Journal of Statistical Physics

, Volume 150, Issue 6, pp 1115–1137 | Cite as

Random Field Sampling for a Simplified Model of Melt-Blowing Considering Turbulent Velocity Fluctuations

  • Florian Hübsch
  • Nicole Marheineke
  • Klaus Ritter
  • Raimund Wegener


In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation (thinning). In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets—that has been neglected so far—are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k–ϵ turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible. Numerical results are discussed for a simplified melt-blowing model consisting of a system of random ordinary differential equations.


Turbulence modeling Gaussian random velocity fields Sampling procedure Random ordinary differential equations Melt-blowing simulations Fiber spinning 



Special thanks go to the Department of Transport Processes, Fraunhofer ITWM for the air flow simulations of the melt-blowing process. This work has been supported by German Bundesministerium für Bildung und Forschung, Schwerpunkt “Mathematik für Innovationen in Industrie und Dienstleistungen”, Projekt 03MS606, and the Fraunhofer Innovationszentrum “Applied System Modeling”, Kaiserslautern.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Florian Hübsch
    • 1
    • 2
  • Nicole Marheineke
    • 3
  • Klaus Ritter
    • 2
  • Raimund Wegener
    • 1
  1. 1.Fraunhofer ITWMKaiserslauternGermany
  2. 2.FB MathematikTU Kaiserslautern, Computational StochasticsKaiserslauternGermany
  3. 3.Lehrstuhl Angewandte Mathematik IFAU Erlangen-NürnbergErlangenGermany

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