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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.101 P.263~270

http://doi.org/10.1631/jzus.2006.AS0263


Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes


Author(s):  Zhang Ming-Kan, Shen Xin-Rong, Ma Jian-Feng, Zhang Ben-Zhao

Affiliation(s):  Institute of Fluid Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   wangtwo@zju.edu.cn

Key Words:  Curved pipe, Galerkin method, Oldroyd-B fluid, Flow characteristic, Axial normal stress


Zhang Ming-Kan, Shen Xin-Rong, Ma Jian-Feng, Zhang Ben-Zhao. Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes[J]. Journal of Zhejiang University Science A, 2006, 7(101): 263~270.

@article{title="Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes",
author="Zhang Ming-Kan, Shen Xin-Rong, Ma Jian-Feng, Zhang Ben-Zhao",
journal="Journal of Zhejiang University Science A",
volume="7",
number="101",
pages="263~270",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.AS0263"
}

%0 Journal Article
%T Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes
%A Zhang Ming-Kan
%A Shen Xin-Rong
%A Ma Jian-Feng
%A Zhang Ben-Zhao
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 101
%P 263~270
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.AS0263

TY - JOUR
T1 - Galerkin method study on flow of Oldroyd-B fluids in curved circular cross-section pipes
A1 - Zhang Ming-Kan
A1 - Shen Xin-Rong
A1 - Ma Jian-Feng
A1 - Zhang Ben-Zhao
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 101
SP - 263
EP - 270
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.AS0263


Abstract: 
A galerkin method was used to investigate steady, fully developed flow of oldroyd-B fluids through curved pipes of circle cross-section. By using galerkin method, large values of curvature ratio, Reynolds number and Weissenberg number can be discussed. The powers of the series of the galerkin method in the present work are chosen carefully. Both effects of Reynolds number and Weissenberg number on axial velocity and stream function are discussed even for large values of the two non-dimensional parameters. It was discovered that the combined effect of large Reynolds number and Weissenberg number decreases the outward shifts of maximum axial velocity and maximum stream function. axial normal stress of creeping flow is also studied here. The large Weissenberg number makes the stress concentration occur on the inner bend of the pipe.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Bolinder, C.J., 1996. Curvilinear coordinates and physical components: an application to the problem of viscous flow and heat transfer in smoothly curved ducts. J. Appl. Mech., 63:985-989.

[2] Bowen, P.J., Davies, A.R., Walters, K., 1991. On viscoelastic effects in swirling flows. J. Non-Newtonian Fluid Mech., 38(2-3):113-126.

[3] Chen, H.J., Zhang, B.Z., Su, X.Y., 2003. Low frequency oscillatory flow in a rotating curved pipe. J. Zhejiang University SCIENCE, 4(4):407-414.

[4] Clegg, D.B., Power, G., 1963. Flow of a Bingham fluid in a slightly curved tube. Appl. Sci. Res., 12:199-212.

[5] Das, B., 1992. Flow of a Bingham fluid in a slightly curved tube. Int. J. Engng. Sci., 30(9):1193-1207.

[6] Dean, R.W., 1927. Note on the motion of fluid in a curved pipe. Phil. Mag., 7(4):208-223.

[7] Dean, R.W., 1928. The stream-line motion of fluid in a curved pipe. Phil. Mag., 7(5):673-695.

[8] Fan, Y.R., Tanner, R.I., Phan-Thien, N., 2001. Fully developed viscous and viscoelastic flows in curved pipes. J. Fluid Mech., 440:327-357.

[9] Ito, H., 1969. Laminar flow in curved pipes. Z. Angew. Math. Mech., 49:653-662.

[10] Jitchote, W., Robertson, A.M., 2000. Flow of second order fluids in curved pipes. J. Non-Newtonian Fluid Mech., 90(1):91-116.

[11] Jones, C.R., 1960. Flow of a non-Newtonian liquid in a curved pipe. Quart. J. Mech. Appl. Math., 13:428-443.

[12] Nandakumar, K., Masliyah, H.J., 1982. Bifurcation in steady laminar flow through curved pipes. J. Fluid. Mech., 119:475-490.

[13] Robertson, A.M., Muller, S.J., 1996. Flow of Oldroyd-B fluids in curved pipes of circular and annular cross-section. J. Non-linear Mech., 31(1):1-20.

[14] Sharma, H.G., Prakash, A., 1977. Flow of second-order fluid in a curved pipe. Indian J. Pure Appl. Math., 8:546-557.

[15] Soh, W.Y., Berger, S.A., 1987. Fully developed flow in a curved pipe of arbitrary curvature ratio. International Journal for Numerical Methods in Fluids, 7(7):733-755.

[16] Thomas, A.H., Walters, K., 1963. On the flow of an elastico-viscous liquid in a curved pipe under a pressure gradient. J. Fluid Mech., 16(2):228-242.

[17] Topakoglu, C.H., 1967. Steady laminar flows of an incompressible viscous fluid in curved pipes. J. Math. Mech., 16:1321-1337.

[18] Xue, L., 2002. Study on laminar flow in helical circular pipes with Galerkin method. Computers & Fluids, 31(1):113- 129.

[19] Zhang, J.S., Zhang, B.Z., 2003. Dean equations extended to rotating helical pipe flow. J. Engrg. Mech., 129(7):823-829.

[20] Zhang, J.S., Zhang, B.Z., Chen, H.J., 2000. Flow in helical annular pipe. J. Engrg. Mech., 126(10):1040-1047.

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