Compressibility and heat release effects in high-speed reactive mixing layers II. Structure of the stabilization zone and modeling issues relevant to turbulent combustion in supersonic flows
Introduction
The renewed interest in high-speed flight motivates the development of hypersonic air-breathing propulsion systems in which the ambient air is used as oxidizer. Such systems have indeed long been recognized as the most well-suited for hypersonic propulsion. From a practical point of view, the traditional ramjet appears as the most appropriate for supersonic speeds (flight Mach number values between 1 and 5) but, due to total pressure losses and corresponding losses of thrust, hypersonic speeds (flight Mach number values ranging from 5 to 15) can be reached only with the use of a scramjet, where combustion takes place at supersonic speeds. Indeed, scramjets are ramjet engines in which the airflow through the whole engine remains supersonic, burning oxygen scooped from the atmosphere. Since the internal flow in a scramjet is supersonic, the flow residence times during which air and fuel must mix at the molecular level are very short, and chemical reactions have to be completed before leaving the engine. The development of supersonic combustion ramjets (scramjets) thus motivates the study of non-premixed combustion in supersonic flows, i.e., in conditions where the reactive flowfield is subject to a strong competition between compressibility effects, turbulent mixing, and chemical kinetics [1]. Some important efforts are therefore directed towards the improvement of available computational models [2], [3], [4], [5] so as to address the numerical simulation of scramjet geometries in realistic conditions. Therefore, there is some need for further detailed investigations of such reactive high-speed flows, which may provide useful insights to elaborate appropriate turbulence-chemistry interaction (TCI) closures for such conditions.
Under conditions of locally supersonic flows the pressure fluctuations at a given point no longer depend on the velocity field over the entire fluid space but only on the velocity field in the forward Mach cone from that point. In comparison to more standard low speed conditions, this specificity induces important modifications in the behavior of the pressure-strain terms in the second-order moment equations. The resulting effects have been early evidenced through the evolution of the spreading rate of mixing layers obtained for increasing values of the convective Mach number Mc. It is worth recalling that, assuming equal densities and free-stream specific heat ratios, this number may be expressed by where U and c denote the free-stream velocity and speed of sound in the each inlet streams. The indices 1 and 2 refer to the high- and the low-speed streams, respectively. In comparison with the study of compressibility effects, the influence of heat release and combustion on the development of such high-speed layers has received much less attention and the amount of available data related to compressible and reacting shear flows still remains relatively scarce. Firm conclusions concerning the ignition and heat release influence on mixing layer development are therefore more difficult to draw. In the low-speed regime, typically for values of Mc below 0.4, only a slight reduction of turbulent shear stresses and mixing layer growth rates has been reported for increasing levels of heat release, see for instance [6]. For high-speed compressible flow regimes, the influence of heat release is even less clear [7], [8]. According to the experimental study of Miller et al. [8], the global structures and normalized growth rates of reactive mixing layers do not seem to be significantly altered with respect to inert cases at similar compressibility levels and this conclusion has been confirmed by recent numerical investigations of spatially-developing compressible reactive mixing layers [10].
The present study is focused on the analysis of the structure and topology of the stabilization zone in such high-speed reactive mixing layers. This paper is organized as follows, in Section 2, the physical models and numerical methodology are briefly presented, the reader is referred to references [10], [11] for further details concerning these aspects. The instantaneous structure of stabilization zone is analyzed in detail in Section 3. Then the combined effects of compressibility and heat release on the overall statistical properties of the reactive flowfield are discussed in Section 4. In Section 5 we scrutinize some assumptions that are currently retained in the modeling of turbulent combustion in supersonic flows. Finally, conclusions are drawn in the last section of the manuscript.
Section snippets
Constitutive equations and conservation laws
The unsteady and three-dimensional compressible Navier-Stokes equations are considered for multicomponent reactive gas mixtures, which are characterized though the set of conservative variables (ρ, ρui, ρet, ρYα), with and . The quantity ρ is the density, ui is the velocity component in direction i, the total specific energy is obtained as the sum of the internal specific energy e and the kinetic energy, Yα denotes the mass fraction of species α, and finally N is
Instantaneous structure of the reactive flowfield
The auto-ignition of mixtures of hydrogen following its release into a supersonic turbulent airflow at elevated temperature is relevant to combustion in hypersonic air breathing propulsion and especially to scramjet engines. Despite this relevance, a detailed understanding of the dynamics of autoignition sites as well as subsequent flame development in supersonic reactive flows is still missing. In a turbulent flow, the interaction between (turbulent) mixing and chemistry determines the regions
Statistical analysis of the high-speed reactive flowfield
For the conditions associated to the R-DT-0.35 case, the minimum ignition time issued from a PSR calculation conducted at a constant pressure equal to the pressure level at the injection stream (i.e., P=94232 Pa) has been evaluated to be [18] and corresponds to ξmr, i.e. the most reactive mixture fraction value [41]. It is noteworthy that the product of τref with the value of the convective velocity Uc leads to an auto-ignition distance value x1, ref approximately equal to 70δω,0,
Inspection of some specific turbulent combustion modeling issues
The modeling of turbulent combustion in high-speed, i.e., supersonic, flows raises several specific issues, e.g., density as well as temperature variations may arise from the heat release due to combustion, from viscous heating and from local compressions and expansions, which may occur as an outcome of the high speeds. Under such conditions changes in velocity may induce significant variations in pressure and static temperature, which result in a coupling between the velocity field and
Conclusions
A new set of DNS of compressible spatially-developing mixing layers has been obtained and analyzed for increasing values of Mc under both inert and reactive conditions. For these high-speed reactive mixing layers, depending on the value of Mc, the thermal runaway occurs in either the mixing layer development zone (small value of Mc) or the fully developed turbulence region (larger value of Mc). For the smallest values of Mc, there is a significant increase in temperature in the auto-ignition
Acknowledgments
The manuscript benefited from the comments and valuable suggestions made by the reviewers. This work benefited from the HPC resources GENCI-IDRIS (Grant 2013-x20132a0912). The authors thank Alexandre Ern (CERMICS, INRIA, France) and Vincent Giovangigli (CMAP, UMR 7641 CNRS and Ecole Polytechnique, France) for providing them with the library EGLIB. They are indebted to Jean-Paul Bonnet and Michel Champion (CNRS, Poitiers) for support and encouragement. Finally, they would like to dedicate this
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