Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis

Abstract

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

A-Priori Assessment of Interfacial Sub-grid Scale Closures in the Two-Phase Flow LES Context

“…Assuming, in a conservative manner, that Re t = Re b and L t = d b yields ≈ 28.2 μ m. One may alternatively estimate ≈ u x,rel g x (Koebe et al 2003) and use = l to obtain the Kolmogorov length scale = ( 3 ∕ ) 1∕4 ≈ 26.8 μ m. The achieved grid spacing is of the same order of magnitude as and can thus be considered sufficient for the evaluation of first-and second-order statistics (Grötzbach 2011). In a closely related setup (bubble Reynolds number ≈ 10 3 , identical fluid properties), a similar grid resolution ( d b ∕ x = 40 ) has also been used in earlier DNS studies (Hasslberger et al 2018) on bubbly flows. However, it may be questioned whether the resolution is fine enough to fully resolve the boundary layers on both sides of the interface.…”

“…The same dominant flow behavior can then be assumed on sub-grid level because in LES, other than in (U)RANS, there is usually a sufficiently high correlation between the strain-vorticity relationship in the DNS and the resolved level (Kobayashi 2005). It has been found in literature (Hasslberger et al 2018) that especially the regions of high interface curvature in bubbly flows are dominated by vortices. In regions characterized by F CS = 0 (strain-vorticity equilibrium), the original formulation (Eq.…”

“…18) is locally recovered. The simplified second formulation BML-SW utilizes the fact that the bubble interior and exterior close to the interface are usually vorticity-and straindominated, respectively (Hasslberger et al 2018). Here, is taken to be the volume fraction of the lighter phase, in which the vorticity tends to accumulate in unsteady turbulent flows (Tripathi et al 2014;Hasslberger et al 2018Hasslberger et al , 2019.…”

“…The simplified second formulation BML-SW utilizes the fact that the bubble interior and exterior close to the interface are usually vorticity-and straindominated, respectively (Hasslberger et al 2018). Here, is taken to be the volume fraction of the lighter phase, in which the vorticity tends to accumulate in unsteady turbulent flows (Tripathi et al 2014;Hasslberger et al 2018Hasslberger et al , 2019. Finally, the scale similarity (SS) ansatz for this term (Chesnel et al 2011) reads where the secondary test filter for any field quantity i,j,k at the discrete location given by the index triple (i, j, k) is implemented according to Anderson and Domaradzki (2012):…”

“…Since the flow behavior in vertical (the direction subject to gravitational acceleration, i.e. the main flow direction) and lateral directions is rather different as shown by Hasslberger et al (2018) who analyzed the flow structure in turbulent bubbly flows in detail by means of a local flow topology analysis, correlation coefficients in both directions are evaluated separately. All models, except the GFM model, show increasing correlation values for decreasing filter width ( ∕ DNS → 1 ) which is an important consistency check.…”