| OCR Text |
Show where Sf is the flame surface per unit mass (m2/kg), P is the flame surface production term which describes the increase of flame area due to the local strain rate whereas the destruction term D represents the flame surface dissipation or flame shortening mechanism due to mutual interaction of adjacent flame elements. In earliers models [5], the production term of Eq. (1) is modelled as P = pEsSj, where Es is the mean strain rate. This term describes the augmentation of material surface by the strain rate. One of the central difficulties in flamelet modelling is the determination of the stretch induced by the turbulent eddies. The strain rate may be determined from velocity gradients of the mean flow (as proposed by Marble and Broadwell [11]). Another way consists in the determination of a small scale strain (Cant et al. [4]) or large scale strain which can be estimated from the turbulent characteristics like the turbulent kinetic energy and its dissipation. Improved methods of evaluation of the effective strain rate producing the flame area have been also devised by Meneveau and Poinsot [12]. It was the aim of our previous work presented in Ref [19 ] to continue the exploration of turbulent premixed combustion based on F S D concept by proposing a new dscription and comparing its predictions with recent experimental and numerical data. The model proposed resolves some of the limits of flamelet models based on flamelet library, by using a new description of the F S D and fuel source term which takes into account the flamelet (laminar flame speed, flame thickness) and turbulence characteristics. The production term in the F S D equation is written such a way that the flame surface production due chemistry and turbulence effects are taken care of. In the present paper, special attention will be devoted to turbulent ducted flame which constitutes one of the simplest geometry that may be studied and also provides a suitable test for models. The following combustors are analysed : 1 - ramjet combustor with lateral injection 2 - combustor with V-shaped stabilizer 3 - combustor with cylindrical rod stabilizer 4 - combustor with backward-facing-step 5 - single and multi-injector furnace 6 - gas turbine combustor Experiments concerning cases 1-3 have been carried out by Montazel [14], Veynante et al. [21], Maistret [9] and Maistret et al. [10] in order to measure the distribution of light emission from C 2 and C H radicals. The spatial distributions of the radiated light m a y be interpreted as giving qualitative and quantitative mappings of the local mean heat release in turbulent premixed propane-air flame. In all these combustors, w e have performed numerical simulation in two-dimensionnal geometry for premixed propane-air turbulent flames. In this paper, results obtained are presented and commented. The text is divided into parts. The first part describes the mathematical model used. In the second part, we begin with a brief description of the new model proposed in Ref [19]. In the third part, 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, the prediction from the combustion model is compared with experimental measurements obtained by Veynante et al. [21], Montazel [14], Maistret [9] and Maistret et al. [10]. This comparison proves that this new combustion model is an efficient tool for further studies of turbulent premixed flame modelling. MATHEMATICAL MODEL 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 c. The mass averaged conservation equations of the model, closed using the classical k-e turbulence model [8], are written in the general form : where <j> stands for any of the dependent variables , and the quantity Tf represents a diffusion coefficient which is given by Tf = pe/(?<t>, <r<f> being the Prandtl or Schmidt number. The effective viscosity, pie, is assumed to be given by //e = p + pt- For the k-e model, the turbulent viscosity is taken as /i< = pC^. 2 |
