Changsheng Zhu

Numerical Simulation of Recalescence of 3-dimensional Isothermal Solidification for Binary Alloy Using phase-field Approach

A accelerated arithmetic algorithm of the dynamic computing regions was designed, and 3-dimensional numerical simulation of isothermal solidification for a binary alloy was implemented. The dendritic growth and the recalescence of Ni-Cu binary alloy during the solidification at different cooling rates were investigated. The effects of cooling rate on dendritic patterns and microsegregation patterns were studied. The computed results indicate that, with the increment of the cooling rate, the dendritic growth velocity increases, both the main branch and side-branches become slender, the secondary dendrite arm spacing becomes smaller, the inadequate solute diffusion in solid aggravates, and the severity of microsegregation ahead of interface aggravates. At a higher cooling rate, the binary alloy presents recalescence; while the cooling rate is small, no recalescence occurs.

Phase-field simulation of forced flow effect on random preferred growth direction of multiple grains

Abstract The random distribution problem of dendrite preferred growth direction was settled by random grid method. This method was used to study the influence of forced laminar flow effect on multiple grains during solidification. Taking high pure succinonitrile (SCN) undercooled melt as an example, the forced laminar flow effect on multiple grains was studied by phase-field model of single grain which coupled with flow equations at non-isothermal condition. The simulation results show that the random grid method can reasonably settle the problem of random distribution and is more effective. When the solid fraction is relatively low, melt particles flow around the downstream side of dendrite, and the flow velocity between two dendrite arms becomes high. At the stage of solidification time less than 1800Δ t , every dendrite grows freely; the upstream dendrites are stronger than the downstream ones. The higher the melt flow rate, the higher the solid fraction. However, when the solid fraction is relatively high, the dendrite arm intertwins and only a little residual melt which is not encapsulated can flow; the solid fraction will gradually tend to equal to solid fraction of melt without flow.

Phase-field simulations of forced flow effect on dendritic growth perpendicular to flow

Abstract The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile (SCN) supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.

Comparative analysis of isothermal and non-isothermal solidification of binary alloys using phase-field model

Abstract Based on the entropy function, a two-dimensional phase field model of binary alloys was established. Meanwhile, an explicit difference method with uniform grid was adopted to solve the phase field and solute field controlled equations. And the alternating direction implicit (ADI) algorithm for solving temperature field controlled equation was also employed to avoid the restriction of time step. Some characteristics of the Ni–Cu alloy were captured in the process of non-isothermal solidification, and the comparative analysis of the isothermal and the non-isothermal solidification was investigated. The simulation results indicate that the non-isothermal model is favorable to simulate the real solidification process of binary alloys, and when the thermal diffusivity decreases, the non-isothermal phase-field model is gradually consistent with the isothermal phase-field model.

Effect of forced lamina flow on microsegregation simulated by phase field method quantitatively

Abstract The influence of supercooled melt forced lamina flow on microsegregation was investigated. The concentration distribution at solid-liquid boundary of binary alloy Ni–Cu was simulated using phase field model coupled with flow field. The microsegregation, concentration maximum value, boundary thickness of concentration near upstream dendrite and normal to flow dendrite, and downstream dendrite were studied quantitatively in the case of forced lamia flow. The simulation results show that solute field and flow field interact complexly. Compared with melt without flow, in front of upstream dendrite tip, the concentration boundary thickness is the lowest and the concentration maximum value is the smallest for melt with flow. However, in front of downstream dendrite tip, the results are just the opposite. The zone of poor Cu in upstream dendrite where is the most severely microsegregation and shrinkage cavity is wider and the concentration is lower for melt with flow than that without flow.

Parameters affecting microsegregation in phase-field simulation

The influence of various material and computational parameters such as interface kinetic coefficient(β), surface energy(σ), anisotropy parameter(γ) and the noise amplitude(α) upon microsegregation patterns during the crystal growth was investigated by using the phase-field model which incorporated the concentration field equations. The computed results indicate that, when the appropriate value is assigned to α, the fluctuant scope of solute composition in the solid is steady, and the influence of α on microsegregation is small; the larger the interface kinetic coefficient β, the more acutely the solute composition in the solid fluctuates, but the severity of microsegregation in the front interface reduces; with the increment of anisotropy parameter γ, the fluctuation of solute composition in the solid becomes more acutely, and the severity of microsegregation in the front interface aggravates; the larger surface energy σ, the smaller the fluctuant scope of solute composition in the solid is, and the smaller the degree of microsegregation is.

Phase-Field Modeling of Solute Trapping in Single-Phase Alloys during Directional Solidification

The evolution of interface morphology for a single-phase Nickel-Copper binary alloy in directional solidification is studied by using a phase-field model cooperated solute concentration gradient corrections. The effect of pulling velocity V and strength of the crystalline anisotropy γ on interface morphology and the solute segregation is formulated. The results indicate that, the transition from plane to cells/fine cellular structures, then to planar structures(plane-cell-plane) will happen with the increment of V, and the level of solute trapping becomes stronger. When the crystal grows with cellular structures, γ crucially influences the interface pattern formation at the lower growth velocity, but the solute partition ratio is not significantly affected by the anisotropy strength. Then, the operating behavior for planar growth is hardly any affected by the crystalline anisotropy.

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

Abstract A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

Zone Partitioning Sequential Calculation Method for Three-Dimensional Phase-Field Material Simulation during Directional Solidification

Complex dendritic structures can be simulated directly by phase field method. However, phase field method needs a very fine mesh computing and memory requirements. A new calculation method named zone partitioning sequential calculation method is proposed to expand the simulation area of phase field method. The simulation area can be divided into several parts, and the parts can be calculated one by one in a certain order by the new method. This new method can reduce the computing and memory requirements of single calculation, because a part of the simulation area is less than the whole simulation area. Although this method could make error in the interface of different parts of the simulation area when the grains go through the interface, but the error has less effect on the grain growth. By using phase field method, coupled with zone partitioning sequential calculation method, the simulation of the directional solidification process of Al-Cu binary alloy is operated. The results show that the new method can be applied to phase field simulation of binary alloy solidification in a large area. The simulation results have certain accuracy and reliability.

Study on the Traffic Behavior of On-Ramp System Considering Driver Behavior

based on the main road into a two lane entrance ramp system the open boundary conditions, using the asymmetric lane changing rules, considering driver behavior characteristics, from standpoint of safety driving ,simulate the entrance ramp system. We get a basic road map different entrance probability of flow, velocity, and analyze the driving safety.compared with reference, and the reference results show that after considering driver behavior, in the ramp at the interface, reduce the interaction with the main ramp,not only the system traffic flow in each section is improved, and but also improve the driving safety.Considering the entrance ramp system driver behavior can be simulated more in line with the running state of the vehicle in real life.