Numarical Simulation Of Indirectly Coupled Electromagnetic-Solidification Transport Process

In the coupled process of electromagnetic-solidification transport process(EM-STP) of multi-component alloys, the heat transport, mass transport and flowof alloy melt are the important transport phenomena in solidification process,which determines the crystalline quality and the ultimate performance of thecasting. The transport of various physical fields in solidification process areclosely interrelated and influenced each other, and those transport phenomenabecome even more complex once the EM-field was introduced. Therefore,establishing a universal unified numerical model for EM-STP during EM-casting(EMC), and proposing an efficient numerical methods for solving these processesare very important theoretically and practically for studying the laws of STP ofdifferent alloys and optimizing the parameters in various EM-casting. Theobjectives in this paper are solving the issues relating to macro-transportphenomena of EM-STP with efficient numerical calculation, by establishing a2D/3D uniform numerical model of EM-STP and expanding and applying theDirect-SIMPLE (Direct Semi-Implicit Method for Pressure Linked Equations)method that solve the coupled process of pressure field and velocity field.Some EM models, including static magnetic field (SMF), traveling/harmonicmagnetic field (TMF/HMF) under two/three dimentional (2D/3D) were calculatedand analised by ANSYS finite element method (FEM) software in detailedly,which were prepared for2D and3D EM-STP numerical calculation such asEM-continous casting (EMCC) and etc. The rusults indicate that the maximummagnitude of magnetic flux denstity (|B|max) increase with current loads linearly in2D and3D EM models. The|B|maxand induced current density of1-pairs of poles(1-POP) TMF are larger than that of2-POP TMF, while it is not homogeneous andsmooth in comprison of2-POP TMF. All of these calculation results and analysisessever as groundwork and provid EM-data for indirect coupled EM-STP.A uniform mathematical model for coupled EM-STP was proposed in thispaper, in which the relative movments between melt/solide phase and mold istaken into account, and it is suitable for the case of only liquid/solide phase existsin the model and that absence or with EM-field. The Direct-SIMPLE method forsolving pressure and velocity (P-V) in2D/3D models was deduced based onstagger grids system. The decompose and correction expressions of velocity andpressure formulas possess clear physical meanings in this method, and iterationcalculations only need to be carried out for pressure coefficient matrix instead ofrepeating iteration correction between pressure and velocity, thus the computational efficiency of numerical simulation be improved greatly.A set of data format convertion method and program were proposed andwrited for2D and3D EM-field data, the data stored with FEM format and finitvolume/difference method (FVM/FDM) format can be converted between twodifferent softwares. All the elements with various shapes are divided intotetrahedron elements uniformly in3D model, and then the center points ofFVM/FDM grids mapping with these new sub-tetrahedron elements, once a centerpoint is confirm to be located in a tetrahedron element, it can be linear interpolatedwith the shape function of tetrahedron element. In a2D model, the shape functionof triangle or quadrilateral element would be directly used to linear interpolat. Thishandling method is not only simple and feasible, but also accurate and efficient.Subsequently, a universal post-process program for displaying scalar/vecter fieldsin2D and3D models was proposed, it can achieve coordinate rotation and datafeedback.SMFs and TMFs exported by ANSYS were coupled to the CC transportcalculation, and an indirect-coupled process of STP with EMF was realized. Theresults show that the appropriate SMF can effectively suppress the circulationflows in the CC-process of slab, the impact of jet on the side wall and theamplitude of level fluctuation as well as the depth of stream decreases withincreasing magnetic flux density. A SMF with|B|max=5.5×10-3T plays a goodbraking effect and can decrease macrosegregtion remarkablely. Once1pair ofpoles (1-POP) or2-POP TMF was applied, the top and lower circulation flows aresignificantly transformed under the influence of the Lorentz force, the flow of meltat meniscus and the front of solidification interface are imforced reasonablely bylinear stirring, the comprehensive effects of2-POP TMF is better than that of1-POP TMF. Finally, the model and numerical method proposed in this paper wasused for the flow and heat transfer simulation in a3D open system of horizontalsingle-belt caster (HSBC), which under the actions of pseudo and the real SMFswith different shapes and intensities. The results show that the EMBr will producea uniform melt conveying to the water-cooled moving single-belt. Among the threecontours of SMF in this paper, a beneficial effect can be achived by the verticaland L-shaped magnetic field, and|B|max=0.4T can decrease the impact of outletflow, bring the solidification shell growth homogeneously on the single-belt andreach a optimal flow pattern in the mold.The zone melting directional solidification (DS) process of Ti-50Al alloywith direct and indirect induction heating were numerical simulated respectively,where they were disigned and experimental verified using the numerical models,algorithms and FEM/FVM indirect-coupled calculation method proposed in thispaper, and directional solidification samples with good quality were obtained. The process design of Ti-Al alloy EM-DS under EM-field as well as the simulation andexperiment of Al-Cu-Si eutectic alloy show that the EM-STP unified numericalmodel, algorithm and indirect-coupled method are simple, accurate and efficient.