Solid Hydrodynamics Research Articles

Nanoscale flow past a colloidal cylinder confined in a slit channel: Lubrication theory and molecular dynamics analysis

Plane Poiseuille flow past a nanoscale cylinder that is arbitrarily confined (i.e., symmetrically or asymmetrically confined) in a slit channel is studied via hydrodynamic lubrication theory and molecular dynamics simulations, considering cases where the cylinder remains static or undergoes thermal motion. Analytical expressions for the drag force and volumetric flow rate valid for high confinement and arbitrary off-center displacements are derived for the first time in this work. Lubrication theory predictions are in close agreement with molecular dynamics simulations of flows having molecularly thin lubrication gaps, despite the presence of significant structural forces induced by the crystalline structure of the modeled solid. While the maximum drag force is observed in symmetric confinement, i.e., when the cylinder is equidistant from both channel walls, the drag decays significantly as the cylinder moves away from the channel centerline and approaches a wall. Hence, significant reductions in the mean drag force on the cylinder and hydraulic resistance of the channel can be observed when thermal motion induces random off-center displacements. Analytical expressions and numerical results in this work provide useful insights into the hydrodynamics of colloidal solids and macromolecules in confinement.

A TFM-KTGF jetting fluidized bed coal gasification model and its validations with data of a bench-scale gasifier

A comprehensive TFM-KTGF simulation was performed with a bench-scale jetting fluidized bed coal gasifier. The numerical results were carefully processed and several key gas–solid hydrodynamic properties, such as the jet height, the bubble size and the amount of solids entrained from the annulus to the jet were validated against literature correlations. The simulated distributions of the bed temperatures, and the gas species compositions (CO, CO2, H2) were validated with reported experiment data (Bi and Kojima, 1996), and compared with those obtained from the TFM-CVM modeling (Gao et al., 2006) as well. It was found that the TFM-KTGF simulation results agreed with the experiment data better than the TFM-CVM, confirming that the TFM-KTGF model could improve the descriptions of gas–solid hydrodynamics of the jetting fluidized bed. The simulation results also showed a high temperature zone in the jet region due to intense char-O2 combustion, whereas the char-H2O, char-CO2 and water gas shift reactions mainly occurred in the annular region, reinforcing the importance of accurately defining and monitoring the jet temperature for an industrial jetting fluidized bed gaisifer.

Critical state and ultimate state surface of soils: a granular solid hydrodynamic perspective

A model predicting the ultimate state surface and critical state of soils is established based on a non-equilibrium thermodynamic approach known as granular solid hydrodynamics. It offers a pressure- and density-dependent approach to assessing the elastic potential energy density of soils while taking soil cohesion into account. The ultimate state surface is quantitatively determined by the convex condition of the elastic potential energy density function with respect to the elastic strain and is compared with the state boundary surface in the critical state soil mechanics. The elastic stress is expressed by a hyper-elastic relationship. Both the critical state and the non-elastic deformation of soils depend on the evolution of elastic relaxation and granular fluctuation, which can be expressed in terms of dissipative forces and dissipative flows. The proposed model allows analysis of the soils critical state, its granular temperature and its effective stress. The predictions of triaxial compression tests of Toyoura sand and Q3 loess show that the model adequately predicts the ultimate state, the critical state and the dilation/contraction or hardening/softening of soils. Limitations of the proposed model in reproducing the density dependency of drained peak shear strength and the rate dependency of critical state are also discussed.

Applying GSH to a wide range of experiments in granular media.

Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, whose wide range of applicability is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: i) static stress distribution, clogging; ii) elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; iii) rapid dense flow: the μ-rheology, Bagnold scaling and the stress minimum; iv) elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and non-local fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that GSH may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

CFD–DEM study of mixing and dispersion behaviors of solid phase in a bubbling fluidized bed

Three-dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) are used to investigate the gas–solid hydrodynamics and mixing characteristics of a three-dimensional rectangular bubbling fluidized bed. The numerical study is conducted referring to the quasi-3D experimental apparatus investigated by Goldschmidt et al. [1]. The simulation results turn out that time-averaged solid volume fraction and instantaneous particle height agree well with the experimental data. To investigate the solid behavior, the solid velocity and flux distribution are extracted and the influence of the gas velocity on the solid velocity is discussed. It is found that higher gas velocity induces the formation of double-recirculation pattern in which solid phase mainly moves from the near wall region to the central region in the lower bed and oppositely in the upper bed. At the same time, the solid mixing is faster under higher inlet velocity, and that particles in vertical directions tend to mix better than those in lateral directions. At last, we find the particle dispersion coefficient is very anisotropic in three normal directions. In accordance with the results of most experiments, the geometry structure strongly influenced the coefficient value. We also find when inlet gas velocity is higher, the dispersion coefficient increases, for the particle velocities are higher due to greater momentum exchange.

Anti-wear beam effects on gas–solid hydrodynamics in a circulating fluidized bed

Anti-wear beams installed on water walls of circulating fluidized bed (CFB) boilers are one of the most effective ways to protect against water-wall erosion. Beam effects from, for example, beam size and superficial gas velocity were investigated on gas–solid hydrodynamics in a CFB test rig using CFD simulations and experimental methods. The downward flow of the wall layer solids is observed to be disrupted by the beam but is then restored some distance further downstream. When falling solids from the wall layer hit the anti-wear beam, the velocity of the falling solids decreases rapidly. A fraction of the solids accumulates on the beam. Below the beams, the falling solids have reduced velocities but upward-moving solids were observed on the wall. The effect of the beam increases with width and superficial gas velocity. Wear occurs mainly above the beam and its variation with width is different above to below the beam. There is an optimum width that, when combined with beam height, results in less erosion.

An integrated methodology for the modeling of Fluid Catalytic Cracking (FCC) riser reactor

Modeling description of the riser reactor is a highly interesting issue in the development of FCC process. However, one of the challenging problems in the modeling of FCC riser reactors is that sophisticated flow-reaction models with high accuracy need long computational time, while simple flow-reaction models give rise to results with fast computation but low accuracy. This dilemma requires new type of coupled flow-reaction models. The goal of this study was to propose a novel integrated model with time-efficient computation and acceptable accuracy. The integrated model, named equivalent reactor network (ERN) model, was established based on Aspen Plus simulator with considering gas–solid hydrodynamics via built-in modules and catalytic reactions via external FORTRAN subroutines, as well as lump mixtures characterized by real components. Through comparing with pilot-scale experimental data and industrial plant data in two case studies, the developed ERN model was justified to be capable of precisely and quickly modeling FCC riser reactors. Furthermore, the proposed methodology is expected to be readily applied to studies on the dynamic simulation, optimization, and control of FCC units in future studies.

Effective stress in saturated soil: a granular solid hydrodynamics approach

Effective stress is one of the most fundamental concepts in soil mechanics. A comprehensive interpretation of its physical essence is important for a better understanding and prediction of the mechanical behaviour of the soil. The granular solid hydrodynamics approach is used in this study to establish a more generalised effective stress principle for saturated soils. In this approach, the stress formulation is theoretically derived from the constraints between conservation laws and thermodynamic principles, in which the energies in soils are quantitatively described by the classical non-equilibrium thermodynamics. Five physical mechanisms of the soil deformation, including the elastic potential, the elastic relaxation, the granular fluctuation, the viscosity and the effect of bound water, are taken into account in the derivation of the stress formulation. Consequently, the effective stress derived in this study is classified into four categories. The first is elastic effective stress that is determined by the elastic potential energy and is limited by a stress state boundary line. The second is granular effective stress that is relevant to the granular fluctuation and is very important to the unrecoverable soil deformation. The third is bound effective stress which is a result of defining the bound water as an independent phase of the soil system. It is an important driving force in the non-isothermal unrecoverable soil deformation induced by the conversion of bound water to free water. The last—viscous stress—is another important part of effective stress.

Particle-Scale Investigation of the Hydrodynamics and Tube Erosion Property in a Three-Dimensional (3-D) Bubbling Fluidized Bed with Immersed Tubes

Particle-scale study of the gas–solid hydrodynamics and the tube erosion in a 3-D bubbling fluidized bed with a tube bundle is conducted in the framework of computational fluid dynamics coupled with the discrete element method. General gas–solid flow behaviors are investigated and the time-averaged properties are obtained to explore the influence of tube configuration on the bed hydrodynamics. Moreover, the erosion patterns of immersed tubes locating in the different regions of system are analyzed. The effect of tube configuration on the erosion property is considered. The results show that the presence of the tube bundle limits the bubble diameter and results in homogeneous distribution of the bubble phase in the tube region. Moreover, inserting the tube bundle into the bed reduces the vertical velocity of the solid phase but results in a uniformly horizontal distribution of its concentration. The vertical intensity of solid dispersion is several times that of the lateral one, and the insertion of tube bundle enhances the solid mixing procedure and enlarges the solid dispersion intensities in both the vertical and lateral directions. Different erosion patterns appear on the immersed tubes locating in different regions of the bed. The intrinsic mechanism behind the erosion distribution can be identified from the solid flux distribution near the tubes.

Influences of operating parameters on the hydrodynamics of a 3-D spout–fluid bed based on DEM modeling approach

Abstract The influences of operating parameters on the gas–solid hydrodynamics of a 3-D spout–fluid bed operated in the flow regime of Jet-In-Fluidization are numerically investigated at the particle-scale level. The gas motion and solid motion are solved under the frameworks of computational fluid dynamics and discrete element method, respectively. The dynamical property of solid phase obtained numerically is compared with the experimental data in literature. Then, the influences of the spouting velocity, the background velocity and the particle diameter on the bed hydrodynamics are discussed. The results show that vigorously lateral motion of solid phase exists in the spout–annulus interface and the vertical transportation intensity is larger than the lateral one. Increasing the spouting velocity enlarges the solid velocity but decreases its concentration in the spout and enhances the solid circulating flux of the system. Meanwhile, the enlargement of background velocity gives rise to an obvious change of voidage in the annulus. However, enlarging the particle diameter lowers the solid motion in three regions of the bed. Spout and annulus interact with each other through the spout–annulus interface. The spout boundary diverges initially, and then keeps nearly constant, finally diverges again until the bed surface. Moreover, the shape of the spouting boundary is strongly influenced by the inlet geometry. Along the bed height, this influence diminishes initially but is enhanced in the vicinity of bed surface. The enlargement of spouting velocity or background velocity leads to the expansion of the spout boundary along the bed height. In contrast, the increase of particle diameter reduces the spout boundary.

Analysis of parameters in granular solid hydrodynamics for triaxial compression tests

Granular materials are omnipresent in industries and in nature. For small strains, elastic-plastic and hypoplastic constitutive relations are widely used in engineering practice, but they are not a significant reflection of the underlying physics. Under a unified thermodynamics framework explaining the physics of materials, granular solid hydrodynamics (GSH) was an extension towards describing granular materials, not only solid-like, but also fluid-like behaviors. In this paper, the fundamentals of GSH are briefly treated and then simplified to analyze quasistatic deformations in triaxial compressions. The calculated stress-strain relations and volumetric strain are compared with experimental results. The influences of the major parameters in GSH, especially their cross coupling influences, are analyzed and their physical meanings are further clarified. After parameters were calibrated, the calculated stress values in the characteristic stress state are found to be within 22% of tested values. Meanwhile, the energy dissipation during triaxial compression is analyzed. The above results support and partially quantify GSH.

Influence of tube configuration on the gas–solid hydrodynamics of an internally circulating fluidized bed: A discrete element study

Three-dimensional modeling of the gas–solid flow in an internally circulating fluidized bed is conducted by means of the computational fluid dynamics combined with the discrete element method to explore the effect of the tube bundle on the gas–solid hydrodynamics of the system. Gas motion is resolved at the computational grid level, while solid motion is obtained in the Lagrangian view. The influences of tube bundle on the interaction of two chambers, the circulating and resident behaviors of solid phase are evaluated. Moreover, solid mixing behavior and tube erosion are discussed. The results show that the immersed tubes obviously enlarge the gas/solid velocity in the vicinity of the partition plate and lower the interaction intensity of the two chambers. Solid cycle time of the system with or without tubes processes a log-normal distribution. Furthermore, different resident behaviors of the solid phase can be obtained in the two chambers, and inserting the tube bundle in the reactor chamber enlarges the solid residence times of the two chambers. More tubes inserted into the bed enlarge both the cycle time and residence time of the solid phase. On the other hand, the presence of tube bundle enhances the solid mixing intensity. Finally, different erosion distributions appear around the circumferential positions of each tube, and the latent erosion pattern can be identified from the distribution of the time-averaged solid flux.

Parallel CFD–DEM modeling of the hydrodynamics in a lab-scale double slot-rectangular spouted bed with a partition plate

This paper presents a numerical modeling of the gas–solid motion in a 3-D lab-scale double slot-rectangular spouted bed with a partition plate under the parallel framework of CFD–DEM coupling approach. Solid motion is tracked with the discrete element method, while the gas motion is solved by the k–ε turbulence model. The bed has two uniform chambers with the diverging base and two parallel slots lying in the bottoms of these two chambers. A total of 2,590,000 glass particles have been tracked with 112 CPUs in a cluster. The distributions of the gas–solid hydrodynamics are investigated initially. Then, the interaction between the spout and the annulus is explored. Finally, the effect of the plate height on the gas–solid motion of the bed is discussed. The results show that the insertion of the partition plate leads to the formation of two parallel fountains without information exchanging and the enlargement of the pressure drop. A velocity peak of the fluid phase or solid phase appears in the central region of each individual chamber. Furthermore, large vertical solid flux appears in the central region of each chamber and shows a distribution strongly related to the slot shape. The slot shape influences the spout–annulus interaction boundary, whereas this effect diminishes obviously with increasing the bed height. Spout–annulus interaction intensity shows the strongest in the conical region of bed and reduces along the axial direction. Finally, the plate height exerts little effect on the solid velocity and voidage distributions.

Three-Dimensional Modeling of Gas–Solid Motion in a Slot-Rectangular Spouted Bed with the Parallel Framework of the Computational Fluid Dynamics–Discrete Element Method Coupling Approach

The gas–solid flow in a three-dimensional slot-rectangular spouted bed is numerically investigated under the parallel framework of the computational fluid dynamics–discrete element method coupling approach. The fluid phase is solved with the k–ε turbulence model at the computational grid level, while the solid phase is tracked individually with the discrete element method at the particle scale. Millions of particles are calculated using a total number of 112 CPUs in a cluster. The predicted pressure drop profiles and the minimum spouting velocities of the calculations under different bed heights agree well with the experimental data. The startup procedure and the solid flow pattern are identified. Then, wall effects on the distribution properties of the gas–solid hydrodynamics are explored. Moreover, the interaction between spout and annulus and the effects of the superficial velocity and bed height on the bed hydrodynamics are discussed. The results show that a larger pressure drop appears in the system with a higher bed height. A bubble with its shape influenced by the slot geometry is formed in the startup procedure. Moreover, the bed hydrodynamics show a strong 3-D behavior along the depth direction. Large vertical solid flux mainly concentrates in the central region of the spout. The spout–annulus interface is dramatically influenced by the slot shape and shows different evolutionary tendencies in the different directions, and this influence becomes weaker along the bed height. The larger the superficial velocity is, the higher the bed height and the larger the spouting height appear. Besides, solid flow patterns under different bed heights with the superficial velocity the same ratio to the corresponding minimum spouting velocity show a similar behavior.

Thermodynamic analysis of simple shear granular flows

Granular flow is the collective moment of a large number of solid particles. A so-called Granular Solid Hydrodynamics (GSH) was recently proposed and expected to provide unifying descriptions of mechanical properties of granular materials. In this work, the simple shear flows with constant volume are firstly simulated with the discrete element method (DEM) where the volume fraction of solids ranges from 0.2 to 0.68. Meanwhile, the conventional kinetic theory is used for dilute systems analysis (i.e. volume fraction less than 0.6 in this study). We found the kinetic theory results about the normal stress with different volume fractions and shear rates agree well with DEM results. After improve the expression of granular temperature, GSH theory is employed to study the granular flows and the obtained results coincide with DEM and kinetic results. It is concluded that the improved GSH theory could coherently describe mechanical behavior of granular flows from quasi-static deformation until rapid flows.

Discrete element simulation of the hydrodynamics in a 3D spouted bed: Influence of tube configuration

Abstract The gas–solid flow in a 3D cylindrical spouted bed with a non-porous draft tube is investigated under the framework of CFD-DEM coupling approach. The gas motion is modeled by the k - e turbulence model, and solid motion is modeled with discrete element method. Flow behavior of the fluid phase, the distribution properties of velocity, the concentration and flux of solid phase in the systems with different tube configurations are compared to evaluate the influence of tube geometry on the system performance. Besides, the erosion characteristic of the draft tube is discussed. Numerical results show that the insertion of draft tube significantly changes the gas–solid hydrodynamics. With the presence of draft tube, the velocity magnitudes of both fluid and solid phases in spout are enlarged significantly. The smaller the entrainment distance below the draft tube is, the larger fluid velocity appears in spout but a more dilute solid concentration in spout will be. Moreover, the extension of the draft tube above the bed surface enhances the solid motion in the central region of bed. Furthermore, the presence of draft tube lowers the solid circular flux of the whole system. For the system with draft tube, large entrainment distance and extension of draft tube above bed surface result in a large circular solid flux. The most severe erosion appears at the upper part of tube while the smallest erosion behavior appears in the lower part of tube. The smaller the entrainment distance is, the less erosion in the bottom of tube will be. Extension of tube above bed surface results in a larger erosion in the upper of the tube.

Proportional paths, Barodesy, and granular solid hydrodynamics

Propotional paths as summed up by the Goldscheider Rule (GR) -- stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components -- is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successfully accounts for data from soil mechanical experiments. Granular solid hydrodynamics (GSH), a theory derived from general principles of physics and two assumptions about the basic behavior of granular media, is constructed to qualitatively account for a wide range of observation -- from elastic waves over elasto-plastic motion to rapid dense flow. In this paper, showing the close resemblance of results from Barodesy and GSH, we further validate GSH and provide an understanding for GR.

Granular materials: Bridging damaged solids and turbulent fluids

Granular materials exhibit abundant dissipations due to fluctuations in both granular motions and configurations (i.e., granular skeleton) evolutions. Twin granular temperatures Tk and Te are introduced accounting for two types of fluctuations, and the so-called twin granular temperatures theory is established as an extension of granular solid hydrodynamics. By using simulations, the nonaffine deformations in a 2D assembly are simulated by using discrete element methods. By analogizing with microdamages in deformed solids, double scalar damage variables, DP and Dq, are proposed to describe the deformed granular solid under triaxial compressions. Granular flows are found intrinsically turbulent due to the presence of Tk and the Naiver–Stokes equation is obtained for granular flows.

Dip of the granular shear stress

Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcing a constant volume does not prevent the local density to vary, and a stress dip may still occur.

Expression for the granular elastic energy

Granular solid hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to deform the grains. The original expression, though useful and simple, has some drawbacks. Therefore a slightly more complicated expression is proposed here that eliminates three of them: (1) The maximal angle at which an inclined layer of grains remains stable is increased from 26^{∘} to the more realistic value of 30^{∘}. (2) Depending on direction and polarization, transverse elastic waves are known to propagate at slightly different velocities. The old expression neglects these differences, the new one successfully reproduces them. (3) Most importantly, the old expression contains only the Drucker-Prager yield surface. The new one contains in addition those named after Coulomb, Lade-Duncan, and Matsuoka-Nakai-realizing each, and interpolating between them, by shifting a single scalar parameter.