基于尼古拉兹实验的层流底层数学模型
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摘要
矿井通风中,巷道壁面处存在的层流底层,对核心区涡的形成、粉尘运移、瓦斯积聚及壁面的换热、换质、减阻等起到重要作用。论文以尼古拉兹实验为基础,通过理论分析得到了层流底层流速分布式;确立了过渡区与水力粗糙管区的分界线;建立了更加精确的层流底层厚度数学模型和边界紊流速度数学模型,验证了层流底层厚度随雷诺数的增加和粗糙度的减少而减少的现象;发现了层流底层能量耗散比例随雷诺数的减少和粗糙度的增加而增加的规律,为矿井通风研究提供了基础。
In the mine ventilation,the laminarsublayer appeared near the wall of roadway not only exerts an important influence on the formation of vortex in the core zone and the accumulation of dust and gas,but also plays a decisive role on the heat transfer,mass transfer and drag reduction with the wall.This paper based on Nikuradse experiment,a velocity distribution formula was derived by theoretical analysis a boundary between transional region and hydraulic rough region was determined.A more precise mathematical model of laminar sublayer thickness was derived and a mathematical model of boundary turbulent velocity was established,which verified that the thickness decreased as the Reynolds number increased and roughness decreased,and found that the ratio of laminar sublayer energy dissipation increased with the Reynolds number decreased and roughness increased.The results could be applied in the analysis of mine ventilation.
In the mine ventilation,the laminarsublayer appeared near the wall of roadway not only exerts an important influence on the formation of vortex in the core zone and the accumulation of dust and gas,but also plays a decisive role on the heat transfer,mass transfer and drag reduction with the wall.This paper based on Nikuradse experiment,a velocity distribution formula was derived by theoretical analysis a boundary between transional region and hydraulic rough region was determined.A more precise mathematical model of laminar sublayer thickness was derived and a mathematical model of boundary turbulent velocity was established,which verified that the thickness decreased as the Reynolds number increased and roughness decreased,and found that the ratio of laminar sublayer energy dissipation increased with the Reynolds number decreased and roughness increased.The results could be applied in the analysis of mine ventilation.
引文
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[13] 孙广臣,傅鹤林,巢万里.桥隧相连工程多源损伤模型试验方法研究[J].铁道学报,2012,34(8):109-116.Sun Guangchen,Fu Helin,Chao Wanli.Study on test method of multiple-source damage model of bridge and tunnel connecting works[J].Journal of the China Railway Society,2012,34(8):109-116.
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[18] Yang B H,Joseph D D.Virtual nikuradse [J].Journal of Turbulence,2009,10(11):1-28.
[19] Lorenzini M,Morini G L,Salvigni S.Laminar,transitional and turbulent friction factors for gas flows in smooth and rough microtubes[J].International Journal of Thermal Sciences,2010,49(2):248-255.
[20] 王松岭.流体力学[M].北京:中国电力出版社,2007.
[2] 张秀华,王李管,冯兴隆.金属矿山通风系统综合评价[J].中国矿业,2010,19(4):93-96.Zhang Xiuhua,Wang Liguan,Feng Xinglong.Fuzzy integrated evaluation for safety of metal mine ventilation system[J].China Mining Magzine,2010,19(4):93-96.
[3] 姜德恩.边界层理论在管内强化传热上应用[J].抚顺石油学院学报,1994,14(1):31-34.Jiang De'en.The application of boundary layer to constrained heat transfer in the pipe[J].Journal of Fushun Petroleum in Stitute,1994,14(1):31-34.
[4] 杨绍琼,姜楠.湍流边界层空间特征尺度的层析TRPIV测量[J].实验力学,2011,26(4):369-376.Yang Shaoqiong,Jiang Nan.On the measurement of spatial characteristic scale in turbulent boundary layer based on tomographic time-resolved PIV [J].Journal of Experimental Mechanics,2011,26(4):369-376.
[5] 吴玉林,刘树红.粘性流体力学[M].北京:中国水利水电出版社,2006.
[6] 罗永豪,赵阳升.煤矿井下不同粗糙度巷道内风速分布的风洞模拟[J].太原理工大学学报,2015,46(2):235-237.Luo Yonghao,Zhao Yangsheng.Wind tunnel simulation on wind speed distribution in coal mine roadways within different roughness[J].Journal of Taiyuan University of Technology,2015,46(2):235-237.
[7] 罗永豪.巷道断面风速分布与煤矿通风系统实时诊断理论研究[D].太原:太原理工大学,2015.
[8] Luo Y,Zhao Y,Wang Y,et al.Distributions of airflow in four rectangular section roadways with different supporting methods in underground coal mines[J].Tunnelling and Underground Space Technology,2015,46:85-93.
[9] 刘亚坤.水力学[M].北京:中国水利水电出版社,2016.
[10] 王亚玲.水力学[M].北京:人民交通出版社,2015.
[11] Gao Ran,Fang Zhiyu,Li Angui,et al.A novel low-resistance tee of ventilation and air conditioning duct based on energy dissipation control[J].Applied Thermal Engineering,2018,132(5):790-800.
[12] 杨加伟.浅谈矿井通风阻力产生的原因及降低阻力的方法[J].采矿技术,2010,10(2):60-62.Yang Jiawei.The reasons of mine ventilation resistance and the method of reducing resistance are discussed[J].Mining Technology,2010,10(2):60-62.
[13] 孙广臣,傅鹤林,巢万里.桥隧相连工程多源损伤模型试验方法研究[J].铁道学报,2012,34(8):109-116.Sun Guangchen,Fu Helin,Chao Wanli.Study on test method of multiple-source damage model of bridge and tunnel connecting works[J].Journal of the China Railway Society,2012,34(8):109-116.
[14] Colebrook C F.Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws[J].Journal of the Institution of Civil Engineers,1939,11(4):133-156.
[15] Nikuradse J.Laws of flow in rough pipes[M].Washington:National Advisory Committee for Aerona-utics,1950.
[16] 张国枢.通风安全学[M].徐州:中国矿业大学出版社,2011.
[17] 李大美,杨小亭.水力学[M].武汉:武汉大学出版社,2015.
[18] Yang B H,Joseph D D.Virtual nikuradse [J].Journal of Turbulence,2009,10(11):1-28.
[19] Lorenzini M,Morini G L,Salvigni S.Laminar,transitional and turbulent friction factors for gas flows in smooth and rough microtubes[J].International Journal of Thermal Sciences,2010,49(2):248-255.
[20] 王松岭.流体力学[M].北京:中国电力出版社,2007.