Investigation into the finite element analysis of enclosed turbulent diffusion flames

• Published in: Applied mathematical modelling Vol. 13; no. 5; pp. 258 - 267
• Main Authors: Benim, A.C., Zinser, W., Schnell, U.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 1989; Elsevier Science
• Subjects: combustion; eddy dissipation concept; Enclosed turbulent diffusion flames; Exact sciences and technology; finite element method; finite elements; k-∈ turbulence model; mathematical models; Mathematics; moment method; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, miscellaneous problems; Sciences and techniques of general use; segregated formulation; turbulent flow; Enclosed turbulent diffusion flames; eddy dissipation concept; k-∈ turbulence model; segregated formulation; moment method; finite elements; Turbulent flame; Finite element method; Equation resolution; Combustion; Diffusion flame; Partial differential equation
• ISSN: 0307-904X
• DOI: 10.1016/0307-904X(89)90069-3

A complete finite element model of enclosed turbulent diffusion flames is presented. A velocity-pressure formulation is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the finite element discretized continuity equation considering the relationships established between the velocity and pressure in the finite element discretized momentum equations. The state of turbulence is defined by a k-∈ model of turbulence. Near solid boundaries, a wall-functions approach is employed. The combustion rates are estimated by the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate elliptic differential equation for the radiation intensity. The proposed finite element model is verified by investigating several examples. The results are compared with experiments and finite difference predictions.