No abstract

Nonpremixed turbulent combustion is studied in situations relevant to those encountered in advanced airbreathing engines operating at high flight Mach number values. Accurate simulations would require modeling both finite rate chemical kinetics and molecular diffusion effects (mixing) as well as the complex compressible flowfield structure associated with the presence of multiple shock and expansion waves that significantly influence combustion. The chemical kinetics are modeled by using a Lagrangian framework for turbulent combustion that has been recently extended to reactive high-speed flows. The corresponding framework incorporates both finite rate kinetics and turbulent molecular mixing rates with minimal additional parameters. An efficient anisotropic mesh adaptation strategy is used to obtain a satisfactory description of both nonreactive and reactive compressible flowfields. The present study confirmed that the proposed approach provides a well-suited framework for future developments devoted to nonpremixed turbulent combustion modeling in high-speed flows. A detailed comparison with data gathered from an experimental study of a laboratory scramjet model indicated the validity of the approach. Nomenclature D = molecular diffusivity D = diffusive flux vector Da = Damköhler number D ;Y = domain of definition of the joint scalar probability density function E = energy F = convective flux vector h = enthalpy k = turbulent kinetic energy Ma = Mach number Mt = turbulent Mach number PY = marginal probability density function of oxygen mass fraction Ỹ P = marginal probability density function of mixture fraction P; Y = joint probability density function of mixture fraction and oxygen mass fraction Y p = pressure q = Reynolds average of quantity q e q = Favre average of quantity q S = source term vector Sc = Schmidt number T = temperature t = time u = velocity U = solution vector (conservative variables) x = Cartesian coordinates Y = oxygen mass fraction = turbulent energy dissipation rate = kinematic viscosity = mixture fraction = density = mixing time scale = test function (finite volume formulation) = scalar dissipation rate = test function (finite element formulation) ! Y = chemical production rate of Y Subscripts k = component k st = stoichiometric t = total (for instance, h t is the total enthalpy) T = turbulent Superscripts 0 = fluctuations with respect to Reynolds average 00 = fluctuations with respect to Favre average

The present work is concerned with the application of a turbulent two-phase §ow combustion model to a spray §ame of Liquid Oxygen (LOx) and Gaseous Hydrogen (GH 2 ). The proposed strategy relies on a joint Eulerian Lagrangian framework. The Probability Density Function (PDF) that characterizes the liquid phase is evaluated by simulating the Williams spray equation [1] thanks to the semi §uid approach introduced in [2]. The Lagrangian approach provides the classical exchange terms with the gaseous phase and, especially, several vaporization source terms. They are required to describe turbulent combustion but di©cult to evaluate from the Eulerian point of view. The turbulent combustion model retained here relies on the consideration of the mixture fraction to evaluate the local fuel-to-oxidizer ratio, and the oxygen mass fraction to follow the deviations from chemical equilibrium. The di©culty associated with the estimation of a joint scalar PDF is circumvented by invoking the sudden chemistry hypothesis [3]. In this manner, the problem reduces to the estimation of the mixture fraction PDF, but with the in §uence of the terms related to vaporization that are the source of additional §uctuations of composition. Following the early proposal of [4], these terms are easily obtained from the Lagrangian framework adopted to describe the two-phase §ows. The resulting computational model is applied to the numerical simulation of LOx GH 2 spray §ames. The test case (Mascotte) is representative of combustion in rocket engine conditions. The results of numerical simulations display a satisfactory agreement with available experimental data.

A Lagrangian framework is set out to describe turbulent non-premixed combustion in high speed coflowing jet flows. The final aim is to provide a robust computational methodology to simulate, in various conditions, the underexpanded GH2/GO2 torch jet that is used to initiate combustion in an expander cycle engine. The proposed approach relies on an early modelling proposal of Borghi and his coworkers. The model is well suited to describe finite rate chemistry effects and its recent extension to high speed flows allows one to take the influence of viscous dissipation phenomena into account. Indeed, since the chemical source terms are highly temperature sensitive, the influence of viscous phenomena on the thermal runaway is likely to be all the more pronounced since the Mach number values are high. The validation of the extended model has been recently performed through the numerical simulation of two distinct well-documented experimental databases. Only a brief summary of this preliminary validation step is provided here. The main purpose of the present work is to proceed with the numerical simulation of geometries that bring together the essential peculiarities of the underexpanded GH2/GO2 torch. The behavior of the corresponding supersonic coflowing jet flames for various conditions is discussed in the light of computational results.