Combustion and Flame 156 (2009) 608–620 Contents lists available at ScienceDirect Combustion and Flame www.elsevier.com/locate/combustflame Counter-gradient transport in the combustion of a premixed CH 4 /air annular jet by combined PIV/OH-LIF G. Troiani a,∗ , M. Marrocco a , S. Giammartini a , C.M. Casciola b a ENEA C.R. Casaccia, via Anguillarese 301, Rome, Italy b Dipartimento di Meccanica e Aeronautica, Facoltà di Ingegneria, Università di Roma “La Sapienza”, Rome, Italy article info abstract Article history: Received 18 April 2008 Received in revised form 23 September 2008 Accepted 15 December 2008 Available online 20 January 2009 Keywords: Premixed combustion Scalar transport Flamelet PIV LIF A combination of PIV/OH laser induced fluorescence technique is used to measure the conditional – burned and unburned – gas velocity in a turbulent premixed CH 4 /air annular bluff-body stabilized burner. By changing the equivalence ratio from lean to almost stoichiometric, the energy budget of the recirculating region anchoring the flame is altered in such a way to increasingly lift the flame away from the jet exit. The overall turbulence intensity interacting with each flame is thus systematically varied in a significant range, allowing for a parametric study of its effect on turbulent scalar transport under well controlled conditions, always well within the flamelet regime. The component of the flux normal to the average front is found to reverse its direction, confirming the Bray number as a good indicator of gradient/counter-gradient behavior, once the actual incoming turbulence level felt locally by the flame is assumed as the proper control parameter.  2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved. 1. Introduction One of the issues in modeling turbulent premixed combustion concerns turbulent fluxes of scalars such as enthalpy or reactive species concentrations [1]. The simplest assumption amounts to a gradient approximation, where the flux is taken to be proportional to the gradient of the averaged field and with opposite direction, with a proportionality constant called turbulent diffusivity. The va- lidity of this assumption has been questioned in [2] and a number of more recent papers where data sets of different origin, numeri- cal and experimental, have been analyzed. At a basic level, the energy balance equation for the instanta- neous thermal enthalpy h reads ρ  ∂ h ∂ t + U ·∇h  = −∇ · q + ǫ + Dp Dt +  α  h α ( ˙ ω α −∇· j α )  , (1) where ρ is the mass density, U the velocity, q is the heat flux, typically expressed in terms of the Fourier law, ǫ is the dissipa- tion rate of mechanical energy, p the pressure, h α the formation enthalpy of the αth species, j α the diffusive flux and ˙ ω α is the source term in the mass balance for the species. The equation for the αth species mass fraction, Y α = ρ α /ρ with ρ α the correspond- ing mass-density is ρ  ∂ Y α ∂ t + U ·∇ Y α  =˙ ω α −∇· j α . * Corresponding author. E-mail address: guido.troiani@casaccia.enea.it (G. Troiani). In combustion modeling, rather than considering the detailed chemistry, one often assumes an effective one-step reaction in- volving a single reactant species (i.e., the fuel F with mass fraction Y going into products). In this case, temperature and mass frac- tion evolve according to the same dynamics, provided that mass and temperature diffusivities are equal, isobaric conditions hold, and one can neglect dissipation of mechanical energy, heat losses and contributions of fluxes of enthalpy associated with mass- diffusion [1]. The two equations can be combined into a single relationship depending on the progress variable C = (T − T r )/(T p − T r ) = (Y r − Y )/(Y r − Y p ), where T r denotes the reactant temper- ature and T p is the adiabatic flame temperature, i.e. the tempera- ture the products would reach in adiabatic combustion. Y r and Y p are the concentrations of fuel before combustion and in the burnt mixture (possibly non-zero for rich mixture). It follows ρ  ∂ C ∂ t + U ·∇ C  =˙ ω C +∇· ( D C ∇ C ), (2) where ˙ ω C =˙ ω F /(Y p − Y r ) is the proper source term. For com- bustion processes occurring at constant pressure, the density de- pends only on temperature and composition of the mixture, hence ρ = ρ (C ). In practice, one is interested in the averaged form of Eq. (2) given in terms of Favre averages,  C = ρ C / ρ , where the over-bar denotes the usual Reynolds averaging ρ ∂  C ∂ t + ρ  U ·∇  C +∇· ( ρ  u ′′ c ′′ ) = ˙ ω C . (3) 0010-2180/$ – see front matter  2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2008.12.010