Entrainment and bulk flow characteristics of heated and unheated transient plumes using direct numerical simulations

Abstract

An off-source volumetrically heated turbulent transient plume, known as transient diabatic plume (TDP), is compared with an unheated transient plume (TP). Both the TDP and TP are simulated using direct numerical simulations at a source Reynolds number (Re) of 2000. The flow is sufficiently resolved till the Kolmogorov (η) scale. The radius of the TP shows a self-similar behavior of linear increase with height after about five diameters from the source hot-patch. However, the velocity does not show a self-similar behavior. The addition of off-source buoyancy in the TDP triples the vertical velocity and also causes an order of magnitude increase in the vorticity magnitude (ω) due to the effect of the baroclinic torque. Compared to the TP, the entrainment coefficient and radius of the TDP increase and this shows enhanced entrainment due to heating. The transient flows fields are analyzed using local scales based on integral quantities of volume, momentum, and buoyancy. Normalizing the vorticity with these integral scales results in a more uniform scaled ωl for both flows. Hence, for both TP and TDP, we use the same values of ωl to quantify the inner and outer boundaries of the turbulent non-turbulent layer (TNTL). The width of the TNTL (δTNTL) decreases by ∼25% due to heating. The conditionally averaged velocity profiles suggest that very close to the outer irrotational boundary (IB) of the TNTL, the TDP exhibits stronger updrafts and downdrafts in comparison to the TP. Entrainment is studied using the mean relative velocity (⟨vn⟩) defined at the IB. The analysis of the components of ⟨vn⟩ reveal that the viscous diffusion component, which is of the order of the Kolmogorov velocity (uη), is balanced by the baroclinic and viscous dissipation components, while the inviscid term is negligible in comparison.