Solid Phase Velocity Research Articles

Autothermal operation of an adiabatic simulated counter current reactor

Periodic operation of several adiabatic fixed beds connected in series is an alternative to conventional steady-state fixed-bed operation or transient reverse flow reactor operation, e.g. to process lean waste gases or to perform efficiently slightly exothermic equilibrium limited reactions. This work explains the periodic operation of a multi-bed reactor network using both a simplified model assuming a true counter current of the phases involved and a more detailed dynamic model. An appropriate expression for relating the switching times and solid phase velocities is applied. The shapes of the thermal waves are studied in a range of relevant switching times. Results of a stability analysis considering both models reveal hysteresis for ignition and extinction of the reactor network. The accompanying regions of multiplicity provide insight in the potential of performing in such reactor networks exothermal reactions for certain ranges of the adiabatic temperature rise.

Hydro-Thermo-Mechanical Model for Highly Deformable Product during Convective Drying

The aim of this work was to simulate in 1D, the spatio-temporal evolution of the moisture content, the temperature and the mechanical stress within a highly deformable and saturated product during convective drying. The hydro-thermal model, written in a fixed coordinate system, consisted of solid mass balance equation, moisture transfer diffusion/advection equation and heat transfer conduction/advection equation. These equations were coupled by the solid phase velocity terms due to hydric shrinkage. Convective boundary conditions completed this set of equations. The hydro-thermal model had been merged with a static mechanical model which was based on the hypothesis of an elastic behavior, of a plane deformation and of an ideal shrinkage. The hydro-thermo-mechanical model had been applied to a parallelepipedical potato sample. Its thickness was small compared to the other dimensions, in order to observe an unidirectional drying and a negligible shear stress case. The transport and equilibrium properties of the product required for the modelling were determined from previous experiments which were independent of the drying trials.

Influence of Blade Outlet Angle on Inner Flow Field of Centrifugal Pump Transporting Salt Aqueous Solution

During transportation of salt aqueous solutions with centrifugal pump, crystallization phenomenon is frequently encountered. For this kind of two-phase flow, it is difficult to be accurately modeled since there are various medium properties and phase change characteristics. In view of experiment, several problems are hampering the implementation of precise measurement. Influences of blade outlet angle and medium temperature on crystallization rate were studied. Sodium sulfate solution was applied to simulate practical fluid in chemical industry. Particle image velocimetry(PIV) was employed to measure velocity distributions in rotating impeller. Crystallization processes in three impellers with different blade outlet angles were investigated. Relations among crystallization and flow parameters such as temperature and velocity were obtained. With the same blade wrap angle, when blade outlet angle is larger, diffusion of single flow passage gets stronger, relative velocity at blade outlet decreases and large scale vortex tends to appear near the blade working surface. For the impact of volume effect of particle phase on fluid viscosity, both liquid and solid phase velocities decrease with continual forming and growing of crystal particles. Velocity of solid phase is greater than that of liquid phase and its direction leans more closely to blade working surface. Solid particles tend to move towards blade working surface, as is more obvious in the impeller with large blade outlet angle. Therefore, collision between solid particles with stern part of blade working surface is more intensive in impeller with large blade outlet angle. Concerning transportation of salt aqueous solution, accurate PIV measurement is conducted in centrifugal impellers with different blade outlet angles. The results are useful and instructive in relevant engineering design and operation.

Deformation of elastic particles in viscous shear flow

In this paper, the dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. To describe the elastic deformation, an evolution equation for the Eulerian Almansi strain tensor is derived. A constitutive equation is thus constructed for an incompressible “Neo–Hookean” elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. The displacement field does not appear in this formulation. A monolithic finite element solver which uses Arbitrary Lagrangian–Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed by two non-dimensional parameters: Reynolds number ( Re) and Capillary number ( Ca, which is defined as the ratio of the viscous force to the elastic force). In the Stokes flow regime and when Ca is small ( Ca < 0.65 ), the particle deforms into an elliptic shape while the material points inside the particle experience a tank-treading like motion with a steady velocity field. The deformation of the elastic particle is observed to vary linearly with Ca, which agrees with theoretical results from a perturbation analysis. Interactions between two particles in a viscous shear flow are also explored. It is observed that after the initial complicated interactions, both particles reach an equilibrium elliptic shape which is consistent with that of a single particle.

Verification and validation study of some polydisperse kinetic theories

The predictions of several polydisperse kinetic theories are presented in this study for the simple shear flow of a binary mixture of powders with varying sizes in a vacuum under zero gravity. These results are compared to published numerical data obtained using discrete molecular dynamics technique. The theory showing the most accurate results is modified so that the sum of the kinetic stresses of two or more identical solid phases adds to that of a monodisperse system with the same properties. Simulation results obtained in a three-dimensional riser for the flow of air and a binary mixture of glass beads are compared with available experimental data for each solid-phase velocity, concentration, and granular temperature. The predictions of the theory compare reasonably well with experimental data when the value of the linear particle–particle restitution coefficient is lowered to take into account the extra energy dissipation due to collisions between pairs of slightly frictional particles.

Horizontal laminar flow of coarse nearly-neutrally buoyant particles in non-Newtonian conveying fluids: CFD and PEPT experiments compared

The horizontal flow of coarse particle suspensions in non-Newtonian carrier fluids was numerically simulated using an Eulerian–Eulerian CFD model. This study was concerned with nearly-neutrally buoyant particles of 5 and 10 mm diameter conveyed by fluids of Ellis rheology in laminar flow, in a 45 mm diameter pipe at concentrations up to 41% v/v. CFD predictions of solid phase velocity profiles and passage times were compared to experimental data obtained by a Positron Emission Particle Tracking (PEPT) technique and Hall effect sensors, and a very good agreement was obtained considering the complexity of the flows studied. CFD predictions of solid–liquid pressure drop were compared to a number of relevant correlations gleaned from the literature. Only one of them showed a good agreement over the whole range of conditions studied. Other correlations generally showed large deviations from CFD, and their limitations in predicting the influence of solids concentration and particle size have been demonstrated. Overall, it emerged that for the flows studied, CFD was capable of giving predictions of pressure drop which were probably better and more reliable than the correlations available in the literature.

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models

In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian–Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366–2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas–solid particle flow in a 90 ∘ bend. A.I.Ch.E. Journal, 41, 2187–2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian–Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well.

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 μm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 μm/s of inlet fluid velocity and 1.45 Pa s viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5×10 −5 Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.

Predictions of the modified Biot–Attenborough model for the dependence of phase velocity on porosity in cancellous bone

The modified Biot–Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c m of solid bone and phase velocity parameter s 2, were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s 2 = 1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c m = 2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3 m/s. The optimized value of s 2 for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c m = 3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.

Dependence of phase velocity on porosity in cancellous bone: Application of the modified Biot-Attenborough model

This study aims to apply the modified Biot-Attenborough (MBA) model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicted that the phase velocity decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed cm of solid bone and phase velocity parameter s2, were determined by comparing the prediction with the previously published measurements in human calcaneus and bovine cancellous bones. The value of the phase velocity parameter s2=1.23 was obtained by curve fitting to the experimental data only for 53 human calcaneus samples with a compressional speed cm=2500 m/s of solid bone. The root-mean-square error (rmse) of the curve fit was 15.3 m/s. The optimized value of s2 for all 75 cancellous bone samples (53 human and 22 bovine samples) was 1.42 with the rmse of 55 m/s. The latter fit was obtained by using cm=3200 m/s. Although the MBA model relies on empirical parameters determined from the experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.

Research on method to calculate velocities of solid phase and liquid phase in debris flow

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham’s rheology equation of liquid phase and Bagnold’s testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.

Estimation of potato moisture diffusivity from convective drying kinetics with correction for shrinkage

The aim of this paper is to report potato moisture diffusivity data determined from experimental convective drying kinetics. Two different methods have been applied to evaluate this coefficient. The first one was based on the analytical solution of a fickian diffusive model which enabled diffusivity determination by simple linear regression over experimental data. The regression was done using the real sample thickness in order to account for shrinkage. The second one was based on a numerical solution of solid mass balance equation and moisture transfer diffusion/convection equation, these equations being coupled by the solid phase velocity due to shrinkage. At each time step of the simulation, the diffusivity was adjusted to minimize the difference between calculated and measured sample mean moisture content. Due to several simplifying hypothesis the first method could only provide approximate results, while the second could be considered as reference. Predictive correlations for moisture diffusivity as function of temperature and moisture content are presented.

Numerical simulation of transport phenomena in electromagnetically stirred semi-solid materials processing

A continuum based integrated mathematical model is developed to analyse momentum, heat and solute transport during an electromagnetically stirred semi-solid materials processing operation. Separate conservation equations are solved to determine the solid phase velocity. Simultaneously, a solid fraction transport equation is solved to take into account the transport of fragmented dendrites and solidification of liquid phases present in the respective elemental volumes. Numerical simulations are performed to reveal the relative contributions of buoyancy and electromagnetic forces. The mathematical model is also tested by confronting present numerical results with reported experimental observations; an excellent agreement can be observed in this regard, thereby establishing the authenticity of the proposed formulation.

Solids flow mapping in a high pressure slurry bubble column

Successful design and scale-up of Slurry Bubble Column Reactors (SBCRs) require proper understanding of how operating conditions affect their flow behavior. Presently, there is little information on the flow dynamics of solids (e.g., distribution of velocities and turbulent parameters) in slurry systems that are operated at industrially relevant conditions of high pressure, high superficial gas velocities, and high solids loading. Computer Automated Radio Particle Tracking (CARPT) is widely recognized as one of a few techniques that can be reliably used even in highly turbulent and opaque slurry flows. This work utilizes an improved CARPT technique to investigate the effect of reactor pressure (0.1–1 MPa) and superficial gas velocity (0.08–0.45 m/s) on solids phase velocity and shear stress in a pilot scale 0.16 m diameter stainless steel column using an air–water–glass beads ( 150 μ m ) system. The solids axial velocity and shear stress were found to increase noticeably with pressure and superficial gas velocity in the churn turbulent flow regime.

Improved subgrid scale model for dense turbulent solid-liquid two-phase flows

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow, the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

Steady Free Surface Flow of a Fluid-Solid Mixture Down an Inclined Plane

The present work is an extension of the investigations performed by Massoudi and Anand (2001). The free surface flow problem is studied here. Numerical solutions for steady free surface flow of a solid-fluid mixture down an inclined plane are presented. The problem is formulated using the mixture theory framework. The resulting set of three coupled nonlinear differential equations is nondimensionalized. A parametric study is conducted to understand the influence of the dimensionless numbers on the velocity and volume fraction. The maximum fluid velocity is found to decrease with increase in the ratio of the drag force to the viscous forces within the fluid phase (D1). The fluid phase velocity was found to decrease with increase in the ratio of the drag force to viscous force within the solid component (D2), and the corresponding solid phase velocity was found to increase.

MODELLING OF MULTICOMPONENT MASS TRANSPORT IN DEFORMABLE MEDIA: APPLICATION TO DEWATERING IMPREGNATION SOAKING PROCESS

The behaviour of a linearly elastic two-phase system is investigated from the point of view of movement of the different species. In this paper, we treat liquid and solid phases as continua and use the method of volume averaging to develop macroscopic transport equations. The solution of the local scale momentum equation of the two-phase medium allows the description of strain distribution and solid phase velocity field. When the liquid phase is a binary mixture, mass transport can occur by diffusion and convective transport. These mechanisms are described without using phenomenological laws that would introduce non-natural driving forces. Notably, the velocity of the liquid phase is deduced from a volume conservation additivity law combined with the solid mass balance. The comparison between experimental and predicted internal mass fraction fields and strain distribution during dewatering impregnation soaking process validates the model.

An implicit method for reconstructing dynamic three-dimensional phase boundaries under low Peclet number conditions

This article develops an implicit inverse method for reconstructing dynamic multidimensional phase boundaries. The technique is suitable for problems having small liquid phase Peclet numbers, Pe r = (V̂ rL̂/ α ̂ ), where V̂ r is the characteristic liquid phase velocity scale evaluated relative to the solid phase velocity scale, L̂ is a characteristic length scale, and α ̂ is a characteristic thermal diffusivity. Under these conditions, a multidimensional Stefan problem emerges. Explicit front-tracking procedures are eliminated by incorporating the latent heat effect in an effective, temperature dependent specific heat. Time-sequential reconstruction is then performed by solving a multidimensional nonlinear inverse heat conduction problem. As an illustration, evolving phase boundaries are reconstructed within moving and stationary plates subject to concentrated, high energy density heat sources. It is found that boundaries can be accurately reconstructed using either exact or noisy temperature measurements.

拡大揚鉱管および背圧装置を用いた深海底鉱物揚鉱用エアリフトポンプの流動特性

In deep-sea mining conditions, abrasion on periphery units of the outlet is predicted at large flow rates of supplied air, because the velocity of solid-phase becomes very large toward the outlet of the conveying pipe owing to very great expansion of the air and corresponding velocities. In this paper, we present flow characteristics of air-lift pumps for deep-sea mining and discuss methods of the countermeasure. That is, some numerical simulations are performed for the flow conditions of air-lift pumps applied one-stepped enlargement pipe in the end part of conveying pipe and/or added excess pressure using back-pressure device at the outlet of conveying pipe. Consequently, it is found to reduce the velocity of solid-phase at the outlet considerably, almost remaining flow rate of lifting slurry. And we demonstrate most appropriate length of enlargement conveying pipe that maximum velocities of solid-phase became equal in main conveying pipe section and enlargement conveying pipe section. As a result, a guideline and fundamental data to design air-lift pumps for deep-sea mining more practically could be shown.

Forced unidirectional infiltration of deformable porous media

We treat the infiltration of an initially dry deformable porous medium by a pressurized liquid, taking into account the influence of variations in permeability within the deformed porous medium. Chief assumptions of our analysis are neglect of gravity, of inertial forces, and of partial saturation in the porous medium. We focus on unidirectional infiltration under constant liquid pressure, and present data from the infiltration of polyurethane sponge by ethylene glycol in a configuration of nearly unidirectional infiltration with reflief from friction effects along sample sides. We find excellent agreement between theory and experiment at longer infiltration times. We examine an additional assumption, namely the neglect of solid-phase velocity compared with average local liquid velicity at lower porous-medium strains. Agreement of this simplified model with experimental data, albeit less good, remains quite acceptable given the considerable computational simplicity it produces.