强迫对流管道内壁结垢层几何形状的逆运算估计

Inverse Estimation for the Unknown Fouling Geometry on the Inner Wall of a Forced-Convection Pipe

利用逆运算法中的共轭梯度法与差异原理,通过测量管壁内的温度,来估算一管流系统内壁结垢层厚度的几何形状.过程中未预先设定结垢层厚度的函数形式.因此,可将这类逆运算问题归类为"函数预测".逆运算过程的管壁温度测量值,可由直接解法所求得的温度数值来仿真实际的测量温度.并用测量误差来检验逆运算分析的正确性.数值实验结果显示,管内壁结垢层厚度的几何形状可获得极佳的估算值.所提出的技术可用作管路维修的预警系统,当管壁结垢层厚度超出某预先设定值时可适时发出维修警示.

A conjugate gradient method based inverse algorithm was applied to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It was assumed that no prior information was available on the functional form of the unknown profile; hence the procedure was classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem were used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the fouling-layer profile can be obtained for the test case considered. The technique presented can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a pre-defined criterion.