Abstracts - KTH Mechanics

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192 Measurements of buoyancy driven turbulence in a vertical pipe Murali R. Cholemari ∗ , Jaywant H. Arakeri ∗ We present measurements of a buoyancy driven turbulent flow in long (length-todiameter ratio = 9) vertical pipes. The flow is created by the density difference across the ends of the vertical tube. We use brine and fresh water for creating the density difference. The flow represents an ‘overturning process’ of the two fluids through the pipe. Since the pipes are long, an axially homogeneous region of turbulence exists away from the ends. In this region the flow is driven by a linear unstable density gradient. The ratio of the diffusivities of momentum and salt, given by the Schmidt number, Sc = ν/α, is about 670. The Rayleigh number based on the diameter d of the pipe and the density gradient, Rag = g(∆ρ/ρL)d 4 /να, which gives the relative importance of the buoyancy and diffusive effects, is of the order of 10 8 . The experimental data consisted of measurements of salt concentration using a conductivity probe and velocity measurements using planar particle image velocimetry (PIV). Velocity measurements show that there is no mean flow. Flow visualization and spatial velocity correlations show that large scales are of the order of the pipe diameter. One dominant motion seems to be heavier particles going down accompanied by lighter particles rising up on the sides. Another motion inferred from the data is the collision of falling and rising fluid particles. The flow is anisotropic, both at large scales as well as at the smallest scales measured 1 . The turbulence in the fully developed region involves the dominance of a single length scale, comparable to the diameter of the pipe. A mixing length model incorporating this feature is shown to agree very well with the experimental measurements of the scalar (salt concentration) flux and velocity measurements. The Nusselt number scales as ∼ Ra 1/2 g Sc 1/2 suggesting that the molecular effects are negligible. This may be compared to the ∼ Ra 1/3 g scaling obtained in turbulent Rayleigh-Bénard convection2 . The unique feature about the present flow is that it is a axially homogeneous purely buoyancy driven turbulent flow. ∗ Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 INDIA. 1 Cholemari, PhD thesis, Indian Inst. Sci., (2004). 2 Cholemari and Arakeri, Int. J. Heat Mass Transfer. 48, 4467 (2005).
Coherent Large-Scale Structures and Hysteresis in Turbulent Convection A. Eidelman, T. Elperin, N. Kleeorin, I. Rogachevskii, I. Sapir-Katiraie Department of Mechanical Engineering Ben-Gurion University of the Negev POB 653, Beer-Sheva 84105 ISRAEL We studied theoretically and experimentally coherent large-scale circulations (semiorganized structures) in turbulent convection in an air flow in a rectangular chamber. Particle Image Velocimetry was used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with twelve sensitive thermocouples was employed to measure the temperature field. We found the hysteresis phenomenon in turbulent convection by varying the temperature difference between the hot bottom wall and cold top wall of the chamber. The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant. We developed a new mean-field theory of turbulent convection. In a shearfree turbulent convection this theory predicts the convective wind instability which causes formation of large-scale semi-organized fluid motions in the form of cells. The developed theory of formation of semi-organized structures in turbulent convection is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. Thermal structure inside the large-scale circulations is neither homogeneous nor isotropic. The warm thermal plumes accumulate at one side of the large-scale circulation, and cold plumes accumulate at the opposite side of the large-scale circulation. The redistribution of the heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection. Predictions of the developed theory are also in a good agreement with the observed semi-organized structures in the atmospheric turbulent convection. 1 193
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