Research On Key Technology Of Dynamic Mesh Based Numerical Simulation Of Die-swell

Viscoelastic fluid is a typical non-Newtonian fluid and has a wide range of applications in industry.As an unique physical phenomenon,die-swell is of great scientific significance in studying the rheological behavior of viscoelastic fluid.With the rapid development of computer science,numerical simulation has become an important method for studying die-swell.However,an accurate and efficient numerical technology to simulate die-swell is facing up to the challenge in achieving accurate free boundary tracking,stable free boundary swelling,accurate error estimation,dynamic grid density adjustment,etc.In order to achieve these objectives,this thesis studies the key technologies of numerical simulations of viscoelastic die-swell based on the dynamic mesh.The main contributions are as follows:1.A novel die-swell simulation framework by coupling Finite Volume Method with Arbitrary Lagrangian–Eulerian Method(FVM-ALE)It is the first time that the Finite Volume Method and the Arbitrary Lagrangian–Eulerian Method are combined together to simulate die-swell.Based on the open source software platform Open FOAM,this thesis designs and implements a die-swell simulation framework.The simulation framework includes the design of the simulation procedure,the realization method of free surface boundary conditions and the design of the internal grids adjustment algorithm.For the first time,a method is proposed in Finite Volume system to satisfy the free surface boundary condition by setting the proper pressure boundary condition on the free boundary and introducing the equilibrium force into the momentum equation.The experimental results show that this method can not only accurately simulate stable viscoelastic extrusion,but also simulate unstable extrusion cases.This thesis provides a platform for the study of rheological properties of viscoelastic fluids.2.Novel error propagation models for free surface position error In order to eliminate the numerical instability of die-swell simulation under high Weissenburg(Wi)numbers,this thesis builds up the propagation models for the position error of free surface grids from two aspects,including the equation discretization and the free surface adjustment algorithm.This thesis establishes the single point error propagation model respectively for time,convection and diffusion terms in the momentum equation.And based on the results,multi-points error superposition formula is proposed and validated.According to the error propagation model based on the free surface adjustment algorithm,a modified first order upwind free surface adjustment algorithm is proposed.Experiments show that the new method can greatly enhance the stability of the numerical simulation of viscoelastic extrusion without affecting the accuracy of the results,which greatly improves the application range of the simulation framework.3.A novel composite defect correction discretization error estimation method for the coupled process when solving equations According to the analysis of current defect correction discretization error estimation methods,this thesis implements a new composite defect correction discretization error estimation method(CDCDEEM)to address problems with several unknown coupled physical quantities.Based on this method,this thesis analyses the sensitive domain and the precision variation process during the simulation.The results show that the discretization error in the domain closed to the die exit is much larger than other domains,which means this area has a greater influence on the final simulation accuracy and requires fine meshes to control the discretization error.4.A novel hybrid dynamic mesh adaptive tracking and refining method for dynamic mesh adjustment According to the limitation of the precision control of the single moving grid point method in traditional die-swell numerical simulation,a hybrid dynamic mesh adaptive tracking and refining method(HDATRM),which couples the grids adjustment method and the mesh refinement method,is proposed.On the basis of the original grid-moving module,the new method adds a two dimensional mesh refinement and mergence module and a data update module.The experimental results show that the new method not only guarantees the accuracy of the final result,but also ensures the accuracy of the result in the simulation process,which verifies the effectiveness of the new method.