Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913385345449984 |
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| author | Samuel, Roshan Samtaney, Ravi Verma, Mahendra K. |
| author_facet | Samuel, Roshan Samtaney, Ravi Verma, Mahendra K. |
| contents | We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh-Bénard convection (RBC) for Rayleigh numbers ranging from $10^6$ to $10^15$ and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. (Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598), albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at $Ra = 10^13$, we use grids that are 1/120 times the grid-resolution as that of the DNS (Iyer et al., Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598). The Reynolds numbers in our simulations span 3 orders of magnitude from 1,000 to 1,700,000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as $Nu \sim Ra^{0.317}$ and $Re \sim Ra^{0.497}$. We also perform LES of RBC with periodic side-walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477 respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers, and hence enable us to test the transition to ultimate convection regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_03697 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers Samuel, Roshan Samtaney, Ravi Verma, Mahendra K. Fluid Dynamics Computational Physics We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh-Bénard convection (RBC) for Rayleigh numbers ranging from $10^6$ to $10^15$ and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. (Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598), albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at $Ra = 10^13$, we use grids that are 1/120 times the grid-resolution as that of the DNS (Iyer et al., Proc. Natl. Acad. Sci., vol 117 (14), 2020, pp. 7594-7598). The Reynolds numbers in our simulations span 3 orders of magnitude from 1,000 to 1,700,000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as $Nu \sim Ra^{0.317}$ and $Re \sim Ra^{0.497}$. We also perform LES of RBC with periodic side-walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477 respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers, and hence enable us to test the transition to ultimate convection regime. |
| title | Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2204.03697 |