Numerical Simulation of Supersonic Nonpremixed Turbulent Combustion in a Scramjet Combustor Model

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

Application and theoretical analysis of the flamelet model for supersonic turbulent combustion flows in the scramjet engine

“…In particular, the obtained pressure distribution on the lower wall fits well with the measured data except for the region near x = 130 mm of the lower wall. Similar results can also be found in other simulations [17,19,39]. Oevermann [17] attributed this difference to two possible reasons: the neglect of the shock wave/boundary layer interaction on the lower wall and the simplification of 2D simulation.…”

“…The grid points are clustered near the upper and lower walls, so that the upper and lower boundary layers are both considered in the present simulation. This also differs from previous simulations [17,19,39,40], where both boundary layers were neglected. In addition, to validate the above 2D approximation for the DLR case, a 3D model with three holes is also established as shown in Figure 4, and a 3D structural mesh with about 1.5 million grid points is generated for the 3D computations.…”

“…The hydrogen is injected parallel to the air stream through 15 holes of diameter 1 mm at the base of the wedge. Due to the symmetry of the combustor about its spanwise centre plane, a 2D approximation for this case was employed in previous studies [17,39]. Obviously, because of the low computational consumptions, 2D simulations would be pretty convenient for the parametric studies of compressibility effects using the flamelet model.…”

A multiple-inlet mixture fraction model for nonpremixed combustion

“…Among the large variety of existing turbulent nonpremixed combustion models, we retain a closure that approximates the Lagrangian trajectory in the mixture fraction space. The main reason for this choice is that the corresponding closure has recently been implemented by us in the N3S_Natur solver [35,50]. The Modèle Intermittent Lagrangien (MIL) was proposed 15.…”

“…It has been previously established to be robust and easy to implement, and it features low computational costs in such a manner that it has been applied to a large variety of situations including nonpremixed combustion [20,52], two-phase flow combustion [27,53], and more recently combustion in nonpremixed high-speed flows [35,50]. The MIL model is a Lagrangian model in the composition space that is based on the knowledge of two scalar variables, namely the mixture fraction n and the mass fraction of oxygen Y O , which follows the departures from chemical equilibrium, i.e., the progress of the chemical reaction.…”