牛顿流体圆管内非稳态Poiseuille流动特性
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摘要
Poiseuille流动初始阶段存在速度发展的非稳态过程,会对测试结果造成偏差。为分析非稳态Poiseuille流动过程对测量黏度造成的偏差,以不可压缩牛顿流体为例,进行恒流量边界与非定常流量边界下的非稳态Poiseuille流动过程研究。以无量纲黏度和无量纲时间表征非稳态过程,建立数值模型,计算给出恒平均速度边界、从0线性增加平均速度边界和恒压力边界条件下无量纲黏度数值的变化规律。结果表明:非稳态过程中无量纲黏度数值随时间逐渐减小并最终趋于1,且不同边界条件下流动达到稳定对应的无量纲时间为定值。当边界类型确定时,非稳态过程的无量纲黏度数值可视为仅与无量纲时间有关的函数;对于不同类型边界条件,从0线性增加的平均速度边界、恒压力边界、恒平均速度边界条件对应的非稳态过程逐渐缩短。
At the initial stage of Hagen-Poiseuille flow,there is an unsteady process for the velocity developing which will cause deviation on the results of measurement. In order to analyze the deviation caused by the unsteady Poiseuille flow for the viscosity measurement,studies were carried out through a numerical model. Taking the incompressible Newtonian fluid as an example,we studied the unsteady Poiseuille flow process at a constant flow rate and unsteady flow rate boundary conditions.The dimensionless viscosity and dimensionless time were used to reflect the unsteady process and a numerical model was built. The variation rules of the dimensionless viscosity under the boundaries of the constant average velocity,the average velocity which increases linearly from 0,and the constant pressure drop were given via numerical calculations. It was found that dimensionless viscosity falls to 1 with the time increasing and the non-dimensional time is a constant when the flow attains the stable state under different boundary conditions. When the types of boundary conditions are decided,the dimensionless viscosity can be viewed as a function only with respect to the dimensionless time in the unsteady process. For different types of boundary conditions,the unsteady processes reduce corresponding to the boundary conditions of the constant average velocity,the constant pressure drop,and the average velocity which increases linearly from 0.
At the initial stage of Hagen-Poiseuille flow,there is an unsteady process for the velocity developing which will cause deviation on the results of measurement. In order to analyze the deviation caused by the unsteady Poiseuille flow for the viscosity measurement,studies were carried out through a numerical model. Taking the incompressible Newtonian fluid as an example,we studied the unsteady Poiseuille flow process at a constant flow rate and unsteady flow rate boundary conditions.The dimensionless viscosity and dimensionless time were used to reflect the unsteady process and a numerical model was built. The variation rules of the dimensionless viscosity under the boundaries of the constant average velocity,the average velocity which increases linearly from 0,and the constant pressure drop were given via numerical calculations. It was found that dimensionless viscosity falls to 1 with the time increasing and the non-dimensional time is a constant when the flow attains the stable state under different boundary conditions. When the types of boundary conditions are decided,the dimensionless viscosity can be viewed as a function only with respect to the dimensionless time in the unsteady process. For different types of boundary conditions,the unsteady processes reduce corresponding to the boundary conditions of the constant average velocity,the constant pressure drop,and the average velocity which increases linearly from 0.
引文
[1]张国忠,高探贵.东黄复线停输再启动过程研究[J].油气储运,1996,15(9):37-40.ZHANG Guozhong,GAO Tangui.A study on the shutdown and restart course of Dong-Huang looping line[J].Oil&Gas Storage and Transportation,1996,15(9):37-40.
[2]张树文,安家荣,张国忠.彩石输油管道停输再启动过程试验研究[J].油气储运,2000,19(10):45-48.ZHANG Shuwen,AN Jiarong,ZHANG Guozhong.Experiment and research on the shut-down and restart in Cainan-Shixi oil pipeline[J].Oil&Gas Storage and Transportation,2000,19(10):45-48.
[3]刘刚.胶凝原油管流特性研究[D].东营:石油大学(华东),2004.LIU Gang.An investigation of the characteristics of the gelled crude oil in pipeline[D].Dongying:the University of Petroleum,China(East China),2004.
[4]PAPANASTASIOU T,GEORGIOU G,ALEXANDROU A N.Viscous fluid flow[M].Boca Raton:CRC Press,1999.
[5]BARI爦S.Some simple unsteady unidirectional flows of a binary mixture of incompressible Newtonian fluids[J].International Journal of Engineering Science,2002,40(18):2023-2040.
[6]ERDOGAN M E.On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient[J].International Journal of Non-linear Mechanics,2002,37(6):1091-1106.
[7]ERDOGAN M E.On the flows produced by sudden application of a constant pressure gradient or by impulsive motion of a boundary[J].International Journal of Non-linear Mechanics,2003,38(5):781-797.
[8]ERDOGAN M E,IMRAK C E.On some unsteady flows of a non-Newtonian fluid[J].Applied Mathematical Modeling,2007,31(2):170-180.
[9]SIDDIQUE I,SAJID Z.Exact solutions for the unsteady axial flow of non-Newtonian fluids through a circular cylinder[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(1):226-238.
[10]FETECAU C.Analytical solutions for non-Newtonian fluid flows in pipe-like domains[J].International Journal of Non-Linear Mechanics,2004,39(2):225-231.
[11]MUZYCHKA Y S,YOVANOVICH M M.Unsteady viscous flows and Stokess first problem[J].International Journal of Thermal Sciences,2010,49(5):820-828.
[12]HAYAT T,ASGHAR S,SIDDIQUI A M.Some unsteady unidirectional flows of a non-Newtonian fluid[J].International Journal of Engineering Science,2000,38(3):337-345.
[13]HAYAT T,KHAN M,SIDDIQUI A M,et al.Transient flows of a second grade fluid[J].International Journal of Non-Linear Mechanics,2004,39(10):1621-1633.
[14]VINAY G,WACHS A,AGASSANT J F.Numerical simulation of weakly compressible Bingham flows:the restart of pipeline flows of waxy crude oils[J].Journal of Non-newtonian Fluid Mechanics,2006,136(2):93-105.
[15]NEGRO C O R,FRANCO A T,ROCHA L L V.A weakly compressible flow model for the restart of thixotropic drilling fluids[J].Journal of Non-Newtonian Fluid Mechanics,2011,166(23):1369-1381.
[16]李传宪.原油流变学[M].东营:中国石油大学出版社,2007.
[17]CHEN Lei,LIU Gang,ZHANG Guozhong,et al.Transient stage comparison of Couette flow under step shear stress and step velocity boundary conditions[J].International Communications in Heat and Mass Transfer,2016,75:232-239.
[18]徐睿妤,刘刚,陈雷,等.同轴圆筒流变仪初始瞬态黏度的解析与数值研究[J].化工学报,2016,5:1784-1790.XU Ruiyu,LIU Gang,CHEN Lei,et al.Analytical and numerical studies on apparent viscosity in coaxial cylinder rotational rheometer during initial unsteady stage[J].CIESC Journal,2016,5:1784-1790.
[19]陈中良.恒流量启动胶凝原油管道初始结构破坏特性研究[D].青岛:中国石油大学(华东),2013.CHEN Zhongliang.Study on initial structural destruction properties of gelled crude oil pipeline under constant start-up flow condition[D].Qingdao:China University of Petroleum(East China),2013.
[20]左栋.胶凝原油恒压力启动特性研究[D].青岛:中国石油大学(华东),2009.ZUO Dong.An investigation of the characteristics of the gelled crude oil on constant pressure startup[D].Qingdao:China University of Petroleum(East China),2009.
[21]兰浩.胶凝原油屈服特性及环道启动过程研究[D].青岛:中国石油大学(华东),2010.LAN Hao.Study on the yield behavior and pipeline restart process of gelled crude oil[D].Qingdao:China University of Petroleum(East China),2010.
[22]蔡少敏.胶凝原油启动波传播及压缩特性研究[D].青岛:中国石油大学(华东),2015.CAI Shaomin.Simulation research on start-up wave propagation and compression characteristic of gelled crude oil[D].Qingdao:China University of Petroleum(East China),2015.
[2]张树文,安家荣,张国忠.彩石输油管道停输再启动过程试验研究[J].油气储运,2000,19(10):45-48.ZHANG Shuwen,AN Jiarong,ZHANG Guozhong.Experiment and research on the shut-down and restart in Cainan-Shixi oil pipeline[J].Oil&Gas Storage and Transportation,2000,19(10):45-48.
[3]刘刚.胶凝原油管流特性研究[D].东营:石油大学(华东),2004.LIU Gang.An investigation of the characteristics of the gelled crude oil in pipeline[D].Dongying:the University of Petroleum,China(East China),2004.
[4]PAPANASTASIOU T,GEORGIOU G,ALEXANDROU A N.Viscous fluid flow[M].Boca Raton:CRC Press,1999.
[5]BARI爦S.Some simple unsteady unidirectional flows of a binary mixture of incompressible Newtonian fluids[J].International Journal of Engineering Science,2002,40(18):2023-2040.
[6]ERDOGAN M E.On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient[J].International Journal of Non-linear Mechanics,2002,37(6):1091-1106.
[7]ERDOGAN M E.On the flows produced by sudden application of a constant pressure gradient or by impulsive motion of a boundary[J].International Journal of Non-linear Mechanics,2003,38(5):781-797.
[8]ERDOGAN M E,IMRAK C E.On some unsteady flows of a non-Newtonian fluid[J].Applied Mathematical Modeling,2007,31(2):170-180.
[9]SIDDIQUE I,SAJID Z.Exact solutions for the unsteady axial flow of non-Newtonian fluids through a circular cylinder[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(1):226-238.
[10]FETECAU C.Analytical solutions for non-Newtonian fluid flows in pipe-like domains[J].International Journal of Non-Linear Mechanics,2004,39(2):225-231.
[11]MUZYCHKA Y S,YOVANOVICH M M.Unsteady viscous flows and Stokess first problem[J].International Journal of Thermal Sciences,2010,49(5):820-828.
[12]HAYAT T,ASGHAR S,SIDDIQUI A M.Some unsteady unidirectional flows of a non-Newtonian fluid[J].International Journal of Engineering Science,2000,38(3):337-345.
[13]HAYAT T,KHAN M,SIDDIQUI A M,et al.Transient flows of a second grade fluid[J].International Journal of Non-Linear Mechanics,2004,39(10):1621-1633.
[14]VINAY G,WACHS A,AGASSANT J F.Numerical simulation of weakly compressible Bingham flows:the restart of pipeline flows of waxy crude oils[J].Journal of Non-newtonian Fluid Mechanics,2006,136(2):93-105.
[15]NEGRO C O R,FRANCO A T,ROCHA L L V.A weakly compressible flow model for the restart of thixotropic drilling fluids[J].Journal of Non-Newtonian Fluid Mechanics,2011,166(23):1369-1381.
[16]李传宪.原油流变学[M].东营:中国石油大学出版社,2007.
[17]CHEN Lei,LIU Gang,ZHANG Guozhong,et al.Transient stage comparison of Couette flow under step shear stress and step velocity boundary conditions[J].International Communications in Heat and Mass Transfer,2016,75:232-239.
[18]徐睿妤,刘刚,陈雷,等.同轴圆筒流变仪初始瞬态黏度的解析与数值研究[J].化工学报,2016,5:1784-1790.XU Ruiyu,LIU Gang,CHEN Lei,et al.Analytical and numerical studies on apparent viscosity in coaxial cylinder rotational rheometer during initial unsteady stage[J].CIESC Journal,2016,5:1784-1790.
[19]陈中良.恒流量启动胶凝原油管道初始结构破坏特性研究[D].青岛:中国石油大学(华东),2013.CHEN Zhongliang.Study on initial structural destruction properties of gelled crude oil pipeline under constant start-up flow condition[D].Qingdao:China University of Petroleum(East China),2013.
[20]左栋.胶凝原油恒压力启动特性研究[D].青岛:中国石油大学(华东),2009.ZUO Dong.An investigation of the characteristics of the gelled crude oil on constant pressure startup[D].Qingdao:China University of Petroleum(East China),2009.
[21]兰浩.胶凝原油屈服特性及环道启动过程研究[D].青岛:中国石油大学(华东),2010.LAN Hao.Study on the yield behavior and pipeline restart process of gelled crude oil[D].Qingdao:China University of Petroleum(East China),2010.
[22]蔡少敏.胶凝原油启动波传播及压缩特性研究[D].青岛:中国石油大学(华东),2015.CAI Shaomin.Simulation research on start-up wave propagation and compression characteristic of gelled crude oil[D].Qingdao:China University of Petroleum(East China),2015.