Entrainment in variable-density jets

The entrainment of ambient fluid into a variable-density jet is typically quantified using an entrainment coefficient $\alpha$ . Here, we investigate the dependence of $\alpha$ on the ratio of the jet's density $\rho _m$ and that of the ambient fluid $\rho _0$ . Current parametrisations of $\alpha$ rely on a scaling inferred from early laboratory experiments (Ricou & Spalding, J. Fluid Mech. , vol. 11, 1961, pp. 21–32). We demonstrate analytically that the experiments preclude definitive conclusions regarding the dependence of $\alpha$ on $\rho _m / \rho _0$ and that the underlying physical processes therefore warrant closer attention. To investigate the physics behind the dependence of entrainment on the density ratio we use a Favre-averaged entrainment decomposition. The decomposition is applied to data from large-eddy simulations of jets characterised by density ratios $\rho _m / \rho _0$ spanning over two orders of magnitude that have been verified against experimental data. Changes in the shape of the velocity profile are a significant contributor to entrainment in the near field due to the breakdown of the potential core, and persist over larger streamwise distances in heavy releases than in light releases. Therefore, to focus exclusively on the effects of density ratio, we study the region where the shape changes have become small but the density ratio is still significant. We show that the dimensionless turbulent kinetic energy production and mean kinetic energy flux depend strongly on the density ratio, both for our large-eddy simulation data and for recent experiments. Despite this, the entrainment coefficient is practically constant in this region and has value $\alpha \approx 0.07$ for all simulations.