Paul Andrews Libby Contribution to Zone-Conditioned Average Transport Equations in Intermittent Turbulent Flows

Abstract

ABSTRACT Professor Paul A. Libby has made lasting contributions to the theory and modeling of turbulent premixed flames. A less known subject of his research relates to the conditioning of the local and instantaneous Navier-Stokes equations for either the turbulent or the irrotational flow regions separated by a thin interface. He postulated an evolution equation for the intermittency function, a generalized function introduced by experimentalists in the decades of 1960 and 1970, which is unity in the vorticity-containing turbulent flow and zero in the surrounding irrotational flow. This intermittency function equation allowed the derivation of transport equations for average variables conditioned either to the turbulent or the vorticity-free regions. Paul A. Libby formalism is explained in this paper. Further research triggered by Libby’s seminal work is then reported. An exact expression is obtained for his “intermittency creation” term, which allows a simple physical interpretation of the entrainment and zone interactions. This methodology is applied to an intermittent scalar in a turbulent flow of a variable density fluid. Various types of intermittent flows with zonal discrimination, based on vorticity, scalar and scalar-gradient criteria, are presented. The analogy of turbulent/nonturbulent interfaces with propagating turbulent premixed flames is remarked.