Meshless Method In Electromagnetic Field And High Frequency Induction Sealing System Of Paper-based Material

In computational electromagnetics, for such problems that the model geometry changes frequently in computation process as electromagnetic field involving moving conductor, the electromagnetic inverse problem, the thin plate problem, and the melting and casting of metal, the grids-based method faces the bottleneck of re-meshing and grid-distortion, so the meshless method due to no grids needed is looked as a potential method to solve the above electromagnetic problems, and attracts the attentions of some researchers. At present, the difficult point and hotspot in computational electromagnetics lie in the research on the coupling or moving electromagnetic problem combined with engineering design. The induction sealing system of paper-based composite material is a nonlinear multi-material system coupling electric, magnetic and thermo. The reliable sealing effect is the key requirement of the induction sealing system in aseptic beverage packaging machine. This paper aims at a few basic problems of meshless method in computational electromagnetic field, including the method for building meshless numerical model, the disposal of interface condition, the meshless method in moving electromagnetic field and so on, systematic researches were carried out. At the same time, based on the study and simulation on the induction sealing problem of paper-based composite material in aseptic beverage packaging machine, an induction sealing system with reliable sealing effect was designed.The foundation of meshless numerical model of electromagnetic field governing equation is the basis of the application of meshless method in electromagnetic problem. Omitting the displacement current and accumulation charge in Maxwell equations and introducing the magnetic vector potential A and the electric scalar potentialφ, the harmonic electromagnetic field governing equation formulated by A-φ-A approach was completed. Then, aiming at the electromagnetic problem which can be expressed in cylindrical coordinates, using the vector and scalar test function, the detailed implementation of the governing equation was described with the meshless method, and the common 3D numerical model in frequency domain was derived by using Galerkin residual method.The disposal of boundary and interface conditions, especially the interface conditions, is the key problem to restrict the application of the meshless method in numerical computation of engineering electromagnetic field. Based on the analysis about the present methods for the discontinuity disposal in meshless method, this paper presents such methods based on the modification of the weak form as Lagrange multiplier method and penalty method to deal with electromagnetic interface conditions. Using above two methods, the detailed disposal process and models of the electromagnetic interface conditions were described further in the meshless method. The application examples used prove that the above meshless method numerical model of electromagnetic field is corrected, and the meshless method is found to be reliable to give reasonable computational results for electromagnetic field; the suggested methods for enforcing the electromagnetic interfaces can introduce the necessary discontinuity and also guarantee the expected continuity; the disposal accuracy of penalty method for electromagnetic interfaces is decided by the value of penalty coefficient, and the suitable value is (1e2-1e5)×(Kii)max; the disposal accuracy of Lagrange multiplier method for electromagnetic interfaces is decided by the number of the interpolation point at interface, the number is larger, the results are more accurate, but too large point number would cause deteriorated result, and even a singular system matrixThe numerical modeling of rigid body motion is an important problem in computational electromagnetics. In this paper, the meshless method was proposed to solve the electromagnetic field governing equation with velocity term, and the computational result indicates that the velocity and the parameter dmax controlling the size of nodal influence domain are the major factors to lead to the numerical oscillation contained in the meshless method solution. The nodal refinement method used can suppress the numerical oscillation, but with the increasing velocity and dmax, the nodal number increases. So, the streamline upwinding stabilization method in FEM was introduced into the meshless method for electromagnetic field involving moving conductor, and the streamline upwinding meshless method numerical model was derived for electromagnetic governing equation with velocity term formulated by A-φ-A method. Different numerical examples show that the combination streamline upwinding and the meshless method can solve effectively the electromagnetic governing equation with velocity term. Although the stabilization factor is no longer optimal in meshless method, the streamline upwinding can still suppress significantly the numerical oscillation in meshless method solution of electromagnetic field governing equation with velocity term. The induction sealing system of paper-based composite material is a nonlinear system coupling electric, magnetic and thermo. In this paper, based on analysis on the factors influencing sealing effect, an induction sealing system was designed, the meshless method model of sealing electromagnetic field was founded, and the coupling of electromagnetic and thermal field was simulated by FEM. The influences of different factors to heating time, eddy current and temperature distribution were studied, and the reference solution of the meshless method solution of sealing system was obtained. The uniform temperature in sealing line can be obtained by the designed induction sealing system. The exciting current is the major factor influencing the seal, the instant seal only can be realized by large current; the larger the current frequency is, the more the eddy current density and Joule heat concentrate to the seal line. The magnetic flux concentrator is necessary to realize the effective and fast sealing of packaging material, and it can increase significantly the eddy current and temperature at the seal line and thickness direction of packaging material. Based on above analyses and simulations, the suitable sealing parameters of paper-based composite material are given, the experiments prove that the proposed sealing parameters are correct.