Two-phase Turbulence Model Research Articles

Characterization of Single and Multiphase Hydrodynamics in Continuous Slab Casting Mold in the Presence of Applied Magnetic Field

A numerical investigation has been carried out to characterize both single and multiphase hydrodynamics in a continuous casting mold under the influence of a superimposed magnetic field. Three-dimensional single- and two-phase magnetohydrodynamic flow and turbulence models have been developed for numerical simulation. The computational model results are in agreement with the plant experimental measurements. In a single phase paradigm, with a functional variation in applied magnetic field distributions, the results have been shown for both conducting and non-conducting media. On the other hand, for multiphase flow, based on the actual magnetic field measurement values at the plant, simulations have been carried out at a representative 6 L/min argon flow rate. Overall, the superimposed magnetic field is observed to subdue the flow velocity magnitude and the distribution of turbulence intensity in the continuous casting mold. A similar phenomenon has also been noticed for multiphase flows.

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

• Numerical simulation of scour around a pipeline using a coupled CFD-DEM model. • Simulated scour evolution is in good agreement with published experimental results. • Detailed information, e.g., particle position, velocity, and force, is obtained to improve the understanding of scour mechanism. • Particle motion and particle–particle interactions are found to be most intense during tunnel erosion stage. • Both pressure gradient and drag forces are important at onset and early stages of scour, but drag is dominant at the last stage. Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.

Two-fluid LES and RANS modeling of sudden-expansion gas-particle flows

Sudden-expansion gas-particle flows are widely encountered in fluid and thermal engineering and are typical cases for basic studies. Both two-fluid large-eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) modeling using a unified second-order (USM) two-phase turbulence model are studied in this paper. The advantage of LES is showing the detailed flow structures and improving the simulation results. For LES most of investigators adopt Eulerian-Lagrangian (E-L) LES approach, in which the widely used are Smagorinsky eddy-viscosity model, Germano dynamic eddy-viscosity model and Kim's SGS energy equation model for single-phase flows and there are no particle SGS stress models. Some researchers proposed gas-phase SGS stress models accounting for the effect of particles in E-L LES. A few investigators proposed particle SGS stress models for two-fluid LES of gas-particle flows, however the particle SGS stress models are simply imitated from the gas SGS stress model, and the interaction between gas and particle SGS stresses is not taken into account. In this paper a kgs-kps-kpgs two-phase SGS stress model for two-fluid LES of gas-particle flows is proposed to simulate sudden-expansion gas-particle flows. Simultaneously, The USM-RANS modeling was made for sudden-expansion gas-particle flows. Also, measurements were made to validate both LES and RANS modeling results. It is shown that LES can reveal the detailed flow structures and surely in most regions of the flow field make some improvements over the USM-RANS modeling.

INFLUENCE OF EXTERNAL PARTICLES ON HETEROGENEOUS CONDENSATION FLOW IN CASCADES

The wet steam nucleation zone is usually concentrated in the lower part of the throat. A double fluid numerical model and a shear stress transport (SST) k-ω-kd two-phase turbulence model were derived for the heterogeneous condensation flow of wet steam. The effect of the particle parameters on the condensation flow and the varying patterns of the nucleation rate and degree of super-cooling were investigated. The results show that external particles have a significant influence on the condensation flow, which weakens the condensation wave, restrains the development of thermodynamic imbalance and improves the flow conditions in the cascade.

Nanofluids heat transfer and flow analysis in vertical spirally coiled tubes using Eulerian two-phase turbulent model

A computation fluid dynamics study has been performed to analyze the nanofluids heat transfer and flow characteristics in the spirally coiled tubes. Eulerian two-phase turbulent model is applied to simulate the heat transfer and flow characteristics in the vertical spirally coiled tube. The spirally coiled tubes are fabricated by bending a 8.50 mm inner diameter straight copper tube into a spiral-coil with two different curvature ratios of 0.035, 0.060. The predicted results are verified with the present measured data. Reasonable agreement is obtained from the comparison between the measured data and the predicted results. In addition, due to the centrifugal force, the induced secondary flow has significant effect on the heat transfer enhancement as flowing through the spirally coiled tube. Effects of curvature, nanofluids concentration and hot water temperature on the nanofluids heat transfer characteristics and pressure drop are considered.

Experimental and Numerical Simulation of an Airlift Pump with Conventional and Modified Air Injection Device

The effect of air injection device on the performance of airlift pump used for water pumping has been studied numerically and experimentally. An airlift pump of dimensions 42mm diameter and 2200 mm length with conventional and modified air injection device was considered. A modification on conventional injection device (normal air-jacket type) was carried out by changing injection angle from 90 (for conventional) to 22.5 (for modified). Continuity and Navier-Stokes equations in turbulent regime with an appropriate two-phase flow model (VOF) and turbulent model ( ) in two dimensions axisymmetry flow were formulated and solved by using the known package FLUENT version (14.5). The numerical and experimental investigations were carried out for both conventional and unconventional air-jackets at submergence ratio of 0.75 and air mass flow rate from 0.5, 2, 10, 50 and 85 kg/hr. Comparisons between the numerical and experimental results for both injection devices were made and fair agreements were found and the main results showed that the performance and maximum efficiency of airlift pump is increased for higher mass flow rate of injected air for the tested submergence ratio using unconventional airjacket performance with average enhancement were 9% and 10% for performance and maximum efficiency respectively.

Phenomenological Study on Fine Particle Misplacement Behavior in Hydrocyclone

In spite of widespread applications of hydrocyclone, imprecise particle separation is an inherent limitation associated with it and led to a significant effect on the grinding operation. Such inefficiency is primarily attributable to the misplacement of significant amount of fine particles in the coarser product stream and commonly known as “bypass” in literature. Concerted research efforts are still continuing at various directions to rationalize the occurrence of such phenomenon in a quantifiable manner. This study reveals a fundamental basis towards the genesis and occurrence of bypass in hydrocyclone based on the hydrodynamic of particulate suspension within the turbulent field. Through a series of experiments, we generated carefully controlled experimental data in a 50.8 mm hydrocyclone to analyse the physical response of different parameters (design and operating) on the bypass. Proceeding with the experimental observations we disclose that fines recovery is not equal to that of water split in the underflow. Following this lead, we concluded that the bypass is principally driven by the hydrodynamic condition and the turbulent dispersion of the suspended particle in the prevailing centrifugal force field. Detailed calculations are presented on the basis of solid–fluid two-phase turbulent model to describe the above phenomenological incident. Although our analysis presented here confined to the small diameter hydrocyclone, we are optimistic that the acquired knowledge will be rationale towards the perception of a physical meaning to bypass even for larger classifying cyclones.

Two-fluid turbulence modeling of swirling gas-particle flows — A review

Swirling gas-particle/droplet flows are commonly encountered in various engineering equipments, such as gas-turbine combustors, gas-solid cyclone separators, cyclone combustors, hydro-cyclones and swirl burners/combustors in furnaces. To better understand the flow behavior by using numerical simulation is important for optimization and scaling-up of design, in order to increase the combustion efficiency and separation efficiency, reduce the pressure drop and pollutant formation, and stabilize the flame. Many-year systematic two-fluid modeling studies of swirling gas-particle flows were done by the research group directed by the present author, including Reynolds-averaged Navier–Stokes simulation (RANS modeling) using k-ε-kp, unified second-order moment (USM), Reynolds-stress-PDF (DSM-PDF), SOM-Monte-Carlo, and non-linear k-ε-kp two-phase turbulence models, proposed by the author and two-fluid large-eddy simulation (LES) using a two-phase sub-grid stress model, proposed by the author. The results give the two-phase time-averaged velocities, two-phase RMS fluctuation velocities, and particle concentration distribution, which indicate the advantage of E–E modeling over the E–L modeling and show the complex recirculation structures in the two-phase axial velocities and the Rankine-vortex (solid-body rotation plus potential vortex) structures in the two-phase tangential velocities, the anisotropic two-phase turbulence properties, and the effect of different closure methods on the two-phase flow behavior of swirling gas-particle flows. These results will help to develop highly efficient and low pollutant separators and combustors. This paper gives a brief review of our studies and will help the readers to understand in more detail the specific features of two-fluid modeling of complex turbulent gas-particle flows

Effects of Reduced Gravity Conditions on Bubble Dispersion Characteristics in the Bubble Column

Bubble-liquid turbulent flow has an excellent heat and mass transfer behaviors than single gas or liquid flow. In order to analyze the effects of normal and reduced gravity on cold bubble-liquid two-phase turbulent flow in bubble column a second-order moment cold bubble-liquid two-phase turbulent model was developed to disclose the bubble dispersion characteristics. Under the reduced gravity condition, volume fraction caused by the decrease of buoyance force is larger than normal gravity level due to bigger bubble solid volume. In addition, bubble frequency is also decreased by in decrease of buoyance force. Normal and shear stresses have strongly anisotropic characteristics at every directions and have larger values under normal gravity than reduced gravity. The liquid turbulent kinetic energy has the two-peak bimodal distribution and weaker than bubble turbulent kinetic energy with one peak unimodal, which is caused by vigorous wake fluctuations. The correlation of fluctuation velocities between bubble and liquid has clearly anisotropic behaviors Under reduced gravity, the bubble motion has a little impact on liquid turbulent flow caused by slight buoyancy force, however, it will greatly reduce the liquid turbulent intensity due to energy cascade transport, which was transformed into bubbles or dissipated by interface friction. Bubble formation and detachment mechanisms affected by gravity conditions lead to the different levels of bubble dispersion distributions.

Three-dimensional CFD modelling of a fluidised bed combustor fuelled by biomass and coal

A computational fluid dynamics analysis of a fluidised bed combustor fuelled by coal and biomass is performed. A discrete phase modelling approach is used to track fuel particles. Combustion is modelled using a two-mixture fraction probability density function approach. The standard k–ɛ two-phase turbulence model is used to describe the gas–solids flow. The residence time of coal particles is found to be greater than that of biomass particles. Contours of char burnout and devolatilisation are obtained and combustion is found to be quantitatively complete, and thus no significant change in combustion efficiency is found under full-load conditions. Velocity vectors are obtained and it is found that the velocity increases from the notch region towards the exit of the furnace, owing to the reduction in cross-sectional area. Heat exchange from in-bed superheater tubes to flue gases is greatest at the highest-temperature regions of the tubes.

Movable-bed coupled analysis model of overtopping failure of concrete face sandy gravel dam

The concrete face holds water in the entire overtopping-induced break process of the concrete face sandy gravel dam. Water flow discharges over the concrete face and engenders reverse vortex. The shear stress of the reverse vortex vertically erodes the dam body. Traditional decoupled mathematical models of concrete face sandy gravel dams are based on simplified conservation equations and are not applicable. A movable-bed coupled analysis model of overtopping failure of concrete face sandy gravel dam is presented in the paper. This model includes the solid–liquid two-phase turbulent flow mathematical model and the sediment incipience module. The sediment incipience module involves bed load surface normal direction, shear stress of vortex and angle of repose. The model was applied to the experiment of overtopping failure of concrete face sandy gravel dam. The model was tested against experimental data, with reasonably good agreement between numerical results and measurements. This shows that this mathematical model can simulate the entire break process of concrete face sandy gravel dams in a meticulous and accurate way, and can clearly depict head-cut migration. Therefore, it is reasonable to believe that this model can serve as an effective tool for further study on the mechanism of overtopping failure of concrete face sandy gravel dams.

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.

Numerical Simulation of Particle Separation in a Hydrocyclone

The mixture two-phase turbulence model and theory of particle dynamics is used to simulate the high concentration water-sand two-phase flow in a hydrocyclone. The article mainly analyzes the particle volumetric concentration distribution and separative efficiency of different diameter particles in a hydrocyclone. The simulation result shows that the particle volumetric concentration distribution of different diameter particles is nonuniform in a hydrocyclone. In the annular space, the small diameter particles are affected by the shortcut flow greatly and have high concentration near the wall of the overflow pipe, while the big diameter particles are mainly distributed near the wall in a hydrocyclone. In cylinder space and cone space, different-diameter particles show a similar distribution, the smaller-diameter particles mainly in inner vortex and the larger-diameter particles in outer vortex.

Simulation of construction ventilation in deep diversion tunnels using Euler–Lagrange method

Removal of harmful components is a major concern in the construction ventilation of deep diversion tunnels with heat exchange. The intersecting tunnels and air leakage along the long duct system increase the difficulty of smoke extraction. A 3D unsteady Euler–Lagrange two-phase turbulence model is utilized with the aim of understanding the pollutant discharge problem caused by the storage heat effects, the intersecting tunnels and air leakage along the long duct system. The effects of air leakage, the gas–solid heat exchange, the gas–solid interaction forces and the particle collision are considered. A grid-sensitivity study was performed to obtain a reasonable mesh resolution. The model is validated based on the in-situ ventilation test data. The construction ventilation for the diversion tunnels of the Jinping Second-cascade Hydropower Station in China is taken as a case. The air field distribution, the distribution of heat transfer coefficient, the air leakage rate per 100m, the particle collision force and dust particles migration tracks are analyzed. The dust particles collisions have a negative influence on ventilation and dust exhaust. Most dust particles move toward the tunnel outlet along the tunnel bottom with the effects of airflow and density flow, whereas part of the dust particles move upwards under the effect of buoyancy.

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.

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.

Study on flow pattern and separation performance of air–water swirl-vane separator

Two-phase mixture has a complicated separating process inside a swirl-vane separator which plays an important role in assuring a low wetness of the steam to turbine. To understand the flow pattern inside the swirl-vane separator and analyze the separation performance, a simplified swirl-vane steam separator made of transparent acrylic resin is studied by experiment in which the mixture of air and water is used as the working fluids. Experimental results reveal that the separation efficiency of the separator strongly depends on the flow pattern and the water velocity. The separation efficiency in the annular flow is higher than that of the mist flow and the churn flow. The pressure drop is mainly affected by the air flow rate and the water droplet diameter. Furthermore, a numerical model assuming water as sphere droplets and neglecting its deformation is developed to simulate the separator with Euler two-phase model and RSM turbulence model. It is founded that although the separation efficiency is not sensitive to the size of the big water droplets, it is affected significantly by the micro scale water droplets. By assuming that 94% water droplet equals the Sauter mean diameter and the other 6% is 0.4 times of the Sauter mean diameter, the separation efficiency predicted agrees well with the experimental results for the studied case.

A two-phase turbulent combustion model and its validation for spray flames

A two-phase turbulent combustion model (FSM) with the inclusion of individual droplet burning behavior was applied in a methanol air spray flame. The FSM model results were compared with the experimental data and results of the traditional two-phase turbulent combustion model (TM). The comparison of the results showed that in most regions the FSM model results were in good agreement with the experimental data. In all the three cases, the FSM model predictions showed the same tendency as the experimental data, which was better than the TM model results. So in the liquid methanol spray flame cases simulated in this paper under atmospheric condition, the FSM model is reasonable for temperature profiles prediction, which could be applied in other liquid fuel combustion simulation in the future.

Effects of momentum transfer on particle dispersions of dense gas–particle two-phase turbulent flows

A modified momentum transfer coefficient of dense gas–particle two-phase turbulent flows is developed and its effect on particle dispersion characteristics in high particle concentration turbulent downer flows has been numerically simulated incorporating into a second-order moment (USM) two-phase turbulent model and the kinetic theory of granular flow (KTGF) to consider particle–particle collisions. The particle fractions, the time-averaged axial particle velocity, the particle velocities fluctuation, and their correlations between gas and particle phases based on the anisotropic behaviors and the particle collision frequency are obtained and compared using traditional momentum transfer coefficients proposed by Wen (1966), Difelice (1985), Lu (2003) and Beetstra (2007). Predicted results of presented model are in good agreement with experimental measurement by Wang et al. (1992). The particle fluctuation velocity and its fluctuation velocity correlations along axial–axial and radial–radial directions have stronger anisotropic behaviors. Furthermore, the presented model is in a better accordance with Lu’s model in light of particle axial velocity fluctuation, particle temperature, particle kinetic energy and correlations of particle–gas axial–axial velocity fluctuation. Also, they are larger than those of other models. Beetstra’s model is not suitable for this downer simulation due to the relative lower particle volume fraction, particle collision and particle kinetic energy.