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Numerical study on unstable surfaces of oblique detonations

Published online by Cambridge University Press:  10 March 2014

Hong Hui Teng ,
Zong Lin Jiang  and
Hoi Dick Ng
Hong Hui Teng*
Affiliation:
State Key Lab of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
Zong Lin Jiang
Affiliation:
State Key Lab of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
Hoi Dick Ng
Affiliation:
Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, Canada H3G 1M8
*
†Email address for correspondence: [email protected]
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Abstract

In this study, the onset of cellular structure on oblique detonation surfaces is investigated numerically using a one-step irreversible Arrhenius reaction kinetic model. Two types of oblique detonations are observed from the simulations. One is weakly unstable characterized by the existence of a planar surface, and the other is strongly unstable characterized by the immediate formation of the cellular structure. It is found that a high degree of overdrive suppresses the formation of cellular structures as confirmed by the results of many previous studies. However, the present investigation demonstrates that cellular structures also appear with degree of overdrive of 2.06 and 2.37, values much higher than ${\sim }$1.8 suggested previously in the literature for the critical value defining the instability boundary of oblique detonations. This contradiction could be explained by the use of differently shaped walls, a straight wall used in this study and a custom-designed curved wedge system so as to induce straight oblique detonations in previous studies. Another possible reason could be due to the low and possibly insufficient resolution used in previously published studies. Hence, simulations with different grid sizes are also performed to examine the effect of resolution on the numerical solutions. Using the present results, analysis also shows that although the characteristic lengths of unstable surfaces are different when the incident Mach number changes, these length scales are proportional to tangential velocities. Hence, the interior time determined by the overdrive degree is identified, and its limitation as the instability parameter is discussed.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Detonation waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 744 , 10 April 2014 , pp. 111 - 128
Copyright
© 2014 Cambridge University Press 

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