Experiments on a reacting plume—2. Conditional concentration statistics

Abstract

Abstract A detailed study is made of reactive scalar statistics conditional on the value of a conserved scalar in a non-buoyant reactive plume of NO in a turbulent grid flow doped with O 3 using the reaction NO + O 3 → NO 2 + O 2 + 200 kJ mol −1 (in the absence of UV radiation). Use of such conditional statistics makes it possible to separate the effects of turbulent mixing and chemical reaction. Simultaneous measurements of two reactive scalars and two orthogonal turbulent velocities are made using high-resolution instruments. Radial profiles of scalar statistics are taken through the plume. It is found that the reactive scalar means conditional on a conserved scalar lack significant dependence on radial position and that conditional variance around the conditional mean is relatively small. This is in agreement with similar findings in completely different types of turbulent reacting flows. Detailed experiments have been conducted at a single location where the ratio of initial reactant concentrations has been varied by a factor of 30 and the Damko¨hler number (the ratio of the flow timescale to that of the chemical reaction) by a factor of 6, but without measurable effect on the flow field. The conditional reactive scalar results are presented and their usefulness for investigating the reactive behaviour of the plume is demonstrated. Use is made of the stoichiometiic distance, the location where the unconditional mean conserved scalar is equal to the initial concentration of ambient reactant. Preliminary results of the conditional moment closure (CMC) model of Klimenko (1990) and Bilger (1993) are compared with conditional experimental data. The CMC model leads to significant simplification of the equations governing variation of reactive scalars in the flow. The equations are solved numerically with low computational requirements. Weighting of the conditional values with the conserved scalar probability density function yields the conventional reactive scalar means. CMC modelling results are shown to be in good agreement with the experimental data. Limiting cases (equilibrium and reaction dominated) for the reactive scalar statistics are derived from the conserved scalar statistics and form bounds on both the experimental and CMC predictions as expected from theoretical considerations. Application of the CMC model to atmospheric flows is discussed. A good estimate of the covariance is also made from the conditional reactive scalar means.