# A Review: Factors Affecting Internal Two-Phase Flow-Induced Vibrations
## 2 Factors Affecting FIV in Internal Two-Phase Flow
### Effect of Void Fraction  
Void fraction or liquid holdup is a dimensionless parameter and can be defined as the ratio of cross-sectional area of pipe \(A_{g}\) occupied by vapor phase or gas to the total cross-sectional area, \(A_{g}+A_{l}\). Void fraction (\(\beta\)) can be calculated using Equation (10) [92], as follows:  
\[\beta=\frac{A_{g}}{A}=\frac{A_{g}}{A_{g}+A_{l}} \tag{13}\]  
[PERSON] and [PERSON] [63] concluded from their experiments on multiphase flow in U-bend that excitation forces are indeed affected by the change in void fraction. In this study, the effect of excitation forces on bends at values of 25%, 50%, 75%, and 95% gas void fraction were studied. The authors reported that for a specific velocity, the excitation forces increase as void fraction increases. Maximum forces are reported between 50% to 60% gas void fraction. Beyond 60% gas void fraction, the excitation forces start to decrease. However, it is noteworthy that this effect is normally due to flow regime change. For void fractions between 50% and 60%, flow regime is normally associated with slug or churn flow, which possesses the maximum momentum flux. In addition, they are more prominent when it comes to excitation forces when compared to bubbly (25%) and annular (95%) flows. [PERSON] et al. [64] conducted experiments to investigate flow-induced vibrations in 52 mm (2 inch) internal diameter U-bend, with a vertically upward two-phase flow. The range of gas void fraction tested during experiments are 25%, 50%, 75%, and 95%. From the force spectra data, it was concluded that the average void fraction signal corresponds to force spectra. It was reported that for a constant velocity, the excitation forces increase with void fraction until 75%, and then decrease with further increase in velocity. This behavior agrees with previous observations [63]. For 25% void fraction, forces start to increase after 3 m/s in bubbly flow. These forces are produced due to propagation of void fraction waves [93; 94]. For 50% void fraction, the force increases with velocity until 7 m/s and after further increase in velocity, the forces do not show any increase, which can be explained by the transition of flow regime from unstable slug flow to bubbly flow regime. The same increasing behavior can be obtained for void fraction of 75% until velocity is increased to 14 m/s and after further increase in velocity, the force decreases. This was due to the transition of flow from unstable slug to churn flow regime. In 95% void fraction, the transition from churn to annular flow is observed at 20 m/s. Forces increase first and then start to decrease after 20 m/s due to less momentum variation in annular flow and void fraction when compared to slug and churn flow regimes. [PERSON] et al. [66] reported that void fraction fluctuations show a similar trend as force fluctuations, and thus it is important to determine the changes in void fraction when the two-phase flow passes through the pipe bend. Moreover, the authors observed the predominant frequency of void fraction fluctuation signals and found that for a fixed liquid superficial velocity, as superficial velocity of gas is increased from bubbly to slug flow, the predominant frequency of void fraction fluctuations reaches a maximum value, upon further increase the predominant frequency decreases in churn flow followed by an increase again in annular flow. [PERSON] et al. [59] reported that when slug flow passes through a 90\({}^{\circ}\) bend, the flow regime transition affects the increase or decrease in void fraction after passing through the pipe bend. For slug flow, at a constant gas superficial velocity, void fraction decreases with the increasing liquid velocity after the slug passes through the pipe bend. However, an increasing gas superficial velocity has a minimal effect on this phenomenon.