Cylindrical Rayleigh Research Articles

Large-scale circulation and oscillation in turbulent Rayleigh–Bénard convection with a Prandtl number Pr = 12.3

An experimental study of the three-dimensional spatial structure of low-frequency temperature oscillations in cylindrical Rayleigh–Bénard convection of a fluid with a Prandtl number Pr = 12.3, aspect ratio Γ ≡ D/L = 1.00 (D is the diameter, and L is the height) and Rayleigh-number 5 × 1010 < Ra < 3 × 1011 is reported. The flow structure was measured using 3 sets of 8 thermal probes, each distributed uniformly around the periphery at heights L/4, L/2, and 3L/4 from the bottom. At the top/bottom layer, the large-scale circulation (LSC) consisted of two well-identified cold/hot flows. These cold/hot flows traveled to mid-height, where only the fluctuation in the temperature reveals the existence of two cold/hot flows. The oscillatory frequency corresponding to the turnover frequency of the LSC was only found at the location where the cold/hot flows were present. There is a discrepancy between the Reynolds number based on the turnover frequency of the LSC in the present work and GL prediction. This discrepancy is consistent with the study by Brown, Funfschilling, and Ahlers (J. Stat. Mech. 2007, P10005-1–P10005-22), indicating that there is a new state in Ra > Ra* where the LSC is no longer a coherent single-roll structure. Ra* for Pr = 12.3 is 1 × 1010.

Natural convection in cylindrical containers with isothermal ring-shaped obstacles

By means of three-dimensional direct numerical simulations, we investigate the influence of the regular roughness of heated and cooled plates on the mean heat transport in a cylindrical Rayleigh–Benard convection cell of aspect ratio one. The roughness is introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The considered Prandtl number $Pr$ equals 1, the Rayleigh number $Ra$ varies from $10^{6}$ to $10^{8}$ , the number of rings on each plate is 1, 2, 4, 8 or 10, the height of the rings is varied from 1.5 % to 49 % of the cylinder height and the gap between the rings is varied from 1.5 % to 18.8 % of the cell diameter. Totally, 135 different cases are analysed. Direct numerical simulations show that with small $Ra$ and wide roughness rings, a small reduction of the mean heat transport (the Nusselt number $Nu$ ) is possible, but, in most cases, the presence of the heated and cooled obstacles generally leads to an increase of $Nu$ , compared to the case of classical Rayleigh–Benard convection with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the $Nu$ versus $Ra$ scaling first increases with growing $Ra$ up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case.

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275031, 11475034, 11575033, and 11274026) and the National Basic Research Program of China (Grant No. 2013CB834100).

Rayleigh–Taylor instability (RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear (WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough, the WN results in planar geometry are recovered.

Vapour-bubble nucleation and dynamics in turbulent Rayleigh–Bénard convection

Vapour bubbles nucleating at micro-cavities etched into the silicon bottom plate of a cylindrical Rayleigh–Bénard sample (diameter $D=8.8$ cm, aspect ratio ${\it\Gamma}\equiv D/L\simeq 1.00$ where $L$ is the sample height) were visualized from the top and from the side. A triangular array of cylindrical micro-cavities (with a diameter of $30~{\rm\mu}\text{m}$ and a depth of $100~{\rm\mu}\text{m}$) covered a circular centred area (diameter of 2.5 cm) of the bottom plate. Heat was applied to the sample only over this central area while cooling was over the entire top-plate area. Bubble sizes and frequencies of departure from the bottom plate are reported for a range of bottom-plate superheats $T_{b}-T_{on}$ ($T_{b}$ is the bottom-plate temperature, $T_{on}$ is the onset temperature of bubble nucleation) from 3 to 12 K for three different cavity separations. The difference $T_{b}-T_{t}\simeq 16$ K between $T_{b}$ and the top plate temperature $T_{t}$ was kept fixed while the mean temperature $T_{m}=(T_{b}+T_{t})/2$ was varied, leading to a small range of the Rayleigh number $Ra$ from $1.4\times 10^{10}$ to $2.0\times 10^{10}$. The time between bubble departures from a given cavity decreased exponentially with increasing superheat and was independent of cavity separation. The contribution of the bubble latent heat to the total enhancement of heat transferred due to bubble nucleation was found to increase with superheat, reaching up to 25 %. The bubbly flow was examined in greater detail for a superheat of 10 K and $Ra\simeq 1.9\times 10^{10}$. The condensation and/or dissolution rates of departed bubbles revealed two regimes: the initial rate was influenced by steep thermal gradients across the thermal boundary layer near the plate and was two orders of magnitude larger than the final condensation and/or dissolution rate that prevailed once the rising bubbles were in the colder bulk flow of nearly uniform temperature. The dynamics of thermal plumes was studied qualitatively in the presence and absence of nucleating bubbles. It was found that bubbles enhanced the plume velocity by a factor of four or so and drove a large-scale circulation (LSC). Nonetheless, even in the presence of bubbles the plumes and LSC had a characteristic velocity which was smaller by a factor of five or so than the bubble-rise velocity in the bulk. In the absence of bubbles there was strongly turbulent convection but no LSC, and plumes on average rose vertically.

Heat-flux enhancement by vapour-bubble nucleation in Rayleigh–Bénard turbulence

We report on the enhancement of turbulent convective heat transport due to vapour-bubble nucleation at the bottom plate of a cylindrical Rayleigh–Bénard sample (aspect ratio 1.00, diameter 8.8 cm) filled with liquid. Microcavities acted as nucleation sites, allowing for well-controlled bubble nucleation. Only the central part of the bottom plate with a triangular array of microcavities (etched over an area with diameter of 2.5 cm) was heated. We studied the influence of the cavity density and of the superheat $T_{b}-T_{on}$ ($T_{b}$ is the bottom-plate temperature and $T_{on}$ is the value of $T_{b}$ below which no nucleation occurred). The effective thermal conductivity, as expressed by the Nusselt number $\mathit{Nu}$, was measured as a function of the superheat by varying $T_{b}$ and keeping a fixed difference $T_{b}-T_{t}\simeq 16$ K ($T_{t}$ is the top-plate temperature). Initially $T_{b}$ was much larger than $T_{on}$ (large superheat), and the cavities vigorously nucleated vapour bubbles, resulting in two-phase flow. Reducing $T_{b}$ in steps until it was below $T_{on}$ resulted in cavity deactivation, i.e. in one-phase flow. Once all cavities were inactive, $T_{b}$ was increased again, but they did not reactivate. This led to one-phase flow for positive superheat. The heat transport of both one- and two-phase flow under nominally the same thermal forcing and degree of superheat was measured. The Nusselt number of the two-phase flow was enhanced relative to the one-phase system by an amount that increased with increasing $T_{b}$. Varying the cavity density (69, 32, 3.2, 1.2 and $0.3~\text{mm}^{-2}$) had only a small effect on the global $\mathit{Nu}$ enhancement; it was found that $\mathit{Nu}$ per active site decreased as the cavity density increased. The heat-flux enhancement of an isolated nucleating site was found to be limited by the rate at which the cavity could generate bubbles. Local bulk temperatures of one- and two-phase flows were measured at two positions along the vertical centreline. Bubbles increased the liquid temperature (compared to one-phase flow) as they rose. The increase was correlated with the heat-flux enhancement. The temperature fluctuations, as well as local thermal gradients, were reduced (relative to one-phase flow) by the vapour bubbles. Blocking the large-scale circulation around the nucleating area, as well as increasing the effective buoyancy of the two-phase flow by thermally isolating the liquid column above the heated area, increased the heat-flux enhancement.

Cylindrical Rayleigh surface waves on a layer-coated cylinder measured by PVDF transducer and defocusing measurement method

This paper develops a measurement method for accurately determining dispersion curves of Rayleigh-type surface waves propagating on layer-coated elastic cylinders. It utilizes PVDF acoustic transducers and a defocusing measurement system. To deal with the cylindrically curved surface, a new cross-correlation waveform processing approach is proposed and verified. Cylindrical Rayleigh wave velocities of layered cylindrical solid samples have been successfully measured over a frequency range from 3 to 20MHz. The measured dispersion curves are in good agreement with their theoretical counterparts. It demonstrates the potential application for non-destructive evaluation of coating layers deposited on cylindrical solids.

Rotating turbulent Rayleigh–Bénard convection subject to harmonically forced flow reversals

The characteristics of turbulent flow in a cylindrical Rayleigh–Bénard convection cell which can be modified considerably in case rotation is included in the dynamics. By incorporating the additional effects of an Euler force, i.e., effects induced by non-constant rotation rates, a remarkably strong intensification of the heat transfer efficiency can be achieved. We consider turbulent convection at Rayleigh number Ra = 109 and Prandtl number σ = 6.4 under a harmonically varying rotation, allowing complete reversals of the direction of the externally imposed rotation in the course of time. The dimensionless amplitude of the oscillation is taken as 1/Ro* = 1 while various modulation frequencies 0.1 ≤ Roω ≤ 1 are applied. Both slow and fast flow-structuring and heat transfer intensification are induced due to the forced flow reversals. Depending on the magnitude of the Euler force, increases in the Nusselt number of up to 400% were observed, compared to the case of constant or no rotation. It is shown that a large thermal flow structure accumulates all along the centreline of the cylinder, which is responsible for the strongly increased heat transfer. This dynamic thermal flow structure develops quite gradually, requiring many periods of modulated flow reversals. In the course of time, the Nusselt number increases in an oscillatory fashion up to a point of global instability, after which a very rapid and striking collapse of the thermal columnar structure is seen. Following such a collapse is another, quite similar episode of gradual accumulation of the next thermal column. We perform direct numerical simulation of the incompressible Navier–Stokes equations to study this system. Both the flow structures and the corresponding heat transfer characteristics are discussed at a range of modulation frequencies. We give an overview of typical time scales of the system response.

Nonlinear saturation amplitude of cylindrical Rayleigh—Taylor instability

The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh—Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the r0/λ (λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When r0/λ is large enough (r0 ≫ λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

Measurement of cylindrical Rayleigh surface waves using line-focused PVDF transducers and defocusing measurement method

Line-focused PVDF transducers and defocusing measurement method are applied in this work to determine the dispersion curve of the Rayleigh-like surface waves propagating along the circumferential direction of a solid cylinder. Conventional waveform processing method has been modified to cope with the non-linear relationship between phase angle of wave interference and defocusing distance induced by a cylindrically curved surface. A cross correlation method is proposed to accurately extract the cylindrical Rayleigh wave velocity from measured data. Experiments have been carried out on one stainless steel and one glass cylinders. The experimentally obtained dispersion curves are in very good agreement with their theoretical counterparts. Variation of cylindrical Rayleigh wave velocity due to the cylindrical curvature is quantitatively verified using this new method. Other potential applications of this measurement method for cylindrical samples will be addressed.

Propagation of Cylindrical Rayleigh Waves in a Transversly Isotropic Thermoelastic Diffusive Solid Half-Space

Abstract The propagation of cylindrical Rayleigh waves in a trans- versely isotropic thermoelastic diffusive solid half-space subjected to stress free, isothermal/insulated and impermeable or isoconcentrated boundary conditions is investigated in the framework of different theories of ther- moelastic diffusion. The dispersion equation of cylindrical Rayleigh waves has been derived. The phase velocity and attenuation coefficients have been computed from the dispersion equation by using Muller’s method. Some special cases of dispersion equation are also deduced

Dynamics and flow coupling in two-layer turbulent thermal convection

AbstractWe present an experimental investigation of the dynamics and flow coupling of convective turbulent flows in a cylindrical Rayleigh–Bénard convection (RBC) cell with two immiscible fluids, water and Fluorinert FC-77 electronic liquid (FC77). With the lighter water above FC77, the latter is under the condition of constant heat flux at its top and bottom boundaries. It is found that one large-scale circulation (LSC) roll exists in each of the fluid layers, and that their circulation planes have two preferred azimuthal orientations separated by ${\sim }\mathrm{\pi} $. A surprising finding of the study is that cessations/reversals of the LSC in FC77 of the two-layer system occur much more frequently than they do in single-layer turbulent RBC, and that a cessation is most likely to result in a flow reversal of the LSC, which is in sharp contrast with the uniform distribution of the orientational angular change of the LSC before and after cessations in single-layer turbulent RBC. This implies that the dynamics governing cessations and reversals in the two systems are very different. Two coupling modes, thermal coupling (the flow directions of the two LSCs are opposite to each other at the fluid–fluid interface) and viscous coupling (the flow directions of the two LSCs are the same at the fluid–fluid interface), are identified, with the former as the predominant mode. That most cessations (in the FC77 layer) end up as reversals can be understood as a symmetry breaking imposed by the orientation of the LSC in the water layer, which remains unchanged most of the time. Furthermore, the frequently occurring cessations and reversals are caused by the system switching between its two metastable states, i.e. thermal and viscous coupling modes. It is also observed that the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally, i.e. the influence of the LSC in one fluid layer on the other is not symmetric.

Linear stability analysis of cylindrical Rayleigh–Bénard convection

AbstractThe instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated sidewall are investigated by linear stability analysis. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1, for aspect ratio $A$ ($A= H/ R= \mathrm{height} / \mathrm{radius} $) equal to 1, 0.9, 0.8, 0.7, respectively. We found that there still exists stable non-trivial axisymmetric flow beyond the second bifurcation in certain ranges of Prandtl number for $A= 1$, $0. 9$ and 0.8, excluding the $A= 0. 7$ case. The finding for $A= 0. 7$ is that very frequent changes of critical mode (azimuthal Fourier mode) of the second bifurcation occur when the Prandtl number is changed, where five kinds of steady modes $m= 1, 2, 8, 9, 10$ and three kinds of oscillatory modes $m= 3, 4, 6$ are presented. These multiple modes indicate different flow structures triggered at the transitions. The instability mechanism of the flow is explained by kinetic energy transfer analysis, which shows that the radial or axial shear of base flow combined with buoyancy mechanism leads to the instability results.

Boundary layers and wind in cylindrical Rayleigh–Bénard cells

AbstractWe analyse the wind and boundary layer properties of turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio one for Prandtl number $\mathit{Pr}= 0. 786$ and Rayleigh numbers ($\mathit{Ra}$) up to $1{0}^{9} $ by means of highly resolved direct numerical simulations. We identify time periods in which the orientation of the large-scale circulation (LSC) is nearly constant in order to perform a statistical analysis of the LSC. The analysis is then reduced to two dimensions by considering only the plane of the LSC. Within this plane the LSC is treated as a wind with thermal and viscous boundary layers developing close to the horizontal plates. Special focus is on the spatial development of the wind magnitude and the boundary layer thicknesses along the bottom plate. A method for the local analysis of the instantaneous boundary layer thicknesses is introduced which shows a dramatically changing wind magnitude along the wind path. Furthermore a linear increase of the viscous and thermal boundary layer thickness along the wind direction is observed for all $\mathit{Ra}$ considered while their ratio is spatially constant but depends weakly on $\mathit{Ra}$. A possible explanation is a strong spatial variation of the wind magnitude and fluctuations in the boundary layer region.

Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.

Modification of turbulence in Rayleigh–Bénard convection by phase change

Heavy or light particles introduced into a liquid trigger motion due to their buoyancy, with the potential to drive flow to a turbulent state. In the case of vapor bubbles present in a liquid near its boiling point, thermal coupling between the liquid and vapor can moderate this additional motion by reducing temperature gradients in the liquid. Whether the destabilizing mechanical feedback or stabilizing thermal feedback will dominate the system response depends on the number of bubbles present and the properties of the phase change. Here we study thermal convection with phase change in a cylindrical Rayleigh–Bénard cell to examine this competition. Using the Reynolds number of the flow as a signature of turbulence and the intensity of the flow, we show that in general the rising vapor bubbles destabilize the system and lead to higher velocities. The exception is a limited regime corresponding to phase change with a high latent heat of vaporization (corresponding to low Jakob number), where the vapor bubbles can eliminate the convective flow by smoothing temperature differences of the fluid.

Reduction of optical forces exerted on nanoparticles covered by scattering cancellation based plasmonic cloaks

Scattering cancellation approach has been recently proposed as a promising route to design invisibility cloaks. However, reduced observability of an object is just one of the potential applications of this technique. In this paper, we investigate the possibility to reduce optical forces exerted on a given nanoparticle by covering it with a properly designed plasmonic cloak. We show, in fact, that conditions similar to those used to make spherical and cylindrical nanoparticles invisible to the electromagnetic field by using the scattering cancellation approach, may be straightforwardly applied also to minimize both gradient and scattering optical forces exerted by the illuminating radiation on the same covered nanoparticles. These results are then validated through full-wave simulations, properly considering both dispersion and losses of the plasmonic materials used to design the cloaks. We also extend our speculations to the case of optical torques exerted on spheroidal and cylindrical Rayleigh particles, deriving the conditions to obtain stable equilibrium positions. This investigation leads to the anomalous result that the usual unstable equilibrium positions of uncovered particles may result stable ones when properly designing the particle cover. Finally, in order to apply the proposed theoretical speculations to more complex cases, we derive the conditions for minimizing optical forces exerted on a cloaked Rayleigh particle placed above a dielectric half space. These results may find interesting applications in different fields of nanotechnology.

A cylindrical Rayleigh–Taylor instability: radial outflow from pipes or stars

The classical Rayleigh–Taylor instability refers to a situation in which two inviscid fluids lie in horizontal layers, with a sharp interface separating them. The upper fluid is heavier, and so disturbances to the interface are unstable and grow with time. The present paper considers the analogous planar flow in cylindrical geometry. A light fluid is being produced by a line source at the origin, and is separated by a sharp interface from a surrounding more dense fluid. As the interface is forced outward, small disturbances to the flow grow with time. There is a finite critical time at which the curvature at the interface evidently becomes infinite, as in the planar case, and inviscid theory fails to be valid beyond this time. By introducing viscosity, it is argued that the high interfacial curvatures in the inviscid model are associated with formation of regions of large vorticity at the interface, and these serve as triggers for the interface to roll up into plume structures. A linearized inviscid theory is presented, and methods for computing nonlinear solutions in the inviscid and viscous models are outlined. Different solution modes exist, in which integer numbers of plumes are formed on the cylindrical outflow, and these are presented and discussed. The second mode, representing bi-polar symmetry, may be of particular relevance in astrophysical applications.

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A0, S0 and A1 modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A0 mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S0 mode with the defect appears, its amplitude is larger than three times of that of S0 mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25,000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry.

Simulation on laser-induced surface acoustic wave on isotropic cylinders by finite element method

Based on the thermoelastic theory, a finite element model is developed to simulate the process of laser inducing ultrasonic field in isotropic cylinders, which can take the temperature dependence of thermal parameters into account. Using the finite element model, we have simulated the ultrasonic fields induced by a pulse laser line source impacting on the generatrix of aluminum cylinders with different diameters. And the intact waveforms of surface acoustic wave (SAW including cylindrical Rayleigh and Whispering gallery (WG) modes) are presented, which are in very good agreement with the calculated and experimental waveforms in other literatures. Furthermore, the dispersion properties of cylindrical Rayleigh waves are analyzed by the method of phase spectral analysis, and the results show that with the increasing frequency, the phase velocity of cylindrical Rayleigh wave rapidly increases to the maximum value, and then gradually decreases to that of plane Rayleigh wave. With the diameter of cylinder decreasing, the maximum value of phase velocity and the corresponding frequency increase.