The dynamics of air bubbles in turbulent Rayleigh–Bénard (RB) convection is described for the first time using laboratory experiments and complementary numerical simulations. We performed experiments at Ra =5.5x10^9 and 1.1x 10^10, where streams of 1 mm bubbles were released at various locations from the bottom of the tank along the path of the roll structure. Using three-dimensional particle tracking velocimetry, we simultaneously tracked a large number of bubbles to inspect the pair dispersion, R2(t), for a range of initial separations, r, spanning one order of magnitude, namely 25η < r < 225η; here η is the local Kolmogorov length scale. Pair dispersion, R2(t), of the bubbles within a quiescent medium was also determined to assess the effect of inhomogeneity and anisotropy induced by the RB convection. Results show that R2(t) underwent a transition phase similar to the ballistic-to-diffusive (t^2-to-t^1) regime in the vicinity of the cell centre; it approached a bulk behavior t3/2 in the diffusive regime as the distance away from the cell centre increased. At small r, R2(t) ~ t^1 is shown in the diffusive regime with a lower magnitude compared to the quiescent case, indicating that the convective turbulence reduced the amplitude of the bubble’s fluctuations.more »
On the dynamics of air bubbles in Rayleigh–Bénard convection
The dynamics of air bubbles in turbulent Rayleigh–Bénard (RB) convection is described for the first time using laboratory experiments and complementary numerical simulations. We performed experiments at $Ra=5.5\times 10^{9}$ and $1.1\times 10^{10}$ , where streams of 1 mm bubbles were released at various locations from the bottom of the tank along the path of the roll structure. Using three-dimensional particle tracking velocimetry, we simultaneously tracked a large number of bubbles to inspect the pair dispersion, $R^{2}(t)$ , for a range of initial separations, $r$ , spanning one order of magnitude, namely $25\unicode[STIX]{x1D702}\leqslant r\leqslant 225\unicode[STIX]{x1D702}$ ; here $\unicode[STIX]{x1D702}$ is the local Kolmogorov length scale. Pair dispersion, $R^{2}(t)$ , of the bubbles within a quiescent medium was also determined to assess the effect of inhomogeneity and anisotropy induced by the RB convection. Results show that $R^{2}(t)$ underwent a transition phase similar to the ballistic-to-diffusive ( $t^{2}$ -to- $t^{1}$ ) regime in the vicinity of the cell centre; it approached a bulk behavior $t^{3/2}$ in the diffusive regime as the distance away from the cell centre increased. At small $r$ , $R^{2}(t)\propto t^{1}$ is shown in the diffusive regime with a lower magnitude compared to the quiescent case, indicating that the convective turbulence reduced more »
- Award ID(s):
- 1912824
- Publication Date:
- NSF-PAR ID:
- 10157234
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 891
- ISSN:
- 0022-1120
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
For each $t\in \mathbb{R}$ , we define the entire function $$\begin{eqnarray}H_{t}(z):=\int _{0}^{\infty }e^{tu^{2}}\unicode[STIX]{x1D6F7}(u)\cos (zu)\,du,\end{eqnarray}$$ where $\unicode[STIX]{x1D6F7}$ is the super-exponentially decaying function $$\begin{eqnarray}\unicode[STIX]{x1D6F7}(u):=\mathop{\sum }_{n=1}^{\infty }(2\unicode[STIX]{x1D70B}^{2}n^{4}e^{9u}-3\unicode[STIX]{x1D70B}n^{2}e^{5u})\exp (-\unicode[STIX]{x1D70B}n^{2}e^{4u}).\end{eqnarray}$$ Newman showed that there exists a finite constant $\unicode[STIX]{x1D6EC}$ (the de Bruijn–Newman constant ) such that the zeros of $H_{t}$ are all real precisely when $t\geqslant \unicode[STIX]{x1D6EC}$ . The Riemann hypothesis is equivalent to the assertion $\unicode[STIX]{x1D6EC}\leqslant 0$ , and Newman conjectured the complementary bound $\unicode[STIX]{x1D6EC}\geqslant 0$ . In this paper, we establish Newman’s conjecture. The argument proceeds by assuming for contradiction that $\unicode[STIX]{x1D6EC}<0$ and then analyzing the dynamics of zeros of $H_{t}$ (building on the work of Csordas, Smith and Varga) to obtain increasingly strong control on the zeros of $H_{t}$ in the range $\unicode[STIX]{x1D6EC}The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al. , J. Fluid Mech. , vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS.more »We mimic a flapping wing through a fluid–structure interaction (FSI) framework based upon a generalized lumped-torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces, wing deformation and self-propelled motion. A phenomenological solution to the linear single-spring structural dynamics equation is established to help offer insight and validate the computations under the limit of small deformation. The cruising velocity and power requirements are evaluated by varying the flapping Reynolds number ( $20\leqslant Re_{f}\leqslant 100$ ), stiffness (represented by frequency ratio, $1\lesssim \unicode[STIX]{x1D714}^{\ast }\leqslant 10$ ) and the ratio of aerodynamic to structural inertia forces (represented by a dimensionless parameter $\unicode[STIX]{x1D713}$ ( $0.1\leqslant \unicode[STIX]{x1D713}\leqslant 3$ )). For structural inertia dominated flows ( $\unicode[STIX]{x1D713}\ll 1$ ), pitching and plunging are shown to always remain in phase ( $\unicode[STIX]{x1D719}\approx 0$ ) with the maximum wing deformation occurring at the end of the stroke. When aerodynamics dominates ( $\unicode[STIX]{x1D713}>1$ ), a large phase difference is induced ( $\unicode[STIX]{x1D719}\approx \unicode[STIX]{x03C0}/2$ ) and the maximum deformation occurs at mid-stroke. Lattice Boltzmann simulations show that there is an optimal $\unicode[STIX]{x1D714}^{\ast }$ at which cruising velocity is maximized and the location of optimum shifts away from unit frequency ratio ( $\unicode[STIX]{x1D714}^{\ast }=1$ ) asmore »Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios ${\rm \pi} /5\leqslant \varGamma \leqslant 4{\rm \pi}$ , where $\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\leqslant Ra\leqslant 10^{11}$ , and four orders of magnitude in the Prandtl number, $10^{-2}\leqslant Pr\leqslant 10^2$ . At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \rightarrow \infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$ . The prefactor of this scaling depends on $\varGamma$ and is largest at $\varGamma \approx 1.9$ . The Reynolds number $Re$ for large- $Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $\varGamma \approx 4.5$ . All of these large- $Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox ( Phys. Fluids , vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $\varGamma$ is smaller.