Axially Homogeneous Turbulent Convection at High Rayleigh Numbers : Scaling Laws for Flux and Spectra
Pawar, Shashikant S
MetadataShow full item record
Natural turbulent convection studies encompass a wide range of flows occurring in nature, for example, atmospheric and oceanic flows, con-vection in the Earth’s mantle, convection in the stars and also in many engineering applications. Rayleigh-Benard convection (RBC), i.e. con-vection in a horizontal fluid layer confined between two plates with a temperature diﬀerential maintained across them, has been a proto-type problem in the studies of turbulent natural convection. Many small scale and global features of the flow in the turbulent regime of RBC are known, yet the flow dynamics is not fully understood, es-pecially at high Rayleigh numbers (Ra). Present work comprises of experimental investigations of a diﬀerent type of flow, high Rayleigh number turbulent convection in a long vertical tube (abbreviated as tube convection or TC). The tube of aspect ratio (length to diameter) of about 10, open at both the ends interconnects two large tanks. The flow driven by an unstable density diﬀerence created between the two tanks, has some unique features, diﬀerent from RBC. The net flow at any tube cross-section is zero and the time averages of the velocities, the Reynolds shear stress and the mean shear are also zero. Turbu-lent energy production is therefore solely due to buoyancy. The flow is axially homogeneous and axisymmetric. In the homogeneous region, the mean density gradient is linear. Rayleigh number in TC is conve-niently defined based on the mean (linear) density gradient (denoted by Rag). Two sets of experiments are carried out. In one set of experiments, the density diﬀerence is created using brine and fresh water and in another set, it is created using heat. The ranges of Rag achieved are 3 × 108 < Rag < 8 × 109 in the experiments using salt (Schmidt number, Sc ≈ 600) and 5 × 104 < Rag < 5 × 106 in the experiments using heat (Prandtl number, P r ≈ 6). From the measured salt and heat fluxes in both the sets of experiments, the non dimensional flux 1 1 scaling above a certain value of Rag is obtained as N ug ∼ Rag2 P r 2 and from the velocity measurements in the experiments using salt, the 1 Reynolds number scaling is obtained as Re ∼ Rag2 P r− 12 . Both these are as per the predicted scalings by the mixing length model proposed by Arakeri et al. (2000) for high Rag convection in the vertical tube. The flux scaling N u ∼ (RaP r)2 , also known as the ‘ultimate regime’ of convection, expected at very high Ra but not yet observed in the experiments in classical RBC, is easily achieved in TC at relatively lower values of Ra. The fluxes and Reynolds numbers in TC are orders of magnitude higher as compared to those obtained in RBC for similar values of Ra and P r. In the lower range of Rag values for P r ≈ 6, a transition to a new flux scaling, N u ∼ (RaP r)0.29 is found. Similar transitions are also found to be present in the results of Tovar (2002) for Sc ≈ 600 and in the DNS results of Schmidt et al. (2012) for P r = 1, at diﬀerent values of Rag. Collecting all these data, it is shown that the transition occurs at a fixed Grashof number of 1.6 × 105, independent of P r. Velocity measurements are carried out using particle image velocime-try (PIV) in the salt experiments. Kinetic energy spectra computed from the velocity fields are presented for the locations from the tube axis to the wall, for the lowest and the highest values of Rag achieved in the experiments. The spatial energy spectrum of lateral velocity at the tube axis follows Kolmogorov-Obukhov (KO) scaling (−5/3 scaling exponent) while the spatial spectrum of longitudinal velocity shows a scaling slightly higher than −5/3 but lower than −11/5 (the Bolgiano-Obukhov (BO) scaling). The scalar spectra is computed from the concentration fields obtained from planar laser induced fluorescence (PLIF) in the experiments using salt, and also from the temperature measurements from the experiments using heat. Both the concentra-tion and temperature fluctuations spectra show some evidence of dual scaling - BO scaling (−7/5 scaling exponent) in the inertial subrange followed by Obukhov-Corrsin (OC) scaling (−5/3 scaling exponent) over a narrow range of scales. Light propagation through the buoyancy driven turbulent flow in TC has also been experimentally investigated. Light propagation through convective turbulence is encountered in many situations. In some cases e.g. in observational astronomy it is undesirable, while in some other cases it is useful, e.g. in remote sensing of meteorological parameters. In the present study, light intensity and angle of arrival fluctuations in a parallel beam of light are measured. Laser shadowgraphy is used in the intensity measurements while the angle of arrival is obtained by measuring deflections of narrow laser beams, created by passing collimated laser light through a mask having equispaced grid of holes. Background oriented schlieren (BOS) measurements have also been carried out to obtain the displacements, which are proportional to the angle of arrivals. The equations for frequency spectrum of intensity and angle of arrival from the literature, developed for isotropic, ho-mogeneous turbulent media, are modified for the flow in the present case and the asymptotic scalings for high and low frequency ranges are obtained. The scalings in the frequency spectra computed from the measurements of intensity and angle of arrival fluctuations are com-pared with the obtained asymptotic scalings. The results from the present work are also compared with results from studies in the atmo-sphere and lab experiments.