Seeking high-performance computing methods to solve the problem of a large amount of calculation,low calculation efficiency,and small simulation scale on the traditional single central processing unit (CPU) platform is of great value to the simulation study of micro-structure.In this study,based on the three-dimensional multi-phase-field model of KKSO coupling phase-field and solute field,the open computing language (OpenCL) + graphics processing unit (GPU) heterogeneous parallel computing technology is used to simulate the eutectoid growth of Fe-C alloy and the end growth process of pearlite under pure diffusion.The effects of initial supercooling and different diffusion coefficients on the growth morphology of lamellar pearlite were investigated.The results show that ferrite and cementite are perpendicular to the front of the solid-solid interface and are coupled and coordinated to grow,and there is no leading phase under the initial supercooling degree of 20 K.With the continuous increase of the initial supercooling degree (19 K-22 K),the morphology changes of the eutectoid layer are as follows:cementite stops growing → slice amplitude increases → regular symmetric growth → oblique growth → layer merge.With the increase of the diffusion coefficient from 3×10^(-13) m^(2)·s^(-1) to 15×10^(-13) m^(2)·s^(-1),the growth rate of the microstructure of the lamellar pearlite increases linearly,and there is no obvious change in the frontal appearance of the pearlite.
Chang-sheng ZhuYu-jie LiFang-lan MaLi FengPeng Lei
We use the phase field method to track the gas-liquid interface based on the gas-liquid two-phase flow in the pool boiling process,and study the bubble nucleation,growth,deformation,departure and other dynamic behaviors on the heating surface under microgravity.By simulating the correlation between liquid undercooling and bubble dynamics,we find that the bubble growth time increases with the increase of liquid undercooling,but the effect of liquid undercooling on bubble height is not significant.Meanwhile,the gas-liquid-solid three-phase contact angle and the gravity level will also have an effect on the bubble growth time and bubble height.With the increase of the contact angle,the bubble growth time and bubble height when the bubble departs also increase.While the effect of gravity level is on the contrary,the smaller the gravity level is,the larger the bubble height and bubble growth time when the bubble separates.
A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.
This work establishes a temperature-controlled sequence function, and a new multi-phase-field model, for liquid- solid-solid multi-phase transformation by coupling the liquid-solid phase transformation model with the solid-solid phase transformation model. Taking an Fe-C alloy as an example, the continuous evolution of a multi-phase transformation is simulated by using this new model. In addition, the growth of grains affected by the grain orientation of the parent phase （generated in liquid-solid phase transformation） in the solid-solid phase transformation is studied. The results show that the morphology of ferrite grains which nucleate at the boundaries of the austenite grains is influenced by the orientation of the parent austenite grains. The growth rate of ferrite grains which nucleate at small-angle austenite grain boundaries is faster than those that nucleate at large-angle austenite grain boundaries. The difference of the growth rate of ferrites grains in different parent phase that nucleate at large-angle austenite grain boundaries, on both sides of the boundaries, is greater than that of ferrites nucleating at small-angle austenite grain boundaries.
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.
Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) < 45o and θ_A < 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.
Li FengNi-ni LuYa-long GaoChang-sheng ZhuJun-he ZhongRong-zhen Xiao
By coupling the phase field model with the continuity equation of incompressible fluid, Navier–Stokes equation,electric field equation, and other governing equations, a multi-field coupling model for multi-bubble coalescence in a viscous fluids is established. The phase field method is used to capture the two-phase interface. The motion and coalescence of a pair of coaxial bubbles under an external uniform electric field and the effects of different electric field strengths on the interaction and coalescence of rising bubbles are studied. The results show that the uniform electric field accelerates the collision and coalescence process of double bubbles in the fluid, and increases the rising velocity of the coalesced bubble.The electric field with an intensity of E = 2 kV/mm is reduced about 2 times compared with that without electric field in coalescence time. When the electric field strength is strong(E ≥ 1 kV/mm), the coalesced bubble will rupture before it rises to the top of the calculation area, and the time of the bubble rupturing also decreases with the increase of the electric field strength. The phase field method is compared with the simulation results of Lattice Boltzmann Method(LBM), and the shape of bubble obtained by the two methods is in good agreement, which verifies the correctness of the calculation model.
Aiming at the interaction and coalescence of bubbles in gas–liquid two-phase flow, a multi-field coupling model was established to simulate deformation and dynamics of multi-bubble in gas–liquid two-phase flow by coupling magnetic field, phase field, continuity equation, and momentum equation. Using the phase field method to capture the interface of two phases, the geometric deformation and dynamics of a pair of coaxial vertical rising bubbles under the applied uniform magnetic field in the vertical direction were investigated. The correctness of results is verified by mass conservation method and the comparison of the existing results. The results show that the applied uniform magnetic field can effectively shorten the distance between the leading bubble and the trailing bubble, the time of bubbles coalescence, and increase the velocity of bubbles coalescence. Within a certain range, as the intensity of the applied uniform magnetic field increases, the velocity of bubbles coalescence is proportional to the intensity of the magnetic field, and the time of bubbles coalescence is inversely proportional to the intensity of the magnetic field.
