Skip to main content
SpringerLink
Log in

Asymptotic Modeling Framework for Fiber-Flow Interactions in a Two-Way Coupling

  • Conference paper
  • First Online:
Progress in Industrial Mathematics at ECMI 2012

Part of the book series: Mathematics in Industry ((TECMI,volume 19))

Abstract

In this work we describe fiber-flow interactions by help of a two-way coupling approach that is based on slender-body theory and the modeling of exchange functions in terms of drag forces and heat sources. The exchange functions are incorporated in the conservation equations for linear momentum and energy with respect to flow and fibers and satisfy a generalized action-reaction principle.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Klar, A., Marheineke, N., Wegener, R.: Hierarchy of mathematical models for production processes of technical textiles. Z. Ang. Math. Mech. 89(12), 941–961 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Mark, A.: A novel immersed-boundary method for multiple moving and interacting bodies. Ph.D. thesis, Chalmers University of Technology (2007)

    Google Scholar 

  3. Marheineke, N., Wegener, R.: Modeling and application of a stochastic drag for fibers in turbulent flows. Int. J. Multiphase Flow 37, 136–148 (2011)

    Article  Google Scholar 

  4. Marheineke, N., Wegener, R.: Fiber dynamics in turbulent flows: general modeling framework. SIAM J. Appl. Math. 66(5), 1703–1726 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Marheineke, N., Liljo, J., Mohring, J., Schnebele, J., Wegener, R.: Multiphysics and multimethods problem of rotational glass fiber melt-spinning. Int. J. Numer. Anal. Model. B 3(3), 330–344 (2012)

    MATH  MathSciNet  Google Scholar 

  6. Arne, W., Marheineke, N., Wegener, R.: Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets. Math. Models Methods Appl. Sci. 21(10), 1987–2018 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Antman, S.: Nonlinear Problems of Elasticity. Springer, New York (2004)

    Google Scholar 

  8. Lamb, H.: On the uniform motion of a sphere through a viscous field. Philos. Mag. 6, 113–121 (1911)

    Google Scholar 

  9. Tomotika, S., Aoi, T.: An expansion formula for the drag on a circular cylinder moving through a viscous fluid at small Reynolds number. Q. J. Mech. Appl. Math. 4, 401–406 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  10. Tomotika, S., Aoi, T., Yosinobu, H.: On the forces acting on a circular cylinder set obliquely in a uniform stream at low values of Reynolds number. Proc. R. Soc. Lond. A 219, 233–244 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  11. Arne, W., Marheineke, N., Schnebele, J., Wegener, R.: Fluid-fiber-interactions in rotational spinning process of glass wool manufacturing. J. Math. Ind. 1, 2 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work has been supported by Bundesministerium für Bildung und Forschung, Verbundprojekt ProFil, 03MS606.

Author information

Authors and Affiliations

  1. Department Mathematik, Friedrich-Alexander-Universität Nürnberg-Erlangen, Cauerstr. 11, 91058, Erlangen, Germany

    Thomas Martin Cibis & Nicole Marheineke

  2. Fraunhofer Institut für Techno- und Wirtschaftsmathematik, Fraunhofer Platz 1, 67663, Kaiserslautern, Germany

    Raimund Wegener

Authors
  1. Thomas Martin Cibis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicole Marheineke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raimund Wegener
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Martin Cibis .

Editor information

Editors and Affiliations

  1. Lunds Universitet, Centre for Mathematical Sciences, Lund, Sweden

    Magnus Fontes

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angew.Math. 1, Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany

    Nicole Marheineke

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Cibis, T.M., Marheineke, N., Wegener, R. (2014). Asymptotic Modeling Framework for Fiber-Flow Interactions in a Two-Way Coupling. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_15

Download citation

Publish with us

Policies and ethics

Search

Navigation