A phase-field model for quasi-incompressible solid–liquid transitions

According to a unified thermodynamic scheme, we derive the general kinetic equation ruling the phase-field evolution in a binary quasi-incompressible mixture for both transition and separation phenomena. When diffusion effects are negligible in comparison with source and production terms, a solid–liquid phase transition induced by temperature and pressure variations is obtained. In particular, we recover the explicit expression of the liquid–pressure curve separating the solid from the liquid stability regions in the pressure–temperature plane. Consistently with physical evidence, its slope is positive (negative) for substances which compress (expand) during the freezing process.     

Venturi-type fluidic sampler for liquid–solid mixtures

Static-type samplers are required for sampling corrosive, toxic, high-temperature, or radioactive liquid–solid fluids. We have designed a compact reverse flow diverter pumping system for transferring liquid–solid mixtures. In accordance with the Venturi principle, an acceptable volume of liquid–solid fluid is automatically collected into a sampling bottle. The effects of sampling needle sizes, sectional area of the T-section, solid concentration, and liquid viscosity on the performance of fluidic samplers were experimentally investigated. The sample volume increased upon the reduction of the sampling needle length and the increase of the sectional area of the T-section, but decreased with the increase of solid concentration and liquid viscosity. Unbiased samples of acceptable volume were produced by the proposed fluidic sampler, even at 10.21 mPa s liquid viscosity, 35 wt% solid concentration, and 6.74 m sampling height.     

Direct numerical simulations of gas–solid–liquid interactions in dilute fluids

The dynamic interactions between gas bubbles, rigid particles and liquid can lead to profound nonlinearities in the aggregate behavior of a multiphase fluid. Predicting the nonlinear dynamics of the multiphase mixture hence requires understanding how the phases interact at the scale of individual interfaces, but these interactions are notoriously difficult to resolve in models. The goal of this paper is to develop and validate a computational method capable of capturing the complex flow interactions between gas bubbles and rigid particles immersed in a Newtonian liquid. We focus on multiphase systems that are dilute enough for the solid and gas components to move through and be moved by the ambient liquid. We use level sets with a topology-preserving advection scheme to track the gas interfaces. To include the motion of the rigid particles, we couple distributed Lagrange multipliers to an immersed-boundary method. The high viscosity contrast between the liquid and the gas requires both time splitting and approximate factorization to efficiently solve the governing equations consisting of the conservation of mass, momentum and energy. To resolve interactions between interfaces that vary drastically in size, we refine our mesh adaptively in the vicinity of the boundary.     

Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes

A computational thermo-metallographic and thermoelastoplastic model for the analysis of the quenching process is developed and validated. The diffusive transfor-mations are modeled according to the Johnson–Mehl–Avrami–Kolmogorov model and the Scheil’s additivity rule. Two different models are investigated for the non-diffusive transformation—the Koistinen–Marburger model and the Yu model. A large displacement formulation is assumed for the deformation analysis, modeling the plastic behavior of the material according to the Prandtl–Reuss model. Two different bilinear hardening models—the isotropic and the kinematic hardening model—are used and compared. The model allows to evaluate the transient stress and strain distributions during the quenching process, the final phases and hardness distributions, and to predict the residual stress and the final deformation of the processed part. A good agreement between computational results and reference data is found     

A coupled model for simulation of the gas–liquid two-phase flow with complex flow patterns

A new model coupling two basic models, the model based on interface tracking method and the two-fluid model, for simulating gas–liquid two-phase flow is presented. The new model can be used to simulate complex multiphase flow in which both large-length-scale interface and small-length-scale gas–liquid interface coexist. By the physical state and the length scale of interface, three phases are divided, including the liquid phase, the large-length-scale-interface phase (LSI phase) and the small-length-scale-interface phase (SSI phase). A unified solution framework shared by the two basic models is built, which makes it convenient to perform the solution process. Based on the unified solution framework, the modified MCBA–SIMPLE algorithm is employed to solve the Navier–Stokes equations for the proposed model. A special treatment called “volume fraction redistribution” is adopted for the special grids containing all three phases. Another treatment is proposed for the advection of large-length-scale interface when some portion of SSI phase coalesces into LSI phase. The movement of the large-length-scale interface is evaluated using VOF/PLIC method. The proposed model is equivalent to the two-fluid model in the zone where only the liquid phase and the SSI phase are present and to the model based on interface tracking method in the zone where only the liquid phase and the LSI phase are present. The characteristics of the proposed model are shown by four problems.     

A growth model for dynamic slugs in gas–liquid horizontal pipes

Long liquid slugs, with sizes reaching 500 pipe diameters or more, may form in gas–liquid horizontal pipe flow at intermediate liquid loadings. Such slugs cause serious operational upsets due to the strong fluctuations in flow supply and pressure. Therefore, predicting the transition from short (hydrodynamic) to long slug flow regimes may play a significant role in preventing or reducing the negative effects caused by the long slugs.     

A compressible two-layer model for transient gas–liquid flows in pipes

This work is dedicated to the modeling of gas–liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas is assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non-conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas–liquid flows through rectangular channels, circular pipes with variable cross section and includes vapor–liquid flows.     

A new drag model for TFM simulation of gas–solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas–solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with experimental data than those of the Gidaspow drag model did.     

A theoretical model for gas–liquid slug flow in down inclined ducts

Analytical solutions are obtained for flows in downwardly inclined ducts, partly filled by a liquid and containing finite amplitude moving jumps. A unified theory for both roll waves and periodic slug flows in rounded ducts of arbitrary cross-section is worked out by means of some simplifications. The article is focused on slugs: a set of equations is obtained, which predicts the transition between roll waves and slug regimes and gives access to all flow characteristics without any need of closure laws concerning either the speed of propagation or the slug length. As a result, we gain a new insight on the physical structure of slug flow. The proposed model is valid for sufficient inclination, small pressure gradient along the duct and negligible superficial tension. Owing to assumptions, only main trends and orders of magnitude observed in experiments are to be checked. In this connection the model fits most of the previously published experimental results obtained in ducts of circular cross-section: the domain of occurrence of downwardly propagating slugs is satisfactorily predicted, the limitations in drift velocity and in liquid layer thickness are demonstrated and upwardly propagating slugs are possible.     

Simulations of vertical jet penetration using a filtered two-fluid model in a gas–solid fluidized bed

The influence of a vertical jet located at the distributor in a cylindrical fluidized bed on the flow behavior of gas and particles was predicted using a filtered two-fluid model proposed by Sundaresan and coworkers. The distributions of volume fraction and the velocity of particles along the lateral direction were investigated for different jet velocities by analyzing the simulated results. The vertical jet penetration lengths at the different gas jet velocities have been obtained and compared with predictions derived from empirical correlations; the predicted air jet penetration length is discussed. Agreement between the numerical simulations and experimental results has been achieved.     

A unifying model for fluid flow and elastic solid deformation: A novel approach for fluid–structure interaction

Fluid–structure coupling is addressed through a unified equation for compressible Newtonian fluid flow and elastic solid deformation. This is done by introducing thermodynamics within Cauchy׳s equation through the isothermal compressibility coefficient that is experimentally measurable for both fluids and solids. The vectorial resolution of the governing equation, where every component of velocity vectors and displacement variation vectors is calculated simultaneously in the overall multi-phase system, is characteristic of a monolithic resolution involving no iterative coupling. For system equation closure, mass density and pressure are both re-actualized from velocity vector divergence, when the shear stress tensor within the solid phase is re-actualized from the displacement variation vectors. This novel approach is first validated on a two-phase system, involving a plane fluid–solid interface, through the two following test cases: (i) steady-state compression and (ii) longitudinal and transverse elastic wave propagations. Then the 3D study of compressive fluid injection towards an elastic solid is analyzed from initial time to steady-state evolution.     

Friction factor correlations for gas–liquid/liquid–liquid flows with drag-reducing polymers in horizontal pipes

In the present paper, two correlations have been developed to predict the effect of DRP on friction factor of two-phase flow for any pipe diameter. The correlations have been verified using published experimental results of DRP added to air–liquid annular flow and for oil–water flows with any flow pattern at the asymptotic state (maximum drag reduction). Such correlations are not available in literature and considered to be very useful in predicting the drag reduction using DRP and in understanding the most significant parameters that affecting the mechanism of drag reduction by polymers in multiphase flow.     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

A reaction–diffusion model for competing languages

The extinction of many of the world’s minority languages is of great concern as language death can lead to the irrevocable loss of cultural information. This often occurs through a process of language shift, where individuals switch from speaking one language to a different, more dominant, language. To prevent the loss of language, it is necessary to determine whether language loss is inevitable or if languages can coexist. We address this question by constructing a nonlinear system of reaction–diffusion equations to model the spread of two competing languages, u and v, which vary temporally and spatially. Language u is assumed to confer a relative status advantage to its speakers, thus individuals may convert from language v to language u. The four constant system equilibria are found. Instability and stability conditions are found for each equilibrium. We conclude that the coexistence of both languages u and v is globally stable, subject to certain constraints on the growth rate of each language and the initial values of both u and v.     

Numerical evaluation of turbulence models for dense to dilute gas–solid flows in vertical conveyor

A two-fluid model (TFM) of multiphase flows based on the kinetic theory and small frictional limit boundary condition of granular flow was used to study the behavior of dense to dilute gas–solid flows in vertical pneumatic conveyor. An axisymmetric 2-dimensional, vertical pipe with 5.6 m length and 0.01 m internal diameter was chosen as the computation domain, same to that used for experimentation in the literature. The chosen particles are spherical, of diameter 1.91 mm and density 2500 kg/m³. Turbulence interaction between the gas and particle phases was investigated by Simonin's and Ahmadi's models and their numerical results were validated for dilute to dense conveying of particles. Flow regimes transition and pressure drop were predicted. Voidage and velocity profiles of each phase were calculated in radial direction at different lengths of the conveying pipe. It was found that the voidage has a minimum, and gas and solid velocities have maximum values along the center line of the conveying pipe and pressure drop has a minimum value in transition from dense slugging to dilute stable flow regime. Slug length and pressure fluctuation reduction were predicted with increasing gas velocity, too. It is shown that solid phase turbulence plays a significant role in numerical prediction of hydrodynamics of conveyor and the capability of particles turbulence models depends on tuning parameters of slip-wall boundary condition.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.     

A thermo-viscoelastic–viscoplastic–viscodamage constitutive model for asphaltic materials

A temperature-dependent viscodamage model is proposed and coupled to the temperature-dependent Schapery’s nonlinear viscoelasticity and the temperature-dependent Perzyna’s viscoplasticity constitutive model presented in Abu Al-Rub et al., 2009, Huang et al., in press in order to model the nonlinear constitutive behavior of asphalt mixes. The thermo-viscodamage model is formulated to be a function of temperature, total effective strain, and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. A systematic procedure for obtaining the thermo-viscodamage model parameters using creep test data at different stress levels and different temperatures is presented. The recursive-iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models, respectively, whereas the viscodamage model is implemented using the effective (undamaged) configuration concept. Numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions with experimental data that include creep-recovery, creep, and uniaxial constant strain rate tests over a range of temperatures, stress levels, and strain rates. It is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.     

Liquid phase heterogeneous photocatalytic ozonation of phenol in liquid–solid fluidized bed: Simplified kinetic modeling

The isotherms of original AC (activated carbon) and photocatalysts (TiO₂-AC) calcined at 500 °C for phenol were measured. The results showed a reversible adsorption of phenol onto both kinds of particles at 25 °C, and could be fitted well to the Freundlich adsorption equation for the dilute solution. Five oxidation processes, namely O₃, O₃/UV, O₃/UV/AC, O₂/UV/TiO₂ and O₃/UV/TiO₂, for phenol degradation in fluidized bed were evaluated and compared, and the photocatalytic ozonation was found to give the highest phenol conversion because of the combined actions of homogenous ozonation in the liquid phase, heterogeneous ozonation on the surface of the catalyst support, i.e. activated carbon, and heterogeneous photocatalytic oxidation on the TiO₂ catalyst surface. With the simplified kinetic model, photolytic ozonation was confirmed to predominantly take place on the particle surface in comparison with the heterogeneous and homogeneous photolytic ozonation. Additionally, the heterogeneous photocatalytic oxidation constant was found to be enhanced by 3.73 times in photocatlaytic ozonation process with ozone as the scavenger compared to the photocatalytic oxidation process with oxygen as the scavenger.