Solid Phase Stress Research Articles

Particle-resolved direct numerical simulation and bottom-up statistical analysis on solid-phase pressure in particle–fluid systems

Solid-phase stress is a major factor shaping the complex behaviors of particle–fluid systems. However, uncertainties and inconsistencies can be found among the various models proposed. This work pays attention to the effect of mesoscale structures, that is, the heterogeneity of particle distribution at a scale of statistical meaning but no significant flow field variation, on the solid-phase normal stress, or pressure. Using a bottom-up statistical method, the solid-phase pressure in liquid- and gas–solid flows is investigated by particle-resolved direct numerical simulation (PR-DNS). It is found that, in almost uniform liquid–solid flows, the solid-phase pressure is not well predicted by classical kinetic theory of granular flow (KTGF) due to the presence of interphase force, although KTGF applies much better to single-phase granular flows. In gas–solid flows, with increasing heterogeneity described by structural functions, the statistical solid-phase pressure becomes significantly larger than that in corresponding homogeneous flows. It reveals that mesoscale structures strongly affect solid-phase pressure, and suggests the deviation from classical KTGF in heterogeneous gas–solid flows can be attributed to both the interphase forces (mainly drag) and mesoscale structures. The coefficients in the solid-phase pressure models in KTFG are modified, fitting the statistical results of both homogeneous and heterogeneous particle–fluid flows.

Machine Learning Approaches to Close the Filtered Two-Fluid Model for Gas–Solid Flows: Models for Subgrid Drag Force and Solid Phase Stress

Machine Learning Approaches to Close the Filtered Two-Fluid Model for Gas–Solid Flows: Models for Subgrid Drag Force and Solid Phase Stress

Rheology of sheared polyhedral granular materials in inclined flows

An investigation of frictional, Platonic solid-shaped particle flows on inclined planes is performed using the discrete element method, and the effects of particle angular shape on rheological properties are analyzed. Higher shear stresses at a specified depth of particle bed are obtained for more angular particles. As particle angularity increases, rapid surges in the coordination number and solid-phase stresses occur at a smaller critical solid volume fraction. The friction and dilatancy laws of polyhedral particle flows are significantly different from those of spherical particle flows, due to particle angularity. Nevertheless, by applying a specific rolling friction to the spherical particles, their rheological properties can match those of the polyhedral particles, indicating that the angular particle shape plays a similar role to the rolling friction in preventing particle rotation. Thus, the flows of spherical particles with a rolling friction incorporated can be used to mimic the flows of angular polyhedral particles. At last, a scaling law is adopted to describe rheological relations for various polyhedral particles based on a bulk friction coefficient, a dimensionless granular temperature, and an inertial number.

Study on formation damage mechanism of carbonate reservoir in Shunbei No.2 area of northwest oil field

A series of experiments were carried out to evaluate and analyze the damage mechanism of carbonate reservoir in Shunbei No.2 Area, Xinjiang, China. According to the analysis of reservoir lithology and physical properties, combined with reservoir fluid characteristics and environmental characteristics, the potential factors of formation core damage were analyzed. The potential damage of reservoir is as follows: solid phase particle intrusion blockage, stress sensitivity and strong water lock damage. The effect of pressure time on permeability was eliminated by fracture stability correction. Fracture stability correction was used to evaluate core sensitivity. There is no velocity sensitive damage in the reservoir core, but weak water sensitive and salt sensitive damage, moderate and weak alkali sensitive damage and strong stress sensitive damage.

Effect of mesoscale structures on solid phase stress in gas–solid flows

Solid phase stress plays an important role in hydrodynamic modeling and simulations of gas–solid flows. However, heterogeneous gas–solid flows are typically regarded as homogeneous systems. Their solid phase stresses are usually calculated by the classical kinetic theory of granular flow (KTGF) without considering mesoscale structures, which is a major source of inaccuracies. This work investigates the effect of mesoscale structures in gas–solid flows via a dilute-dense two-phase partition, and proposes a phase-specific model to predict solid phase stress. Subsequently, the sensitive of threshold for phase partition is discussed, and a specific threshold is utilized in the proposed model to investigate the effect of mesoscale structures on solid phase stress with large-scale particle-resolved direct numerical simulation (PR-DNS) data. Numerical results show that classical KTGF underestimates the solid phase stress due to the ignorance of these structures.

Assessment of kinetic theory for gas–solid flows using discrete particle method

Kinetic theory is a common choice for closing the solid phase stress in the continuum theory for dilute and moderate dense gas–solid flows. In this article, methods are proposed for postprocessing the data obtained from discrete particle simulations, and the results are then used to critically assess the fundamental assumptions of kinetic theory. It is shown that (i) the fundamental assumptions and predictions of kinetic theory are, respectively, valid and accurate in homogeneous granular flows, as expected. Those results prove that the methods for data postprocessing are effective; (ii) in the case of nonequilibrium and heterogeneous gas–solid flows, nearly all fundamental assumptions get challenged, and the predictions of kinetic theory, in terms of collision frequency and particle pressure, deviate significantly from the statistical results of discrete particle simulation. Therefore, the standard kinetic theory is insufficient to provide the constitutive laws for continuum modeling of heterogeneous gas–solid flows.

Jamming in granular shear flows of frictional, polydisperse cylindrical particles

In this work, frictional, cylindrical particle shear flows with different size distributions (monodisperse, binary, Gaussian, uniform) are simulated using the Discrete Element Method (DEM). The influences of particle size distribution and interparticle friction coefficient on the solid phase stresses, bulk friction coefficient, and jamming transition are investigated. In frictional dense flows, shear stresses rise rapidly with the increasing solid volume fraction when jamming occurs. The results suggest that at the jamming volume fraction, stress fluctuation and granular temperature achieve the maximum values, and the rate of the stress increase with increasing solid volume fraction approaches the peak value. Meanwhile, the degree of cylindrical particle alignment approaches a valley value. In the polydisperse flows, the jamming volume fraction exhibits significant dependences on the fraction of the longer particles and the particle size distribution. Two models considering the effect of particle size distribution are discussed for predicting the jamming volume fractions of polydisperse flows with frictional, cylindrical particles.

Frictional granular flows of rod and disk mixtures with particle shape distributions

Three-dimensional simulations of polydisperse shear flows of rod and disk mixtures are performed using the discrete element method. The effects of particle shape distribution on flow behaviors are investigated assuming that all particles have the same volume and density but different shapes in the simulations. The solid phase stresses and bulk friction coefficients show a strong dependence on the particle alignment and the structural anisotropy of interparticle contacts. The combined effects of interparticle friction and particle shape difference lead to larger stresses for mixtures of different particle shapes than the pure particle species in dense shear flows. For frictionless and frictional flows with particle shape distributions, it is observed that the particle fluctuating velocities follow non-Maxwellian distributions and the fluctuating kinetic energies are unequally partitioned among the different particle species.

Effect of turbulence modeling on hydrodynamics of a turbulent contact absorber

A computational fluid dynamics (CFD) study is conducted to find a suitable two equation turbulence model for accurate prediction of hydrodynamics of an inhouse turbulence contact absorber (TCA) at high gas and liquid velocities. Based on the multi-fluid Eulerian approach, hydrodynamics of TCA is simulated by incorporating three turbulence models i.e. standard k–ε model, RNG k–ε model and SST k–ω model in ANSYS Fluent®. The solid phase stresses were closed by using the kinetic theory of granular flows (KTGF). TCA hydrodynamics parameters; expanded bed height and bed pressure drop were used to compare the results of this study with experimental data and also with earlier numerical study published with laminar viscous model. It was found that the RNG k–ε model predicted the bed height and pressure drop better than its counterparts. To accurately find the effects of secondary phase turbulence, two RNG k–ε model options i-e. per phase and dispersed were also evaluated. The results show that the “per phase” option of RNG k–ε model produced the expanded bed height and pressure drop in close agreement with available experimental data at similar operating conditions.

Modeling of the filtered drag force in gas–solid flows via a deep learning approach

A deep learning approach based on a proposed artificial neural network (ANN) is exploited to predict the filtered drag force, which is a desirable term for coarse-grid simulations of gas–solid flows. The proposed ANN model includes one input layer, five hidden layers and one output layer. The hidden layers are composed of three convolutional layers and two fully-connected layers. The results show that the proposed ANN model is superior to the multi-layered perceptron (MLP) model and the best available traditional functional model over a wide range of the filter size. The results also indicate that the use of the information on neighboring coarse grids is necessary for accurate estimation of the filtered drag force at the considered filter sizes. This finding is substantiated by a budget analysis which demonstrates that the diffusion of the Reynolds stress and solid phase stress significantly affects the filtered drag force.

An in situ Study of the Kinetics of a Solid-Phase Reaction Activated by the Energy of Elastic Stresses Arisen upon the Formation of the Cu/As2Se3 Nanosized Film Structure

For the first time, the kinetics of a solid-phase chemical reaction activated by the energy of elastic stresses generated upon the formation of the Cu/As2Se3 nanosized film structure is investigated in situ. It is shown that the time at which a solid-phase chemical reaction starts, as well as the voltage of the Cu/As2Se3 heterolayer, significantly depends on the thickness of the As2Se3 film. At a critical thickness of the As2Se3 film, which is equal to 110 nm, a threshold value of the energy of elastic stresses is achieved. Relaxation of this energy over new defects (micropores and microcracks) generated in the film system leads to the activation of a solid-phase chemical reaction and an increase in its rate. A mechanism of the operation of a positive feedback between the chemical reaction in a solid phase and elastic stresses is proposed.

Hip chondrolabral mechanics during activities of daily living: Role of the labrum and interstitial fluid pressurization

Osteoarthritis of the hip can result from mechanical factors, which can be studied using finite element (FE) analysis. FE studies of the hip often assume there is no significant loss of fluid pressurization in the articular cartilage during simulated activities and approximate the material as incompressible and elastic. This study examined the conditions under which interstitial fluid load support remains sustained during physiological motions, as well as the role of the labrum in maintaining fluid load support and the effect of its presence on the solid phase of the surrounding cartilage. We found that dynamic motions of gait and squatting maintained consistent fluid load support between cycles, while static single-leg stance experienced slight fluid depressurization with significant reduction of solid phase stress and strain. Presence of the labrum did not significantly influence fluid load support within the articular cartilage, but prevented deformation at the cartilage edge, leading to lower stress and strain conditions in the cartilage. A morphologically accurate representation of collagen fibril orientation through the thickness of the articular cartilage was not necessary to predict fluid load support. However, comparison with simplified fibril reinforcement underscored the physiological importance. The results of this study demonstrate that an elastic incompressible material approximation is reasonable for modeling a limited number of cyclic motions of gait and squatting without significant loss of accuracy, but is not appropriate for static motions or numerous repeated motions. Additionally, effects seen from removal of the labrum motivate evaluation of labral reattachment strategies in the context of labral repair.

Discrete element simulation studies of angles of repose and shear flow of wet, flexible fibers.

A discrete element method (DEM) model is developed to simulate the dynamics of wet, flexible fibers. The angles of repose of dry and wet fibers are simulated, and the simulation results are in good agreement with experimental results, validating the wet, flexible fiber model. To study wet fiber flow behavior, the model is used to simulate shear flows of wet fibers in a periodic domain under Lees-Edwards boundary conditions. Significant agglomeration is observed in dilute shear flows of wet fibers. The size of the largest agglomerate in the flow is found to depend on a Bond number, which is proportional to liquid surface tension and inversely proportional to the square of the shear strain rate. This Bond number reflects the relative importance of the liquid-bridge force to the particle's inertial force, with a larger Bond number leading to a larger agglomerate. As the fiber aspect ratio (AR) increases, the size of the largest agglomerate increases, while the coordination number in the largest agglomerate initially decreases and then increases when the AR is greater than four. A larger agglomerate with a larger coordination number is more likely to form for more flexible fibers with a smaller bond elastic modulus due to better connectivity between the more flexible fibers. Liquid viscous force resists pulling of liquid bridges and separation of contacting fibers, and therefore it facilitates larger agglomerate formation. The effect of liquid viscous force is more significant at larger shear strain rates. The solid-phase shear stress is increased due to the presence of liquid bridges in moderately dense flows. As the solid volume fraction increases, the effect of fiber-fiber friction coefficient increases sharply. When the solid volume fraction approaches the maximum packing density, the fiber-fiber friction coefficient can be a more dominant factor than the liquid bridge force in determining the solid-phase shear stress.

Исследование in situ кинетики твердофазной реакции, активированной энергией упругих напряжений при формировании наноразмерной пленочной структуры Cu/As-=SUB=-2-=/SUB=-Se-=SUB=-3-=/SUB=-

AbstractFor the first time, the kinetics of a solid-phase chemical reaction activated by the energy of elastic stresses generated upon the formation of the Cu/As_2Se_3 nanosized film structure is investigated in situ. It is shown that the time at which a solid-phase chemical reaction starts, as well as the voltage of the Cu/As_2Se_3 heterolayer, significantly depends on the thickness of the As_2Se_3 film. At a critical thickness of the As_2Se_3 film, which is equal to 110 nm, a threshold value of the energy of elastic stresses is achieved. Relaxation of this energy over new defects (micropores and microcracks) generated in the film system leads to the activation of a solid-phase chemical reaction and an increase in its rate. A mechanism of the operation of a positive feedback between the chemical reaction in a solid phase and elastic stresses is proposed.

Triple Phase Simulation of Bubbling Fluidized Beds of Geldart “A” Particles with a Bubble-Based Drag Model

A triple-phase numerical model was developed for the simulations of gas-solid bubbling fluidized beds with Geldart “A” particles. In the model, the gas-solids suspension was modeled as a primary gas phase presented in the emulsion, a secondary gas phase presented in the bubble, and a third phase consisting of solids. A bubble-based drag model was derived taking into account of the heterogeneous flow structures of the emulsion phase. The KTGF model was used to describe the solid phase stresses. Simulations were conducted for two different scales bubbling fluidized beds of Group “A” particles. Mesh independences were confirmed up to a radial grid size of 200 times particle diameter, and the sensitivity of the transitional results on the time-steps was investigated. The predicted bed expansion and the voidage distribution, axial and radial solids volume fraction profiles, and the solids velocity vectors have been validated against literature data.

An Inverse Problem in the Darcian Mechanics of Porous Media

The constitutive relation between the solid-phase stress and the solid-phase concentration is sought. Since this characteristic is difficult to measure, the equations of Darcian mechanics are applied in order to derive a correspondence between the studied quantities and a set of data which are easy to measure. The utilized data originate from a set of 50 experiments carried out with a suspension of water and kaolin; the height of a suspension column was measured as a function of time. Inversion based on the equations of porous media mechanics makes it possible to convert the obtained relationship between mass and height of the suspension column to the sought relationship between the solid-phase stress and the solid-phase concentration. Two different forms of the result are found and presented. A particular result is the threshold value of concentration at which the solid-phase stress becomes nonzero.

An elastic-viscoplastic model for saturated frozen soils

From the material science point of view, saturated frozen soil is a natural particulate composite, composed of solid grains, ice and unfrozen water. The mechanical behaviour of such a material is strongly affected by the amount of ice. The amount of ice depends on the temperature and the applied mechanical stresses. The influence of ice content and temperature on the mechanical behaviour and the coupling effects on the reverse direction can be mentioned as the main difference between frozen and unfrozen soils. On the other hand, considering the highly rate-dependent behaviour of ice, rate-sensitive behaviour of frozen soils is expected. This rate dependency is also affected by the amount of ice existed in the composite. In the light of these differences, an elastic-viscoplastic constitutive model for describing the mechanical behaviour of saturated frozen soils is proposed. By dividing the total stress into fluid pressure and solid phase stress, in addition to consideration of the cryogenic suction, the model is formulated within the framework of two stress-state variables. The rate-dependent behaviour is considered using the so-called over-stress method. In unfrozen state, the model becomes a conventional elastic-viscoplastic critical state model. Model predictions are compared with the available test results and reasonable agreement is achieved.

Constitutive model for rate-independent behavior of saturated frozen soils

The mechanical behavior of frozen soils is strongly affected by the amount of ice. The amount of ice depends on the temperature and the applied mechanical stresses. The influence of ice content and temperature on the mechanical behavior and the coupling effects on the reverse direction can be mentioned as the main difference between frozen and unfrozen soils. In the light of this difference, an elastoplastic constitutive model for describing the stress–strain behavior of saturated frozen soils is proposed. By dividing the total stress into fluid pressure and solid phase stress, in addition to consideration of the cryogenic suction, the model is formulated within the framework of two-stress state variables. The proposed model is able to represent many of the fundamental features of the behavior of frozen soils, such as ice segregation phenomenon and strength weakening due to pressure melting. In the unfrozen state the model becomes a conventional critical state model. Typical predictions of the model for simulating the characteristic trends of the frozen soil behavior is described qualitatively. Model predictions are also compared with the available test results and reasonable agreement is achieved.

A simplified two-fluid model coupled with EMMS drag for gas-solid flows

A simplified two-fluid model (STFM) combined with energy-minimization multi-scale (EMMS) drag was proposed for accurate and fast simulation of gas-solid flows. In the proposed approach, the solid phase viscosity is neglected, the solid phase pressure is calculated with an empirical formulation, and the interphase momentum transfer is modeled with EMMS drag, which takes the effects of meso-scale structures into consideration. Three typical fluidization cases, namely, a 2D circulating fluidized bed, a 3D lab-scale bubbling fluidized bed, and a 3D lab-scale full-loop circulating fluidized bed, were successfully simulated with this approach. The numerical results are compared with those of full two-fluid model (FTFM, i.e., the two-fluid model using the kinetic theory for granular flow to close solid phase stress term), as well as experimental data. Predictions of STFM coupled with EMMS drag are comparable with those of FTFM coupled with EMMS drag, and both agree well with experimental data. However, computational cost of STFM is significantly reduced compared with that of FTFM. It is suggested that drag model has a dominant effect on gas-solid simulation, and the effect of solid phase stress term seems to play a minor role, demonstrating the feasibility and practicality of STFM with EMMS drag for describing the hydrodynamics of heterogeneous gas-solid flows.

Prediction of Solid Recirculation Rate and Solid Volume Fraction in an Internally Circulating Fluidized Bed

This paper presents a numerical study of gas and solid flow in an internally circulating fluidized bed (ICFB). Two-fluid Eulerian model with kinetic theory of granular flow option for solid phase stress closure and various drag laws were used to predict the hydrodynamic behavior of ICFB. 2D and 3D geometries were used to run the simulations. The 2D simulation results by various drag laws show that the Arastoopour and Gibilaro drag models able to predict the fluidization dynamics in terms of flow patterns, void fractions and axial velocity fields close to the experimental data. The effect of superficial gas velocity, presence of draft tube on solid hold-up distribution, solid circulation pattern, and variations in gas bypassing fraction for the 3D ICFB are investigated. The mechanism governing the solid circulation and solids concentration in an ICFB has been explained based on gas and solid dynamics obtained from the simulations. Predicted total granular temperature distributions in the draft tube and annular zones qualitatively agree with experimental data. The total granular temperature tends to increase with increasing solids concentration in the dilute region (ε < 0.1) and decreases with an increase of solids concentration in the dense region (ε > 0.1). In the dense zone, the decreasing trend in the granular temperature is mainly due to the reduction of the mean free path of the solid particles.