CAJ | 학술논문

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.
침대고방사성핵폐물지하처치고근장포화렬극암체배경,제출일충유분포열원、포화단렬극화량측무한대암석구성적삼유수류-전열간화모형,건립료공제미분방정화기우랍씨변환역격림함수적적분방정;채용구형단원파렬극면역리산화,이용겁좌표하적해석방법계산포함기점적단원적분,이용수치방법계산분포열원화불포함기점적단원적분,건립랍씨변환역적선성대수방정조,구해후,이용랍씨수치역변환,계산임의시각렬극수화암석적온도분포.대량개무내열원、류장학정적계산모형진행료계산,여부고필암석연렬극면법향일유열전도적해석해진행료대비.계산분석료분포열원작용하포화단렬극암체적삼유수류-전열특정급기대렬극수류속、암석열전도계수화열원열류집도적민감도.계산결과표명:여직접채용고사수치적분상비,제출적해석법기이적분정도교고;취렬극수온도이언,단렬극암체삼유수류-전열반해석계산방법여해석법득도적결과기본일치,단유우반해석계산방법고필료암석적삼유열전도,사득렬극수적상유온도교저,이하유온도교고;무분포열원작용시,암석열전도계수월대,렬극수온도월저;렬극수류속월대,렬극진수온도대렬극수화암석온도분포적영향월명현;유우수도렬극수류동전열적작용,분포열원대렬극수온도화암석온도적영향재렬극수류적하유구역비교현저.
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.