A FULLY COUPLED, IMPLICIT, NUMERICAL SCHEME FOR LAMINAR AND TURBULENT PARABOLIC FLOWS

A fully coupled, implicit, numerical scheme has been developed for solving highly sti¤ systems of parabolic conservation equations. The Þnite-domain equations are formed by integration of the governing conservation equations, expressed in vector notation, over control volumes. The central idea is to put the discretized vector equations as Di¤erential/Algebraic equations (DAE) in the context of numerically solving a system of sti¤ ordinary di¤erential equations. One of the beneÞts of the present numerical method is that the Jacobian matrix retains its banded property and thus the problems related to computer storage are eliminated. The mathematical interface that the code employs is a computer program that is most e¦cient for solving the sti¤ equations usually found in chemical kinetics. The method has shown good convergence rate and numerical stability. The mathematical formulation is capable of modelling laminar and turbulent ßows. Two study cases are considered in this work to illustrate the applicability of the numerical method. Case one corresponds to a numerical simulation of a laminar non-premixed methaneÐair ßame. The chemical processes are described with a four-step reduced mechanism that derives from a larger mechanism with twenty-Þve reaction steps. The predicted velocity, temperature, and mole fractions of the conÞned laminar round-jet ßame investigated here are compared with experimental data taken from the literature. The versatility of the present solver for predicting high Reynolds number ßows is demonstrated by simulating an isothermal turbulent air jet, labelled as case two. A standard two-equation turbulence model is used to simulate the turbulence processes. The analytical velocity distribution for a turbulent submerged jet is used as a benchmark to test the performance of the model for turbulent jets.