Study On Multi-physics Model Coupled With Heat,Fluid Flow And Electromagnetic Field For Continuous Casting Billet

The solidification process of continuous casting billet is the process of molten steel turning into billet,and its essence is a multi-physical field coupling process.The physical fields include temperature field,flow field and electromagnetic field,which determine the internal quality of continuous casting billet,including macrosegregation of continuous casting billet.Therefore,it is of great significance to study the interaction among temperature field,flow field and electromagnetic field in continuous casting slab for clarifying the formation mechanism of macrosegregation of continuous casting slab and optimizing the technological parameters of continuous casting.In this paper,the thermal-magnetic-fluid multi-field coupling model of 65#steel billet is established and solved.The main contents of this thesis are as follows:(1)The mathematical model of electromagnetic stirring in continuous casting is established and solved by finite element method.Maxwell's equations are simplified according to the environment and technological characteristics of electromagnetic stirring in continuous casting,and then the expression under the time-harmonic field is obtained.The governing equations of electromagnetic stirring in continuous casting are derived while the electromagnetic potential function is selected as A-? and the boundary conditions at the interface of different media are derived.The finite electromagnetic field in continuous casting is deduced by Galerkin method.The element equations and their matrix forms are given,and the solution methods of stiffness matrix parameters under different shape elements are given.(2)A mathematical model of continuous casting billet flow field is established.The flow state of molten steel in continuous casting billet is analyzed and Reynolds time-averaged method is selected to solve the flow field model.The governing equations of flow field in continuous casting billet under low Reynolds number k-? model were derived from NavierStokes equation of incompressible fluid.The heat transfer equation is added to simulate the solidification phenomenon of continuous casting billet and a coupled thermal-fluid model is established.In order to solve the uncertain flow field calculation domain and the mushy zone caused by solidification,the continuous medium model and porous medium model were introduced to modify the governing equations of the flow field.(3)The multi-physics model coupled with heat transfer,fluid flow and electromagnetic is solved by ANSYS.In order to simplify the solution of the thermal-magnetic-fluid coupling model,the coupling relationship between the physical fields is analyzed and the secondary coupling relationship is neglected.The finite element solution of electromagnetic stirring in mold and final stage of solidification is completed by APDL language,and the electromagnetic force and Joule heat produced in the two regions were obtained.The coupled model of thermalmagnetic-fluid is solved by FLUENT,the calculation results were analyzed,and the influence of stirring parameters on the flow field is studied,the result shows that stirring speed will increase with the increase of the current and frequency.(4)The accuracy of the multi-physics model is verified.The electromagnetic field model is verified by measuring the magnetic induction intensity distribution at the mold and final stage of solidification in the continuous casting production site and comparing it with the numerical simulation results.The result of the temperature field is verified by comparing with the calculation results of solidification heat transfer model.The flow field calculation is verified by comparing with the existing research on the flow field of continuous casting billet.The influence of grid density on the flow field calculation results is also analyzed.Numerical results show that the accuracy of the calculation results can be guaranteed only when the cross section of 0.16m×0.16m billet reaches 30720 nodes.Results show that the average absolute error of numerical simulation results is 2.2 mT and the average relative error is 8.1%compared with the field measurement results of electromagnetic field.Compared with the solidification heat transfer model,the average absolute error of temperature field calculation results is 18? and the average relative error is 2.0%.The trend of velocity change is consistent with the existing research results,and the speed is similar.However,due to the different steel types and the corresponding continuous casting process parameters,the specific values can't be compared.In summary,it can be concluded that the multi-physics model coupled with heat transfer,fluid flow and electromagnetic for billet continuous casting established in this thesis is accurate.