Numerical predictions of oblique detonation stability boundaries

Grismer, Matthew J.; Powers, Joseph M.

doi:10.1007/bf02510995

Cited by 37 publications

(27 citation statements)

References 22 publications

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“…This result differs from the previous studies, which suggest the overdrive degree for the stability boundary is just slightly below 1.8, a value close to the stability boundary for one-dimensional normal detonation (i.e. f = 1.73) (Grismer & Powers 1996;Verreault et al 2013). A possible explanation of this difference could originate from the wedge shape used by different researchers resulting in different types of initial disturbance near the wall.…”

Section: Resultscontrasting

confidence: 90%

“…For convenience, the coordinate is rotated to the direction along the wedge surface, and simulations are carried out in the region enclosed by the dashed line. Similar to previous numerical studies on oblique detonations (Li, Kailasanath & Oran 1993;Grismer & Powers 1996;Papalexandris 2000;Choi et al 2007;Gui et al 2011;Teng & Jiang 2012;Verreault et al 2013), the present study is also based on the inviscid assumption. In the present study, non-dimensional Euler equations with one-step irreversible Arrhenius kinetic model are used as the governing equations, i.e.…”

Section: Methodsmentioning

confidence: 61%

“…It is worth noting that a resolution of 20 points per half reaction zone length, l 1/2 , of the detonation wave is often suggested as a minimum to capture the longitudinal instability in one-dimensional pulsating detonations. This applies to cases with a high degree of overdrive factor or moderate activation energy; or when seeking only a reasonable estimation of the stability boundary using numerical simulations (Grismer & Powers 1996;Bourlioux et al 1991;Sharpe & Falle 1999;Hwang et al 2000). For sufficiently regular detonation cells as for the case with high degree of overdrive, Bourlioux & Majda (1992) simulated detonation cells using a similar grid resolution of about 20 points/l 1/2 and agreement was obtained between computed detonation cell sizes and predictions from stability theories.…”

Section: Resultsmentioning

confidence: 99%

“…The reaction is controlled by the activation energy E a and pre-exponential factor k. The latter is chosen to define the spatial and temporal scales. In this study, the dimensionless parameters are fixed with the values q = 50, E a = 50 and γ = 1.20 often used in previous studies of both oblique and normal onedimensional pulsating detonations (Bourlioux & Majda 1992;Grismer & Powers 1996;Short & Stewart 1998;Papalexandris 2000;Verreault et al 2013). The governing equations are discretized on Cartesian orthogonal uniform grids and solved with the MUSCL-Hancock scheme with Strang's splitting.…”

Section: Methodsmentioning

confidence: 99%

“…Oblique detonations are overdriven and, hence, Grismer & Powers (1996) introduced the overdrive degree as one controlling parameter to define stability boundaries for oblique detonations. Using the two-dimensional reactive Euler model with a custom-designed curved wedge so as to induce a straight shock with a formally irrotational downstream flow field, their computational study predicted both steady and unsteady oblique detonation solutions when the overdrive factor was varied.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study on unstable surfaces of oblique detonations

2014

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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 ∼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.

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Section: Resultscontrasting

confidence: 90%