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.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.

A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows

In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin （SUPG/PSPG） extended finite element method （XFEM） is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.

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.

Velocity Slip and Interfacial Momentum Transfer in the Transient Section of Supersonic Gas-Droplet Two-Phase Flows

Modelling and simulations are conducted on velocity slip and interfacial momentum transfer for supersonic two-pha.se (gas-droplet) flow in the transient section inside and outside a Laval jet(LJ). The initial velocity slip between gas and droplets causes an interfacial momentum transfer flux as high as (2.0-5.0) x 104 Pa. The relaxation time corresponding to this transient process is in the range of 0.015-0.090ms for the two-phase flow formed inside the LJ and less than 0.5ms outside the LJ. It demonstrates the unique performance of this system for application to fast chemical reactions using electrically active media with a lifetime in the order of 1 ms. Through the simulations of the transient processes with initial Mach number Mg from 2.783 to 4.194 at different axial positions inside the LJ, it is found that Mg has the strongest effect on the process. The momentum flux increases as the Mach number decreases. Due to compression by the shock wave at the end of the LJ, the flow pattern becomes two dimensional and viscous outside the LJ. Laser Doppler velocirneter (LDV) measurements of droplet velocities outside the LJ are in reasonably good agreement with the results of the simulation.

An Experimental Study on the Void Fraction for Gas-Liquid Two-Phase Flows in a Horizontal Pipe

The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.

Numerical Simulation of the Gas-solid Two-phase Flows in a Precalciner

The gas-solid two-phase flous of the precalciner were simulated by different multiphase models,such as mixture model,the Enderium model,including mixture and dispersed,and discrete phase model（DPM）,The results of the different multiphase models were analyzed and compared.showing the rationality of the diffusion and mixture of the cenment raic meals and coal poroder some extent Moreover,the results also shose the rationality of the given inlets parameters of actual process of the precalciner.

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.

A hybrid scheme for computing incompressible two-phase flows

We propose a hybrid scheme for computations of incompressible two-phase flows. The incompressible constraint has been replaced by a pressure Poisson-like equation and then the pressure is updated by the modified marker and cell method. Meanwhile, the moment equations in the incompressible Navier-Stokes equations are solved by our semidiscrete Hermite central-upwind scheme, and the interface between the two fluids is considered to be continuous and is described implicitly as the 0.5 level set of a smooth function being a smeared out Heaviside function. It is here named the hybrid scheme. Some numerical experiments are successfully carried out, which verify the desired efficiency and accuracy of our hybrid scheme.

A K-εTWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.

Analysis of choked two-phase flows of gas and particle in a C-D nozzle

Particle-gas two-phase flows show significantly different behaviors compared to single gas flow through a convergent-divergent nozzle. Non-equilibrium effects, thermal and velocity lag results to the inefficiency of nozzle performance. In the present studies, theoretical analysis and numerical simulations were carried out to investigate particle-gas flows in a C-D nozzle. Homogeneous equilibrium model that no lag in velocity and temperature occurs between particles and gas phase was used to derive mass flow rate and sound speed of multiphase flows. Two-phase flows are regarded as isentropic flows that isentropic relations can be used for homogeneous equilibrium model. Discrete phase model （DPM） where interaction with continuous phase and discrete random walk model were considered was used to calculate particle- gas flows. Particle mass loadings were varied to investigate their effects on choking phenomena of particle-gas flows. Mass flow rate and sound speed of mixture flows were theoretically calculated by homogeneous equilibrium model and compared with numerical results. Shock wave structure and particle number density were also obtained to be different at different particle mass loading and operating pressure conditions.

NUMERICAL SIMULATION OF 1-D UNSTEADY TWO-PHASE FLOWS WITH SHOCKS

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.

Phase identification by a novel needle-contact capacitance probe in gas-liquid two-phase flows

In this paper,we propose a novel probe to identify phases in any two-phase flows where one phase is conductive and the other nonconductive.We can further obtain many parameters such as void fraction,bubble velocity,and interfacial area concentration.Compared with the traditional probe,the novel probe has unique advantages that it is less dependent on water conductance or distance between the electrodes,and that the amplitude is bigger between high and low levels.Theoretical analyses showed that the measurement error became higher when water conductance decreases or distance increases,which is consistent with the theoretical analyses.Experimental results showed that the output signal kept constant with salt content of 0-5% and electrode distance of 0-30 mm in tap water.The level difference was up to 6.4 V,resulting in identifying two phases easily.Time traces of phase identification were completely consistent with the flow structures.

Experimental investigations on characteristics of water-air two-phase flows during water-fillings in undulation pipelines

Visual and pressurized pipeline systems with single- and multi-undulation layouts were used to study experimentally and analyze theoretically the transient characteristics of water-air two-phase flow during water fillings in undulation pipelines based on the combination action analyses of both the communicating pipe and the gravity of the water-air two-phase flows in the descending pipe. For the single undulation pipeline, the complex two-phase flow-pattern evolutions including full pipe flow and stratified flow for low, medium, high water-filling velocity cases, respectively, lead to a great difference in transient pressure, flow pattern and the water-filling duration. Especially for low and medium water-filling velocity cases, the hydraulic theories related to hydraulic drop and hydraulic jump were employed to investigate the entrapped air pocket evolutions in the descending pipe, and the mechanism of negative pressure at the top of the undulation pipes was analyzed. For the same multi-undulation pipeline, due to the different elevations of the three undulation points along flow direction, namely three different types of pipeline layout, high-medium-low case (high elevation undulation point, medium one, and low one), low-medium-high and high-low-medium ones, their water-filling durations are significantly different, i.e., approximately 80.02 s, 227.34 s and 617.78 s. Meanwhile, there are significant differences in flow patterns in water filling, namely larger entrapped air pockets in three descending pipes for the high-medium-low case, entrapped air pockets in the first two descending pipes and open channel stratified flow in the last one for low-medium-high case, some bubbles in three descending pipes for the high-low-medium case.

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.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Entropic Multi-Relaxation-Time Lattice Boltzmann Model for Large Density Ratio Two-Phase Flows

We propose a multiple relaxation time entropic realization of a recent twophase flow lattice Boltzmann model[S.A.Hosseini,B.Dorschner,and I.V.Karlin,Journal of Fluid Mechanics 953(2022)].While the original model with a single relaxation time allows us to reach large density ratios,it is limited in terms of stability with respect to non-dimensional viscosity and velocity.Herewe showthat the entropic multiple relaxation time model extends the stability limits of the model significantly,which allows us to reach larger Reynolds numbers for a given grid resolution.The thermodynamic properties of the solver,using the Peng-Robinson equation of state,are studied first using simple configurations.Co-existence densities and temperature scaling of both the interface thickness and the surface tension are shown to agree well with theory.The model is then used to simulate the impact of a drop onto a thin liquid film with density and viscosity ratios matching those of water and air both in two and three dimensions.The results are in very good agreement with theoretically predicted scaling laws and experimental data.

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.