Dynamics of flame/vortex interactions
Introduction
Vortices naturally occur in many reacting flows of technological interest. Vortical structures are found for example in continuous combustors where their production is related to the streams injected into the chamber and to the developing turbulent motion. Vortex motion is also established in internal combustion engines as a result of reactant injection and exhaust processes. In general, concentrated vorticity constitutes the large-scale structure of the turbulent shear flows found in combustion systems. Studies in turbulence carried out during the last 30 years indicate that mixing is controlled to a great extent by vortex motion and specifically by the large-scale vortices developing in the highly sheared regions of the flow. Much experimental evidence indicates that turbulence may be described as an organized motion at the largest scale superposed on a fine grain random background of fluctuations in the small scales. This picture has evolved from experiments carried out on plane shear layers [1] and has received further confirmation from studies on jets and wakes (see for example Ref. [2]). These data have suggested that turbulent combustion could be viewed as a process dominated by the continuous distortion, extension, production and dissipation of the flame surface by vortices of different scales. This conceptual description has given rise to a variety of “flamelet” models for turbulent combustion [3]. The elementary interaction between a vortex and a flame thus appears as a key process in the description of turbulent reactive flows.
Vortex structures also arise when a flame traveling in a duct interacts with bluff obstacles, a mechanism which may lead to significant levels of flame acceleration (Fig. 1(a)). A starting vortex is also observed when jets or plumes are formed by a sudden injection or expansion of a mass of gases into a quiescent medium. The jet features a characteristic mushroom vortex cap (Fig. 1(b)). When dealing with supersonic flows, it has been known from early experiments on supersonic combustion that natural mixing was slow and that combustors could not operate in the supersonic range without some method of mixing enhancement. One possible scheme for improving the rate of span-wise mixing relies on vorticity created by the interaction between weak shock waves and the hydrogen stream (Fig. 1(c)). This process has been extensively investigated in relation with developments of supersonic ramjet combustors [4].
Vortex structures may also appear as a result of flow instability. There is growing evidence that combustors operating in regimes of oscillation are driven by organized vortices (Fig. 2). In many cases, the ignition and subsequent reaction of these structures constitute the sustaining mechanism by which energy is fed into the oscillation [5]. Vortex roll-up often governs the transport of fresh reactants into burning regions and this process determines the rate of reaction in the flow and the amplitude of the pressure pulse associated with the vortex burn-out.
This panoramic view of practical devices and modes of operation clearly indicates that vorticity and its dynamical interaction with combustion are of great practical importance.
Vortex/flame interactions constitute also a fundamental problem in combustion theory. The problem is generic as it typifies the more complex situations found in turbulent flows or in special modes of operation like those found under combustion oscillation or in pulse combustion devices. It is also valuable as an example of flame development in a non-uniform configuration. One of the simplest examples of the effect of flow non-uniformity on a flame is provided by the positive straining motion obtained for example in the vicinity of a counterflow stagnation point, possibly varying the strain-rate in time. This specific problem has bee investigated most extensively because it allows basic studies of flame structure, quenching and ignition conditions, effects of strain on reaction rates, flame response and dynamics etc. Flames submitted to constant or variable strain rate provide a remarkably rich example of the effect of flow non-uniformity. The flame/vortex interaction constitutes the next step in the search for simple model geometries. This case offers new possibilities, as it allows for example investigations of straining and curvature effects in the same configuration.
Much has been learned in the recent past from theoretical, numerical and experimental studies of flame/vortex interactions. Problems which may be examined in this geometry relate to the structure of the flame when it is wound up by a vortex, formation of a central core, secondary vorticity generation, quenching of the reaction zone, ignition dynamics, mixing and combustion enhancement.
This article provides a review of the research effort devoted to the problem of a flame interacting with a vortex. This survey is restricted to situations where vortex structures are isolated (single vortex, vortex pair, vortex rows, vortex ring) or form a well-organized pattern [15]. It does not touch upon the more complex situation encountered in turbulence where the vortex filaments are randomly distributed in space. The review begins in Section 2 with some background material on vortex dynamics, stability and decay, structure, and gives some ideas of the difficulties involved in flame/vortex interaction studies. The third section reviews a set of theoretical studies of simplified geometries including non-premixed and premixed flames interacting with a single vortex or a pair of vortices. Numerical calculations are also surveyed in this section, and the main formulations used for these theoretical investigations are given. A short description of the main experimental setups follow (Section 3.3). The most significant results for both non-premixed (Section 4) and premixed (Section 5) configurations are then detailed on the theoretical, numerical, and experimental levels. To give an idea of the usefulness of flame/vortex interactions studies, their use in improving turbulent combustion diagrams is briefly described in Section 6, along with the latest versions of these diagrams.
Section snippets
Structure and occurrence of vortices
Before dealing with flame/vortex interactions, it is first useful to provide some background on vortex structures in non-reactive streams, give some elements on their experimental and numerical generation and discuss stability issues.
Two-dimensional vortex dipoles (or pairs) and axisymmetrical vortex rings are common in nature. Vortex dipoles feature circular streamlines with two cores symmetrically located on the two sides of the propagation axis. Their structure is well described by a Lamb
Configurations
As already indicated, a basic issue in flame/vortex interactions studies is to define the configuration which allows the simplest interpretation. Theoretical studies are restricted to simple geometries that are not always close to reality, but they give insight in the basic mechanisms. Numerical and experimental studies allow investigations of more realistic cases, even if they are also limited with respect to the attainable parameters. An experimental setup should allow an easy optical access
Theoretical results for non-premixed flames
Theoretical studies of flame/vortex interactions were initiated by an elegant analysis devised by Marble [65] to understand the basic features of the problem. The configuration investigated comprises a simple plane diffusion flame initially at rest along the horizontal axis. A vortex with a circulation Γ is established at the origin at the initial time t=0 (Fig. 23(a)).
The vortex induces an aximuthal motion described by Eq. (14). It is assumed that the chemistry is infinitely fast and that the
Theoretical results for the premixed case
The theory of premixed flame roll-up by vortices is less developed. The configurations which have been considered are sketched in Fig. 29. With the exception of the study due to Peters and Williams [172], most investigations of premixed flame/vortex interactions are numerical or experimental and they will be reviewed later in this article. Peters and Williams show that for the initial geometry of Fig. 29(a), the roll-up gives rise to a reacted core as in the non-premixed case. The core radius
Turbulent combustion diagrams
Studies of flame/vortex interactions provide detailed information on the complicated process which take place when a flame spreads in a turbulent flow field. The identification and classification of regimes of combustion progressed to a great extent mainly because of simulations and experiments on flame/vortex configurations.
Early attempts to classify turbulent flames in different regimes in diagrams are due to Barrère [198], Bray [199], Borghi [200], Williams [74] and Peters [3] for premixed
Conclusion
The present article reviews past and recent progress in the field of flame/vortex interactions. Flame/vortex interactions are defined as an intermediate configuration between plane strained flames and turbulent flames and they may be used to study basic mechanisms of combustion dynamics. The means employed to investigate the physical processes are of three kinds.
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Some theoretical analyses were carried out and have provided considerable insight in a variety of processes (flame structure, reacted
Acknowledgements
The authors wish to thank the Délégation Générale pour l'Armement for the PhD fellowship of P.H. Renard. This work is part of a collaboration with the Air Force Research Laboratory of the Wright Patterson Air Force Base of Dayton (USA), the PCI laboratory of the University of Bielefeld (Germany) and the LAERTE of ONERA (France).
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