Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence–chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N ₂ and CO ₂ mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl’s micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.     

Implementation problems of manifolds-based model reduction and their generic solution

During the last decades, tabulated chemistry approaches, like manifold-based concepts to implement model reduction, have become a widespread, promising and accurate method to take chemical reactions into account in computing reacting flows. However, there is a number of crucial issues concerning the generation and implementation of the tabulated chemistry approaches. These concern the way manifolds of the arbitrary dimension are generated, parametrised (i.e. tabulated) preserving fast/slow decomposition and implemented rigorously by the formulation of a reduced model in a coordinate independent manner.

This study discusses these problems in detail and suggests generic solutions based on the Reaction–Diffusion Manifolds (REDIM) method. A REDIM tabulated chemistry concept obtained by using the hierarchical nature of the invariant slow system manifolds is presented. Numerical aspects of the implementation are in the focus of the paper. It is shown how the concept is implemented to overcome most problems without a-priori knowledge of the considered system behaviour. As a basic example for discussion and illustration synthesis, gas/air combustion in premixed, freely propagating flames is used.