M. Oevermann

A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces

We present a finite volume method for the solution of the two-dimensional elliptic equation ??(s(x)?u(x))=f(x) with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution u(x) resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the L∞ and L2 norm.

A sharp interface finite volume method for elliptic equations on Cartesian grids

We present a second order sharp interface finite volume method for the solution of the three-dimensional elliptic equation ? ? ( ? ( x ? ) ? u ( x ? ) ) = f ( x ? ) with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewise trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in M. Oevermann, R. Klein, A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, Journal of Computational Physics 219 (2006) 749-769] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases - including large ? -ratios and non-smooth interfaces - the method achieves second order of accuracy in the L ∞ and L 2 norm.

Dust in brown dwarfs I. Dust formation under turbulent conditions on microscopic scales

Dust formation in turbulent media is studied adopting the example of brown dwarf atmospheres. By combining asymptotic techniques and time-dependent, multi-dimensional numerical simulations, we show that acoustic waves originating from convective motions provide a mechanism to initiate dust nucleation in otherwise dust-hostile environments. The subsequently growing particles cause a radiative cooling strong enough to re-initiate efficient dust formation resulting in a strongly inhomogeneous distribution of dust in such environments. Recent observations bear indications for such cloudy dust distributions in brown dwarf atmospheres.

CFD Modeling of the Influence of Fuel Staging on the Mixing Quality and Flame Characteristics in a Lean Premixed Combustor

In this paper, we investigate the feasibility and limitation of modeling non reacting and reacting flows of a premixed burner with steady RANS. The burner investigated here is a standard industrial swirl-inducing burner equipped with a staging of fuel injection. The simulation results on mixing quality, flame shape and position and convective time delays are compared to measurements which are performed in a water test rig and in a combustion chamber. The RANS simulations can qualitatively capture the trends observed from experimental data. The simulated mixing quality evolves in a similar way as the experimental data when the fuel distribution is changed. Using a turbulent Schmidt number of 0.2, the absolute values are in good agreement with the measured ones. Variations of the fuel injection distribution lead to changes in the flame shape and its stabilization location. The simulated reacting flow optimized with respect to the turbulent Schmidt/Prandtl number (Sct /Prt = 0.55) is able to predict the changes in flame shape and flame position. However, the shifting of the flame is not as distinct as observed in the experiments. This explains that variations in simulated convective time delays are also smaller than in reality. Nevertheless, the qualitative characteristics of the time delays depending on the fuel distribution parameter can be reproduced and absolute values are generally similar to those of the measurements.Copyright

The impact of periodical ow forcing on the mixing quality and ow structure in a swirl burner: numerical and experimental studies

ow structure of a combustor allows to control combustion instabilities and to reduce pollutant emissions. The investigations are conducted with unsteady RANS simulations and experimental measurements in a water test rig for cold ow congurations. Studies on axial mass ow excitations with the dominant frequency of the coherent struc- ture are performed. The unforced ow eld exhibits a helical structure which switches to an axis-symmetric one when forcing at the natural frequency is applied. The concentration eld at the burner exit becomes more homogeneous, i.e. the mixing quality increases, with forcing. The simulations are able to reproduce the main features of the inuence of forcing on mixing characteristics and ow structure.