We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers (105 &lt; Ra &lt; 1011) and at three Prandtl numbers (Pr = 0.7, 5.2, 602). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (Lp/A), made dimensionless by the near-wall length scale in turbulent convection (Z w), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to Lp H/A for a given fluid layer of height H. The increase in Pr has a weak influence in decreasing Lp/A. These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces. © 2011 Cambridge University Press.

Baburaj A. Puthenveettil

Department of Applied Mechanics

BUOYANT BOUNDARY LAYERS

FLUID LAYER

GEOMETRIC CONSTRAINT

HORIZONTAL SURFACES

Laminar natural convection

Length scale

NEAR-WALL

Per unit

PLUME LENGTH

PLUME SPACING

PLUMES/THERMALS

Rayleigh number

Total length

TURBULENT CONVECTION

Natural convection

Nusselt number

Laminar boundary layer

convection

CONVECTIVE BOUNDARY LAYER

Laminar flow

Plume

Turbulent boundary layer

Fulltext

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IIT Madras

Journal of Fluid Mechanics

We study the dynamics of line plumes on the bottom horizontal plate in turbulent convection over six decades of Rayleigh number .105 &lt; Raw &lt; 1011/ and two decades of Prandtl number or Schmidt number (0:7 &lt; Pr &lt; 5:3, Sc D 602). From the visualisations of these plumes in a horizontal plane close to the plate, we identify the main dynamics as (i) motion along the plumes, (ii) lateral merging of the plumes and (iii) initiation of the plumes; various other minor types of motion also occur along with these main dynamics. In quantifying the three main motions, we first find that the spatiotemporal mean velocity along the length of the plumes (Vsh) scales as the large-scale flow velocity (VLS), with the fraction of the length of the plumes affected by shear increasing with Raw as Lps=Lp ∼ Ra0:054w Pr-0:12. The mean time of initiation of the plumes t∼, scales as the diffusive time scale near the plate, Z2w =≈, where Zw is the appropriate length scale near the plate, in agreement with Howard (Proc. 11th Int. Congress Applied Mechanics, Munich, 1964, pp. 1109-1115). Merging occurs in a large fraction of the area of the plate, with ∼70% of the length of the plumes undergoing merging at Raw ∼ 1011 and Sc D 602. The fraction of the length of the plumes that undergoes merging decreases with increase in Ra w as, Lpm=Lp ∼ Raw -0:054 Pr0:12; the exponents of Raw and Pr being of the same magnitude but of opposite sign as that in the relation for L ps=Lp. Measurements of the locational means of the velocities of merging of the plumes .Vm/ show that Vm is a constant during each merging cycle at any location. However, the values of these constant velocities depend on the location and the time of measurement, since the merging velocities are affected by the local shear, which is a function of space and time at any Raw -Pr combination. The merging velocities at all Raw and Pr have a common lognormal distribution, but their mean and variance increased with increasing Raw and decreasing Pr. Using mass and momentum balance of the region between two merging plumes, we show that the spatiotemporal mean merging velocities (Vm), which are an order lower than Vsh, scale as the entrainment velocity at the sides of the plumes, averaged over the height of the diffusive layer near the plate. This implies that Vm scales as the diffusive velocity scale near the plate ∼=Zw. The Reynolds number in terms of Vm and the layer height H(ReH) scales as Raw 1=3, in the same way as the Nusselt number (Nu) scales approximately; therefore ReH ∼ Nu. These relations imply that Rew D VmZw=∼ a Reynolds number near the plate, is an invariant for a given fluid in turbulent convection. © 2014 Cambridge University Press.

Dynamics of line plumes on horizontal surfaces in turbulent convection

In natural convection, driven by an unstable density difference due to a heavier fluid (brine) above a lighter fluid (water) across a horizontal permeable membrane, we discover a new regime of convection, where the Sherwood number (Sh) scales approximately as the Rayleigh number (Ra). Inferring from the planforms of plume structure on the membrane and the estimates of velocity through the membrane, we show that such a regime occurs when advection balances diffusion in the membrane, i.e. the Péclet number based on the membrane thickness (Pe) is of order one. The advection is inferred to be caused by the impingement of the large-scale flow on the membrane. Utilizing mass balance and symmetry assumptions in the top and the bottom fluids, we derive an expression for the concentration profile in the membrane pore in the new regime by solving the convection-diffusion equation in the membrane pore; this helps us to obtain the concentration drops above and below the membrane that drive the convection. We find that the net flux, normalised by the diffusive flux corresponding to the concentration drop on the side opposite to the impingement of the large-scale flow remains constant throughout the new regime. On the basis of this finding, we then obtain an expression for the flux scaling in the new regime which matches with the experiments; the expression has the correct asymptotes of flux scaling in the advection and the diffusion regimes. The plume spacings in the new regime are distributed lognormally, and their mean follows the trend in the advection regime. © 2011 Cambridge University Press.

The Pe ∼ 1 regime of convection across a horizontal permeable membrane

We study natural convection driven by unstable concentration differences of sodium chloride (NaCl) across a horizontal permeable membrane at Rayleigh numbers (Ra) of 1010 to 1011 and Schmidt number (Sc) = 600. A layer of brine lies over a layer of distilled water, separated by the membrane, in square-cross-section tanks. The membrane is permeable enough to allow a small flow across it at higher driving potentials. Based on the predominant mode of transport across the membrane, three regimes of convection, namely an advection regime, a diffusion regime and a combined regime, are identified. The near-membrane flow in all the regimes consists of sheet plumes formed from the unstable layers of fluid near the membrane. In the advection regime observed at higher concentration differences (ΔC) across the membrane, there is a slow overturning through-flow across the membrane; the transport across the membrane occurs mostly by advection. This phenomenology explains the observed Nub ∼ Ra2/Sc scaling of the Nusselt number. The planforms of sheet plumes near the membrane show a dendritic structure due to the combined influence of the mean shear due to the large-scale flow and the entrainment flow of the adjacent plumes. The near-membrane dynamics show initiation, elongation and merger of plumes; a movie is available with the online version of the paper. Increase in Ra results in a larger number of closely and regularly spaced sheet plumes. The mean plume spacing in the advection regime λb, is larger than the mean plume spacing in Rayleigh-Bénard convection (λ), and shows a different Ra-dependence. The plume spacings in the advection regime (λb) show a common log-normal probability density function at all Ra. We propose a phenomenology which predicts λb ∼ √ZwZVi, where Zw and ZVi are, respectively, the near-wall length scales in Rayleigh-Bénard convection (RBC) and due to the advection velocity. In the combined regime, which occurs at intermediate values of ΔC, the flux scales as (ΔC/2)4/3. At lower driving potentials, in the diffusion regime, the flux scaling is similar to that in turbulent RBC. © 2008 Cambridge University Press.

Convection due to an unstable density difference across a permeable membrane

Near-wall structures in turbulent natural convection at Rayleigh numbers of 1010 to 1011 at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR = 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. The mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in Rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log-normal probability distribution function, independent of the Rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-Rayleigh-number turbulent natural convection are likely to be laminar mixed convection type. © 2005 Cambridge University Press.

Plume structure in high-Rayleigh-number convection

New Journal of Physics

Physical and geometrical properties of thermal plumes in turbulent Rayleigh–Bénard convection

Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection

Length of near-wall plumes in turbulent convection

Journal	Journal of Fluid Mechanics
ISSN	00221120
Open Access	Yes