Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

Abstract

Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Δρ/(2⟨ρ⟩)=1.15×10−2] in a long circular tube tilted at an angle θ=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

Buoyancy-induced turbulence in a tilted pipe

“…In particular, they found 'hard' turbulence (for which the above 'ultimate' scaling holds) to occur for Θ 20 • at large enough Rayleigh numbers, followed by 'soft' turbulence (for which the Nusselt number varies as the square of the Rayleigh number) at larger Θ. For Θ 20 • , the corresponding mean velocity and shear stress profiles are similar to those of Znaien et al (2009), and the smaller Θ the lower the critical Rayleigh number required to reach the 'hard' regime. New data by the same group in the range 5 • Θ 20 • (Salort et al 2013) were interpreted in the light of a mixing length model, but the observed Θ-dependence of the mean velocity profile could only be recovered by altering the usual time scale of Prandtl's original model (i.e.…”

“…At low-to-moderate Reynolds numbers, the effective diffusivity and front velocity were shown to decrease as the inverse of the three-half and three-quarter powers of the Reynolds number, respectively (Séon et al 2007). The local characteristics of the turbulent field, especially the distribution of the variance of velocity fluctuations and that of the turbulent shear stress, started to be explored, both experimentally (using PIV) and computationally (with the present code), by Znaien et al (2009). This study revealed that the near-wall region plays little role in the streamwise mean momentum transfer and showed existence of a four-roll mean secondary flow, the generation mechanism and scaling of which were elucidated by .…”

“…Some of the most recent ones employed PIV to investigate the instantaneous flow field and the large-scale turbulent statistics in the vertical midplane of the channel or pipe, providing mean velocity and shear stress profiles. However none of them explored the complete three-dimensional structure of the velocity and density fields which is of importance in the mixing process, as emphasized by the discovery of the mean secondary flow in the circular pipe configuration (Znaien et al 2009). Also, apart from those by Odier et al (2009Odier et al ( , 2012, no joint measurement of the velocity and scalar fields has been reported so far.…”

Recirculation cells in a wide channel

“…Based on these measurements, we use a depth-averaged model to evaluate the momentum transfer by these structures, and find that it is comparable with the classical turbulent transfer. They appear in rapid granular flows 1 , in Rayleigh-Bénard-Poiseuille flows 2 , in the superficial layers of sea and lakes 3 , in straight tubes 4,5 , as well as in straight channels and natural rivers [6][7][8] .…”

Exchange flow of two immiscible fluids and the principle of maximum flux

“…Frigaard & Scherzer 1998, Moyers-Gonzalez & Frigaard 2004. There is also associated work on exchange problems involving miscible fluids, tilted tubes or channels, and unsteady solutions (see the recent articles by Seon et al 2007, Znaien et al 2009and Taghavi et al 2009.…”