|
|
|
| Analytical solution of steady state temperature field of a few freezing pipes arranged near a right angle adiabatic boundary |
| HU Xiang-dong,GUO Wang,ZHANG Luo-yu |
Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground
Engineering of Ministry of Education, Tongji University, Shanghai 200092, China |
|
|
|
Abstract Aiming at the actual situation that the development of frozen soil often subjects to existing underground structures in artificial ground freezing projects, the engineering problem of the temperature field of a few freezing pipes arranged near right angle structures was studied. The study subjects were abstracted into quarter-plane problems of a few point cold sources arranged near a right-angle adiabatic boundary. A solution method combining the potential superposition method with the mirror image method was proposed. With the quarter-plane problems mapped into infinite region problems by the mirror image method, the potential superposition method was then employed for the solution. After theoretical derivations, the steady-state temperature fields of single-piped and double-piped freezing near a right-angle adiabatic boundary were obtained analytically. All the analytical formulas for different arrangements of freezing pipes were verified by thermal numerical simulation, and the results showed that the temperature fields calculated by the analytical formulas were well consistent with those by thermal numerical simulation for the same conditions.
|
|
Published: 10 June 2018
|
|
|
直角绝热边界附近少量冻结管稳态温度场解析解
针对地层在进行人工冻结时,由于冻土帷幕受到既有地下构筑物的限制而无法自由发展的实际情况,研究直角构筑物附近少量冻结管温度场这一工程问题.将该工程问题抽象成1/4平面内直角绝热边界附近布置少量点冷源稳态温度场问题,提出势函数叠加法结合镜像法的求解方法.采用镜像法将1/4平面问题映射成无限区域问题,应用势函数叠加法进行求解.通过理论推导,求得了直角绝热边界附近单管和双管冻结的稳态温度场解析解.采用热学数值模拟方法对冻结管布置不同时的解析解分别进行验证,结果表明,解析解计算温度场与数值模拟结果吻合.
|
|
| ［1］ ТРУПАК Н Г. Замораживание горных пород при проходке стволов［M］. Москва: Углетехиздат, 1954．
TRUPAK N G. Ground freezing in shaft sinking ［M］. Moscow: Coal Technology Press, 1954. (in Russian)
［2］ БАХОЛДИН Б В. Выбор оптимального режима замораживания грунтов в строительных целях［M］. Москва: Госстройиздат, 1963．
BAKHOLDIN B V. Selection of optimized mode of ground freezing for construction purpose ［M］. Moscow. State Construction Press, 1963. (in Russian)
［3］ SANGER F J, SAYLES F H. Thermal and rheological computations for artificially frozen ground construction ［J］. Engineering Geology, 1979, 13(1-4): 311337．
［4］ 戸部 暢, 秋元 攻. 凍土内温度分布計算式と,その応用［J］. 冷凍, 1979, 54(8):3-11．
TOBE N, AKIMOTO O. Temperature distribution formula in frozen soil and its application ［J］. Refrigeration, 1979, 54(8):3-11.
［5］ 加藤 哲治,伊豆田 久雄,櫛田 幸弘.温度分布凍土ばりの曲げ強さの解析と凍土設計平均温度評価法の考察［J］. 土木学会論文集F, 2007, 63(1): 97-106．
KATO T, IZUTA H, KUSHIDA Y. Bending strength of frozen soil beam with temperature distribution and consideration of average temperature evaluation method［J］. Doboku Gakkai Ronbunshuu F, 2007, 63(1):97106．
［6］ 陈文豹, 汤志斌. 潘集矿区冻结壁平均温度及冻结孔布置圈径的探讨［J］. 煤炭学报, 1982, 7(1): 46-52．
CHEN Wen-bao, TANG Zhi-bin. The average temperature in ice wall and the diameter of frozen circle in Panji Coal Field ［J］. Journal of China Coal Society, 1982, 7(1): 46-52．
［7］ HU Xiang-dong. Average Temperature model of double-row-pipe frozen soil wall by equivalent trapezoid method［C］∥ Proceedings of the Second International Symposium on Computational Mechanics and the Twelfth International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science. New York: American Institute of Physics, 2009: 1333-1338.
［8］ 胡向东, 黄峰, 白楠. 考虑土层冻结温度时人工冻结温度场模型［J］. 中国矿业大学学报, 2008, 37(4): 550-555．
HU Xiang-dong, HUANG Feng, BAI Nan. Models of artificial frozen temperature field considering soil freezing point ［J］. Journal of China University of Mining & Technology, 2008, 37(4): 550-555．
［9］ 胡向东, 白楠, 余锋. 单排管冻结温度场ТРУПАК和БАХОЛДИН公式的适用性［J］. 同济大学学报：自然科学版, 2008, 36(7): 906-910．
HU Xiang-dong, BAI Nan, YU Feng. Analysis of Trupak and Bakholdin formulas for temperature field of single-row-pipe frozen soil wall［J］. Journal of Tongji University ：Natural Science, 2008, 36(7): 906-910．
［10］ 胡向东, 何挺秀. 多排管直线冻土墙平均温度的等效梯形计算方法［J］. 煤炭学报, 2009, 34(11): 1465-1469．
HU Xiang-dong, HE Ting-xiu. Equivalent-trapezoid method of average temperature calculation for multi-row-pipe straight frozen soil wall ［J］. Journal of China Coal Society, 2009, 34(11): 1465-1469．
［11］ 胡传鹏, 胡向东, 朱合华. 单排管冻结巴霍尔金温度场控制参数敏感度分析［J］. 煤炭学报, 2011, 36(8): 938-944．
Hu Chuan-peng, Hu Xiang-dong, Zhu He-hua. Sensitivity analysis of control parameters of Bakholdin solution in single-row-pipe freezing ［J］. Journal of China Coal Society, 2011, 36(8): 938-944．
［12］ 胡向东, 赵俊杰. 人工冻结温度场巴霍尔金模型准确性研究\
[J\]. 地下空间与工程学报, 2010, 6(1): 96-101．
HU Xiang-dong, ZHAO Jun-jie. Research on precision of Bakholdin model for temperature field of artificial ground freezing［J］. Chinese Journal of Underground Space and Engineering, 2010, 6(1): 96-101．
［13］ 胡向东. 直线形单排管冻土帷幕平均温度计算方法［J］. 冰川冻土, 2010, 32(4): 778-785．
HU Xiang-dong. Average temperature calculation for the straight single-row-pipe frozen soil wall ［J］. Journal of Glaciology and Geocryology, 2010, 32(4): 778-785．
［14］ 胡向东, 赵飞, 佘思源, 等. 直线双排管冻结壁平均温度的等效抛物弓形模型［J］. 煤炭学报, 2012, 37(1): 28-32．
HU Xiang-dong, ZHAO Fei, SHE Si-yuan, et al. Equivalent parabolic arch method of average temperature calculation for straight double-row- pipe frozen soil wall ［J］. Journal of China Coal Society, 2012, 37(1): 28-32．
［15］ 胡向东, 汪洋. 三排管冻结温度场的势函数叠加法解析解［J］. 岩石力学与工程学报, 2012, 31(5): 1071-1080．
HU Xiang-dong, WANG Yang. Analytical solution of three-row-piped frozen temperature field by means of superposition of potential ［J］. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(5): 1071-1080． |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
