The Eddy Structure Model of Turbulent Flamelet Propagation, the Expanding Spherical and Steady Planar Cases

Abstract

A structural model of turbulence, composed of vortex tubes which are based on direct simulations of turbulence, is used to model the flame area enhancement found in direct simulations of passive flame propagation. The resulting model produces a turbulent premixed flame speed ST within a chamber which has the experimentally observed integral length scale and turbulence intensity behavior. The excess flame area is proportional to where R, is the flame radius,. is the Taylor length scale and the diameter of the vortex tube, u’ is the turbulence intensity and SL is the burning velocity. This first model yields a linear dependence between and and additionally, gives as the steady-state planar propagation, where A is the integral scale. This planar relation can also be expressed as s/t/ReJ\5SL, and this relation has been shown to correlate experimental turbulent flame speed results and direct turbulence simulations of passive flamelet propagation. A second propagation model uses a function that exhibits a maximum value of to replace the in the above excess area estimate. This eddy structure model yields departure from the linear u’/SL behavior of the first model, and this departure agrees with the experimental results. The maximum in is caused by vortical structures which are not space filling, and depends upon the ratio of. The two constants in this eddy structure model are determined from experimental results, however, their values are close to those estimated from the spatial structure of vorticity. A model of flame propagation for internal combustion applications is proposed and the effect of the chamber geometry upon the turbulent flame speed is discussed.