Stabilisation of Pre-Mixed Laminar Oxy/Acetylene Flame Simulations by means of a Multigrid Solver for the Pressure Correction Equation

Oxy/acetylene flames from ordinary welding torclies can be successfully used for the chemical vapour deposition of diamond. The fluid dynamics, transport phenomena and complex combustion mechanisms, that are present in the resulting pre-mixed laminar flames, are not completely understood. This hampers the scale-up of the process to fllms of approximately 1000mm^2 as required for most practical applications. Therefore, a numerical study was started at the Kramers Laboratorium voor Fysische Technologie in cooperation with the Eindhoven University of Technology, where the chemical reactions and fluid dynamics were studied in more detail. The in-house developed code CVDMODEL is used at the Kramers Laboratory for the simulations of laminar flames and CVD processes. Although laminar methane flames were successfully simulated, it was not possible to get satisfying result with the simulation of oxy/acetylene flames. The flame sheet showed wave-like instabilities, especially on flne computational grids. The CVDMODEL code uses the SIMPLE method. One equations in particular, the pressure correction equation, plays an important role in this method. This equation eliminates the mass sources, when it is solved accurately. Because the calculation of the chemical reactions depends on these mass sources, the simulation is affected by the way of solving the pressure correction equation. The adjustment of the solving method of the pressure correction equation seemed a reasonable continuation in the development of the CVDMODEL code. In this thesis, a multigrid solver is presented that can be used in combination with the CVDMODEL code. The solver is, in contrary to basic iterative solvers, capable of solving large linear systems with a good rate of convergence. The Galerkin coarse grid approximation method was chosen to obtain the required information for the multigrid solver, i.e. the coarse grid coefficient matrices. Several tests were done with the standard GCA method and an optimal setting was found for the solving of the pressure correction equation. For good results of the multigrid solver with the CVDMODEL code, the standard GCA method had to be adjusted. The creation of the coarse grid coefficient matrices and the restriction of grid values must be altered when blocks and fixed pressure points are present. When the pressure correction equation is accurately solved {i.e. down to machine accuracy) with the multigrid solver, the SIMPLE method follows a more controlled path towards a steady solution. Nevertheless, it is more efficient to perform the SIMPLE iteration witliout tlie multigrid solver when the simulation concerns only one species. With the laminar oxy/acetylene flame simulations, the simulation are controlled with a false time step. The multigrid solver makes it possible to apply larger time steps. Also, the SIMPLE procedure becomes more robust when the pressure correction equation is accurately solved. Although the SIMPLE method requires more CPU time when the multigrid solver is used, a more efficient method will be the result. To ensure stability, the adjusted multigrid solver should be used for the simulation of laminar oxy/acetylene fiames.Kramers Laboratorium voor Fysische TechnologieApplied Science