Flow, Turbulence and Combustion

, Volume 91, Issue 2, pp 281–317 | Cite as

On the Application of the Levenberg–Marquardt Method in Conjunction with an Explicit Runge–Kutta and an Implicit Rosenbrock Method to Assess Burning Velocities from Confined Deflagrations

  • A. E. Dahoe
  • T. Skjold
  • D. J. E. M. Roekaerts
  • H. J. Pasman
  • R. K. Eckhoff
  • K. Hanjalic
  • M. Donze
Article

Abstract

The potential of the Levenberg–Marquardt method combined with an explicit Runge–Kutta method for non-stiff systems, and, an implicit Rosenbrock method for stiff systems to investigate burning velocities using explosion bombs was explored. The implementation of this combination of methods was verified on three benchmark test problems, and, by the application of two integral balance models to laminar hydrogen-air and methane-air explosions. The methodology described here was subsequently applied to quantify the coefficients of a turbulent burning velocity correlation for a methane-air explosion in the decaying flow field of the standard 20-litre explosion sphere. The outcome of this research indicates that the usefulness of the 20-litre sphere can be extended beyond the measurement of practical explosion parameters. When combined with the methodology in this paper, turbulent burning velocity correlations can be assessed in different parts of the Borghi-diagram.

Keywords

Deflagration Burning velocity Flame thickness Least-squares minimisation Stiff integration 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • A. E. Dahoe
    • 1
  • T. Skjold
    • 2
  • D. J. E. M. Roekaerts
    • 3
  • H. J. Pasman
    • 4
  • R. K. Eckhoff
    • 5
  • K. Hanjalic
    • 6
    • 7
  • M. Donze
    • 8
  1. 1.Faculty of Art, Design and the Built EnvironmentUniversity of UlsterNorthern IrelandUK
  2. 2.Department of Physics and TechnologyUniversity of Bergen & GexCon ASBergenNorway
  3. 3.Section Fluid Mechanics, Department Process and EnergyDelft University of TechnologyDelftThe Netherlands
  4. 4.Mary Kay O’Connor Process Safety CenterTexas A&M UniversityCollege StationUSA
  5. 5.Department of Physics and TechnologyUniversity of BergenBergenNorway
  6. 6.Chemical Engineering DepartmentDelft University of TechnologyDelftThe Netherlands
  7. 7.Novosibirsk State UniversityNovosibirskRussia
  8. 8.Faculty Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands

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