Estimation of solid concentration in solid–liquid two-phase flow in horizontal pipeline using inverse-problem approach

In this study, an inverse-problem method was applied to estimate the solid concentration in a solid–liquid two-phase flow. An algebraic slip mixture model was introduced to solve the forward problem of solid–liquid convective heat transfer. The time-average conservation equations of mass, momentum, energy, as well as the volume fraction equation were computed in a computational fluid dynamics (CFD) simulation. The solid concentration in the CFD model was controlled using an external program that included the inversion iteration, and an optimal estimation was performed via experimental measurements. Experiments using a fly-ash–water mixture and sand–water mixture with different solid concentrations in a horizontal pipeline were conducted to verify the accuracy of the inverse-problem method. The estimated results were rectified using a method based on the relationship between the estimated results and estimation error; consequently, the accuracy of the corrected inversion results improved significantly. After a verification through experiments, the inverse-problem method was concluded to be feasible for predicting the solid concentration, as the estimation error of the corrected results was within 7% for all experimental samples for a solid concentration of less than 50%. The inverse-problem method is expected to provide accurate predictions of the solid concentration in solid–liquid two-phase flow systems.     

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.     

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     

Clustering behavior of solid particles in two-dimensional liquid-solid fluidized-beds

In this paper, the clustering behavior of solid particles in a two-dimensional （2D） liquid-solid fluidized-bed was studied by using the charge coupled devices （CCD） imaging measuring and processing technique and was characterized by fractal analysis. CCD images show that the distribution of solid particles in the 2D liquid-solid fluidised-bed is not uniform and self-organization behavior of solid particles was observed under the present experimental conditions. The solid particles move up in the 2D fluidized-bed in groups or clusters whose configurations are often in the form of horizontal strands. The box fractal dimension of the cluster images in the 2D liquid-solid fluidized-bed increases with the rising of solid holdup and reduces with the increment of solid particle diameter and superficial liquid velocity. At given solid holdup and solid particle size, the lighter particles show smaller fractal dimensions.     

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.     

Aerodynamic characteristics of solid particles�� acceleration by shock waves

In this study, the interaction of a planar shock wave with a group of particles has been investigated using high-speed photography and dynamic pressure measurements. Experiments were carried out in a horizontal circular shock tube. The influence of the particle loading ratio, particle diameter, driving gas and shock wave Mach number on the acceleration was studied. It was found that the higher the particle loading ratio, the greater was the particle velocity. This is due to the higher driving pressure. Helium and nitrogen gases play quite different roles in acceleration. Pressure multiplication during shock wave interaction with particles also appears. Based on the experimental results, the discussion regarding partial quantitative velocities and accelerations of particle groups, as well as the attenuation factors when shock waves pass through the particles, is given.     

Blockage of constrictions by particles in fluid–solid transport

Blockage is an important phenomenon in particulate flow. Work was undertaken to provide a better understanding of key hydrodynamic multiphase flow factors which cause, or contribute to, stalling and blockage in particulate feeding systems such as those used for feeding biomass into reactors. Rubber and plastic particles were hydraulically conveyed along a horizontal rectangular duct leading to constrictions of different geometries. Experimental results showed that large size, irregular shape, high volumetric concentrations of particles, small constriction dimensions and particle compressibility all increased the likelihood of blockage. Reynolds number also had a significant effect on particle behaviour and blockage propensity. The pressure drop needed to break a blockage is also considered, based on a simple horizontal packed bed model.     

An unsteady point vortex method for coupled fluid–solid problems

A method is proposed for the study of the two-dimensional coupled motion of a general sharp-edged solid body and a surrounding inviscid flow. The formation of vorticity at the body’s edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices’ intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown–Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices’ position and intensity, thereby providing an explicit formulation of the vortex–solid coupled problem as a set of non-linear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadside-on fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reduced-order representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.      

Orientation of cylindrical particles in gas–solid circulating fluidized bed

The orientation of cylindrical particles in a gas–solid circulating fluidized bed was investigated by establishing a three-dimensional Euler–Lagrange model on the basis of rigid kinetics, impact kinetics and gas–solid two-phase flow theory. The resulting simulation indicated that the model could well illustrate the orientation of cylindrical particles in a riser during fluidization. The influences of bed structure and operation parameters on orientation of cylindrical particles were then studied and compared with related experimental results. The simulation results showed that the majority of cylindrical particles move with small nutation angles in the riser, the orientation of cylindrical particles is affected more obviously by their positions than by their slenderness and local gas velocities. The simulation results well agree with experiments, thus validating the proposed model and computation.     

Hydrodynamics in a new liquid–solid circulating conventional fluidized bed

A new type of liquid–solid fluidized bed, named circulating conventional fluidized bed (CCFB) which operates below particle terminal velocity was proposed and experimentally studied. The hydrodynamic behavior was systematically studied in a liquid–solid CCFB of 0.032 m I.D. and 4.5 m in height with five different types of particles. Liquid–solid fluidization with external particle circulation was experimentally realized below the particle terminal velocity. The axial distribution of local solids holdup was obtained and found to be fairly uniform in a wide range of liquid velocities and solids circulation rates. The average solids holdup is found to be significantly increased compared with conventional fluidization at similar conditions. The effect of particle properties and operating conditions on bed behavior was investigated as well. Results show that particles with higher terminal velocity have higher average solids holdup.     

A review of multiscale CFD for gas–solid CFB modeling

Meso-scale structure is of critical importance to circulating fluidized bed (CFB) applications. Computational fluid dynamics (CFD) with consideration of meso-scale structures can help understand the structure-oriented coupling between flow, heat/mass transfer and reactions. This article is to review our recent progress on the so-called multiscale CFD (MSCFD), which characterizes the sub-grid meso-scale structure with stability criteria in addition to conservation equations. It is found that the mesh-independent solution of fine-grid two-fluid model (TFM) without sub-grid structures is inexact, in the sense that it overestimates the drag coefficient and fails to capture the characteristic S-shaped axial profile of voidage in a CFB riser. By comparison, MSCFD approach in terms of EMMS/matrix seems to reach a mesh-independent solution of the sub-grid structure, and succeeds in predicting the axial profile and flow regime transitions. Further application of MSCFD finds that neglect of geometric factors is one of the major reasons that cause disputes in understanding the flow regime transitions in a CFB. The operating diagram should, accordingly, include geometric factors besides commonly believed operating parameters for the intrinsic flow regime diagram. Recent extension of MSCFD to mass transfer finds that Reynolds number is insufficient for correlating the overall Sherwood number in a CFB. This is believed the main reason why the conventional correlations of Sherwood number scatter by several orders of magnitude. Certain jump change of state of motion around Reynolds number of 50–100 can be expected to clarify the abrupt decay of Sherwood number in both classical- and circulating-fluidized beds. Finally, we expect that the real-size, 3-D, full-loop, time-dependent multiscale simulation of CFB is an emerging paradigm that will realize virtual experiment of CFBs.     

Reference map technique for finite-strain elasticity and fluid–solid interaction

The reference map, defined as the inverse motion function, is utilized in an Eulerian-frame representation of continuum solid mechanics, leading to a simple, explicit finite-difference method for solids undergoing finite deformations. We investigate the accuracy and applicability of the technique for a range of finite-strain elasticity laws under various geometries and loadings. Capacity to model dynamic, static, and quasi-static conditions is shown. Specifications of the approach are demonstrated for handling irregularly shaped and/or moving boundaries, as well as shock solutions. The technique is also integrated within a fluid–solid framework using a level-set to discern phases and using a standard explicit fluid solver for the fluid phases. We employ a sharp-interface method to institute the interfacial conditions, and the resulting scheme is shown to efficiently capture fluid–solid interaction solutions in several examples.     

Novel multistage solid–liquid circulating fluidized bed: Hydrodynamic characteristics

The present work proposes a novel radially cross-flow multistage solid–liquid circulating fluidized bed (SLCFB). The SLCFB primarily consists of a single multistage column (having an inner diameter of 100 mm and length of 1.40 m), which is divided into two sections wherein both the steps of utilization or loading (e.g., adsorption and catalytic reaction) and regeneration of the solid phase can be carried out simultaneously in continuous mode. The hydrodynamic characteristics were studied using ion exchange resin as the solid phase and water as the fluidizing medium. The loading and flooding states were determined for three particle sizes; i.e., 0.30, 0.42, and 0.61 mm. The effects of the superficial liquid velocity and solid feed rate on the solid hold-up were investigated under loading and flooding conditions. The solid hold-up increases with an increase in the solid feed rate and decreases with an increase in the superficial liquid velocity. An artificial-intelligence formalism, namely the multilayer perceptron neural network (MLPNN), was employed for the prediction of the solid hold-up. The input space of MLPNN-based model consists of four parameters, representing operating and system parameters of the proposed SLCFB. The developed MLPNN-based model has excellent prediction accuracy and generalization capability.     

Characterization of gas–solid fluidized bed hydrodynamics by vibration signature analysis

Vibration measurement, as a non-intrusive technique, was used to characterize the hydrodynamics of fluidized beds. A series of experiments were performed in a lab-scale fluidized bed using two accelerometers for measuring the vibration of the bed and a pressure probe for measuring pressure fluctuations. The output signals were analyzed by statistical methods. The results show that the vibration technique can predict transition velocities at high velocities and indicate that analyzing the vibration signals can be an effective non-intrusive technique to characterize the hydrodynamics of fluidized beds. It was shown that transition from bubbling to turbulent velocity can be determined from the variation of standard deviation and kurtosis of vibration signals against superficial gas velocity of the bed. However, this point could be determined only from standard deviation of pressure fluctuations, and not from skewness or kurtosis of pressure fluctuations.     

Discontinuous solid solutions of anthracene–phenanthrene: Thermodynamics and crystallization kinetics

We explored such issues as the formation mechanism, structure and propriety of the solid solutions of anthracene (ANT)–phenanthrene (PHE). Solution crystallization and solid-state grinding were employed to prepare solid solutions under different conditions. The thermal behavior and PXRD scanning results revealed the formation of discontinuous solid solutions, whose melting points and crystal lattices varied linearly with mixed ratio. Combing with Materials Studio, the formation possibility of solid solutions were investigated by evaluating the change of the energy. The crystal morphology of the solid solutions have a positive correlation with the change of the major part. Finally, the solution crystallization process of solid solution were studied using the population balance model.     

Liquid suspensions of single and binary component solid particles—An overview

In this paper theoretical approaches and experimental findings relative to the hydrodynamics of liquid suspensions of solid particles by liquids are reported and discussed. For the single particle specie systems, advantages and possible faults of well known empirical correlations are discussed. For binary-solid mixture suspensions, experimental evidence are reviewed and approaches capable of successfully describing observed behaviour are reported.     

Magnetic resonance studies of jets in a gas–solid fluidised bed

Magnetic resonance imaging (MRI) has been used to study the behaviour of jets at the distributor of a 50 mm diameter fluidised bed of 0.5 mm diameter poppy seeds. Two perforated-plate distributors were examined, containing either 10 or 14 holes, each 1 mm diameter. Ultra-fast MR imaging was able to show the transient nature of the upper parts of the jets, where discrete bubbles are formed. Imaging in 3D showed that the central jets were the longest for flow rates below minimum fluidisation. Above minimum fluidisation, the outer jets, nearest the wall of the fluidised bed, arched inward towards the central axis. In this latter case, interpretation of the time-averaged 3D image required the use of ultra-fast MR imaging to identify the approximate height above the distributor at which discrete bubbles were formed. The apparently continuous void extending along the central axis above this height in the time-averaged 3D image was thus identified, using ultra-fast MR imaging, as representing the averaged paths of released bubbles. Time-averaged MR velocity mapping was also used to identify dead zones of stationary particles resting on the distributor between the jets. The dead zones could be observed when the superficial velocity of the gas approached minimum fluidisation, but they were smaller than those observed at lower gas superficial velocity. Comparable images of a single jet through 1.2 mm diameter poppy seeds from MRI and electrical capacitance volume tomography (ECVT) are also demonstrated.     

Numerical simulations of gas–liquid–solid flows in a hydrocyclone separator

The flow behavior in hydrocyclones is quite complex. In this study, the computational fluid dynamics (CFD) method was used to simulate the flow fields inside a hydrocyclone in order to investigate its separation efficiency. In the computational fluid dynamics study of hydrocyclones, the air-core dimension is a key to predicting the mass split between the underflow and overflow. In turn, the mass split influences the prediction of the size classification curve. Three models, the model, the Reynolds stress model (RSM) without considering the air-core, and the Reynolds stress turbulence model with the volume of fluid (VOF) multiphase model for simulating the air-core, were compared in terms of their predictions of velocity, axial and tangential velocity distributions, and separation proportion. The RSM with air-core simulation model, since it reproduces some detailed features of the turbulence and multiphase, clearly predicted the experimental data more closely than did the other two models.