Solid Velocity Research Articles

Theoretical and numerical analysis of key sub-grid quantities' effect on filtered Eulerian drag force

An expression of the filtered Eulerian drag force is proposed based on the second order Taylor polynomial approximation of a microscopic drag coefficient. Theoretical computations of the expression at low particle Reynolds numbers show that four sub-grid quantities, the gas drift velocity, the solid drift velocity, the scalar variance of solid volume fraction and a third-order moment, are significant for an accurate estimation of the filtered drag force. Various drag models with different combinations of the four sub-grid quantities are proposed and their coefficients are optimized based on fine-grid two fluid model results. The gas drift velocity is demonstrated to be the most important marker in predicting the filtered drag force. The model with the solid drift velocity and the scalar variance of the solid volume fraction is found to be promising in computational fluid dynamic-discrete element model simulations due to the ready availability of the two sub-grid quantities.

Multi-fluid modelling of hydrodynamics in a dual circulating fluidized bed

In this work, a multi-fluid model based on the Eulerian-Eulerian framework is used to study the gas-solid hydrodynamics, such as solid distribution, particle motion and solid velocity, in a three-dimensional (3D) dual circulating fluidized bed (DCFB). The influence of four different drag force models, including two classic models, i.e. Gidaspow, EMMS drag model and two recent drag models, i.e. Rong and Tang drag model, on hydrodynamics in DCFB are assessed. Numerical results show that the characteristics of solid distribution and velocity in different sections are distinct. For qualitative analysis, all the drag models can predict a reasonable radial solid distribution and pressure distribution, but only the EMMS, Rong and Tang drag model can capture the phenomenon of dense solid concentration in the low part. For quantitative analysis, the solid circulating rate predicted by the EMMS drag model is the closest to the experimental value while the Gidaspow drag model shows the most significant deviation. The overall assessments confirm that the drag model selection has a significant influence on the simulations of gas-solid flow in DCFBs. This study sheds lights on the design and optimization of fluidized bed apparatuses.

Sdfibm: a signed distance field based discrete forcing immersed boundary method in OpenFOAM

In this paper we present the algorithm and implementation of an open-source immersed boundary code sdfibm, which is based on OpenFOAM v6 and written in C++. The immersed boundary method (“ibm” of the name) treats the velocity field as the volume average of fluid and solid velocities, and applies the volume-average discrete forcing to account for the fluid–solid interaction. The signed distance field (“sdf” of the name) representation of the solid shape, together with the proposed pyramid decomposition method, allow accurate calculations of the volume fraction field created by solids overlapping with an arbitrary unstructured fluid mesh. SDF removes the need of intersection test between the solid and fluid mesh, or the discretization and re-sampling of the solid shape. Users can freely combine different components (shapes, materials, and motion constraints) into new solids within the plain-text input file, and implement new shapes and motion constrains easily. sdfibm is an efficient and robust tool for exploring complex fluid–solid interactions in a fully-resolved sense, and can generate data for closure models in upscaling procedures. Program summaryProgram title:sdfibmCPC Library link to program files:http://dx.doi.org/10.17632/hcvtddjngv.1Licensing provisions: GNU General Public License 3Programming language: C++Nature of problem: Fluid–structure interaction and particle-laden multi-phase flow problems, with the structure/solid phase being rigid bodies. Examples range from classic flows passing stationary cylinder or sphere, to the sedimentation of a cluster of particles. Thanks to the fully-resolved direct numerical simulation, detail data of the flow field and particle motion are obtained as part of the solution, which can be used to analyze the dynamic process and to build coarse-grain models for industrial scale simulations.Solution method: The solution method can be divided into the fluid part and the solid part. For the fluid part, the Navier–Stokes equations are solved via the projection method. Because of the collocated arrangement of variables, a mesh face based flux field is used to enforce the divergence-free condition. The solid part follows Newtonian dynamics and is solved using linear multi-step method. The coupling of the two is via volume-average discrete forcing, which is an immersed boundary formulation suitable for rigid bodies. To find the forcing, the solid volume fraction at each fluid mesh cell is needed, which is calculated accurately on arbitrary unstructured meshes using signed distance field.

Quantification of Solid Mixing in Bubbling Fluidized Beds via Two-Fluid Model Simulations

The influence of particle density and fluidization velocity on the mixing behavior of Geldart B particles was investigated in bubbling fluidized beds for various operating conditions using a two-fluid model approach. The simulation results proved that the predicted solid flow pattern for a wide range of Geldart B particles differs from particles of Geldart B/D classification at identical fluidization numbers. Quantitative analysis of the predicted solid velocity variances revealed that the solid axial dispersion rate is higher than the lateral one. In detail, a Peclet number of 1.54 and 3.92 was predicted for axial and lateral mixings, respectively. Also, the solid dispersion and diffusion coefficients were linearly correlated with the excess gas velocity for a range of particle properties. Finally, the characteristic global particle mixing times were computed. Thereby, the characteristic mixing time can be correlated with the particle Froude number, expanded bed height, and solid dispersion coefficient with high accuracy.

Evaluation of sorption-enhanced reforming over catalyst-sorbent bi-functional particles in an internally circulating fluidized bed

An internally circulating fluidized bed (ICFB) has been applied in various industrial processes owing to its potential in the reduction of heat loss and compact size. In this work, the sorption-enhanced reforming process in the ICFB is investigated. The dense discrete phase model (DDPM) is employed to evaluate the performance of catalyst-sorbent bi-functional particles, considering the particle size distribution. The results demonstrate that the utilization of bi-functional particles can significantly increase hydrogen production. The impacts of operating parameters including solid loading and regenerator velocity on solid circulation rate and gas leakage are examined. It is found that the gas leakage between reactors is increased by 46.6% when the regenerator gas velocity varies from 1.8 m/s to 2.4 m/s so as to weaken the hydrogen yield.

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The mathematical model is a simplified case of the seven-equation Baer–Nunziato model of compressible multi-phase flows. The resulting governing PDE system is a nonlinear system of hyperbolic conservation laws with non-conservative products. The geometry of the solid bodies is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume. This allows the discretization of arbitrarily complex geometries on simple uniform or adaptive Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero, while it is unitary inside the fluid phase. Due to the diffuse interface nature of the model, the volume fraction function can assume any value between zero and one in mixed cells that are occupied by both, fluid and solid.We also prove that at the material interface, i.e. where the volume fraction jumps from unity to zero, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity. This result can be directly derived from the governing equations, either via Riemann invariants or from the generalized Rankine Hugoniot conditions according to the theory of Dal Maso et al. (1995)[89], which justifies the use of a path-conservative approach for treating the non-conservative products.The governing partial differential equations of our new model are solved on simple uniform Cartesian grids via a high order path-conservative ADER discontinuous Galerkin (DG) finite element method with a posteriori sub-cell finite volume (FV) limiter. Since the numerical method is of the shock capturing type, the fluid-solid boundary is never explicitly tracked by the numerical method, neither via interface reconstruction, nor via mesh motion.The effectiveness of the proposed approach is tested on a set of different numerical test problems, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies.

3D model simulating the hydro-mechanical state of unsaturated and deformable material during hot air drying

A three dimensional model to predict the hydro-mechanical state of unsaturated and deformable material during hot air drying has been proposed. The material viscoelastic behaviour was formulated using Bishop’s effective stress theory for partially saturated material using the liquid saturation as the Bishop parameter. The hydro-thermal and mechanical equations were coupled by the fluid pressure and the solid matter velocity. The model was applied to a deformable material (innovative clay-cellulose fibers composite) subjected to convective drying. A generalized Maxwell model with five elements, whose parameters were measured experimentally and correlated to water content was used to describe the material’s viscoelastic behavior. The hydro-thermal part of the proposed model was validated on the basis of a comparison of experimental and simulated drying rate curves. The Von Mises stress was simulated and compared to the experimental tensile strength in order to predict the time and the region of material failure. For a drying process at95°C, the region of failure risk was identified. The failure may occur on the lateral surface of the slab in contact with air at a drying time of 2.5h.

Analysis of Suspended Sediment in the Anavilhanas Archipelago, Rio Negro, Amazon Basin

This article analyzes the flows of water and total suspended sediment in different reaches in the lower course of the Negro River, the largest fluvial blackwater system in the world. The area under study is the Anavilhanas Archipelago, which is a complex multichannel reach on the Negro River. Between the years 2016 and 2019, data about water discharge, velocity, and concentration of total suspended solids (TSS) were acquired in sample sections of the Negro River channels located upstream, inside, and downstream of the Anavilhanas Archipelago. In the study area, the Negro River drains an area greater than 700,000 km2, and the mean water discharge observed before the Anavilhanas was about 28.655 m3·s−1, of which 97% flows through two channels of the Archipelago close to the right and left banks. The mean TSS concentration of the Negro River upstream and downstream the Archipelago was 3.28 mg·L−1 and 1.63 mg·L−1, respectively. Within the Archipelago, we observed more TSS in the channel on the left bank of the Negro River (mean of 4.50 mg·L−1). The total suspended sediment discharge of the Negro River before (3.14 Mt·year−1) and after (1.43 Mt·year−1) the Anavilhanas Archipelago indicates a 55% retention of the suspended load due to the low water slope and reduced flow velocity caused by the backwater effect of Solimões River on the Negro River. The hydro-sedimentary scenario of the low course of the Negro River characterized in this study indicates a slow and continuous sedimentation process in the Anavilhanas Archipelago. The results presented will serve as a baseline to assess the impacts of the dams on the Branco River, the main tributary for both water and sediment in the Negro River basin.

Effect of process parameters on circulating fluidized bed coal gasification using 3D full‐loop CFD simulation

AbstractThis article presents a 3D full‐loop computational fluid dynamics (CFD) simulation of a circulating fluidized bed gasifier (CFBG). The simulation results are validated against the experimental data and found to be in good agreement. Thereupon, the effect of the process parameters, ie, temperature, pressure, air/coal (A/C) ratio, and steam/coal (S/C) ratio, on the performance of the gasifier is analyzed. The effect of temperature on the hydrodynamics was found to be small. The CO and H2 increase, whereas the CO2 and H2O decrease with an increase in temperature. While the effect of pressure on the outlet species mole fraction is negligible, the gas and solid axial velocity decrease with an increase in pressure. With an increasing A/C ratio or decreasing S/C ratio, the combustion products (CO2 and H2O) increase, whereas the gasification products (CO and H2) decrease due to the increase in the O2 concentration. In addition, temperature increases with an increase in the A/C ratio or a decrease in the S/C ratio. The feed velocity increases with an increasing A/C or S/C ratio, and, accordingly, the pressure increases and bed height decreases. The CH4 decreases in all of the cases as it is being consumed in gasification as well as combustion reactions.

Macroscopic model of fluid structure interaction in cylinder arrangement using theory of mixture

In the framework of the theory of mixture, the dynamic behaviour of solid cylinder bundles submitted to external hydrodynamic load exerted by surrounding viscous fluid flow is described. Mass conservation and momentum balance formulated on an elementary domain made of a given volume of mixture give rise to a system of coupled equations governing solid space-averaged displacement, fluid velocity and pressure provided that near-wall hydrodynamic load on each vibrating cylinder is expressed as a function of both fluid and solid space-averaged velocity fields.Then, the ability of the macroscopic model to reproduce over time an averaged flow surrounding vibrating cylinders in a large array in the context of small magnitude displacements is pointed out. Numerical solutions obtained on a two-dimensional configuration involving an array of several hundreds of cylinders subjected to an impulsional load are compared to those provided by averaged well-resolved microscopic-scale solutions. The relative error is less than 3% in terms of displacement magnitude and 5% for frequency delay.The proposed macroscopic model does not include any assumption on relative effect contributions to mechanical exchanges occurring in the full domain. Therefore it features interesting properties in terms of fluid solid interaction prediction capabilities. Moreover it contributes to a significant gain in terms of computational time and resources. Further developments are now required in order to extent the formulation to large magnitude displacements including three-dimensional effects. This could be recommended for investigations on fuel assembly vibration risk assessment in Pressure Water, Fast Breeder reactors at a whole core scale or any other large-scale mechanical system involving some kind of periodic geometry.

A low-error calibration function for an electrostatic gas-solid flow meter obtained via machine learning techniques with experimental data

In this paper, modeling and machine learning with experimental data and a novel calibration function for a gas-solid flow sensor fusion are presented. Sensor fusion is the use of software that intelligently combines data from multiple sensors in order to improve overall system performance. This technique can be applied to measurement of mass flow rate of solids in a pipeline with non-intrusive electrostatic techniques. Data fusion from multiple heterogeneous/homogenous sensors can overcome the limitations of an individual sensor and measured variable. It is shown that the output voltage of a ring-shaped electrode is predominantly a function of solids mass flow rate and velocity for a flow of bulk solids in a pipeline, when particle size, properties and ambient conditions remain constant. By incorporating solids flow velocity in a proposed mathematical model (obtained via machine learning), meter output voltage could be predicted with superior accuracy, for wide range of different flow parameters from numerous experiments with a pneumatic conveying system. Transposing the model yields a new calibration function which, when deployed in signal processing software, enables accurate mass flow measurement with velocity compensation. The described method also de-necessitates determination of air solids ratio or solids volumetric concentration, thereby enabling simplification of the overall measurement system whilst yielding higher accuracy than calibration methods from previous studies. Accurate flow measurement facilitates enhanced monitoring and controllability of blast furnaces, power stations, chemical reactors, process plants etc. where there are bulk solids flows in pipelines. Optimization of such highly materially consumptive and energy intensive processes can yield significant reductions in waste and emissions (CO2, NOx) and increased efficiencies in global production of energy and materials.

Investigation on Erosion Resistance of Downhole Throttle with Ultra-high Pressure

The throttling nozzle, the core element of downhole throttling tool, is seriously eroded in the producing-sand gas well. In this paper, the fixed downhole throttle developed by Petro China Southwest Oil and Gasfield Company is taken as the research object, and the flow state of gas and the movement of sand particles are expressed by RNG k – ε model and DPM model respectively. Through Fluent numerical simulation, the internal flow field distribution rule of throttle with diameter of 70mm is discussed, the most serious erosion area of throttle is obtained, and the influence of solid particle velocity, solid particle diameter and solid particle mass flow rate on the erosion of throttle are analyzed. It is meaningful to design and improve throttle according to working parameters of gas well. According to the simulation, it is believed that the fixed downhole throttle will contribute to a better understanding for erosion resistance of downhole throttle with ultra-high pressure.

Effects of Riser Diameter on Solids Holdup and Particle Velocity Profiles in Circulating Fluidized Bed Riser Systems

Abstract Tests were performed in a 0.1-m diameter small circulating fluidized bed (SCFB) and 0.3 m diameter cold flow circulating fluidized bed (CFCFB) riser systems located at the National Energy Technology Laboratory (NETL) to study the effects of riser diameter on the riser hydrodynamics. These tests were performed at solids circulation rates of Gs = 20 and 75 kg/m2 s and superficial gas velocities of Ug = 5.8 and 6.5 m/s using high-density polyethylene (HDPE) pellets with a density of 0.863 g/cm3, particle size range of 600–1400 µm (with a Sauter mean diameter of 871 µm, placing them in the Geldart B classification). Comparisons of riser axial pressure and solids fraction profiles, radial particle velocity profiles, and radial profiles of higher statistical moments and select chaos analysis parameters were considered. The results showed that for a given Ug and Gs, the smaller diameter riser exhibited characteristics associated with more dilute solids flow than that observed in the larger diameter riser. Additionally, the larger diameter riser exhibited a downward flow of solids near the wall under all test conditions, whereas the smaller diameter riser data exhibited little or no indications of solids downflow near the wall. These findings suggest that, from an industrial standpoint, a direct scaleup of small-scale tests cannot readily be accomplished as the solids holdup and the solids velocity profiles in small units (those normally tested in the laboratory) are not similar to those of large units and the performance of large units can therefore not be predicted from small-scale tests.

A phase field method for the numerical simulation of rigid particulate in two-phase flows

In this paper, we propose a phase field method for the numerical simulations of a moving solid object in two-phase flows. A three-phase Cahn–Hilliard and Navier–Stokes model is employed for this problem. The solid region is represented by a single phase in the three-phase system. The rigidity constraint of the solid phase and the no-slip boundary condition on the solid-fluid interface is imposed by attributing a high viscosity to the solid phase. The solid velocity is then averaged over the solid phase region by the momentum conservation of solid phase. In the aspect of numerics, we design an efficient adaptive finite element method to solve the problem. Several numerical simulation results are given to show the capacity and efficiency of our model and numerical method.

3D CPFD Simulation of Circulating Fluidized Bed Downer and Riser: Comparisons of Flow Structure and Solids Back-Mixing Behavior

The difference of gas-solids flow between a circulating fluidized bed (CFB) downer and riser was compared by computational particle fluid dynamics (CPFD) approach. The comparison was conducted under the same operating conditions. Simulation results demonstrated that the downer showed much more uniform solids holdup and solids velocity distribution compared with the riser. The radial non-uniformity index of the solids holdup in the riser was over 10 times than that in the downer. In addition, small clusters tended to be present in the whole downer, large clusters tended to be present near the wall in riser. It was found that the different cluster behavior is important in determining the different flow behaviors of solids in the downer and riser. While the particle residence time increased evenly along the downward direction in the downer, particles with both shorter and longer residence time were predicted in the whole riser. The nearly vertical cumulative residence time distribution (RTD) curve in the downer further demonstrated that the solids back-mixing in the downer is limited while that in the riser is severe. Solids turbulence in the downer was much weaker compared with the riser, while the large clusters formation near the wall in the riser would hinder solids transportation ability.

Investigation on gas–solid flow behavior in a multistage fluidized bed by using numerical simulation

Poor gas–solid flow structure is one of the primary factors restricting desulfurization efficiency in dry process. A multistage fluidized bed was developed to improve dynamic characterizations. A 3D numerical simulation based on two-fluid model was applied to systematically study the gas–solid flow behavior in the multistage fluidized bed. The model was first verified by comparison with experimental data, and good agreement was achieved between the experiment and simulation. Results showed that the axial flow uniformity decreased in the multistage fluidized bed. Solid holdup and turbulent intensity increased significantly in enlarged sections, together with reducing solid velocity. The radial profiles of gas–solid two phases became uniform along the height of enlarged section. Moreover, superficial gas velocity and solid mass flux exerted different effects on radial distributions. Hydrodynamic profiles maintained similar tendencies between two enlarged sections. Though gas–solid flow exhibited weak behavior in the upper enlarged section, the total flow development was fast in comparison with the lower enlarged section. The comparison results of hydrodynamic characteristics between the enlarged and traditional beds showed that a gas–solid flow structure contributed to the improvement of reaction performance for desulfurization was obtained in the multistage fluidized bed.

Heavily loaded line EHL contacts with thin adsorbed soft layers

Studies of thin soft polymeric or metal layers adsorbed on the surfaces of lubricated solids showed lower friction coefficients and energy losses. The degree to which this reduction happens depends on the coating material nature, its rheology, and coating thicknesses, as well as other factors. To an extent, the application of such soft coatings is in its infancy and it is still not clear which parameters affect the performance of lubricated joints, and how. This paper attempts to model such coated lubricated contacts and to understand how soft coatings affect the joint performance. The paper presents a model of heavily loaded elastohydrodynamically lubricated (EHL) contacts of solids made of elastic homogeneous materials, the surfaces of which are covered by thin coating layers made of soft elastic material. The model incorporates not only normal but also tangential contact stresses and displacements. First, the effect of tangential contact stresses and displacements on the problem parameters is determined, and then the EHL problem is formulated and analyzed. It is necessary to account for variations in the solid surface linear velocities caused by tangential contact stresses. The deformation and displacement processes in thin coating layers are asymptotically modeled by certain boundary conditions. This is done using the Fourier transform with respect to the coordinate along the contact and making the necessary simplifications of the equations. The formulated EHL problem incorporates the normal and tangential contact surface displacements caused by normal and tangential contact stresses. The difference between the classic EHL problems and the problem at hand is due to variations in the linear surface velocities compared with the nominal ones. This causes significant changes in the contact friction parameters. The solution of the EHL problem is obtained numerically. A parametric analysis of the EHL problem solution is performed.

Scale-up effect analysis and modeling of liquid–solid circulating fluidized bed risers using multigene genetic programming

Understanding scale-up effects on the hydrodynamics of a liquid‒solid circulating fluidized bed (LSCFB) unit requires both experimental and theoretical analysis. We implement multigene genetic programming (MGGP) to investigate the solid holdup and distribution in three LSCFB systems with different heights. In addition to data obtained here, we also use a portion of data sets of LSCFB systems developed by Zheng (1999) and Liang et al. (1996). Model predictions are in good agreement with the experimental data in both radial and axial directions and at different normalized superficial liquid and solid velocities. The radial profiles of the solid holdup are approximately identical at a fixed average cross-sectional solid holdup for the three LSCFB systems studied. Statistical performance indicators including the mean absolute percentage error (6.19%) and correlation coefficient (0.985) are within an acceptable range. The results suggest that a MGGP modeling approach is suitable for predicting the solid holdup and distribution of a scaled-up LSCFB system.

Numerical simulation of a 3D full loop iG-CLC system including a two-stage counter-flow moving bed air reactor

A three-dimensional two-fluid model is established for an in-situ gasification chemical looping combustion system to predict its dynamic characteristics and non-uniformity in gas-solid distribution. In the experiment, the fuel reactor (FR) and air reactor (AR) were designed as a high-velocity riser and a novel low-velocity moving bed, respectively. Simulations results show that the predicted pressure distributions agree reasonably well with the experimental data. AR operation did not show any obvious influence on oscillations in the full-loop particle circulation. Each stage of the moving bed AR is found to operate better at relatively lower gas fluidizing number, and the maximum allowable fluidizing number is estimated to be around 0.7. With increase in fluidizing number in AR, gas concentration, gas velocity and solid velocity uniformity index increase, while solid concentration uniformity index decreases. Compared to the parallel arrangement of gas distributors and exhausts, gas concentration and velocity uniformity indices are smaller except for the near-exhaust section under the vertical arrangement of gas distributors and exhausts. Increase in first-stage or second-stage AR outlet pressure has an opposite influence on gas leakage in both the first-stage AR and second-stage AR.

Heat transfer studies in a laboratory vertical riser system suitable for waste heat recovery from industrial waste exhaust gases

Waste heat recovery from effluent hot gases in an energy-intensive production unit like cement manufacture contributes significantly to the profitability of the plant. Modern cement plants employ a suspension preheater (SP) system, claiming recovery of 75% of the waste heat. Lack of information, characterizing flow and heat transfer in the SP system, in literature prompted this study. A prototype experimental setup is fabricated and is used for heat transfer characterization. Solid particles are introduced into an upward moving air in a vertical metallic fluid particle heat exchanger and gas and solid temperatures are measured at different heights of riser. Three different solids – sand, limestone, and chalcopyrite are studied. Solid flow rate and gas velocities are varied to obtain instantaneous gas and particle temperature profiles experimentally. Rate of heat transfer and overall heat transfer coefficients are determined at different solid and gas feed rates. Regression analysis of the collected heat transfer data yielded an empirical correlation – which is recommended for cement industry and diverse other industries, where waste heat recovery is possible.