High Rayleigh number convection in a cubic cell with adiabatic sidewalls

Vasiliev, A.; Sukhanovskii, A.; Frick, Peter; Budnikov, A. V.; Фомичев, В. М.; Bol’shukhin, M. A.; Romanov, R. I.

doi:10.1016/j.ijheatmasstransfer.2016.06.015

Cited by 50 publications

(37 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The Large Scale Circulation (LSC) associated with these states consists of a dominant roll in one of the two diagonal planes x = y or x = 1 − y with a clockwise or anticlockwise motion as shown in figure 1. These four flow states have been reported by other researchers in numerical studies (Foroozani et al 2017;Giannakis et al 2018;Vasiliev et al 2018) and experimental studies (Bai et al 2016;Vasiliev et al 2016)).…”

Section: Large-scale Flow Structuressupporting

confidence: 83%

“…Unlike the cylindrical geometry, the cubic container does not possess an azimuthal symmetry and the LSC stabilizes in one of the two diagonal vertical planes leading to four potential quasi-stable states for the flow (the two diagonal planes combined with clockwise or anticlockwise motion). Random low-frequency reorientations between these quasi-stable states have been observed in experiments (Vasiliev et al 2016) and numerical simulations (Foroozani et al 2017) which consist in a rotation of the LSC from one diagonal plane to the other. No cessation-led reorientation events have been reported yet, although the study of Giannakis et al (2018) suggests that reversals (reorientations of an angle π) can happen.…”

Section: Introductionmentioning

confidence: 91%

See 1 more Smart Citation

Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

et al. 2019

View full text Add to dashboard Cite

This paper investigates the large-scale flow reorientations of Rayleigh–Bénard convection in a cubic cell using proper orthogonal decomposition (POD) analysis and modelling. A direct numerical simulation is performed for air at a Rayleigh number of $10^{7}$ and shows that the flow is characterized by four quasi-stable states, corresponding to a large-scale circulation lying in one of the two diagonal planes of the cube with a clockwise or anticlockwise motion, with occasional brief reorientations. Proper orthogonal decomposition is applied to the joint velocity and temperature fields of an enriched database which captures the statistical symmetries of the flow. We found that each quasi-stable state consists of a superposition of four spatial modes representing three types of structures: (i) a mean-flow mode consisting of two stacked counter-rotating torus-like structures; (ii) two large-scale two-dimensional rolls (pair of degenerated modes) which form large-scale diagonal rolls when combined together; and (iii) an eight-roll mode that transports fluid from one corner to the other and strengthens the circulation along the diagonal. In addition, we identified three other modes that play a role in the reorientation process: two boundary-layer modes (pair of degenerated modes) that connect the core region with the horizontal boundary layers and one mode associated with corner rolls. The symmetries of the different POD modes are discussed, as well as their temporal dynamics. A description of the reorientation process in terms of POD modes is provided and compared with other modal approaches available in the literature. Finally, Galerkin projection is used to derive a POD-based reduced-order model. Unresolved modes are accounted for in the model by an extra dissipation term and the addition of noise. A seven-mode model is able to reproduce the low-frequency dynamics of the large-scale reorientations as well as the high-frequency dynamics associated with the large-scale circulation rotation. Linear stability analysis and sensitivity analysis confirm the role of the boundary-layer modes and the corner-rolls mode in the reorientation process.

show abstract

Section: Large-scale Flow Structuressupporting

confidence: 83%

Section: Introductionmentioning

confidence: 91%

Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

et al. 2019

View full text Add to dashboard Cite

show abstract

“…From his work, it is concluded that for aspect ratios greater than 2 the influence of the temperature distribution across the different walls on the mean Nusselt number is negligible. Vasiliev et al (2016) developed a numerical and experimental study in a cubic cell with turbulent Rayleigh-Bénard convection using two similar (but not identical) experimental setups in different laboratories. Both teams conducted experiments for the same set of Prandtl and Ra numbers (Pr = 3.5, Pr = 6.1, Ra = 2.0 • 10 9 , Ra = 6.0 • 10 9 , Ra = 1.6 • 10 10 ).…”

Section: Previous Numerical Work On Horizontal Surfacesmentioning

confidence: 99%

New natural convection heat transfer correlations in enclosures for building performance simulation

Rincón-Casado

Flor

Vera

et al. 2017

Engineering Applications of Computational Fluid Mechanics

View full text Add to dashboard Cite

This paper presents new correlations to calculate natural convection heat transfer coefficients (CHTC) in enclosures for building performance simulation. Current work related to the development of correlations is not oriented to building enclosures, and the influence of high numbers of Rayleigh (Ra) and aspect ratio on the CHTC has not been studied in detail. In this work, two new correlations have been developed for a vertical wall, one in laminar regime (Ra < 10 7) and another one in turbulent regime (10 7 < Ra < 10 11). Moreover, two new correlations have been developed for floor and ceiling, one in laminar regime (Ra < 10 6) and another one in turbulent regime (Ra > 10 6). All correlations have been developed as function of the aspect ratio (H/L) and Ra numbers calculated from the enclosure average air temperature and wall surface temperature. By contrast, in previous works the Ra numbers have been calculated from the temperature difference of opposite walls. Computer Fluid Dynamics (CFD) simulations for different aspect ratios (H/L = 0.5-1-2) and Ra numbers (10 3-10 11) have been carried out in order to obtain these correlations. The SIMPLE algorithm has been used for the solution of the Navier-Stokes equations and the realizable turbulence k-ε model with an enhanced wall-function treatment has been used. The correlations developed follow the expected trend for the low number of Ra in comparison with the expressions developed by other authors. For a high number of Ra, our correlations improve the previous correlations, because it is a function of the aspect ratio of the enclosure and the average air temperature of the enclosure. This approach is simple to implement in the construction of thermal simulation programs with low computational cost.

show abstract

“…However, recent large-eddy numerical simulations [57] of thermal convection in a cube for Pr = 0.7, and Ra = 10 8 exhibits flow reversals. Note that, Vasiliev et al [58] observed random reorientations of LSC in a cubic cell; they also studied the sensitivity of LSC on experimental design. Hence, we need to carry out further analysis to test whether Taylor's hypothesis will be applicable in a cube in which LSC exhibits flow reversals.…”

Section: Introductionmentioning

confidence: 99%

Applicability of Taylor's hypothesis in thermally driven turbulence

Kumar

Verma

2018

R. Soc. open sci.

View full text Add to dashboard Cite

In this paper, we show that, in the presence of large-scale circulation (LSC), Taylor’s hypothesis can be invoked to deduce the energy spectrum in thermal convection using real-space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov’s spectrum (k−5/3). We also record the velocity time series using real-space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov’s spectrum (f−5/3), thus validating Taylor’s hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real-space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence.

show abstract

High Rayleigh number convection in a cubic cell with adiabatic sidewalls

Cited by 50 publications

References 42 publications

Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell

New natural convection heat transfer correlations in enclosures for building performance simulation

Applicability of Taylor's hypothesis in thermally driven turbulence

Contact Info

Product

Resources

About