OCR Text |
Show kinetics and multicomponents diffusion (Sennoun [20]). A database called a flamelet library is first assembled, constituting a numerical description of the evolution of the gas composition and temperature across the flame front as a function of the input values of composition, temperature and pressure and of the characteristic suain rate as well as ignition and extinction conditions that are required in the computation of the turbulent flow field. In order to be applied to practical combustors, this flamelet library must cover a large range of equivalence ratios, strain rates, fresh gas temperatures and pressures. This kind of study is burdensome in terms of C P U time and can work only for one type of fuel. It is the aim of the present paper to continue the exploration of turbulent premixed combustion based on F S D concept by proposing a new description and comparing its predictions with recent experimental and numerical data. The model proposed in this paper resolves some of the limits mentioned above by implementing a new description of the F S D and fuel source terms which no longer needs a flamelet library and which take into account the flamelet (laminar flame speed, flame thickness) and turbulence characteristics. The production term in the F S D equation is written in such a way that it takes into account flame surface production due to chemistry and turbulence effects. The action of the turbulent flow and chemistry on the flame surface (convection, diffusion, production and destruction) is described through the F S D by introducing a new formulation of the source term in the F S D balance equations. The combusting flow investigated numerically in the present study corresponds to a ramjet combustor with lateral injection (Figure 1) previously studied experimentally and numerically by Montazel [15] and Veynante et al. [23]. The study of this configuration bears considerable interest: a) on a fundamental aspect, for the analysis of turbulent combustion in a flow of interacting jets, which has been given little attention to date, b) in relation with the assessement and validation of new turbulent combustion models. Very few experimental and numerical results are available for this configuration. The recent work performed by Montazel [15] and Veynante et al. [23] have brought many new ideas on the structure of the turbulent premixed flames and a wealth of high quality data. The text is divided into parts. The first part describes the mathematical model used. In the second part, w e will specifically consider combustion models based on the F S D concept. W e begin with a brief background of the coherent flame model ( C F M ) and w e will end this part by the description of the new model proposed in this paper. In the third part of this paper, the computational domain, numerical method and initial and boundary conditions are then reviewed, followed by the numerical solution of the two-dimensional control volume equations for conservation of mass, momentum, energy, chemical species and flame surface density. Finally, predictions from the combustion model are compared with experimental measurements obtained by Veynante et al. [23 ] and Montazel [15]. This comparison proves that the new combustion model is an efficient tool for further studies in turbulent premixed flame modelling. GOVERNING EQUATIONS The independent variables of the problem are the two components (x, y) of a cartesian co-ordinate system. The main dependent variables characterising the turbulent flow are the two velocity components (u, v), the pressure p, enthalpy h, the kinetic energy of turbulence k, and the energy dissipation rate e. The mass averaged conservation equations of the model, closed by using the classical k-e turbulence model [11], are written in the following general form : where y?stands for any of the dependent variables , and the quantity Tf represents a diffusion coefficient which is given by Tf = / i e / ^ . where <r^ is the Prandtl or Schmidt number. The effective viscosity, //e, is assumed to be given by ne = // + //*. For the k-e model, the turbulent viscosity is taken as fit = pC^ - . The equation set simulates a two-dimensional turbulent reactive flow. Equations are solved for <f> equal to time-mean axial and tangential velocities u and v, stagnation enthalpy h, fuel mass fraction Yfu, turbulent kinetic energy k, dissipation rate e, and flame surface density Sf. This last quantity requires a special attention in our model, since it represents the key of the success of turbulent combustion description based on mis approach. The next section is devoted to the description of the flame surface density balance equation. The exchange coefficients Tf, source terms SJ,, and the values of the constants in the k-€ model are compiled in Table 1. 2 |