Liquid-Gas Two-Phase Flow Simulation in Mold Filling Process with Level Set Method

Air entrapped in liquid metal during the mold filling process seriously affects the casting quality, thus it is important to track its behavior in the mold cavity. A liquid-gas two-phase flow model is developed to describe the mold filling process and predict the air entrapment defect. The model is based on the combination of SOLA and Level Set Method. The pressure and velocity fields are calculated by SOLA,and the interface movement is simulated by Level Set method as the most common interface tracking method in recent years.In order to validate the feasibility of the model,the liquid-gas two-phase simulation results were tested by the broken dam problem and the S-shaped experiment. Comparison between the experiments and simulation results show that Level Set method might be a very promising tool in two-phase flow simulation during the mold filling process.

Simulation of Gas-Water Two-Phase Flow in Tight Gas Reservoirs Considering the Gas Slip Effect

A mathematical model for the gas-water two-phase flow in tight gas reservoirs is elaborated.The model can account for the gas slip effect,stress sensitivity,and high-speed non-Darcy factors.The related equations are solved in the framework of a finite element method.The results are validated against those obtained by using the commercial software CMG(Computer Modeling Group software for advanced recovery process simulation).It is shown that the proposed method is reliable.It can capture the fracture rejection characteristics of tight gas reservoirs better than the CMG.A sensitivity analysis of various control factors(initial water saturation,reservoir parameters,and fracturing parameters)affecting the production in tight gas wells is conducted accordingly.Finally,a series of theoretical arguments are provided for a rational and effective development/exploitation of tight sandstone gas reservoirs.

Simulation of gas–liquid two-phase flow in a flow-focusing microchannel with the lattice Boltzmann method

A lattice Boltzmann method for gas–liquid two-phase flow involving non-Newtonian fluids is developed. Bubble formation in a flow-focusing microchannel is simulated by the method. The influences of flow rate ratio, surface tension,wetting properties, and rheological characteristics of the fluid on the two-phase flow are analyzed. The results indicate that the flow pattern transfers from slug flow to dry-plug flow with a sufficiently small capillary number. Due to the presence of three-phase contact lines, the contact angle has a more significant effect on the dry-plug flow pattern than on the slug flow pattern. The deformation of the front and rear meniscus of a bubble in the shear-thinning fluid can be explained by the variation of the capillary number. The reduced viscosity and increased contact angle are beneficial for the drag reduction in a microchannel. It also demonstrates the effectiveness of the current method to simulate the gas–liquid two-phase flow in a microchannel.

Numerical Simulation of a Two-Phase Flow with Low Permeability anda Start-Up Pressure Gradient

A new numerical model for low-permeability reservoirs is developed.The model incorporates the nonlinear characteristics of oil-water two-phase flows while taking into account the initiation pressure gradient.Related numerical solutions are obtained using a finite difference method.The correctness of the method is demonstrated using a two-dimensional inhomogeneous low permeability example.Then,the differences in the cumulative oil and water production are investigated for different starting water saturations.It is shown that when the initial water saturation grows,the water content of the block continues to rise and the cumulative oil production gradually decreases.

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.

Numerical simulation on the multiphase flow and reoxidation of the molten steel in a two-strand tundish during ladle change

A 3D mathematical model was proposed to investigate the molten steel–slag–air multiphase flow in a two-strand slab continuous casting(CC)tundish during ladle change.The study focused on the exposure of the molten steel and the subsequent reoxidation occurrence.The exposure of the molten steel was calculated using the coupled realizable k–εmodel and volume of fluid(VOF)model.The diffusion of dissolved oxygen was determined by solving the user-defined scalar(UDS)equation.Moreover,the user-defined function(UDF)was used to describe the source term in the UDS equation and determine the oxidation rate and oxidation position.The effect of the refilling speed on the molten steel exposure and dissolved oxygen content was also discussed.Increasing the refilling speed during ladle change reduced the refilling time and the exposure duration of the molten steel.However,the elevated refilling speed enlarged the slag eyes and increased the average dissolved oxygen content within the tundish,thereby exacerbating the reoxidation phenomenon.In addition,the time required for the molten steel with a high dissolved oxygen content to exit the tundish varied with the refilling speed.When the inlet speed was 3.0 m·s^(-1)during ladle change,the molten steel with a high dissolved oxygen content exited the outlet in a short period,reaching a maximum dissolved oxygen content of 0.000525wt%.Conversely,when the inlet speed was 1.8 m·s^(-1),the maximum dissolved oxygen content was 0.000382wt%.The refilling speed during the ladle change process must be appropriately decreased to minimize reoxidation effects and enhance the steel product quality.

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.

Flow field, sedimentation, and erosion characteristics around folded linear HDPE sheet sand fence: Numerical simulation study

Wind and sand hazards are serious in the Milan Gobi area of the Xinjiang section of the Korla Railway. In order to ensure the safe operation of railroads, there is a need for wind and sand protection in heavily sandy areas. The wind and sand flow in the region is notably bi-directional. To shield railroads from sand, a unique sand fence made of folded linear high-density polyethylene(HDPE) is used, aligning with the principle that the dominant wind direction is perpendicular to the fence. This study employed field observations and numerical simulations to investigate the effectiveness of these HDPE sand fences in altering flow field distribution and offering protection. It also explored how these fences affect the deposition and erosion of sand particles. Findings revealed a significant reduction in wind speed near the fence corner;the minimum horizontal wind speed on the leeward side of the first sand fence(LSF) decreased dramatically from 3 m/s to 0.64 m/s. The vortex area on the LSF markedly impacted horizontal wind speeds. Within the LSF, sand deposition was a primary occurrence. As wind speeds increased, the deposition zone shrank, whereas the positive erosion zone expanded. Close to the folded corners of the HDPE sand fence, there was a notable shift from the positive erosion zone to a deposition zone. Field tests and numerical simulations confirmed the high windproof efficiency(WE) and sand resistance efficiency(SE) in the HDPE sand fence. Folded linear HDPE sheet sand fence can effectively slow down the incoming flow and reduce the sand content, thus achieving good wind and sand protection. This study provides essential theoretical guidance for the design and improvement of wind and sand protection systems in railroad engineering.

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 Simulations of the Flow Field around a Cylindrical Lightning Rod

As an important lightning protection device in substations,lightning rods are susceptible to vibration and potential structural damage under wind loads.In order to understand their vibration mechanism,it is necessary to conduct flow analysis.In this study,numerical simulations of the flow field around a 330 kV cylindrical lightning rod with different diameters were performed using the SST k-ωmodel.The flow patterns in different segments of the lightning rod at the same reference wind speed(wind speed at a height of 10 m)and the flow patterns in the same segment at different reference wind speeds were investigated.The variations of lift coefficient,drag coefficient,and vorticity distribution were obtained.The results showed that vortex shedding phenomena occurred in all segments of the lightning rod,and the strength of vortex shedding increased with decreasing diameter.The vorticity magnitude and the root mean square magnitudes of the lift coefficient and drag coefficient also increased accordingly.The time history curves of the lift coefficient and drag coefficient on the surface of the lightning rod exhibited sinusoidal patterns with a single dominant frequency.For the same segment,as the wind speed increased in a certain range,the root mean square values of the lift coefficient and drag coefficient decreased,while their dominant frequencies increased.Moreover,there was a proportional relationship between the dominant frequencies of the lift coefficient and drag coefficient.The findings of this study can provide valuable insights for the refined design of lightning rods with similar structures.

Analysis of debris flow control effect and hazard assessment in Xinqiao Gully,Wenchuan M_(s)8.0 earthquake area based on numerical simulation

Xinqiao Gully is located in the area of the 2008 Wenchuan M_(s)8.0 earthquake in Sichuan province,China.Based on the investigation of the 2023"6-26"Xinqiao Gully debris flow event,this study assessed the effectiveness of the debris flow control project and evaluated the debris flow hazards.Through field investigation and numerical simulation methods,the indicators of flow intensity reduction rate and storage capacity fullness were proposed to quantify the effectiveness of the engineering measures in the debris flow event.The simulation results show that the debris flow control project reduced the flow intensity by41.05%to 64.61%.The storage capacity of the dam decreases gradually from upstream to the mouth of the gully,thus effectively intercepting and controlling the debris flow.By evaluating the debris flow of different recurrence intervals,further measures are recommended for managing debris flow events.

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.

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.

Numerical Simulation and Analysis of Solid-liquid Two-phase Flow in Centrifugal Pump

The flow with solid-liquid two-phase media inside centrifugal pumps is very complicated and the relevant method for the hydraulic design is still immature so far. There exist two main problems in the operation of the two-phase flow pumps, i.e., low overall efficiency and severe abrasion. In this study, the three-dimensional, steady, incompressible, and turbulent solid-liquid two-phase flows in a low-specific-speed centrifugal pump are numerically simulated and analyzed by using a computational fluid dynamics （CFD） code based on the mixture model of the two-phase flow and the RNG k-~ two-equation turbulence model, in which the influences of rotation and curvature are fully taken into account. The coupling between impeller and volute is implemented by means of the frozen rotor method. The simulation results predicted indicate that the solid phase properties in two-phase flow, especially the concentration, the particle diameter and the density, have strong effects on the hydraulic performance of the pump. Both the pump head and the efficiency are reduced with increasing particle diameter or concentration. However, the effect of particle density on the performance is relatively minor. An obvious jet-wake flow structure is presented near the volute tongue and becomes more remarkable with increasing solid phase concentration. The suction side of the blade is subject to much more severe abrasion than the pressure side. The obtained results preliminarily reveal the characteristics of solid-liquid two-phase flow in the centrifugal pump, and are helpful for improvement and empirical correction in the hydraulic design of centrifugal pumps.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

Numerical simulation of gas-liquid two-phase jet flow in air-bubble generator

Air-bubble generator is the key part of the self-inspiration type swirl flotation machines,whose flow field structure has a great effect on flotation.The multiphase volume of fluid(VOF),standard k-ε turbulent model and the SIMPLE method were chosen to simulate the present model;the first order upwind difference scheme was utilized to perform a discrete solution for momentum equation.The distributing law of the velocity,pressure,turbulent kinetic energy of every section along the flow direction of air-bubble generator was analyzed.The results indicate that the bubbles are heavily broken up in the middle cross section of throat sect and the entrance of diffuser sect along the flow direction,and the turbulent kinetic energy of diffuser sect is larger than the entrance of throat sect and mixing chamber.

Two-dimensional Dynamics Simulation of Two-phase Debris Flow

To investigate the movement mechanism of debris flow, a two-dimensional, two-phase, depthintegrated model is introduced. The model uses Mohr-Coulomb plasticity for the solid rheology, and the fluid stress is modeled as a Newtonian fluid. The interaction between solid and liquid phases, which plays a major role in debris flow movement, is assumed to consist of drag and buoyancy forces. The applicability of drag force formulas is discussed. Considering the complex interaction between debris flow and the bed surface, a combined friction boundary condition is imposed on the bottom, and this is also discussed. To solve the complex model equations, a numerical method with second-order accuracy based on the finite volume method is proposed. Several numerical experiments are performed to verify the feasibilities of model and numerical schemes. Numerical results demonstrate that different solid volume fractions substantially affect debris flow movement.

Numerical simulation of flow focusing pattern and morphological changes in two-phase flow inside nozzle

The flow focusing nozzle is a new type of nozzle that performs effective atomization of the discrete phase by means of high-speed motion of the continuous phase.The flow pattern and its morphological changes have a significant effect on the atomization, but the influence of different parameters on the morphological change of the flow pattern remains unclear.The flow focusing pattern and morphological changes in the two-phase flow inside the nozzle were simulated numerically, based on the volume of fluid method.The results demonstrate that the ratio of the nozzle-to-capillary distance and capillary diameter, the gas–liquid velocity ratio, and capillary diameter have significant effects on the flow pattern.When the ratio of the nozzle-to-capillary distance H and capillary diameter D increases, or the capillary diameter D increases, the flow pattern tends to transform into a laminar form; however, when the gas–liquid velocity ratio V increases, the flow pattern tends to transform into a turbulence form.Furthermore, we define the cone-shaped expansion rate, cone-shaped focusing rate,and cone angle in order to study the morphological changes in the cone shape inside the nozzle.The results indicate that the morphological change of the cone shape and flow pattern transformation is interrelated.When the cone shape tends to be unstable, the flow pattern changes towards flow blurring, whereas, a stable cone indicates that the flow tends to exhibit a droplet pattern.

Simulation of two-phase debris flow scouring bridge pier

Debris flows are typical two-phase flows, which commonly accompany erosion in mountainous areas, and may destroy bridge engineering by scouring. In this study, a physically-based two-phase model is applied for the simulation of debris flow scouring of bridge pier. In this model, the shear stress of debris flow on an erodible bed is considered to be a function of the solid shear stress, fluid shear stress, and volume fraction; accordingly, the erosion is incorporated into the two-phase model. Using a highaccuracy computational scheme based on the finite volume method, the model is employed for simulating a dynamic debris flow over an erodible bed. The numerical results are consistent with the experimental data, and verify the feasibility of the two-phase model. Moreover, a simple numerical test is performed to exhibit the fundamental behaviour of debris flow scouring of bridge pier, which shows that the degree of erosion on each side of the pier is higher compared to other areas. The scouring depth is influenced by the variations of solid volume fraction and velocity of debris flow and pier width.