分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法

›› 2013, Vol. 34 ›› Issue (3): 685-695.

分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法

张勇，项彦勇

北京交通大学土木建筑工程学院，北京 100044

收稿日期:2012-02-16 出版日期:2013-03-11 发布日期:2013-03-20
作者简介:张勇，男，1986年生，博士研究生，主要从事岩土工程方面的研究工作。
基金资助:
中央高校基本科研业务费专项资金资助项目(No. 2011YJS259)；国家自然科学基金资助项目(No. 50778014)。

A semi-analytical method for calculation of three-dimensional water flow and heat transfer in single-fracture rock with distributed heat sources

ZHANG Yong，XIANG Yan-yong

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Received:2012-02-16 Online:2013-03-11 Published:2013-03-20

摘要/Abstract

摘要： 针对高放射性核废物地下处置库近场饱和裂隙岩体环境，提出一种由分布热源、饱和单裂隙和两侧无限大岩石构成的三维水流-传热简化模型，建立了控制微分方程和基于拉氏变换域格林函数的积分方程；采用矩形单元把裂隙面域离散化，利用极坐标下的解析方法计算包含奇点的单元积分，利用数值方法计算分布热源和不包含奇点的单元积分，建立拉氏变换域的线性代数方程组，求解后，利用拉氏数值逆变换，计算任意时刻裂隙水和岩石的温度分布。对两个无内热源、流场确定的计算模型进行了计算，与仅考虑岩石沿裂隙面法向一维热传导的解析解进行了对比。计算分析了分布热源作用下饱和单裂隙岩体的三维水流-传热特征及其对裂隙水流速、岩石热传导系数和热源热流集度的敏感度。计算结果表明：与直接采用高斯数值积分相比，提出的解析法奇异积分精度较高；就裂隙水温度而言，单裂隙岩体三维水流-传热半解析计算方法与解析法得到的结果基本一致，但由于半解析计算方法考虑了岩石的三维热传导，使得裂隙水的上游温度较低，而下游温度较高；无分布热源作用时，岩石热传导系数越大，裂隙水温度越低；裂隙水流速越大，裂隙进水温度对裂隙水和岩石温度分布的影响越明显；由于受到裂隙水流动传热的作用，分布热源对裂隙水温度和岩石温度的影响在裂隙水流的下游区域比较显著。

关键词: 核废物处置库, 裂隙岩体, 裂隙水流, 三维传热, 格林函数, 奇异积分

Abstract: Taking the near field of nuclear waste repositories in fractured rocks as the subject of study, a simplified conceptual model for three-dimensional water flow and heat transfer in single-fracture rock is proposed. The mathematical model, taking into account of distributed heat source and saturated single-fracture rock of infinite extent, is formulated and solved by using a Green function approach, in which a fundamental solution of the governing differential equations after Laplace transform is employed. The fracture surface is discretized by rectangular elements. The singularities in the integral equation are handled through analytical integration in polar coordinates; and a numerical procedure is developed to solve the transient temperature distributions in fracture water and rock matrix. Two numerical examples with special flow field are provided for illustration of the proposed method with comparison of an analytical solution based on 1D rock thermal conduction; and other numerical examples with distributed heat sources are extended for characteristics of flow and heat transfer in single-fracture rock and the sensitivities to flow velocity, rock thermal conductivity and heat source intensity. The calculations show the following observations: Comparing with the direct Gaussian method, the proposed analytical approach to handling the singular integrals is more accurate. The temperature of water in the fracture calculated by using the semi-analytical method is lower in upstream and higher in downstream than the analytical solution, due to the fact that the former method takes into account 3D thermal conduction in the rock matrix, whereas the latter assumes 1D conduction. Without interior heat source, the greater the rock thermal conductivity, the lower the temperature of facture water, due to more heat exchange between fracture water and rock matrix. The larger the fracture water velocity, the more significant of the influence of the inlet fracture water temperature on the temperatures of fracture water and rock matrix. The effects of the distributed heat source on the temperatures of fracture water and rock are more sensitive in downstream as a result of the heat advection of fracture fluid flow.

Key words: nuclear waste repository, fractured rock, fracture water flow, 3D heat transfer, Green function, singular integral

中图分类号:

TU 451

张勇，项彦勇. 分布热源作用下单裂隙岩体三维水流-传热的半解析计算方法[J]. , 2013, 34(3): 685-695.

ZHANG Yong，XIANG Yan-yong. A semi-analytical method for calculation of three-dimensional water flow and heat transfer in single-fracture rock with distributed heat sources[J]. , 2013, 34(3): 685-695.

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