On the Three-dimensional Central Moment Lattice Boltzmann Method

A three-dimensional (3D) lattice Boltzmann method based on central moments is derived. Two main elements are the local attractors in the collision term and the source terms representing the effect of external and/or self-consistent internal forces. For suitable choices of the orthogonal moment basis for the three-dimensional, twenty seven velocity (D3Q27), and, its subset, fifteen velocity (D3Q15) lattice models, attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work; the corresponding source terms are specified to correctly influence lower order hydrodynamic fields, while avoiding aliasing effects for higher order moments. These are achieved by successively matching the corresponding continuous and discrete central moments at various orders, with the final expressions written in terms of raw moments via a transformation based on the binomial theorem. Furthermore, to alleviate the discrete effects with the source terms, they are treated to be temporally semi-implicit and second-order, with the implicitness subsequently removed by means of a transformation. As a result, the approach is frame-invariant by construction and its emergent dynamics describing fully 3D fluid motion in the presence of force fields is Galilean invariant. Numerical experiments for a set of benchmark problems demonstrate its accuracy.Comment: 55 pages, 8 figure

A numerical investigation of flame lift-off in diesel jets

Flame lift-off heights are modeled in diesel jets by using diffusion flamelet extinction as a criterion for identifying the lift-off. It is shown that the axial distance in the jet where the stoichiometric scalar dissipation rate matches computed extinction scalar dissipation rate correlates with the lift-off height. The influence of injection pressures (40–138 MPa), chamber densities (14.8–58.5 kg/m³), chamber temperatures (1000–1300 K) and O₂ molar concentrations (10–21%) are studied. N-heptane is chosen as a surrogate for diesel fuel. Two chemical kinetic mechanisms, a 37-species, 56-step mechanism and a 159-species, 1540-step mechanism, are employed. Consistent with experimental findings, the computed results indicate that the flame lift-off height decreases with increase in chamber temperature, chamber density and oxygen concentration and increases when the injection velocity is increased. It is observed that across the range of chamber conditions considered, the computed extinction scalar dissipation rates correlate well with the measured lift-off heights. When chamber temperatures and O₂ concentrations are varied, the results are found to be sensitive to the choice of the chemical kinetic mechanism.Rishikesh Venugopal and John Abraha