A New Method for Accurate Calculation of the Bingham Fluid Axial Laminar Flow Pressure Drop and Velocity Distribution in Circular Pipes

ZHAO Shan-shan; WU Xiao-ming; LIU Yao-dong

doi:10.3879/j.issn.1000-0887.2015.04.012

Volume 36 Issue 4

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(4): 440-448

ZHAO Shan-shan, WU Xiao-ming, LIU Yao-dong. 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, 36(4): 440-448. doi: 10.3879/j.issn.1000-0887.2015.04.012

Citation:

PDF( 1216 KB)

A New Method for Accurate Calculation of the Bingham Fluid Axial Laminar Flow Pressure Drop and Velocity Distribution in Circular Pipes

doi: 10.3879/j.issn.1000-0887.2015.04.012

¹Faculty of Engineering, China University of Geoscicences(Wuhan), Wuhan 430074, P.R.China;²Guangdong Heli Civil Engineering Co., Ltd., Guangzhou 510403, P.R.China

Received Date: 2014-10-27
Rev Recd Date: 2015-01-28
Publish Date: 2015-04-15

Abstract

Abstract

Based on the Bingham model, the analytical calculations of axial laminar flow pressure drop in circular pipes often involve the general formula for viscous fluid, with the Bingham fluid constitutive equations introduced into the calculation to get only the analytical solution of pressure drop. A new method combining the Bingham fluid constitutive equation and the motion equation to establish the mechanical equilibrium equations was proposed, to solve the circular pipe laminar flow nonlinear equations according to the algebraic equation radical solution theory, and directly get the analytical solution of the axial laminar flow pressure drop, the velocity flow core zone radius and the flow velocity. The results show that, the direct influential factors on the Bingham fluid pipe laminar flow velocity are flow rate, plastic viscosity and yield value, and the flow core zone width is proportional to the yield value and inversely proportional to the flow velocity or the plastic viscosity. Besides, the wider the velocity flow core zone is, the lower the flow velocity in the core zone is.
- hydraulic parameter,
- velocity flow core zone radius,
- Bingham fluid,
- laminar flow,
- analytical solution

FullText(HTML)

References(16)

References

[1]	张景富. 钻井流体力学[M]. 北京: 石油工业出版社, 1994.(ZHANG Jing-fu. Drilling Fluid Mechanics [M]. Beijing: Petroleum Industry Press, 1994.(in Chinese))
[2]	陈家琅. 钻井泥浆的管流公式集[J]. 大庆石油学院学报, 1981(3): 99-111.(CHEN Jia-lang. Circular flow formula of drilling mud[J].Journal of Daqing Petroleum Institute,1981(3): 99-111.(in Chinese))
[3]	陈家琅. 钻井泥浆的管流公式集(续)[J]. 大庆石油学院学报, 1983(2): 111-115.(CHEN Jia-lang. Circular flow formula of drilling mud (sequel)[J].Journal of Daqing Petroleum Institute,1983(2): 111-115.(in Chinese))
[4]	von Schowalter W R.Mechanics of Non-Newtonian Fluids [M]. Oxford: Pergamon Press, 1978: 138-139.
[5]	汪海阁, 苏义脑. Robertson-Stiff流体在偏心环空中的流动[J]. 应用数学和力学, 1998,19(10): 931-940.(WANG Hai-ge, SU Yi-nao. Flow of Robertson-Stiff fluids through an eccentric annulus[J].Applied Mathematics and Mechanics,1998,19(10): 931-940.(in Chinese))
[6]	Govier G W, Aziz K.The Flow of Complex Mixtures in Pipes [M]. New York: Van Nostrand Reinhold, 1972: 183-185.
[7]	Herzog R O, Weissenberg K. Ueber die thermische, mechanische und rntgenoptische analyse der Quellung[J].Kolloid-Zeitschrift,1928,46(4): 277-289.
[8]	Rabinowitsch B. Uber die viskositt und elastizitt von Solen[J].Z Phys Chem A,1929,145: 1-26.
[9]	Monney M. Explicit formulas for slip and fluidity[J].Journal of Rheology,1931, 2(2): 210-222.
[10]	高远文, 鲁港, 杨龙, 佟长海, 孙忠国. 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), 2010,37(3): 5-7.(GAO Yuan-wen, LU Gang, YANG Long, TONG Chang-hai, SUN Zhong-guo. 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,〖STHZ〗 37(3): 5-7.(in Chinese))
[11]	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 Yu-fa. Use quartic equation root 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))
[12]	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.Mathematics Handbook [M]. Beijing: People’s Education Press, 1979.(in Chinese)）
[13]	陈尚伟. 宾汉塑性流体层流压强降的分析解[J]. 化学世界, 1990(8): 369-372.(CHEN Shang-wei. Bingham plastic fluid laminar analysis solution of the pressure drop[J].Chemical World,1990(8): 369-372.(in Chinese))
[14]	樊洪海, 彭齐, 腾学清, 周号博, 李朝玮, 汤化沙. 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 Hong-hai, PENG Qi, TENG Xue-qing, ZHOU Hao-bo, LI Zhao-wei, TANG Hua-sha. 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))
[15]	白家祉, 姚荣魁. 《带屈服值的假塑性流体的双曲模式方程与压降计算式》一文的实验验证[J]. 石油学报, 1980,1(3): 49-57.(BAI Jia-zhi, YAO Rong-kui. Experimental verifications on “a new hyperbolic model equation for yield-pseudoplastic fluids and related pressure drop formulas”[J].Acta Petrolei Sinica,1980,1(3): 49-57.(in Chinese))
[16]	李兆敏, 王渊, 张琪. 宾汉流体在环空中流动时的速度分布规律[J]. 石油学报, 2002,23(2): 87-91.(LI Zhao-min, WANG Yuan, ZHANG Qi. The law of velocity distribution of Bingham fluid’s flowing in the encircle pipe[J].Acta Petrolei Sinica,2002,23(2): 87-91.(in Chinese))