低温裂隙岩体的各向异性传热模型
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摘要
低温裂隙岩体属于典型的非连续介质,其传热特性具有明显的各向异性特性和时变性。从传热学的基本原理出发,对含冰–水相变低温裂隙岩体的传热特性进行了研究。首先通过类比电阻,推导考虑冰水相变及热对流作用的低温单裂隙热阻模型。在此基础上,根据能量守恒定律并考虑对流换热作用对裂隙岩体等效传热特性的影响,推导低温单裂隙代表性体元的传热模型。基于传热性能的可叠加性,构建含多组优势节理低温岩体的各向异性传热模型,从而实现低温裂隙岩体传热性能的等效连续化处理。最后通过一个含水平裂隙岩样和理想岩质边坡对各向异性传热模型进行了验证,最大误差不超过1.0℃。该传热模型的精度满足实际低温裂隙岩体工程的要求。
The fractured rock mass in cold regions is a typical discontinuous medium,whose heat-transfer characteristics have obviously anisotropy and time-variation. Based on the basic principles of heat transfer,the heat-transfer characteristics of fractured rock mass with ice-water phase change were carried out in this paper.Firstly,the thermal resistance model of single fracture under minus temperature was derived by drawing from the definition of resistance,which has considered the effect of ice-water phase change and thermal convection. Then,based on the law of energy conservation,the heat-transfer model of the representative volume element(RVE) of single fracture rock mass was developed by considering the effect of convective heat transfer on the equivalent heat-transfer property. Based on the additivity of heat-transfer,the anisotropic heat-transfer model of rock mass with several sets of fractures in cold regions was established,thus enabling the equivalent continuous treatment of heat-transfer property of fractured rock mass in cold regions. Finally,the model were verified by a rock sample with a set of horizontal fractures and a rockmass slope. The results indicate that the maximum error is less than1.0 ℃,which means the accuracy of this model could meet the needs of the real fractured rock mass engineering in cold regions.
The fractured rock mass in cold regions is a typical discontinuous medium,whose heat-transfer characteristics have obviously anisotropy and time-variation. Based on the basic principles of heat transfer,the heat-transfer characteristics of fractured rock mass with ice-water phase change were carried out in this paper.Firstly,the thermal resistance model of single fracture under minus temperature was derived by drawing from the definition of resistance,which has considered the effect of ice-water phase change and thermal convection. Then,based on the law of energy conservation,the heat-transfer model of the representative volume element(RVE) of single fracture rock mass was developed by considering the effect of convective heat transfer on the equivalent heat-transfer property. Based on the additivity of heat-transfer,the anisotropic heat-transfer model of rock mass with several sets of fractures in cold regions was established,thus enabling the equivalent continuous treatment of heat-transfer property of fractured rock mass in cold regions. Finally,the model were verified by a rock sample with a set of horizontal fractures and a rockmass slope. The results indicate that the maximum error is less than1.0 ℃,which means the accuracy of this model could meet the needs of the real fractured rock mass engineering in cold regions.
引文
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[15]LI Z W,FENG X T,ZHANG Y J,et al.Experimental research on the convection heat transfer characteristics of distilled water in manmade smooth and rough rock fractures[J].Energy,2017,133:206-218.
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[17]王世东,虎维岳,张文忠,等.深部裂隙岩体温度场及其控制因素[J].太原理工大学学报,2010,41(5):613-615.(WANG Shidong,HUWeiyue,ZHANG Wenzhong,et al.Study on the temperature fields of deep rock mass and the main influencing factors[J].Journal of Taiyuan University of Technology,2010,41(5):613-615.(in Chinese))
[18]张树光,赵亮,徐义洪.裂隙岩体传热的流热耦合分析[J].扬州大学学报:自然科学版,2010,13(4):61-64.(ZHANG Shuguang,ZHAO Liang,XU Yihong.Fluid-heat coupling analysis on heattransfer in fracture rock mass[J].Journal of Yangzhou University:Natural Science,2010,13(4):61-64.(in Chinese))
[19]徐彬.大型液化天然气(LNG)地下储气库裂隙围岩的热力耦合断裂损伤分析研究[博士学位论文][D].西安:西安理工大学,2008.(XU Bin.Research on thermo-mechanical coupling damage behavior in jointed rocks surrounding large scale rock cavern for refrigerated LNG(liquided natural gas)storage[Ph.D.Thesis][D].Xi?an:Xi?an University of Technology,2008.(in Chinese))
[20]WU Y S,MUKHOPADHYAY S,ZHANG K,et al.A mountain-scale thermal-hydrologic model for simulating fluid flow and heat transfer in unsaturated fractured rock[J].Journal of Contaminant Hydrology,2006,86(1):128-159.
[21]SHAIK A R,RAHMAN S S,TRAN N H,et al.Numerical simulation of fluid-rock coupling heat transfer in naturally fractured geothermal system[J].Applied Thermal Engineering,2011,31(10):1 600-1 606.
[22]HEINZE T,HAMIDI S,GALVAN B.A dynamic heat transfer coefficient between fractured rock and flowing fluid[J].Geothermics,2017,65:10-16.
[23]GIBSON R D.The contact resistance for a semi-infinite cylinder in vacuum[J].Applied Energy,1976,(2):57-65.
[2]徐斅祖,王家澄,张立新.冻土物理学[M].北京:科学出版社,2001:5-80.(XU Xiaozu,WANG Jiacheng,ZHANG Lixin.Permafrost physics[M].Beijing:Science Press,2001:5-80.(in Chinese))
[3]谭贤君.高海拔寒区隧道冻胀机理及其保温技术研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2010.(TAN Xianjun.Study on the mechanism of frost heave of tunnel in cold region with high altitude and related insulation technology[Ph.D.Thesis][D].Wuhan:Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,2010.(in Chinese))
[4]杨更社,周春华,田应国,等.软岩类材料冻融过程水热迁移的实验研究初探[J].岩石力学与工程学报,2006,25(9):1 765-1 770.(YANG Gengshe,ZHOU Chunhua,TIAN Yingguo,et al.Primary experimental study on moisture and heat transfer of soft rock material during its freezing and thawing[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(9):1 765-1 770.(in Chinese))
[5]MURTON J B,PETERSON R,OZOUF J C.Bedrock fracture by ice segregation in cold regions[J].Science,2006,314(5802):1 127.
[6]赵延林,王卫军,曹平,等.不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现[J].岩土力学,2010,31(2):638-644.(ZHAO Yanlin,WANG Weijun,CAO Ping,et al.Numerical implementation of discontinuities in dual media 3D model for thermohydro-mechanical coupling[J].Rock and Soil Mechanics,2010,31(2):638-644.(in Chinese))
[7]KELKAR S,LEWIS K,KARRA S,et al.A simulator for modeling coupled thermo-hydro-mechanical processes in subsurface geological media[J].International Journal of Rock Mechanics and Mining Sciences,2014,70(70):569-580.
[8]张勤.脆性岩石热-力-损伤耦合机理及数值模拟研究[博士学位论文][D].武汉:武汉大学,2013.(ZHANG Qin.Numerical modeling of coupled thermo-mechanical-damage behaviors for brittle rocks[Ph.D.Thesis][D].Wuhan:Wuhan University,2013.(in Chinese))
[9]申艳军,杨更社,荣腾龙,等.低温环境下含表面裂隙硬岩温度场及冻胀演化过程分析[J].岩土力学,2016,37(增1):521-529.(SHEN Yanjun,YANG Gengshe,RONG Tenglong,et al.Analysis of evolution of temperature field and frost heaving in hard rock with surface cracks under low temperature environment[J].Rock and Soil Mechanics,2016,37(Supp.1):521-529.(in Chinese))
[10]黄诗冰,刘泉声,程爱平,等.低温裂隙岩体水-热耦合模型研究及数值分析[J].岩土力学,2018,39(2):735-744.(HUANGShibing,LIU Quansheng,CHENG Aiping,et al.A coupled hydrothermal model of fractured rock mass under low temperature and its numerical analysis[J].Rock and Soil Mechanics,2018,39(2):735-744.(in Chinese))
[11]BAI B,HE Y Y,LI X C,et al.Experimental and analytical study of the overall heat transfer coefficient of water flowing through a single fracture in a granite core[J].Applied Thermal Engineering,2017,116:79-90.
[12]HUANG X X,ZHU J,LI J,et al.Fluid friction and heat transfer through a single rough fracture in granitic rock under confining pressure[J].International Communications in Heat and Mass Transfer,2016,75(1):78-85.
[13]张玉军,徐刚,杨朝帅.裂隙刚度随应力变化对双重孔隙介质热-水-应力耦合影响的有限元分析[J].岩土力学,2012,33(11):3 426-3 432.(ZHANG Yujun,XU Gang,YANG Chaoshuai.Finite element analysis of influence of fracture stiffness changing with stress on thermo-hydro-mechanical coupling in dual-porosity medium[J].Rock and Soil Mechanics,2012,33(11):3 426-3 432.(in Chinese))
[14]王宏伟,荣航.流热耦合作用下组合岩体等效导热系数研究[J].煤炭学报,2013,38(10):1 781-1 785.(WANG Hongwei,RONGHang.Study on the equivalence heat conduction coefficients of combined rock in fluid-thermal coupling[J].Journal of China Coal Society,2013,38(10):1 781-1 785.(in Chinese))
[15]LI Z W,FENG X T,ZHANG Y J,et al.Experimental research on the convection heat transfer characteristics of distilled water in manmade smooth and rough rock fractures[J].Energy,2017,133:206-218.
[16]罗爽,宋二祥.热储岩层单条裂隙换热概念模型的解及相关讨论[J].防灾减灾工程学报,2017,37(4):627-635.(LUO Shuang,SONGErxiang.Semi-analytic solutions to thermal exchange conceptual models for a single fracture in a geothermal reservior and related discussions[J].Journal of Disaster Prevention and Mitigation Engineering,2017,37(4):627-635.(in Chinese))
[17]王世东,虎维岳,张文忠,等.深部裂隙岩体温度场及其控制因素[J].太原理工大学学报,2010,41(5):613-615.(WANG Shidong,HUWeiyue,ZHANG Wenzhong,et al.Study on the temperature fields of deep rock mass and the main influencing factors[J].Journal of Taiyuan University of Technology,2010,41(5):613-615.(in Chinese))
[18]张树光,赵亮,徐义洪.裂隙岩体传热的流热耦合分析[J].扬州大学学报:自然科学版,2010,13(4):61-64.(ZHANG Shuguang,ZHAO Liang,XU Yihong.Fluid-heat coupling analysis on heattransfer in fracture rock mass[J].Journal of Yangzhou University:Natural Science,2010,13(4):61-64.(in Chinese))
[19]徐彬.大型液化天然气(LNG)地下储气库裂隙围岩的热力耦合断裂损伤分析研究[博士学位论文][D].西安:西安理工大学,2008.(XU Bin.Research on thermo-mechanical coupling damage behavior in jointed rocks surrounding large scale rock cavern for refrigerated LNG(liquided natural gas)storage[Ph.D.Thesis][D].Xi?an:Xi?an University of Technology,2008.(in Chinese))
[20]WU Y S,MUKHOPADHYAY S,ZHANG K,et al.A mountain-scale thermal-hydrologic model for simulating fluid flow and heat transfer in unsaturated fractured rock[J].Journal of Contaminant Hydrology,2006,86(1):128-159.
[21]SHAIK A R,RAHMAN S S,TRAN N H,et al.Numerical simulation of fluid-rock coupling heat transfer in naturally fractured geothermal system[J].Applied Thermal Engineering,2011,31(10):1 600-1 606.
[22]HEINZE T,HAMIDI S,GALVAN B.A dynamic heat transfer coefficient between fractured rock and flowing fluid[J].Geothermics,2017,65:10-16.
[23]GIBSON R D.The contact resistance for a semi-infinite cylinder in vacuum[J].Applied Energy,1976,(2):57-65.