Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

doi:10.1007/s10483-018-2300-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (2): 169-180.doi: https://doi.org/10.1007/s10483-018-2300-6

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

Xinyin ZOU¹, Xiang QIU², Jianping LUO¹, Jiahua LI³, P. N. KALONI⁴, Yulu LIU^2,5

1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
2. School of Science, Shanghai Institute of Technology, Shanghai 201418, China;
3. College of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
4. Department of Mathematics and Statistics, University of Windsor, Ontario N9B 3P4, Canada;
5. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2017-02-06 修回日期:2017-09-08 出版日期:2018-02-01 发布日期:2018-02-01
通讯作者: Xiang QIU E-mail:qiux@sit.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11572203 and 11332006)

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

Xinyin ZOU¹, Xiang QIU², Jianping LUO¹, Jiahua LI³, P. N. KALONI⁴, Yulu LIU^2,5

1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
2. School of Science, Shanghai Institute of Technology, Shanghai 201418, China;
3. College of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai 201418, China;
4. Department of Mathematics and Statistics, University of Windsor, Ontario N9B 3P4, Canada;
5. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Received:2017-02-06 Revised:2017-09-08 Online:2018-02-01 Published:2018-02-01
Contact: Xiang QIU E-mail:qiux@sit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11572203 and 11332006)

摘要/Abstract

摘要： A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.

关键词: principal axis representation, principal axis intrinsic method, tensor equation, velocity distribution, Johnson-Segalman (J-S) fluid, double perturbation strategy, slowly varying pipe

Abstract: A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.

Key words: velocity distribution, principal axis representation, principal axis intrinsic method, tensor equation, slowly varying pipe, Johnson-Segalman (J-S) fluid, double perturbation strategy

中图分类号:

76A05

Xinyin ZOU, Xiang QIU, Jianping LUO, Jiahua LI, P. N. KALONI, Yulu LIU. Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 169-180.

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Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

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