Second-order model of entrainment in planar turbulent jets at low Reynolds number

Abstract

Turbulent jets and plumes are commonly encountered in natural and industrial environments, and have been the objects of seminal works on turbulent free shear flows. The dynamics of turbulent jets is most often described as a function of the so-called entrainment coefficient, α, which quantifies the entrainment of ambient fluid into the jets. This key parameter has been determined in numerous and extensive experimental, numerical, and theoretical studies of axisymmetric jets. However, data remain scarce on turbulent planar jets. Available studies have shown that at low distance from the source, α increases with the source Reynolds number, and that α increases with distance from the source for large source Reynolds number. But no link has been made between these two kinds of observation so far. To study the relative influence of source Reynolds number, Re0, and distance from source on entrainment in planar turbulent jets, we perform new experiments at low Re0 (between 59 and 424) with three different aspect ratio (185, 370, and 925) and at small and large distances from the source. Our experimental results show no systematic variations of α as a function of Re0 or as a function of the distance from the source. To interpret these observations, we develop a formalism based on the flow velocity profiles, which yields an expression of α as a function of the evolution of the Reynolds shear stress and of the turbulent fluctuations of the radial and vertical velocities. We obtain that the main contribution to entrainment is related to the turbulent shear stress, and that second-order fluctuations of the velocity account for the observed variations of α. The evolution to a fully self-similar regime in which these fluctuations are fully negligible is too slow at small Re0 for this regime to be observed in our experiments, even at the largest distances from the source.