Penetrative internally heated convection in two and three dimensions

D. Goluskin, Erwin van der Poel

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

Abstract

Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that penetrates into the stably stratified lower region. The fraction of produced heat escaping across the bottom plate, which is one half without convection, initially decreases as convection strengthens. Entering the turbulent regime, this decrease reverses in two dimensions but continues monotonically in three dimensions. The mean fluid temperature, which grows proportionally to the heating rate (H) without convection, grows proportionally to H4=5 when convection is strong in both two and three dimensions. The ratio of the heating rate to the fluid temperature is likened to the Nusselt number of Rayleigh–Bénard convection. Simulations are reported for Prandtl numbers between 0.1 and 10 and for Rayleigh numbers (defined in terms of the heating rate) up to 5 1010.
Original languageEnglish
Pages (from-to)R6-1-R6-13
Number of pages13
JournalJournal of fluid mechanics
Volume791
DOIs
Publication statusPublished - 24 Feb 2016

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convection
Heating rate
heating
Fluids
fluids
Prandtl number
Direct numerical simulation
Rayleigh number
Nusselt number
Convection
direct numerical simulation
Temperature
temperature
heat
simulation

Keywords

  • METIS-316100
  • IR-100118

Cite this

Goluskin, D. ; van der Poel, Erwin. / Penetrative internally heated convection in two and three dimensions. In: Journal of fluid mechanics. 2016 ; Vol. 791. pp. R6-1-R6-13.
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Penetrative internally heated convection in two and three dimensions. / Goluskin, D.; van der Poel, Erwin.

In: Journal of fluid mechanics, Vol. 791, 24.02.2016, p. R6-1-R6-13.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Penetrative internally heated convection in two and three dimensions

AU - Goluskin, D.

AU - van der Poel, Erwin

PY - 2016/2/24

Y1 - 2016/2/24

N2 - Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that penetrates into the stably stratified lower region. The fraction of produced heat escaping across the bottom plate, which is one half without convection, initially decreases as convection strengthens. Entering the turbulent regime, this decrease reverses in two dimensions but continues monotonically in three dimensions. The mean fluid temperature, which grows proportionally to the heating rate (H) without convection, grows proportionally to H4=5 when convection is strong in both two and three dimensions. The ratio of the heating rate to the fluid temperature is likened to the Nusselt number of Rayleigh–Bénard convection. Simulations are reported for Prandtl numbers between 0.1 and 10 and for Rayleigh numbers (defined in terms of the heating rate) up to 5 1010.

AB - Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that penetrates into the stably stratified lower region. The fraction of produced heat escaping across the bottom plate, which is one half without convection, initially decreases as convection strengthens. Entering the turbulent regime, this decrease reverses in two dimensions but continues monotonically in three dimensions. The mean fluid temperature, which grows proportionally to the heating rate (H) without convection, grows proportionally to H4=5 when convection is strong in both two and three dimensions. The ratio of the heating rate to the fluid temperature is likened to the Nusselt number of Rayleigh–Bénard convection. Simulations are reported for Prandtl numbers between 0.1 and 10 and for Rayleigh numbers (defined in terms of the heating rate) up to 5 1010.

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