Flow topology dynamics in a three-dimensional phase space for turbulent Rayleigh-Bénard convection

Dabbagh, F.; Trias, F. X.; Gorobets, A.; Oliva, A.

doi:10.1103/physrevfluids.5.024603

Cited by 15 publications

(6 citation statements)

References 35 publications

(60 reference statements)

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“…Contrary to this, our philosophy is that operator symmetries are critical to the dynamics of turbulence and Rayleigh-Bénard configuration studied in Ref. [3]. Instantaneous temperature field at Ra = 10 10 (left) and instantaneous velocity magnitude at Ra = 10 11 (right) for a span-wise cross section are shown.…”

Section: Introductionmentioning

confidence: 93%

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

Trias¹,

Valle²,

Gorobets³

et al. 2021

14th WCCM-ECCOMAS Congress

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The essence of turbulence are the smallest scales of motion. They result from a subtle balance between convective transport and diffusive dissipation. Mathematically, these terms are governed by two differential operators differing in symmetry: the convective operator is skew-symmetric, whereas the diffusive is symmetric and positive-definite. On the other hand, accuracy and stability need to be reconciled for numerical simulations of turbulent flows around complex configurations. With this in mind, a fully-conservative discretization method for general unstructured grids was proposed [Trias et al., J.Comp.Phys. 258, 246-267, 2014]: it exactly preserves the symmetries of the underlying differential operators on a collocated mesh. However, any pressure-correction method on collocated grids suffer from the same drawbacks: the cell-centered velocity field is not exactly incompressible and some artificial dissipation is inevitable introduced. On the other hand, for staggered velocity fields, the projection onto a divergence-free space is a well-posed problem: given a velocity field, it can be uniquely decomposed into a solenoidal vector and the gradient of a scalar (pressure) field. This can be easily done without introducing any dissipation as it should be from a physical point-of-view. In this work, we explore the possibility to build up staggered formulations based on collocated discrete operators.

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Section: Introductionmentioning

confidence: 93%

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

Trias¹,

Valle²,

Gorobets³

et al. 2021

14th WCCM-ECCOMAS Congress

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“…The analyzed data corresponds to the bulk region of the air-filled Rayleigh-Bénard configuration at Ra = 10 11 studied in Ref. [10].…”

Section: Nonlinear Sgs Heat Flux Models For Large-eddy Simulationmentioning

confidence: 99%

“…For more details the reader is referred to [9]. Our future research plans include the extension of this analysis to higher Ra and testing a posteriori the new non-linear SGS heat flux models for air-filled RBC at Ra up to 10 11 [10]. Prior to that, we aim to properly discretize tensorial eddy-diffusivity models.…”

Section: Assessment Of Eddy-viscosity Models At Very Low Prandtl Numbersmentioning

confidence: 99%

On a Proper Tensorial Subgrid Heat Flux Model

Trias¹,

Dabbagh²,

Santos³

et al. 2021

14th WCCM-ECCOMAS Congress

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In this work, we aim to shed light to the following research question: can we find a nonlinear tensorial subgrid-scale (SGS) heat flux model with good physical and numerical properties, such that we can obtain satisfactory predictions for buoyancy-driven turbulent flows? This is motivated by our findings showing that the classical (linear) eddy-diffusivity assumption, q eddy ∝ ∇T , fails to provide a reasonable approximation for the actual SGS heat flux, q = uT − uT : namely, a priori analysis for airfilled Rayleigh-Bénard convection (RBC) clearly shows a strong misalignment. In the quest for more accurate models, we firstly study and confirm the suitability of the eddy-viscosity assumption for RBC carrying out a posteriori tests for different models at very low Prandtl numbers (liquid sodium, Pr = 0.005) where no heat flux SGS activity is expected. Then, different (nonlinear) tensor-diffusivity SGS heat flux models are studied a priori using DNS data of an air-filled (Pr = 0.7) RBC at Rayleigh numbers up to 10 11. Apart from having good alignment trends with the actual SGS heat flux, we also restrict ourselves to models that are numerically stable per se and have the proper cubic near-wall behavior. This analysis leads to a new family of SGS heat flux models based on the symmetric positive semi-definite tensor GG T where G ≡ ∇u, i.e. q ∝ GG T ∇T , and the invariants of the GG T tensor. Finally, relevant numerical aspects regarding the implementation of this type of models are discussed in detail. A list of physical and numerical properties is identified and subsequently imposed, leading to a symmetrypreserving discretization that is based on discrete operators already available in any CFD code.

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“…Tsinober 16 postulated that the enstrophy production is large in S4 topology whereas the strain rate production is concentrated in regions of S1 topology. The flow topology distributions in Rayleigh-Bénard convection, where temperature and velocity fields are intrinsically coupled, are yet to be analysed in detail [17][18][19][20] in comparison to the vast body of literature (e.g. Refs.…”

mentioning

confidence: 99%

“…The analyses by Dabbagh et al [17][18][19] revealed the existence of the teardrop shape in the bulk region away from the walls in Rayleigh-Bénard convection but the small scale structures in the vicinity of the hot and cold walls have not been discussed there in terms of Q and R. Xi et al 20 reported a transition of flow topologies from a quadruple structure to a dipole structure based on Rayleigh number in turbulent Rayleigh-Bénard convection, which has implications on the Nusselt number (or heat transfer rate). A recent analysis revealed that large-scale circulation in Rayleigh-Bénard convection is affected by Prandtl number 21 .…”

mentioning

confidence: 99%

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh–Bénard convection

Yiğit

Haßlberger

Klein

et al. 2020

Sci Rep

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The statistical behaviours of the invariants of the velocity gradient tensor and flow topologies for Rayleigh–Bénard convection of Newtonian fluids in cubic enclosures have been analysed using Direct Numerical Simulations (DNS) for a range of different values of Rayleigh (i.e. $$Ra=10^7-10^9$$ R a = 10 7 - 10 9 ) and Prandtl (i.e. $$Pr=1$$ P r = 1 and 320) numbers. The behaviours of second and third invariants of the velocity gradient tensor suggest that the bulk region of the flow at the core of the domain is vorticity-dominated whereas the regions in the vicinity of cold and hot walls, in particular in the boundary layers, are found to be strain rate-dominated and this behaviour has been found to be independent of the choice of Ra and Pr values within the range considered here. Accordingly, it has been found that the focal topologies S1 and S4 remain predominant in the bulk region of the flow and the volume fraction of nodal topologies increases in the vicinity of the active hot and cold walls for all cases considered here. However, remarkable differences in the behaviours of the joint probability density functions (PDFs) between second and third invariants of the velocity gradient tensor (i.e. Q and R) have been found in response to the variations of Pr. The classical teardrop shape of the joint PDF between Q and R has been observed away from active walls for all values of Pr, but this behavior changes close to the heated and cooled walls for high values of Pr (e.g. $$Pr=320$$ P r = 320 ) where the joint PDF exhibits a shape mirrored at the vertical Q-axis. It has been demonstrated that the junctions at the edges of convection cells are responsible for this behaviour for $$Pr=320$$ P r = 320 , which also increases the probability of finding S3 topologies with large negative magnitudes of Q and R. By contrast, this behaviour is not observed in the $$Pr=1$$ P r = 1 case and these differences between flow topology distributions in Rayleigh–Bénard convection in response to Pr suggest that the modelling strategy for turbulent natural convection of gaseous fluids may not be equally well suited for simulations of turbulent natural convection of liquids with high values of Pr.

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Flow topology dynamics in a three-dimensional phase space for turbulent Rayleigh-Bénard convection

Cited by 15 publications

References 35 publications

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

Symmetry-Preserving Discretization of Navier-Stokes on Unstructured Grids: Collocated Vs Staggered

On a Proper Tensorial Subgrid Heat Flux Model

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh–Bénard convection

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