## Abstract

In the present study, focusing on characterizing the bubble-induced agitation (turbulence), spatially varying flow statistics of gas and liquid phases in laminar upward bubbly flows (Reynolds number of 750) with varying mean void fraction are investigated using a two-phase high-speed particle image velocimetry. As the flow develops along the vertical direction, bubbles with small-to-moderate void fractions, which were intentionally distributed asymmetrically at the inlet, migrate fast and show symmetric distributions of wall or intermediate peaking. Meanwhile, the mean liquid velocity saturates relatively slowly to a flat distribution at the core region. Despite small void fractions considered, the bubbles generate a substantial turbulence, which increases with increasing mean void fraction. Interestingly, it is found that the mean vertical velocity, bubble-induced normal stress in radial direction, and Reynolds stress profiles match well with those of a single-phase turbulent flow at a moderate Reynolds number (e.g., 10^{4}), indicating the similarity between the bubble-induced turbulence and wall-shear-generated turbulence in a single-phase flow. Previously suggested scaling relations are confirmed such that the mean bubble rise velocity and bubble-induced normal stress (in both vertical and radial directions) scale with mean volume void fraction as a power of −0.1 and 0.4, respectively. Finally, based on the analysis of measured bubble dynamics (rise in an oscillating path), a theoretical model for two-phase turbulent (Reynolds) stress is proposed, which includes the contributions by the non-uniform distributions of local void fraction and relative bubble rise velocity, and is further validated with the present experimental data to show a good agreement with each other.

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## Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (NRF-2012M2A8A4055647, NRF-2013R1A1A1008373) via SNU-IAMD, and the Aspiring Researcher Program through Seoul National University (SNU) in 2014, Korea.

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Kim, M., Lee, J.H. & Park, H. Study of bubble-induced turbulence in upward laminar bubbly pipe flows measured with a two-phase particle image velocimetry.
*Exp Fluids* **57**, 55 (2016). https://doi.org/10.1007/s00348-016-2144-6

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DOI: https://doi.org/10.1007/s00348-016-2144-6

### Keywords

- Void Fraction
- Liquid Velocity
- Bubbly Flow
- Volume Void Fraction
- Void Distribution