A flamelet-based model for supersonic combustion

The renewed interest in high-speed flight has recently demonstrated the need for the development of hypersonic air-breathing propulsion systems, i.e., in which the ambient air is used as oxidizer. These systems have long been recognized as the most well-suited for hypersonic propulsion. Although a traditional ramjet is most appropriate for supersonic speeds (Mach 3 to 5), hypersonic speeds (Mach 6 to15) can be reached only with the use of a scramjet, where combustion takes place at supersonic speeds. Because the internal flow in a scramjet is supersonic, the flow has a very short residence time during which air and fuel must mix on a molecular level, and chemical reactions have to be completed before leaving the engine. Moreover, the inlet flow is often accompanied by oblique shocks so that mixing, sustained combustion and flame anchoring become critical. Although some ground and flight experiments have successfully demonstrated the feasibility of supersonic combustion (e.g., Gardner et al. 2004; Smart, Hass & Paull 2006), experimental testing requires a large investment and presents numerous difficulties. Computational tools are thus a key element toward the development of an efficient, high-performance scramjet engine, and because mixing and heat release are at the heart of a scramjet operation, the implementation of an accurate combustion model for supersonic combustion is critical. The vast majority of computational work in supersonic turbulent combustion has so far relied on simplified/reduced mechanisms and the explicit transport of the involved species (Bray 1996). Such approaches require the closure of the chemical source term in the species transport equation. This can be achieved, for example, with simpler but low-accuracy models such as Arrhenius law (Davidenko et al. 2003), which neglects closure , the Eddy Dissipation Concept model (Chakraborty, Paul & Mukunda 2000), or with closure based on assumed (Baurle & Girimaji 2003; Karl et al. 2008) or transported (Baurle, Hsu & Hassan 1995) probability distribution functions (PDF). Some authors have also used the Linear Eddy Mixing model (LEM) (Genin, Chernyavsky & Menon 2004). But due to the strong non-linearity of the source term and the wide range of time scales associated with the chemistry, those equations are very stiff and difficult to solve. Moreover, due to very short residence times in such high speed flows, flame stabilization mechanisms are governed by auto-ignition. It is critical to model accurately such ignition and extinction phenomena in order to predict the stability of scramjet combustion. Therefore, prediction …