16:15
Turbulent Convection 3
16:15
15 mins
#410
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The influence of spatial boundary heat distribution on turbulent convection
Johanna Mader, John Craske, Maarten van Reeuwijk
Abstract: We investigate the effects of different spatial heating and cooling distributions on the top and bottom walls of a closed domain using direct numerical simulation (DNS). The boundary buoyancy sources on the top and bottom walls are of equal strength and opposite sign. Localised heating and cooling is realised via line sources of buoyancy of strength Fl, giving rise to turbulent planar plumes. The remaining boundary area acts as a distributed source of buoyancy of strength Fd, such that the total heat flux across the boundary remains constant for all simulations. Six simulations are presented for Rayleigh number Ra=3e7 and Prandtl number Pr=0.7, which differ only in the distribution ratio G=Fd/Fl of the boundary buoyancy fluxes.
Purely localised heating (G=0) results in the formation of a stable two-layer stratification. In contrast, distributed heating from a horizontal source induces vertical mixing and thus produces an approximately uniform temperature profile. Combining both types of buoyancy sources (G>0) creates a competition between the stabilising effect of localised heating and the destabilising effect of distributed heating. This results in a decreasing buoyancy difference between the layers, as G is increased, and an increasing tilt of the stable stratification due to a lateral gradient in the buoyancy. For the largest value of G considered, the distributed source becomes so strong that that the stratification breaks down entirely and a Rayleigh-Benard-like flow develops. The transition is clearly observable in the probability density functions of the buoyancy, which have two distinct peaks for all but the highest G simulation.
We developed two theoretical models of increasing complexity that are able to predict the buoyancy difference between the layers and, in case of the second model, the tilt of the stratification. Both models are able to predict the heating distribution ratio G at which the stratification breaks down.
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16:30
15 mins
#390
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Transition to the ultimate regime in a radiatively driven convection experiment
Basile Gallet, Vincent Bouillaut, Simon Lepot, Sébastien Aumaître
Abstract: I will report on the transition between two regimes of heat transport in a radiatively driven convection experiment, where a fluid gets heated up within a tunable heating length l in the vicinity of the bottom of the tank. The first regime is similar to the one observed in standard Rayleigh-Bénard experiments, the Nusselt number Nu being related to the Rayleigh number Ra through the power-law Nu = const. Ra^{1/3}. The second regime corresponds to the "ultimate" or mixing-length scaling regime of thermal convection, where Nu varies as the square-root of Ra. Evidence for these two scaling regimes have been reported in Lepot et al. (PNAS, 2018), and I will present a detailed study of the transition from one regime to the other. I will introduce a simple model describing radiatively driven convection in the mixing-length regime, which leads to the scaling relation Nu = const. (l/H) Pr^{1/2} Ra^{1/2}, where H is the height of the cell and Pr the Prandtl number. From this model, one can deduce the values of Ra and Nu at which the system transitions from one regime to the other. These predictions are confirmed by the experimental data gathered at various Ra and l.
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16:45
15 mins
#173
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Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection
Xiaozhou He, Yin Wang, Penger Tong
Abstract: We report an experimental study of local temperature $T(t)$ and thermal dissipation rate $\epsilon(t)$ in free turbulent thermal convection for the Rayleigh numbers $10^9 \alt \Ra \alt 9 \times 10^{10}$ and the Prandtl number $\Pra = 4.3$. The data were taken at the center of a cylindrical convection cell of the aspect ratio $\Gamma = 1$. We show that because of the dynamic heterogeneity in RBC, non-Gaussian fluctuations can be generated by a convolution of Gaussian-like dynamic modes, to which the central limit theorem applies \cite{WKBG12}. In RBC, we found that $\epsilon$ is the correct dynamic variable that characterizes the non-Gaussian temperature fluctuations. At a constant $\epsilon$, the conditional temperature $(\delta T\vert \epsilon)$ follows a Gaussian distribution. The variance $\sigma_T^2(\epsilon)$ of the conditional temperature for varying $\epsilon$ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential temperature PDF \cite{HWT18}.
\begin{equation}
P(\delta T) = \frac{1}{\sqrt{2}\sigma_0} e^{-\sqrt{2}|\delta T/\sigma_0|} \ . \\
\label{eq1}
\end{equation}
Figure 1 shows the measured unconditional PDF $P(\delta T)$ at the cell center for three different values of $\Ra$. Although the measured temperature root-mean-square (rms) $\sigma_0$ varies considerably for different $Ra$, the PDFs collapse onto a single master curve, once the normalized variable $\delta T/\sigma_0$ is used. Except for a small roundoff near the origin, all of the PDFs have an exponential tail (solid line), as given by Eq.(\ref{eq1}). \\
Figure 2 shows a representative set of the conditional PDFs $G(\delta T \vert \epsilon)$ for 5 different values of $\epsilon$, which are obtained at the cell center with $Ra=8.3\times 10^9$. It is seen that all of the conditional PDFs can be well described by a Gaussian function $G(\delta T \vert \epsilon) = \frac{1}{\sqrt{2\pi}\sigma_T(\epsilon)}e^{-\delta T^2/[2\sigma_T^2(\epsilon)]}$ with $\sigma^2_T(\epsilon)$ being the variance of the conditionally sampled $\delta T(t_i)$. Obtained $G(\delta T \vert \epsilon)$ for other values of $\Ra$ were found to have the same Gaussian form.
\begin{figure}[H]
\setcaptionwidth{0.45\linewidth}
\begin{minipage}{0.5\linewidth}
\vskip -13pt
\centering
\includegraphics[width=0.8\textwidth]{fig1.eps}
\caption{Measured unconditional PDF $P(\delta T)$ of temperature fluctuations $\delta T$ at the cell center for three different values of Ra: $1.3\times 10^9$ (blue squares), $3.8 \times 10^9$ (black triangles), and $8.3 \times 10^9$ (red circles). In the plot, $\delta T$ is normalized by its rms value $\sigma_0$, and the error bars show the standard deviation of the red circles. The solid line shows a plot of Eq. $P(\delta T) = \frac{1}{\sqrt{2}\sigma_0} e^{-\sqrt{2}|\delta T/\sigma_0|}$.}
\label{1}
\end{minipage}%
\begin{minipage}{0.5\linewidth}
\centering
\includegraphics[width=0.8\textwidth]{fig2.eps}
\caption{Conditional PDF $G(\delta T \vert \epsilon)$ measured at the cell center with $\Ra = 8.3 \times 10^9$ for varying $\epsilon$ in units of their rms value $\sigma_{\epsilon}$ (from bottom to top): $\epsilon/\sigma_{\epsilon}=0.2$ (black circles), 0.5 (red circles), 2 (blue circles), 5 (green circles) and 10 (purple circles). For clarity, the vertical scale of the four PDFs with $\epsilon/\sigma_{\epsilon} \geq 0.5$ is multiplied by a factor $10$, $10^2$, $10^3$ and $10^4$, respectively. Solid lines represent Gaussian functions $G(\delta T\vert \epsilon) = \frac{1}{\sqrt{2\pi}\sigma_T(\epsilon)}e^{-\delta T^2/[2\sigma_T^2(\epsilon)]}$ with varying $\sigma^2_T(\epsilon)$.}
\label{2}
\end{minipage}
\end{figure}
\bibliographystyle{plainbv}
%\bibliography{biblio}
% Alternatively use this for the bibliography :
%
\begin{thebibliography}{1}
\bibitem{WKBG12}
B. Wang, J. Kuo, S. C. Bae, and S. Granick, When Brownian diffusion is not Gaussian, \textit{Nat. Mater.} \textbf{11}, 481 2012.
\bibitem{HWT18}
X. He, Y. Wang, and P. Tong, Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection, \textit{Phys. Rev. Fluids} \textbf{3} 052401, 2018.
\end{thebibliography}
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17:00
15 mins
#631
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DENSE LAGRANGIAN PARTICLE TRACKING OF TURBULENT RAYLEIGH BÉNARD CONVECTION IN A CYLINDRICAL SAMPLE USING SHAKE-THE-BOX
Johannes Bosbach, Daniel Schanz, Philipp Godbersen, Andreas Schröder
Abstract: We present spatially and temporally resolved velocity and acceleration measurements of turbulent Rayleigh-Bénard convection covering the complete volume of a cylindrical sample with aspect ratio one. Using the Shake-The-Box Lagrangian particle tracking algorithm, we are able to instantaneously track up to ~ 600,000 particles in the complete sample volume (~ 1 m³). The data assimilation scheme FlowFit with continuity and Navier-Stokes-constraints is used to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid, enabling to recover the smallest flow scales. The frame rate was chosen to be at least 7 times faster than the Kolmogorov time scale. In the presentation, we show Lagrangian and Eulerian visualizations of the large scale circulation (LSC) as well as small scale structures, such as thermal plumes and turbulent background fluctuations and unveil the dynamics of their complex interplay. Rare dynamic events, such as cessations and reorientations of the LSC will be presented in addition to combined and conditioned Lagrangian and Eulerian statistics of turbulent quantities.
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17:15
15 mins
#13
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The influence of thermal boundary conditions on turbulent forced convection pipe flow
Steffen Straub, Pourya Forooghi, Luca Marocco, Ricardo Vinuesa, Philipp Schlatter, Thomas Wetzel, Bettina Frohnapfel
Abstract: Different types of thermal boundary conditions are conceivable to accurately mimic convective heat transfer.
In this study, a turbulent forced convection pipe flow is used to compare isoflux, isothermal and mixed-type thermal boundary conditions at a range of Reynolds numbers of $Re_b=5300$ to $Re_b=37700$ and two Prandtl numbers $Pr=0.71$ and $Pr=0.025$.
It is found that, while the Nusselt number is unaffected by the type of thermal boundary condition for $Pr=0.71$, the isothermal boundary condition yields $\approx 20 \, \%$ lower Nusselt numbers at the low Prandtl number.
Furthermore, first and second order thermal statistics together with power spectra expose the influence of the type of thermal boundary conditions from the wall up to the core region of the flow.
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17:30
15 mins
#584
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Numerical study of radiatively driven convection: Influence of the Prandtl number on the heat flux in the mixing-length regime
Miquel Benjamin, Vincent Bouillaut, Sebastien Aumaitre, Basile Gallet
Abstract:
Buoyancy driven turbulent flows pertain to numerous geo- and astrophysical systems, where they have far reaching consequences: understanding them in atmospheric and oceanographic contexts is of paramount importance for climate modelling; in planetary and stellar cores, they control magnetic field generation via the dynamo effect, to cite a few examples.
Experimentally, convective flows have often been driven by heat fluxes from the boundaries. This setup is conducive to the formation of boundary layers that throttle the heat transfer, resulting in a diffusivity-controlled heat transfer, even for a turbulent bulk: Nu ~ Ra^{1/3} (Malkus 1954). By contrast, when heat is deposited directly in volume, thereby by-passing boundary layers, a recent experiment (Lepot et al. 2018) has evidenced an inviscid heat-transfer regime (sometimes referred to as the ``ultimate regime'' or the ``mixing length regime''): Nu ~ Ra^{1/2} (Kraichnan 1962, Spiegel 1963). In this experiment, dyed water is heated through a transparent bottom by means of a powerful spotlight. Further, the transition between the two regimes has been analyzed when the typical depth of injection of heat varies (Bouillaut et al. 2019).
I will briefly summarize those recent experimental results, and will complement them with a numerical study of the Boussinesq equations of motion performed with the HPC solver Coral. In particular, the influence of the Prandtl number (intimately linked to the fluid and therefore tuned with difficulty in experiments) will be discussed, and two distinct regimes will be decribed for low and high Prandtl number values.
Finally, I will comment on the influence of rotation, a key ingredient of natural flows.
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17:45
15 mins
#374
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Design process of a vertical backward facing step experiment for forced- and mixed-convection low Prandtl number flows
Thomas Schaub, Kevin Krauth, Joachim Konrad
Abstract: Low-Prandtl (low-Pr) number flows do not present scale similarity between viscous and thermal scales for all turbulent convection regimes, particularly for the highly anisotropic mixed- and natural convection cases [1]. A higher order moment description of Reynolds stresses and the turbulent heat flux is thought to be the minimum requirement for transversal heat transfer calculations in all convection regimes [1]. To test this hypothesis, precise experimental data is needed, which, unfortunately, is rare and highly scattered for the liquid metal case. The reasons are the complex measurement techniques associated with liquid metal flows and the difficult handling of liquid metals in practice. These issues have forced researchers to adopt compromises between high flow quality and clearly defined boundary conditions with performing experiments at all. To contribute towards a better understanding of low-Prandtl number convective flows is that the DITEFA 2 facility, a modular liquid metal loop, has been designed and is prior to be commissioned, see figure 1. A vertical backward facing step with channel expansion ratio of 2 and a channel aspect ratio of 1 after the step is installed in the test section. Hence, turbulent secondary flow and its implications cannot be neglected in this experiment. The used working fluid is the eutectic alloy gallium-indium-tin (Pr ~ 0,025). Special efforts have been put to guarantee good flow quality and controllable, describable and reproducible boundary conditions in the experiment. Existing know-how found in the literature of high quality flow experiments in water and air was thoughtfully transferred to the liquid metal case. Instrumentation techniques for local velocity and temperature measurement developed in the past [2] were brought to the current state of art. The design process of the DITEFA 2 facility will be overviewed and special considerations for the liquid metal case will be highlighted. If available, preliminary experimental results for Richardson numbers (Ri) in the range of 0.005 ≤ Ri ≤ 0.8 will be presented.
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18:00
15 mins
#564
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Mechanisms of helicity excitation in large-scale convection in closed volumes
Rodion Stepanov, Andrei Vasiliev, Peter Frick, Andrei Sukhanovskii, Valerij Titov, Frank Stefani
Abstract: Thermal convection in closed volumes of different shapes has many interesting features including a variety of patterns and complex temporal dynamics. One of the most interesting phenomena is the formation of large-scale circulation (LSC) known also as a mean wind in turbulent convection. Small scale structures of the flow are mutually linked to the dynamics of LSC. We address the problem of excitation of helicity which plays an important role in turbulence research in general, and is an essential building block of dynamo theory in particular. The α-effect, which is closely related to it, is an important mechanism for magnetic field self-excitation in planets, stars and galaxies. While in the solar dynamo the transformation of poloidal field into toroidal field is unambiguously ascribed to the Ω-effect in the strong shear regions within (and close to) the tachocline, the origin and “working site” of the α-effect (for regenerating the poloidal field) is still under debate. In this work the large-scale circulation (LSC) in turbulent Rayleigh - Bénard convection in cubic and cylindrical cells is shown to be able to generate a flow with a pronounced helicity. We have found that in the cube the total value of helicity is close to zero as it should be since there is no pseudoscalar in our problem. However local values of helicity can reach significant levels. Helicity is concentrated in structures related to the corner rolls. The diagonal plane of the LSC separates rolls with opposite signs of helicity. We note that this mechanism of spatial helicity separation is a consequence of the mirror symmetry breaking due to global rotation of LSC. Rayleigh - Bénard convection in a cylindrical volume is considered with an additional periodic perturbation with azimuthal wave number m=2. There is a particular interest to reproduce the resonant amplification of helicity oscillations, connected with the Tayler instability with azimuthal wave number m=1, by tide-like perturbation. This is a key element for a special Tayler-Spruit type dynamo model which might explain the amazing empirical synchronization of the solar cycle with the 11.07 years conjunction cycle of the tidally dominant Venus-Earth-Jupiter system. Results of the numerical simulations show spatial and temporal evolution of the helicity distribution in a cylinder.
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