Modeling Of Transport Phenomena Research Articles

CFD modeling of a fixed-bed biofilm reactor coupling hydrodynamics and biokinetics

Rigorous modeling of transport phenomena is essential to reproduce accurately biofiltration systems performance. In this sense, the aim of this study was to investigate the effect of integrating fluid flow dynamics in the development of these bioreactor models, mimicking their hydrodynamics and behavior in a fixed biofilm reactor. 2D bioreactor models were developed using three different well-established tools for modeling bioreactors (AQUASIM, MATLAB, and Computational Fluid Dynamics – CFD), considering from ideal flow patterns to more complex fluid dynamics. A detailed comparison was performed among the results, taking into account the simulation of dissolved oxygen profiles in the liquid phase, inside the biofilm and in the boundary layer along a bioreactor. These models were validated by comparing the simulations with direct measurements obtained by means of dissolved oxygen microsensors of high spatial resolution. In all cases, deviations were below 6%, nevertheless CFD predictions obtained the lowest deviations below 3.5%. Thus, these results underline that CFD techniques are appropriate to model more accurately the performance of fixed-bed biofilm reactors, allowing the study in detail of all the hydrodynamics variables involved in the process. In addition, a 3D CFD model, combining hydrodynamics and biological reactions, was developed and solved to simulate local transient flow and dynamic behaviors of oxygen consumption in the bioreactor. The results of CFD simulations were evaluated in order to know the effect of mass transport phenomena (advection and diffusion) by characterizing hydrodynamics and, finally, to predict the oxygen degradation along the bioreactor.

Numerical modeling of interfacial heat and mass transport phenomena during a phase change using ANSYS-Fluent

ABSTRACTNumerical modeling of phase change requires accurate estimations of heat and mass transport at the interface. The present work develops a model in ANSYS-Fluent with user-defined functions to address phase change with a planar interface. An interface boundary method determines the heat fluxes with the exact location of the interface without interpolation functions. Five cases are analyzed based on the classic Stefan problem for validating the model. The numerical model is validated against closed form theoretical solutions with agreement within 0.55%. This work can be extended to include curvature effects and the interaction between the interface and heterogeneous surfaces.

Modeling Transport Phenomena in Selective Catalytic Reductant Catalytic Converter with NH3 as Reductant for NO Degradation

In the current study, reduction of nitrogen oxide from exhaust gas in the presence of NH3 as reductant on selective catalytic reductant (SCR) impregnated catalytic converter was simulated using Comsol© software. Mass transfer (one-dimensional) and heat transfer (three-dimensional) governing equations were taken into account to model the unsteady state behavior of the catalytic converter. Modeling results of reaction rate indicated good agreement with the experimental data. Results showed that the cumulative conversion exceeded 98 percent for both NO and NH3 components in the outflow gas emitted from the converter. In addition, temperature distribution graphs showed that the exhaust gas temperature varied from 450 K at the converter inlet to 550 K at the outlet. According to the results, the temperature tolerance inside the converter was less than 20 °C. Moreover, radial temperature gradient was sharper than axial one because of lesser energy accumulation in the direction of the convective flow.

Uncertainty quantification in modelling equiaxed alloy solidification

Numerical simulations can provide insight into physical phenomena during alloy solidification processes that cannot be observed experimentally. These model predictions depend on the material, process and numerical parameters which contain inherit uncertainties due to their origin in experimental measurements or model assumptions. As a step towards understanding the effect of uncertain inputs on solidification process modelling, uncertainty quantification and sensitivity analysis are performed on a transient model of transport phenomena during the solidification of grain refined Al-4.5 wt.% Cu in a rectangular cavity. The effect of microstructural model parameters, thermal boundary conditions and material property input uncertainties are examined for their effect on macrosegregation levels and solidification time. Predictions of the macrosegregation level are most sensitive to the dendrite arm spacing of the rigid mushy zone.

Multiscale modelling of transport phenomena for materials with n-layered embedded fibres. Part II: Investigation of fibre packing effects

The case of molecular diffusion is investigated and a method is proposed to predict the effective diffusion properties of transversely isotropic composite materials. This paper is the second one of a set of two consecutive papers published in this volume. The general modelling strategy was devised in the first paper (Hervé-Luanco and Joannès, 2016) and applied to the biphasic case in this one. Closed-form analytical expressions are given to investigate fibre packing effects on the effective transverse diffusivity of any unidirectional composite. The specific case of insulated fibres embedded in a diffusive matrix is studied and a clear procedure is then described to determine the model parameters. It is worth noting that only a very simple cross-section image analysis of the unidirectional composite medium is required to provide the two morphological parameters needed to predict the overall diffusivity tensor. Finally, an application on a real microstructure is provided to demonstrate the efficiency of the suggested turnkey method. Very simple analytical calculations make possible parametric studies less expensive than numerical or experimental characterizations.

Modeling of transport phenomena in fixed-bed reactors for the Fischer-Tropsch reaction: a brief literature review

Abstract Currently, few processes can be considered practical alternatives to the use of petroleum for liquid fuel production. Among these alternatives, the Fischer-Tropsch synthesis (FTS) reaction has been successfully applied commercially. Nevertheless, many of the fundamentals of this process are difficult to understand because of its complexity, which depends strongly on the catalyst and the reactor design and operating conditions, as the reaction is seriously affected by mass and heat transport issues. Thus, studying this reaction system with transport phenomena models can help to elucidate the impact of different parameters on the reaction. According to the literature, modeling FTS systems with 1D models provides valuable information for understanding the phenomena that occur during this process. However, 2D models must be used to simulate the reactor to correctly predict the reactor variables, particularly the temperature, which is a critical parameter to achieve a suitable distribution of products during the reaction. Thus, this work provides a general resume of the current findings on the modeling of transport phenomena on a particle/pellet level in a tubular fixed-bed reactor.

Mathematical modeling of transport phenomena during waterpipe smoking—a parametric study

Waterpipe (WP) smoking has spread worldwide and emerged as a global health issue in recent years. Yet only little is known on the details of transport phenomena and the compositions of smoke and particulates released during WP smoking. In this paper a general mathematical model is developed to study various processes occurring during the use of a WP. The model is used to assess the role of various design and operating conditions on the WP performance. In particular, the influence of water temperature, diameter of body pipe, depth of WP body immersed in the water, puff volume, water volume and puff frequency on the bubble hydrodynamics, the gaseous phase absorption and the removal of aerosols has been studied. Numerical results have indicated that the rate of gas absorption increases with the increase in depth of WP body immersed in the water, puff volume and the amount of water, and also with decrease in water temperature, diameter of body pipe and puff frequency. In addition, the removal of aerosols is improved with the increase in depth, radius and density of particles. The model results have also revealed that the major part of the pressure drop occurs in the water bowl.

Neoclassical toroidal plasma viscosity with effects of finite banana width for finite aspect ratio tokamaks

Theory for neoclassical toroidal plasma viscosity has been developed to model transport phenomena, especially, toroidal plasma rotation for tokamaks with broken symmetry. Theoretical predictions are in agreement with the results of the numerical codes in the large aspect ratio limit. The theory has since been extended to include effects of finite aspect ratio and finite plasma β. Here, β is the ratio of the plasma thermal pressure to the magnetic field pressure. However, there are cases where the radial wavelength of the self-consistent perturbed magnetic field strength B on the perturbed magnetic surface is comparable to the width of the trapped particles, i.e., bananas. To accommodate those cases, the theory for neoclassical toroidal plasma viscosity is further extended here to include the effects of the finite banana width. The extended theory is developed using the orbit averaged drift kinetic equation in the low collisionality regimes. The results of the theory can now be used to model plasma transport, including toroidal plasma rotation, in real finite aspect ratio, and finite plasma β tokamaks with the radial wavelength of the perturbed symmetry breaking magnetic field strength comparable to or longer than the banana width.

Multiscale modelling of transport phenomena for materials with n-layered embedded fibres. Part I: Analytical and numerical-based approaches

• The overall diffusivity tensor of a multi-layered fibre-reinforced material is given. • Diffusivity is derived from a Morphological Representative Pattern-based approach. • Closed-form analytical relations are proposed depending on morphological parameters. • Diffusivity effects of interphase areas are investigated. Numerical and analytical modelling approaches are often competing to describe a desired phenomenon. However, there is no reason to look for a single method and complementarities between distinct modelling ways are always profitable. This paper, the first of a set of two consecutive papers published in this volume, provides such a modelling methods reconciliation in the case of transport phenomena acting in transversely isotropic multi-phased materials. Microstructural Finite Element Modelling (FEM) helps supplying the analytical implementation for a better description of interactions between the constituents. As an application example, the case of molecular diffusion within a unidirectional composite medium is investigated without any restriction for considering any other transport mechanism. Based on a rational microstructure description, this study proposes a model able to predict the overall diffusion tensor of the composite and investigates more particularly diffusivity effects of interphase areas and fibre packings. For this purpose, a “ n -phase” Generalized Self-Consistent Scheme (GSCS) coupled with a Morphologically Representative Pattern (MRP) approach has been developed. This first part is focused on the modelling strategy and the concept of “transfer matrices” has been used. This approach is applied in Part II (Joannès and Hervé-Luanco, 2016) to study the influence of fibre packings on the effective behaviour of composite materials made of insulated fibres embedded in a diffusive matrix.

Modeling transport phenomena of ice slurry in an ice forming unit

In this article, multiphase convective and solidification transport phenomena of ice slurry is investigated by developing a one-domain macroscopic model to simulate its formation in a rectangular ice forming unit. Convection, sedimentation, interfacial drag, permeability, remelting and viscosity variations are incorporated into this model through the appropriate governing multiphase transport equations. Validation studies with literature data are performed to determine the most suitable drag law by comparing the position of the interface between the coherent and non-coherent zones. After establishing modified Stokes' Law as the best-suited drag model, solidification study of an aqueous ammonium chloride solution is performed. The results for the evolution of ice fraction, species distribution, temperature profile and multiphase velocity field are presented. Solid fraction gradient, due to the generation of ice particles, has a major influence on the density gradient leading to a counter-clockwise flow current resulting in the homogenization of temperature and species in the generated ice slurry.

Finite Element Simulation of Nonlinear Convective Heat and Mass Transfer in a Micropolar Fluid-Filled Enclosure with Rayleigh Number Effects

A mathematical model is presented to study the double-diffusive convective heat and mass transfer of a micropolar biofluid in a rectangular enclosure, as a model of transport phenomena in a bioreactor. The vertical walls of the enclosure are maintained at constant but different temperatures and concentrations. The conservation equations for linear momentum, angular momentum, energy and species concentration are formulated subject to appropriate boundary conditions and solved using both finite element and finite difference numerical techniques. Results are shown to be in excellent agreement between these methods. Several special cases of the flow regime are discussed. The distributions for streamline, isotemperature, isoconcentration and (isomicrorotation) are presented graphically for different Lewis number, buoyancy parameter, micropolar vortex viscosity parameter, gyration viscosity parameter, Rayleigh number, Prandtl number and micro-inertia parameter. Micropolar material parameters are shown to considerably influence the flow regime. The flow model has important applications in hybrid aerobic bioreactor systems exploiting rheological suspensions e.g. fermentation.

Effects of laser beam spatial distribution on laser-material interaction

The efficiency of any laser materials processing depends on the efficient energy transfer from the laser to a substrate. One of the critical factors in the process is the spatial distribution or the “mode” of the laser beam. Although an inverse Bremsstrahlung initiates the photon to electron energy transfer, a major part of the process is transport phenomena created by the absorbed energy. A mathematical model for transport phenomena during laser materials interaction is developed that includes multiple reflections, capillary and thermocapillary forces, recoil pressure, temperature distribution, melt pool flow, and phase changes. This model simulates interaction between a CO2 laser (λ = 10.6 μm) with four different spatial distributions and iron. The results of a simulation for fundamental understanding of this laser-material interaction are presented in this paper. First, overall keyhole behaviors are compared in terms of response time, penetration hole geometry, and absorptivity. Furthermore, a dimensionless parameter is developed to examine keyhole collapse quantitatively. Finally, velocity, temperature, and, intensity fields are analyzed.

Modeling Transport Phenomena in Ammonia Fuel Cells

Introduction Ammonia has been considered as a potential fuel for alkaline fuel cells. Ammonia can be produced at low cost, and inexpensive catalysts can be used in Ammonia Fuel Cells (AFC) [1, 2]. In AFC, ammonia is oxidized at the anode side and OH-, nitrogen and water are produced (1). OH- anion moves through membrane and reduced into water at the cathode side (2). 1/3 NH3 + OH- ↔ 1/6 N2 + H2O + e-, E0=0.40V ----- Eqn. 1 1/4 O2 + 1/2 H2O + e- ↔ OH-, E0=0.40V ----- Eqn. 2 The theoretical open-circuit voltage (OCV) of the AFC is 1.17 V at standard conditions. The value is less than that of Hydrogen Fuel Cells (HFC), but AFC has a higher energy efficiency, 88.7%, than HFC of 83% [1]. Performance and durability of hydrogen PEM fuel cells has been improved over the last decade by extensive experiments and computations. In particular, continuum modeling has been an important tool for understanding and insight into processes and phenomena, which cannot be captured through experiments [3]. Recently, AFCs have attracted the attention of fuel cell researchers due to its high potential for a clean future energy device. However, AFCs show some problems in related to mass transfer and fuel crossover in the membrane electrode assembly. In this study, transport phenomena in AFCs are analyzed using a computational model. Objective When the AFC is in operation, complex phenomena occur in the Membrane Electrode Assembly (MEA) including mass and heat transfer, electrochemical reactions, and charge (OH- and electron) transport (Fig.1). Therefore, a continuum model was developed to simulate the phenomena in MEA. Figure 1. Illustration of Mass Transport in Membrane Electrode Assembly depicting individual layers and chemical components. cCL and aCL depict the cathode and anode catalyst layers respectively, while cGDL and aGDL depict the cathode and anode gas diffusion layers respectively. Results Using the model, potential and species distribution in MEA, and the extent of electrochemical reaction in catalyst layer were calculated. In addition, the effect of different operating conditions on these phenomena were analyzed. These results, along with the effect of water transfer and ammonia crossover on cell performance will be discussed. Detailed accounts of the governing equations and their numerical solving procedure will also be provided.

(Invited) Interfacial and Transport Phenomena in Hybrid Pseudocapacitors

Electrochemical capacitors have attracted significant attention in recent years due to their promise as electrical energy storage devices for high energy and power applications. They are typically classified as either electric double layer capacitors (EDLCs) or pseudocapacitors depending on the energy storage mechanism. EDLCs store energy physically in the electric double layers (EDLs) forming near the electrode/electrolyte interfaces. Thus, EDLCs feature highly reversible charge storage and long cycle life. However, their energy density remains low compared with that of batteries. On the other hand, pseudocapacitors store energy via the electric double layers as well as via reversible oxidation-reduction (redox) reactions with or without insertion or intercalation. Pseudocapacitors tend to feature larger capacitances and energy densities than EDLCs because the amount of charge they can store is not limited by the surface area of the electrode/electrolyte interface. Finally, hybrid pseudocapacitors are devices combining a pseudocapacitive electrode made of a porous transition metal oxide (e.g., RuO2, MnO2, Nb2O5, MoO3) and an EDLC-type electrode typically made of porous carbon. This invited talk will present recent advances in physical modeling of interfacial, transport, and electrochemical phenomena in pseudocapacitors. It aims to provide physical interpretation of cyclic voltammograms obtained experimentally either from hybrid pseudocapacitors or from pseudocapacitive electrodes using three-electrode systems. First, it will present a continuum model simultaneously accounting for (i) charge transport in electrodes and electrolyte, (ii) the dynamics of the electric double layer, (iii) steric repulsion due to finite ion sizes, (iv) redox reactions, and (v) intercalation. Second, it will report selected numerical simulations of CV curves for different electrode thickness and electron and ion transport properties in the electrodes and electrolyte, representative of actual situations. These results will be used to elucidate the respective contributions of faradaic reactions and electric double layer formation to charge storage in pseudocapacitors. Particular attention will be paid to the so-called b-value characterizing the power law evolution of the total current with respect to scan rate for a given potential. Special effort will be made to systematically compare model predictions with experimental data.

Stationary Currents in Particle Systems with Constrained Hopping Rates

Abstract We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of zero range processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced by Cirillo et al. (Does communication enhance pedestrians transport in the dark? To appear in C. R. Mécanique 344 (2016), 19–23) and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians, but finds also applications in the modeling of various transport phenomena.

Determination of thermal conductivity of baled agricultural biomass

Modeling of transport phenomena in materials with porous bed features requires thermophysical properties, such as porosity, permeability and thermal conductivity be known.The paper presents experimental data obtained in the course of investigation focused on analysis of stagnant thermal conductivity of biomass. Experiments were conducted using a custom designed and constructed experimental setup and implementing original experimental procedure. Results obtained enabled stagnant thermal conductivity of biomass to be determined for different biomass porosity values.Analysis of the experimental data enabled functional dependence of stagnant thermal conductivity on porosity to be determined, with porosity varied in a range 0.50–0.85. Results obtained indicate that reduced bed porosity, down to the value of 0.65, causes stagnant thermal conductivity of the bed to be reduced. Further porosity reduction, below the value of 0.65, results in increased stagnant thermal conductivity of the bed.Experimental procedure developed shall be useful for gathering experimental data on different materials planned to be analyzed when examining transport phenomena occurring during combustion of biomass bales. In addition, data to be acquired shall be helpful in modeling the transport phenomena associated with combustion in porous beds.

The Role of Transport Phenomena and Modeling in the Development of Thermal Plasma Technology

A brief overview is presented of the principal areas where thermal plasmas had a significant technological impact over the past century. This is followed by an analysis of the specific role played by modelling and studies of transport phenomena under plasma conditions for three specific examples. The first dealing with the development of inductively coupled plasma sources. The following two examples deals with process development for the in-flight melting and spheroidization of powders, and the synthesis of nano-powders. Emphasis is placed on the critical role of plasma–particle interactions under dense loading conditions. A proposal is made for a relatively simple thermodynamic model which can be used for the estimation of the theoretical limits for the processing rates possible with different powders in each of these two cases. The model takes into account radiative energy losses from the surface of the particles and from the formed vapor cloud in the plasma, as well as the residual energy in the gases at the exit of the plasma reactor which are not accessible for process needs.

Plasma arc and weld pool coupled modeling of transport phenomena in keyhole welding

Plasma arc welding involves intricate thermal, electrical, magnetic and fluid dynamics phenomena. To date, tremendous research has been carried out on the weld pool or the thermal plasma arc separately. Yet few studies have integrated the both aspects, much less the keyhole effect in addition. Accordingly, as an endeavor to advance the understanding of the transport phenomena in keyhole welding with plasma arc, a unified model coupling plasma arc and weld pool has been developed to help gain access to the more complete knowledge of energy conversion in the thermal plasma process and heat transfer to the weld pool with the consideration of keyhole effect. By solving a series of governing equations that contain the mass, the momentum and the combined thermal, electric and magnetic energy, both temperature and velocity fields in the arc region and in the weld pool were exhibited. Results show that about 10% of plasma arc outflows from the keyhole exit. The heat conduction flux is more than two times of the electron condensation flux in the welding process. It is also found that the Marangoni shear takes obvious priority over the electromagnetic force, and two circular flows appear in the weld pool. Moreover, arc flows, electrical potential, current density and electromagnetic force were all predicted to further the understanding of thermal plasma process. Two velocity-transition points were found within the keyhole, from which the arc begins to flow outwards and upwards and finally outflows through the top metal surface. Finally, experiment was conducted on the stainless steel plate, and the measured weld pool is close to that calculated by our model.

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

The paper presents the potential of an efficient front tracking method on a fixed control-volume grid in micro–macroscopic numerical modeling of both binary alloy solidification and a solid–liquid phase transition of single-component or doped optically functioning materials. In the former case, the method, basing on the assumption that an envelope of columnar dendrite tips moves locally according to a single crystal growth law, allows more precise identification of zones of different dendritic structures developing within the two-phase region, and thus more detailed analysis of some closing models. It is shown, by exploiting the commonly used benchmark problem that a porous medium model of the columnar mush must be carefully chosen since it strongly affects the predicted macro-segregation pattern. In the case of solidification of a single-component or doped semi-transparent material the combination of the front tracking method with the immersed boundary technique provides a new simulation method, which can handle different thermo-physical and optical properties of liquid and solid phases, processes of emission, absorption, reflection and refraction or transmission of thermal radiation at a diffusive or specular distinct solid–liquid interface detected by the front tracking technique. The method has been used in a detailed parametric analysis where the impact of different optical configurations of both phases and their various optical properties as well as variable transmissivity of solid–liquid interface on the phase change process development has been addressed.

Influence of the Interfacial Water Transfer on the Analysis of Dynamic Sorption and Desorption Experiments in Nafion® Membrane

Water sorption and desorption in Nafion ® 117 membranes in acid form were studied by means of dynamic experiments as a response of relative humidity steps from 20% to 80% using a balance IGASORP (Hiden Isochema Ltd) which allows the measurement of very small mass variations with an accuracy of about 1 mg. The recorded mass variations with time of the membrane samples were analyzed by means of the least squares method based on a model that takes into account a transfer resistance at the interface between the membrane and the surrounding humid gas [1]. As the diffusion time is small (the diffusion coefficient being large), the diffusive internal resistance can be neglected compared to the interfacial resistance so that the water content of the membrane can be assumed uniform, which was confirmed using NMR imaging [2]. The model predicts than the kinetics of sorption is much faster than the kinetics of desorption, and the comparisons with the experimental results show a good agreement and give the value of the corresponding mass transfer coefficients (Figure 1). These results also agree with the results reported by Satterfield and Benziger [3] and they contribute to the debate concerning the existence of an interfacial resistance as reported in the recent review of Weber et al. [4]. For the experimental conditions considered in this study, the membrane is in equilibrium with the humid gas at the interface but the main resistance to water transfer is located in the humid gas phase. REFERENCES C.W. Monroe, T. Romero,W. Merida, M. Eikerling, Journal of Membrane Science 324 (2008) 1-6M. Klein, J.-C. Perrin, S. Leclerc, L. Guendouz, J. Dillet and O. Lottin, ECS Transactions, 58 (1) 283-289 (2013)M.B. Satterfield and J.B. Benziger, Non-Fickian vapor sorption dynamics by Nafion membranes, J. Phys. Chem. B, 2008, 3693-3704Weber et al. A critical review of modeling transport phenomena in polymer-electrolyte fuel cells. Journal of the electrochemical society, 161 (12), F1254-F1299 (2014) Figure 1