Xiaofeng Niu

New algorithm for solving 3D incompressible viscous equations based on projection method

Abstract A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure. The calculation region can be divided into different regions according to Reynolds number. In the far-wall region, the thermal melt flow was calculated as Newtonian flow. In the near-wall region, the thermal melt flow was calculated as non-Newtonian flow. It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment. The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.

Application of Fuzzy Set Theory to Quantitative Analysis of Correctness of the Mathematical Model Based on the ADI Method during Solidification

The explicit finite difference (EFD) method is used to calculate the casting temperature field during the solidification process. Because of its limited time step, the computational efficiency of the EFD method is lower than that of the alternating direction implicit (ADI) method. A model based on the equivalent specific heat method and the ADI method that improves computational efficiency is established. The error of temperature field simulation comes from model simplification, the acceptable hypotheses and calculation errors caused by different time steps, and the different mesh numbers that are involved in the process of numerical simulation. This paper quantitatively analyzes the degree of similarity between simulated and experimental results by the hamming distance (HD). For a thick-walled position, the time step influences the simulation results of the temperature field and the number of casting meshes has little influence on the simulation results of temperature field. For a thin-walled position, the time step has minimal influence on the simulation results of the temperature field and the number of casting meshes has a larger influence on the simulation results of temperature field.

Numerical Simulation of Casting Filling Process of Composites Reinforced with Nano SiC Based on Smoothed Particle Hydrodynamics

The actual casting filling process can be deemed as the coupled flow of air, molten metal and solid-phase particles (such as slag) inside the cavity, which may cause air entrapment, slag inclusion and other casting defects, and affect the quality of casting. Through computation simulation of the casting filling process on the basis of smoothed particle hydrodynamics (SPH) method, it can not only precisely track the motion trajectories of air, molten metal and slag particles, but also precisely predict air entrapment, slag inclusion and other casting defects. This paper established a mathematical model of gas-liquid-solid three-phase flow for the SPH-based casting filling process. The model eliminated the instability of gas-liquid interface pressure by introducing the corrected gas-liquid two-phase momentum equation, and maintained a clear interface between air and molten metal by introducing the surface tension model. In addition, it introduced the motion model of rigid body to deal with the coupled flow process of slag, air and molten metal. The mathematical model established in this paper was used to calculate the bubble floating and the flowing process of the gas-liquid two-phase during mold filling through the bottom side of the injection cavity and of the gas-liquid-solid three-phase flow during mold filling for casting of plate (the plate was composite reinforced with nano SiC, and the viscosity of the composite melt was calculated from the viscosity formula of the composite melt). The calculated results were compared with the experimental results to verify the accuracy and validity of the mathematical model established.

New numerical algorithm of gas–liquid two-phase flow considering characteristics of liquid metal during mold filling

Abstract A new program is developed for gas–liquid two-phase mold filling simulation in casting. The gas fluid, the superheated liquid metal and the liquid metal containing solid grains are assumed to be governed by Navier-Stokes equations and solved through Projection method. The Level set method is used to track the gas–liquid interface boundary. In order to demonstrate the correctness of this new program for simulation of gas–liquid two-phase mold filling in casting, a benchmark filling experiment is simulated (this benchmark test is designed by XU and the filling process is recorded by a 16-mm film camera). The simulated results agree very well with the experimental results, showing that this new program can be used to properly predicate the gas–liquid two-phase mold filling simulation in casting.

A New Implicit Finite Difference Algorithm of Thermal Melt Flow during Filling Process

In the SOLA-VOF method of casting simulation, the explicit difference method is often used for calculating the 3D incompressible viscous equations in filling simulation. Because the time step is limited, the computational efficiency is low. In this work, the new algorithm based on the projection method with the implicit finite difference technique is established to calculate the velocity fields and the pressure. It is proved that the new algorithm based on the projection method with the implicit technique is correct through the nonparametric statistics method and experiments. The simulation results show that the new algorithm based on the projection method with the implicit technique is more quickly than the SOLA-VOF method using the explicit difference method.