Natural versus forced convection in laminar starting plumes

Abstract

A starting plume or jet has a well-defined, evolving head that is driven through the surrounding quiescent fluid by a localized flux of either buoyancy or momentum, or both. We studied the scaling and morphology of starting plumes produced by a constant flux of buoyant fluid from a small, submerged outlet. The plumes were laminar and spanned a wide range of plume Richardson numbers Ri. Ri is the dimensionless ratio of the buoyancy forces to inertial effects, and is thus our measurements crossed over the transition between buoyancy-driven plumes and momentum-driven jets. We found that the ascent velocity of the plume, nondimensionalized by Ri, exhibits a power law relationship with Re, the Reynolds number of the injected fluid in the outlet pipe. We also found that as the threshold between buoyancy-driven and momentum-driven flow was crossed, two distinct types of plume head mophologies existed: confined heads, produced in the Ri > 1 regime, and dispersed heads, which are found in the Ri < 1 regime. Head dispersal is caused by a breakdown of overturning motion in the head, and a local Kelvin-Helmholtz instability on the exterior of the plume.Comment: 8 pages, 8 figures, accepted for publication in Physics of Fluids (final version with corrections

Temperature and velocity measurements of a rising thermal plume

“…For example, various alternate scaling relationships have been proposed for the rise velocity of plumes [ Batchelor , ; Whitehead and Luther , ; Griffiths and Campbell , ; Moses et al ., ]. This may in part be because several studies have examined plumes generated by the injection of buoyant fluid [e.g., Olson and Singer , ; Griffiths and Campbell , ; Rogers and Morris , ; Bercovici and Mahoney , ], rather than those generated by a heater (which is closer to the nature of the heating in the mantle). The use of injection systems creates an additional controlling variable, the volume flow rate, and the difference in the source of buoyancy is likely to have a significant effect on the fluid dynamics.…”

Dynamics of a laminar plume in a cavity: The influence of boundaries on the steady state stem structure

“…He further suggested that the buoyancy of the head increases since the head is fed by the stem as a result of the slower upwards motion of the head compared with the steady stem below it. Since then, much effort has been devoted to understand plume dynamics and to provide scalings for plume ascent velocity [ Whitehead and Luther , ; Shlien , ; Olson and Singer , ; Chay and Shlien , ; Griffiths and Campbell , ; Moses et al ., ; Couliette and Loper , ; van Keken , ; Kaminski and Jaupart , ; Rogers and Morris , ; Davaille et al ., ] or for steady state plume stem structure [ Batchelor , ; Fujii , ; Shlien and Boxman , ; Tanny and Shlien , ; Worster , ; Moses et al ., ; Olson et al ., ; Couliette and Loper , ; Vasquez et al ., ; Laudenbach and Christensen , ; Whittaker and Lister , , 2006b; Davaille et al ., ]. Additionally, plume growth by entrainment of fluid by thermal diffusion, continuous feeding from the source, laminar entrainment of surrounding material at the rear of a leading vortical head has been studied [ Griffiths and Campbell , ; Moses et al ., ; Couliette and Loper , ; Kumagai , ].…”

Autocatalytic plume pinch-off

“…In their early stages, the external appearances of autocatalytic plumes are similar to non-reacting, laminar plumes [1,6,7]. This suggests that the interior flow profiles of autocatalytic and non-reacting laminar plumes might be similar, at least initially.…”

“…In order to quantify the thermal and compositional contributions to buoyancy separately, we define two Rayleigh-like numbers [25,26]. The thermal and concentration Rayleigh numbers are Ra T = gα T L 3 νD ∆T and Ra c = gα c L 3 νD ∆c, (7) respectively. Here, L is a length scale that we choose to be equal to the diffusive thickness of the reaction front, defined by = √ Dτ , where τ is a reaction time scale.…”

“…(Color online) The aspect ratio w h / h for autocatalytic plumes in a 30% (dark circles, blue online) and 40% (light circles, orange online) glycerol solution. The horizontal grey line indicates the constant value of w h / h = 1.24 ± 0.04 for non-reacting forced plumes[7]. Here, t = 0 corresponds approximately to when a vortex ring first forms in the head, not to the moment when the reaction front emerges from the capillary tube.…”