and geometrical considerations with no adjustable parameters in order to reconcile the theoretical work with the experimental data of the literature. Finally, this model is validated for two marginal cases (i.e. ‘slim’ and ‘fat’ foams).     

Statistical distribution of residence time and tortuosity of flow through open-cell foams

A new method to analyse properties such as pressure loss of open-cell foams is given by the rise in computational speed, which makes it possible to handle even the flow within these structures with conventional CFD methods. In the present study air flows through several structures have been calculated explicitly using the standard Navier-Stokes equations. The structures comprised reconstructed tomographic data obtained by means of MRI as well as model structures of various complexity. Numerical determination and variation of tortuosity by closing structure windows provided a possibility to match the pressure drop calculated in modelled structures with experimental literature data.     

气固并流式轴向移动床过滤器的压降特性

通过冷模实验,改变移动床表观气速、颗粒循环速率、入口气体含尘浓度等操作参数,研究了轴向移动床过滤器的压降特性和合适的操作条件,结合移动床内气固两相运动特点,修正了Ergun公式,在加尘条件下分析了床内滤饼对压降稳定性的影响。结果表明,在无尘负荷条件下(“纯”移动床操作),颗粒的循环速率由0增至2.26 kg/(m2?s)时,设备的压降减小0.03 kPa。表观气速为0.126 m/s、入口气体含尘浓度为89.10 g/m3时,移动床内滤饼形成和破损呈动态平衡,过滤500 s后,压降可稳定在0.88 kPa,此时设备具有较高的除尘性能,粉尘捕集效率可达96%以上。     

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 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 gas bypassing in recirculating fluidized beds

The effect of different operating and design parameters on the pressure drop profile for a recirculating fluidized bed has been studied. A mathematical model was developed for the pressure drop in the recirculating fluidized bed. The different parameters considered were flow rate, inventory of solids and spacing between the draft-tube bottom and the distribution plate. Geldart D and B particles were used for the study. The gas bypassing from the jet towards the downcomer was calculated on the basis of the mathematical model and the effect of various parameters on gas bypassing were analyzed.     

Effect of a severe form of initial gas maldistribution on pressure drop of a structured packing bed

The results of an experimental study devoted to establishing the relation between a severe form of initial gas distribution, as created by a chordal blockage set-up used in a recent FRI study, and the hydraulics of a structured packing bed are presented. Both dry and wet bed experiments were conducted with air/water system under ambient conditions, using a 1.4 m i.d. Plexiglas column in conjunction with Montz-pak B1-250 packing bed of the approximately same length, employing liquid loads corresponding to that from the FRI study. From dry and wet experiments it appeared that chordal blanking of 30% of cross-sectional area at gas inlet can influence the pressure drop significantly, particularly that in the lower part of the bed.     

Very-viscous-oil/water/air flow through horizontal pipes: Pressure drop measurement and prediction

Core annular flow pattern, where a low viscosity liquid surrounds a very-viscous one, may be very interesting for heavy oil transportation. However, in oil production, oil and water rarely flow alone and gas is usually present. Despite several publications on liquid-liquid core annular flow, no much work has been done towards a proper characterization of the effect of gas on pressure drop. The aim of this paper is twofold: to provide a new data base on three-phase (very-viscous-oil/water/air) flow, and to propose a simple model for the determination of pressure drop.     

On the modeling of non-Newtonian purely viscous flow through high porosity synthetic foams

In a previous paper a model was proposed for the prediction of non-Newtonian, purely viscous flow, through isotropic high porosity synthetic foams. However, based on work done for creep flow of a Newtonian fluid through two-dimensional arrays of squares, an adaptation to the existing model is discussed and a volumetric partitioning is proposed which facilitates the introduction of possible stagnant regions within the flow domain. Three models, for non-Newtonian purely viscous flow, were derived that allow for various staggering configuration, namely doubly, singly staggered and non-staggered configurations. Results from the proposed model for a doubly staggered configuration compared favorably to experimental pressure gradient data.     

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.     

Evaluation of models and correlations for pressure drop estimation in dense phase pneumatic conveying and an experimental analysis

This study reviews the models and correlations for dense phase conveying in an effort to explore existing and new data on the subject and to provide guidance to the designer on the best pressure drop model. Using various data sets the Mi (Konrad)-based model was found to be best for predicting the pressure drop across dense phase plugs. A series of industrial scale tests also shows agreement with the Mi (Konrad)-based model.