Edward Baudrez

Accuracy and convergence rate of steady-state simulation of one-dimensional, reactive gas flow with molar expansion

A coupled and a decoupled solution method are applied to the steady-state simulation of one-dimensional, reactive gas flow. The accuracy of the numerical steady-state solution depends to a significant extent on the molar expansion of the gas. The convergence rate of the coupled solution method is almost independent of molar expansion. The convergence rate of the decoupled solution method is at least 50% lower for strong molar expansion than for nonexistent molar expansion. By adding a transport equation for molar mass, the convergence rate of the decoupled solution method becomes almost independent of molar expansion. The results for the decoupled solution method apply to other methods in which composition is determined on a fixed flow field. A tool is presented to quantify the perturbation of the flow field by the chemical reactions.

Preconditioning for Eulerian-Eulerian Gas-Solid Flow Calculations

Local preconditioning for Eulerian-Eulerian gas-solid flow calculations is investigated. The gas-solid drag source terms are at the origin of a solid volume fraction and frequency dependency of the mixture speed of sound. Whereas the solid volume fraction dependency of the mixture speed of sound is straightforward to account for in the gas-solid preconditioner, this is not the case with the frequency dependency. Not accounting for the frequency dependency of the mixture speed of sound in the gas-solid preconditioner results, however, in drastic convergence slow down. Possible approaches to account for the frequency dependency of the mixture speed of sound in the gas-solid preconditioner are investigated. It is shown that the gas-solid preconditioner does not need to remove the frequency dependency of the mixture speed of sound, but should account for it and be scaled according to the mixture speed of sound at the highest frequency calculated, that is the filter frequency mixture speed of sound, which logically depends on the local mesh resolution. Accounting for the filter frequency mixture speed of sound in the gassolid preconditioner as good as eliminates the reduction of the convergence speed by the gas-solid drag source terms. The addition of a drag history force to the gas-solid preconditioner to properly rescale frequencies lower than the filter frequency hardly alters the convergence behavior. The convergence speed is determined by propagation at the highest, i.e. filter frequency.

Simultaneous Solution Algorithms for Gas-Solid Flows: an Efficient Parallel Line Solver

A pointwise simultaneous solution algorithm based on dual time stepping was developed by De Wilde et al. (2002). With increasing grid aspect ratios, the efficiency of the point method quickly drops. Most realistic flow cases, however, require high grid aspect ratio grids, with the highest grid spacing in the streamwise direction. In this direction, the stiffness is efficiently removed by applying preconditioning (Weiss and Smith, 1995). In the direction perpendicular to the stream wise direction, stiffness remains because of the viscous and the acoustic terms. To resolve this problem, a line method is presented. All nodes in a plane perpendicular to the stream wise direction, a so-called line, are solved simultaneously. This allows a fully implicit treatment of the fluxes in the line, removing the stiffness in the line wise directions. Calculations with different grid aspect ratios are presented to investigate the convergence behavior of the line method. The line method presented is particularly suited for parallelization. At each pseudo-time step, the lines (typically hundreds) can be solved independently of each other. The Message Passing Interface (MPI) standard (Snir et al., 1996) is used. The communication between the processors can be easily reduced by solving a block of lines per processor. The communication is then limited to information regarding only the outer lines of the block. In common practice, the number of lines is much higher than the number of processors available. In this region of the lines/processor space, the reduction of the calculation time is linear with the number of processors that is used.Copyright