Experimental study of three-scalar mixing in a turbulent coaxial jet

Abstract

In the present study we investigate three-scalar mixing in a turbulent coaxial jet. In this flow a centre jet and an annular flow, consisting of acetone-doped air and ethylene respectively, are mixed with the co-flow air. A unique aspect of this study compared to previous studies of three-scalar mixing is that two of the scalars (the centre jet and air) are separated by the third (annular flow); therefore, this flow better approximates the mixing process in a non-premixed turbulent reactive flow. Planar laser-induced fluorescence and Rayleigh scattering are employed to measure the mass fractions of the acetone-doped air and ethylene. The results show that the most unique aspects of the three-scalar mixing occur in the near field of the flow. The mixing process in this part of the flow are analysed in detail using the scalar means, variances, correlation coefficient, joint probability density function (JPDF), conditional diffusion, conditional dissipation rates and conditional cross-dissipation rate. The diffusion velocity streamlines in scalar space representing the conditional diffusion generally converge quickly to a manifold along which they continue at a lower rate. A widely used mixing model, interaction through exchange with mean, does not exhibit such a trend. The approach to the manifold is generally in the direction of the ethylene mass fraction. The difference in the magnitudes of the diffusion velocity components for the two scalars cannot be accounted for by the difference in their dissipation time scales. The mixing processes during the approach to the manifold, therefore, cannot be modelled by using different dissipation time scales alone. While the three scalars in this flow have similar distances in scalar space, mixing between two of the scalars can occur only through the third, forcing a detour of the manifold (mixing path) in scalar space. This mixing path presents a challenging test for mixing models since most mixing models use only scalar-space variables and do not take into account the spatial (physical-space) scalar structure. The scalar JPDF and the conditional dissipation rates obtained in the present study have similarities to those of mixture fraction and temperature in turbulent flames. The results in the present study provide a basis for understanding and modelling multiscalar mixing in reactive flows.

Joint probabilities and mixing of isolated scalars emitted from parallel jets

“…JPDFs are reported for homogenous isotropic turbulence (Juneja & Pope 1996), scalar mixing layers (Bilger, Saetran & Krishnamoorthy 1991;Sawford & de Bruyn Kops 2008) and coaxial jets (Cai et al 2011;Rowinski & Pope 2013). In the binary scalar topology, the mixing path between the two scalars falls on a straight line where Φ A + Φ B = 1 (Sawford & de Bruyn Kops 2008).…”

“…In the binary scalar topology, the mixing path between the two scalars falls on a straight line where Φ A + Φ B = 1 (Sawford & de Bruyn Kops 2008). In the isolated topology, scalars must first mix with ambient fluid before mixing with each other (Cai et al 2011). The result is the mixing path between the two scalars must first make a detour toward the ambient state (Sawford & de Bruyn Kops 2008;Cai et al 2011); however, the size and shape of this detour depends on the separation between the scalars and the nature of the turbulence.…”

“…In the isolated topology, scalars must first mix with ambient fluid before mixing with each other (Cai et al 2011). The result is the mixing path between the two scalars must first make a detour toward the ambient state (Sawford & de Bruyn Kops 2008;Cai et al 2011); however, the size and shape of this detour depends on the separation between the scalars and the nature of the turbulence. For reactive flows, the mixing path also depends on travel time and reactivity of the two scalars expressed as the Damköhler number (Bilger et al 1991).…”

“…In scalar space the conditional diffusion has two vector components, γ A and γ B , describing the transport velocity of the JPDF (Cai et al 2011). The magnitude and direction of the conditional diffusion is important as it describes not only the mixing path of the two scalars, but also the speeds of various mixing processes in the flow.…”

“…The magnitudes of the diffusion velocity vary considerably across scalar space (compare with Cai et al 2011). Scalars that still exist in strong concentrations (e.g.…”