Richardson and Reynolds number effects on the near field of buoyant plumes: flow statistics and fluxes

Abstract

The near-field characteristics of highly buoyant plumes, commonly referred to as lazy plumes, remain relatively poorly understood across a range of flow conditions, particularly compared with our understanding of far-field characteristics. Here, we perform fully resolved three-dimensional numerical simulations of round helium plumes to characterize the effects of different inlet Richardson, ${Ri}_0$ , and Reynolds, ${Re}_0$ , numbers on first- and second-order statistical moments as well as average vertical fluxes in the near field. For sufficiently high ${Re}_0$ at a particular ${Ri}_0$ , heavy air can penetrate the core of the plume, reminiscent of spikes in the classical Rayleigh–Taylor instability. In the most turbulent simulation, this penetration becomes so strong that a recirculation zone forms along the centreline of the plume. Vertical fluxes are found to scale linearly with vertical distance from the plume inlet, consistent with experimental and numerical observations (Jiang & Luo, Flow Turbul. Combust., vol. 64, 2000, pp. 43–69; Kaye & Hunt, Intl J. Heat Fluid Flow, vol. 30, 2009, pp. 1099–1105). We analytically derive this linear scaling from the governing equations by making a radial entrainment hypothesis whereby ambient fluid is entrained, on average, only in the radial direction at a finite distance from the inlet. Through this derivation, we identify physical mechanisms that can cause these relationships to remain only approximately valid for the present simulations. Lastly, we identify near-field power-law scaling relations for the flux magnitudes based on ${Ri}_0$ , and also examine vertical profiles of the non-dimensional Richardson number flux. Ultimately, insights from the present simulations are used to define near-, intermediate- and far-field regions in buoyant plumes.