Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

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.

Multi-physical fields distribution in billet during helical electromagnetic stirring:A numerical simulation research

Electromagnetic stirring is one of the widely applied techniques to modify the quality of casting billets.Different from conventional rotate stirring,the helical stirring is more professional in assisting multi-dimensional flow of molten metal and eliminating solidification defects.In this study,the single-winding helical stirring(SWHS)was introduced,offering advantages such as smaller volume and lower electromagnetic shielding compared to traditional helical stirring methods.Following a comprehensive numerical simulation,the stirring parameters of SWHS were adjusted to yoke inclination angle of 43°and frequency of 12 Hz.The higher electromagnetic force and flow velocity in drawing direction,as well as the lower temperature gradient induced by the SWHS,are positive factors for homogeneous solidification of billet.The experimental results on Al-8%Si alloy and 0.4%C-1.1%Mn steel demonstrate that compared to rotate stirring,the SWHS process can induce better billet quality and is more effective in accelerating the equiaxed expansion and reducing element segregation.The SWHS process can enhance the equiaxed ratio of the billet by 58.3%and reduce segregation degree of carbon element by 10.97%.Consequently,SWHS holds great promise as a potential approach for improving the quality of continuous casting billets.

Numerical Simulation and Entropy Production Analysis of Centrifugal Pump with Various Viscosity

The fluid’s viscosity significantly affects the performance of a centrifugal pump.The entropy production method and leakage are employed to analyze the performance changes under various viscosities by numerical simulation and validated by experiments.The results showed that increasing viscosity reduces both the pump head and efficiency.In addition,the optimal operating point shifts to the left.Leakage is influenced by vortex distribution in the front chamber and boundary layer thickness in wear-ring clearance,leading to an initial increase and subsequent decrease in leakage with increasing viscosity.The total entropy production Spro,Total inside the pump rises with increasing viscosity.The different mechanisms dominate under varying conditions:Turbulent dissipation dominates at low viscosity.Under high-viscosity conditions,energy loss is primarily caused by direct dissipation Spro,D and wall entropy production Spro,W.This study provides a deeper and more objective understanding of the energy characteristics of centrifugal pumps handling fluids of various viscosity,potentially aiding in optimizing pump design and improving energy conversion efficiency.

In-situ measurement via the flow-through method and numerical simulations for radon exhalation during measurements of the radon exhalation rate

Small-scale measurements of the radon exhalation rate using the flow-through and closed-loop methods were conducted on the surface of a uranium tailing pond to better understand the differences between the two methods.An abnormal radon exhalation behavior was observed,leading to computational fluid dynamics(CFD)-based simulations in which dynamic radon migration in a porous medium and accumulation chamber was considered.Based on the in-situ experimental and numerical simulation results,variations in the radon exhalation rate subject to permeability,flow rate,and insertion depth were quantified and analyzed.The in-situ radon exhalation rates measured using the flow-through method were higher than those measured using the closed-loop method,which could be explained by the negative pressure difference between the inside and outside of the chamber during the measurements.The consistency of the variations in the radon exhalation rate between the experiments and simulations suggests the reliability of CFD-based techniques in obtaining the dynamic evolution of transient radon exhalation rates for diffusion and convection at the porous medium-air interface.The synergistic effects of the three factors(insertion depth,flow rate,and permeability)on the negative pressure difference and measured exhalation rate were quantified,and multivariate regression models were established,with positive correlations in most cases;the exhalation rate decreased with increasing insertion depth at a permeability of 1×10^(−11) m^(2).CFD-based simulations can provide theoretical guidance for improving the flow-through method and thus achieve accurate measurements.

Numerical simulation of melt flow and temperature field during DC casting 2024 aluminium alloy under different casting conditions

Casting speed,casting temperature and secondary cooling water flow rate are the main process parameters affecting the DC casting process.These parameters significantly influence the flow and temperature fields during casting,which are crucial for the quality of the ingot and can determine the success or failure of the casting operation.Numerical simulation,with the advantages of low cost,rapid execution,and visualized results,is an important method to study and optimize the DC casting process.In the present work,a simulation model of DC casting 2024 aluminum alloy was established,and the reliability of the model was verified.Then,the influence of casting parameters on flow field and temperature field was studied in detail by numerical simulation method.Results show that with the increase of casting speed,the melt flow becomes faster,the depths of slurry zone and mushy zone increase,and the variation of slurry zone depth is greater than that of mushy zone.With an increase in casting temperature,the melt flow rate increases,the depth of the slurry zone becomes shallower,and the depth of the mushy zone experiences only minor changes.The simulation results further indicate that the increase of the flow rate of the secondary cooling water slightly reduces the depths of both slurry and mushy zone.

Numerical simulations for radon migration and exhalation behavior during measuring radon exhalation rate with closed-loop method

Accurate measurements of the radon exhalation rate help identify and evaluate radon risk regions in the environment.Among these measurement methods,the closed-loop method is frequently used.However,traditional experiments are insufficient or cannot analyze the radon migration and exhalation patterns at the gas–solid interface in the accumulation chamber.The CFD-based technique was applied to predict the radon concentration distribution in a limited space,allowing radon accumulation and exhalation inside the chamber intuitively and visually.In this study,three radon exhalation rates were defined,and two structural ventilation tubes were designed for the chamber.The consistency of the simulated results with the variation in the radon exhalation rate in a previous experiment or analytical solution was verified.The effects of the vent tube structure and flow rate on the radon uniformity in the chamber;permeability,insertion depth,and flow rate on the radon exhalation rate and the effective diffusion coefficient on back-diffusion were investigated.Based on the results,increasing the inser-tion depth from 1 to 5 cm decreased the effective decay constant by 19.55%,whereas the curve-fitted radon exhalation rate decreased(lower than the initial value)as the deviation from the initial value increased by approximately 7%.Increasing the effective diffusion coefficient from 2.77×10^(-7) to 7.77×10^(-6) m^(2) s^(-1) made the deviation expand from 2.14 to 15.96%.The conclusion is that an increased insertion depth helps reduce leakage in the chamber,subject to notable back-diffusion,and that the closed-loop method is reasonably used for porous media with a low effective diffusion coefficient in view of the back-diffusion effect.The CFD-based simulation is expected to provide guidance for the optimization of the radon exhalation rate measurement method and,thus,the accurate measurement of the radon exhalation rate.

Numerical simulation of flow field deposition and erosion characteristics around bridge-road transition section

Wind-sand flow generates erosion and deposition around obstacles such as bridges and roadbeds, resulting in sand damage and endangering railway systems in sandy regions. Previous studies have mainly focused on the flow field around roadbeds, overlooking detailed examinations of sand particle erosion and deposition patterns near bridges and roadbeds. This study employs numerical simulations to analyze the influence of varying heights and wind speeds on sand deposition and erosion characteristics at different locations: the bridge-road transition section(side piers), middle piers, and roadbeds. The results show that the side piers, experience greater accumulation than the middle piers. Similarly, the leeward side of the roadbed witnesses more deposition compared to the windward side. Another finding reveals a reduced sand deposition length as the vertical profile, in alignment with the wind direction, moves further from the bridge abutments at the same clearance height. As wind speeds rise, there’s a decline in sand deposition and a marked increase in erosion around the side piers, middle piers and roadbeds. In conclusion, a bridge clearance that’s too low can cause intense sand damage near the side piers, while an extremely high roadbed may lead to extensive surface sand deposition. Hence, railway bridges in areas prone to sandy winds should strike a balance in clearance height. This research provides valuable guidelines for determining the most suitable bridge and roadbed heights in regions affected by wind and sand.

Numerical Simulation and Parallel Computing of Acoustic Wave Equation in Isotropic-Heterogeneous Media

In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.

Determination method of mesh size for numerical simulation of blast load in near-ground detonation

In order to improve the overall resilience of the urban infrastructures, it is required to conduct blast resistant design for important building structures in the city. For complex terrain in the city, it is recommended to determine the blast load on the structures via numerical simulation. Since the mesh size of the numerical model highly depends on the explosion scenario, there is no generally applicable approach for the mesh size selection. An efficient method to determine the mesh size of the numerical model of near-ground detonation based on explosion scenarios is proposed in this study. The effect of mesh size on the propagation of blast wave under different explosive weights was studied, and the correlations between the mesh size effect and the charge weight or the scaled distance was described. Based on the principle of the finite element method and Hopkinson-Cranz scaling law, a mesh size measurement unit related to the explosive weight was proposed as the criterion for determining the mesh size in the numerical simulation. Finally, the applicability of the method proposed in this paper was verified by comparing the results from numerical simulation and the explosion tests and was verified in AUTODYN.

Coupled CFD-DEM Numerical Simulation of the Interaction of a Flow-Transported Rag with a Solid Cylinder

A coupled Computational Fluid Dynamics-Discrete Element Method(CFD-DEM)approach is used to calculate the interaction of a flexible rag transported by a fluid current with a fixed solid cylinder.More specifically a hybrid Eulerian-Lagrangian approach is used with the rag being modeled as a set of interconnected particles.The influence of various parameters is considered,namely the inlet velocity(1.5,2.0,and 2.5 m/s,respectively),the angle formed by the initially straight rag with the flow direction(45°,60°and 90°,respectively),and the inlet position(90,100,and 110 mm,respectively).The results show that the flow rate has a significant impact on the permeability of the rag.The higher the flow rate,the higher the permeability and the rag speed difference.The angle has a minor effect on rag permeability,with 45°being the most favorable angle for permeability.The inlet position has a small impact on rag permeability,while reducing the initial distance between the rag an the cylinder makes it easier for rags to pass through.

Numerical simulation on sand sedimentation and erosion characteristics around HDPE sheet sand barrier under different wind angles

For the safety of railroad operations,sand barriers are utilized to mitigate wind-sand disaster effects.These disasters,characterized by multi-directional wind patterns,result in diverse angles among the barriers.In this study,using numerical simulations,we examined the behavior of High Density Polyethylene(HDPE)sheet sand barriers under different wind angles,focusing on flow field distribution,windproof efficiency,and sedimentation erosion dynamics.This study discovered that at a steady wind speed,airflow velocity varies as the angle between the airflow and the HDPE barrier changes.Specifically,a 90°angle results in the widest low-speed airflow area on the barrier’s downwind side.If the airflow is not perpendicular to the barrier,it prompts a lateral airflow movement which decreases as the angle expands.The windproof efficiency correlates directly with this angle but inversely with the wind’s speed.Notably,with a wind angle of 90°,wind speed drops by 81%.The minimum wind speed is found at 5.1H(the sand barrier height)on the barrier’s downwind side.As the angle grows,the barrier’s windproof efficiency improves,extending its protective reach.Sedimentation is most prominent on the barrier’s downwind side,as the wind angle shifts from 30°to 90°,the sand sedimentation area on the barrier’s downwind side enlarges by 14.8H.As the angle grows,sedimentation intensifies,eventually overtakes the forward erosion and enlarges the sedimentation area.

Explosion resistance performance of reinforced concrete box girder coated with polyurea:Model test and numerical simulation

To study the anti-explosion protection effect of polyurea coating on reinforced concrete box girder,two segmental girder specimens were made at a scale of 1:3,numbered as G(without polyurea coating)and PCG(with polyurea coating).The failure characteristics and dynamic responses of the specimens were compared through conducting explosion tests.The reliability of the numerical simulation using LS-DYNA software was verified by the test results.The effects of different scaled distances,reinforcement ratios,concrete strengths,coating thicknesses and ranges of polyurea were studied.The results show that the polyurea coating can effectively enhance the anti-explosion performance of the girder.The top plate of middle chamber in specimen G forms an elliptical penetrating hole,while that in specimen PCG only shows a very slight local dent.The peak vertical displacement and residual displacement of PCG decrease by 74.8% and 73.7%,respectively,compared with those of specimen G.For the TNT explosion with small equivalent,the polyurea coating has a more significant protective effect on reducing the size of fracture.With the increase of TNT equivalent,the protective effect of polyurea on reducing girder displacement becomes more significant.The optimal reinforcement ratio,concrete strength,thickness and range of polyurea coating were also drawn.

Experimental and Three-Dimensional Numerical Simulation of Phenomena Induced by Submerged Oblique Jet Scouring

Scouring experiments were conducted using a three-dimensional laser scanning technology for angles of the jet spanning the interval from 0°to 30°,and the characteristics of the scour hole in equilibrium conditions were investigated accordingly.The results indicate that the optimal scouring effects occur when the jet angle is in the ranges between 15°and 20°.Moreover,the dimensionless profiles of the scour hole exhibit a high degree of similarity at different jet angles.Numerical simulations conducted using the Flow-3D software to investigate the bed shear stress along the jet impingement surface have shown that this stress is influenced by both the resultant force and the jet impingement surface area.It reaches its maximum value when the jet is vertical,decreases rapidly as the jet starts to tilt,then increases slightly,and decreases again significantly when the angle exceeds 20°.

Investigations on High-Speed Flash Boiling Atomization of Fuel Based on Numerical Simulations

Flash boiling atomization(FBA)is a promising approach for enhancing spray atomization,which can generate a fine and more evenly distributed spray by increasing the fuel injection temperature or reducing the ambient pressure.However,when the outlet speed of the nozzle exceeds 400 m/s,investigating high-speed flash boiling atomization(HFBA)becomes quite challenging.This difficulty arises fromthe involvement ofmany complex physical processes and the requirement for a very fine mesh in numerical simulations.In this study,an HFBA model for gasoline direct injection(GDI)is established.This model incorporates primary and secondary atomization,as well as vaporization and boilingmodels,to describe the development process of the flash boiling spray.Compared to lowspeed FBA,these physical processes significantly impact HFBA.In this model,the Eulerian description is utilized for modeling the gas,and the Lagrangian description is applied to model the droplets,which effectively captures the movement of the droplets and avoids excessive mesh in the Eulerian coordinates.Under various conditions,numerical solutions of the Sauter mean diameter(SMD)for GDI show good agreement with experimental data,validating the proposed model’s performance.Simulations based on this HFBA model investigate the influences of fuel injection temperature and ambient pressure on the atomization process.Numerical analyses of the velocity field,temperature field,vapor mass fraction distribution,particle size distribution,and spray penetration length under different superheat degrees reveal that high injection temperature or low ambient pressure significantly affects the formation of small and dispersed droplet distribution.This effect is conducive to the refinement of spray particles and enhances atomization.

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.

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.

Numerical Simulation of Slurry Diffusion in Fractured Rocks Considering a Time-Varying Viscosity

To analyze the effects of a time-varying viscosity on the penetration length of grouting,in this study cement slur-ries with varying water-cement ratios have been investigated using the Bingham’sfluidflow equation and a dis-crete element method.Afluid-solid coupling numerical model has been introduced accordingly,and its accuracy has been validated through comparison of theoretical and numerical solutions.For different fracture forms(a single fracture,a branch fracture,and a fracture network),the influence of the time-varying viscosity on the slurry length range has been investigated,considering the change in the fracture aperture.The results show that under different fracture forms and the same grouting process conditions,the influence of the time-varying viscosity on the seepage length is 0.350 m.

Coupled Numerical Simulation of Electromagnetic and Flow Fields in a Magnetohydrodynamic Induction Pump

Magnetohydrodynamic(MHD)induction pumps are contactless pumps able to withstand harsh environments.The rate of fluid flow through the pump directly affects the efficiency and stability of the device.To explore the influence of induction pump settings on the related delivery speed,in this study,a numerical model for coupled electromagnetic and flow field effects is introduced and used to simulate liquid metal lithium flow in the induction pump.The effects of current intensity,frequency,coil turns and coil winding size on the velocity of the working fluid are analyzed.It is shown that the first three parameters have a significant impact,while changes in the coil turns have a negligible influence.The maximum increase in working fluid velocity within the pump for the parameter combination investigated in this paper is approximately 618%.As the frequency is increased from 20 to 60 Hz,the maximum increase in the mean flow rate of the working fluid is approximately 241%.These research findings are intended to support the design and optimization of these devices.

High-Precision Flow Numerical Simulation and Productivity Evaluation of Shale Oil Considering Stress Sensitivity

Continental shale oil reservoirs,characterized by numerous bedding planes and micro-nano scale pores,feature significantly higher stress sensitivity compared to other types of reservoirs.However,research on suitable stress sensitivity characterization models is still limited.In this study,three commonly used stress sensitivity models for shale oil reservoirs were considered,and experiments on representative core samples were conducted.By fitting and comparing the data,the“exponential model”was identified as a characterization model that accurately represents stress sensitivity in continental shale oil reservoirs.To validate the accuracy of the model,a two-phase seepage mathematical model for shale oil reservoirs coupled with the exponential model was introduced.The model was discretely solved using the finite volume method,and its accuracy was verified through the commercial simulator CMG.The study evaluated the productivity of a typical horizontal well under different engineering,geological,and fracture conditions.The results indicate that considering stress sensitivity leads to a 13.57%reduction in production for the same matrix permeability.Additionally,as the fracture half-length and the number of fractures increase,and the bottomhole flowing pressure decreases,the reservoir stress sensitivity becomes higher.