Development of an algebraic reaction rate closure for the numerical calculation of turbulent premixed methane, ethylene, and propane/air flames for pressures up to 1.0 MPa

In this work a simplified but effective closure for the numerical simulation of turbulent premixed flames is developed, being applicable for pressures up to 1.0 MPa. Here the reaction source term of the reaction progress variable is modeled with an algebraic relation for the flame-wrinkling ratio AT/A¯. The closure is based on a three-parameter description, including an explicit pressure term. In order to determine the fit parameters, an extensive numerical optimization study is performed, where the calculated and measured flame angles of 101 different Bunsen-type flames are compared for operating pressures between 0.1 and 1.0 MPa. Experimental data on 20-mm Bunsen-type flames for lean methane/air, ethylene/air, and propane/air mixtures for different flow and turbulence inlet conditions were provided by the group of Kobayashi (Japan). For each fuel the three parameters of the algebraic relation are varied such that a minimum least-square deviation between computed and measured flame cone angles is achieved. It is found that for all the fuels investigated this relation collapses to a unique equation, in which the Lewis number of the fuel/air mixture is included. It has been proposed recently that differential molecular transport effects, as described by the Lewis number, may be related not only to laminar flame instability effects at low turbulence but also to visible effects at higher degrees of turbulence. This fits to our finding of the explicit Lewis number dependency in the source term. It is possible to substantiate the applicability of this algebraic closure for methane/air flames for higher pressures up to 3 MPa in reasonable agreement with experimental data, as described in Appendix A.