Effect of a polymer additive on heat transport in turbulent Rayleigh-B\'enard convection

Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-B\'enard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range 5\times 10^9 \alt Ra \alt 7 \times 10^{10} $Nu$ is smaller than it is for pure water by up to 10%.Comment: 3 pages, 2 figure

Absense of slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh-Benard convection

We report experimental results for the influence of a tilt angle beta relative to gravity on turbulent Rayleigh-Benard convection of cylindrical samples. The measurements were made at Rayleigh numbers R up to 10^11 with two samples of height L equal to the diameter D (aspect ratio Gamma = D/L = 1). The fluid was water with a Prandtl number sigma = 4.38. In contrast to the experiences reported by Chilla et. al. (2004) for a similar sample but with Gamma = 0.5 (D = 0.5 and L = 1.0 m), we found no long relaxation times. For R = 9.4 times 10^10 we measured the Nusselt number N as a function of tilt angle beta and obtained a small beta dependence about a factor of 50 smaller than the result found by Chilla et. al. (2004) for their Gamma = 0.5 sample. We measured side-wall temperatures at eight equally spaced azimuthal locations on the horizontal mid-plane of the sample and used their cross-correlation functions to find the turn-over time of the large-scale circulation (LSC). The resulting Reynolds numbers R_e^cc were found to increase with beta. An important conclusion is that the increase of R_e^cc with beta of the LSC does not significantly influence the heat transport. Over the range 10^9 < R < 10^11 the enhancement of R_e^cc at constant beta due to the tilt could be described by a power law of R with an exponent of -1/6, consistent with a simple model that balances the additional buoyancy due to the tilt angle by the shear stress across the boundary layers. Even a small tilt angle dramatically suppressed the azimuthal meandering and the sudden reorientations characteristic of the LSC in a sample with beta = 0. The azimuthal mean of the temperature at the horizontal mid-plane within our resolution was independent of beta.Comment: 32 pages, 17 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 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 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

Orientation changes of the large-scale circulation in turbulent Rayleigh-Benard convection

We present measurements of the orientation theta_0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in cylindrical cells of aspect ratio 1. theta_0(t) undergoes irregular reorientations. It contains reorientation events by rotation through angles Delta theta with a monotonically decreasing probability distribution p(Delta theta), and by cessations (where the LSC stops temporarily) with a uniform p(Delta theta). Reorientations have Poissonian statistics in time. The amplitude of the LSC and the magnitude of the azimuthal rotation rate have a negative correlation.Comment: 4 pages, 5 figures. Under consideration for publication in Physical Review Letters. Some new content has been added, and some content has been removed to make spac

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements