Initial-value problem for perturbations of idealized detonations in circular pipes

Ivan Shalaev, Anatoli Tumin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The initial-value problem for perturbations of an idealized one-reaction detonation in a circular pipe is solved using the Laplace transformin time, Fourier series in the azimuthal angle, and expansion into Bessel's functions of the radial variable. For each radial and azimuthal mode, the inverse Laplace transform can be presented as an expansion of the solution into the normal modes of discrete and continuous spectra. The dispersion relation for the discrete spectrumrequires solving the homogeneous ordinary differential equations for the adjoint system and evaluating an integral through the reaction zone. The solution of the initial-value problem gives a tool for analysis of the flow receptivity to various types of perturbations in the reaction zone and in the quiescent gas.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalCombustion Theory and Modelling
Issue number1
StatePublished - Feb 2010


  • Circular pipe
  • Detonation
  • Initial-value problem
  • Receptivity
  • Stability

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Modeling and Simulation
  • Fuel Technology
  • Energy Engineering and Power Technology
  • Physics and Astronomy(all)


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