Symmetries and turbulence modeling

Klingenberg, Dario; Oberlack, Martin; Pluemacher, Dominik

doi:10.1063/1.5141165

Cited by 14 publications

(3 citation statements)

References 36 publications

(76 reference statements)

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“…It permits to speed up significantly the calculation but necessitates the modelling of subgrid terms. The Lie group theory has been used to analyze classical turbulence models in [116][117][118][119]. These works conclude that many turbulence models used in litterature break the symmetries of the equations.…”

Section: Symmetry Group Of the Equations Of A Mechanical Problemmentioning

confidence: 93%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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Section: Symmetry Group Of the Equations Of A Mechanical Problemmentioning

confidence: 93%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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“…The emphasis of this paper is quite different as we are interested in free turbulence (also called isotropic or homogeneous turbulence) that develops far away of the boundary and is rather governed by suitable scaling symmetries in the sense of Oberlack [14] and Klingenberg et al. [15]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

On the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence

Mielke

Naumann

2022

Z Angew Math Mech

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This paper is concerned with Kolmogorov's two‐equation model for turbulence in double-struckR3$\mathbb {R}^3$ involving the mean velocity u, the pressure p, an average frequency ω>0$\omega >0$, and a mean turbulent kinetic energy k. We consider the system with space‐periodic boundary conditions in a cube normalΩ=(false]0,afalse[)3$\Omega =({]0,a[}){}^3$, which is a good choice for studying the decay of free turbulent motion sufficiently far away from boundaries. In particular, this choice is compatible with the rich set of similarity transformations for turbulence. The main part of this work consists in proving existence of global weak solutions of this model. For this we approximate the system by adding a suitable regularizing r‐Laplacian and invoke existence result for evolutionary equations with pseudo‐monotone operators. An important point constitutes the derivation of pointwise a priori estimates for ω (upper and lower) and k (only lower) that are independent of the box size a, thus allow us to control the parabolicity of the diffusion operators.

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“…More precisely, the statistical symmetries developed in this work should be incorporated into turbulence models to make them reproduce the derived scaling laws. This was recently published by the research team in [105]. It was shown how the statistical symmetries can be considered and a first base-model was developed.…”

Section: Discussionmentioning

confidence: 99%

Study of the thermal field of turbulent channel flows via Direct Numerical Simulations

Avila¹

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The main goal of this thesis is the study of heat transfer in turbulent channels to obtain a better knowledge about the phenomenon of turbulence. For this, a study has been carried out from the point of view of computational fluid mechanics, specifically, the technique of direct numerical simulations (DNS) has been used. This type of simulation is very computationally expensive, but the results they provide are highly accurate and faithful to reality, as long as the discretization schemes are correct. The main idea of the simulations conducted has been to expand the current state of the art, regarding the two main parameters that characterize the flow: the friction Reynolds number, Re τ and the Prandtl number, P r . Two flow configurations have been used: Poiseuille flow and Couette flow, the former being the main focus of the study. Regarding the temperature field, a mixed boundary condition has been used and it has been considered as a passive scalar.Thus, the simulated friction Reynolds numbers for a Poisuille flow have been Re τ = 500, 1000 and 2000, for Prandtl numbers ranging from 0.007 (molten metals) up to 10 (water) , passing through 0.71 which is the most used value since this is the Prandtl number of the air. Also, a simulation has been performed with Re τ = 5000 and P r = 0.71, which is the thermal DNS with the highest friction Reynolds number up to date. A first distinction of heat flux can be made for Prandtl numbers less or greater than P r = 0.3. When the Prandtl number is less than 0.3, the conductive region extends above the logarithmic layer, and even penetrates to the central region of the channel, forming a practically laminar thermal field, for the lowest Prandtl numbers. For thermal fields where the logarithmic layer begins to emerge, the value of the von Kármán thermal constant, κ t tends to a constant value of approximately κ t = 0.44 as the Reynolds number tends to infinity, and that value is independent of the Prandtl number. Regarding the variance of the temperature, θ + and the turbulent heat flow in the direction of the current, u + θ + , the collapse in the outer region is determined by the friction Péclet number, P e τ = Re τ P r, instead of the Reynolds or Prandtl number. Furthermore, it has been observed that for the highest Prandtl numbers, the maximum value of the variance of the temperature is constant. This has a significant impact on the scaling of the θ + budget terms. Specifically, the dissipation and viscous diffusion, which scale with much greater precision near the wall for high Prandtl numbers. This is an important result, since many models of the energy equation are based on these budget equations, so obtaining good scaling for different parameters means greater reliability of the models. Finally, it should be noted that new correlations have been presented for the Nusselt number, N u, valid for the ranges of Re τ and P r studied.Finally, with regard to Poiseuille flow simulations, the isothermal case has been studied with Re τ = 10000, which is also the largest DNS o...

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Symmetries and turbulence modeling

Cited by 14 publications

References 36 publications

Lie groups and continuum mechanics: where do we stand today?

Lie groups and continuum mechanics: where do we stand today?

On the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence

Study of the thermal field of turbulent channel flows via Direct Numerical Simulations

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