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Curved quasi-steady detonations: Asymptotic analysis and detailed chemical kinetics

Klein, R. and Krok, J. C. and Shepherd, J. E. (1995) Curved quasi-steady detonations: Asymptotic analysis and detailed chemical kinetics. California Institute of Technology , Pasadena, CA. (Unpublished)

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We consider the problem of slightly-curved, quasi-steady diverging detonation waves. For sufficiently small curvature, the reaction zone structure equations can be formulated as a two point boundary value problem for solutions containing a sonic point. Analytical solutions to this boundary value problem are obtained for the case of a one-step Arrhenius reaction in the limit of high activation energy. The analytic solution results in a nonlinear relationship between detonation velocity and curvature. For extremely small curvature, this relationship is consistent with previous linear analyses, whereas in the nonlinear regime it predicts a critical maximum curvature, beyond which no quasi-steady solutions with a sonic point can be found. We also analyse the curved detonation structure for the gaseous fuel-oxidizer combination of H_2 and O_2 with various diluents. Using a standard shooting method we generate numerical solutions of the two-point boundary value problem based on realistic thermochemistry and a detailed chemical reaction mechanism. Similar to the large activation energy results, the numerical solutions reveal a nonlinear detonation speed-curvature relation and a critical maximum curvature for the existence of quasi-steady solutions. The relation of this critical curvature to the critical scales of multi-dimensional detonation is discussed.

Item Type:Report or Paper (Technical Report)
Shepherd, J. E.0000-0003-3181-9310
Additional Information:© 1995 California Institute of Technology.
Group:Graduate Aeronautical Laboratories (Fluid Mechanics), GALCIT
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Classification Code:PACS numbers: 47.40-x, 47.70.Fw
Record Number:CaltechAUTHORS:20141111-095800953
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51558
Deposited On:11 Nov 2014 21:24
Last Modified:17 Nov 2021 17:35

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