# 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  
The flow behaviors in small diameter pipe bends and large diameter pipe bends are different. [PERSON] et al. [68] reported that pipes can be characterized as small or large based on non-dimensional hydraulic diameter, \(D_{H}^{*}\), as shown in Equation (2). Small pipes have \(D_{H}^{*}\) less than 18.6 and larger pipes have \(D_{H}^{*}\) greater than 40. With relevance to air-water two-phase flow, diameters < 0.0507 m correspond to \(D_{H}^{*}\) = 16.8, while diameters >0.1091 m represent \(D_{H}^{*}\) = 40. The region between these two extremes is known as the transition region and affects both large and small diameter pipes, as observed. [PERSON] and [PERSON] [69] and [PERSON] et al. [68] reported that bubbly flow regime is present in small as well as large diameter pipes. Beyond the bubbly flow regime, as the superficial velocities increase, gas bubbles with larger dimensions begin to form in both small and larger diameter pipes. In small pipes, these bubbles grow and fill the entire pipe, creating long slugs, which are known as slug flow regime. In large pipes, these bubbles form cap bubbles, which are known as cap bubbly flow regime. By further increasing the velocity, the flow in smaller pipes remains as a stable slug flow, while a churn turbulent flow regime develops in pipes with a larger diameter. \[D_{H}^{*}=\frac{D_{H}}{\sqrt{\frac{\sigma}{g\Delta\rho}}} \tag{2}\]  
where \(D_{H}\), \(g\), \(\sigma\), and \(\Delta\rho\), are hydraulic diameter, gravitational acceleration, liquid phase surface tension, and difference of density between two phases, respectively. [PERSON] and [PERSON] [8] investigated three different pipe diameters (6.35, 15.9, 25.4 mm) and reported that unsteady momentum fluxes decrease as the pipe diameter increases. This is primarily due to the fact that phases are mixed better in large pipes when compared to small pipes. Overall, the pipe diameter has a very little effect on predominant frequency. The authors also reported that high transverse vibrations were observed in rectangular pipes, which were not observed in round pipes. These transverse vibrations can be attributed to the fact that rectangular pipes have low natural frequency. [PERSON] et al. [64] investigated the effect of four different diameters (12, 15, 20, 52 mm) of U-bends on FIV for a vertically upward two-phase flow. For all conditions tested, the RMS force increased with the tube internal diameter. The increasing trend in RMS force was D\({}^{1.38}\), D\({}^{1.52}\), and D\({}^{1.9}\) on average for 50%, 75%, and 95% void fraction, respectively. It was reported that the peak/main frequency on force spectrum generally decreases with the tube diameter. [PERSON] et al. [70] reported a variation in the fluctuating forces with diameter. A validated numerical modelling approach, which was used for 52.5 mm (2 inch) internal diameter pipe geometry by [PERSON] et al. [65] was applied to a 203.2 mm (8 inch) internal diameter pipe geometry. It was reported that peak frequencies for gas superficial velocities between 0.773 and 9.04 m/s were higher in pipes with smaller diameter compared to larger diameter pipes for similar flow conditions. Peak frequency was higher in churn flow regime for the large internal diameter pipe and in slug flow regime for the small pipes. Therefore, slug flow is critical for multiphase fluid-induced vibrations in small diameter pipes and churn flow is important when large diameter pipes are involved. The fluctuation force displayed a similar behavior in both pipe sizes by increasing monotonically with gas superficial velocity. Moreover, the study showed that for large to small pipe diameter ratio of 4, fluctuation forces were about 10\(\times\) higher in the large dimeter pipe when compared to the small diameter pipe. Later, [PERSON] et al. [71] extended this study to investigate different diameter pipes (0.0525, 0.1016, 0.2032 mm).