Rankine-Hugoniot Relations in Relativistic Combustion Waves

As a foundational element describing relativistic reacting waves of relevance to astrophysical phenomena, the Rankine-Hugoniot relations classifying the various propagation modes of detonation and deflagration are analyzed in the relativistic regime, with the results properly degenerating to the non-relativistic and highlyrelativistic limits. The existence of negative-pressure downstream flows is noted for relativistic shocks, which could be of interest in the understanding of the nature of dark energy. Entropy analysis for relativistic shock waves are also performed for relativistic fluids with different equations of state (EoS), denoting the existence of rarefaction shocks in fluids with adiabatic index \Gamma < 1 in their EoS. The analysis further shows that weak detonations and strong deflagrations, which are rare phenomena in terrestrial environments, are expected to exist more commonly in astrophysical systems because of the various endothermic reactions present therein. Additional topics of relevance to astrophysical phenomena are also discussed.Comment: 34 pages, 9 figures, accepted for publication in Ap

Pointwise Green function bounds and stability of combustion waves

Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave solutions of an abstract viscous combustion model including both Majda's model and the full reacting compressible Navier--Stokes equations with artificial viscosity with general multi-species reaction and reaction-dependent equation of state, % under the necessary conditions of strong spectral stability, i.e., stable point spectrum of the linearized operator about the wave, transversality of the profile as a connection in the traveling-wave ODE, and hyperbolic stability of the associated Chapman--Jouguet (square-wave) approximation. Notably, our results apply to combustion waves of any type: weak or strong, detonations or deflagrations, reducing the study of stability to verification of a readily numerically checkable Evans function condition. Together with spectral results of Lyng and Zumbrun, this gives immediately stability of small-amplitude strong detonations in the small heat-release (i.e., fluid-dynamical) limit, simplifying and greatly extending previous results obtained by energy methods by Liu--Ying and Tesei--Tan for Majda's model and the reactive Navier--Stokes equations, respectively

Canonical solutions for unsteady flow fields

The initial value problem of one-dimensional gas-dynamics involving discontinuous, nonuniform initial data is discussed. Canonical solutions which are valid in a small x, t region aroung a discontinuity, and which include the first order effects of nonuniformities in the data, are derived explicitly. The theory is derived by considering a group of elementary piston problems. Solutions with a shock or with a centered expansion wave are worked out individually in order to relate initial flow properties and their gradients to the speed and acceleration of the discontinuity waves. They are then combined to represent the solution of a general initial value problem by regarding the piston path as a contact line. In addition, problems with chemical reaction are discussed in terms of elementary piston problems which involve strong detonation waves, Chapman-Jouguet detonation waves, and deflagration waves

Stability of cosmological detonation fronts

The steady state propagation of a phase transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.Comment: 34 pages, 11 figures. v2: typos corrected and minor change

LES study of deflagration to detonation mechanisms in a downsized spark ignition engine

Using 15 LES cycles of a high load/low speed spark ignition engine operating point, two different fresh gases autoignition regimes called knock and super-knock are analyzed. A direct “a posteriori” analysis of pressure waves and autoignition heat release observed in LES is proposed. It reveals that low to moderate knock intensity, corresponding to late spark timings (ST) is characterized by one or several random autoignition (AI) spots which consume the surrounding fresh gases without coupling with the AI heat release. On the contrary, the highest knock intensities correspond to what is usually called super-knock, a very intense knock observed under pre-ignition conditions or for very early ST, as done in this study. LES shows that the pressure waves generated by one or a couple of AI spots are strong enough to induce locally a strong fresh gases temperature increase leading itself to a substantial decrease of the AI delay. This allows to generate a coupling between the pressure wave and the AI reaction rate which reinforce each other, leading to maximum pressures and propagation speeds close to those of a detonation. These results therefore strongly support the hypothesis proposed in the literature that super-knock is characterized by a deflagration to detonation transition (DDT). An “a priori” analysis is also performed thanks to the use of a local detonation indicator based on Bradley’s DDT diagram. It is shown that this tool not only predicts the change of combustion regime as a function of the ST, but it also roughly succeeds in predicting the location and time of appearance of the DDT in the chamber. Unfortunately, the first AI spot is not always responsible for the DDT, implying that using cold flow LES to calculate the detonation indicator instead of a reacting LES as proposed here, would lead to a failure of the indicator in many cases

General concept for autoignitive reaction wave covering from subsonic to supersonic regimes

We consider a one-dimensional (1D) autoignitive reaction wave in reactive flow system comprising unburned premixed gas entering from the inlet boundary and burned gas exiting from the outlet boundary. In such a 1D system at given initial temperature, it is generally accepted that steady-state solutions can only exist if the inlet velocity matches either the velocity of deflagration wave, as determined by the burning rate eigenvalue in the subsonic regime or the velocity of detonation wave as dictated by the Chapman-Jouguet (CJ) condition in the supersonic regime. In this study, we developed the general concept of "autoignitive reaction wave" and theoretically demonstrate that two distinct regimes that can maintain steady-state solutions both in subsonic and supersonic conditions. Based on this theory, we selected inlet velocities that are predicted to yield either steady-state or flashback solutions, and conducted numerical simulations. This novel approach revealed that steady-state solutions are possible not only at the velocity of the deflagration wave in the subsonic regime and the velocity of the detonation wave in the supersonic regime, but also across a broad range of inlet velocities. Furthermore, we identify a highly stable "autoignitive reaction wave" that emerges when the inlet velocity surpasses the velocity of detonation wave, devoid of the typical shock wave commonly seen in detonation waves. This "supersonic autoignitive reaction wave" lacks the instability-inducing detonation cell structure, suggesting the potential for the development of novel combustor concepts.Comment: Prior to publication please use: "The following article has been submitted to Physics of Fluids. After it is published, it will be found at Link.

Detonations and deflagrations in cosmological phase transitions

We study the steady state motion of bubble walls in cosmological phase transitions. Taking into account the boundary and continuity conditions for the fluid variables, we calculate numerically the wall velocity as a function of the nucleation temperature, the latent heat, and a friction parameter. We determine regions in the space of these parameters in which detonations and/or deflagrations are allowed. In order to apply the results to a physical case, we calculate these quantities in a specific model, which consists of an extension of the Standard Model with singlet scalar fields. We also obtain analytic approximations for the wall velocity, both in the case of deflagrations and of detonations.Comment: 31 pages, 14 figures. v2: several clarifications added, a change of notation. v3: reference added. Version to appear in Nucl. Phys.

Quasi-steady stages in the process of premixed flame acceleration in narrow channels

The present paper addresses the phenomenon of spontaneous acceleration of a pre-mixed flame front propagating in micro-channels, with subsequent deflagration-to-detonation transition. It has recently been shown experimentally [M. Wu, M. Burke, S. Son, and R. Yetter, Proc. Combust. Inst. 31, 2429 (2007)], computationally [D. Valiev, V. Bychkov, V. Akkerman, and L.-E. Eriksson, Phys. Rev. E 80, 036317 (2009)], and analytically [V. Bychkov, V. Akkerman, D. Valiev, and C. K. Law, Phys. Rev. E 81, 026309 (2010)] that the flame acceleration undergoes different stages, from an initial exponential regime to quasi-steady fast deflagration with saturated velocity. The present work focuses on the final saturation stages in the process of flame acceleration, when the flame propagates with supersonic velocity with respect to the channel walls. It is shown that an intermediate stage may occur during acceleration with quasi-steady velocity, noticeably below the Chapman-Jouguet deflagration speed. The intermediate stage is followed by additional flame acceleration and subsequent saturation to the Chapman-Jouguet deflagration regime. We elucidate the intermediate stage by the joint effect of gas pre-compression ahead of the flame front and the hydraulic resistance. The additional acceleration is related to viscous heating at the channel walls, being of key importance at the final stages. The possibility of explosion triggering is also demonstrated