Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection

Grötzbach, G.

doi:10.1016/0021-9991(83)90125-0

Cited by 276 publications

(169 citation statements)

References 20 publications

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“…The first is the one proposed by Grötzbach [44] for the Rayleigh-Bénard convection where the thermal boundary layer thickness is about δ ϑ = H/2Nu (here the Nusselt number is estimated as Nu = 0.124 Ra 0.309 [39]). The second criteria is the one proposed by Patterson and Imberger [45] for a boundary layer in a differential heated cavity δ ϑ ∼ H/Ra 0.5 .…”

Section: Towards the Cfdandht Modelling Of The Molten Salt Tankmentioning

confidence: 99%

“…Using Grötzbach [44] criteria as reference for evaluating the smallest scales of the flow, η ∼ π(Ra Pr Nu) −0.25 H ms , the total number of control volumes (NCV ) have been estimated (see table 4). Since these constraints must be attained, special care is taken when constructing the computational meshes, considering that at least 3 control volumes must be located within the boundary layer [44].…”

Section: Towards the Cfdandht Modelling Of The Molten Salt Tankmentioning

confidence: 99%

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Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants

et al. 2013

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Two-tank molten salt storages are the most widespread thermal energy storage technology within concentrated solar power plants. In spite of this, there are design aspects such as thermal losses control, optimisation of the storage or how these devices scale up with the increase in power capacity of the plant which still should be considered. In this sense, numerical modelling of these systems can be a powerful tool for reducing their cost. The present work aims at modelling molten salt tanks by proposing a parallel modular object-oriented methodology which considers the different elements of the storage (e.g. tank walls, insulation material, tank foundation, molten salt storage media, etc.) as independent systems. Each of these elements can be solved independently and using different levels of modelling (from global to fully three-dimensional models), while at the same time they are to linked each other through their boundary conditions. The mathematical models used, together with some illustrative examples of the application of the proposed methodology, are presented and discussed in detail. Keywords

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Section: Towards the Cfdandht Modelling Of The Molten Salt Tankmentioning

confidence: 99%

Section: Towards the Cfdandht Modelling Of The Molten Salt Tankmentioning

confidence: 99%

Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants

et al. 2013

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“…The Reynolds number defined in this way follows Re = 0.33Ra 0.475 . In addition, we list the corresponding grid resolutions in azimuthal, radial and vertical directions (N φ , Nr, Nz), the grid spacing due to Grötzbach (1983), ∆G, and the maximum of the geometric mean of the grid spacings for the present simulations as given by (2.6),∆. δT is the thermal boundary layer thickness, which is determined as H/(2N u).…”

Section: Equations Of Motion and Numerical Modelmentioning

confidence: 99%

“…Table 1 lists the parameters of the present simulations: Ra, P r, Γ, the resulting Reynolds and Nusselt numbers and the corresponding grid resolutions. The table also shows the grid spacing due to the resolution criterion of Grötzbach (1983) (see also Kerr (1996) for a discussion) which is given by…”

Section: Equations Of Motion and Numerical Modelmentioning

confidence: 99%

Fine-scale statistics of temperature and its derivatives in convective turbulence

Emran

Schumacher

2008

J. Fluid Mech.

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We study the fine-scale statistics of temperature and its derivatives in turbulent RayleighBénard convection. Direct numerical simulations are carried out in a cylindrical cell with unit aspect ratio filled with a fluid with Prandtl number equal to 0.7 for Rayleigh numbers between 10 7 and 10 9 . The probability density function of the temperature or its fluctuations is found to be always non-Gaussian. The asymmetry and strength of deviations from the Gaussian distribution are quantified as a function of the cell height. The deviations of the temperature fluctuations from the local isotropy, as measured by the skewness of the vertical derivative of the temperature fluctuations, decrease in the bulk, but increase in the thermal boundary layer for growing Rayleigh number, respectively. Similar to the passive scalar mixing, the probability density function of the thermal dissipation rate deviates significantly from a log-normal distribution. The distribution is fitted well by a stretched exponential form. The tails become more extended with increasing Rayleigh number which displays an increasing degree of small-scale intermittency of the thermal dissipation field for both the bulk and the thermal boundary layer. We find that the thermal dissipation rate due to the temperature fluctuations is not only dominant in the bulk of the convection cell, but also yields a significant contribution to the total thermal dissipation in the thermal boundary layer. This is in contrast to the ansatz used in scaling theories and can explain the differences in the scaling of the total thermal dissipation rate with respect to the Rayleigh number.

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“…Special attention is given to the proper resolution of the steep temperature gradients in the proximity of the horizontal walls. In accordance with Grötzbach [11], 5-10 CVs are used for accurate representation of the thermal boundary layers along horizontal walls. The central part of the simulated domain is represented by a coarser mesh with ≈ (5 − 10)η K , which should be sufficient for a LES approach.…”

Section: Methodsmentioning

confidence: 99%

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

Kenjereš

2009

Theor. Comput. Fluid Dyn.

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We conducted a large eddy simulation (LES) of a locally applied electromagnetic control of turbulent thermal convection of an electrically conductive fluid (electrolyte solution) inside of a slender enclosure. Generic configurations, consisting of two or three magnets of opposite polarities located below the lower wall, and two oppositely charged electrodes along the side walls, are considered. The neutral situation (pure thermal convection) is selected to be in turbulent regime at Ra = 10 7 , Pr = 7. A magnetically extended Smagorinsky type model for the subgrid turbulent stresses and a simple-gradient diffusion model for the subgrid turbulent heat fluxes are used. Different intensities of applied DC current through electrodes are imposed. The effects of the resulting Lorentz force on flow, turbulence reorganisation and wall-heat transfer are analysed. It is demonstrated that significant flow and turbulence structure reorganisation takes place in the proximity of the lower horizontal wall and in the central parts of the enclosure-even for weak DC current of I = 1 A. Significant turbulence increase, generated by the elevated electromagnetic mixing, produced significant enhancements of the wall-heat transfer-up to 70% for the 2-magnet configuration.

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Spatial resolution requirements for direct numerical simulation of the Rayleigh-Bénard convection

Cited by 276 publications

References 20 publications

Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants

Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants

Fine-scale statistics of temperature and its derivatives in convective turbulence

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

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