基于傅立叶级数解的导温系数现场测定

Thermal Diffusivity Field Determination Based on Fourier Series

摘要:

将路面温度场抽象为1维瞬态热传导方程,由分离变量法导出满足方程的傅立叶级数,推导出在已知界面温度时确定1维层状体瞬态温度分布的解答.基于路面温度场实测数据,提出用牛顿法反算路面材料导温系数的方法.在路面降温过程中路面温度沿深度单调变化时,傅立叶级数解取50项就能够达到0.01 ℃的精度.实测数据分析结果表明:路面沥青层中上部导温系数较下部稍大,中面层AC16导温系数为0.002 4 m2·h-1,底面层AC25为0.001 6 m2·h-1,比大多实验室测定值低.

Abstract:

Pavement temperature field was abstracted as onedimensional transient heat conduction equation.Fourier series that compatibility with the equation was obtained by separation of variables.Then instantaneous temperature distribution of one dimensional layered body in terms of known interface temperature was derived based on Fourier series.The Newton method that backcalculation the thermal diffusivity of pavement material in related to measuring temperature distribution in field was presented.In cooling process as pavement temperature changes along the depth monotony,Fourier series with 50 items can attain the accuracy of 0.01℃.Results derived from measured data show that thermal diffusivity of top asphalt concrete layer is larger than that of bottom layer,with 0.002 4 m2·h-1 for AC16 and 0.001 6 m2·h-1 for AC25,which is lower than most of the laboratory measured values.