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Local wall heat flux in turbulent Rayleigh-Bénard convection

Local wall heat flux in turbulent Rayleigh-Bénard convection. Ronald du Puits Ilmenau University of Technology Department of Mechanical Engineering POB 100565, D-98693 Ilmenau, GERMANY contact: ronald.dupuits@tu-ilmenau.de. Collaboration: André Thess, Jörg Schumacher (Ilmenau)

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Local wall heat flux in turbulent Rayleigh-Bénard convection

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  1. Local wall heat flux in turbulent Rayleigh-Bénard convection Ronald du Puits Ilmenau University of Technology Department of Mechanical Engineering POB 100565, D-98693 Ilmenau, GERMANY contact: ronald.dupuits@tu-ilmenau.de Collaboration: André Thess, Jörg Schumacher (Ilmenau) Philippe Roche (Grenoble) Technicians: Vigimantas Mitschunas, Klaus Henschel, Helmut Hoppe Financial support: German Research Foundation Federal Ministry of Education and Research Thuringian Government EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  2. Outline • Motivation to measure the local wall heat flux • Heat flux sensor and measurement technique • Local heat flux and plume dynamics • Local heat flux and the large-scale circulation • 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

  3. 1. Motivation Rayleigh-Bénard convection reflects a large number of natural and technical flow phenomena. 1. Motivation 2. Measurementtechnique 3. Plume dynamics Atmosheric flows Oceanic flows 4. Large-scale circulation 5. Conclusion Earth core convection Star convection EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  4. 1. Extremely high level of turbulence  large Rayleigh number e.g. Earth atmosphere: 1020 Pacific Ocean: 1021 Outer earth core: > 1020Sun‘s convective zone: 1023 2. Small thickness compared with lateral extent  large aspect ratio e.g. Earth atmosphere: 4000 Pacific Ocean: 3000 Outer earth core: 10Sun‘s convective zone: 6 1. Motivation Characteristics of those flows: 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

  5. Actual high Rayleigh number experiments: • Triest (I), Ramax = 1017, G = 0.5…4, liquid He Grenoble (Fr), Ramax = 1015, G = 0.5…1, liquid He Goettingen (D) , Ramax = 1015, G = 0.5…1, SF6 (15bar) Santa Barbara (US) , Ramax = 1014, G = 0.28…6, various liquids Hongkong (CN) , Ramax = 1014, G = 1….20, water Ilmenau (D) , Ramax = 1012, G = 1…100, Air 1. Motivation Requirements for experiments to model geophysical flows: • high Rayleigh numbers 2. large aspect ratios 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

  6. 1. Motivation The best known geometry is the G = 1 cell of cylindrical shape. For high Ra convection we know many features of the flow. • Prediction of the global heat flux in terms of Nu = f(Ra, Pr). 1. Motivation The boundary layers play a crucial role for the global heat transport . 2. Measurementtechnique The boundary layers interact with the bulk by thermal plumes. 3. Plume dynamics 4. Large-scale circulation 5. Conclusion The dynamics of the large-scale circulation, one single role exists, cessations, rotations, reversals can occur, mean plane oscillatesin angular direction, sloshing mode EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  7. 1. Motivation Can we simply transfer this knowledge to flows at higher aspect ratio? local heat flux sensor 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion What can we learn from local heat flux measurements at the surface of the heating and the cooling plate? EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  8. Accessible parameter range full-size barrel small barrel DNS 2. Experimental facility Main features: • High Ra numbers up to Ra = 1012 Continuously variable aspect ratioG ≈ 1…100 1. Motivation 2. Measurementtechnique H < 6.30 m 3. Plume dynamics 4. Large-scale circulation 5. Conclusion Large-scale experimental facility `Barrel of Ilmenau‘ www.ilmenauer-fass.de D = 7.15 m EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  9. 2. Heat flux sensor Sensor: The local wall heat fluxes were measured using special sensors called heat flux plates. 1. Motivation Convection flow 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation heat flux sensor (fcutoff=3Hz)qw (t) 1.5mm 5. Conclusion 20mm heating/cooling plate EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  10. 2. Heat flux sensor Where we are with our heat flux sensor? – Ra ≈ 5x1011, G ≈ 1 z[mm] T(z) ‹v›(z) 20 1. Motivation 2. Measurementtechnique 10 Thickness of the sensor 3. Plume dynamics 4. Large-scale circulation 5. Conclusion The heat flux sensor reflects the local convection coefficient adepending on the local velocity v(t) and the local temperature difference DT(t). EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  11. 3. Local heat flux and plume dynamics A thermal plume develops at the surface of the cooled top plate. 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 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) 5. Conclusion EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  12. 3. Local heat flux and plume dynamics Thermal plumes arise from the heated bottom plate and fall down from the cooled top plate. 1. Motivation They organize themselve to a large scale motion of one single role occupying the whole space of the cell. 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 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) 5. Conclusion EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  13. 3. Local heat flux and plume dynamics 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion Generalized sketch of the plume motion in turbulent convection. Can we generalize this picture to other fluids, e.g. with Pr = 0.7. Can we generalize it to aspect ratios G > 1. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  14. 3. Local heat flux and plume dynamics Hypothesis: • The plume has to be reflected as a positive burst in the time series of the local heat flux. 1. Motivation For a given velocity of the LSC the width can be calculated from the time of the burst. 2. Measurementtechnique w 3. Plume dynamics v 4. Large-scale circulation 5. Conclusion t EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  15. 3. Local heat flux and plume dynamics Time resolved local heat flux at the surface of the cooling plate.position: centre; G=1.13, Ra=4.27x1011, Pr=0.7 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion • The local heat flux fluctuates over the time by ≈ 40%. Positive eruptions occur as often as negative ones do. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  16. 3. Local heat flux and plume dynamics 8s 1. Motivation 2. Measurementtechnique 3. Plume dynamics 7s 4. Large-scale circulation 5. Conclusion • The typical time of a strong eruption is ≈ 8s. 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! EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  17. 3. Local heat flux and plume dynamics Probability density of the local heat flux at the surface of the heating plate.position: centre; G=1.13, Ra=4.27x1011, Pr=0.7, meas. time: 53 hours 1. Motivation 2. Measurementtechnique gaussian 3. Plume dynamics 4. Large-scale circulation 5. Conclusion • For aspect ratio G = 1.13the fluctuations of the local heatflux are distributed gaussian. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  18. 3. Local heat flux and plume dynamics Question: Is the local heat flux symmetrical at the heating and the cooling plate? Ra=4.27x1011, DT=20K 1. Motivation heating plate cooling plate 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion • The mean local heat flux and the fluctuations at the heatingand the cooling plate differ, but both are distributet gaussian. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  19. 3. Local heat flux and plume dynamics Question: Does it depend on aspect ratio? second measurement position: centre; G=4.00, Ra=4.00x109, Pr=0.7 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion • For aspect ratios G ≈ 4 the fluctuations of the local heat flux are notdistributet gaussian, there are more positive than negative eruptions. There is a sharp cut towards lower heat fluxes. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  20. 3. Local heat flux and plume dynamics Question: How can we interpret these results? G ≈ 4, Pr ≈ 1 G ≈ 1, Pr ≈ 1 1. Motivation 2. Measurementtechnique fluctuating boundary layer LSC LSC 3. Plume dynamics d 4. Large-scale circulation • For aspect ratios G ≈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) For aspect ratios G ≈ 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 5. Conclusion EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  21. 3. Local heat flux and the large-scale circul. Question: Are the boundary layers coupled by the large scale circu-lation and is the emission of plumes a periodic process? 1. Motivation 2. Measurementtechnique Sketch of the large-scale circulation shearing the boundary layers.Villermaux, PRL 75, 4619 (1995) 3. Plume dynamics 4. Large-scale circulation The Model of Villermaux: 5. Conclusion • Boundary layer instabilities (plumes) are emerged at one plate. They travel within the large-scale circulation to the other plate and create a second instability (plume) there. The process runs periodically and can be described by a model of two coupled oscillators. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  22. 3. Local heat flux and the large-scale circul. Local heat flux sensors We compute the cross-correlation function Cxy 1. Motivation 2. Measurementtechnique G = 1.13, Ra = 4.27x1011, Pr = 0.7 3. Plume dynamics 4. Large-scale circulation 5. Conclusion For G ≈1 and Pr ≈1 the local heat fluxes at the centre of the heating and the cooling plate are not correlated. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  23. 3. Local heat flux and the large-scale circul. Local heat flux sensors G = 2.00, Ra = 0.52x1011, Pr = 0.7 1. Motivation 100s 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation For G ≈ 2 and Pr ≈ 1 the local heat fluxes at the centre of the heating and the cooling plate are correlated. 5. Conclusion Thermal plumes emerging from the cooling plate arrive at the heating plate and vice versa. Both boundary layers are coupled by the large-scale circulation. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  24. 3. Local heat flux and the large-scale circul. Local heat flux sensors G = 4.00, Ra = 4.00x109, Pr = 0.7 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 24/29

  25. 3. Local heat flux and the large-scale circul. Question: Can we identify the recently found „sloshing mode“ of the large-scale circulation also in RB convection at Pr ≈ 1? Xi et al., PRL 102, 044503 (2009) Brown et al., JFM 638, 383 (2009) oscillatory mode 1. Motivation 2. Measurementtechnique 3. Plume dynamics sloshing mode 4. Large-scale circulation 5. Conclusion Model of the large-scale circulation with the „oscillatory“ mode (red) and the „sloshing mode“ (green). EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  26. 3. Local heat flux and the large-scale circul. We compute the auto-correlation function Cxx 1. Motivation G = 1.13, Ra = 4.27x1011, Pr = 0.7 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion For Pr ≈ 1 and G ≈ 1 the sloshing mode could not be identified. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  27. 3. Local heat flux and the large-scale circul. ? ? G = 4.00, Ra = 4.00x109, Pr = 0.7 G = 2.00, Ra = 0.52x1011, Pr = 0.7 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion Auto-correlation function of the local heat flux for larger aspect ratios G. For larger aspect ratios G = 2 and G = 4 (Pr ≈ 1) we do not have sufficient information to interprete these results. EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  28. 4. Conclusion and Outlook Conclusion: • 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 G ≈ 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 G ≈ 1 and Pr ≈ 5 could not be found in a Pr ≈ 1 cell. 1. Motivation 2. Measurementtechnique 3. Plume dynamics 4. Large-scale circulation 5. Conclusion It would be nice to have a complete picture of the distribution of the heat flux at the plates! EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  29. MANY THANKS! EUROMECH Colloquium #520, High Rayleigh number convection, Les Houches, 24.-29.01.2010

  30. 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 30/29

  31. 4. Conclusion and Outlook Outlook: • 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. 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

  32. 1. Motivation INPUT RESPONSE • Aspect ratio (geometry): • Nusselt number (heat transport): • Rayleigh number (buoyancy): • Reynolds number (velocity): 1. Motivation 2. Measurementtechnique • Prandtl number (fluid prop.): 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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