Heat transport by turbulent Rayleigh-Benard Convection in cylindrical samples with aspect ratio one and larger

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number sigma = 4.38) with diameters D = 49.7, 24.8, and 9.2 cm, all with aspect ratio Gamma = D/L = 1 (L is the sample height). In addition, we present data for D = 49.7 and Gamma = 1.5, 2, 3, and 6. For each sample the data cover a range of a little over a decade of R. For Gamma = 1 they jointly span the range 10^7 < R < 10^11. Where needed, the data were corrected for the influence of the finite conductivity of the top and bottom plates and of the side walls on the heat transport in the fluid to obtain estimates of N_infinity for plates with infinite conductivity and sidewalls of zero conductivity. For Gamma = 1 the effective exponent gamma_eff of N_infinity = N_0 R^gamma_eff ranges from 0.28 near R = 10^8 to 0.333 near R = 7 times10^10. For R < 10^10 the results are consistent with the Grossmann-Lohse model. For larger R, where the data indicate that N_infinity(R) = R^1/3, the theory has a smaller gamma_eff than 1/3 and falls below the data. The data for Gamma > 1 are only a few percent smaller than the Gamma = 1 results.Comment: 10 pages, 5 figures. Under consideration for publication in J. Fluid Mec

Heat transport by turbulent Rayleigh-B'enard Convection in cylindrical cells with aspect ratio one and less

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number sigma = 4.4) with a diameter D of 49.7 cm and heights L = 116.3, 74.6, and 50.6 cm, as well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Gamma = D/L = 0.28, 0.43, 0.67, and 0.98 the data cover a range of a little over a decade of R. The maximum R ~= 10^12 and Nusselt number N ~= 600 were reached for Gamma = 0.43 and D = 49.7. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of N_infty for plates with infinite conductivity. The results for N_infty and Gamma >= 0.43 are nearly independent of Gamma. For Gamma = 0.275 N_infty falls about 2.5 % below the other data. For R ~<= 10^11, the effective exponent gamma_eff of N_infty = N_0 R^gamma_eff is about 0.321, larger than those of the Grossmann-Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for Gamma = 0.98, 0.67, and 0.43, gamma_eff saturates at the asymptotic value gamma = 1/3 of the Grossmann-Lohse model. The data do not reveal any crossover to a Kraichnan regime with gamma_eff > 1/3.Comment: 10 pages, 5 figure

Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity

We describe three apparatus, known as the large, medium, and small apparatus, used for high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600 was reached for Gamma = 0.43. Measurements were made with both Aluminum and Copper top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N_infinity for plates with infinite conductivity was estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 - exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Gamma for the large apparatus and showed a small Gamma-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.Comment: 35 pages, 11 figures. Under consideration for publication in Phys. of Fluid

Effects of polymer additives in the bulk of turbulent thermal convection

We present experimental evidence that a minute amount of polymer additives can significantly enhance heat transport in the bulk region of turbulent thermal convection. The effects of polymer additives are found to be the \textit{suppression} of turbulent background fluctuations that give rise to incoherent heat fluxes that make no net contribution to heat transport, and at the same time to \textit{increase} the coherency of temperature and velocity fields. The suppression of small-scale turbulent fluctuations leads to more coherent thermal plumes that result in the heat transport enhancement. The fact that polymer additives can increase the coherency of thermal plumes is supported by the measurements of a number of local quantities, such as the extracted plume amplitude and width, the velocity autocorrelation functions and the velocity-temperature cross-correlation coefficient. The results from local measurements also suggest the existence of a threshold value for the polymer concentration, only above which can significant modification of the plume coherent properties and enhancement of the local heat flux be observed. Estimation of the plume emission rate suggests that the second effect of polymer additives is to stabilize the thermal boundary layers.Comment: 8 figures, 11 page

Enhanced heat transport by turbulent two-phase Rayleigh-B\'enard convection

We report measurements of turbulent heat-transport in samples of ethane (C$_2$H$_6$) heated from below while the applied temperature difference $\Delta T$ straddled the liquid-vapor co-existance curve $T_\phi(P)$. When the sample top temperature $T_t$ decreased below $T_\phi$, droplet condensation occurred and the latent heat of vaporization $H$ provided an additional heat-transport mechanism.The effective conductivity $\lambda_{eff}$ increased linearly with decreasing $T_t$, and reached a maximum value $\lambda_{eff}^*$ that was an order of magnitude larger than the single-phase $\lambda_{eff}$. As $P$ approached the critical pressure, $\lambda_{eff}^*$ increased dramatically even though $H$ vanished. We attribute this phenomenon to an enhanced droplet-nucleation rate as the critical point is approached.Comment: 4 gages, 6 figure

Experimental study of path instability of rising bubbles

Experimental study of path instability of rising bubbles Abstract: The main objective is to study the path instability of a freely ascending air bubble in water and silicon oil at varied Bond numbers (ratio of body forces to surface tension) and Galileo numbers (ratio of gravitational force to viscous force). Below a certain threshold of the Galileo number, the path of the bubble remains straight. But above a critical Galileo number (related to the size of the bubble) a new regime sets in, and the bubble changes its shape and follows a zig-zagging path. Experimental investigation is needed because earlier existing numerical work suffers from simplifications likely to bias predictions, such as the assumption of fixed shape [1,2] and recent simulations accounting fully for shape deformation are either still too sparse to provide a reliably established marginal stability curve [3,4] or bring controversial results [5]. Our work aims to contribute reliable observations of the onset of instability using various silicon oils. In our experimental set up, bubbles of variable size are released in a rectangular tank filled with silicon oil known to present no problem of free surface impurities. Images obtained by a fast camera and are post-processed to determine the size and shapes of the bubbles and their trajectory in the fluid. Bond and Galileo numbers are calculated based on the volume of bubble and on the physical properties of the used working fluid.  Experiments will be conducted with silicon oils of varying viscosity to obtain as many points in the Galileo ? Bond number parameter plane as possible. Bibilography : [1] Tchoufag J., Magnaudet J. and Fabre D., Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble, Physics of Fluids, 25 (2013) 052108 [2] Cano-Lozano J.C., Bohorquez P. and Martinez-Bazán C., Wake instability of a fixed axisymmetric bubble of realistic shape, Int. J. Multiphase Flow, 51 (2013) 11. [3] Tripathi M.K., Saku K.C. and Govindarajan R., Nature Comm., 6:6268, (2015). [4] Cano-Lozano J.C. , Martinez-Bazán, Magnaudet J. and Tchoufag J., Paths and wakes of deformable nearly spherical rising bubbles close to the transition to path instability, Phys. Rev. Fluids 1, 053604 (2016). [5] Zhou W. and Dusek J., Marginal stability curve of a deformable bubble, Int. J. Multiphase Flow, 89 (2017) 218

Experimental evidence for the boundary zonal flow in rotating Rayleigh-Benard convection

We report on the presence of the boundary zonal flow in rotating Rayleigh-Benard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio between its diameter (D) and height (H) of G=D/H=1. As the working fluid we used various mixtures of water and glycerol, leading to Prandtl numbers in the range 6.6<Pr<75. The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range 10e8 < Ra < 6.3e9. The effect of rotation is quantified by the Ekman number which was between 1.5e-5<Ek< 1.2e-3 in our experiment. With our results we show the first direct measurements of the boundary zonal flow - BZF that develops near the sidewall and was recently discovered in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness of the BZF as well as its maximal velocity as function of Pr, Ra, and Ek, and compare these results with previous DNS results

Plume motion and large-scale circulation in a cylindrical Rayleigh-B\'enard cell

We used the time correlation of shadowgraph images to determine the angle $\Theta$ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-B\'enard cell of aspect ratio $\Gamma \equiv D/L = 1$ ($D$ is the diameter and $L \simeq 87$ mm the height) in the Rayleigh-number range $7\times 10^7 \leq R \leq 3\times 10^{9}$ for a Prandtl number $\sigma = 6$. We expect that $\Theta$ gives the direction of the large-scale circulation. It oscillates time-periodically. Near the top and bottom plates $\Theta(t)$ has the same frequency but is anti-correlated.Comment: 4 pages, 6 figure