TY - JOUR

T1 - Numerical simulation of nonlinear dynamics of 1D pulsating detonations

AU - Borisov, S. P.

AU - Kudryavtsev, A. N.

PY - 2017/10/22

Y1 - 2017/10/22

N2 - The development of 1D instability of a detonation wave is numerically simulated for a two-stage chemical model. The shock-fitting approach is employed to track the leading detonation front. In order to determine its motion, the equation for the acceleration of the shock wave derived from the Rankine-Hugoniot conditions and the characteristic relations is integrated along with the reactive Euler equations. The fifth-order WENO scheme is used, time stepping is performed with the four-stage Runge-Kutta-Gill method. It is shown that in a certain range of parameters of the problem (the degree of overdrive f, the dissociation energy Ed and the activation energy Ea ), the Zeldovich-Neumann-Döring stationary solution is unstable with respect to 1D disturbances. The evolution of disturbances at later nonlinear stages is studied. Nonlinear saturation of the growth of disturbances leads to the formation of a stable limit cycle. When changing the parameters of the problem, the period doubling bifurcation can occur leading to the appearance of pulsations with two different maxima of the amplitude.

AB - The development of 1D instability of a detonation wave is numerically simulated for a two-stage chemical model. The shock-fitting approach is employed to track the leading detonation front. In order to determine its motion, the equation for the acceleration of the shock wave derived from the Rankine-Hugoniot conditions and the characteristic relations is integrated along with the reactive Euler equations. The fifth-order WENO scheme is used, time stepping is performed with the four-stage Runge-Kutta-Gill method. It is shown that in a certain range of parameters of the problem (the degree of overdrive f, the dissociation energy Ed and the activation energy Ea ), the Zeldovich-Neumann-Döring stationary solution is unstable with respect to 1D disturbances. The evolution of disturbances at later nonlinear stages is studied. Nonlinear saturation of the growth of disturbances leads to the formation of a stable limit cycle. When changing the parameters of the problem, the period doubling bifurcation can occur leading to the appearance of pulsations with two different maxima of the amplitude.

KW - ONE-DIMENSIONAL DETONATIONS

KW - GASES

UR - http://www.scopus.com/inward/record.url?scp=85033211421&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/894/1/012013

DO - 10.1088/1742-6596/894/1/012013

M3 - Article

AN - SCOPUS:85033211421

VL - 894

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012013

ER -