Unsteady axial mixing by natural convection in a vertical column

Baird, M. H. I.; Kannan, A.; Rao, N. V. Rama; Chadam, John; Peirce, Anthony

doi:10.1002/aic.690381113

Cited by 47 publications

(31 citation statements)

References 12 publications

(16 reference statements)

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“…The sizes of these eddies are typically of the order of the width of the tank, and their speed decreases with increasing distance from the source of buoyancy located at the top of the tank. These are similar observations to those made for the mixing of dense source fluid in the experiments discussed by Baird et al (1992), Debacq et al (2001), Dalziel et al (2008), VS12 and VS13. …”

Section: Methodssupporting

confidence: 89%

Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

2014

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We perform experiments to study the mixing of passive scalar by a buoyancy-induced turbulent flow in a long narrow vertical tank. The turbulent flow is associated with the downward mixing of a small flux of dense aqueous saline solution into a relatively large upward flux of fresh water. In steady state, the mixing region is of finite extent, and the intensity of the buoyancy-driven mixing is described by a spatially varying turbulent diffusion coefficient κ v (z) which decreases linearly with distance z from the top of the tank. We release a pulse of passive scalar into either the fresh water at the base of the tank, or the saline solution at the top of the tank, and we measure the subsequent mixing of the passive scalar by the flow using image analysis. In both cases, the mixing of the passive scalar (the dye) is well-described by an advection-diffusion equation, using the same turbulent diffusion coefficient κ v (z) associated with the buoyancy-driven mixing of the dynamic scalar. Using this advection-diffusion equation with spatially varying turbulent diffusion coefficient κ v (z), we calculate the residence time distribution (RTD) of a unit mass of passive scalar released as a pulse at the bottom of the tank. The variance in this RTD is equivalent to that produced by a uniform eddy diffusion coefficient with value κ e = 0.88 κ v , where κ v is the vertically averaged eddy diffusivity. The structure of the RTD is also qualitatively different from that produced by a flow with uniform eddy diffusion coefficient. The RTD using κ v has a larger peak value and smaller values at early times, associated with the reduced diffusivity at the bottom of the tank, and manifested mathematically by a skewness γ 1 ≈ 1.60 and an excess kurtosis γ 2 ≈ 4.19 compared to the skewness and excess kurtosis of γ 1 ≈ 1.46, γ 2 ≈ 3.50 of the RTD produced by a constant eddy diffusion coefficient with the same variance.

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Section: Methodssupporting

confidence: 89%

Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

2014

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“…Related studies of miscible flows have focused on the effect of buoyancy in inducing mixing in the context of chemical, oil-and-gas and environmental settings [45]. A typical system studied involves two, initially stratified, miscible fluids of different densities in vertical and tilted tubes, with the more dense fluid overlying the less dense one [46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Pressure-driven miscible two-fluid channel flow with density gradients

et al. 2009

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We study the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations. The flow dynamics are governed by the continuity and NavierStokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity and density. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. We present results showing the spatio-temporal evolution of the flow together with an integral measure of mixing. *

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“…These flows often take place in confined geometries such as tubes or narrow channels ͑for instance, in artificial wells or in chemical reactors͒. [3][4][5] The corresponding mixing flows strongly differ both from buoyant flows in open geometries and from pressure-driven flows in pipes or channels. A particularly interesting case is provided by long tilted pipes 6,7 in which, for a zero net axial flow, mixing results from the combined effects of the axial gravity that drives the interpenetration, shear instabilities that induce the transverse mixing, and transverse gravity that moderates it.…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

et al. 2009

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Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Δρ/(2⟨ρ⟩)=1.15×10−2] in a long circular tube tilted at an angle θ=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

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Unsteady axial mixing by natural convection in a vertical column

Cited by 47 publications

References 12 publications

Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

Pressure-driven miscible two-fluid channel flow with density gradients

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

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