Exploration of the coupled lattice Boltzmann model based on a multiphase field model:A study of the solid-liquid-gas interaction mechanism in the solidification process

A multiphase field model coupled with a lattice Boltzmann(PF-LBM)model is proposed to simulate the distribution mechanism of bubbles and solutes at the solid-liquid interface,the interaction between dendrites and bubbles,and the effects of different temperatures,anisotropic strengths and tilting angles on the solidified organization of the SCN-0.24wt.%butanedinitrile alloy during the solidification process.The model adopts a multiphase field model to simulate the growth of dendrites,calculates the growth motions of dendrites based on the interfacial solute equilibrium;and adopts a lattice Boltzmann model(LBM)based on the Shan-Chen multiphase flow to simulate the growth and motions of bubbles in the liquid phase,which includes the interaction between solid-liquid-gas phases.The simulation results show that during the directional growth of columnar dendrites,bubbles first precipitate out slowly at the very bottom of the dendrites,and then rise up due to the different solid-liquid densities and pressure differences.The bubbles will interact with the dendrite in the process of flow migration,such as extrusion,overflow,fusion and disappearance.In the case of wide gaps in the dendrite channels,bubbles will fuse to form larger irregular bubbles,and in the case of dense channels,bubbles will deform due to the extrusion of dendrites.In the simulated region,as the dendrites converge and diverge,the bubbles precipitate out of the dendrites by compression and diffusion,which also causes physical phenomena such as fusion and spillage of the bubbles.These results reveal the physical mechanisms of bubble nucleation,growth and kinematic evolution during solidification and interaction with dendrite growth.

Water Modeling of Optimizing Tundish Flow Field

In the water modeling experiments, three cases were considered, i. e, , a bare tundish, a tundish equipped with a turbulence inhibitor, and a rectangular tundish equipped with weirs （dams） and a turbulence inhibitor. Comparing the RTD curves, inclusion separation, and the result of the streamline experiment, it can be found that the tundish equipped with weirs （dams） and a turbulence inhibitor has a great effect on the flow field and the inclusion separation when compared with the sole use or no use of the turbulent inhibitor or weirs （dams）. In addition, the enlargement of the distance between the weir and dam will result in a better effect when the tundish equipped with weirs （dam） and a turbulence inhibitor was used.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Development of Mathematical Model of Slag Flow Field and Temperature Field in ESR System

The heat transfer phenomena and driving forces of slag bath flow in ESR process were analyzed, and the mathematical models in ESR system were reviewed and evaluated. The electromagnetic force is the main driving force for the flow formation in the ESR slag pool, and the temperature difference in the pool creates a convective flow in the system. The shape of the electrode tip has an effect on electromagnetic field distribution in slag pool, thus affects the flow pattern. Finally an improved mathematical model of slag pool flow was proposed.

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymer chain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense in continuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to as envelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, a phenomenological viscoelastic model is derived. The model is tested in simple shear flow, simple elongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The results show that the model works well to predict the change of internal structure and viscoelastic performance of polymer melts in flow fields.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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Flow Field and Temperature Field in GaN-MOCVD Reactor Based on Computational Fluid Dynamics Modeling

Metal organic chenlical vapor deposition （AIOCVD） growth systems arc one of the. main types of equipment used for growing single crystal materials, such as GaN. To obtain fihn epitaxial materials with uniform performanee, the flow field and ternperature field in a GaN-MOCVD reactor are investigated by modeling and simulating. To make the simulation results more consistent with the actual situation, the gases in the reactor are considered to be compressible, making it possible to investigate the distributions of gas density and pressure in the reactor. The computational fluid dynamics method is used to stud,v the effects of inlet gas flow velocity, pressure in the reactor, rotational speed of graphite susceptor, and gases used in the growth, which has great guiding~ significance for the growth of GaN fihn materials.

The Erupting-Flow Model and Erupting-Flow Types in Yangbajain Geothermal Field in China

Erupting-flow types of geothermal wells in the Yangbajain geothermal field, China, are proposed based on internal energy of geothermal fluids and hydrogeologic-dynamic conditions of wellbore. An erupting-flow model, which is adaptable to the steaming and erupting of flow from wells in the field, has been verified by actual cases.

Mathematical Wave Functions and 3D Finite Element Modelling of the Electron and Positron

The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.

Fluid Flow and Solidification Simulation in Beam Blank Continuous Casting Process With 3D Coupled Model

Based on turbulent theory, a 3D coupled model of fluid flow and solidification was built using finite difference method and used to study the influence of superheating degree and casting speed on fluid flow and solidification, analyze the interaction between shell and molten steel, and compare the temperature distribution under different technological conditions. The results indicate that high superheating degree can lengthen the liquid-core depth and make the crack and breakout possible, so suitable superheating should be controlled within 35℃ according to the simulation results. Casting speed which is one of the most important technological parameters of improving production rate, should be controlled between 0. 85 m/min and 1.05 m/min and the caster has great potential in the improvement of blank quality.

Performance Optimization of Torque Converters Based on Modified 1D Flow Model

A methodology for performance optimization of torque converters is put forward based on the one-dimensional (1D) flow model. It is found that the inaccuracy of 1D flow model for predicting hydraulic performance at the low speed ratio is mainly caused by the separation phenomenon at the stator cascade which is induced by large flow impinging at the pressure side of the stator blades. A semi-empirical separation model is presented and incorporated to the original 1D flow model. It is illustrated that the improved model is able to predict the circumferential velocity components accurately, which can be applied to performance optimization. Then, the Pareto front is obtained by using the genetic algorithm (GA) in order to inspect the coupled relationship among stalling impeller torque capacity, stalling torque ratio and efficiency. The efficiency is maximized on the premise that a target stalling impeller torque capacity and torque ratio are achieved. Finally, the optimized result is verified by the computational fluid dynamics(CFD) simulation, which indicates that the maximal efficiency is increased by 0.96%.

Numerical Simulation and Experimental Study of the Effects of Disposal Space on the Flow Field Around the Combined Three-Tube Reefs

The artificial reefs placed on the seabed with different layouts and disposal spaces will produce variational flow field. The intensity and scale of the combined three-tube artificial reefs with different layouts at five Reynolds numbers（Re） are numerically investigated by use of the RNG k-ε turbulent model and SIMPLEC algorithm. A stationary no-slip boundary condition is used on the models and the bottoms, and the free surface is treated as a ＂moving wall＂ with zero shear force and the same velocity with inflow. In order to validate the simulation results, a particle image velocimetry（PIV） experiment is carried out to analyze the flow field. The numerical simulation results are consistent with the data obtained from experiment. The corresponding errors are all below 20%. Based on the validation, the effects of disposal space on flow field are simulated and analyzed. According to the simulation, in a parallel combination, a better artificial reef effect is obtained when the disposal space between two parallel reefs is 1.0L（L is the length of the combined three-tube reef model）. In a vertical combination, when the disposal space between two vertical reefs is 1.0L to 2.0L, the artificial reef effect is better.

Flow and Temperature Fields in Slab Continuous Casting Molds

In order to develop super-board and super-thick slabs, the flow and temperatur fields were studied in slab continuous casting molds under different practical conditions, such as slab dimensions, with-drawing slab speed, design of nozzles, and superheat tempera-ture. The results showed that it is preferred to incline nozzle bores downwards and the submerged depth of the nozzles is best kept be-tween 250-300 mm. In addition, the solidified shell is thicker at the wide face than that at the narrow face, while the thin points alongthe wide face ekist both in the center and in the some area toward each respective end.

Analysis of the Flow Field Characteristics Associated with the Dynamic Rock Breaking Process Induced by a Multi-Hole Combined External Rotary Bit

The characteristics of the flow field associated with a multi-hole combined external rotary bit have been studied by means of numerical simulation in the framework of an RNG k-εturbulence model,and compared with the results of dedicated rock breaking drilling experiments.The numerical results show that the nozzle velocity and dynamic pressure of the nozzle decrease with an increase in the jet distance,and the axial velocity of the nozzle decays regularly with an increase in the dimensionless jet distance.Moreover,the axial velocity related to the nozzle with inclination angle 20°and 30°can produce a higher hole depth,while the radial velocity of the nozzle with 60°inclination can enlarge the hole diameter.The outcomes of the CFD simulations are consistent with the actual dynamic rock breaking and pore forming process,which lends credence to the present results and indicates that they could be used as a reference for the future optimization of systems based on the multi-hole combined external rotary bit technology.

Semi-Automatic Modeling Technique of Torque Converter Flow Passage

The modeling technique of hydrodynamic torque converter flow passage was investigated. The semi-automatic modeling technique of torque converter flow passage was proposed. The flow passage model of each converter wheel is considered as a revolution entity sliced by two curved surfaces. In order to generate the revolution entity, a new approximation method, condition optimum arc approximation, was proposed. The method was used to approximate the meridional streamlines of the inner and outer wall. As a result, the three-dimensional revolution entity can be conveniently generated. In order to create slice surfaces, the central stream surface of flow passage was approximated with a quadric surface. The normal vector of the quadric surface and the thickness/thickness-function of bade were used to calculate the discrete point coordinates of blade surfaces. Via the rotation transformation to the coordinates, the discrete point coordinates of slice surfaces were obtained. A parameterized program code used for the hydrodynamic torque converter design and semi-automatic modeling was developed. Modeling errors were calculated and analyzed. The flow passage model was generated in several minutes with the help of the program code, Auto CAD and Solidworks software. Finally, the model was inputted into Gambit, and the pre-processing task used for the numerical simulation of torque converter flow field was successfully completed. The investigation results show that the semi-automatic modeling not only can ensure the accuracy of modeling, but also librates the research and design workers of torque converter from the time-consuming modeling work, which paves the way for the numerical simulation of the complex flow field of the hydrodynamic torque converter.

MATHEMATICAL MODELLING OF FLOW PHENOMENA IN METAL BATH COVERED WITH MOLTEN SLAG

By use of the two-component LDA and high speed camera,the water model of the flow field in metal bath under molten slag layer has been tested.On the basis of experimental results,the flow boundary conditions of liquid metal at the slag-metal interface of a gas injecting bath were deduced.The flow field and the turbulent parameters of the metal bath covered with slag were solved by the vorticity-stream function method.The results reveal that the flow velocity, turbulent energy and circulating rate of the melt under slag are lower than that of without slagcover.Another one “dead zone” of the lowest turbulent energy is formed in the top layer under cover of slag near the ladle linning.

NUMERICAL SIMULATION OF THE FLOW FIELD IN A THERMAL PLASMA REACTOR

A numerical simulation is presented for a thermal plasma reactor with particle-trajectory model in this paper. Turbulance is considered by using simple SGS model. The governing equations are solved by means of the algorithm of SIMPLER. The calculated results give the velocity and the temperature fields within plasma reactor, and the trajectories of the injected particles.

Coupled Modeling of Electromagnetic Fleld,Fluid Flow,Heat Transfer and Solidification During Conventional DC Casting and Low Ftequency Electrmagnetic Casting of 7xxx Aluminum Alloys

A comprehensive mathematical model has been developed to describe the interaction of the multiple physics fields during the conventional DC casting and LFEC (low frequency electromagnetic casting) process. The model is based on a combination of the commercial finite element package ANSYS and the commercial finite volume package FLUENT, with the former for the calculation of the electromagnetic field and the latter for the calculation of the magnetic driven fluid flow, heat transfer and solidification. Moreover, the model has been verified against the temperature measurements obtained from two 7XXX aluminum alloy billets of 200mm diameter, cast during the conventional DC casting and the LFEC casting processes. In addition, a measurement of the sump shape of the billets were carried out by using addition melting metal of Al-30%Cu alloy into the billets during casting process. There was a good agreement between the calculated results and the measured results. Further, comparison of the calculated results during the LFEC process with that during the conventional DC casting process indicated that velocity patterns, temperature profiles and the sump depth are strongly modified by the application of a low frequency electromagnetic field during the DC casting.

Effect of electromagnetic stirring on flow field in mold under submerged entry nozzle clogging

A physical model with mercury as analog was developed to investigate the influences of electromagnetic stirring（EMS） on flow field in slab continuous casting when the submerged entry nozzle（SEN） was clogged with different clogging rates（0,10% ,25% ,and 50% ）. The flow field in mold under different EMS currents（0, 40 A, and 60 A） was measured by an ultrasonic Doppler velocimeter. The results proved that the flow field in the mold was a typical double roll structure under non-clogging SEN. As the SEN clogging rate increased, the flow field structure was transformed from a double roll to asymmetry flow. When the clogging rate reached 50%, the up circulation disappeared on the clogged side. The zone under the meniscus near the narrow face was a non-flowing area. EMS could correct bias flow caused by SEN clogging and improve the symmetry of the flow field during SEN clogging.

Numerical Simulation of the Influence of Water Flow on the Piers of a Bridge for Different Incidence Angles

A two-dimensional mathematical model is used to simulate the influence of water flow on the piers of a bridge for different incidence angles.In particular,a finite volume method is used to discretize the Navier-Stokes control equations and calculate the circumferential pressure coefficient distribution on the bridge piers’surface.The results show that the deflection of the flow is non-monotonic.It first increases and then decreases with an increase in the skew angle.