Two-phase Stress Research Articles

Hydrodynamic Predictions of the Ultralight Particle Dispersions in a Bubbling Fluidized Bed

Particle and gas flow characteristics are numerically simulated by means of a proposed gas–particle second-order moment two-fluid model with particle kinetic–friction stress model in a bubbling fluidized bed. Anisotropic behaviors of gas–solid two-phase stresses and their interactions are fully considered by the two-phase Reynolds stress model and their closure correlations. The dispersion behaviors of the non-spherical expand graphite and spherical heavy particles are predicted by using the parameters of distributions of particle velocity, porosity, granular temperature, and dominant frequency. Compared to particles density 2700 kg/m3, ultralight particles exhibit the higher voidages with big bubbles and larger axial-averaged velocity of particles and stronger dispersion behaviors. Maximum granular temperature is approximately 3.0 times greater than that one, and dominant frequency for axial porosity fluctuations is 1.5 Hz that is 1/3 time as larger as that heavy particle.

Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling

Multi-scale finite element analysis is performed to ascertain the effect of geometrical changes at multiple structural scales on the mechanical properties of cortical bone. Finite element models are developed, with reference to experimental data from existing literature, to account for bone's viscoelastic behaviour and anisotropic structure from the most fundamental level of bone consisting of mineralised collagen fibrils, up to the macroscopic level consisting of osteons and the Haversian canals. A statistical approach is incorporated to perform sensitivity analyses on the effects of different geometrical parameters on the effective material properties of cortical bone at each length scale. Numerical results indicate that there is an exponential correlation between the mineral volume fraction and the effective stiffness constants at each length scale. This contributes to the exponential behaviour of the instantaneous moduli describing cortical bone's two-phase stress relaxation process: a fast and slow response relaxation behaviour. Results indicate that the fast response relaxation time is independent of bone's structural anisotropy, whilst being dependent on variations in the global mineral volume fraction between length scales. However, the slow response relaxation time is independent of the changes in mineral volume fraction. It is also observed that the slow response relaxation time varies with bone's anisotropic structure, and therefore, contributes to the anisotropic properties of bone.

A Comprehensive Model for Estimating Stimulated Reservoir Volume Based on Flowback Data in Shale Gas Reservoirs

Stimulated reservoir volume (SRV) which is generated by horizontal drilling with multistage hydraulic fracturing governs the production in the shale gas reservoirs. Although microseismic data has been used to estimate the SRV, it is high-priced and sometimes overestimated. Additionally, the effect of stress sensitivity on SRV is not considered in abnormal overpressure areas. Thus, the objective of this work is to characterize subsurface fracture networks with stress sensitivity of permeability through the shale gas well production data of the early flowback stage. The flowback regions are first identified with the flowback data of two shale gas wells in South China. Then, we measured the permeability stress sensitivity of the core after fracturing, coupled to the dynamic relative permeability (DRP) calculation to obtain an accurate and simple DRP curve. After that, a comprehensive model is built considering dynamic two-phase relative permeability function and stress sensitivity. Finally, we compared the calculated results with the microseismic data. The results show that the proposed model could reasonably predict the SRV using the flowback data after fracturing. Additionally, compared with the microseismic data, the stress sensitivity should be included, especially in the abnormal overpressure block. It is believed that this mathematical model is accurate and useful. The work provides an efficient approach to estimate stimulated reservoir volume in the shale gas reservoirs.

Deriving the Oil-Water Seepage Pressure Distribution from Two-Phase Oil-Water Flow Stress Gradient

The characteristics of oil-water two-phase flow in low-permeability reservoirs have been insufficiently studied. In the present article, we estimate the oil-water seepage parameters using a flow stress gradient model with a nonuniform radial distribution of the water saturation coefficient in a low-permeability reservoir. We apply the oil-water relative permeability curves and the Buckley-Leverett equation to determine the oil-water mobility ratio and the functional relationship between the two-phase flow stress gradient, the radial distribution, and the oil saturation. In this way, we construct an oil-water radial flow model based on the oil-water two-phase flow stress to derive the pressure distribution equation. Calculation results show that there is a linear relationship between the oil-water two-phase flow stress gradient and the oil saturation and a quadratic relationship between the oil-water two-phase mobility ratio and the oil saturation. The strata/ pressure distribution for low-permeability reservoirs is highly sensitive to the oil-water two-phase flow stress gradient, and the effect is more noticeable near the wellbore.

Two-phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-particle Flows and Coal Combustion

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.

Effects of bubble–liquid two‐phase turbulent hydrodynamics on cell damage in sparged bioreactor

According to recent experimental studies on sparged bioreactors, significant cell damage may occur at the gas inlet region near the sparger. Although shear stress was proposed to be one of the potential causes for cell damage, detailed hydrodynamic studies at the gas inlet region of gas–liquid bioreactors have not been performed to date. In this work, a second-order moment (SOM) bubble–liquid two-phase turbulent model based on the two-fluid continuum approach is used to investigate the gas–liquid hydrodynamics in the bubble column reactor and their potential impacts on cell viability, especially at the gas inlet region. By establishing fluctuation velocity and bubble–liquid two-phase fluctuation velocities correlation transport equations, the anisotropy of two-phase stresses and the bubble– liquid interactions are fully considered. Simulation results from the SOM model indicate that shear and normal stresses, turbulent energy dissipation rate, and the turbulent kinetic energy are generally smaller at the gas inlet region when compared with those in the fully developed region. In comparison, a newly proposed correlation expression, stress-induced turbulent energy production (STEP), is found to correlate well with the unusually high cell death rate at the gas inlet region. Therefore, STEP, which represents turbulent energy transfer to a controlled volume induced by a combination of shear and normal stresses, has the potential to provide better explanation for increased cell death at the sparger region.

Effects of Particles Collision on Separating Gas–Particle Two-Phase Turbulent Flows

A second-order moment two-phase turbulence model incorporating a particle temperature model based on the kinetic theory of granular flow is applied to investigate the effects of particles collision on separating gas–particle two-phase turbulent flows. In this model, the anisotropy of gas and solid phase two-phase Reynolds stresses and their correlation of velocity fluctuation are fully considered using a presented Reynolds stress model and the transport equation of two-phase stress correlation. Experimental measurements (Xu and Zhou in ASME-FED Summer Meeting, San Francisco, Paper FEDSM99-7909, 1999) are used to validate this model, source codes and prediction results. It showed that the particles collision leads to decrease in the intensity of gas and particle vortices and takes a larger effect on particle turbulent fluctuations. The time-averaged velocity, the fluctuation velocity of gas and particle phase considering particles collision are in good agreement with experimental measurements. Particle kinetic energy is always smaller than gas phase due to energy dissipation from particle collision. Moreover, axial–axial and radial–radial fluctuation velocity correlations have stronger anisotropic behaviors.

Effects of higher wall roughness on dense particle–laden dispersion behaviors

To analyze the effects of higher wall roughness on dense particle–laden dispersion behaviors under reduced gravity environments, a dense gas–particle two-phase second-order-moment turbulent model are developed. In this model, the wall roughness function and the kinetic theory of granular flows are coupled and closed. Anisotropy of gas–solid two-phase stresses and the interaction between gas–particle are fully considered using two-phase Reynolds stress model and the two-phase correlation transport equation. Numerical simulation test is validated by Sommerfeld and Kussin (2003) experiments data with higher wall roughness 8.32μm. Predicted results showed that the particle concentration distribution, particle fluctuation velocity, particle temperature and particle collision frequency are greatly affected by higher wall roughness, as well as particle Reynolds stress and interactions between gas and particle turbulent flows are redistributed. Under microgravity conditions, particle temperature and collision frequency are greatly less than those of earth and lunar gravity.

Effects of particle–particle collisions on sudden expansion gas-particle flows via a two-phase kinetic energy-particle temperature model

In the framework of the gas–particle two-fluid mode, an improved gas–particle two-phase kinetic energy incorporating into a particles collision model (k–kp–θ) is proposed to study the sudden expansion gas–particle turbulent flows in a cylindrical pipe section. Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are considered by means of a transport equation of two-phase fluctuation velocity correlation. Xu and Zhou [10] experimental data is used to quantitatively validate k–kp–θ and k–kp model for analysis the effects of particle–particle collision. Numerical predicted results show that time-averaged velocity, fluctuation velocity of gas and particle and correlation of two-phase fluctuation velocity considering particles collision are better than those of the without particle temperature model and they are in good agreement with experimental data. Larger particle concentration and particle temperature located at shear layer adjacent to wall surface and re-circulation region. Energy dissipation due to smaller scale particles collision contributes to homogeneous distribution of Reynolds stress and affects the particle transportation behavior together with particle inertia.

Influence of Low-Temperature Freezing Treatment on Micro-Area Hardness and Residual Stress of SiCp/Al Composites

In order to study the effect of freezing treatment on the mechanical properties of SiCp/Al composites, SiCp/Al composites were froze by liquid nitrogen for different time. The micro-area hardness, two-phase residual stress and interface combination status of were analyzed with micro hardness tester, x-ray diffractometer and SEM before and after freezing treatment. The results show that the hardness of Al matrix after freezing is higher than that of before freezing, while the hardness of SiC particles does not show much change. Low-temperature freezing makes the residual compressive stress of matrix phase and the residual tensile stress of reinforcing phase reduce. With the increasing of freezing time, the difference value between the measured residual stress and the primary residual stress of Al matrix and SiC particles both turn out to be greater. Freezing can not destroy the interface combination status between the matrix phase and the reinforcing phase.

Second-order moment modeling of dispersed two-phase turbulence-Part 2-USM-Θ two-phase turbulence model and USM-SGS two-phase stress model

Dense gas-particle flows are frequently encountered in fluidized beds, riser and downer reactors, pneumatic transport and the near-wall zone of dilute gas-particle flows. Particle-particle collision plays an important role in the behavior of two-phase flows. In this paper a USM-Q two-phase turbulence model for dense gas-particle flows is proposed to account for both two-phase turbulence and inter-particle collision. For two-fluid large-eddy simulation of gas-particle flows, the author proposed a unified second-order moment (USM) two-phase SGS stress model and a two-phase k-kp SGS energy-equation stress model. The proposed models can fully account for the interaction between the gas and particle SGS stresses.

Numerical prediction effects of particle–particle collisions on gas–particle flows in swirl chamber

In this paper, a unified-second-order-moment two-phase turbulent model incorporating into the kinetic theory of granular flows for considering particle–particle collision (USM-θ) is proposed to study the turbulent gas–particle flows in swirl chamber. Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are fully considered by constructing a two-phase Reynolds stress model and a transport equation of two-phase stress correlation. Sommerfeld et al. (1991) experimental data is used to quantitatively validate USM-θ and USM model for analysis the effects of particle–particle collision. Numerical predicted results show that time-averaged velocity and fluctuation velocity of gas and particle using particle temperature model are better than those of without particle temperature model. Maximum particle concentration and temperature located at thin shear layer adjacent to wall surface due to particle inertia. Small-scale particle fluctuation due to particle–particle collision is smaller than large-scale gas–particle turbulence fluctuation. Particle–particle collision leads to the redistribution dissipation of Reynolds stress and particle turbulence kinetic energy.

Numerical investigation on gas–particle flows in horizontal channel under the reduced gravity environments

A unified second-order-moment gas–particle two-phase turbulent model incorporated with kinetic theory of granular flows (USM-θ) is developed to study the particle dispersion behavior of dense gas–particle flows in horizontal channel with 6.96 μm wall roughness and with earth, lunar and microgravity environments, respectively. Anisotropy of gas and particle two-phase stresses and the interaction between two-phase stresses are fully considered by constructing two-phase Reynolds stress model and the transport equation of two-phase stress correlation. The flow behavior of particles in a horizontal channel of Kussin and Sommerfeld [12] experiments is numerically simulated. Results show that the reduced gravity conditions affect the particle concentration distribution, particle velocity and fluctuation velocity, particle temperature, axial–axial fluctuation velocity correlation of gas and particle and particle collision frequency. Under microgravity conditions, particle temperature and collision frequency are much less than those of earth and lunar gravity. Compared with earth gravity, anisotropic of two-phase flow and sedimentation are weaker.

Hydrodynamic predictions of dense gas–particle flows using a second-order-moment frictional stress model

Based on the Eulerian–Eulerian two-fluid continuum approach, an improved unified second-order-moment two-phase turbulence model combining with the kinetic theory of particle collision frictional stress model is developed to simulate the dense gas–particle flows in downer, where the effective coefficient of restitution is incorporated into the particle–particle collision. The interaction term between gas and particle turbulence is fully taken into account by the transport equation of two-phase stress correlation. Hydrodynamics of high density particle flow, measured by Wang et al. [27] are predicted and the simulated results are in good agreement with experimental data. On the conditions of considering the realistic energy dissipation due to frictional stress, particle concentration and particle axial averaged velocity are closely the measured and they are better than without frictional stress model. Furthermore, the particle Reynolds stress is redistributed and the particle temperature is reduced. Effect of frictional stress leads to increase obviously the collision frequency at the outlet and inlet regions and the magnitude of frequency of particle collisions is 102.

Hydrodynamic Modeling of Dense Gas-Particle Turbulence Flows Under Microgravity Space Environments

An Euler–Euler two-fluid model based on the second-order-moment closure approach and the granular kinetic theory of dense gas-particle flows was presented. Anisotropy of gas-solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. Under the microgravity space environments, hydrodynamic characters and particle dispersion behaviors of dense gas-particle turbulence flows are numerically simulated. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Decreased gravity can decrease the particle dispersion and can weaken the particle–particle collision as well as it is in favor of producing isotropic flow structures. Moreover, axial–axial fluctuation velocity correlation of gas and particle in earth gravity is approximately 3.0 times greater than those of microgravity and it is smaller than axial particle velocity fluctuation due to larger particle inertia and the larger particle turbulence diffusions.

Numerical prediction of particle dispersions in downer under different gravity environments

Abstract Particle dispersion behavior of dense gas–particle flows in a downer affected by gravity environment is numerically simulated using an Euler–Euler two-fluid approach incorporating unified-second-order-moment two-phase turbulent models and kinetic theory of granular flows (USM-θ). Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are fully considered by two-phase Reynolds stress model and the transport equation of two-phase stress correlation. The flow behavior of particles in a downer of Wang et al. (1992) [27] experiments is predicted under earth gravity, lunar gravity and microgravity environment. Simulation results of particle concentration and particle velocity are in good agreement with measurement data under earth gravity environment. Comparison earth gravity to lunar and microgravity condition, peak value of particle concentration is shifted to near center region and axial particle fluctuation velocity is larger than that of approximately 3.0 times. Particle temperature, particle heterogeneities dispersion and particle–particle collision are weakened due to decrease gravity. Furthermore, roles of particle and gas kinetic energy in particle–fluid system are alternated. Both particle kinetic energy and gas kinetic energy are greater than ones under earth gravity conditions.

96/01897 The character of ash deposits and the thermal performance of furnaces

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.