Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session E34: Free and Rayleigh-Benard Convection I |
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Chair: Joseph Niemela, International Center for Theoretical Physics Room: Georgia World Congress Center B406 |
Sunday, November 18, 2018 5:10PM - 5:23PM |
E34.00001: Direct numerical simulations towards ultimate turbulence Richard Stevens, Roberto Verzicco, Detlef Lohse Both in experiments and simulations of Rayleigh-Bénard (RB) convection it is a major challenge to reach the ultimate regime in which the boundary layers transition from laminar to turbulent. In the ultimate regime the scaling exponent γ in the relation Nu∼Ra^{γ}, where Nusselt Nu is the dimensionless heat transport and Rayleigh Ra is the dimensionless temperature difference between the plates, increases. The critical Rayleigh number (Ra*) for the transition to the ultimate regime has been observed in the Göttingen experiments around Ra*≈2x10^{13}. So far, the highest Ra obtained in direct numerical simulations (DNS) is Ra=2x10^{12 }for aspect ratio Γ=0.5 (Stevens, Lohse, Verzicco, JFM 688, 31 (2011)). Here we present a comparison between the Göttingen experiments and DNS up to Ra=10^{13}. We find perfect agreement between experiments and simulations, both for the heat transfer and for the mean and temperature variance profiles close to the sidewall. We will also provide flow visualizations and analysis, and results from resolution checks up to Ra=10^{13}. In addition, we discuss simulations for Γ=0.23 up to Ra=10^{14}, which are performed on grids with almost 100x10^{9} nodes. These results agree well with measurements by Roche et al., NJP 12, 085014 (2010). |
Sunday, November 18, 2018 5:23PM - 5:36PM |
E34.00002: Revealing ultimate Rayleigh-Bénard turbulence through scaling analysis of the temperature structure functions Dominik Krug, Xiaojue Zhu, Daniel Chung, Roberto Verzicco, Ivan Marusic, Detlef Lohse The transition to the so-called ultimate regime, in which the boundary layers (BL) are of turbulent type, in turbulent Rayleigh-Bénard convection (RBC) has been observed in some experiments and very recently in direct numerical simulations (DNS) of 2D RBC at Ra = 10^{13}. Here, we make use of the same DNS to analyse the scaling properties of temperature structure functions S_{p} ≡ ⟨Δθ(r)^{2p}⟩^{1/p} in the BLs, where 2p is the (even) order and Δθ(r) the temperature difference across a lateral distance r. Based on e.g. the attached-eddy framework, it is possible to derive a scaling S_{p}(r) ∼ ln(r) for velocity structure functions in the logarithmic region. By employing extended self-similarity (ESS) ( i.e., plotting the structure functions against each other, rather than r), we have previously demonstrated that this scaling emerges even at low Reynolds numbers with universal relative slopes. In RBC, we find no ESS scaling below the transition and in the near wall region. However, beyond the transition and for large enough wall distance z^{+ }> 100, we find clear ESS behaviour. Our analysis gives strong evidence that the observed transition in the global Nusselt number at Ra ≈ 10^{13} indeed is the transition from a laminar type BL to a turbulent type BL. |
Sunday, November 18, 2018 5:36PM - 5:49PM |
E34.00003: Universal properties in penetrative turbulent Rayleigh-B\'enard convection Zhen-Hua Wan, Qi Wang, De-Jun Sun Penetrative convection refers to the phenomenon whenever convection in thermally unstable fluid layers penetrate into adjacent stable layers. In this work, we study penetrative turbulent Rayleigh-B\'enard convection which depends on the density maximum of water near 4°C using two-dimensional and three-dimensional direct numerical simulations. The working fluid is water near 4°C with reference Prandtl number Pr=11.57. The considered Rayleigh numbers Ra range from 10^{7} to 10^{10}. The density inversion parameter T_{m} varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thickness (F_{λ}=λ_{t}^{Θ}/λ_{b}^{Θ}) increases with increasing T_{m}, and the relationship between F_{λ} and T_{m} seems to be independent of Ra. The center temperature T_{c} is enhanced compared to that of the Oberbeck-Boussinesq (OB) cases, and T_{c} is also found to have a universal relationship with T_{m} which is independent of Ra. T_{c} is related to F_{λ} with 1/T_{c}=1/F_{λ}+1. Moreover, the normalized Nu(T_{m})/Nu(0) and Re(T_{m})/Re(0) also have universal relationships with T_{m} which seem to be independent of both Ra and the aspect ratio Γ. The scaling exponents of Nu~Ra^{α} and Re~Ra^{β} are found to be insensitive to T_{m}. |
Sunday, November 18, 2018 5:49PM - 6:02PM |
E34.00004: Nusselt number enhancement and flow structures in Rotating Rayleigh-Benard convection Yantao Yang, Roberto Verzicco, Detlef Lohse, Richard Stevens It is well known that external rotation may enhance the heat transfer in Rayleigh-Benard (RB) convection through Ekman pumping. In this talk we focus on the Nusselt numbers enhancement regime of the rotating RB flow. We show that for low Rayleigh number, the optimal rotating rate which generates the highest heat transfer can be well explained by a cross-over of the boundary layer thicknesses of the momentum and thermal field. However, when Rayleigh number is larger than a critical value, such explanation breaks down. The optimal rotating rate is different for periodic and cylindrical domains, as well as cylindrical domains with different aspect ratios. By looking into the autocorrelation of the vertical velocity we found that characteristic height of the coherent structures in the bulk is strongly affected by the horizontal boundary conditions. Therefore different domains reach optimal heat transfer at different rotating rates. |
Sunday, November 18, 2018 6:02PM - 6:15PM |
E34.00005: Prandtl number dependence of the transition to the geostrophic regime of rotating Rayleigh-Bénard convection Andres Aguirre Guzman, Rodolfo Ostilla Monico, Herman Clercx, Rudie Kunnen In the rotating Rayleigh-Bénard (RRB) configuration different regimes of turbulent rotating convection can be reached depending on the strength of the buoyant forcing (Rayleigh number, Ra), the strength of rotation (Ekman number, Ek) and the fluid properties (Prandtl number, Pr). The transition between regimes has been widely studied for moderate values of the Prandtl number (Pr≥1). We directly simulate the RRB flow to specifically investigate the transition to the geostrophic turbulent regime for different Prandtl numbers. We include cases at Pr=0.1, relevant to liquid metals and to numerous geophysical and astrophysical scenarios, and Pr=1 and ∼5 that corresponds to water as used by many laboratory experiments and relevant to oceanic processes. For the different Prandtl numbers we find a transition between geostrophic turbulence and the rotation-affected regime. We highlight the presence of a large-scale vortical structure in the geostrophic turbulent regime for our lowest Pr case with no-slip top/bottom boundaries in the RRB setup. Similar large-scale coherent structures have been observed for stress-free boundaries, but not yet confirmed for the no-slip case until now. Our results expose the active role of the Prandtl number in the dynamics of the flow. |
Sunday, November 18, 2018 6:15PM - 6:28PM |
E34.00006: Convective heat transfer over ratchet surfaces in vertical natural convection Hechuan Jiang, Xiaojue Zhu, Varghese Mathai, Xianjun Yang, Roberto Verzicco, Detlef Lohse, Chao Sun We report on a combined experimental and numerical study on convective heat transfer over ratchet surfaces in vertical natural convection (VC). Due to the asymmetry of the convection system caused by the asymmetric ratchet-like wall roughness, two distinct states exist with different orientations of the large-scale circulation roll and different heat transport capacities. The statistical analysis shows that the heat transport efficiency depends on the strength of the large-scale recirculation. We observe that, when the large-scale wind sweeps the ratchets along the smaller slopes, the convective roll is stronger and the heat transport larger than the case in which the mean flow has the opposite direction. The result on the heat transfer differs from standard Rayleigh-B\'enard convection (RBC) where the heat transfer is stronger in the second configuration. We show that the reason for the opposite behavior of VC as compared to RBC is that the flow is more turbulent in RBC than that in VC at the same Ra. This work helps to understand the mechanisms of heat transport in turbulent thermal convection with asymmetric roughness and sheds new light on heat transport enhancement and flow control in engineering. |
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