# A Review: Factors Affecting Internal Two-Phase Flow-Induced Vibrations
## 2 Factors Affecting FIV in Internal Two-Phase Flow
### Effect of Flow Velocity  
The effect of flow velocity on FIV was reported in research conducted on multiphase FIV at bends with 20.6 mm internal diameter [48; 63]. A piezoelectric force sensor was used to record excitation force signal and an optical probe was used to record void fraction data. It was reported that the amplitude and predominant frequency of excitation forces increase linearly with flow velocity, for a given void fraction. As the velocity of the fluid increases, the higher modes become excited. Moreover, the authors correlated the root mean square of excitation force (\(F_{RMS}\)) with inlet superficial mixture velocity (\(V_{m}\)). The experimental results on U-bends suggested that the relationship between excitation forces and superficial velocities can be expressed in Equation (1), as shown below:  
\[F_{RMS}\propto V_{m}\lx@note{footnote}{footnoteThe same trend was also reported by [PERSON] et al. [64]. The authors conducted experiments to investigate FIV for various diameters of U-bends, for a vertically upward two-phase flow. The experiments were conducted for volumetric quality or gas void fraction, \(\beta\), of 25%, 50%, 75%, and 95%, and superficial mixture velocity between 1-12, 2-14, 2-20, and 5-30 m/s, respectively. These conditions represent bubbly, churn, slug, and annular flow regimes. It was concluded that for a specific value of void fraction, excitation forces on bends increase with an increase in the mixture velocity. This was true for the volumetric quality values of 50%, 75%, and 95%. However, in the case of 25% void fraction, there is a large decrease in forces between 2 and 3 m/s mixture velocity. This is attributed to the fact that in this range, a transition from slug/bubbly flow to finely dispersed bubbly flow occurs. Force spectrum data demonstrated that the peak/dominant frequency shows a linear increasing trend with superficial velocity for all the observed conditions. [PERSON] et al. [65] reported the effect of superficial velocities on excitation forces and dominant frequency for an upward two-phase flow in a vertical 90\({}^{\circ}\) elbow of internal diameter 0.0525 m (2 inch) and curvature radius of 0.0762 m (3 inch), specifically for slug and churn flows. To study the effect of superficial liquid velocity (\(V_{sl}\)), it was varied from 0.642 to 5 m/s, while maintaining a constant superficial gas velocity (\(V_{sg}\)) at 5 m/s. Furthermore, to study the effect of superficial gas velocity, it was varied from 0.5 to 9.04 m/s, while maintaining a constant superficial gas velocity at 0.642 m/s. It was observed that the magnitude of excitation force increases and the predominant frequency decreases with the increasing gas superficial velocity, while both frequency and force magnitude increase with the increasing liquid superficial velocity. The effect of superficial velocity on force fluctuations and peak frequency was studied by [PERSON] et al. [66], for vertically upward two-phase flow in 52.6 mm (2 inch) internal diameter pipe with a bend having a radius of 76.2 mm (3 inch). The ranges for liquid and gas phase superficial velocities investigated are 0.61-2.31 m/s and 0.1-18 m/s, respectively, covering slug, churn, annular, and bubbly flow regimes. For a fixed liquid superficial velocity, the RMS force increases monotonically with an increase in superficial velocity of gas. Moreover, the RMS force increases with liquid flow rates, but with a few exceptions, which can be attributed to flow regime transition. In the case of predominant frequency, for a constant liquid phase flow rate, the peak frequency increased to its maximum value when flow transitioned from bubbly to slug flow. A further increase in flow rate of gas phase, caused the peak frequency to decrease first for slug and churn flow regimes and increase again for annular flow regime. For a fixed flow rate of gaseous phase, the peak/dominant frequency increased with the liquid phase flow rate in general. Experimental and numerical techniques were used by [PERSON] et al.