In this paper, we extend Grossmann and Lohse’s (GL) model [S. Grossmann and D. Lohse, “Thermal convection for large Prandtl numbers,” Phys. Rev. Lett. 86, 3316 (2001)] for the predictions of Reynolds number (Re) and Nusselt number (Nu) in turbulent Rayleigh–Bénard convection. Toward this objective, we use functional forms for the prefactors of the dissipation rates in the bulk and boundary layers. The functional forms arise due to inhibition of nonlinear interactions in the presence of walls and buoyancy compared to free turbulence, along with a deviation of the viscous boundary layer profile from Prandtl–Blasius theory. We perform 60 numerical runs on a three-dimensional unit box for a range of Rayleigh numbers (Ra) and Prandtl numbers (Pr) and determine the aforementioned functional forms using machine learning. The revised predictions are in better agreement with the past numerical and experimental results than those of the GL model, especially for extreme Prandtl numbers.
Skip Nav Destination
Article navigation
January 2021
Research Article|
January 11 2021
Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
Shashwat Bhattacharya
;
Shashwat Bhattacharya
a)
1
Department of Mechanical Engineering, Indian Institute of Technology Kanpur
, Kanpur 208016, India
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Mahendra K. Verma
;
Mahendra K. Verma
2
Department of Physics, Indian Institute of Technology Kanpur
, Kanpur 208016, India
Search for other works by this author on:
Ravi Samtaney
Ravi Samtaney
3
Mechanical Engineering, Division of Physical Science and Engineering, King Abdullah University of Science and Technology
, Thuwal 23955, Saudi Arabia
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 33, 015113 (2021)
Article history
Received:
October 08 2020
Accepted:
December 19 2020
Citation
Shashwat Bhattacharya, Mahendra K. Verma, Ravi Samtaney; Revisiting Reynolds and Nusselt numbers in turbulent thermal convection. Physics of Fluids 1 January 2021; 33 (1): 015113. https://doi.org/10.1063/5.0032498
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
On Oreology, the fracture and flow of “milk's favorite cookie®”
Crystal E. Owens, Max R. Fan (范瑞), et al.
Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
Hamidreza Eivazi, Mojtaba Tahani, et al.
Chinese Academy of Science Journal Ranking System (2015–2023)
Cruz Y. Li (李雨桐), 李雨桐, et al.
Related Content
Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
Physics of Fluids (February 2022)
Rayleigh and Prandtl number scaling in the bulk of Rayleigh–Bénard turbulence
Physics of Fluids (May 2005)
Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water
Physics of Fluids (May 2014)
Rayleigh–Bénard convection: Improved bounds on the Nusselt number
J. Math. Phys. (August 2011)
Multiple scaling in the ultimate regime of thermal convection
Physics of Fluids (April 2011)