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Numerical Simulation of Cellular Structure of Detonation Wave and Evaluation of Linear Instability Analysis

Barkhordari, Alireza | 2016

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 48680 (48)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Farshchi, Mohammad
  7. Abstract:
  8. Experimental studies of regular cell structure of a weak detonation wave in a gaseous mixture of hydrogen and oxygen diluted with argon have shown that for a constant initial thermodynamic condition, the final cell size differs by repeating the tests. The question is that if these different final cell sizes for a constant initial condition are because of test errors, or the experiments would lead to a domain of solution in the form of different final cell sizes? Therefore, the aim of this study is to investigate, numerically, the evolution process and domain of variation of cellular structure of a weak detonation, and their dependency to unstable wavelengths obtained from linear instability analysis of detonation waves for an ideal mixture of hydrogen, oxygen, and argon. Two dimentional reactive Euler equations with an idealized one-step Arrhenius type reaction model are solved using powerful combination of the PPM scheme coupled with the exact Riemann solver. Computational grid has been generated by introducing grid patching technique. This technique leads to enormous decreasing in computational time, memory and cost. Long-time numerical simulations results of cellular structures are produced by two-dimensional sinusoidal perturbations imposed on a ZND detonation wave. The initial sinusoidal perturbation wavelengths are predicted from linear instability analysis. The results show that for a given mixture with an initial thermodynamic condition, there is not just a single final cell size. Instead, depending on the initial perturbation wavelength, the cellular dynamics reaches a final equilibrium state with the corresponding final cell size that belongs to a specific band of unstable wavelengths predicted by the linear stability analysis. It has been shown that, every initial perturbation wavelength within this specific band (Zone II) would result in a cellular structure with the same size as the initial perturbation wavelength. We have argued that the lower boundary of this band of unstable wavelengths is approximated by the average thickness of the heat release layer for the detonation wave, and its upper boundary is approximated by the upper neutral growth rate of the case with maximum overdrive velocity possible within the detonation front. Perturbations with wavelengths outside this band (Zone II) will initially damp out, but later random numerical noises consistently result in a cellular structure with a cell size which is independent of the initial perturbation wavelengths and is placed in Zone II with a length of about 10 to 12.5 times the half-reaction length
  9. Keywords:
  10. Cellular Structure ; Triple Point ; Transverse Waves ; Detonation Wave ; Chemical Kinetic ; Linear Instability Analysis ; Premixed Mixture

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