Assessment and calibration of an algebraic turbulent heat flux model for low-Prandtl fluids

Shams, A.; Roelofs, F.; Baglietto, Emilio; Lardeau, Sylvain; Kenjereš, Saša

doi:10.1016/j.ijheatmasstransfer.2014.08.018

Cited by 92 publications

(61 citation statements)

References 13 publications

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“…An analysis of vorticity generation mechanisms in such flows and a comparison with other turbulent flows, which requires the resolution of spatial derivatives of the turbulent fields, is still missing. These details are, however, essential to improve parameterizations of the small-scale turbulence in low-Prandtl-number fluids such as algebraic heat flux and other subgrid-scale models (21,22).…”

mentioning

confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr = 0.7 and in liquid mercury at Pr = 0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large-and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. T urbulent convection depends strongly on the material properties of the working fluid that are quantified by the Prandtl number, the ratio of kinematic viscosity of the fluid to thermal diffusivity of the temperature, Pr = ν=κ. Compared with the vast number of investigations at Pr ≥ 1 (1, 2), the very-low-Pr regime appears almost as a "terra incognita" despite many applications. Turbulent convection in the Sun is present at Prandtl numbers Pr < 10 −3 (3-5). The Prandtl number in the liquid metal core of the Earth is Pr ∼ 10 −2 (6). Convection in material processing (7), nuclear engineering (8), or liquid metal batteries (9) has Prandtl numbers between 3 × 10 −2 and 10 −3 . Rayleigh-Bénard convection (RBC), a fluid flow in a layer that is cooled from above and heated from below, is a paradigm for all of these examples. One reason for significantly fewer low-Pr RBC studies is that laboratory measurements have to be conducted in opaque liquid metals such as mercury or gallium at Pr = 0.021 (10-12). The lowest value for a Prandtl number that can be obtained in optically transparent fluids is Pr = 0.2 for binary gas mixtures (13), i.e., an order of magnitude larger than in liquid metals. Direct numerical simulations (DNS) are currently the only way to gain access to the full 3D convective turbulent fields in low-Pr convection (14-18). These simulations turn out to become very demanding if the...

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mentioning

confidence: 99%

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Schumacher

Götzfried

Scheel

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…This choice is similar to the one adopted by Shams et al (2014), who proposed a Present Set of parameters for AHFM to be used in STAR-CCM+ for heat transfer to liquid metals, considering a constant fluid density. In their paper, it is suggested using a constant value of R = 0.5, providing correct results for the addressed fluids.…”

Section: Adopted Methodologymentioning

confidence: 99%

“…Concerning the use of STAR-CCM+ with similar models, it must be mentioned that Shams et al (2014) recently implemented an AHFM in the code for cases with constant density fluids aiming at paving the way for analyses applicable to the Gen IV liquid metal cooled reactors. They compared their results with DNS data obtaining good coherence between the two approaches.…”

Section: Nomenclaturementioning

confidence: 99%

Prediction of heat transfer to supercritical fluids by the use of Algebraic Heat Flux Models

Pucciarelli

Sharabi

Ambrosini

2016

Nuclear Engineering and Design

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“…Some known issues of this type of modeling are that the dependence on the geometry does not allow to study various configurations of the flow without prior information and that the model could be too much dependent on the problems for which it has been developed. Another approach is to use a more complex model based on an approximate solution of the turbulent heat flux equation together with a proper definition and computation of a time scale for the thermal turbulence [1,[9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The (7) and (8) can be employed for a convection dominated flow, while to study mixed or natural convection they should be modified properly [13,14]. Moreover the model presented and validated in this work could be improved with a different definition of (7) and (8) and some additional terms in the model equations in order to account for anisotropic effects [3,18].…”

Section: Introductionmentioning

confidence: 99%

Assessment and calibration of an algebraic turbulent heat flux model for low-Prandtl fluids

Cited by 92 publications

References 13 publications

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Prediction of heat transfer to supercritical fluids by the use of Algebraic Heat Flux Models

A k–Ω–kθ–
Vià
¹
,
Manservisi
²
,
Menghini
³

2016
International Journal of Heat and Mass Transfer
23
0
14
0
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Assessment and calibration of an algebraic turbulent heat flux model for low-Prandtl fluids

Cited by 92 publications

References 13 publications

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

Prediction of heat transfer to supercritical fluids by the use of Algebraic Heat Flux Models

A k–Ω–kθ–Vià1, Manservisi2, Menghini3 2016International Journal of Heat and Mass Transfer230140View full textAdd to dashboardCite

Contact Info

Product

Resources

About

A k–Ω–kθ–
Vià
¹
,
Manservisi
²
,
Menghini
³

2016
International Journal of Heat and Mass Transfer
23
0
14
0
View full text Add to dashboard Cite