Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session G14: Convection and Buoyancy-driven Flows: Rayleigh-Benard |
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Chair: Herman Clercx, Eindhoven University of Technology Room: 307/308 |
Sunday, November 24, 2019 3:48PM - 4:01PM |
G14.00001: Do steady rolls maximize heat transport in truncated models of Rayleigh–-B\'enard convection? David Goluskin, Charles R. Doering, Anuj Kumar, Matthew Olson In Rayleigh–-B\'enard convection, steady rolls are the simplest nonlinear states. They exist for all Rayleigh numbers (Ra) above the primary instability but are unstable at large Ra. Heat transport by steady rolls is comparable to that by turbulent convection if the aspect ratio of rolls is varied with Ra to maximize heat transport (Waleffe et al., Phys. Fluids 27, 2015). Here we ask: do steady rolls transport more heat than any other flows, including turbulent or unstable time-periodic flows? Answering this question in the affirmative requires computing exact upper bounds on heat transport, and showing that steady rolls saturate the bounds. Exact bounds for the governing PDEs are beyond current capabilities, so we instead study ODE models of increasing dimension, each derived as a Galerkin truncation of the PDEs governing 2D convection between free-slip plates. For the ODEs we compute sharp upper bounds on heat transport by using polynomial optimization. In particular, upper bounds are provided by solutions to convex optimization problems, whose constraints require certain expressions to be sums of squares of polynomials, and which are solved numerically using semidefinite programming. To find the states that saturate these bounds, we perform numerical bifurcation analysis. [Preview Abstract] |
Sunday, November 24, 2019 4:01PM - 4:14PM |
G14.00002: Numerical study of thermal transfer in Rayleigh-Benard convection under rarefied gas conditions Gianluca Di Staso, Bijan Goshayeshi, Federico Toschi, Herman Clercx The Rayleigh-B\'{e}nard problem has been analyzed in depth theoretically, experimentally and numerically under a broad range of conditions such as small and large Prandtl number, high Rayleigh number turbulent convection, non-negligible compressibility effects, as well as under rotation. The large majority of these studies have in common the underlying assumption of a continuum flow, i.e. the molecular mean free path is much smaller than any characteristic macroscopic spatial scale of the flow. In this contribution, we depart from this assumption and we numerically study the final state of a 2D Rayleigh-B\'{e}nard system under rarefied gas conditions using the Direct Simulation Monte Carlo method (DSMC), the standard particle-based numerical method for simulating rarefied gas flows. By collecting a large number of statistical samples, we quantitatively measure the heat flux enhancement when convection is present and we determine the influence of rarefaction conditions on the maximum attainable heat flux. Finally, we show that onset of convection is found only for a limited range of Rayleigh number and this range is reduced as the degree of rarefaction increases. [Preview Abstract] |
Sunday, November 24, 2019 4:14PM - 4:27PM |
G14.00003: Transition of the flow dynamics in two-dimensional Rayleigh-Bénard convection Zhenyuan Gao, Yun Bao, Shidi Huang We investigate the flow dynamics in two-dimensional Rayleigh-Bénard convection through high resolution direct numerical simulation, with the Rayleigh number Ra range being 10$^{\mathrm{7}}$\textasciitilde 10$^{\mathrm{12}}$ and the Prandtl number Pr fixed at 4.3. It is found that there exists a transitional Rayleigh number Ra$_{\mathrm{c}}$ at which the flow pattern changes significantly and the large-scale circulation (LSC) evolves from an elliptical shape into a circular one. Detailed Fourier mode analysis reveals that, while the single-roll mode becomes weaker and other modes become stronger during the transition, all the flow modes experience violent fluctuations. This is also manifested by the sharp change of the local turbulent fluctuations near Ra$_{\mathrm{c}}$, in both magnitude and Ra-dependent scaling. We understand this transition by stability analysis. [Preview Abstract] |
Sunday, November 24, 2019 4:27PM - 4:40PM |
G14.00004: Using Persistent Homology to Compare Chaotic Dynamics Between Experiments on and Simulations of Rayleigh-B\'enard Convection Brett Tregoning, Saikat Mukherjee, Rachel Levanger, Mu Xu, Jacek Cyranka, Konstantin Mischaikow, Mark Paul, Michael Schatz Persistent homology is a tool from algebraic topology that can be used to efficiently detect pattern features in image data. In the spatio-temporally chaotic flow known as spiral defect chaos in Rayleigh-B\'enard convection, we explore the use of pattern features detected by persistent homology as a proxy for fundamental dynamical quantities that are not observable in experimental data but can be calculated from simulations, such as leading-order Lyapunov vectors. In simulations, we have identified that convective plumes are highly correlated with the leading-order Lyapunov vectors; however, we find that plumes appear in experiments at distinctly different rates than for Boussinesq simulations at the same parameter values. We describe work to resolve this discrepancy by accounting for non-Boussinesq effects in both experiments and simulations. [Preview Abstract] |
Sunday, November 24, 2019 4:40PM - 4:53PM |
G14.00005: Marginally stable Rayleigh--B\'{e}nard convection Baole Wen, Zijing Ding, Gregory Chini, Rich Kerswell We propose a new strategy to predict the heat transport in 2D Rayleigh--B\'{e}nard convection between stress-free isothermal boundaries. The Constantin--Doering--Hopf (CDH) variational framework, in which the temperature is decomposed into a background profile plus a fluctuation field and the background profile is required to satisfy a marginal energy-stability constraint, provides a formalism for determining an upper bound on the heat flux, i.e., the Nusselt number $Nu$. Although this scheme yields a rigorous upper bound on the flux scaling at large values of Rayleigh number $Ra$, i.e., $Nu\le 0.106Ra^{5/12}$ (Wen \emph{et al.} 2015), the resulting horizontal mean (background plus fluctuation average) temperature profile exhibits much thinner thermal boundary layers than are observed in DNS and laboratory experiments. Here, we incorporate an additional, marginal \emph{linear-stability} constraint on the horizontal mean temperature profile to thicken the boundary layers and thereby bring the predicted and observed profiles into closer agreement. We then develop a time-marching method to numerically solve the modified upper-bound problem. Our analysis reproduces the Malkus/Howard $Nu\sim Ra^{1/3}$ scaling but with a prefactor that closely matches the DNS results. [Preview Abstract] |
Sunday, November 24, 2019 4:53PM - 5:06PM |
G14.00006: Effect of aspect ratio on the Rayleigh convection of Maxwell viscoelastic fluids in a cavity heated from below Ildebrando Perez-Reyes, Alejandro Sebastian Ortiz-Perez, Nestor Gutierrez-Mendez Interesting results, of the effect the parity of convective rolls, on the Rayleigh convection in a Maxwell viscoelastic fluid confined in a 2D cavity are presented. A linear stability analysis have shown how the fluid stability changes for different values of the aspect ratio ranging from 0.1 to 10. It was found that vertical and horizontal parity of the temperature and velocity solutions, related to parity of the number of rolls distributed horizontally or vertically, gives different stability scenarios. On the other hand, kinks also appear in the curves of criticallity, which is also found in the stability of newtonian fluids which also depend on the symmetry of the solutions. Results and physical mechanisms shall be presented in terms of plots of the critical Rayleigh number and the frequency of oscillation for different cases encompassing perfect thermal conducting, or insulating, lateral, or horizontal, walls. Different values of the dimensionless relaxation time F are considered to discuss the physical mechanism of instability for fixed values of the Prandtl number Pr as well. [Preview Abstract] |
Sunday, November 24, 2019 5:06PM - 5:19PM |
G14.00007: Thermal convection over a fractal surface Srikanth Toppaladoddi, Andrew Wells, Charles Doering, John Wettlaufer We use well resolved numerical simulations to study Rayleigh-B\'enard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $Ra \in \left[10^7, 2.15 \times 10^9\right]$. The fractal boundaries are functions characterized by power spectral densities $S(k)$ that decay with wavenumber as $S(k) \sim k^{p}$ ($p < 0$). The degree of roughness is quantified by the exponent $p$ with $p < -3$ for smooth (differentiable) surfaces and $-3 \le p < -1$ for rough surfaces with Hausdorff dimension $D_f=\frac{1}{2}(p+5)$. By computing the exponent $\beta$ in power law fits $Nu \sim Ra^{\beta}$, where $Nu$ and $Ra$ are the Nusselt and the Rayleigh numbers, we observe that heat transport increases with roughness. For $p$ $= -3.0$, $-2.0$ and $-1.5$ we find, respectively, $\beta = 0.256, 0.281$ and $0.306$. For a given value of $p$ we observe that the mean heat flux is insensitive to the details of the roughness. [Preview Abstract] |
Sunday, November 24, 2019 5:19PM - 5:32PM |
G14.00008: On non-Oberbeck-Boussinesq effects in Rayleigh-Benard convection in air Zhenhua Wan, Ben Wang, Qi Wang, Shu-Ning Xia, Quan Zhou, De-Jun Sun Direct numerical simulations (DNS) of non-Oberbeck-Boussinesq (NOB) Rayleigh-B\'enard (RB) convection are performed in two-dimensional (2-D) and three-dimensional (3-D) cells. Perfect air is chosen as the operating fluid and the Prandtl number ($Pr$) is fixed to 0.71 for the reference state. Strong NOB effects are induced by large temperature differences at moderate Rayleigh numbers ($Ra$). Due to top-down symmetry breaking under NOB conditions, an increase of the centre temperature $T_c$ is found compared to the arithmetic mean temperature $T_m$, and the shifts of $T_c$ are strongly dependent on Rayleigh number $Ra$ and temperature differential $\epsilon$. The NOB effects on the Nusselt number ($Nu$) are quite small ($<2\%$). The power-law scalings of $Nu$ versus $Ra$ are robust against NOB effects, even though the temperature difference reaches up to 240 K. The Reynolds numbers $Re$, as well as the scalings of $Re$ versus $Ra$, are also insensitive to NOB effects. It is noteworthy that the influence of NOB effects on $Nu$ and $Re$ in 3-D RB flow is weaker than its 2-D counterpart. [Preview Abstract] |
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