IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

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.

Department of Applied Mechanics

Fulltext

Journal of Fluid Mechanics

Length of near-wall plumes 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.

World University root node

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

We study convection driven by an unstable concentration difference across a horizontal permeable membrane due to a layer of brine lying over a layer of water across the membrane. The flow through the membrane changes the phenomena drastically from those in Rayleigh Benard convection; different regimes of convection across the membrane are observed &nbsp;[5]. By using a coarser membrane compared to that by [5], we find a new regime of convection where the Sherwood number scales linearly with the Rayleigh number. The planform plume-structure in this regime is presented. &nbsp;Phenomenology proposed is able to explain the flux scaling in the new regime.

Fluid Mechanics and Fluid Power conference

THE TRANSITION FROM ADVECTION TO DIFFUSION IN CONVECTION ACROSS A HORIZONTAL PERMEABLE MEMBRANE

We present results on parametrically forced capillary waves in a circular cylinder, obtained in the limit of large fluid depth, using two low-viscosity liquids whose surface tensions differ by an order of magnitude. The evolution of the wave patterns from the instability to the wave-breaking threshold is investigated in a forcing frequency range (f = ω/2π = 25-100 Hz) that is around the crossover frequency (ωot) from gravity to capillary waves (ωot/2≤ω/2 ≤ 4ωot). As expected, near the instability threshold the wave pattern depends on the container geometry, but as the forcing amplitude is increased the wave pattern becomes random, and the wall effects are insignificant. Near breaking, the distribution of random wavelengths can be fitted by a Gaussian. A new gravity-capillary scaling is introduced that is more appropriate, than the usual viscous scaling, for low-viscosity fluids and forcing frequencies &lt; 103 Hz. In terms of these scales, a criterion is derived to predict the crossover from capillary- to gravity-dominated breaking. A wave-breaking model is developed that gives the relation between the container and the wave accelerations in agreement with experiments. The measured drop size distribution of the ejected drops above the breaking threshold is well approximated by a gamma distribution. The mean drop diameter is proportional to the wavelength determined from the dispersion relation; this wavelength is also close to the most likely wavelength of the random waves at drop ejection. The dimensionless drop ejection rate is shown to have a cubic power law dependence on the dimensionless excess acceleration ε′d an inertial-gravitational ligament formation model is consistent with such a power law. © 2009 Cambridge University Press.

Evolution and breaking of parametrically forced capillary waves in a circular cylinder

We investigate the effects of wall-normal velocity ($V_b$) on high Schmidt number ($Sc&gt;600$) natural convection boundary layers formed on permeable horizontal surfaces. Using integral boundary layer equations, we define a blowing parameter, &nbsp;$S = (Re_L^5/ Gr_L)^{1/8}$ to characterize the strength of blowing relative to the buoyancy and the viscous effects. The analysis is performed for $0.1\leq S \leq 0.26$. The upper limit being given by $Re_d = V_b\delta_v/\nue &lt;1$ so that inertial effects in the boundary layer are small. The lower limit of $S$ ensures that there is negligible diffusive mass transfer in the species boundary layer. As expected, blowing increases the velocity boundary layer thickness and the species boundary layer thickness; the effect is felt more on the species boundary layer thickness. Blowing also increases the horizontal velocity in the boundary layers. We show that the species boundary layer thickness scales as $x(Re_x/Gr_x)^{1/4}$ while the horizontal velocity scales as $V_b (Gr_x/Re_x)^{1/4}$.

12th Asian Congress of Fluid Mechanics

EFFECT OF WALL-NORMAL FLOW ON HIGH Sc NATURAL CONVECTION BOUNDARY LAYERS

We investigate the effects of uniform wall-normal velocity ($V_b$) on high Schmidt number ($Sc$&gt;600) indirect natural convection boundary layers. The study is limited for the negligible inertial effects ($Re = V_b\delta_v/n$) and negligible diffusive mass transfer in $\delta_d$. Using integral boundary layer equations, we define a non-dimensional blowing parameter, $S = (Re_L^5/ Gr_L)^{1/8}$ to quantify the strength of normal blowing relative to buoyancy and viscous effects. The analysis is conducted for $0.1&lt;S&lt;0.26$. Blowing increases the velocity boundary layer thickness ($\delta_v$), the species boundary layer thickness ($\delta_d$), the horizontal velocity (u) and the wall shear stress ($\tau_w$). We show that $\delta_d/x = 1.59(Re_x/Gr_x)^{1/4}$ and $u(\eta,x)/V_b = u(\eta) (Gr_x/Re_x)^{1/4}$. Unlike in shear boundary layers, $t_w$ increases with increase in blowing parameter and the coefficient of drag, $C_D$ scales as $2.4/Re_L$. The concentration in the species boundary layer averaged over half of the mean plume spacing, $\lambda/2$ has a quadratic dependence on the vertical coordinate.

IISc Centenary – International Conference on Advances in Mechanical Engineering (IC-ICAME)

High Schmidt number natural convection boundary layers with blowing

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

The geometrically different planforms of near-wall plume structure in turbulent natural convection, visualized 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 1010-1011 at Schmidt number of 602. The scaling is seen for a length scale range of 25 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 for the near-wall plume structures. © 2005 Cambridge University Press.

The multifractal nature of 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 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

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.

Department of Mathematics

Integral Analysis of Laminar Indirect Free Convection Boundary Layers with Weak Blowing for Schmidt No. ∼ 1

We present the dissolution characteristics of lac dye from lac resin. Lac samples of various mass ML are agitated at various rates (ω) in different volumes of water (Vw) having various granule size (SL ) and the concentration of dye in water was measured as a function of time. We show that the remaining amount of lac dye in the lac samples reduce exponentially with time. Time for achieving 30% of the initial mass of the dye in the lac sample (t30) is seen to decrease with increase in surface area of the lac (SL), agitation rate (ω) and the volume of the water. We obtain a relation for t30 as t30ω=f(ζ) where ζ=(C_(ⅆ_i ) ρ_L S_L v_w^(1/3))/ML&nbsp; and f(ζ) is an exponential function. This relation could now be used to design intervention strategies in the washing process to improve the process.