Received: 30 April 1996/Accepted: 2 September 1997 C. Ghenai, I. Gokalp Centre National de la Recherche Scientifique Laboratoire de Combustion et Syste ` mes Re ´ actifs F-45071 Orle ´ ans ce ´ dex 2, France Correspondence to: C. Ghenai During its different stages, this work was supported by the CNRS, the Conseil Regional Centre, the French Army Research Office, and the European Commission Joule Program. Experiments in Fluids 24 (1998) 347— 353  Springer-Verlag 1998 Correlation coefficients of the fluctuating density in turbulent premixed flames C. Ghenai, I. Gokalp Abstract Two-point density measurements by laser induced Rayleigh scattering are used in this study to fully characterise the scalar field in a Bunsen type turbulent premixed flame. The two points are separated within the flame brush in the axial or radial directions. Correlation coefficients are obtained by comparing the evolution of one-point density fluctuations in time or the two-point density fluctuations in both space and time. Time and length scales of the scalar field, and the mean convection velocity of the turbulent scalar structures are deduced from these correlation coefficients. Time scales are calculated from the auto-correlation coefficients, length scales are determined from the space correlation coefficients and the mean convection velocity of the scalar structures in the axial direction is deduced from the space—time correlation coef- ficients. The relevance of these results for analysing and modelling the structure of turbulent premixed flames is discussed. List of symbols r radial separation  time separation z axial separation x spatial separation I  Rayleigh scattering intensity l integral length scale lz integral length scale in the axial direction T integral time scale U 0 exit cold flow velocity R () auto-correlation coefficient R (x) space correlation coefficient R (x, ) space-time correlation coefficient V c convection velocity of the scalar turbulent struc- tures z axial position  equivalence ratio  density Subscripts  mean value , fluctuation 0 reference condition 1 Introduction The structure of turbulent premixed flames depends on many parameters related to the composition of the mixture, as well as to its turbulence structure. Recent developments in this research area emphasis the importance of the scalar fields, which are related to the space and time dynamics of instan- taneous flame fronts within the average flame brush. For example, when the turbulence Reynolds number is high and the chemistry is fast (high Damkohler number), flamelet models are able to predict, at least qualitatively, the mean local reaction rates. One such model, the Bray—Moss—Cham- pion—Libby model, in its temporal or spatial versions, proposes closure assumptions for the chemical source term based on the space and time statistics of instantaneous flame fronts (Bray et al. 1988; Bray 1990). Also, all the models based on the flame surface density concept make use of the scalar field character- istics of turbulent premixed flames (Bray and Peters 1994; Veynante et al. 1994; Trouve ´ and Poinsot 1994). The introduc- tion of the models based on the scalar dissipation rate (Mante and Borghi 1994; O’Young and Bilger 1997) equally strengthen the usefulness of a thorough characterisation of the scalar field in turbulent premixed flames. Several experimental studies have been reported in the literature to characterise the time statistics of the scalar field in turbulent premixed flames by using one-point laser induced Rayleigh light scattering measurements (Gouldin and Haltore 1986; Boukhalfa and Gokalp 1988; Deschamps et al. 1992); but these studies give no direct information on the length scales associated with the fluctuating scalar field and the induced flamelet morphology. Two-point laser induced Rayleigh scattering measurements of the scalar field in methane-air Bunsen type turbulent premixed flames are reported in this study to provide directly and simultaneously the time and length scales of flamelet dynamics, and also other important statistical information (Ghenai et al. 1996). This paper focuses on the determination of space—time correlations of the scalar field from which the associated time and length scales are deduced. The two-point