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Dynamics of line plumes on horizontal surfaces in turbulent convection
- G. S. Gunasegarane, Baburaj A. Puthenveettil
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- Journal:
- Journal of Fluid Mechanics / Volume 749 / 25 June 2014
- Published online by Cambridge University Press:
- 14 May 2014, pp. 37-78
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We study the dynamics of line plumes on the bottom horizontal plate in turbulent convection over six decades of Rayleigh number $(10^5<\mathit{Ra}_w<10^{11})$ and two decades of Prandtl number or Schmidt number ($0.7<\mathit{Pr}<5.3$, $\mathit{Sc}=602$). 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 ($\overline{V_{sh}}$) scales as the large-scale flow velocity ($V_{LS}$), with the fraction of the length of the plumes affected by shear increasing with $\mathit{Ra}_w$ as $L_{ps}/L_p\sim \mathit{Ra}_w^{0.054} \mathit{Pr}^{-0.12}$. The mean time of initiation of the plumes $\overline{t^{*}}$, scales as the diffusive time scale near the plate, $Z_w^2/\alpha $, where $Z_w$ 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 ${\sim }70\, \%$ of the length of the plumes undergoing merging at $\mathit{Ra}_w\approx 10^{11}$ and $\mathit{Sc}= 602$. The fraction of the length of the plumes that undergoes merging decreases with increase in $\mathit{Ra}_w$ as, $L_{pm}/L_p \sim \mathit{Ra}_w^{-0.054} \mathit{Pr}^{0.12}$; the exponents of $\mathit{Ra}_w$ and $\mathit{Pr}$ being of the same magnitude but of opposite sign as that in the relation for $L_{ps}/L_p$. Measurements of the locational means of the velocities of merging of the plumes $(V_m)$ show that $V_m$ 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 $\mathit{Ra}_w-\mathit{Pr}$ combination. The merging velocities at all $\mathit{Ra}_w$ and $\mathit{Pr}$ have a common lognormal distribution, but their mean and variance increased with increasing $\mathit{Ra}_w$ and decreasing $\mathit{Pr}$. Using mass and momentum balance of the region between two merging plumes, we show that the spatiotemporal mean merging velocities ($\overline{V_m}$), which are an order lower than $\overline{V_{sh}}$, 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 $\overline{V_m}$ scales as the diffusive velocity scale near the plate $\nu /Z_w$. The Reynolds number in terms of $\overline{V_m}$ and the layer height $H(\mathit{Re}_H)$ scales as $\mathit{Ra}_w^{1/3}$, in the same way as the Nusselt number ($\mathit{Nu}$) scales approximately; therefore $\mathit{Re}_{H}\sim \mathit{Nu}$. These relations imply that $\mathit{Re}_w= \overline{V_m}Z_w/\nu $ a Reynolds number near the plate, is an invariant for a given fluid in turbulent convection.
Length of near-wall plumes in turbulent convection
- Baburaj A. Puthenveettil, G. S. Gunasegarane, Yogesh K. Agrawal, Daniel Schmeling, Johannes Bosbach, Jaywant H. Arakeri
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- Journal:
- Journal of Fluid Mechanics / Volume 685 / 25 October 2011
- Published online by Cambridge University Press:
- 20 September 2011, pp. 335-364
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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 () and at three Prandtl numbers (). 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 (), made dimensionless by the near-wall length scale in turbulent convection (), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to for a given fluid layer of height . The increase in has a weak influence in decreasing . 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.