一类热流耦合模型边界条件的反演计算方法
Inversion Method of Boundary Condition for a Class of Coupled Heat Flow Models
刘唐伟 1欧阳旺林 1阮晓晴 1李柯瑶 1唐阿敏1
作者信息
- 1. 东华理工大学理学院,330013,南昌
- 折叠
摘要
提出一种裂隙岩体中热流耦合模型边界条件的反演计算方法.基于单裂隙热流耦合模型,利用部分温度观测数据,反演计算出岩体和流体接触边界上的温度、温度梯度和对流换热系数.首先,利用分离变量法将热传导边值问题转化成第一类Fredholm积分方程,然后,基于正则化方法求解积分方程,得到岩体和流体接触边界上的温度和温度梯度,再得到局部换热系数,再利用梯度下降法求解一类无约束优化问题,得到总体对流换热系数,最后,对热流耦合方程进行数值计算.结果表明,提出的计算方法能克服反演问题的不适定性,具有较高的精度和较好的稳定性.
Abstract
An inversion method for calculating the boundary conditions of heat flow coupled model in fractured rock mass is proposed.Based on single fracture heat flow coupled model and using partial temperature observation data,the temperature,temperature gradient,and convective heat transfer coefficients at the interface between the rock and fluid have been calculated.Firstly,the separation variable method is used to transform the boundary value problem of heat conduction into the first Fredholm integral equation,and then the integral equation is solved based on the regularization method to obtain the temperature and temperature gradient on the contact boundary between rock mass and fluid,and the local heat transfer coefficient is calculated.An unconstrained optimization problem is solved using the gradient descent method to determine the overall convective heat transfer coefficient.Finally,the heat flow coupled equation is numerically calculated.The numerical results show that the proposed method can overcome the uneasiness of the inversion problem and has high accuracy and stability.
关键词
热-流耦合模型/换热系数/不适定性/侧边值反问题/反演计算Key words
heat-flow coupled model/heat transfer coefficient/ill-posedness/sideways problem/inversion computation引用本文复制引用
基金项目
国家自然科学基金(41962019)
国家自然科学基金(42264007)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据