Robust And Efficient Three-dimensional Simulation Of Mold Filling In Plastic Injection Molding

Numerical simulation technology has been widely in the optimization procedure of mold structure and molding processes in the industry of plastic injection molding,and plays an important role in improving product quality,shortening the development cycle and reducing the development cost.With the increasing diversity,complexity,and precision of plastic injection molding products,the traditional numerical simulation technology based on the Hele-Shaw model has become increasingly unable to meet the simulation accuracy requirements in practical applications due to its introduction of some simplifications.The three-dimensional(3D)simulation technology,which abandons the simplifications in the Hele-Shaw model,has gradually become a mainstream choice and an inevitable trend.Unstructured finite volume(FV)methods have been widely adopted in 3D filling simulation of plastic injection molding because of its inherent local conservation,computational economy,and geometric flexibility.However,the existing unstructured FVbased simulation methods for plastic injection molding still has some problems and shortcomings in terms of robustness and efficiency,which mainly include:(1)the computational stability on poor quality meshes is insufficient;(2)the abrupt changes of fluid viscosity across the gas-liquid interface lead to non-physical oscillations of the velocity field;(3)a melt mass loss problem arises with the use of VOF methods to capture the gas-liquid interface;(4)the SIMPLE algorithm for solving the coupled governing equations has slow convergence rate and poor stability.These problems and shortcomings are more severe in engineering applications.In view of the existing problems and shortcomings of current unstructured FV-based simulation methods for plastic injection molding,this dissertation proposed a series of improvements in the discretization schemes of the governing equations,the gas-liquid interface prediction method and the solution algorithm of the discretized governing equations,which improve the robustness and efficiency of 3D filling simulations.The research work of this dissertation mainly includes the following aspects.First,the mathematical model of the filling process in plastic injection molding is established.Based on the single-fluid two-phase flow model and the incompressible,generalized Newtonian fluid assumption,the governing equations describing the 3D flow in the filling process are given.In terms of boundary conditions,by applied dynamic outlet boundary conditions at the cavity walls,the air is able to exit from the cavity when the melt is injected into the cavity.For the discretization of the governing equations,a stable unstructured FV discretization model is established.To improve the computational stability on poor quality meshes,the cellface normal derivatives are discretized using the over-relaxed approach,and the cell center gradients of variables are calculated using the Green-Gauss vertex-based method.To solve the non-physical oscillations of the velocity field caused by the abrupt changes of the viscosity at the gas-liquid interface,the problem existing in the traditional calculation scheme of the cell-face volume flux is analyzed,and an improved calculation scheme by employing a different interpolation method of the cell-face pressure gradient is proposed.For the prediction of the gas-liquid interface in the filling process,an accurate and efficient gas-liquid interface capturing method based on the algebraic VOF method is established.The volume fraction convection equation is discretized by the CICSAM method,which maintains the sharpness of the interface and ensures the boundedness of the volume fraction.In order to solve the problem of melt mass loss in the filling simulation on the VOF framework,an efficient melt mass compensation method is proposed,which compensates the melt mass at the gas-liquid interface and considers the advancing velocity of the gas-liquid interface.For the solution of the discretized governing equations,an efficient solution method based on the velocity-pressure fully coupled algorithm and parallel computing technology is established.Considering the strong coupling relationship between velocity and pressure in the filling flow governing equations,the velocity-pressure fully coupled algorithm is employed to solve the discretized governing equations in order to improve the convergence rate and stability of the solution.To further improve the computational efficiency,the computational code is parallelized using the single program multiple data(SPMD)parallel model.Finally,the numerical simulation method proposed in this dissertation is verified and analyzed by a series of cases in terms of accuracy,stability and efficiency.In terms of accuracy,the comparisons show that the simulation results of the proposed method are in good agreement with the analytical solution and experimental results in terms of flow field calculation and interface prediction.The test results also demonstrate that the melt mass compensation method proposed in this dissertation can ensure that the melt mass is strictly conserved during the filling process.In terms of stability,the test results indicate that the discretization schemes used in this dissertation can significantly improve the computational stability on poor quality meshes,and the proposed cell-face volume flux calculation scheme can also effectively solve the problem of non-physical oscillations of the velocity field caused by the abrupt changes of the viscosity at the gas-liquid interface.In terms of computational efficiency,the results of cases with different mesh sizes show that the velocity-pressure fully coupled algorithm employed in this dissertation has a significantly faster convergence rate than the traditional SIMPLE algorithm(increasing by more than 1.4 times),and its total computation time is also significantly less than the SIMPLE algorithm(reducing more than 32%).In addition,the parallel computing performance test results also indicate good parallel efficiency of the parallel computing model used in this dissertation,and the speed-up factor can reach 5 or more when using 8 computing cores.