Conditional and unconditional second-order structure functions in bubbly channel flows of power-law fluids

E Trautner,M Klein,J Hasslberger,F Bräuer

doi:10.1063/5.0049799

Abstract

The influence of non-Newtonian fluid behavior and the Eötvös number on conditional and unconditional second-order structure functions of bubbly channel flows has been investigated by conducting a series of direct numerical simulations at a friction Reynolds number of 127.3. Two Eötvös numbers have been considered (Eo = 0.3125 and Eo = 3.75) together with three different power-law indexes representing shear-thinning (n = 0.7), Newtonian (n = 1.0), and shear-thickening (n = 1.3) fluid behavior. The scaling of the second-order structure functions (SFs) can be translated into an inertial range scaling of the turbulent kinetic energy spectrum. However, because of the discontinuous character of the fluid properties in bubbly flows, SFs are more easily accessible than turbulence spectra, which are based on Fourier transform. It has been found that the different parameters (i.e., Eo, n) have an influence on the energy content as well as the peak location of the compensated second-order SFs (i.e., the dimensions of the large scales). However, after appropriate scaling, the curves nearly collapse. To confirm and further explain the above findings, directional length scales have been evaluated and discussed in detail. Finally, the anisotropy of the Reynolds stress tensor and dissipation tensor has been analyzed in terms of the Lumley triangle, showing that bubbly channel flows are less isotropic than their single-phase counterpart, although they are more homogeneous in the channel center. While the dissipation tensor is slightly more isotropic than the Reynolds stress tensor in the bulk region of the channel flow, overall, a very similar behavior is observed.

Highlights

Flows are found in a large number of technical applications, e.g., in thermal power plants, in boiling water reactors, in cooling systems of nuclear reactors, in compressed air lifters in the oil industry, and, above all, in chemical process engineering
The anisotropy of the Reynolds stress tensor and dissipation tensor has been analyzed in terms of the Lumley triangle, showing that bubbly channel flows are less isotropic than their single-phase counterpart, they are more homogeneous in the channel center
The inertial range scaling in bubbly two-phase flows is still discussed controversially and even less is known for non-Newtonian two-phase flow behavior

Summary

Introduction

Flows are found in a large number of technical applications, e.g., in thermal power plants, in boiling water reactors, in cooling systems of nuclear reactors, in compressed air lifters in the oil industry, and, above all, in chemical process engineering. It was observed that the bubble oscillations increase with decreasing power-law index Besides such statistics, the knowledge of the distribution of energy on the wide range of spatial and temporal scales is of fundamental importance for understanding and modeling turbulent multiphase flows. The knowledge of the distribution of energy on the wide range of spatial and temporal scales is of fundamental importance for understanding and modeling turbulent multiphase flows In their pioneering work, Lance and Bataille[26] found that the one-dimensional spectra exhibit a large range of high frequencies associated with the wakes of the bubbles and that the

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Conclusion