A Split-Operator, Finite-Difference Solution for Axisymmetric Laminar-Jet Biffusion Flames

Abstract

A split-operator numerical method is developed to solve the steady laminar diffusion flame problem. Splitting the chemical kinetic terms from the fluid-mechanical terms ameliorates some of the difficulties associated with the disparate time scales and stiffness in the set of equations which describes highly exothermic diffusion flames. Implicit differencing methods enhance the numerical stability of both operators. Special care is taken to maintain the accuracy of the solution, and the coordinate system is varied continuously to follow the flame shape. The present method allows a detailed study of the complex interaction between the fluid mechanics and the finite-rate chemical kinetics in a flame. Cpk = Dk g Nomenclature constant-pressure heat capacity of the gas mixture constant-pressure heat capacity of the kth species trace diffusion coefficient of kth species acceleration due to gravity enthalpy of species A: per unit mass number of radial nodes number of species pressure radial dimension universal gas constant, ergs/mole-K source term in general transport equation temperature axial velocity radial velocity transformed radial velocity formation rate of kth species by chemical reaction molecular weight of kth species axial dimension mass fraction of kth species coordinate spread angle transformed axial dimension origin of coordinate system referenced to nozzle exit transport coefficient in general transport equation conductivity transformed radial coordinate mass density of the gas mixture viscosity chemical symbol for kth species J K p r R S T u v V &k Wk x Yk a £0 e X rj p fjL Xk Subscripts I = axial node index j ' • = radial node index & — species index n — reaction index e = edge condition