# A Review: Factors Affecting Internal Two-Phase Flow-Induced Vibrations
## 2 Factors Affecting FIV in Internal Two-Phase Flow
### Effect of Flow Regimes  
Two-phase flow can be divided into different flow regimes depending on their properties and appearances. Various flow regime maps are introduced over time to identify flow regimes using visual inspection and flow rates of phases involved [81; 82]. [PERSON] and [PERSON] [69] used void fraction to identify criteria for different flow regimes and established a flow regime map with gas superficial velocity and liquid superficial velocity as horizonal and vertical coordinates. This criterion was developed for vertical two-phase flow and their results are comparable with the existing literature. More advanced methods, such as the measurement of void fraction using X-rays [83], electrical capacitance tomography [84], rotating electric field conductance gauge [85], conductivity and electrical impedance [86] are also being used to identify different flow regimes. Different flow regime visualizations are shown in Figure 4 to help in understanding and better visualizing the different types of flow regimes. Flow regime is a critical parameter when discussing FIV in two-phase flow and different flow regimes cause different magnitudes of vibrations. [PERSON] et al. [76; 77] investigated the effect of two-phase flow on FIV in a 6-mm pipe with bend in different configurations. It was reported that slug flow showed the highest absolute forces followed by annular flow, while stratified flow showed the lowest forces. These observations were also verified in another research [75]. [PERSON] et al. [76] developed a simple slug unit model by considering momentum fluctuation and neglecting turbulence and friction effects. This model could explain the forces generated by slug flow, but it was unable to describe forces due to annular and stratified flow regimes since no distinct slugs travel through the pipe in these flow regimes. Instead, a mixture model was presented to estimate excitation forces due to annular and stratified flows. This model is analogous to single-phase conditions, where a simple mixture momentum is considered. The results of these models were comparable to experimental results, but the accuracy can be further increased by considering parameters, such as random excitations due to turbulence, friction, gravity, and impact force. [PERSON] et al. [66] conducted experiments on vertically upward two-phase flow in 52.6 mm (2 inch) internal diameter pipe with a bend radius of curvature of 76.2 mm (3 inch). In this study, 36 multiphase flow cases, which include bubbly, slug, churn, and annular flow regimes, were studied. The investigated superficial velocities range of gas and liquid are 0.61-2.31 m/s and 0.1-18 m/s, respectively. For all the flow regimes, the high frequency component (>20 Hz) measured by the force sensor was insignificant. RMS values of force fluctuations were recorded in x and z directions and their peak frequency was plotted. The  
Figure 4: Flow visualization. (**a**) Flow patterns in horizontal pipe, (**b**) flow patterns in vertical pipe. RMS of force fluctuation in x and z directions are the lowest for bubbly flow regime and the value increases as the flow enters slug and churn flow regimes. In addition, it reaches the maximum value after the flow transitions into an annular flow. On the other hand, the peak frequency of force fluctuation is almost zero in bubbly flow, except for the 7-Hz peak at liquid superficial velocity of 1.78 m/s and air superficial velocity of 0.407 m/s. This random peak did not show a significant amplitude and was due to the absence of system fluctuations. When the flow transitioned into slug and churn flows, the peak frequency increased instantly to its overall maximum value due to the formation of slug bubbles in vertical section, and then decreased a little before transitioning into annular flow. The peak frequency increased again in annular flow, which was due to the disturbance wave effect. Overall, slug and churn flow regimes showed the highest peak frequencies in the range of 8 to 10 Hz.