COMPARISON OF TURBULENT FLAME SPEEDS FROM COMPLETE AVERAGING AND THE G-EQUATION

A popular contemporary approach in predicting enhanced flame speeds in premixed turbulent combustion involves averaging or closure theories for the G-equation involving both large-scale flows and small-scale tu rbulence. The G-equation is a Hamilton-Jacobi equation involving advec tion by an incompressible velocity field and nonlinear dependence on t he laminar flame speed; this G-equation has been derived from the comp lete Navier-Stokes equations under the tacit assumptions that the velo city field varies on only the integral stale and that the ratio of the flame thickness to this integral scale is small. Thus there is a pote ntial source of error in using the averaged G-equation with turbulent velocities varying on length scales smaller than the integral scale in predicting enhanced flame speeds. Here these issues are discussed in the simplest context involving velocity fields varying on two scales w here a complete theory of nonlinear averaging for predicting enhanced flame speeds without any nd hoc approximations has been developed rece ntly by the authors. The predictions for enhanced flame speeds of this complete averaging theory versus the averaging approach utilizing the G-equation are compared here in the simplest context involving a cons tant mean flow and a small-scale steady periodic flow where both theor ies can be solved exactly through analytical formulas. The results of this comparison are summarized briefly as follows: The predictions of enhanced flame speeds through the averaged G-equation always underesti mate those computed by complete averaging. Nevertheless, when the tran sverse component of the mean flow relative to the shear is less than o ne in magnitude, the agreement between the two approaches is excellent . However, when the transverse component of the mean flow relative to the shear exceeds one in magnitude, the predictions of the enhanced fl ame speed by the averaged G-equation significantly underestimate those computed through complete nonlinear averaging, and in some cases, by more than an order of magnitude. (C) 1995 American Institute of Physic s.