等离子喷涂中基板传热的无网格分析

Meshless Analysis of the Substrate Temperature Evolution during Plasma Spray Process

基于无网格彼得洛夫-伽辽金法(MLPG)建立了热喷涂中基板的三维传热数学模型。温度场由权函数、多项式基和一组未知系数近似构造,利用二次样条函数作为移动最小二乘中的权函数和局部弱形式的试函数,并采用罚函数法处理本征边界条件。详细研究了比例系数对数值精度的影响。与有限元法相比,无网格法可取得更好的收敛性和较高的精度。利用该方法计算等离子喷涂中基板温度,其计算结果与实验结果基本一致,表明该模型可用于求解热喷涂中的基板传热问题。

This paper focused on establishing a sound 3--D heat transfer formulation based on the meshless local Petrov--Galerkin（MLPG） method and was used to solve transient heat transfers in the plasma spraying. The unknown temperature functions were approximated and constructed by a weight function, a polynomial basis and a set of non--constant coefficients. A quartic spline function was selected as the moving least--squares weight and test function. A penalty technique was introduced to enforce the essential boundary conditions. The effect of scaling parameters on numerical solutions was discussed in detail. The substrate temperature was computed using this formulation numerically. It is found that MLPG solutions can achieve better convergence and higher accuracy compared with FEM and are in good agreement with those from the experiments, suggesting that the MLPG is feasible and efficient and therefore applicable to heat transfer problems during the plasma spray process.