Skip to main content
SpringerLink
Log in

Stokes flow through a coiled tube

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Stokes flow through a coiled tube with arbitrary cross-section is investigated by perturbation expansions in the limit where the helical pitch is either small or large compared to the radius of the helical centerline. The problem is formulated using two alternative non-orthogonal helical coordinate systems applicable to these two opposing limits. The solutions of the respective zeroth-, first-, and second-order perturbation problems are computed by finite element methods for unidirectional, axisymmetric, and two-dimensional Stokes flow. Computations are carried out for tubes with circular and square cross-sections oriented in different ways. The results illustrate the effect of the tube geometry on the hydraulic conductivity and kinematic structure of the flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • R. Aris (1962) Vectors, tensors, and the basic equations of fluid mechanics Prentice-Hall New Jersey Occurrence Handle0123.41502

    MATH  Google Scholar 

  • M. G. Blyth C. Pozrikidis (2007) ArticleTitleStokes flow through a single-screw extruder AIChEJ. 53 69–77 Occurrence Handle10.1002/aic.11050

    Article  Google Scholar 

  • S. A. Berger L. Talbot L.-S. Yao (1983) ArticleTitleFlow in curved pipes Ann. Rev. Fluid Mech. 15 461–512 Occurrence Handle10.1146/annurev.fl.15.010183.002333

    Article  Google Scholar 

  • W. R. Dean (1927) ArticleTitleNote on the motion of fluid in a curved pipe Phil. Mag. Ser. 7 4 208–223

    Google Scholar 

  • W. R. Dean (1928) ArticleTitleThe streamline motion of fluid in a curved pipe Phil. Mag. Ser. 7 5 673–695

    Google Scholar 

  • J. Eustice (1910) ArticleTitleFlow of water in curved pipes Proc. R. Soc. Lond. A 84 107–118

    Google Scholar 

  • J. Eustice (1911) ArticleTitleExperiments of streamline motion in curved pipes Proc. R. Soc. Lond. A 85 119–131

    Google Scholar 

  • M. Germano (1982) ArticleTitleOn the effect of torsion on a helical pipe flow J. Fluid Mech. 125 1–8 Occurrence Handle0533.76029 Occurrence Handle10.1017/S0022112082003206

    Article  MATH  Google Scholar 

  • M. Germano (1989) ArticleTitleThe Dean equations extended to a helical pipe flow J. Fluid Mech. 203 289–305 Occurrence Handle0675.76040 Occurrence Handle10.1017/S0022112089001473

    Article  MATH  Google Scholar 

  • T. J. Hüttl R. Friedrich (2001) ArticleTitleDirect numerical simulation of turbulent flows in curved and helically coiled pipes Computers & Fluids 30 591–605 Occurrence Handle0990.76030 Occurrence Handle10.1016/S0045-7930(01)00008-1

    Article  MATH  Google Scholar 

  • T. J. Hüttl C. Wagner R. Friedrich (1999) ArticleTitleNavier-Stokes solutions of laminar flows based on orthogonal helical coordinates Int. J. Numer. Meth. Fluids 29 749–763 Occurrence Handle0949.76053 Occurrence Handle10.1002/(SICI)1097-0363(19990415)29:7<749::AID-FLD815>3.0.CO;2-4

    Article  MATH  Google Scholar 

  • H. C. Kao (1987) ArticleTitleTorsion effect on fully developed flow in a helical pipe J. Fluid Mech. 184 335–356 Occurrence Handle0645.76045 Occurrence Handle10.1017/S002211208700291X

    Article  MATH  Google Scholar 

  • J. Larrain C. F. Bonilla (1970) ArticleTitleTheoretical analysis of pressure drop in the laminar flow of fluid in a coiled pipe Trans. Soc. Rheol. 142 135–147 Occurrence Handle10.1122/1.549184

    Article  Google Scholar 

  • S. Liu J. H. Masliyah (1993) ArticleTitleAxially invariant laminar flow in helical pipes with a finite pitch J. Fluid Mech. 251 315–353 Occurrence Handle0775.76036 Occurrence Handle10.1017/S002211209300343X

    Article  MATH  Google Scholar 

  • S. Murata Y. Miyake T. Inaba H. Ogawa (1981) ArticleTitleLaminar flow in a helically coiled pipe Bull. Japanese Soc. Mech. Engng. 24 355–362 Occurrence Handle610876

    MathSciNet  Google Scholar 

  • C. Pozrikidis (1997) Introduction to theoretical and computational fluid dynamics Oxford University Press New York Occurrence Handle0886.76002

    MATH  Google Scholar 

  • C. Pozrikidis (2005) Introduction to finite and spectral element methods using Matlab Chapman & Hall/CRC Boca Raton Occurrence Handle1078.65109

    MATH  Google Scholar 

  • C. Pozrikidis (2006) ArticleTitleStokes flow through a twisted tube J. Fluid Mech. 567 261–280 Occurrence Handle05122396 Occurrence Handle10.1017/S0022112006002242 Occurrence Handle2271559

    Article  MATH  MathSciNet  Google Scholar 

  • Rennie, T. J.: Numerical and experimental studies of a double-pipe helical heat exchanger. McGill University, Montreal: Ph.D. Thesis (2004).

  • T. T. Tung R. L. Laurence (1975) ArticleTitleA coordinate frame for helical flows Polym. Engng. Sci. 15 401–405 Occurrence Handle10.1002/pen.760150602

    Article  Google Scholar 

  • E. R. Tuttle (1990) ArticleTitleLaminar flow in twisted pipes J. Fluid Mech. 219 545–570 Occurrence Handle0706.76040 Occurrence Handle10.1017/S002211209000307X

    Article  MATH  Google Scholar 

  • C. Y. Wang (1981) ArticleTitleOn the low-Reynolds-number flow in a helical pipe J. Fluid Mech. 108 185–194 Occurrence Handle0483.76040 Occurrence Handle10.1017/S0022112081002073

    Article  MATH  Google Scholar 

  • C. Y. Wang (2006) ArticleTitleEffect of helical corrugations on low-Reynolds-number flow in a tube AIChE J. 52 2008–2012 Occurrence Handle10.1002/aic.10817

    Article  Google Scholar 

  • J.-W. Wang J. R. G. Andrews (1995) ArticleTitleNumerical simulation of flow in helical ducts AIChE J. 41 1071–1080 Occurrence Handle10.1002/aic.690410504

    Article  Google Scholar 

  • G. S. Williams C. W. Hubbell G. F. Fenkell (1902) ArticleTitleExperiments at Detroit, MI, on the effect of curvature upon the flow of water in pipes Trans. ASCE 47 1–196

    Google Scholar 

  • D. G. Xie (1990) ArticleTitleTorsion effect on secondary flow in a helical pipe Int. J. Heat Fluid Flow 11 114–119 Occurrence Handle10.1016/0142-727X(90)90004-U

    Article  Google Scholar 

  • Q. Yu G.-H. Hu (1997) ArticleTitleDevelopment of a helical coordinate system and its application to analysis of polymer flow in screw extruders, Part I. The balance equations in a helical coordinate system J. Non-Newt. Fluid Mech. 69 155–167 Occurrence Handle10.1016/S0377-0257(96)01534-0

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California, 92093-0411, USA

    C. Pozrikidis

Authors
  1. C. Pozrikidis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Pozrikidis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pozrikidis, C. Stokes flow through a coiled tube. Acta Mechanica 190, 93–114 (2007). https://doi.org/10.1007/s00707-006-0425-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-006-0425-5

Keywords

Search

Navigation