scholarly journals Observation of a link between energy dissipation rate and oscillation frequency of the large-scale circulation in dry and moist Rayleigh-Bénard turbulence

2018 ◽  
Vol 3 (8) ◽  
Author(s):  
Dennis Niedermeier ◽  
Kelken Chang ◽  
Will Cantrell ◽  
Kamal Kant Chandrakar ◽  
David Ciochetto ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Oscillation Frequency ◽  
Dissipation Rate ◽  
Large Scale ◽  
Energy Dissipation Rate ◽  
Large Scale Circulation ◽  
Rayleigh Benard

scholarly journals Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 582 ◽  
Author(s):  
Hui Yang ◽  
Yikun Wei ◽  
Zuchao Zhu ◽  
Huashu Dou ◽  
Yuehong Qian
Keyword(s):  
Heat Transfer ◽  
Structure Function ◽  
Dissipation Rate ◽  
Large Scale ◽  
Thermal Dissipation ◽  
Small Scale ◽  
Linear Scaling ◽  
Two Dimensional ◽  
Large Scale Circulation ◽  
Rayleigh Benard

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

Turbulent flow in the bulk of Rayleigh–Bénard convection: aspect-ratio dependence of the small-scale properties

2014 ◽  
Vol 747 ◽  
pp. 73-102 ◽  
Author(s):  
Matthias Kaczorowski ◽  
Kai-Leong Chong ◽  
Ke-Qing Xia
Keyword(s):  
Heat Flux ◽  
Energy Dissipation ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Thermal Plumes ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Very High

AbstractGeometrical confinement of turbulent Rayleigh–Bénard convection (RBC) in Cartesian geometries is found to reduce the local Bolgiano length scale in the centre of the cell $L_{B,centre}$ and can therefore be used to study cascade processes in the bulk of RBC. The dependence of $L_{B,centre}$ versus $\varGamma $ suggests a cut-off to the local $L_B$, which depends on the Prandtl number $Pr$ and is of the order of the cell’s smallest dimension. It is also observed that geometrical confinement changes the topology of the flow, causing the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate (averaged over the centre of the cell and normalized by their respective global averages) to exhibit a maximum at a certain $\varGamma $, which roughly coincides with the aspect ratio at which the viscous and thermal boundary layers of the two opposite lateral walls merge. As a result the mean heat flux through the core region also exhibits a maximum. Unlike in the cubic case, we find that geometrical confinement of the flow results in a local balance of the heat flux and the turbulent kinetic energy dissipation rate for $Pr= 4.38$ for all values of the Rayleigh number $Ra$ (up to $10^{10}$), while no balance is observed for $Pr= 0.7$. The need for very high bulk resolution to accurately resolve the gradients of the flow field at high $Ra$ is shown by analysing the second-order structure functions of the vertical velocity and temperature in the bulk of RBC. Under-resolution of the temperature field yields a large error in the dissipative range scaling, which is believed to be an effect of intermittently penetrating thermal plumes. The resolution contrast resulting from the requirement to resolve the thermal plumes and the homogeneous and isotropic background turbulence scales as $\delta _T / \langle \eta _k \rangle _{centre} \sim Ra^{0.1}$ and should therefore be taken into account when tackling very high $Ra$. In the case studied here, under-resolution can have a significant effect on the local heat flux through the centre of the cell.

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

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