Gaseous diffusion ¯ames: simple structures and their interaction A. Cavaliere a, * , R. Ragucci b a Dip. di Ingegneria Chimica, Universita Á degli Studi Federico II, Piazzale Tecchio 80, 80125 Naples, Italy b Istituto di Ricerche sulla Combustione C.N.R., Naples, Italy Received 10 November 1999; accepted 21 November 2000 Abstract This is a synoptic overview of a selection of works dealing with single diffusive structures, with their mutual interaction in simple ¯ows and their statistical modeling in complex ¯ows. The focus is on reacting conditions pertaining to gaseous diffusion ¯ames, but isothermal structures are also described when they are of some conceptual interest. This paper considers only few representative works for each subject, which are functional in explaining the key characteristics of the diffusive structures. The extension, given to single subjects, is not weighed according to the number of related publications but on the relevance to the basic understanding of the general framework concerning diffusion ¯ames. One-dimensional structures are ®rst discussed. They are ordered according to the number of balance equation terms needed for their description. Two-dimensional 2D) structures are then introduced following an order based on their convolution level. Some pioneering work on three-dimensional structures is further quoted. The temporal evolution of simple structures in quiescent or simple ¯owing 2D systems is considered. The latter case is exploited to present classi®cation of diffusion-controlled mixing regimes. Modeling characterization approach of turbulent diffusion ¯ames is also described in order to yield a self-suf®cient didactic presentation. The approach based on the ¯ame surface density model is speci®cally discussed because of its potential use in the determination of qualitative and quantitative features of simple diffusion ¯ames. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Diffusion ¯ames; Mixing; Structure Contents 1. Introduction .................................................................. 548 2. De®nitions ................................................................... 549 2.1. Conserved and material variables, tracers ......................................... 549 2.2. Reference surfaces ......................................................... 551 2.2.1. Eulerian surfaces interface, isosurface) .................................... 551 2.2.2. Lagrangian surfaces material, intermaterial) ................................ 552 2.2.3. Eulerian±Lagrangian surfaces ........................................... 553 2.2.4. Surface evolution .................................................... 553 3. Methodological approaches ....................................................... 555 3.1. Experimental approaches ..................................................... 555 3.2. Theoretical approaches ...................................................... 555 3.3. Numerical approaches ....................................................... 556 4. Simple diffusion ®elds and ¯ames .................................................. 556 4.1. Simple 1D plane structure .................................................... 557 4.1.1. Unsteady, diffusive layers .............................................. 557 Progress in Energy and Combustion Science 27 2001) 547±585 PERGAMON www.elsevier.com/locate/pecs 0360-1285/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0360-128500)00031-9 * Corresponding author. Tel.: 139-81-768-2264; fax: 139-81-513-6936. E-mail address: antcaval@unina.it A. Cavaliere).