TY - JOUR
T1 - On a transitional and turbulent natural convection in spherical shells
AU - Feldman, Yuri
AU - Colonius, Tim
N1 - Funding Information:
This research was funded by the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration. We are grateful to the JPL for a granted access to their supercomputer facilities. We are also thankful to Dr. Jeffrey Hall for his helpful inputs during this project.
PY - 2013/5/29
Y1 - 2013/5/29
N2 - Laminar and turbulent natural convection inside concentric spherical shells with isothermal cold and hot boundaries is numerically investigated up to Rayleigh number values Ra ≤ 1012 and Pr = 0.71. The study utilizes direct numerical simulation (DNS), large eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) approaches for investigation of the laminar, transitional and fully developed turbulent flow regimes, respectively. Three-dimensional flow patterns for slightly supercritical oscillatory flow regime inside the shell, with internal/external diameter ratio equal to D i/Do = 0.714 are presented and may be potentially useful for verification of the future linear stability analysis results. Particular attention has been given to the complex, fully three-dimensional unsteady flows occurring in narrow shell geometries characterized by 0.85 ≤ D i/Do ≤ 0.95. For this geometry considerable deviations in predicted heat flux rate through the shell boundaries are observed when compared with existing heat transfer correlations for the entire range of Ra numbers. The deviations tend to increase for transitional and fully turbulent flows. A new correlation for the heat transfer rate is suggested for laminar and transitional flow regimes.
AB - Laminar and turbulent natural convection inside concentric spherical shells with isothermal cold and hot boundaries is numerically investigated up to Rayleigh number values Ra ≤ 1012 and Pr = 0.71. The study utilizes direct numerical simulation (DNS), large eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) approaches for investigation of the laminar, transitional and fully developed turbulent flow regimes, respectively. Three-dimensional flow patterns for slightly supercritical oscillatory flow regime inside the shell, with internal/external diameter ratio equal to D i/Do = 0.714 are presented and may be potentially useful for verification of the future linear stability analysis results. Particular attention has been given to the complex, fully three-dimensional unsteady flows occurring in narrow shell geometries characterized by 0.85 ≤ D i/Do ≤ 0.95. For this geometry considerable deviations in predicted heat flux rate through the shell boundaries are observed when compared with existing heat transfer correlations for the entire range of Ra numbers. The deviations tend to increase for transitional and fully turbulent flows. A new correlation for the heat transfer rate is suggested for laminar and transitional flow regimes.
KW - Laminar and turbulent natural convection
KW - Narrow spherical shells
KW - Nu-Ra functional relation
UR - http://www.scopus.com/inward/record.url?scp=84878144834&partnerID=8YFLogxK
U2 - 10.1016/j.ijheatmasstransfer.2013.04.042
DO - 10.1016/j.ijheatmasstransfer.2013.04.042
M3 - Article
AN - SCOPUS:84878144834
SN - 0017-9310
VL - 64
SP - 514
EP - 525
JO - International Journal of Heat and Mass Transfer
JF - International Journal of Heat and Mass Transfer
ER -