NUMERICAL MODELING OF 3-D TURBULENT TWO-PHASE FLOW AND COAL COMBUSTION IN A PULVERIZED-COAL COMBUSTOR

In the present paper, a multifluid model of two-phase flows with pulverized-coal combustion, based on a continuum-trajectory model with reacting particle phase, is developed and employed to simulate the 3-D turbulent two-phase hows and combustion in a new type of pulverized-coal combustor with one primary-air jet placed along the wall of the combustor. The results show that: (1) this continuum-trajectory model with reacting particle phase can be used in practical engineering to qualitatively predict the flame stability, concentrations of gas species, possibilities of slag formation and soot deposition, etc.; (2) large recirculation zones can be created in the combustor, which is favorable to the ignition and flame stabilization.

Numerical simulation of stratified turbulent two-phase flow in aquatic environment

The two fluid model of stratified turbulent two phase flow in aquatic environment is developed in this paper. The motion of each phase is described by a unified multi fluid model in an Eulerian coordinate system. The laws of turbulent transportation for each phase, and the restriction of each other between the two phases are completely simulated. The complex two phase turbulence with strong buoyancy effects is selected to examine numerically. The extensive experimental data obtained in stratified flow are used here. Comparison of the results of numerical simulation with the experimental data is conducted. It has shown that the results of numerical simulation are satisfactory.

Heat and Mass Transfers in a Two-Phase Stratified Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction

This research focused on the study of heat and mass transfers in a two-phase stratified turbulent fluid flow in a geothermal pipe with chemical reaction. The derived non-linear partial differential equations governing the flow were solved using the Finite Difference Method. The effects of various physical parameters on the concentration, skin friction, heat, and mass transfers have been determined. Analysis of the results obtained indicated that the coefficient of skin friction decreased with an increase in Reynolds number and solutal Grasholf number, the rate of heat transfer increased with an increase in Eckert number, Prandtl number, and angle of inclination, and the rate of mass transfer increased with increase in Reynolds number, Chemical reaction parameter and angle of inclination. The findings would be useful to engineers in designing and maintaining geothermal pipelines more effectively.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Integrated numerical simulation of hydraulic fracturing and production in shale gas well considering gas-water two-phase flow

Based on the displacement discontinuity method and the discrete fracture unified pipe network model,a sequential iterative numerical method was used to build a fracturing-production integrated numerical model of shale gas well considering the two-phase flow of gas and water.The model accounts for the influence of natural fractures and matrix properties on the fracturing process and directly applies post-fracturing formation pressure and water saturation distribution to subsequent well shut-in and production simulation,allowing for a more accurate fracturing-production integrated simulation.The results show that the reservoir physical properties have great impacts on fracture propagation,and the reasonable prediction of formation pressure and reservoir fluid distribution after the fracturing is critical to accurately predict the gas and fluid production of the shale gas wells.Compared with the conventional method,the proposed model can more accurately simulate the water and gas production by considering the impact of fracturing on both matrix pressure and water saturation.The established model is applied to the integrated fracturing-production simulation of practical horizontal shale gas wells.The simulation results are in good agreement with the practical production data,thus verifying the accuracy of the model.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.

Identifying the enhancement mechanism of Al/MoO_(3) reactive multilayered films on the ignition ability of semiconductor bridge using a one-dimensional gas-solid two-phase flow model

Energetic Semiconductor bridge(ESCB)based on reactive multilayered films(RMFs)has a promising application in the miniature and intelligence of initiator and pyrotechnics device.Understanding the ignition enhancement mechanism of RMFs on semiconductor bridge(SCB)during the ignition process is crucial for the engineering and practical application of advanced initiator and pyrotechnics devices.In this study,a one-dimensional(1D)gas-solid two-phase flow ignition model was established to study the ignition process of ESCB to charge particles based on the reactivity of Al/MoO_(3) RMFs.In order to fully consider the coupled exothermic between the RMFs and the SCB plasma during the ignition process,the heat release of chemical reaction in RMFs was used as an internal heat source in this model.It is found that the exothermal reaction in RMFs improved the ignition performance of SCB.In the process of plasma rapid condensation with heat release,the product of RMFs enhanced the heat transfer process between the gas phase and the solid charge particle,which accelerated the expansion of hot plasma,and heated the solid charge particle as well as gas phase region with low temperature.In addition,it made up for pressure loss in the gas phase.During the plasma dissipation process,the exothermal chemical reaction in RMFs acted as the main heating source to heat the charge particle,making the surface temperature of the charge particle,gas pressure,and gas temperature rise continuously.This result may yield significant advantages in providing a universal ignition model for miniaturized ignition devices.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

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.

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 1–Turbulence properties and particle chord time and length

This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅰ) Turbulent Gas-Solid Flow-Reaction Model

Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅱ) Numerical Simulation on the Gas-Solid Two-Phase Turbulent Flow

Numerical simulation on the flow,heat transfer and cracking reactions in commercial fluid catalyticcracking(FCC)riser reactors were carried out employing the developed turbulent gas-solid two-phase flow-reac-tion model for FCC riser reactors given in Part Ⅰ of the present paper.Detailed information about the turbulentflow fields in the riser reactor obtained revealed the basic characteristics of the gas-solid two-phase turbulentflows when heat transfer and catalytic cracking reactions were co-existing in the riser.Results showed that thedistributions of the flow,the turbulence kinetic energy and the catalyst particle concentration are not uniform inthe axial,radial and tangential directions.The most complicated part of the riser reactor is the feed injectingzone.The complicated configuration of the turbulent gas-solid two-phase flows would exert a great influence onthe results of interphase heat transfer and cracking reactions.

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

To predict the characteristics of dense liquid-solid two-phase flow, K-Ε-T model is established, in which the turbulent flow of fluid phase was described with fluid turbulent kinetic energy Kf and its dissipation rate Εf, and the particles random motion was described with particle turbulent energy Kp and its dissipation rate Εp and pseudothermal temperature Tp. The governing equations were also derived. With K-Ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.

Deduction and Validation of an Eulerian-Eulerian Model for Turbulent Dilute Two-Phase Flows by Means of the Phase Indicator Function-Disperse Elements Probability Density Function

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

NUMERICAL MODELING OF TURBULENTEVAPORATING GAS-DROPLET TWO-PHASE FLOWS IN AN AFTERBURNER DIFFUSOR OF TURBO-FAN JET ENGINES

The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.