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Local wall heat flux in turbulent Rayleigh-Bénard convection
Ronald du Puits Ilmenau University of Technology
Department of Mechanical EngineeringPOB 100565, D-98693 Ilmenau, GERMANY
contact: ronald.dupuits@tu-ilmenau.de
Technicians:Vigimantas Mitschunas, Klaus Henschel, Helmut Hoppe
Financial support: German Research Foundation Federal Ministry of Education and ResearchThuringian Government
Collaboration:André Thess, Jörg Schumacher (Ilmenau)
Philippe Roche (Grenoble)
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 2/29
Outline
1. Motivation to measure the local wall heat flux
2. Heat flux sensor and measurement technique
3. Local heat flux and plume dynamics
4. Local heat flux and the large-scale circulation
5. Conclusion and outlook
1. Motivation
2. Measurementtechnique
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 3/29
1. Motivation
1. Motivation
2. Measurementtechnique
Rayleigh-Bénard convection reflects a large number of natural and technical flow phenomena.
Atmosheric flows Oceanic flows
Earth core convection Star convection
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 4/29
1. Motivation
2. Measurementtechnique
Characteristics of those flows:
2. Small thickness compared with lateral extent large aspect ratio
e.g.
Earth atmosphere: 4000Pacific Ocean: 3000Outer earth core: 10Sun‘s convective zone: 6
HL
1. Extremely high level of turbulence large Rayleigh number
e.g.
Earth atmosphere: 1020
Pacific Ocean: 1021
Outer earth core: > 1020 Sun‘s convective zone: 1023
/3HTgRa
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 5/29
1. Motivation
2. Measurementtechnique
Requirements for experiments to model geophysical flows:
1. high Rayleigh numbers
2. large aspect ratios
Actual high Rayleigh number experiments:
1. Triest (I), Ramax = 1017, = 0.5…4, liquid He
2. Grenoble (Fr), Ramax = 1015, = 0.5…1, liquid He
5. Hongkong (CN) , Ramax = 1014, = 1….20, water
3. Goettingen (D) , Ramax = 1015, = 0.5…1, SF6 (15bar)
6. Ilmenau (D) , Ramax = 1012, = 1…100, Air
4. Santa Barbara (US) , Ramax = 1014, = 0.28…6, various liquids
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 6/29
1. Motivation
2. Measurementtechnique
1. Prediction of the global heat flux in terms of Nu = f(Ra, Pr).
2. The boundary layers play a crucial role for the global heat transport .
1. MotivationThe best known geometry is the = 1 cell of cylindrical shape.
For high Ra convection we know many features of the flow.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
q3. The boundary layers interact with the bulk
by thermal plumes.
4. The dynamics of the large-scale circulation, one single role exists, cessations, rotations, reversals can occur, mean plane oscillatesin angular direction, sloshing mode
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1. Motivation
2. Measurementtechnique
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Can we simply transfer this knowledge to flows at higher aspect ratio?
q
local heat flux sensor
What can we learn from local heat flux measurements at the surface of the heating and the cooling plate?
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2. Experimental facility
2. Measurementtechnique
Large-scale experimental facility `Barrel of Ilmenau‘
www.ilmenauer-fass.de
H <
6.3
0 m
D = 7.15 m
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Main features:
1. High Ra numbers up to Ra = 1012
2. Continuously variable aspect ratio ≈ 1…100
DNS
small barrel
full-size barrel
Accessible parameter range
1
10
100
5 7 9 11 13
log Ra
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2. Heat flux sensor
heating/cooling plate
heat flux sensor (fcutoff=3Hz)qw (t)
Convection flow
20mm
1.5m
m
Sensor: The local wall heat fluxes were measured using special sensors called heat flux plates.
1. Motivation
2. Measurementtechnique
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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2. Measurementtechnique
20
10
z[mm]T(z)
Where we are with our heat flux sensor? – Ra ≈ 5x1011, ≈ 1
‹v›(z)
bhp TTq
The heat flux sensor reflects the local convection coefficient depending on the local velocity v(t) and the local temperature difference T(t).
Thickness of the sensor
2. Heat flux sensor
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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3. Local heat flux and plume dynamics
1. Motivation
3. Plume dynamics
Thermal plumes at the cooling plate of a RB cell filled with water , Pr ≈ 5 and at Ra = 2.6x109 .
(Y. Du and P. Tong, 52nd APS meeting, Nov 21-23, 1999, New Orleans, Louisiana)
2. Measurementtechnique
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
1. A thermal plume develops at the surface of the cooled top plate.
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3. Local heat flux and plume dynamics
1. Motivation
3. Plume dynamics
Thermal plumes in an aspect ratio one cell filled with Dipropylene glycol withPr = 596 and at Ra = 6.8x108 .(Shang et al., PRL 90, 074501)
2. Measurementtechnique
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
1. Thermal plumes arise from the heated bottom plate and fall down from the cooled top plate.
2. They organize themselve to a large scale motion of one single role occupying the whole space of the cell.
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3. Local heat flux and plume dynamics
1. Motivation
3. Plume dynamics
Generalized sketch of the plume motion in turbulent convection.
Can we generalize this picture to other fluids, e.g. with Pr = 0.7.
2. Measurementtechnique
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Can we generalize it to aspect ratios > 1.
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3. Local heat flux and plume dynamics
1. Motivation
v
Hypothesis:
1. The plume has to be reflected as a positive burst in the time series of the local heat flux.
2. For a given velocity of the LSC the width can be calculated from the time of the burst.
vtww
t
q
2. Measurementtechnique
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
Time resolved local heat flux at the surface of the cooling plate.position: centre; =1.13, Ra=4.27x1011, Pr=0.7
1. The local heat flux fluctuates over the time by ≈ 40%.
0 1000 2000 3000 4000 500070
80
90
100
110
120
130
time [s]
he
at
flu
x [W
/m²]
2. Positive eruptions occur as often as negative ones do.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
1800 1850 1900 1950 200080
90
100
110
120
time [s]
he
at
flu
x [W
/m²]
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
1. The typical time of a strong eruption is ≈ 8s.
2. According to a typical mean velocity of the LSC the width of such an eruption is w = v*t = 0.34 ms-1
*8 s = 2.72 m!
7s
8s
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
75 80 85 90 950
0.02
0.04
0.06
0.08
0.1
0.12
heat flux [W/m²]
pro
ba
bili
ty
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
Probability density of the local heat flux at the surface of the heating plate.position: centre; =1.13, Ra=4.27x1011, Pr=0.7, meas. time: 53 hours
492.3kurt
307.0skew
Wm27.3std
Wm7.85
2
2
q
q
q
q
1. For aspect ratio = 1.13 the fluctuations of the local heatflux are distributed gaussian.
gaussian
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
1. The mean local heat flux and the fluctuations at the heatingand the cooling plate differ, but both are distributet gaussian.
Is the local heat flux symmetrical at the heating and the cooling plate?
Question:
67.3kurt
34.0skew
Wm00.4std
Wm8.98
2
2
q
q
q
q
heating plate cooling plate
49.3kurt
31.0skew
Wm27.3std
Wm7.85
2
2
q
q
q
q
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
70 80 90 100 110 1150
0.05
0.1
0.15
heat flux [W/m²]
pro
ba
bili
ty
Ra=4.27x1011, T=20K
22 24 26 28 30 32 34 360
0.05
0.1
0.15
0.2
0.25
heat flux [W/m²]
pro
ba
bili
ty
200 250 3000
0.01
0.02
0.03
=7
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
1. For aspect ratios ≈ 4 the fluctuations of the local heat flux are notdistributet gaussian, there are more positive than negative eruptions.
Question:
03.4kurt
76.0skew
Wm92.1std
Wm6.28
2
2
q
q
q
q
Does it depend on aspect ratio?
second measurementposition: centre; =4.00, Ra=4.00x109, Pr=0.7
2. There is a sharp cut towards lower heat fluxes.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
94.2kurt
28.0skew
Wm25.15std
Wm9.245
2
2
q
q
q
q
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3. Local heat flux and plume dynamics
1. Motivation
2. Measurementtechnique
1. For aspect ratios ≈ 1 and Pr ≈ 1 the LSC is stronger as the localadvection of plumes. In this case the interface between bulk and boundary layer fluctuates.(K.-Q. Xia, ETC 11, Marburg)
Question: How can we interpret these results?
≈ 1, Pr ≈ 1
≈ 4, Pr ≈ 1
fluctuating boundary layer
LSC LSC
2. For aspect ratios ≈ 4 and Pr ≈ 1 the LSC is weak, plumes
can emerge freely, the sharp cut towards low heat fluxes can be associated with maximum boundary layer thickness
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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3. Local heat flux and the large-scale circul.
1. Motivation
2. Measurementtechnique
Question: Are the boundary layers coupled by the large scale circu-lation and is the emission of plumes a periodic process?
Sketch of the large-scale circulation shearing the boundary layers.Villermaux, PRL 75, 4619 (1995)
1. Boundary layer instabilities (plumes) are emerged at one plate.
The Model of Villermaux:
2. They travel within the large-scale circulation to the other plate and create a second instability (plume) there.
3. The process runs periodically and can be described by a model of two coupled oscillators.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
-5000 -2500 0 2500 5000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
Cx
y
-100 -50 0 50 100-0.2
0
0.2
0.4
0.6
0.8
1
[s]
Cxy
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1. Motivation
2. Measurementtechnique
Local heat flux sensors
= 1.13, Ra = 4.27x1011, Pr = 0.7
11
0
myxmC n
mN
nmnxy
We compute the cross-correlation function Cxy
1. For ≈ 1 and Pr ≈ 1 the local heat fluxes at the centre of the heating and the cooling plate are not correlated.
3. Local heat flux and the large-scale circul.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 23/29
1. Motivation
2. Measurementtechnique
Local heat flux sensors
= 2.00, Ra = 0.52x1011, Pr = 0.7
1. For ≈ 2 and Pr ≈ 1 the local heat fluxes at the centre of the heating and the cooling plate are correlated.
-5000 -2500 0 2500 5000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
Cx
y
-250 -125 0 125 250-0.2
0
0.2
[s]
Cxy
100s
3. Both boundary layers are coupled by the large-scale circulation.
2. Thermal plumes emerging from the cooling plate arrive at the heating plate and vice versa.
3. Local heat flux and the large-scale circul.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
-5000 -2500 0 2500 5000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
Cxy
-1000 -500 0 500 1000-0.2
0
0.2
[s]C
xy
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1. Motivation
2. Measurementtechnique
Local heat flux sensors
= 4.00, Ra = 4.00x109, Pr = 0.7
3. Local heat flux and the large-scale circul.
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 25/29
1. Motivation
2. Measurementtechnique
Question: Can we identify the recently found „sloshing mode“ of the large-scale circulation also in RB convection at Pr ≈ 1?
3. Local heat flux and the large-scale circul.
Model of the large-scale circulation with the „oscillatory“ mode (red) and the „sloshing mode“ (green) .
Xi et al., PRL 102, 044503 (2009)Brown et al., JFM 638, 383 (2009)
q
t
q
t
oscillatory mode
sloshing mode3. Plume dynamics
4. Large-scale circulation
5. Conclusion
0 1000 2000 3000 4000 5000-0.2
0
0.2
0.4
0.6
0.8
1
1.2
[s]
Cxx
0 50 100 150 200-0.5
0
0.5
1
[s]
Cxx
Page 26/29
1. Motivation
2. Measurementtechnique
1. For Pr ≈ 1 and ≈ 1 the sloshing mode could not be identified.
3. Local heat flux and the large-scale circul.
= 1.13, Ra = 4.27x1011, Pr = 0.7
11
0
mxxmC n
mN
nmnxx
We compute the auto-correlation function Cxx
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 27/29
1. Motivation
2. Measurementtechnique
0 2000 4000 6000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
0 300 600 900-0.2
0
0.2
0 2000 4000 6000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
0 300 600 900-0.2
0
0.2
Auto-correlation function of the local heat flux for larger aspect ratios .
1. For larger aspect ratios 2 and 4 (Pr ≈ 1) we do not have sufficient information to interprete these results.
3. Local heat flux and the large-scale circul.
= 4.00, Ra = 4.00x109, Pr = 0.7
= 2.00, Ra = 0.52x1011, Pr = 0.7
? ?
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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2. Measurementtechnique
• Local heat flux measurements have been carried out at the surface of the heating and the cooling plate.
• The advection of plumes is a stochastic process which depends on the geometry of the cell.
• For aspect ratio ≈ 1 and Pr ≈ 1 the boundary layers at the centre of the cell are not coupled by the large-scale circulation while for larger aspect ratios correlations have been found.
• The „sloshing mode“ of the large-scale circulation in cylindrical samples of ≈ 1 and Pr ≈ 5 could not be found in a Pr ≈ 1 cell.
Conclusion:
4. Conclusion and Outlook
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
It would be nice to have a complete picture of the distribution of the heat flux at the plates!
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1. Motivation
2. Measurementtechnique
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
-5000 -2500 0 2500 5000-0.2
0
0.2
0.4
0.6
0.8
1
[s]
Cxy
-1000 -500 0 500 1000-0.2
0
0.2
[s]
Cxy
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2. Measurementtechnique
• In an ongoing national Research Group we are going to study particularly these boundary layer dynamics like local heat fluxes, plume emissions etc.
• The group runs from 2010 to 2015 and the following groups will participate:- Bruno Eckardt (Uni Marburg) - C. Egbers (Uni Cottbus) - A. Delgado (Uni Erlangen)- B. Hof (MPI Goettingen)- J. Schumacher (Uni Ilmenau)- R. du Puits (Uni Ilmenau)
• Aim: to find similarities in the boundary layer transport in turbulent RB convection, TC- and pipe flow.
Outlook:
4. Conclusion and Outlook
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
Page 32/29
1. Motivation
2. Measurementtechnique
D
HT ,qu
INPUT
HdΓ
3THgRa
Pr
• Rayleigh number (buoyancy):
• Prandtl number (fluid prop.):
• Aspect ratio (geometry):
RESPONSE
dqqNu
HuRe
• Nusselt number (heat transport):
• Reynolds number (velocity):
1. Motivation
3. Plume dynamics
4. Large-scale circulation
5. Conclusion
EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010
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