The Stokes flow in a cylindrical quadrant duct with a rotating wall was analytically and numerically studied. Based on mathematics and fluid dynamics theory, the analytical expressions of three velocity components were achieved by solving a Poisson's equation and a biharmonic equation. Especially, a closed-form analytical expression of axial velocity was obtained, which can greatly improve the calculating accuracy and speed in analyzing Stokes flow. The velocity distributions for different Reynolds numbers were investigated numerically to insure the accuracy of the analytical results at low Reynolds numbers and to confirm the error range of the analytic results at higher Reynolds numbers. The conclusion indicates that there exists an infinite sequence of eddies that decrease exponentially in size towards the sectorial vertex. The width of the first eddy region reached 99.4% of the sector radius; the sum of the width of other eddies is only 0.6% of the sector radius, which cannot be easily displayed graphically, while the sequence of eddies contributes to form the chaotic flow. The maximum deviations of the velocity components between the analytical results and simulated ones are all less than 1% when Re < 0.1, which verifies the validity and accuracy of the analytical expressions in the creeping flow regime. The analytical expressions are not only suitable for creeping flow but also for laminar flow with smaller Reynolds number (Re < 50).
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November 2014
Research-Article
Stokes Flow Characteristics in a Cylindrical Quadrant Duct With Rotating Outer Wall
Zongyong Wang,
Zongyong Wang
School of Energy and Power Engineering,
e-mail: syuctwzy@163.com
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
e-mail: syuctwzy@163.com
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Jiayu Zhao,
Jiayu Zhao
1
School of Energy and Power Engineering,
e-mail: zhaojiayu.456@163.com
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
e-mail: zhaojiayu.456@163.com
1Corresponding author.
Search for other works by this author on:
Jianhua Wu
Jianhua Wu
School of Energy and Power Engineering,
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
Search for other works by this author on:
Zongyong Wang
School of Energy and Power Engineering,
e-mail: syuctwzy@163.com
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
e-mail: syuctwzy@163.com
Jiayu Zhao
School of Energy and Power Engineering,
e-mail: zhaojiayu.456@163.com
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
e-mail: zhaojiayu.456@163.com
Jianhua Wu
School of Energy and Power Engineering,
Shenyang University of Chemical Technology
,Shenyang 110142, Liaoning
, China
1Corresponding author.
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 17, 2013; final manuscript received April 30, 2014; published online September 4, 2014. Editor: Malcolm J. Andrews.
J. Fluids Eng. Nov 2014, 136(11): 111202 (11 pages)
Published Online: September 4, 2014
Article history
Received:
July 17, 2013
Revision Received:
April 30, 2014
Citation
Wang, Z., Zhao, J., and Wu, J. (September 4, 2014). "Stokes Flow Characteristics in a Cylindrical Quadrant Duct With Rotating Outer Wall." ASME. J. Fluids Eng. November 2014; 136(11): 111202. https://doi.org/10.1115/1.4027586
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