应用高精度差分格式求解涡轮叶片热传导方程  

Solve Heat Transfer in Turbo Engine Blade with High Accuracy Difference Scheme

作　　者：郭兆元[1] 周驰[1] 王松涛[1] 冯国泰[1] 

机构地区：[1]哈尔滨工业大学推进理论与技术所,哈尔滨150001

出　　处：《科学技术与工程》2009年第14期3941-3944,共4页Science Technology and Engineering

基　　金：国家自然科学基金项目(50476028)资助

摘　　要：为了提高涡轮气热弹耦合计算时叶片热传导的计算精度,给出热传导方程在任意曲线坐标系中的表达形式,并将所得一次项和交叉项作为方程源项,推导出了数值求解三维复杂几何体热传导方程的精度为O(Δτ+Δh4)的ADI紧致格式,研究了源项求解精度为O(Δh4)的紧致格式,并采用Fourier法分析了格式的稳定性。通过数值实验结果验证所得方法的精确性和可靠性,该方法适用于涡轮叶片的热传导的计算,并分析了某涡轮叶片热传导。Heat transfer equation in curvilinear coordinate has been given, and first order item and cross item is deal as source item, then 3-D ADI compact difference scheme with the accuracy O（△τ＋△h^4 ）for numerical simulating heat transfer equation in complex computation zone,forth order difference accuracy scheme is studied for solving source item, finely stability of the scheme is validated by the solution of Fourier. To validate accuracy and reliability,analytic solution was selected , and the numerical results agreed well with the experimental data, the solution for solving heat transfer in complex computation zones can be using in engineering,analysing heat transfer in turbo blade with a cavity.

关 键 词：热传导方程 紧致格式 高精度 叶片热传导 

分 类 号：O241.82[理学—计算数学]