Numerical Simulation of Erosion-Corrosion in the Liquid-Solid Two-Phase Flow

Erosion-corrosion of liquid-solid two-phase flow occurring in a pipe with sudden expansion in cross-section is numerically simulated in this paper. The global model for erosion-corrosion process includes three main components: the liquid-solid two-phase flow model, erosion model and corrosion model. The Eulerian-Lagrangian approach is used to simulate liquid-solid two-phase flow, while the stochastic trajectory model was adopted to obtain properties of particle phase. Two-way coupling effect between the fluid and the particle phase is considered in the model. The accuracy of the models is tested by the data in the reference. The comparison shows that the model is basically correct and feasible.

Pressure Drop of Liquid–Solid Two-Phase Flow in the Vertical Tube Bundle of a Cold-Model Circulating Fluidized Bed Evaporator

A cold-model vertical multi-tube circulating fluidized bed evaporator was designed and built to conduct a visualization study on the pressure drop of a liquid–solid two-phase flow and the corresponding particle distribution.Water and polyformaldehyde particle(POM)were used as the liquid and solid phases,respectively.The effects of operating parameters such as the amount of added particles,circulating flow rate,and particle size were systematically investigated.The results showed that the addition of the particles increased the pressure drop in the vertical tube bundle.The maximum pressure drop ratios were 18.65%,21.15%,18.00%,and 21.15%within the experimental range of the amount of added particles for POM1,POM2,POM3,and POM4,respectively.The pressure drop ratio basically decreased with the increase in the circulating flow rate but fluctuated with the increase in the amount of added particles and particle size.The difference in pressure drop ratio decreased with the increase in the circulating flow rate.As the amount of added particles increased,the difference in pressure drop ratio fluctuated at low circulating flow rate but basically decreased at high circulating flow rate.The pressure drop in the vertical tube bundle accounted for about 70%of the overall pressure drop in the up-flow heating chamber and was the main component of the overall pressure within the experimental range.Three-dimensional phase diagrams were established to display the variation ranges of the pressure drop and pressure drop ratio in the vertical tube bundle corresponding to the operating parameters.The research results can provide some reference for the application of the fluidized bed heat transfer technology in the industry.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

BASIC EQUATIONS AND WAVE THEORY OF GAS-LIQUID TWO-PHASE TRANSIENT FLOW

This paper systematically discussed the equations for two-phase transient flow and pressure wave and interfacial wave. The behaviour of basic equations was analyzed. The formulas for the wave speed of the pressure wave and the interfacial wave were derived. It was proved that various mathematical models can be uniformed by the integrating model and various wave speed formulas can be uniformed by the universal formula derived. The basic equations for the separated flow model are ill-conditioned because of the unreasonable neglect of the pressure differences between the phases and interfaces. Drift flux model can improve the accuracy if some additional equations are provided. The basic equations for homogeneous flow model are well-conditioned and they can be used in two-phase transient flow, especially in the cases of no velocity slips between various phases fluid.

Two Phase Flow Simulation of Fractal Oil Reservoir Based on Meshless Method

The reservoir is the networked rock skeleton of an oil and gas trap,as well as the generic term for the fluid contained within pore fractures and karst caves.Heterogeneity and a complex internal pore structure characterize the reservoir rock.By introducing the fractal permeability formula,this paper establishes a fractal mathematical model of oil-water two-phase flow in an oil reservoir with heterogeneity characteristics and numerically solves the mathematical model using the weighted least squares meshless method.Additionally,the method’s correctness is verified by comparison to the exact solution.The numerical results demonstrate that the fractal oil-water two-phase flow mathematical model developed using the meshless method is capable of more accurately and efficiently describing the flow characteristics of the oil-water two-phase migration process.In comparison to the conventional numerical model,this method achieves a greater degree of convergence and stability.This paper examines the effect of varying the initial viscosity of the oil,the initial formation pressure,and the production and injection ratios on daily oil production per well,water cut in the block,and accumulated oil in the block.For 10 and 60 cp initial crude oil viscosities,the water cut can be 0.62 and 0.80,with 3100 and 1900 m^(3)cumulative oil production.Initial pressures have little effect on production.In this case,the daily oil production of well PRO1 is 1.7 m^(3)at 7 and 10 MPa initial pressure.Block cumulative oil production is 3465.4 and 2149.9m^(3)when the production injection ratio is 1.4 and 0.8.The two-phase meshless method described in this paper is essential for a rational and effective study of production dynamics patterns in complex reservoirs and the development of reservoir simulations of oil-water flow in heterogeneous reservoirs.

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study,a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed.Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop.One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore,and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations.Predictions are compared with experimental data measured by Lali et al.,where the computed porosities from model B are closer to the measured data than other models.Furthermore,the predicted pressure drop rises as liquid velocity increases,while it decreases with the increase of particle size.Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient,and particle concentration,granular temperature,granular pressure,and granular viscosity go down accordingly.

Numerical simulation of counter-current flow field in the downcomer of a liquid-solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid-solid circulating fluidized bed （LSCFB） is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian-Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superfcial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB,

Study on the solid-liquid suspension behavior in a tank stirred by the long-short blades impeller

We investigated the solid–liquid suspension characteristics in the tank with a liquid height/tank diameter ratio of 1.5 stirred by a novel long-short blades(LSB) impeller by the Euler granular flow model coupled with the standard k–ε turbulence model. After validation of the local solid holdup by experiments,numerical predictions have been successfully used to explain the influences of impeller rotating speed,particle density, particle size, liquid viscosity and initial solid loading on the solid suspension behavior,i.e. smaller particles with lower density are more likely to be suspended evenly in the liquid with higher liquid viscosity. At a low impeller rotating speed(N), increase in N leads to an obvious improvement in the solid distribution homogeneity. Moreover, the proposed LSB impeller has obvious advantages in the uniform distribution of the solid particles compared with single Rushton turbine(RT), dual RT impellers or CBY hydrofoil impeller under the same power consumption.

Effects of CO₂Injection on the Seismic Velocity of Sandstone Saturated with Saline Water

Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essential on ascertaining movement, volumes and locations of injected CO2 in the sequestration reservoir. One technique is to use time-lapsed seismic survey mapping to provide spatial distribution of seismic wave velocity as an indicator of CO2 migration and volumes in a storage reservoir with time. To examine the use of time-lapsed seismic survey mapping as a monitoring tool for CO2 sequestration, this paper presents mathematical and experimental studies of the effects of supercritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The mathematical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible pore fluids. The experimental study uses a high pressure and high temperature triaxial cell to clarify the seismic response of a sample of Berea sandstone to supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2 injection in the sandstone sample show the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2 injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus. The empirical relation of Brie et al. for the bulk modulus of mixtures of two-phase immiscible fluids, in combination with the Biot-Gassmann theory, was found to satisfactorily represent the pore-fluid dependent acoustic P-wave velocity of sandstone.

Wall-scaling prevention in cryogenic external cooler of ammonium chloride solution by liquid-solid fluidization

A double-tube cooler with liquid-solid circulating fluidization operation and corresponding parameter measuring system are developed to avoid fouling of inner walls of heat exchange tubes in a cryogenic temperature external cooler of ammonium chloride solution in soda ash production.Wall-scaling prevention performance of the cooling process is experimentally evaluated using convection and overall coefficients,enhancement factor,wall temperature and fouling resistance.Effects of different volume fractions of added particles,particle size,superficial liquid velocity,and cooling medium temperature on heat transfer are examined.Under present conditions,convection coefficient of liquid-solid flow inside the tube of external cooler is higher than that of the liquid phase flow,increased by 0.7–2.8 times,enhancing cooling performance obviously.Convection coefficient initially increases and then decreases as the volume fraction of added particles increases,reaching its maximum value at a volume fraction of 2.0%.The wall-scaling prevention effect of glass beads mainly depends on the volume fraction of added particles;optimal anti-fouling effects are achieved when adding particles at a volume fraction of 2.0%,regardless of changes in superficial liquid velocity or cooling medium temperature.This study lays a foundation for industrial applications of this new technique of fluidized bed external coolers.

Hyperconcentrated flows as influenced by coupled wind-water processes

Using data from more than 40 rivers in the middle Yellow River basin, a study has been made of the influence of coupled wind-water processes on hyperconcentrated flows. A simple “vehicle” model has been proposed to describe hyperconcentrated flows. The liquid phase of two-phase flows is a “vehicle”, in which coarse sediment particles are carried as solid-phase. The formation and characteristics of hyperconcentrated flows are closely related with the forma-tion and characteristics of this liquid-phase and solid-phase. Surface materials and geomorphic agents of the middle Yellow River basin form some patterns of combination, which have deep influence on the formation and characteristics of liquid- and solid-phases of hyperconcentrated flows. The combination of high percentages of relatively coarse material with low percentages of fine material appears in the area predominated by the wind process, where the supply of rela-tively coarse sediment is sufficient, but the supply of relatively coarse sediment is not. The com-bination of low percentages of relatively coarse material with high percentages of fine material appears in the area predominated by the water process, where the supply of fine sediment is sufficient, but the supply of fine sediment is not. In the area predominated by coupled wind-water processes appears the combination of medium percentages of coarse and fine materials, and thus both coarse and fine sediments are in relatively sufficient supply. The manner in which the mean annual sediment concentrations of liquid- and solid-phases vary with total suspended sediment concentration is different. With the increased total suspended sediment concentration, mean annual sediment concentration of liquid-phase increased to a limit and then remained constant; however, mean annual sediment concentrations of solid-phase in-creased continuously. Thus, the magnitude of total suspended sediment concentration depends on the supply conditions of relatively coarse sediment and the ability of the flow to carry these relatively coarse sediment particles. In the area predominated by wind process, both the liquid- and the solid-phases cannot develop well, and their concentrations are low. In the area pre-dominated by the water process, the mean annual sediment concentrations of liquid- and solid-phases are also low. Only in the area predominated by coupled wind-water processes, can the conditions most favor the development of both the liquid- and solid-phases, and then the peaks of mean annual sediment concentrations of liquid- and solid-phases appear. Low values of suspended sediment concentrations appear in the areas predominated by the wind process or by the water process, a fact indicating that the predominating wind process or water process does not favor the development of hyperconcentrated flows. Peak values appear in the area where the coupled wind-water processes are predominated, indicating that the cou-pled wind-water processes most favor the development of hyperconcentrated flows.

Numerical prediction of flow hydrodynamics of wet molecular sieve particles in a liquid-fluidized bed

The Eulerian-Eulerian framework was used in the numerical simulation of liquid hydrodynamics and particle motion in liquid-fluidized beds. The kinetic theory of granular flow, which accounts for the viscous drag influence on the interstitial liquid phase, was used in combination with two-fluid models to simulate unsteady liquid-solid two-phase flows. We focus on local unsteady features predicted by the numerical models. The solid fraction power spectrum was analyzed. A typical flow pattern, such as core annular flow and particle back-mixing near the wall region of liquid-solid fluidized beds is obtained from this calculation. Effects of the restitution coefficient of particle-particle collisions on the distribution of granular pressure and temperature are discussed. Good agreement was achieved between the simulated results and experimental findings.

Numerical simulation and experimental study on eggshell membrane separation device

In order to provide theoretical guidance for separating egg membrane from eggshell by using mechanical agitation,CFD was used to explore the flow characteristics in stirred tank,using the Sliding Grid method to deal with the impeller rotational velocity zone in flow field,and using the Euler model to deal with liquid-solid two-phase flow.This study explored the influence of dish-shape bottom or flat-shape bottom,the clearance size between baffle and the side wall,and the axial height of impeller to bottom on suspension state of particles,solids holdup distribution,solid phase velocity and power number by CFD.Simulation results showed that better particles suspension effect in dish-shape tank can reduce particles accumulation at the bottom and power consumption.If there was a small clearance size(S)between the baffle and the side wall of the stirred tank,it would reduce particles accumulation at the bottom,and reduce the power consumption.However,too large S would decrease the suspension height of particles,not only cannot strengthen the main flow,but also lead to most fluid through clearance forming tangential flow,simulation results showed that S=6 mm was perfect.While decreased axial height of impeller(C)to bottom,particles accumulation at the bottom was decreased,but power consumption would increase,simulation results showed that C=H/5(H is height of liquid surface)was perfect.According to the simulation results,the structure of the stirring tank was optimized.At the same time,the influences of stirring rotational velocity,stirring time,solid-liquid ratio and separating medium temperature on egg membrane recovery were also studied by experiment,and optimal parameter combination of factors was obtained.The experiment results showed while the stirring time was 17.1 min,stirring rotational velocity was 350 r/min,solid-liquid ratio was 1:17 g/mL,the separating medium temperature was 32℃,the membrane recovery rate can reach above 89%.The device improves the recovery and utilization of discarded eggshell,and provides a reference for the solid-liquid two-phase flow and related study.

Time-Periodic Solution to the Compressible Navier–Stokes/Allen–Cahn System

In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.