Phase Conservation Equations Research Articles

Experimental and numerical investigation of iron ore pellet firing using coupled CFD-DEM method

Iron ore pellets are the main feedstock in ironmaking processes. While extensive research has addressed numerical modeling of the iron ore pellet induration process, little effort has been made to describe the intricate thermochemical processes occurring within the reactor starting from the pellet and particularly at the intra-particle scale. In this regard, discrete-continuous methods like CFD-DEM can generate more realistic, irregular particle assemblies, which leads to significantly more accurate predictions of voidage variation, wall effects, temperature distribution, and associated mass transfer phenomena. This study presents a numerical model based on computational fluid dynamics (CFD) coupled with the discrete element method (DEM) to simulate the thermal induration process of iron ore pellets. The presented model solving heat, mass, and momentum conservation equations for both continuous and discrete phases, provides detailed information on the thermochemical aspects of the process. Pilot-scale induration experiment was conducted to validate model predictions in terms of thermal history and final conversion fraction. It was found that inlet charge specifications, such as particle and pellet size, significantly impact the productivity of pelletizing plants, highlighting the potential of the presented model to optimize the process and improve plant productivity.

Analysis of Rod Withdrawal at Power (RWAP) Accident using ATHLET Mod 2.2 Cycle A and RELAP5/mod 3.3 Codes

The system code ATHLET (Analysis of THermal-hydraulics of Leaks and Transients) is being developed by the Gesellschaft für Anlagen-und Reaktorsicherheit (GRS) mbH in Garching, Germany. In the paper, an overview of activities performed at Faculty of Electrical Engineering and Computing (FER), University of Zagreb, in application of system code ATHLET in transient analyses for NPP Krško (NEK) is presented. Newly, the NEK input deck for the released ATHLET version (Mod 2.2 Cycle A) has been developed. For that purpose, the NEK data base that has been developed and maintained at FER for the last two decades primarily for development of standard input deck for RELAP5 code was used. The ATHLET model has been validated by analyzing the Rod Withdrawal At Power (RWAP) accident at nominal power. The results for steady state calculation as well as RWAP transient were assessed against the analysis performed by RELAP5/mod 3.3 code. In both ATHLET and RELAP5 calculation, the RWAP accident was simulated by constant reactivity insertion rate equal to 2.4 pcm/sec. For ATHLET analysis, two fluid dynamic options were tested for the primary side: a) base case analysis with 5 conservation equations and mixture level model and b) two-fluid model with separate conservation equations for liquid and vapour phases for all the volumes except for the pressurizer where 5 equations+mixture level model was retained. The Steam Generators (SGs) were built using basic ATHLET elements together with the dedicated separator model. For RELAP5/mod 3.3 analysis, a standard option with thermal and mechanical non-equilibrium (6 equations) was used. The results of the steady state calculation for the ATHLET model have shown a very good agreement with RELAP5 calculation. In the transient analysis very small differences for the main physical parameters between ATHLET and RELAP5 as well as between the two ATHLET models were obtained.

Computational Modeling of Bubbles Growth Using the Coupled Level Set-Volume of Fluid Method.

Understanding the generation, growth, and dynamics of bubbles as they absorb or release dissolved gas in reactive flows is crucial for optimizing the efficiency of electrochemically gas-evolving systems like alkaline water electrolysis or hydrogen production. To better model these bubbly flow systems, we use a coupled level set and volume of fluid approach integrated with a one-fluid transport of species model to study the dynamics of stationary and rising bubbles in reactive two-phase flows. To accomplish this, source terms are incorporated into the continuity and phase conservation equations to allow the bubble to grow or shrink as the species moves through the interface. Verification of the hydrodynamics of the solver for non-reactive systems demonstrates the requisite high fidelity interface capturing and mass conservation necessary to incorporate transport of species. In reactive systems where the species impacts the bubble volume, the model reproduces the theoretically predicted and experimentally measured diffusion-controlled growth rate (i.e., R(t) ∝ t0.5). The model is then applied to rising bubbles to demonstrate the impact of transport of species on both the bubble velocity and shape as well as the concentration field in its wake. This improved model enables the incorporation of electric fields and chemical reactions that are essential for studying the physicochemical hydrodynamics in multiphysics systems.

Numerical Solotion of a Problem of Fluid Filtration in a Viscoelastic Porous Medium

The paper considers a model for filtering a viscous incompressible fluid in a deformable porous medium. The filtration process can be described by a system consisting of mass conservation equations for liquid and solid phases, Darcy's law, rheological relation for a porous medium, and the law of conservation of balance of forces. This paper assumes that the poroelastic medium has both viscous and elastic properties. In the one-dimensional case, the transition to Lagrange variables allows us to reduce the initial system of governing equations to a system of two equations for effective pressure and porosity, respectively. The aim of the work is a numerical study of the emerging initial-boundary value problem. Paragraph 1 gives the statement of the problem and a brief review of the literature on works close to this topic. In paragraph 2, the initial system of equations is transformed, as a result of which a second-order equation for effective pressure and the first-order equation for porosity arise. Paragraph 3 proposes an algorithm to solve the initial-boundary value problem numerically. A difference scheme for the heat equation with the righthand side and a Runge–Kutta second-order approximation scheme are used for numerical implementation.

OpenFOAM을 이용한 EOM 기반 2차원 수치 파 생성에 관한 파라메트릭 연구

The consistency of the initially designed waves in the domain is essential for accurate calculation of the added resistance in waves through CFD. In particular, unwanted reflected waves at domain boundaries can cause incorrect numerical solutions due to the superposition with initially designed waves. Euler Overlay Method(EOM) is one of the methods for reducing wave reflections by adding an additional source term to momentum and phase conservation equations, respectively. In this study, we apply the Euler Overlay Method(EOM) to the open-source CFD library, OpenFOAM®, to simulate the accurate free-surface waves in the domain and the parametric study is performed for efficient implementation of Euler Overlay Method(EOM). Considering that the damping efficiency depends on the selection of the overlay parameter in the added source terms, the size of overlay zone and the wave steepness, the influences of these factors are tested through the wave elevation measured at constant time intervals in the 2D numerical wave tank. Through this process, guidelines for selection of optimal overlay parameter and overlay zone size that can be applied according to the scaling law are finally presented.

A general formulation of relative motion between two phases in sediment-laden water flows

A general formulation for the relative velocity between the two phases in sediment-laden water flows is established in this study. The purpose of this effort is to obtain more affordable tools for the simulation of sediment-laden flows at different scales. To this end, an enhanced Eulerian–Eulerian two-phase flow model, which encompasses the mass and momentum conservation equations for both water and sediment phases and a modified k−ɛ model including sediment effects on fluid turbulence, is first presented and then validated for steady-state, open-channel as well as oscillatory flows. Starting from the aforementioned two-phase flow model, the relative velocity between the two phases is obtained by manipulating the momentum equations for the two phases, thus leading to a simplified expression which saves computational time. Based on numerical experiments, it is found that that in the vertical direction pressure and shear stress are predominant as compared to other factors, while in the horizontal direction, lift force and advection effect are also important to some extent, particularly when accurate results are expected. Interestingly, the simplified form of the formulation is shown to provide similar accuracy as the two-phase flow model does.

A fully-coupled gas-water two phase productivity equations for low-permeability CBM wells

To date, much attention has been focused on the high-permeability CBM reservoirs, which results in ignorance of pressure and saturation gradients in the coal seams of previous productivity equations. However, for the low-permeability CBM reservoirs (<1 mD), the pressure and saturation gradients are too large to be neglected during the production process. The CBM reservoirs exhibit stress-dependent permeability changes during early dewatering operation and a strong matrix-shrinkage effect once below the desorption pressure. Thus, considering the pressure profile will enable us to capture the absolute permeability profile in the coal seams. In addition, the gas-water two phase flow will further aggravate the complexity of this issue. Similarity, considering the saturation profile will enable us to capture the relative permeability profile of gas/water phase in the coal seams. Hence, the objective of this research is to develop the productivity equations for low-permeability CBM wells considering both pressure and saturation gradients. Firstly, the previous gas/water phase pseudo-pressure is modified by considering the gas/water phase effective permeability. Secondly, on the basis of gas-water two phase conservation equations of mass and momentum, the relationship between pressure and saturation is established through rigorously derivation. Subsequently, combined with gas-water two phase relative permeability curve, we present an iterative algorithm to obtain the pressure-saturation relationship. As a result, the gas/water phase effective permeability can be described as the unique function of pressure. Finally, according to the relationship between gas/water phase effective permeability and pressure, the fully-coupled productivity equations for low-permeability CBM wells are developed. The reliability of the proposed equations is successfully validated through comparisons with commercial numerical simulation and previous productivity equations. After that, the analysis of sensitive factors is implemented to quantify the corresponding effects on production performance and several key implications are drawn.

A multiphase flow in the antroduodenum: some results of the mathematical modelling and computational simulation

This work is devoted to a problem of creation of a multiphase flow model in an antroduodenum that includes the lower part of the stomach and the upper part of the small intestine (duodenum). The mathematical model is developed for the next purposes: description of the process of digestion in normal physiological state and with functional disorders, prediction of the flow characteristics in distinct conditions. The antroduodenum is considered as a complex form canal with moving boundaries. The mathematical statement of the problem includes mass and momentum conservation equations for phases and components as well as initial and boundary conditions with peristaltic movement. To describe secretion and absorption processes we use mass sources/sinks in a layer adjacent to the tract wall. Using computational simulation we got the digestion processes characteristics in dynamic: pH of the medium, components and phases velocities and fractions. In some scenarios with secretory and motor disorders we identified zones of abnormal acidity. The results of the simulation showed that motor functionality of the antrum and pyloric sphincter affect the stomach evacuation. Additionally, the chemical absorption rate is analyzed in scenarios with distinct food parameters (size, viscosity, density).

Inter-group mass transfer modeling in the two-group two-fluid model with interfacial area transport equation in condensing flow

The two-group two-fluid model with interfacial area transport equation is analyzed in gas-dispersed condensing flow. Past work on the inter-group mass transfer model, required for closure of the dispersed phase conservation equations and interfacial area transport equations, has only considered the condition of expansion of group-1 bubbles to group-2 bubbles with inter-group transfer from group-2 to group-1 only through group-2 breakup. However, in condensing flows, the condensation of large group-2 bubbles provide a significant source of mass and interfacial area to group-1 bubbles. Therefore, the inter-group mass transfer model is revisited in this work to derive a more general form suitable to any heat transfer and pressure change condition. The resulting model requires a second inter-group transfer coefficient. In analogy to the original model, a general case of the group distributions is considered to describe a preliminary treatment of the new inter-group transfer coefficients. The simulation employs a coupled calculation of the void transport equations and interfacial area transport equations for both bubble groups. Validation against existing data shows results consistent with the physics of the flow field.

Severity and exposure associated with tsunami actions in urban waterfronts: the case of Lisbon, Portugal

The Tagus estuary is bordered by the largest metropolitan area in Portugal, the Lisbon capital city council. It has suffered the impact of several major tsunamis in the past, as shown by a recent revision of the catalogue of tsunamis that struck the Portuguese coast over the past two millennia. Hence, the exposure of populations and infrastructure established along the riverfront comprises a critical concern for the civil protection services. The main objectives of this work are to determine critical inundation areas in Lisbon and to quantify the associated severity through a simple index derived from the local maximum of momentum flux per unit mass and width. The employed methodology is based on the mathematical modelling of a tsunami propagating along the estuary, resembling the one occurred on the 1 November of 1755 that followed the 8.5 Mw Great Lisbon Earthquake. The employed simulation tool was STAV-2D, a shallow-flow solver coupled with conservation equations for fine solid phases, and now featuring the novelty of discrete Lagrangian tracking of large debris. Different sets of initial conditions were studied, combining distinct tidal, atmospheric and fluvial scenarios, so that the civil protection services were provided with comprehensive information to devise public warning and alert systems and post-event mitigation intervention. For the most severe scenario, the obtained results have shown a maximum inundation extent of 1.29 km at the Alcântara valley and water depths reaching nearly 10 m across Lisbon’s riverfront.

On the dynamics and kinematics of two‐fluid‐phase flow in porous media

AbstractA model formulated in terms of both conservation and kinematic equations for phases and interfaces in two‐fluid‐phase flow in a porous medium system is summarized. Macroscale kinematic equations are derived as extensions of averaging theorems and do not rely on conservation principles. Models based on both conservation and kinematic equations can describe multiphase flow with varying fidelity. When only phase‐based equations are considered, a model similar in form to the traditional model for two‐fluid‐phase flow results. When interface conservation and kinematic equations are also included, a novel formulation results that naturally includes evolution equations that express dynamic changes in fluid saturations, pressures, the capillary pressure, and the fluid‐fluid interfacial area density in a two‐fluid‐system. This dynamic equation set is unique to this work, and the importance of the modeled physics is shown through both microfluidic experiments and high‐resolution lattice Boltzmann simulations. The validation work shows that the relaxation of interface distribution and shape toward an equilibrium state is a slow process relative to the time scale typically allowed for a system to approach an apparent equilibrium state based upon observations of fluid saturations and external pressure measurements. Consequently, most pressure‐saturation data intended to denote an equilibrium state are likely a sampling from a dynamic system undergoing changes of interfacial curvatures that are not typically monitored. The results confirm the importance of kinematic analysis in combination with conservation equations for faithful modeling of system physics.

Identifying the roles of reduced gravity and pressure on the piloted ignition of solid combustibles

The influence of environmental conditions on solid fuel ignition is of particular interest in spacecraft fire safety because of the large difference in environments between a spacecraft and earth (low gravity, low gas flow velocities, low pressure, elevated oxygen concentration). Considering that fire safety is essential when dealing with spacecraft vehicles, where space is confined and egress is difficult or almost impossible, low gravity fire initiation has a prominent importance. In addition to microgravity, low cabin pressure may further decrease the convective heat losses from the solid, leading to a faster heating of the materials and therefore raising the fire hazard on board. A numerical model developed with the CFD code Fire Dynamics Simulator (FDS) was used to analyze the effect of reduced gravity and ambient pressure on the transport processes taking place in the piloted ignition of an externally irradiated solid fuel. The model simultaneously solves the gas phase and solid phase conservation equations, using a one-step second order Arrhenius reaction rate for the gas phase kinetics and a one-step global Arrhenius reaction rate for the solid phase decomposition. The transition from an incipient premixed reaction at the pilot to the establishment of a self-sustained diffusion flame anchored on the solid fuel surface is analyzed and described in detail and compared for several cases of reduced pressure and gravity. The influence of these parameters on the ignition delay time and the mass flux at ignition is also calculated and compared to experiments at 1g for a range of sub-atmospheric pressures. The results show that reduced pressure and reduced gravity have similar effects on the piloted ignition of a solid fuel in low velocity flows, indicating that heating and pyrolysis of the solid are the primary mechanisms in the process. The results of this work may guide in the selection of materials in future space exploration vehicles and indicate when microgravity testing may be substituted by reduced ambient pressure conditions to analyze their ignition properties.

On Conservation Equation Combinations and Closure Relations

Fundamental conservation equations for mass, momentum and energy of chemical species can be combined with thermodynamic relations to obtain secondary forms, such as conservation equations for phases, an internal energy balance and a mechanical energy balance. In fact, the forms of secondary equations are infinite and depend on the criteria used in determining which species-based equations to employ and how to combine them. If one uses these secondary forms in developing an entropy inequality to be used in formulating closure relations, care must be employed to ensure that the appropriate equations are used, or problematic results can develop for multispecies systems. We show here that the use of the fundamental forms minimizes the chance of an erroneous formulation in terms of secondary forms and also provides guidance as to which secondary forms should be used if one uses them as a starting point.

Stabilization of the outflow temperature of a packed-bed thermal energy storage by combining rocks with phase change materials

A new thermal energy storage (TES) configuration for concentrated solar thermal power is proposed for stabilizing the outflow temperature of a packed bed of rocks during discharging. This concept is based on the combination of sensible and latent heat storage by adding a relatively small amount of phase change material (PCM) to the top of the bed. Transient simulations solving the energy conservation equations for fluid, solid, and molten phases show that the outflow temperature during discharging can be kept constant around the PCM melting temperature, thereby eliminating the inherent temperature drop of TES based on sensible heat storage only. A PCM volume of only 1.33% of the total storage volume is sufficient to accomplish stabilization, corresponding to 4.4% of the total thermal energy stored as latent heat.

Simulation of Drying Characteristics of Evaporation from a Wet Particle in a Turbulent Pulsed Opposing Jet Contactor

The motion and drying characteristics of a single particle in a novel two-dimensional pulsed opposing jet contactor (POJC) are modeled and discussed. Hot air is used as the drying medium. To simulate particle drying, the gas phase and dispersed phase conservation equations are considered in the Eulerian reference frame and the Lagrangian reference frame, respectively. The RNG turbulence model is used to determine the turbulent characteristics of the gas phase. The particle motion is described by the BBO (Basset-Boussinesq-Oseen) equation. The effects of the key parameters, such as the jet Reynolds number, amplitude of pulsation, frequency of pulsation, particle diameter, location of release of particle from one jet as well as velocity profile on residence time (RT) and particle penetration depth (PN) into the opposite jet, are examined. Results show that POJC has strong potential for particulate heat transfer as well as drying; it can improve evaporation rate relative to the corresponding steady OJC by up to 30% as a result of increased residence time in the impingement zone within the parameter ranges simulated.

Verification and validation in CFD for a free-surface gas-liquid flow in channels

This work deals with experimental and numerical studies of a 3-D transient free-surface two-phase flow in a bench-scale channel flow. The aim was to determine how well the homogeneous model can predict the fluid dynamics behavior and to validate the model. The model was validated with experimental data acquired for two hydrodynamic situations. The mathematical model was based on the mass conservation equations for liquid and gas phases and on the momentum conservation equation for the mixture, assuming interpenetrating, continuum and homogeneous hypotheses. Turbulence has been considered for the mixture through the standard k-e model. The numerical methods were the finite volume method with pressure-velocity coupling and a numerical grid on a generalized Cartesian coordinate system. Good qualitative and quantitative agreements were found for both cases, making the prediction of the fluid dynamics behavior quite robust.

Investigation of particle size effect on flame velocity in the combustion of nano/micron-sized aluminum particles in air

It is observed that a diffusion-controlled mechanism applied to the burning of micron-sized particles is not applicable to the combustion of nano-sized particles burning under kinetically controlled conditions. Furthermore, when heat transfer occurs between micron-sized particles and air, Nusselt number can be assumed to be constant and equal to 2, while this number is a function of Knudsen number when heat transfer occurs between nano-sized particles and air. Ignition temperatures of micron- and nano-sized particles are also different. In this article, mass and energy conservation equations for both particle and gas phases are solved. By doing so, flame velocity is obtained. Afterwards, with respect to different combustion characteristics of micron-and nano-sized particles such as ignition temperature, burning time, and Nusselt number, the effect of particle size on the flame velocity of aluminum particles combustion in air is studied and compared with experimental and numerical results. At the equivalence ratio of 0.85, it is shown that flame velocity is proportional to d−0.94 and d−0.56 for micron- and nano-sized aluminum particles, respectively.

Studies on Transport Phenomena during Continuous Casting of an Al-Alloy in Presence of Electromagnetic Stirring

In the present work, a numerical study is performed to predict the transport phenomena during continuous casting of an aluminum alloy (A356) in presence of weak stirring. A set of volume averaged single phase conservation equations (mass, momentum, energy and species) is used to represent the casting process. The electromagnetic forces are incorporated in the momentum equations. The governing equations are solved based on the pressure-based finite volume method according to the SIMPLER algorithm using TDMA solver along with an enthalpy update scheme. The simulation predicts the temperature, solid fraction and species in the computational domain. A parametric study is also performed.

Numerical Simulation of Roughness Effects Inside a Brick-lined Cyclone Separator

An industrial cyclone used for separating dust from a hot gas mixture was studied by means of numerical simulation. Because of the high gas temperatures (about 1075 K), the inner surfaces of the cyclone separator and the inlet pipe must be lined with refractory bricks, causing high wall roughness. The virtual wall model was used to simulate this roughness, and a new model extension accounting for joints between the bricks is proposed and validated experimentally. As the cyclone inlet mass load was relatively low (0.01 kg/kg), the Eulerian-Lagrangian approach was used for the simulations. The continuous phase conservation equations were solved in the Eulerian reference frame on a fixed grid, whereas the discrete phase properties were determined by computing particle trajectories through the computational domain in a Lagrangian reference frame. Besides inlet particle diameters ranging from 1 μm to 100 μm, different particle materials with varying particle densities had to be considered. The measurements and the Muschelknautz analytical model were compared to the numerical simulations regarding pressure loss, particle spectra at the outlet, and the fractional separation efficiency. The Muschelknautz model exhibited some difficulties with the kind of wall roughness considered here (especially joints between bricks). Moreover, this method was not designed to handle multiple different particle densities simultaneously. Nevertheless, comparisons show good agreement between numerical simulations, measurements and theoretical predictions.

Work input for unsaturated elastic porous media

The work input for unsaturated elastic porous media is investigated based on averaged conservation equations for phases, interfaces, and common curves. In this analysis, the interfaces between the air–water interfaces are allowed to move and the surface tension appears explicitly in the analysis. Expressions for the work of the solid alone and for the medium are obtained. Conditions under which the result obtained here for the medium reduces to a more traditional expression are indicated. In this analysis, a form of the solid phase stress tensor, recently derived within the framework of thermodynamically constrained averaging theory for phase and interface properties, is used.