Modes of mild ignition in shock tubes: Origins and classification

Abstract

The paper analyses numerically the scenarios of ignition kernels formation in the shock tube in the intermediate temperature range. Three modes of mild ignition are distinguished among which are: ignition related to the shear heating in the developed boundary layer, ignition due to the shear heating in the recirculation zone behind the reflected shock and ignition in the central region of the tube due to the axial compression. All three modes define short ignition delays at low temperatures compared to the ideal shock-tube values. Moreover, it is shown that the gas-dynamic mechanisms responsible for additional local heating of the test mixture provide close rates of heating. As a result, all the data on ignition delays fall in a certain range defined by the mixture composition and pressure, independent on the particular mode of mild ignition.

Introduction

The shock tube is one of the most widely used reactors for studying combustion kinetics. The main advantage of the shock tube technique is the ability to control the thermodynamic conditions of the ignition. Thus, according to the ideal theory of the shock tube, the ignition arises in the mixture compressed via Hugoniot adiabat up to a particular thermodynamic state. So, in the ideal case, all the parameters, including temperature and pressure, are known. However, the ideal conditions are achieved only in the case of rather high reaction rates, for example, at high temperatures. The reaction starts immediately behind the shock front, and the visible heat release is observed first directly at the contact surface if the incident shock wave is strong enough, or on the end-wall. In the case of lower reactivity, the ignition can arise via the so-called mild ignition scenario [1]. The ignition occurs inside the localized kernels at a certain distance from the end wall [1], [2], [3]. They can arise either in the boundary region near the sidewall of the tube [4] or in the bulk flow [5], [6]. Sometimes, the ignitions can be registered both in the boundary region and in the bulk flow but with a certain time delay [7]. The switch between different modes of localized ignition can take place in a quite narrow range of parameters (e.g. ignition temperature or shock wave intensity) [8]. Such a complex behavior exacerbates interpretation of the experimental data [9], and one should apply more complex diagnostics systems when mild ignition scenarios take place [10]. Given this, it is challenging to analyze in detail the mild ignition scenarios and to distinguish the physical mechanisms responsible for their development. In this context, for example, in the work [11] it is proposed to treat localized ignition events as a reason for much earlier experimental registration of ignition compared to the numerical predictions [12], [13]. According to theoretical assessments [11], [14], [15], such an assumption seems to be quite reasonable. Thus, it is of paramount interest to study the key mechanisms of ignition kernels formation and examine further combustion development.

As it was mentioned above, the ignition can arise at a different distance from the end wall and sidewall of the tube. So it is reasonable to assume that different mechanisms can take part in the ignition kernel formation. Let us briefly overview the data on gas-dynamical mechanisms of the ignition kernels formation in the shock tube. In papers [16], [17], authors carried out a one-dimensional numerical analysis of the ignition behind the reflected shock. They have shown that both dissipation and noise provide conditions for ignition at a certain distance from the end wall. In real experiments, such noise can be related to the multidimensional structure of the flow. For example, the flow separation from the wall behind the reflected shock leads to the formation of the non-uniform temperature field in the vicinity of the end wall [18], [19]. Under such conditions, the ignition arises locally in the region of the highest temperature value and progresses in the form of the kernel with a complex spatial structure. At different parameters, a similar mechanism of localized ignition can be observed in the bulk flow or vortexes separated from the wall [20].The role of flow separation from the wall in the ignition kernels formation was examined in [21]. The authors observed two different modes, involving either small vortexes formed directly near the end wall or intense vortex in the recirculation zone behind the reflected shock wave. The scenario with three types of subsequent ignitions, first near the sidewall, then inside the bulk flow and finally on the end wall, was reproduced numerically in [22]. Recently in [23], [24], it was shown that an important role in the temperature field formation belongs to the boundary layer structure. The gas-dynamical instability of the boundary layer determines the formation of the roller vortexes, which can be responsible for local ignition kernels formation. This mechanism is valid even in argon-diluted mixtures, where visible flow separation behind the reflected shock is not observed contrary to the cases of undiluted mixtures, where the shock wave bifurcation plays the leading role [25]. In [26], it was also shown that the structure of the boundary layer could define such a phenomenon as multi-kernel ignition reported in [27], [28].

Despite that various scenarios are discovered and described in numerous papers, there is still no systematization of all the possible ignition modes. Besides, there is no data on how the ignition delay depends on the particular ignition mode. So, the main goal of this paper is to analyze different possible scenarios of mild ignition and to match each of them to the corresponding changes in ignition delay. Distinct to previous works in this field, here it is decided to focus primarily on the detailed analysis of the flow evolution. It is proposed to analyze the effect of the tube diameter on the process to achieve a comprehensive view on the gas dynamics. Thinner tubes are considered in addition to quite wide tubes of 52–154 mm diameter used in the experiments, that expands the area of application of obtained results for different test mixtures.