6 results
Rotating turbulent thermal convection at very large Rayleigh numbers
- Marcel Wedi, Dennis P.M. van Gils, Eberhard Bodenschatz, Stephan Weiss
-
- Journal:
- Journal of Fluid Mechanics / Volume 912 / 10 April 2021
- Published online by Cambridge University Press:
- 15 February 2021, A30
-
- Article
-
- You have access Access
- Open access
- HTML
- Export citation
-
We report on turbulent thermal convection experiments in a rotating cylinder with a diameter ($D$) to height ($H$) aspect ratio of $\varGamma =D/H=0.5$. Using nitrogen and pressurised sulphur hexafluoride we cover Rayleigh numbers (Ra) from $8\times 10^{9}$ to $8\times 10^{14}$ at Prandtl numbers $0.72\lesssim {\textit {Pr}}\lesssim 0.94$. For these Ra we measure the global vertical heat flux (i.e. the Nusselt number – Nu), as well as statistical quantities of local temperature measurements, as a function of the rotation rate, i.e. the inverse Rossby number – 1/Ro. In contrast to measurements in fluids with a higher Pr we do not find a heat transport enhancement, but only a decrease of Nu with increasing 1/Ro. When normalised with Nu(0) for the non-rotating system, data for all different Ra collapse and, for sufficiently large 1/Ro, follow a power law ${\textit {Nu}}/{\textit {Nu}}_0\propto (1/{\textit {Ro}})^{-0.43}$. Furthermore, we find that both the heat transport and the temperature field qualitatively change at rotation rates $1/{\textit {Ro}}^*_1=0.8$ and $1/{\textit {Ro}}^*_2=4$. We interpret the first transition at $1/{\textit {Ro}}^*_1$ as change from a large-scale circulation roll to the recently discovered boundary zonal flow (BZF). The second transition at rotation rate $1/{\textit {Ro}}^*_2$ is not associated with a change of the flow morphology, but is rather the rotation rate for which the BZF is at its maximum. For faster rotation the vertical transport of warm and cold fluid near the sidewall within the BZF decreases and hence so does Nu.
Experimental investigation of heat transport in homogeneous bubbly flow
- Biljana Gvozdić, Elise Alméras, Varghese Mathai, Xiaojue Zhu, Dennis P. M. van Gils, Roberto Verzicco, Sander G. Huisman, Chao Sun, Detlef Lohse
-
- Journal:
- Journal of Fluid Mechanics / Volume 845 / 25 June 2018
- Published online by Cambridge University Press:
- 20 April 2018, pp. 226-244
-
- Article
-
- You have access Access
- Open access
- HTML
- Export citation
-
We present results on the global and local characterisation of heat transport in homogeneous bubbly flow. Experimental measurements were performed with and without the injection of ${\sim}2.5~\text{mm}$ diameter bubbles (corresponding to bubble Reynolds number $Re_{b}\approx 600$) in a rectangular water column heated from one side and cooled from the other. The gas volume fraction $\unicode[STIX]{x1D6FC}$ was varied in the range 0 %–5 %, and the Rayleigh number $Ra_{H}$ in the range $4.0\times 10^{9}{-}1.2\times 10^{11}$. We find that the global heat transfer is enhanced up to 20 times due to bubble injection. Interestingly, for bubbly flow, for our lowest concentration $\unicode[STIX]{x1D6FC}=0.5\,\%$ onwards, the Nusselt number $\overline{Nu}$ is nearly independent of $Ra_{H}$, and depends solely on the gas volume fraction $\unicode[STIX]{x1D6FC}$. We observe the scaling $\overline{Nu}\,\propto \,\unicode[STIX]{x1D6FC}^{0.45}$, which is suggestive of a diffusive transport mechanism, as found by Alméras et al. (J. Fluid Mech., vol. 776, 2015, pp. 458–474). Through local temperature measurements, we show that the bubbles induce a huge increase in the strength of liquid temperature fluctuations, e.g. by a factor of 200 for $\unicode[STIX]{x1D6FC}=0.9\,\%$. Further, we compare the power spectra of the temperature fluctuations for the single- and two-phase cases. In the single-phase cases, most of the spectral power of the temperature fluctuations is concentrated in the large-scale rolls/motions. However, with the injection of bubbles, we observe intense fluctuations over a wide range of scales, extending up to very high frequencies. Thus, while in the single-phase flow the thermal boundary layers control the heat transport, once the bubbles are injected, the bubble-induced liquid agitation governs the process from a very small bubble concentration onwards. Our findings demonstrate that the mixing induced by high Reynolds number bubbles ($Re_{b}\approx 600$) offers a powerful mechanism for heat transport enhancement in natural convection systems.
Optimal Taylor–Couette flow: radius ratio dependence
- Rodolfo Ostilla-Mónico, Sander G. Huisman, Tim J. G. Jannink, Dennis P. M. Van Gils, Roberto Verzicco, Siegfried Grossmann, Chao Sun, Detlef Lohse
-
- Journal:
- Journal of Fluid Mechanics / Volume 747 / 25 May 2014
- Published online by Cambridge University Press:
- 10 April 2014, pp. 1-29
-
- Article
- Export citation
-
Taylor–Couette flow with independently rotating inner ($i$) and outer ($o$) cylinders is explored numerically and experimentally to determine the effects of the radius ratio $\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to $\mathit{Re}_i=9.5\times 10^3$ and $\mathit{Re}_o=5\times 10^3$, corresponding to Taylor numbers of up to $\mathit{Ta}=10^8$ for four different radius ratios $\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ($\mathrm{T^3C}$) set-up, reach Reynolds numbers of up to $\mathit{Re}_i=2\times 10^6$ and $\mathit{Re}_o=1.5\times 10^6$, corresponding to $\mathit{Ta}=5\times 10^{12}$ for $\eta =0.714\mbox{--}0.909$. Effective scaling laws for the torque $J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving $\mathit{Ta}$ are independent of the radius ratio $\eta $. As previously reported for $\eta =0.714$, optimum transport at a non-zero Rossby number $\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here $\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between $\mathit{Ta}\sim 3\times 10^{8}$ and $\mathit{Ta}\sim 10^{10}$, $\mathit{Ro}_{opt}$ saturates to an asymptotic $\eta $-dependent value. Theoretical predictions for the asymptotic value of $\mathit{Ro}_{opt}$ are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.
The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor–Couette flow
- Dennis P. M. van Gils, Daniela Narezo Guzman, Chao Sun, Detlef Lohse
-
- Journal:
- Journal of Fluid Mechanics / Volume 722 / 10 May 2013
- Published online by Cambridge University Press:
- 28 March 2013, pp. 317-347
-
- Article
- Export citation
-
Bubbly turbulent Taylor–Couette (TC) flow is globally and locally studied at Reynolds numbers of $\mathit{Re}= 5\times 1{0}^{5} $ to $2\times 1{0}^{6} $ with a stationary outer cylinder and a mean bubble diameter around 1 mm. We measure the drag reduction (DR) based on the global dimensional torque as a function of the global gas volume fraction ${\alpha }_{global} $ over the range 0–4 %. We observe a moderate DR of up to 7 % for $\mathit{Re}= 5. 1\times 1{0}^{5} $. Significantly stronger DR is achieved for $\mathit{Re}= 1. 0\times 1{0}^{6} $ and $2. 0\times 1{0}^{6} $ with, remarkably, more than $40\hspace{0.167em} \% $ of DR at $\mathit{Re}= 2. 0\times 1{0}^{6} $ and ${\alpha }_{global} = 4\hspace{0.167em} \% $. To shed light on the two apparently different regimes of moderate DR and strong DR, we investigate the local liquid flow velocity and the local bubble statistics, in particular the radial gas concentration profiles and the bubble size distribution, for the two different cases: $\mathit{Re}= 5. 1\times 1{0}^{5} $ in the moderate DR regime and $\mathit{Re}= 1. 0\times 1{0}^{6} $ in the strong DR regime, both at ${\alpha }_{global} = 3\pm 0. 5\hspace{0.167em} \% $. In both cases the bubbles mostly accumulate close to the inner cylinder (IC). Surprisingly, the maximum local gas concentration near the IC for $\mathit{Re}= 1. 0\times 1{0}^{6} $ is ${\approx }2. 3$ times lower than that for $\mathit{Re}= 5. 1\times 1{0}^{5} $, in spite of the stronger DR. Evidently, a higher local gas concentration near the inner wall does not guarantee a larger DR. By defining and measuring a local bubble Weber number ($\mathit{We}$) in the TC gap close to the IC wall, we observe that the cross-over from the moderate to the strong DR regime occurs roughly at the cross-over of $\mathit{We}\sim 1$. In the strong DR regime at $\mathit{Re}= 1. 0\times 1{0}^{6} $ we find $\mathit{We}\gt 1$, reaching a value of $9(+ 7, - 2)$ when approaching the inner wall, indicating that the bubbles increasingly deform as they draw near the inner wall. In the moderate DR regime at $\mathit{Re}= 5. 1\times 1{0}^{5} $ we find $\mathit{We}\approx 1$, indicating more rigid bubbles, even though the mean bubble diameter is larger, namely $1. 2(+ 0. 7, - 0. 1)~\mathrm{mm} $, as compared with the $\mathit{Re}= 1. 0\times 1{0}^{6} $ case, where it is $0. 9(+ 0. 6, - 0. 1)~\mathrm{mm} $. We conclude that bubble deformability is a relevant mechanism behind the observed strong DR. These local results match and extend the conclusions from the global flow experiments as found by van den Berg et al. (Phys. Rev. Lett., vol. 94, 2005, p. 044501) and from the numerical simulations by Lu, Fernandez & Tryggvason (Phys. Fluids, vol. 17, 2005, p. 95102).
Optimal Taylor–Couette turbulence
- Dennis P. M. van Gils, Sander G. Huisman, Siegfried Grossmann, Chao Sun, Detlef Lohse
-
- Journal:
- Journal of Fluid Mechanics / Volume 706 / 10 September 2012
- Published online by Cambridge University Press:
- 03 July 2012, pp. 118-149
-
- Article
- Export citation
-
Strongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux as a function of the Taylor number and the angular velocity ratio in the large-Taylor-number regime and well off the inviscid stability borders (Rayleigh lines) for co-rotation and for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux , with an amplitude and an exponent . The data are consistent with one effective exponent for all , but we discuss a possible dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of , i.e. along the line . This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position of the neutral line, defined by for fixed height . For these large values, the ratio , which is close to , is distinguished by a zero angular velocity gradient in the bulk. While for moderate counter-rotation , the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.
On bubble clustering and energy spectra in pseudo-turbulence
- JULIÁN MARTÍNEZ MERCADO, DANIEL CHEHATA GÓMEZ, DENNIS VAN GILS, CHAO SUN, DETLEF LOHSE
-
- Journal:
- Journal of Fluid Mechanics / Volume 650 / 10 May 2010
- Published online by Cambridge University Press:
- 24 March 2010, pp. 287-306
-
- Article
- Export citation
-
Three-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulence.