scholarly journals How heat transfer efficiencies in turbulent thermal convection depend on internal flow modes

2011 ◽  
Vol 676 ◽  
pp. 1-4 ◽  
Author(s):  
KE-QING XIA
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Thermal Convection ◽  
Large Scale ◽  
Internal Flow ◽  
Global Transport ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Flow States

How internal flow states can influence the global transport properties in a turbulent system has always been an intriguing question. Weiss & Ahlers (J. Fluid Mech., this issue, vol. 676, 2011, pp. 5–40) have provided an example by measuring the instantaneous Nusselt number in turbulent Rayleigh-Bénard convection and correlating it to the different modes of large-scale flow.

High-Rayleigh-number convection of pressurized gases in a horizontal enclosure

2002 ◽  
Vol 469 ◽  
pp. 1-12 ◽  
Author(s):  
A. S. FLEISCHER ◽  
R. J. GOLDSTEIN
Keyword(s):  
Heat Transfer ◽  
High Pressure ◽  
Rayleigh Number ◽  
Flow Field ◽  
Large Scale ◽  
Data Set ◽  
Video Images ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

High-pressure gases are used to study high-Rayleigh-number Rayleigh–Bénard convection in cylindrical horizontal enclosures. The Nusselt–Rayleigh heat transfer relationship is investigated for 1×109 < Ra < 1.7×1012. Schlieren video images of the flow field are recorded through optical viewports in the pressure vessel. The data set is well correlated by Nu = 0.071Ra0.328. The schlieren results confirm the existence of a large-scale flow that periodically interrupts the ascending and descending plumes. The intensity of both the plumes and the large-scale flow increases with Rayleigh number.

Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109

2010 ◽  
Vol 662 ◽  
pp. 409-446 ◽  
Author(s):  
G. SILANO ◽  
K. R. SREENIVASAN ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Multiple Solutions ◽  
Large Scale ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.

scholarly journals Dynamics of reorientations and reversals of large-scale flow in Rayleigh–Bénard convection

2010 ◽  
Vol 668 ◽  
pp. 480-499 ◽  
Author(s):  
P. K. MISHRA ◽  
A. K. DE ◽  
M. K. VERMA ◽  
V. ESWARAN
Keyword(s):  
Vertical Velocity ◽  
Large Scale ◽  
Numerical Study ◽  
Phase Changes ◽  
Fourier Mode ◽  
Complete Reversal ◽  
Large Scale Flow ◽  
Convective Fluid ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We present a numerical study of the reversals and reorientations of the large-scale circulation (LSC) of convective fluid in a cylindrical container of aspect ratio one. We take Prandtl number to be 0.7 and Rayleigh numbers in the range from 6 × 105 to 3 × 107. It is observed that the reversals of the LSC are induced by its reorientation along the azimuthal direction, which are quantified using the phases of the first Fourier mode of the vertical velocity measured near the lateral surface in the midplane. During a ‘complete reversal’, the above phase changes by around 180°, leading to reversals of the vertical velocity at all the probes. On the contrary, the vertical velocity reverses only at some of the probes during a ‘partial reversal’ with phase change other than 180°. Numerically, we observe rotation-led and cessation-led reorientations, in agreement with earlier experimental results. The ratio of the amplitude of the second Fourier mode and the first Fourier mode rises sharply during the cessation-led reorientations. This observation is consistent with the quadrupolar dominant temperature profile observed during the cessations. We also observe reorientations involving double cessation.

scholarly journals Mixed thermal conditions in convection: how do continents affect the mantle’s circulation?

2017 ◽  
Vol 822 ◽  
pp. 1-4 ◽  
Author(s):  
R. Ostilla-Mónico
Keyword(s):  
Boundary Conditions ◽  
Plate Tectonics ◽  
Large Scale ◽  
Thermal Conditions ◽  
Experimental Proof ◽  
Bénard Convection ◽  
Benard Convection ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Natural convection is omnipresent on Earth. A basic and well-studied model for it is Rayleigh–Bénard convection, the fluid flow in a layer heated from below and cooled from above. Most explorations of Rayleigh–Bénard convection focus on spatially uniform, perfectly conducting thermal boundary conditions, but many important geophysical phenomena are characterized by boundary conditions which are a mixture of conducting and adiabatic materials. For example, the differences in thermal conductivity between continental and oceanic lithospheres are believed to play an important role in plate tectonics. To study this, Wang et al. (J. Fluid Mech., vol. 817, 2017, R1), measure the effect of mixed adiabatic–conducting boundary conditions on turbulent Rayleigh–Bénard convection, finding experimental proof that even if the total heat transfer is primarily affected by the adiabatic fraction, the arrangement of adiabatic and conducting plates is crucial in determining the large-scale flow dynamics.

Effects of geometric confinement in quasi-2-D turbulent Rayleigh–Bénard convection

2016 ◽  
Vol 794 ◽  
pp. 639-654 ◽  
Author(s):  
Shi-Di Huang ◽  
Ke-Qing Xia
Keyword(s):  
Heat Transport ◽  
Large Scale ◽  
Lateral Aspect ◽  
Bénard Convection ◽  
Benard Convection ◽  
Reversal Frequency ◽  
Geometric Confinement ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We report an experimental study of confinement effects in quasi-2-D turbulent Rayleigh–Bénard convection. The experiments were conducted in five rectangular cells with their height $H$ and length $L$ being the same and fixed, while the width $W$ was different for each cell to produce lateral aspect ratios (${\it\Gamma}=W/H$) of 0.6, 0.3, 0.2, 0.15 and 0.1. Direct flow field measurements reveal that the large-scale flow slows down as ${\it\Gamma}$ decreases and there are more plumes travelling through the bulk region. Moreover, the reversal frequency of the large-scale flow is found to increase drastically in smaller ${\it\Gamma}$ cells, by more than 1000-fold for the highest value of Rayleigh number reached in the experiment. The reversal frequency can be well described by a stochastic model developed by Ni et al. (J. Fluid Mech., vol. 778, 2015, R5) and the probability density functions (PDF) of the time interval between successive reversals are found to follow Poisson statistics as in the 3-D system. It is further observed that the bulk temperature fluctuation increases significantly and its PDF changes from exponential to Gaussian as ${\it\Gamma}$ decreases. The influences of geometric confinement on the global heat transport are also investigated. The measured Nu–Ra relationship suggests that, as the lateral aspect ratio decreases, the relative weight of the boundary layer contribution in the global heat transport increases compared to that from the bulk. These results demonstrate that in the quasi-2-D geometry, geometric confinement has strong effects on both the global and local properties in turbulent convective flows, which are very different from the previous findings in 3-D and true 2-D systems.

Thermal convection in inclined cylindrical containers

2016 ◽  
Vol 790 ◽  
Author(s):  
Olga Shishkina ◽  
Susanne Horn
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Large Scale ◽  
Direct Numerical Simulations ◽  
Large Scale Circulation ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard ◽  
Small Inclination

By means of direct numerical simulations (DNS) we investigate the effect of a tilt angle ${\it\beta}$, $0\leqslant {\it\beta}\leqslant {\rm\pi}/2$, of a Rayleigh–Bénard convection (RBC) cell of aspect ratio 1, on the Nusselt number $\mathit{Nu}$ and Reynolds number $\mathit{Re}$. The considered Rayleigh numbers $\mathit{Ra}$ range from $10^{6}$ to $10^{8}$, the Prandtl numbers range from 0.1 to 100 and the total number of the studied cases is 108. We show that the $\mathit{Nu}\,({\it\beta})/\mathit{Nu}(0)$ dependence is not universal and is strongly influenced by a combination of $\mathit{Ra}$ and $\mathit{Pr}$. Thus, with a small inclination ${\it\beta}$ of the RBC cell, the Nusselt number can decrease or increase, compared to that in the RBC case, for large and small $\mathit{Pr}$, respectively. A slight cell tilt may not only stabilize the plane of the large-scale circulation (LSC) but can also enforce an LSC for cases when the preferred state in the perfect RBC case is not an LSC but a more complicated multiple-roll state. Close to ${\it\beta}={\rm\pi}/2$, $\mathit{Nu}$ and $\mathit{Re}$ decrease with increasing ${\it\beta}$ in all considered cases. Generally, the $\mathit{Nu}({\it\beta})/\mathit{Nu}(0)$ dependence is a complicated, non-monotonic function of ${\it\beta}$.

Some Observations on the Computational Sensitivity of Rotating Cavity Flows

2020 ◽  
Author(s):  
Tom Hickling ◽  
Li He
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Internal Flow ◽  
Systematic Investigation ◽  
Small Scale ◽  
Rotating Cavity ◽  
Ekman Layers ◽  
Inertial Wave ◽  
Wall Flow ◽  
Large Scale Flow

Abstract Heat transfer inside rotating cavities plays an important role in gas turbine engineering. Flows in both compressors and turbine internal flow cavities exhibit self-generated large-scale inertial wave structures, and buoyancy effects are often important. Across the open literature on the topic, there seems to be no clear consensus on what the most suitable modelling fidelity is — although it is a widely held opinion that URANS approaches are less suitable than LES, many authors have succeeded in getting reasonable heat transfer results with URANS. There is also little knowledge of the validity of hybrid URANS/LES type approaches (such as DES) when it comes to predicting the heat transfer in these flows, and furthermore, on the sensitivity of the flow model validity to local driving aerothermal mechanisms in different parts of the cavity. This paper presents the results of a systematic investigation of a rotating cavity with axial throughflow at a Grashof number of 3 × 109. It is found that, for the case investigated, the disk Ekman layers remain laminar. This causes the disk heat transfer to be relatively insensitive to the modelling fidelity used with URANS, DES, and LES giving similar results. The effect of the disk thermal boundary condition is also investigated — it is found to have a significant effect on the direction of the near-wall flow at high radii, despite the large-scale flow structure within the cavity remaining essentially unchanged. This feedback of the disk heat transfer to the near-disk aerodynamics implies that conjugate heat transfer computations of rotating cavities may be worth investigating. On the shroud, URANS fails to resolve the heat transfer enhancement from small-scale buoyancy driven streaks, whilst these are captured by LES. DES also captures these streaks, as the URANS layer within which they are located returns a very small eddy viscosity, and behaves in a similar manner to LES.

Large-scale flow and spiral core instability in Rayleigh-Bénard convection

1997 ◽  
Vol 55 (5) ◽  
pp. R4877-R4880 ◽  
Author(s):  
Igor Aranson ◽  
Michel Assenheimer ◽  
Victor Steinberg ◽  
Lev S. Tsimring
Keyword(s):  
Large Scale ◽  
Bénard Convection ◽  
Benard Convection ◽  
Large Scale Flow ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard
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