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Show Preconditioned Navier-Stokes Solution Technique for Laminar Methane-Air Non-Premixed Combustion Albert D. Harvey III* The Dow Chemical Company Plaquemme, Louisiana 70765 Jack R. Edwardsf North Carolina State University Raleigh, North Carolina 27695 Abstract A solution-adaptive Navier-Stokes technique is presented which incorporates a fully implicit solution algorithm with low Mach number preconditioning. The equations are formulated for generalized n-species/ra-reactions Arrhenius chemistry and are cast in a generalized coordinate frame for application to arbitrary geometries. The grid adaption strategy employs a line-by-line equi-distribution concept in which grid points are re-distributed along each coordinate line during the course of the solution process according to gradients of user specified dependent variables. The solution technique is demonstrated on a laminar methane-air diffusion flame using a 17-species/58-reaction chemistry mechanism. Computed results for temperature, mole fraction, and velocity compare favorably with experimental results. Typical computations require a few hours C P U time on a standard desktop engineering workstation. The accuracy of the computed results illustrate that the solution strategy presented in this paper is an attractive means of computing reacting flows with detailed chemistry. Introduction There have been significant advances in the development of algorithms for modeling of turbulent combustion in the last several years. This continued progress together with the ever improving performance of desktop computer hardware will eventually render combustion calculations tractable to industry for some applications. However, turbulent combustion in real industrial type geometries such as pyrolysis furnaces containing sophisticated low NOj- burner designs and process heaters with multiple fuel and air feed locations will continue to be in the forefront of research for years to come. Computation of these real industrial type problems in three-dimensional geometries is still, for the most part, intractable. In this paper we describe a computational strategy capable of addressing large scale reacting flow problems and we successfully demonstrate these techniques on a laminar non-premixed flame with detailed finite rate chemistry. The expense in computing flows with detailed chemistry mechanisms is due primarily to the additional cost associated with solving a large number of species equations. The large variations in time scales associated with the chemistry and the fluid dynamics can result in the large equation set being numerically stiff or poorly conditioned. Another source of complexity arises in solving reacting flows when the convective speed is significantly less than the acoustical speed. * Research Associate, Research & Development; correspondence to: bharvey@dow.com f Assistant Professor, Department of Mechanical and Aerospace Engineering Since very low Mach number flows are most common in the petrochemical industry, a solution to this particular problem is of primary interest. The large differences in the convective and acoustical velocities result in poor coupling of the velocity and pressure fields and introduce additional numerical stiffness. The release of heat by many exothermic reacting systems such as thermal chlorination, incineration and combustion causes interactions between the chemistry and fluids that are strong. Furthermore, the high temperatures associated with exothermic reactions lead to thermophysi-cal property variations of an order of magnitude within the reaction zone. Combustion represents the intersection of two highly non-linear phenomenon turbulence and chemistry, both of which possess multiple time and length scales. All these characteristics of reacting flows command a numerical approach which prescribes strong physical coupling between each transport equation. This paper presents a preconditioned Navier-Stokes method which uses a strongly coupled solution procedure for the finite rate chemistry. The type of flow algorithms outline in Patankar (1980) provide the necessary coupling between the velocity and pressure fields for an incompressible flow through the sequential solution of a Poisson equation in pressure and the momentum equations to update the velocity. Using this technique for flows with chemical reactions, additional species transport equations are solved one-by-one, in a sequential fashion using "frozen" velocity, pressure, and species concentration fields. This de-coupled method of solution is inefficient for time dependent solutions of non-reacting compress- 1 |