Post on 14-Feb-2017
transcript
Heat transfer in convective
turbulence
Jörg Schumacher
Theoretical Fluid MechanicsTechnische Universität Ilmenau
Germany
Where is Ilmenau?
Johann W. Goethe Karlheinz
Brandenburg
Barrel of Ilmenau
Über allen GipfelnIst Ruh'In allen WipfelnSpürest DuKaum einen Hauch;Die Vögelein schweigen im WaldeWarte nur, baldeRuhest Du auch.
Outline
IntroductionLocal: Boundary layer structureLocal: Temperature and thermal dissipationGlobal: Large-scale flow patternsLocal: Lagrangian fingerprintGlobal: Plume clusters?Outlook
Hydrostatic equilibrium
warmer fluidelement
colder fluidelement
fluid element
Ttop Tbottom
Nusselt number
Rayleigh instabilityRayleigh, Philos. Mag. 1916; Jeffreys, Philos. Mag. 1926;
Schlüter, Lortz & Busse, J. Fluid Mech. 1965
Further bifurcations Transition to convective turbulence
stable unstable
Ra
Heatconductiononly
Heatconduction &convection
unstable branch
Model equations
Rotation (opt.) Buoyancy
Approximations
• Density is linear function of temperature Boussinesq-Approximation
• Flow is incompressible (u much smaller than speed of sound)
Oberbeck, Ann. Phys. Chem. 1879; Boussinesq, Théorie Analytique de la Chaleur, 1903
Rayleigh-Bénard convection
HDimensionless controlparameters
Examples
Semiconductor chips, Ra=106
Buildings, Ra=1012
Atmosphere, Ra=1020
Sun, Ra=1023
Rayleigh-Bénard convection
H
„System response“
Power law for heat transfer (for fixed Pr)
=2/7 or 1/3?Shraiman & Siggia, Phys. Rev. A 1991; Großmann & Lohse, J. Fluid Mech.
2000
Deviation by morethan 100% !!!
Niemela et al., Nature
2000
Different models for the velocity boundary layer
Regions in convective turbulence
Bulk Boundary layer
Mixing zone?
Mixing zone?
Plume
Boundarylayer
thickness:0.01
Turbulenttemperature
field
Mean temperature
Heig
ht
Turbulent
structureMean profile Transport law
„Perturbation“„Response“
Why study mean profiles?
7 Meters
„Barrel of Ilmenau“
Worlds biggest convection experiment
Accessible range in the Barrel
6 9 12 15 18
log(Ra)
log
(R
)
Fitzjarrald (1976)
Castaing (1989)
Niemela (2000)
Barrel of Ilmenau (2000)50000
5000
500
50
R=Size of Experiment
Size of Sensor
Luft
Luft
Helium
Helium
Air
Air
Velocity measurements
LD
A
du Puits, Resagk & Thess, Phys. Rev. Lett. 2007
Laser-Doppler-Anemometry vx
Theoretical model
Resolve
boundary
layers!!
vy
Data
Numerical simulations in cylindrical cell
T =0.00005 HRa=1017
T =0.0014 HRa=1012
T =0.016 HRa=109
Proper resolution of boundary layerslimits accessible Ra
Verzicco & Orlandi, JCP 1996
No-slip boundaries, adiabatic side walls
Second-order finite difference scheme
Temperature & temperature derivativeEmran & Schumacher, J. Fluid Mech., in revision
BL Bulk
BLBulk
Strong vertical dependence of statistics of turbulent temperature field
Deviations from local isotropySchumacher & Sreenivasan, Phys. Rev. Lett. 2003
BLBulk
Return to local isotropy (K41) for temperature fluctuations in bulk Formation of „superconducting core“ in high-Ra turbulence
Niemela & Sreenivasan, Phys. Rev. Lett. 2008
Thermal dissipation rateEmran & Schumacher, J. Fluid Mech., in revision
Significant contribution to dissipation due to temperature fluctuations Does not enter the Großmann-Lohse scaling theory!
Großmann & Lohse, J. Fluid Mech. 2000
„Wind of turbulence“
Mean (114 double frames) andsnapshot
Ra=1011, =2
z
x
Barrel: Visualisation with He bubbles
Geometry dependence of heat transport
10% effect
POD analysis
Time-averaged streamlines
Pair dispersion in turbulent convectionSchumacher, Phys. Rev. Lett. 2008
Lagrangian fingerprint of thermal plumes
L
H
Successively flatter cells
W
Cartesian geometry
Free-slip b.c. in zPeriodic b.c. in x and y
Pseudospectral method
Volumetric 3D-FFT
xy
z
y1. r2c in x
2.
kx kx
3. c2c in y
4.z
ky
5. c2c in z
One more communication step necessary !
kz
3
2
1
0
0
1
2
3
Nx = Ny >> Nz is possible as necessary for our studies
N2 processors can be used 2D processor grid(iproc,jproc)
iproc=2
jproc=2
pencil
D. Pekurovsky (SDSC), p3dfft package
Massively parallel supercomputing
Production jobs on 4096 CPUs
Schumacher & Pütz, Proceedings of PARCO 2007
Effect of rotation
Temperature
Temperature
Ta=0
Ta=2.5 108
Mean temperature and heat transfer
Rotation diminishesfluctuations and thus heat
transport
Rotationincreases
Temperature patternsHartlep, Tilgner & Busse, J. Fluid Mech. 2005; von Hardenberg et al., Phys. Letters A
2008
Plume clusters?
... the road ahead
Scale analysis of plume clusters (image segmentation)
Lagrangian analysis in large-aspect-ratio convectioncells temporal persistence of plume clusters?
Statistical significance of thermal plumes with increasingRayleigh number (BL thickness ~ 1/Nu)
Together with O. Pauluis (NYU): simple extension tomoist convection
condensation at saturation level piecewise linear dependence of buoyancy on S and q dry and moist lapse rates allow to tune stability
Summary
Boundary layers (BL): neither laminar Blasius type nor turbulentPrandtl type Scaling theories of heat transfer
Turbulent temperature fluctuations contribute significantly tothermal dissipation in BL
Lateral dispersion of Lagrangian tracers is Richardson-like
Rotation prohibits formation of horizontal large-scale patterns
Clusters of thermal plumes seem to cause large-scaletemperature patterns in non-rotating case
Thanks to
Mohammad Emran, Jorge Bailon-Cuba (TU Ilmenau)
Ronald du Puits, Christian Resagk, Andre Thess (TU Ilmenau)
Katepalli R. Sreenivasan (ICTP Trieste / UMD College Park)
Roberto Verzicco (U Roma II)
Matthias Pütz (IBM Germany)
Jülich Supercomputing Centre (Germany)