scholarly journals Rayleigh-Bénard convection in air: out-of-plane vorticity from stereoscopic PIV measurements

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Valori Valentina ◽  
Alexander Thieme ◽  
Christian Cierpka ◽  
Joerg Schumacher
Keyword(s):  
Pressure Vessel ◽  
Piv Measurements ◽  
Stereoscopic Piv ◽  
Bénard Convection ◽  
Benard Convection ◽  
Out Of Plane ◽  
Set Up ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We present results from stereoscopic PIV measurements in a Rayleigh-Benard convection (RBC) cell filled with (compressed) air at Rayleigh numbers: Ra = 1.5×104,  2×104, 1×105, 2×105, 5×105, and Prandtl number Pr ' 0.7. The three largest Rayleigh numbers are obtained pressurising the whole set-up including cameras and objective lenses, up to 4.5 bars. The main goal of this study is to reproduce DNS data that are acquired at the same Rayleigh numbers to study far-tail events of the out-of-plane vorticity component (ωz). The measurements are performed in a RBC cell with aspect ratio Γ = W/H = 10, where W is the width and H = 3 cm is the height of the domain. The cell is equipped with a transparent bottom plate heated by a thin oxide layer (for details see Kastner et al. (2018)), which allows us to measure 3C2D velocity fields on ¨a horizontal plane at mid height of the cell. The RBC cell set-up is inserted in the SCALEX facility of TU Ilmenau, a pressure vessel with several optical accesses that can be pressurised up to 10 bars The experiments aim firstly at improving the quality of previous measurements performed in the sameset-up [Kastner et al. (2018), Cierpka et al. (2019)], regarding the accuracy of the out-of-plane velocity ¨component. This has been realised by positioning the cameras at a larger stereo angle (about 25◦), which is possible by placing them inside the pressure vessel. Major challenges of the current measurements are caused by optical distortions due to the temperature gradients that are typical for thermal convection (see Valori (2018), Valori et al. (2019)). Probability Density Functions (PDFs) of ωz from stereo PIV experiments and from DNS data are shown respectively in figure 1(a) and 1(b) for all Rayleigh numbers studied. We can observe that for both kind of data the tails of the PDF becomes wider while increasing the Rayleigh number, which may be connected to intermittency. This crossover from Gaussian to intermittent statistic was recently studied in Valori and Schumacher (2021) from DNS. Figure2(a) shows the temporal evolution of ωz at the position of its largest (extreme) value at Ra = 2.5 × 105, while figure2(b) shows the spatial distribution of ωz at the time of its extreme event in the experiments. The experimental results are able to reproduce well the statistics of DNS data of the same flow, and allow the study of extreme events of ωz.

Randomly forced Rayleigh-Bénard convection

1980 ◽  
Vol 98 (2) ◽  
pp. 329-348 ◽  
Author(s):  
Bharat Jhaveri ◽  
G. M. Homsy
Keyword(s):  
Convective Transport ◽  
Time Intervals ◽  
Onset Of Convection ◽  
Nonlinear Convection ◽  
Bénard Convection ◽  
Benard Convection ◽  
Random Fluctuations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We consider the onset of Rayleigh–Bénard convection from random fluctuations arising within a fluid. In the specific case in which the fluctuations are thermodynamically determined, we reduce the problem to a random initial value problem for the Fourier modes. For the case of weak nonlinear convection, it is possible to truncate the number of modes and this truncated set is solved both by a Monte Carlo technique and by moment methods for various Rayleigh numbers. We find three stages in the evolution of ordered convection from random fluctuations which correspond to time intervals in which the fluctuations and the nonlinearity have different degrees of importance. It is shown that no simple moment truncation method will succeed and that the time for onset of convection is a mean over a distribution of times for which members of an ensemble exhibit appreciable convective transport.

The effect of distant side-walls on the evolution and stability of finite-amplitude Rayleigh-Bénard convection

1981 ◽  
Vol 378 (1775) ◽  
pp. 539-566 ◽  
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Side Walls ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

A recent study by Cross et al . (1980) has described a class of finite-amplitude phase-winding solutions of the problem of two-dimensional Rayleigh-Bénard convection in a shallow fluid layer of aspect ratio 2 L (≫ 1) confined laterally by rigid side-walls. These solutions arise at Rayleigh numbers R = R 0 + O ( L -1 ) where R 0 is the critical Rayleigh number for the corresponding infinite layer. Nonlinear solutions of constant phase exist for Rayleigh numbers R = R 0 + O ( L -2 ) but of these only the two that bifurcate at the lowest value of R are stable to two-dimensional linearized disturbances in this range (Daniels 1978). In the present paper one set of the class of phase-winding solutions is found to be stable to two-dimensional disturbances. For certain values of the Prandtl number of the fluid and for stress-free horizontal boundaries the results predict that to preserve stability there must be a continual readjustment of the roll pattern as the Rayleigh number is raised, with a corresponding increase in wavelength proportional to R - R 0 . These solutions also exhibit hysteresis as the Rayleigh number is raised and lowered. For other values of the Prandtl number the number of rolls remains unchanged as the Rayleigh number is raised, and the wavelength remains close to its critical value. It is proposed that the complete evolution of the flow pattern from a static state must take place on a number of different time scales of which t = O(( R - R 0 ) -1 ) and t = O(( R - R 0 ) -2 ) are the most significant. When t = O(( R - R 0 ) -1 ) the amplitude of convection rises from zero to its steady-state value, but the final lateral positioning of the rolls is only completed on the much longer time scale t = O(( R - R 0 ) -2 ).

scholarly journals Prandtl and Rayleigh numbers dependences in Rayleigh-Bénard convection

2002 ◽  
Vol 58 (5) ◽  
pp. 693-698 ◽  
Author(s):  
P.-E Roche ◽  
B Castaing ◽  
B Chabaud ◽  
B Hébral
Keyword(s):  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

Has the ultimate state of turbulent thermal convection been observed?

2015 ◽  
Vol 785 ◽  
pp. 270-282 ◽  
Author(s):  
L. Skrbek ◽  
P. Urban
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Ultimate State ◽  
Logarithmic Factor ◽  
Aspect Ratios ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

An important question in turbulent Rayleigh–Bénard convection is the scaling of the Nusselt number with the Rayleigh number in the so-called ultimate state, corresponding to asymptotically high Rayleigh numbers. A related but separate question is whether the measurements support the so-called Kraichnan law, according to which the Nusselt number varies as the square root of the Rayleigh number (modulo a logarithmic factor). Although there have been claims that the Kraichnan regime has been observed in laboratory experiments with low aspect ratios, the totality of existing experimental results presents a conflicting picture in the high-Rayleigh-number regime. We analyse the experimental data to show that the claims on the ultimate state leave open an important consideration relating to non-Oberbeck–Boussinesq effects. Thus, the nature of scaling in the ultimate state of Rayleigh–Bénard convection remains open.

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