scholarly journals The Zoo of Modes of Convection in Liquids Vibrated along the Direction of the Temperature Gradient

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Georgie Crewdson ◽  
Marcello Lappa
Keyword(s):  
Temperature Gradient ◽  
Linear Equations ◽  
Fluid Motion ◽  
Spatial Behavior ◽  
Quiescent State ◽  
Reference Case ◽  
Fluid Systems ◽  
Periodic Acceleration ◽  
Rayleigh Benard ◽  
Time Periodic

Thermovibrational flow can be seen as a variant of standard thermogravitational convection where steady gravity is replaced by a time-periodic acceleration. As in the parent phenomena, this type of thermal flow is extremely sensitive to the relative directions of the acceleration and the prevailing temperature gradient. Starting from the realization that the overwhelming majority of research has focused on circumstances where the directions of vibrations and of the imposed temperature difference are perpendicular, we concentrate on the companion case in which they are parallel. The increased complexity of this situation essentially stems from the properties that are inherited from the corresponding case with steady gravity, i.e., the standard Rayleigh–Bénard convection. The need to overcome a threshold to induce convection from an initial quiescent state, together with the opposite tendency of acceleration to damp fluid motion when its sign is reversed, causes a variety of possible solutions that can display synchronous, non-synchronous, time-periodic, and multi-frequency responses. Assuming a square cavity as a reference case and a fluid with Pr = 15, we tackle the problem in a numerical framework based on the solution of the governing time-dependent and non-linear equations considering different amplitudes and frequencies of the applied vibrations. The corresponding vibrational Rayleigh number spans the interval from Raω = 104 to Raω = 106. It is shown that a kaleidoscope of possible variants exist whose nature and variety calls for the simultaneous analysis of their temporal and spatial behavior, thermofluid-dynamic (TFD) distortions, and the Nusselt number, in synergy with existing theories on the effect of periodic accelerations on fluid systems.

scholarly journals Bulk scaling in wall-bounded and homogeneous vertical natural convection

2018 ◽  
Vol 841 ◽  
pp. 825-850 ◽  
Author(s):  
Chong Shen Ng ◽  
Andrew Ooi ◽  
Detlef Lohse ◽  
Daniel Chung
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Temperature Gradient ◽  
Power Law ◽  
Exact Relation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Previous numerical studies on homogeneous Rayleigh–Bénard convection, which is Rayleigh–Bénard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($\mathit{Nu}$) and the Reynolds number ($\mathit{Re}$) vary with the Rayleigh number ($\mathit{Ra}$) according to $\mathit{Nu}\sim \mathit{Ra}^{1/2}$ and $\mathit{Re}\sim \mathit{Ra}^{1/2}$ at small Prandtl numbers ($\mathit{Pr}$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel to it; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $\mathit{Nu}$, $\mathit{Re}$ and $\mathit{Ra}$ and to find physical arguments for closure, rather than making use of the exact relation between $\mathit{Nu}$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous set-up, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focusing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $\mathit{Ra}$, $\mathit{Re}$ and $\mathit{Nu}$. From a stability perspective, at low- to moderate-$\mathit{Ra}$, we find that the time evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

scholarly journals Suppression of Rayleigh-Taylor turbulence by time-periodic acceleration

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
G. Boffetta ◽  
M. Magnani ◽  
S. Musacchio
Keyword(s):  
Periodic Acceleration ◽  
Time Periodic

scholarly journals The role of Stewartson and Ekman layers in turbulent rotating Rayleigh–Bénard convection

2011 ◽  
Vol 688 ◽  
pp. 422-442 ◽  
Author(s):  
Rudie P. J. Kunnen ◽  
Richard J. A. M. Stevens ◽  
Jim Overkamp ◽  
Chao Sun ◽  
GertJan F. van Heijst ◽  
...  
Keyword(s):  
Temperature Gradient ◽  
Wall Temperature ◽  
Large Scale ◽  
Vertical Wall ◽  
Vertical Axis ◽  
Dominant Feature ◽  
A Cell ◽  
Vertically Aligned ◽  
Boundary Layer Dynamics ◽  
Rayleigh Benard

AbstractWhen the classical Rayleigh–Bénard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large-scale circulation (LSC) is the dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at $\mathit{Ra}\ensuremath{\sim} 1{0}^{8} \text{{\ndash}} 1{0}^{9} $ ($\mathit{Pr}= 4\text{{\ndash}} 6$) and $0\lesssim 1/ \mathit{Ro}\lesssim 25$ we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regimes II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part.

Convective instability by active stress

1969 ◽  
Vol 310 (1501) ◽  
pp. 183-219 ◽  
Keyword(s):  
Convective Instability ◽  
Pure Shear ◽  
Fluid Motion ◽  
Transformation Process ◽  
The Body ◽  
Equivalent Transformation ◽  
Quiescent State ◽  
Concentration Gradients ◽  
Active Stress ◽  
The Galerkin Method

Composition-dependent stress fields in continuous and mechanically isolated material can, it is shown, initiate and maintain conversion of chemical to kinetic energy. Though the process is analogous to natural convection, neither the body force of the well-known buoyancy mechanism nor the singular inhomogeneity and anisotropy of the interfacial tension mechanism is required. In the cases examined, the material is represented by the constitutive relation for incompressible Newtonian fluid augmented by an active stress which must be anisotropic or nonlinear in concentration gradients (or other, equivalent gradients) in accordance with the oft-misquoted Curie principle. The concentration gradients are supposed to be sustained by steady chemical reaction (or an equivalent transformation process) throughout the material and by exchange with surroundings. Conventional linear analysis of asymptotic stability is used to identify types of stress/concentration-gradient coupling that can render a quiescent state of reaction and diffusion unstable when concentration gradients exceed critical values. It is found that both deviatoric (pure shear) and antisymmetric active stress can support two-dimensional convective instability in a cylinder of material in which the quiescent state is circularly symmetric. Certain cases of stationary instability are solved exactly. Others involving both stationary and oscillatory instability are treated by a new version of the Galerkin method. The results establish the possibility of generating fluid motion by mechanochemical means in continuous material having appropriate subcontinuum structure. Whatever their relevance to protoplasmic movement in biological systems they do contain challenges for experimental and theoretical fluid mechanics and related areas of rheology and chemistry.

Unsteady Heating of Rayleigh-Benard Convection

2004 ◽  
Vol 59 (4-5) ◽  
pp. 266-274
Author(s):  
B. S. Bhadauria
Keyword(s):  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Dependent Part ◽  
Prandtl Numbers ◽  
Periodic Temperature ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Unsteady Heating ◽  
Horizontal Fluid Layer ◽  
Time Periodic

The linear thermal instability of a horizontal fluid layer with time-periodic temperature distribution is studied with the help of the Floquet theory. The time-dependent part of the temperature has been expressed in Fourier series. Disturbances are assumed to be infinitesimal. Only even solutions are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. It is found that the disturbances are either synchronous with the primary temperature field or have half its frequency. - 2000 Mathematics Subject Classification: 76E06, 76R10.

Stability and resonant wave interactions of confined two-layer Rayleigh–Bénard systems

2014 ◽  
Vol 754 ◽  
pp. 415-455 ◽  
Author(s):  
S. V. Diwakar ◽  
Shaligram Tiwari ◽  
Sarit K. Das ◽  
T. Sundararajan
Keyword(s):  
Travelling Waves ◽  
Current Work ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Aspect Ratios ◽  
Fluid Systems ◽  
Dimensional Parameters ◽  
The Individual ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractThe current work analyses the onset characteristics of Rayleigh–Bénard convection in confined two-dimensional two-layer systems. Owing to the interfacial interactions and the possibilities of convection onset in the individual layers, the two-layer systems typically exhibit diverse excitation modes. While the attributes of these modes range from the non-oscillatory mechanical/thermal couplings to the oscillatory standing/travelling waves, their regimes of occurrence are determined by the numerous system parameters and property ratios. In this regard, the current work aims at characterising their respective influence via methodical linear and fully nonlinear analyses, carried out on fluid systems that have been selected using the concept of balanced contrasts. Consequently, the occurrence of oscillatory modes is found to be associated with certain favourable fluid combinations and interfacial heights. The further branching of oscillatory modes into standing and travelling waves seems to additionally rely on the aspect ratio of the confined cavity. Specifically, the modulated travelling waves have been observed to occur (amidst standing wave modes) at discrete aspect ratios for which the onset of oscillatory convection happens at unequal fluid heights. This behaviour corresponds to the typical $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}m$:$n$ resonance where the critical wavenumbers of convection onset in the layers are dissimilar. Based on all of these observations, an attempt has been made in the present work to identify the oscillatory excitation modes with a reduced number of non-dimensional parameters.

scholarly journals Nonlinear theory for thermoacoustic waves in a narrow channel and pore subject to a temperature gradient

2016 ◽  
Vol 797 ◽  
pp. 765-801 ◽  
Author(s):  
N. Sugimoto
Keyword(s):  
Temperature Gradient ◽  
Nonlinear Theory ◽  
Narrow Channel ◽  
Excess Pressure ◽  
Advection Equation ◽  
Quiescent State ◽  
Dynamical Equations ◽  
Mean Values ◽  
Small Parameters ◽  
The Mean

A nonlinear theory for thermoacoustic waves in a gas-filled, narrow channel and pore subject to an axial temperature gradient is developed based on the fluid dynamical equations for an ideal gas. Under the narrow-tube approximation, three small parameters are introduced as asymptotic parameters, one being the ratio of a span length to a typical thickness of the thermoviscous diffusion layer, another the ratio of the typical propagation speed of thermoacoustic waves to an adiabatic sound speed and the final parameter is the ratio of the typical magnitude of a pressure disturbance to uniform pressure in a quiescent state. No thermal interaction between the gas and the solid wall is taken into account on assuming that the wall has a large heat capacity. Using the three small parameters, the fluid dynamical equations are approximated asymptotically to be reduced to a single nonlinear diffusion wave (advection) equation for an excess pressure. All field variables are determined consistently in terms of the excess pressure so as to satisfy the boundary conditions on the wall. Supposing a time-periodic solution to the equation derived, the mean value of the excess pressure over one period is examined. It is shown that while the mean vanishes in the linear theory, it decreases monotonically due to nonlinearity. It is also shown that mean values of the shear stress and the heat flux at the wall, as well as those of the vector fields of the mass and energy fluxes representing, respectively, acoustic and thermoacoustic streaming, are expressed in terms of the mean values of the products of the spatial and/or temporal pressure gradients, which are reduced to the spatial derivatives of the mean pressure.

Effect of non-uniform basic temperature gradient on Rayleigh–Benard–Marangoni convection in ferrofluids

2002 ◽  
Vol 248 (3) ◽  
pp. 379-395 ◽  
Author(s):  
I.S. Shivakumara ◽  
N. Rudraiah ◽  
C.E. Nanjundappa
Keyword(s):  
Temperature Gradient ◽  
Marangoni Convection ◽  
Basic Temperature ◽  
Rayleigh Benard
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