15THEUROPEANTURBULENCECONFERENCE, 25-28 AUGUST, 2015, DELFT, THENETHERLANDS
TEMPERATURE SMALL SCALES STATISTICS IN TURBULENT CONVECTIVE TILTED
CHANNEL FLOW
Eléonore RUSAOUEN
1,2, Julien SALORT
1, Bernard CASTAING
1, & Francesca CHILLA
1 1Laboratoire de Physique, ENS de Lyon, Lyon, France
2
Institut Néel, CNRS, Grenoble, France
Abstract We report here the small scales statistics of velocity en temperature in a turbulent convective flow : a channel connecting two chambers. This flow, differently from Rayleigh-Bénard, is independent from the thermal boundary layers and can be influenced by stratification if tilted. The probability distribution functions of the temperature and velocity are gaussian while the temperature power spectra exhibit a Bolgiano-Obukov scaling at all angles.
CONTEXT AND PURPOSE
Free convection is responsible for most natural flows.While its driving mechanism is conceptually simple, it can result in very complex flows, due to the interplay between mixing, buoyancy, and transport for the active scalar. One still opened question is the behavior of the temperature small scales properties. Is the temperature an active or a passive scalar? Some works and measurements give for the Raylegh Bénard system a not ambiguous but not easy to explain answer : the temporal spectra of temperature exhibit a Bolgiano-Obukov ’59 (BO59) scaling while the spatial structure functions of both velocity and temperature have a close to Kolmogorov scaling. The probability distribution function of the temperature are not gaussian [1]. We choose here to look at the temperature statistics in an other convective system : a channel connecting a top cold and a bottom hot chambers. This system has two important special characteristics :it is independent of the thermal boundary layers (trough with the energy is injected in the flow) and exhibits a pure inertial low for the heat flux transport : N u ∝ (P rRa)12 [2]. It can be assimilated to a Rayleigh-Bénard bulk. This channel can
be tilted to add stratification effects. When the channel is tilted the temperature has a gaussian distribution function, a BO59 scaling is found for the temporal power spectra of temperature, while spatial velocity power spectra are close to Kolmogorov −5/3 scaling law.
EXPERIMENTAL SET-UP
The experiment consists in two conical chambers, based by thick plates, connected with a square duct d × d of inner dimensions, of length D, filled with water. The cold (top) chamber is temperature regulated by a water bath. The hot (bottom) chamber is Joule heated by a spiral resistor. The channel has transverse dimensions d =20cm, and length D = 80cm. The used power varies between 100W and 1000W , the Rayleigh number varies between 109 and 1010.
The temperature is measured in the middle of the channel, by means of a thermistor of typical size 0.4mm, and 0.1s of response time.
MEASUREMENTS
Turbulence is completely developed and the probability distribution functions of velocity are gaussian at all the explored angles. Nevertheless when the channel is tilted stratification begin to act, deforming the mean velocity profiles [3]. Differently from the Rayleigh Bénard [4] case the probability distribution functions of temperature are gaussian. This is true for vertical or inclined case at least till ψ = 30◦of inclination, the maximum we can attain. In figure 2 are shown the probability distribution functions at different power at an angle of ψ = 15◦. Temporal power spectra of temperature have a scaling close to −7/5 indicating a Bolgiano-Obukov scaling as shown in figure 3. Those results are independent from the tilting angle.
Figure 2. Probability distribution function of the temperature fluctuation at an angle of ψ = 15◦.
Figure 3. Temporal power spectra of temperature at an angle of ψ = 15◦.
References
[1] D. Lohse and K.Q. Xia, "Small scale properties of turbulent Rayleigh-Bénard convection", Annual Review of Fluids Mecanics, 2010.
[2] X. Riedinger, J.-C. Tisserand, F. Seychelles, B. Castaing, and F. Chillà, “Heat transport regimes in an inclined channel ” Phys. Fluids 25, 015117 (2013).
[3] J. Salort, X. Riedinger, E. Rusaouën, J.C. Tisserand, F. Seychelles, B. Castaing, F. Chillà, “Turbulent velocity profiles in a tilted heat pipe”, Phys. Fluids, 25, 105110 (2013).
