Challenges in low-Prandtl number heat transfer simulation and modelling

Grötzbach, G.

doi:10.1016/j.nucengdes.2012.09.039

Cited by 130 publications

(54 citation statements)

References 71 publications

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“…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.…”

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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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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“…The calculated Nu values for fully developed liquid NaK-78 flows are compared to those reported experimentally by Talanov and Ushakov [14]. The experimental Nu values are correlated in terms of Pe, and the developed correlation is compared to those reported by others for liquid Na, NaK-78, and NaK-56 flows [19][20][21][22] in uniformly heated circular tubes of various lengths.…”

Section: Comparsion Of Cfd and Experiments Resultsmentioning

confidence: 77%

“…A challenge in performing CFD analyses of convection heat transfer for alkali liquid metals is their very low Prandtl numbers, which vary from $0.003 to 0.008, depending on temperature [17][18][19][20][21]. The analyses of liquid NaK-78 flow in the uniformly heated circular tube and the tri-lobe channel in Fig.…”

Section: Cfd Analyses Modelsmentioning

confidence: 99%

“…The RANS models employ a turbulent Prandtl number, Pr t , which is the ratio of the eddy viscosity and eddy heat diffusivity. In the STAR-CCM+ code, the default Pr t , a constant 0.9, is not suitable for modeling the convection heat transfer of alkali liquid metals, such as Na, NaK-78, and NaK-56 [19][20][21][22]. To account for the high thermal diffusivity and the low momentum diffusivity of these liquids, the Reynolds equation is used [22], which gives a higher Pr t ($1.5-2.2) than the default value in the STAR-CCM+ code.…”

Section: Cfd Analyses Modelsmentioning

confidence: 99%

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Convection heat transfer of NaK-78 liquid metal in a circular tube and a tri-lobe channel

Schriener

El‐Genk

2015

International Journal of Heat and Mass Transfer

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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%

Challenges in low-Prandtl number heat transfer simulation and modelling

Cited by 130 publications

References 71 publications

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

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

Convection heat transfer of NaK-78 liquid metal in a circular tube and a tri-lobe channel

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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Challenges in low-Prandtl number heat transfer simulation and modelling

Cited by 130 publications

References 71 publications

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

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

Convection heat transfer of NaK-78 liquid metal in a circular tube and a tri-lobe channel

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

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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