Mean structure of one-dimensional unstable detonations with friction

Abstract

WOS:000332844200022International audienceThis investigation deals with the study of the mean structure of a mildly unstable non-ideal detonation wave. The analysis is based on the integration of one-dimensional reactive Euler equations with friction forces using a third-order Runge-Kutta scheme and a fifth-order weighted essentially non-oscillatory (WENO5) spatial discretization. A one-step Arrhenius reaction mechanism is used for modelling the chemical reaction. When the frictional forces are active, the limit cycle based on the post-shock pressure reveals an enhanced pulsating behaviour of the downstream subsonic reaction zone compared to the ideal case. The results show that the detonation-velocity deficit increases as the mean reaction zone becomes thicker compared to the generalized ZND model. A new master equation, based on the Favre-averaged quantities, is derived and analysed along with new sonicity and thermicity conditions. The analysis of the species, momentum and energy balances reveals that the presence of mechanical fluctuations within the reaction zone constitutes another source of energy withdrawal, meaning that the detonation deviates from its laminar structure. Furthermore, the compressibility of the flow is analysed and the relationships between the fluctuations of temperature, velocity and reactive scalar are discussed in terms of strong Reynolds analogies

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

“…First, the results of select cases are analyzed via a densityweighted (Favre), spatio-temporal averaging method. Using this analysis, which was introduced to the field of detonation by Lee and Radulescu [3], Radulescu et al [4], and Sow et al [19]. Mi et al interpreted the super-CJ propagation, resulting from a system with highly concentrated sources that instantaneously deposit energy after a fixed delay time, as weak detonations owing to the non-equilibrium condition at the average sonic surface.…”

Computational study of non-ideal and mildly-unstable detonation waves

“…The chemical source term is set to zero when the mass fraction goes below a threshold of 10 6 . In Sow et al [30], we show that the work of friction which is expressed by the product of friction force by the velocity implies that the only source of entropy production is due to the irreversible chemical reaction. In the present study, the thermal heat transfer should be added as another source of entropy production.…”

“…Then the numerical results are post-treated in the instantaneous shock-attached frame to define the mean structure of the detonation wave. In contrast with Gamezo et al [28] and Radulescu et al [29], the Favre-averaged procedure, which is detailed in [30] is conditioned by the position of the shock. Based on this analysis, a new Favre-averaged Master Equation (ME) defining the mean sonic locus has been obtained…”

On a stabilization mechanism for low-velocity detonations

“…The presence of losses leads to the increased instability of the wave (Zhang & Lee 1994;Dionne et al 2000;Sow et al 2014). Figure 3 shows the period-one and period-two limit cycles arising from the instability of solutions at points a and b.…”