A Similarity Subgrid Model for Premixed Turbulent Combustion

Abstract

The accuracy of large-eddy simulation (LES) of a turbulent premixed Bunsen flame is investigated in this paper. To distinguish between discretization and modeling errors, multiple LES, using different grid sizes h but the same filterwidth , are compared with the direct numerical simulation (DNS). In addition, LES using various values of but the same ratio / h are compared. The chemistry in the LES and DNS is parametrized with the standard steady premixed flamelet for stochiometric methane-air combustion. The subgrid terms are closed with an eddyviscosity or eddy-diffusivity approach, with an exception of the dominant subgrid term, which is the subgrid part of the chemical source term. The latter subgrid contribution is modeled by a similarity model based upon 2 , which is found to be superior to such a model based upon . Using the 2 similarity model for the subgrid chemistry the LES produces good results, certainly in view of the fact that the LES is completely wrong if the subgrid chemistry model is omitted. The grid refinements of the LES show that the results for = h do depend on the numerical scheme, much more than for h = /2 and h = /4. Nevertheless, modeling errors and discretization error may partially cancel each other; occasionally the = h results were more accurate than the h ≤ results. Finally, for this flame LES results obtained with the present similarity model are shown to be slightly better than those obtained with standard β-pdf closure for the subgrid chemistry.

Modulation of a methane Bunsen flame by upstream perturbations

“…For the scalar transport equation, which describes the evolution of combustion, the Van Leer third-order MUSCL scheme is applied in the discretisation of the advective term. Closely following [19], the dynamic viscosity μ is a function of temperature and modelled using Sutherland's law, with the diffusion coefficient D c in (1c) modelled considering the ratio between the temperature diffusivity and the Lewis number of the progress variable chosen, i.e. D c = λ/c p Le CO 2 , where Le CO 2 =1.384.…”

“…The code is based on a low-Mach formulation [19]. Note that although in the treatment considered the density varies because of its dependence on the progress variable, (cf.…”

“…Therefore, in the present formulation the pressure field is obtained by solving a Poisson equation. For completeness, we briefly outline the steps to obtain the equation for the pressure correction, closely following [19]. Namely, from (1b) we obtain the following relation for the unknown momentum at time level n + 1:…”

“…where in the low-Mach approach used, the unknown flux of momentum at n + 1 is obtained from (1a) [19]:…”

“…and other tabulated properties from the manifold database using a linear interpolation procedure, which retrieves these properties using the local value of the scalars c at level n + 1 as entries [19]. Next we introduce the computational domain and the boundary conditions for the set of numerical simulations performed.…”