一种预测流动和传热问题的快速算法

Fast Algorithm for Prediction of Fluid Flow and Heat Transfer

将湍流拟序结构分析中的最佳正交分解技术运用到流动和传热问题中,并在最佳正交分解技术的基础上提出了一种快速预测流动和传热问题的算法.通过对样本矩阵实施最佳正交分解得到一组特征函数.这些特征函数具有能量最优的特性,即以这些特征函数为基函数,可以用非常少的基函数将原物理问题准确地表示出来.特征系数用样条曲线插值的方式计算得到.以同心圆环内的自然对流为例验证此算法,参数Ro/Ri为2.6,Pr为0.71,5 000≤Ra≤1×105.利用该算法可以准确地预测温度场和速度场,与准确解之间的相对误差仅为0.7%,并且比SIMPLE算法快100倍.该算法有较广的使用范围,不受几何结构和流态的限制,只要有一组准确的样本便可使用.

A fast and efficient algorithm based on the proper orthogonal decomposition （POD） technique for predicting heat transfer and fluid flow was proposed. The POD technique was applied to a set of numerical simulation results to obtain the eigenfunctions that represent the dynamics of the physical problerm.The function space considered in the physical problem was limited to the smallest linear subspace when employing these eigenfunctions as basis functions. In stead of projecting the governing equations onto these eigenfunctions, the spectral coefficients were obtained with a simple cubic spline interpolation procedure. The presented algorithm was verified with an example of natural convection in a two dimensional concentric cylinder with a radius ratio of 2.6, and the Rayleigh number varying from 5 000 to 1×10^5. The results show that this algorithm can predict the flow and temperature fields with a relative error of 0.7 % compared with the exact numerical results, moreover, it is more than 100 times faster than the SIMPLE algorithm.