Interface Finite Element Method with Lower Calculation Amount for Step Size-varying Electro-quasistatic Field Problem

A novel FEM called interface finite element method(I-FEM)is proposed for the step size-varying electro-quasistatic field(EQS)in this paper.First,the corresponding equation and interface conditions for I-FEM are given.Then,the numerical principle of I-FEM is conducted.In the proposed method,by the inverse matrix modification lemma,the calculation amount of I-FEM is decreased greatly.Furthermore,the corresponding example is given to verify the effectiveness and correctness of IFEM.At last,the error analysis and universal promotion of the proposed I-FEM are given.Compared with the normal FEM,I-FEM can greatly decrease the calculation amount while the numerical accuracy of I-FEM is even better than the normal FEM in some case.

Interface Finite Volume Method with Low Calculating Amount for Step Size Varying Electro-Quasistatic Field Problem

In this paper,a novel numerical method called interface finite volume method(I-FVM)for calculation of step-varying Electro-quasistatic(EQS)field is proposed.First,the principle of I-FVM is derived.Then,with numerical example of double layers parallel plate structure under step voltage which has an analytical solution,effectiveness and correctness of the I-FVM are verified.It can be found the calculating time of I-FVM is only 30%of normal FVM without decreasing accuracy during the whole calculating process.Furthermore,an engineering example about the electric field of DBC(Direct Bonding Copper)structure in a high voltage IGBT device is given.It can be found that accuracy of the I-FVM is the same as normal FVM,while time cost of I-FVM is only 20.8%of normal FVM.At last,the I-FVM is extended to one dimension based on the two-direction tri-diagonal matrix algorithm(TDMA)method given in this paper which can save processing of LU decomposition compared to one-dimensional traditional TDMA.In conclusion,the novel method called I-FVM proposed in this paper can decrease calculating amount for a step size varying electro-quasistatic field calculation problem.It may be a good method for large-scale EQS field calculation.

Heterogeneous particle structure formation during post-crystallization of spray-dried powder

The formation of heterogeneous particle structure in skim milk powder has been investigated in a post- crystallization facility using experimental and a mathematical model. Various processing conditions were used to produce these heterogeneous structures. The experimental process parameters were used as initial and boundary conditions for the model. The modelled data agreed well with the experimental data. The experimental and modelling results show that the powder processed at high water activity （aw = 0.7） with low initial moisture content （X0 = 0.01 kg/kg） developed a crystalline surface layer while the core of the particle remained amorphous. This structure is referred to as an egg-shell structure. The powder that was processed at low water activity （αw = 0.1） with high initial moisture content （X0 = 0.2 kg/kg） developed a crystalline core while the surface of the particle remained amorphous. This structure is referred to as an egg-yolk structure. Understanding the dependency of particle microstructures on the processing conditions could be useful when developing procedures to control the drying equipment because the particle microstructure affects the physicochemical properties of the powder and potential applications and behaviour of the powder.