A Puthenveettil Baburaj

In Rayleigh Bénard convection, for a range of Prandtl numbers and Rayleigh numbers, we study the effect of shear by the inherent large-scale flow (LSF) on the local boundary layers on the hot plate. The velocity distribution in a horizontal plane within the boundary layers at each, at any instant, is (A) unimodal with a peak at approximately the natural convection boundary layer velocities; (B) bimodal with the first peak between and, the shear velocities created by the LSF close to the plate; or (C) unimodal with the peak at approximately. Type A distributions occur more at lower, while type C occur more at higher, with type B occurring more at intermediate. We show that the second peak of the bimodal type B distributions, and the peak of the unimodal type C distributions, scale as scales with. We then show that the areas of such regions that have velocities of the order of increase exponentially with increase in and then saturate. The velocities in the remaining regions, which contribute to the first peak of the bimodal type B distributions and the single peak of type A distributions, are also affected by the shear. We show that the Reynolds number based on these velocities scale as, the Reynolds number based on the boundary layer velocities forced externally by the shear due to the LSF, which we obtained as a perturbation solution of the scaling relations derived from integral boundary layer equations. For and aspect ratio, for small shear, similar to the observed flux scaling in a possible ultimate regime. The velocity at the edge of the natural convection boundary layers was found to increase with as; since, this suggests a possible shear domination of the boundary layers at high. The effect of shear, however, decreases with increase in and with increase in, and becomes negligible for at or for at, causing.

We study the spreading of a film from ethanol-water droplets of radii 0:9 mm

We study the effect of shear on the coherent structures near the hot surface, namely, line plumes, in turbulent Rayleigh-Bénard convection (RBC) and turbulent mixed convection (MC) for the range of near-surface Rayleigh numbers 5.75×107≤Raw≤2.17×109 and shear Reynolds numbers 8.02×102≤Re≤15×103 for a Prandtl number range of 10.1≥Pr≥0.7 in water and air. Plumes are visualized by particle scattering in MC in air while they are extracted from the particle image velocimetry fields in RBC in water. We also use the planforms of plume structure obtained by Gilpin et al. [J. Heat Transfer 100, 71 (1978)JHTRAO0022-148110.1115/1.3450506] in MC in water using electrochemical visualization, as well as those obtained by Pirozzoli et al. [J. Fluid Mech. 821, 482 (2017)JFLSA70022-112010.1017/jfm.2017.216] in simulations. The planforms of plume structure show that shear aligns the line plumes and increases their mean spacing λ. An increase in Raw decreases λ, while the resulting increase in Re in RBC, due to the increase of larger large-scale flow strength, counteracts this effect. Further, plumes are seen more spaced and smeared in air, compared to that in water, due to the lower Pr. We show that these complex dependences of λ on Raw, Re, and Pr in RBC and MC can be described by a common scaling law λ∗=λ-λ0=SZsh/D, where λ0 is the mean plume spacing in the absence of shear, S=Re3/Raw is a shear parameter, Zsh=ν/Ush is the viscous-shear length, and D a function of Pr.

We study the expansion of a vortex ring generated due to the spreading of ethanol-water droplets, with ethanol concentration range of 20%≤Ce ≤ 100%, on the surface of a 50-mm-deep water layer. Once deposited on the water layer, the surface tension difference leads to some part of the lighter ethanol droplet spreading as a thin film over the water layer. We observe an expanding vortex ring below the radially spreading film front. We visualize the film spreading from top using aluminum particles, while the vortex is visualized from the side using polyamide particles with laser induced fluorescence (LIF) from the dyed drop used to distinguish the alcohol from the water. Particle image velocimetry (PIV) is used to obtain the velocity and the vorticity fields below the spreading film. Vortex regions and their centers, identified by the λ2 method from the velocity fields, are tracked to determine the vortex expansion. We show that the vortex ring expands with the same velocity of expansion as that of the spreading ethanol film at the free surface, possibly since the vortex ring is created due to the surface tension difference across the film front. Using dimensional arguments, we also propose a scaling for the upward velocity,uΓ, induced by this expanding vortex ring and show that uΓ ∼ t−1/2.

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.

We study concentration-driven natural convection boundary layers on horizontal surfaces, subjected to a weak, surface normal, uniform blowing velocity Vi for three orders of range of the dimensionless blowing parameter 10-8 ≥ J = Re3x/Grx ≥ 10-5, where Rex and Grx are the local Reynolds and Grashof numbers at the horizontal location x, based respectively on Vi and ΔC, the concentration difference across the boundary layer. We formulate the integral boundary layer equations, with the assumption of no concentration drop within the species boundary layer, which is valid for weak blowing into the thin species boundary layers that occur at the high Schmidt number (Sc - 600) of concentration-driven convection. The equations are then numerically solved to show that the species boundary layer thickness δd = 1.6 x(Rex/Grx )1/4, the velocity boundary layer thickness δv = δdSc1/5, the horizontal velocity u = Vi(Grx/Rex )1/4f (n), where n = y/δv, and the drag coefficient based on Vi, CD = 2.32/vJ.We find that the vertical profile of the horizontally averaged dimensionless concentration across the boundary layer becomes, surprisingly, independent of the blowing and the species diffusion effects to follow aGr2/3y scaling, where Gry is the Grashof number based on the vertical location y within the boundary layer.We then show that the above profile matches the experimentally observed mean concentration profile within the boundary layers that form on the top surface of a membrane, when a weak flow is forced gravitationally from below the horizontal membrane that has brine above it and water below it. A similar match between the theoretical scaling of the species boundary layer thickness and its experimentally observed variation is also shown to occur.

We present scaling laws for the jet velocity resulting from bubble collapse at a liquid surface which bring out the effects of gravity and viscosity. The present experiments conducted in the range of Bond numbers < 0.004

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 < 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.

We consider the motion of the drop sedimenting down an inclined glass plate in viscous fluid. The density difference between the two fluids causes the motion of the drop along the glass plate. The drop motion for Reynolds number, Re << 1 and Bond number, B << 1 for inclination angle, 0.174 < α < 0.523 was studied. In that regime, Stokes drag over the drop balances the driving force. The proposed scaling law was compared with Hodges theoretical relation and with the experiments. The outer flow field visualization of the drop was done using particle imaging velocimetry technique. A small recirculation zone was observed just above the drop from the PIV image.

We study the generation of vorticity at a water–air interface due to the spreading of ethanol–water droplets for ethanol concentrations in the drop ranging from 20% ≤ Ce≤ 100% on the surface of a 50 mm deep water layer. On deposition onto the water layer, the lighter, miscible ethanol droplet spreads as a film on the water surface due to the ethanol–water surface tension difference. Simultaneous to the film spreading, an expanding vortex ring is found below the tip of the spreading film front. The phenomenon in the water layer is visualized using particles, and 2D PIV is used to obtain the velocity field. Vortex regions are identified using the λ2 method for various time instants. The average vorticity generation in between the time instants is calculated. A scaling law is proposed for the dimensionless vorticity at a given instant based on the experimental observations.