Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting

Abstract

We report an experimental study of the properties of the velocity boundary layer in turbulent Rayleigh-Bénard convection in a cylindrical cell. The measurements were made at Rayleigh numbers Ra in the range 2.8 × 10 8 < Ra < 5.6 × 10 9 and were conducted with the convection cell tilted with an angle θ relative to gravity, at θ = 0. and 3.4 o , respectively. The fluid was water with Prandtl number P r = 5.3. It is found that at small tilt angles (θ 1 o ), the measured viscous boundary layer thickness δ v scales with the Reynolds number Re with an exponent close to that for a Prandtl-Blasius laminar boundary layer, i.e. δ v ∼ Re −0.46±0.03 . For larger tilt angles, the scaling exponent of δ v with Re decreases with θ. The normalized mean horizontal velocity profiles measured at the same tilt angle but with different Ra are found to have an invariant shape. But for different tilt angles, the shape of the normalized profiles is different.It is also found that the Reynolds number Re based on the maximum mean horizontal velocity scales with Ra as Re ∼ Ra 0.43 and the Reynolds number Re σ based on the maximum rms velocity scales with Ra as Re σ ∼ Ra 0.55 , with both exponents do not seem to depend on the tilt angle θ.Several wall quantities are also measured directly and their dependency on Re are found to agree well with those predicted for a classical laminar boundary layer. These are the wall shear stress τ (∼ Re 1.46 ), the viscous sublayer δ w (∼ Re 0.75 ), the friction velocity u τ (∼ Re −0.86 ) and the skin friction coefficient c f (∼ Re −0.46 ). Again, all these near-wall quantities do not seem to depend on the tilt angle.We also examined the dynamical scaling method proposed bys Zhou and Xia [Phys. Rev. Lett. 104, 104301 (2010)] and found that in both the laboratory and the dynamical frames the mean velocity profiles show deviations from the theoretical Prandtl-Blasius profile, with the deviations increase with Ra. But profiles obtained from dynamical scaling in general have better agreement with the theoretical profile. It is also found that the effectiveness of this method appears to be independent of Ra.1. Introduction Rayleigh-Bénard convectionRayleigh-Bénard (RB) convection, which is a fluid layer heated from below and cooled from the top, is an idealized model to study turbulent flows involving heat transport and has attracted much attention during the past few decades (Siggia 1994;Kadanoff 2001;Ahlers, Grossmann & Lohse 2009;. The system is characterized by two control parameters: the Rayleigh number Ra, Prandtl number P r, which are defined arXiv:1209.6415v1 [physics.flu-dyn]

Quasistatic magnetoconvection: heat transport enhancement and boundary layer crossing

“…To obtain the asymptotic behaviour of δ v in the limit of Re Ha, we fit a power law to its values at Ha = 0, which is shown in figure 15(a). The obtained power law exponent of −0.20 agrees excellently with previous measured values (see, for example, Xin, Xia & Tong 1996;Wei & Xia 2013). For the Re-Ra relationship, we show in figure 15(b) a plot of the zero-Ha Reynolds number Re 0 versus Ra; a power law fit gives Re 0 = 0.014Ra 0.53±0.01 .…”

Boundary layer structure in turbulent Rayleigh–Bénard convection in a slim box

“…The data collected for comparison with experimental and other DNS studies include the viscous BL thickness and heat flux. Two sets of experimental measurements [35,36] and two sets of DNS from [37] with different aspect ratios, and from Stevens et al [38] for a cylindrical box with aspect ratio Γ = 1/2 at higher Ra of 2 × 10 10 , 2 × 10 11 and 2 × 10 12 . Streamwise mean velocity measurements from du Puits et al [39] at several Ras around 10 11 and mean temperature measurements from Ahlers et al [13] are also considered.…”

The effect of cell tilting on turbulent thermal convection in a rectangular cell

“…The velocity components u and w are in the x and z directions, Effect of cell tilting on turbulent thermal convection 277 respectively. The application of PIV to the RBC system has been described in previous works Sun, Xia & Tong 2005b;Wei & Xia 2013). In the present study, a double-cavity neodymium-doped yttrium aluminium garnet (Nd:YAG) laser, with an interval time 0.068 s, provides a light sheet (∼3 mm thick) to illuminate the convection cell.…”

“…Bairi, Laraqi & de María (2007) performed natural convection both experimentally and numerically over a range of tilt angles 0 < β < 2π, but the range of Ra was small (Ra < 10 8 ). Recently, Wei & Xia (2013) reported the effect of cell tilting on the boundary layer properties of RBC. Their experiments were carried out in a cylindrical cell with 2.8 × 10 8 < Ra < 5.6 × 10 9 , Pr = 5.3, Γ 1 and β 3.4 • .…”