基于四种曲线不同当量半径算法的对比研究

为探讨不同曲线代替拱形断面地下工程顶部曲线对当量半径及围护结构传热的影响趋势,利用圆弧、椭圆、抛物线和双曲线分别代替求得当量半径值的计算公式。基于MATLAB和COMSOL软件针对宽度参数L、起拱高度H和拱高h进行模拟,分析结果发现,在不考虑明显偏离情况下,3个参数对当量半径值的影响趋势总体上分别保持一致,R_dif-s与R_dif-p的差值在对应L、H和h的变化条件下最大分别可达0.43 m、0.45 m和0.65 m。对比发现,湿周法所得当量半径值均大于截面积法,两者差值在对应参数变化条件下最大分别可达1.03 m、0.91 m和0.94 m。且从工程最高温度的角度分析,采用截面积法计算模拟宜选择椭圆,采用湿周法则宜选择抛物线。若给定相同热流密度,则湿周法计算所得的温升大于截面积法。

Comparative Study on Different Equivalent Radius Algorithms Based on Four Curves

In order to study the effect of different curves in place of the top curve of arch section in underground engineering on the equivalent radius and the heat-transfer of envelope, theoretical formulas of equivalent radius are obtained by using circular arc, ellipse, parabola and hyperbolic respectively. According to the simulation to the width parameter L, the springing height H and the height h of arch based on MATLAB and COMSOL, the results show that the overall impact of each parameter on the equivalent radius is consistent without considering the obvious deviation and that the biggest difference between R_dif-s and R_dif-p in the corresponding L, H and h changes can respectively reach up to 0.45 m, 0.43 m and 0.65 m. It is found by comparison that the equivalent radius of the wetted perimeter method is larger than that of the cross section method and that the biggest difference between the two methods in the corresponding L, H and h changes can respectively reach up to 1.03 m, 0.91 m and 0.94m. And from the view of the maximum temperature of engineering, ellipse and parabola should be respectively selected when using the cross section method and wetted perimeter method to simulate. Given the same heat flux, the temperature rise of the wetted perimeter method is larger than that of the cross section method.