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Introduction
Multiphase fluid, especially gas–liquid fluid and gas–liquid–solid fluid, has been the research hotspot in fluid mechanics. Since the flow characteristics of multiphase fluid are influenced by initialization/boundary conditions, fluid properties, and even temperatures and pressures, existing methods mainly focused on simulations and/or experiments, which summarize and analyze characteristics of multiphase fluids by observed results and experiences. Researchers have conducted various experiments and simulations on gas–liquid multiphase fluids in vertical pipes. Recently, Lin et al.1 studied void fraction, bubble size, liquid velocity, bubble rise velocity, and solid fraction in gas–liquid fluids through experiments. They indicated that radial forces become more uneven if bubbles in fluids are bigger, thus making bubble shape changeable and influencing the flowing properties of the whole fluid. Therefore, bubble size is one of the influencing factor of flow regime. On the other hand, they found in experiments that big bubbles concentrate in center, while small ones are close to pipe walls. This was later verified by Ozar et al.2 and Wang.3 According to the above-mentioned experimental results, although the accurate relationship between void fraction and flow regime could not be gained, it can be sure that void fraction and gas-phase fluid velocity under the turbulence are higher than those under steady flow regime. Julia et al.2,4 explored void fraction, bubble size, and flow regime in annulus used in deep sea drilling thoroughly. For fresh water–air fluid, the flow regime basically has linear relationships with void fraction and bubble size. The fluid is basically identified as bubble flow regime when void fraction is lower than 0.3, when most...