Flux scaling and plume structure in high Ra - high Sc turbulent convection

The arrangement of brine above water across a micro porous permeable membrane is used to study high Rayleigh Number($10^{11}- 10^{10}$) high Schmidt number(650)turbulent convection. The flux shows 4/3$^{rd}$ scaling with line plume as the near wall coherent structures. Shifting of multiple large scale flow cells result in changing near membrane mean shear directions for large aspect ratios. Lower aspect ratios show single large scale flow cell and constant sense of mean shear.Comment: 7 pages, 7 Figures, Published in Proceedings of the Tenth Asian Congress of Fluid Mechanics 17--21, May 2004, Peradeniya, Srilank

Multifractal nature of plume structure in high Rayleigh number convection

The geometrically different plan forms of near wall plume structure in turbulent natural convection, visualised by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range $10^{10}- 10^{11}$ at Schmidt number of 602. The scaling is seen for a length scale range of $2^5$ and is independent of the Rayleigh number, the flux, the strength and nature of the large scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non trivial spatial scaling is proposed to be due to the same underlying generating process of the near wall plume structures.Comment: 11pages, 16 figures Accepted in Journal of Fluid mechanics. Revised version. Added two more figures and related discussion on suggestion of referee

Integral analysis of laminar indirect free convection boundary layers with weak blowing for Schmidt no. ~ 1

Laminar natural convection at unity Schmidt number over a horizontal surface with a weak normal velocity at the wall is studied using an integral analysis. To characterise the strength of the blowing, we define a non-dimensional parameter called the blowing parameter. After benchmarking with the no blowing case, the effect of the blowing parameter on boundary layer thickness, velocity and concentration profiles is obtained. Weak blowing is seen to increase the wall shear stress. For blowing parameters greater than unity, the diffusional flux at the wall becomes negligible and the flux is almost entirely due to the blowing.Comment: 10 pages, published in International Communications in heat and mass transfer,Vol31,No8, 2004, pp 1199 -120

Dynamics of collapse of free-surface bubbles: effects of gravity and viscosity

The rupture of the thin film at the top of a bubble floating at a liquid-gas interface leads to the axisymmetric collapse of the bubble cavity. We present scaling laws for such a cavity collapse, established from experiments conducted with bubbles spanning a wide range of Bond (${10^{-3}<Bo\leq1}$) and Ohnesorge numbers (${10^{-3}<Oh<10^{-1}}$), defined with the bubble radius $R$. The cavity collapse is a capillary-driven process, with a dependency on viscosity and gravity affecting, respectively, precursory capillary waves on the cavity boundary, and the static bubble shape. The collapse is characterised by tangential and normal velocities of the kink, formed by the intersection of the concave cavity opening after the top thin film rupture, with the convex bubble cavity boundary. The tangential velocity $U_t$ is constant during the collapse and is shown to be $U_t=4.5~U_c{\mathcal{W}}_R$, where $U_c$ is the capillary velocity and ${\mathcal{W}}_R(Oh,Bo)={(1-\sqrt{Oh {\mathscr{L}}} )^{-1/2}}$ is the wave resistance factor due to the precursory capillary waves, with $\mathscr{L}(Bo)$ being the path correction of the kink motion. The movement of the kink in the normal direction is part of the inward shrinkage of the whole cavity due to the sudden reduction of gas pressure inside the bubble cavity after the thin film rupture. This normal velocity is shown to scale as $U_c$ in the equatorial plane, while at the bottom of the cavity $\overline{U}_{nb}=U_c(Z_c/R)({\mathcal{W}_R}/ {\mathscr{L}})$, where $Z_c(Bo)$ is the static cavity depth. The total volume flux of cavity-filling, which is entirely contributed by this shrinking, scales as ${Q_T\simeq 2\pi R Z_c U_c}$; remains a constant throughout the collapse.Comment: 22 page

Plume structure in high-Rayleigh-number convection

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 NaCl. 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

Convection due to an unstable density difference across a 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 10<SUP>10</SUP> to 10<SUP>11</SUP> 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 (Δ C) 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 Nu<SUB>b</SUB>~Ra<SUP>2</SUP>/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 λ̅<SUB>b</SUB> , is larger than the mean plume spacing in Rayleigh-Bénard convection (λ̅), and shows a different Ra-dependence. The plume spacings in the advection regime (λ<SUB>b</SUB>) show a common log-normal probability density function at all Ra. We propose a phenomenology which predicts λ̅<SUB>b</SUB> ~√ Z<SUB>w</SUB>Z<SUB>v<SUB>i</SUB></SUB>, where Z<SUB>w</SUB> and Z<SUB>v<SUB>i</SUB></SUB> 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 Δ C, the flux scales as (Δ C/2)<SUP>4/3</SUP>. At lower driving potentials, in the diffusion regime, the flux scaling is similar to that in turbulent RBC