Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number
Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws...
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| Veröffentlicht in: | Journal of fluid mechanics 2023-12, Vol.977, Article A26 |
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| creator | Rein, F. Carénini, L. Fichot, F. Favier, B. Le Bars, M. |
| description | Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions. |
| doi_str_mv | 10.1017/jfm.2023.922 |
| format | Article |
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We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2023.922</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Asymptotic properties ; Boundary conditions ; Convection ; Cooling ; Direct numerical simulation ; Flow structures ; Fluid Dynamics ; Free convection ; Heat transfer ; JFM Papers ; Mathematical models ; Nuclear accidents & safety ; Nuclear power plants ; Nuclear reactors ; Nuclear safety ; One dimensional models ; Physics ; Prandtl number ; Rayleigh-Benard convection ; Scaling ; Scaling laws ; Temperature differences ; Temperature gradients ; Temperature profile ; Temperature profiles</subject><ispartof>Journal of fluid mechanics, 2023-12, Vol.977, Article A26</ispartof><rights>The Author(s), 2023. 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Fluid Mech</addtitle><description>Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). 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Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2023.922</doi><tpages>27</tpages><orcidid>https://orcid.org/0009-0007-8090-3726</orcidid><orcidid>https://orcid.org/0009-0006-2060-7362</orcidid><orcidid>https://orcid.org/0000-0002-4884-6190</orcidid><orcidid>https://orcid.org/0000-0002-1184-2989</orcidid><orcidid>https://orcid.org/0000-0002-2134-3948</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of fluid mechanics, 2023-12, Vol.977, Article A26 |
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| subjects | Asymptotic properties Boundary conditions Convection Cooling Direct numerical simulation Flow structures Fluid Dynamics Free convection Heat transfer JFM Papers Mathematical models Nuclear accidents & safety Nuclear power plants Nuclear reactors Nuclear safety One dimensional models Physics Prandtl number Rayleigh-Benard convection Scaling Scaling laws Temperature differences Temperature gradients Temperature profile Temperature profiles |
| title | Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number |
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