Non-Oberbeck-Boussinesq effects in strongly turbulent Rayleigh-Benard convection

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Non-Oberbeck-Boussinesq effects in strongly
turbulent Rayleigh-Benard convection
Guenter Ahlers, Eric Brown, Denis Funfschilling
Physics Department, Santa Barbara
F. Fontenele Araujo, Kazu Sugiyama, Enrico
Calzavarini, Siegfried Grossmann, Detlef Lohse
Physics of Fluids, University of Twente, The
Netherlands
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Oberbeck-Boussinesq dynamics
?, ?, ?, ?
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Oberbeck-Boussinesq dynamics
Conflict of interest!
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Large Ra regime
Non-Oberbeck-Boussinesq (NOB) effects?
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Systematically explore NOB effects in water
small L9.5cm
medium L24.8cm
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Effect of NOB top-down symmetry broken
OB
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Notation
Control parameter
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Characterization of (input) NOB effects
100 effect for ??, ? !
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Characterizations of NOB effects(response of
system)
Measured
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Experimental results on ?
about 15 effect
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Experimental results on Nu
small cell
medium cell
large cell
1.5 effect (tiny decrease)
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Experimental results on Re
NOB data No effect within 2 error bars
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TheoryCalculation of Tc(and thus ?)
gtExtended Prandtl-Blasius BL theory
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Extended velocity equation
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Nondimensionalize
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NOB version of Prandtl equation
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Temperature equation
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Non-dimensionalize
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NOB version of temperature equation
How to determine ?c?
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Coupling between top bottom BL
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Temperature profiles
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Center temperature Tc
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Theory vs experiment ?
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Nusselt number cannot yet be calculated
within extended Prandtl-Blasius BL theory
without additional assumptions
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What can be answeredWhy is Nu so robust
towards NOB effects?
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Heat flux conservation at top bottom
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Robustness of Nu

• Only sums of top bottom BL contributions
  appear
• NOB corrections to Nu depend on quadratic
  contributions to NOB deviations of the
  material parameters

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Origin of NOB deviation for Nu
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NuNOB/NuOB exp vs theory
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Numerics2D NOB simulations

• with Kazu Sugiyama and Enrico Calzavarini

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Solve full Navier-Stokes eqs
with temperature and thus space dependent
material properties
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Ra107
Water
OB
60
40
D 40K
20
Tm40oC
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Central temperature vs D
BL theory
No convection
/K
Tm40oC
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Ra108
Tm40oC
/K
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Is F11 a general features?

• gt try glycerol where the viscosity strongly
  depends on temperature

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Ra107
Glycerol
OB
60
40
DT 40K
20
Tm40oC
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Central temperature vs D
Ra104 (steady)
Tm40oC
/K
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Tc vs ? for Ra107
/K
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Nusselt number deviation
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F11 is no general features,

• but is incidental for water at Tm40oC and ?lt40K
• NOB-extended BL theory still works very
  accurately for F2

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/K
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Summary

• 100 effect in ?, ?, 10 effect in ? (for
  water)
• 15 effect in Tc and
• less 2 effect in Nu and Re
• robustness theoretically understood
• NOB-extended BL theory works nicely for Tc and ?
  
• agreement with 2D numerics for water and
  glycerol
• in general, Nu cannot yet be theoretically
  calculated

Ref. G. Ahlers et al., J. Fluid Mech., in press
(2006).
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Acknowledgements

• Financial support from
• FOM

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Failure of Wu-Libchaber NOB theory
Wu Libchaber (PRA43, 2833 (1991)) introduce

and assume
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Heat flux
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Experimental Tc
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