# A Review: Factors Affecting Internal Two-Phase Flow-Induced Vibrations
## 2 Factors Affecting FIV in Internal Two-Phase Flow
### Effect of Pipe Geometry and Sizes
It was reported that at a constant liquid phase superficial velocity, the predominant frequency of force fluctuations increases with the increase in gas superficial velocity within the slug flow regime and drops when the flow regime transitioned into churn flow for 0.0525 mm (2 inch) and 0.2032 mm (8 inch) diameter pipe. For the case of 0.1016 mm (4 inch), the behavior of the pipe was more irregular. It was also reported that the presence of internal two-phase flow changes the natural frequency of all pipes, but the effect was more dominant in small diameter pipes when compared to large pipes. [PERSON] et al. [72] conducted experimentations to investigate the effects of FIV in large diameter pipes (i.e., 6 inch). Two different bend configurations were used with a radius of 1.5 D, one elbow and another consisted of an elbow with a U-bend upstream. The results obtained were reported to be higher than smaller diameter pipes, but were comparable with large diameter pipes (70 and 100 mm) [73; 74]. A correlation to determine forces was introduced using the quasi-steady approach, as shown in Equation (3). A constant, \(C\), of 25 and 10 is recommended to determine \(F_{RMS}\) for large and small pipes, respectively, as follows:  
\[F_{RMS}=C\Big{(}\rho_{l}{V_{m}}^{2}A\Big{)}We^{-0.4} \tag{3}\]  
where \(\rho_{l}\) is the liquid phase density, \(V_{m}\) is the mixture velocity, \(A\) is the cross-sectional area of pipe, \(C\) is a constant, and \(We\) is the Weber number. [PERSON] and [PERSON] [63] performed experiments on bends with different radii of curvature, R/D, (0.5, 2, 5, 7.2) and reported that R/D of the bend has a minimal effect on excitation forces. A similar conclusion regarding the minimal effect of bend radius was derived by [PERSON] et al. [75]. Moreover, [PERSON] et al. [76; 77] reported the effect of radius of curvature on excitation forces. In their experiments, it was found that a larger bend radius showed greater forces when compared to a smaller bend radius. This increase in forces was attributed to the larger pressure drop in the bend with larger radius of curvature, which causes larger excitations due to the larger pressure difference. [PERSON] et al. [78] reported that the bend radius has a direct effect on the distribution and development of local parameters. Moreover, it changes the void fraction and effects phase separation at the elbow. [PERSON] et al. [79; 80] investigated the effect of two different radii of curvature (1 and 1.5) on FIV and reported that flow separation is continuous in short elbow and intermittent in larger elbow at the exit. Moreover, the authors observed the secondary flow behavior at the elbow, which showed that the position of high-turbulence intensity region and separation region was affected by the radius of curvature. In summary, the excitation forces increase with the increasing diameter, while the dominant frequency decreases with the increasing diameter. The majority of these findings are based on small diameter pipes. According to [PERSON] et al. [68], flow behavior in small and large pipe diameters is different. Therefore, it would be inappropriate to derive conclusions regarding FIV behavior in large pipes based on conclusions derived for small pipes and vice versa. This is also true when comparing horizontal and vertical two-phase flows. The database available on large diameter pipes is almost non-existent and further studies on their behavior are needed since the majority of practical industrial pipes are with larger diameters. In addition, it is noted that the literature on the effect of bend radius is not explored properly, and very limited variations and cases are studied. [PERSON] and [PERSON] [63] only studied four different bend radii and other research involved studied two different radii [76; 79; 80]. Therefore, there is a big gap in the body of knowledge. A further exploration on different bend radii is highly recommended, considering the dimension of bend radius effect parameters, such as void fraction, pressure drop, and phase separation.