PNF管内层流压降数值计算模型及偏差分析
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摘要
为了建立管道非连续流体(PNF)输送时管内层流压降数值模型,基于牛顿流体和宾汉流体管内层流压降模型,考虑实际工程中气体在管道中低速运动的阻力对PNF输送阻力的影响,对PNF压降模型进行简化。结合工程实践详细分析了PNF管内层流压降近似表达式和相对精确表达式,并分析了二者之间的偏差。结合对工程数据的分析,验证了PNF管内层流压降模型的有效性。结果表明:当PNF流量增大或输送管管径减小时,使用压降近似公式与压降相对精确公式计算出的压降值之间的偏差会减小。通过与实测值对比表明,本文模型较好地描述了PNF输送时的压降。其中压降近似模型的精度更优(计算值与实测值的偏差率为1.16%~8.33%),且求解更方便。
In order to establish the pressure drop numerical model of pipe noncontinuous fluid(PNF) under laminar tube flow transportation, based on the pressure drop numerical model of laminar tube flow in Newtonian fluid and Bingham fluid, and considering the influence of gas resistance while low-speed moving in engineering practice to the PNF transportation, the pressure drop numerical model of PNF is simplified. Combining with engineering practice, the approximation solution formula and the relative exact solution formula of PNF's laminar pressure drop is analyzed and then the deviation between the two solutions is discussed. The validity of the PNF's laminar pressure drop model is verified through analysis of engineering data. The results show the fact that the deviation will decrease while the quantity of flow increases, and also decrease while the radius of the conveying pipe decreases. By comparing the measured value with the calculated value, it can be concluded that the models established describe the pressure drop in PNF transportation very well. The approximate model is better in accuracy and easier to be solved, the deviation between approximate solution and measured value ranges from 1.16% to 8.33% and the deviation between relative exact solution and measured value ranges from 1.96% to 13.33%.
In order to establish the pressure drop numerical model of pipe noncontinuous fluid(PNF) under laminar tube flow transportation, based on the pressure drop numerical model of laminar tube flow in Newtonian fluid and Bingham fluid, and considering the influence of gas resistance while low-speed moving in engineering practice to the PNF transportation, the pressure drop numerical model of PNF is simplified. Combining with engineering practice, the approximation solution formula and the relative exact solution formula of PNF's laminar pressure drop is analyzed and then the deviation between the two solutions is discussed. The validity of the PNF's laminar pressure drop model is verified through analysis of engineering data. The results show the fact that the deviation will decrease while the quantity of flow increases, and also decrease while the radius of the conveying pipe decreases. By comparing the measured value with the calculated value, it can be concluded that the models established describe the pressure drop in PNF transportation very well. The approximate model is better in accuracy and easier to be solved, the deviation between approximate solution and measured value ranges from 1.16% to 8.33% and the deviation between relative exact solution and measured value ranges from 1.96% to 13.33%.
引文
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[12]滕一峰,郭少华,陈勇民,等.管道非连续流体层流、边界层表达式及减阻分析[J].矿山机械,2016(3):68-73.(Teng Yifeng,Guo Shaohua,Chen Yongmin,et al.Analysis on expression of laminar flow and boundary layer and drag reducing in PNF[J].Mining&Processing Equipment,2016(3):68-73(in Chinese)).
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[15]陶松垒,李未材,陶钧炳,等.一种新型的清淤输泥设备[J].水利水电技术,2004(5):108-110.(Tao Songlei,Li Weicai,Tao Junbing,et al.A new type of dredging and mud flow conveying system[J].Water Resources and Hydropower Engineering,2004(5):108-110(in Chinese)).
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[19]陶松垒.气力输送软粘物料的研究与应用[J].水利管理技术,1997,17(3):54-58.(Tao Songlei.Pneumatic conveying research and application of soft clay material[J].Water Resources Development and Management,1997,17(3):54-58(in Chinese)).
[20]数学手册编写组.数学手册[M].北京:人民教育出版社,1979.(Mathematical Manual Writing Committee.Mathematic handbook[M].Beijing:People’s Education Press,1979(in Chinese)).
[2]Chilton R A,Stainsby R.Pressure loss equations for laminar and turbulent non-Newtonian pipe flow[J].Journal of Hydraulic Engineering,1998,124(5):522-529.
[3]Grozdek M,Khodabandeh R,Lundqvist P.Experimental investigation of ice slurry flow pressure drop in horizontal tubes[J].Experimental Thermal and Fluid Science,2009,33(2):357-370.
[4]石玉发.使用四次方程求根公式精确计算宾汉流体圆管轴向层流压降[J].科技创新导报,2009(7):91.(Shi Yufa.Use quartic equation radical formula accurately calculating the Bingham fluid axial laminar flow pressure drop in circular pipe[J].Science and Technology Innovation Herald,2009(7):91(in Chinese)).
[5]Monteiro A C S,Bansal P K.Pressure drop characteristics and rheological modeling of ice slurry flow in pipes[J].International Journal of Refrigeration,2010,33(8):1523-1532.
[6]高远文,鲁港,杨龙,等.宾汉钻井液圆管轴向层流压降的数值计算[J].探矿工程:岩土钻掘工程,2010(3):5-7.(Gao Yuanwen,Lu Gang,Yang Long,et al.Numerical calculation for axial laminar flow pressure drop of the Bingham drilling fluid in circular pipe[J].Exploration Engineering:Rock&Soil Drilling and Tunneling,2010(3):5-7(in Chinese)).
[7]Mika?.Pressure loss coefficients of ice slurry in horizontally installed flow dividers[J].Experimental Thermal&Fluid Science,2013,45(2):249-258.
[8]Bechtel T B.Laminar pipeline flow of wastewater sludge:computational fluid dynamics approach[J].American Society of Civil Engineers,2014,129(2):153-158.
[9]樊洪海,彭齐,腾学清,等.不同流变模式钻井流体圆管层流压耗的通用精确算法[J].中国石油大学学报:自然科学版,2014,38(1):70-74.(Fan Honghai,Peng Qi,Teng Xueqing,et al.A high precision method for calculating laminar pressure drop of drilling fluid in pipe flow with different rheological models[J].Journal of China University of Petroleum:Edition of Natural Science,2014,38(1):70-74(in Chinese)).
[10]赵珊珊,乌效鸣,刘耀东.精确计算Bingham流体圆管层流压降及速度分布规律的新方法[J].应用数学和力学,2015(4):440-448.(Zhao Shanshan,Wu Xiaoming,Liu Yaodong.A new method for accurate calculation of the Bingham fluid axial laminar flow pressure drop and velocity distribution in circular pipes[J].Applied Mathematics and Mechanics,2015(4):440-448(in Chinese)).
[11]王树刚,吕燕捷,王继红,等.水平直管内冰浆流动压降分相叠加算法[J].高校化学工程学报,2015(1):43-48.(Wang Shugang,Lv Yanjie,Wang Jihong,et al.Phase splitting algorithm for flowing pressure drop of ice slurry in horizontal straight pipe[J].Journal of Chemical Engineering of Chinese Universities,2015(1):43-48(in Chinese)).
[12]滕一峰,郭少华,陈勇民,等.管道非连续流体层流、边界层表达式及减阻分析[J].矿山机械,2016(3):68-73.(Teng Yifeng,Guo Shaohua,Chen Yongmin,et al.Analysis on expression of laminar flow and boundary layer and drag reducing in PNF[J].Mining&Processing Equipment,2016(3):68-73(in Chinese)).
[13]Hirt C W,Nichols B D.Volume of fluid(VOF)method for the dynamics of free boundaries[J].Journal of Computational Physics,1981,39(1):201-225.
[14]方杰.VOF方法在水利水电工程中的应用和探索[D].南京:河海大学,2005.(Fang Jie.Implication and research of the fractional volume of fluid method in water conservancy and hydropower engineering[D].Nanjing:Hohai University,2005(in Chinese)).
[15]陶松垒,李未材,陶钧炳,等.一种新型的清淤输泥设备[J].水利水电技术,2004(5):108-110.(Tao Songlei,Li Weicai,Tao Junbing,et al.A new type of dredging and mud flow conveying system[J].Water Resources and Hydropower Engineering,2004(5):108-110(in Chinese)).
[16]Yamaguchi H.Engineering fluid mechanics[M].Berlin:Springer,2008.
[17]Wilkinson W L.Non-Newtonian fluids:fluid mechanics,mixing and heat transfer[M].London:Pergamon Press,1960.
[18]陶松垒.气力输送软站物料的研究与应用[J].建设机械技术与管理,1996,9(5):18-23.(Tao Songlei.Pneumatic conveying research and application of soft clay material[J].Construction Machinery Technology and Management,1996,9(5):18-23(in Chinese)).
[19]陶松垒.气力输送软粘物料的研究与应用[J].水利管理技术,1997,17(3):54-58.(Tao Songlei.Pneumatic conveying research and application of soft clay material[J].Water Resources Development and Management,1997,17(3):54-58(in Chinese)).
[20]数学手册编写组.数学手册[M].北京:人民教育出版社,1979.(Mathematical Manual Writing Committee.Mathematic handbook[M].Beijing:People’s Education Press,1979(in Chinese)).