A numerical procedure for the computation of confined, axisymmetric, turbulent diffusion flames is developed. The governing elliptic partial differential equations are solved by the finite-element method to generate the flexible mesh in flow regions with physical and geometrical complexity. This algorithm adopts a sequential velocity-pressure formulation that allows the uncoupling of pressure and velocity. In order to minimize the numerical diffusion, the streamline upwind/Petrov-Galerkin formulation is employed. Turbulence is represented by the k-e model, and the combustion process involves an irreversible one-step reaction at an infinite rate. The time-averaged mixture properties are obtained by weighting the property function with a beta probability density function (pdf). Predictions are made for turbulent reacting and nonreacting flow systems with recirculation, and the results are compared with experimental data. Nomenclature a,b -parameter in /3 function pdf C p = specific heat C^ = constants in the turbulent model / = mixture fraction g = square of fluctuations of mixture fraction h = enthalpy of mixture Hf U = heat of reaction k = kinetic energy of turbulence M = molecular weight P = pressure R = universal gas constant r = distance in radial direction s = stoichiometric mass of oxidant T = temperature u = axial velocity component v -radial velocity component W = weighting function x = axial coordinate distance j8 = conserved scalar £ = nondimensional mixture fraction e = rate of dissipation of turbulence energy fji = molecular viscosity Ht = turbulent viscosity p = mixture density $ = continuous weighting function = discontinuous weighting function Subscripts A = airstream F = fuel stream fu -fuel ox = oxidant pr = product Superscripts = correction * = estimation

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