## 1 Introduction  
Two-phase bubbly flow is a common phenomenon in many industrial processes such as chemical production, thermal power plants, and nuclear reactors. In Light-Water Reactor (LWR) nuclear power plants, especially those involving the Boiling Water Reactor (BWR), the phenomenon occurs with coolant in the nuclear reactor core and influences plant operation, i.e., the power level of the reactor and safety function. To understand the characteristics of this phenomenon, multi-scale modeling has been developed to analyze and predict the characteristic of two-phase bubbly flow [1; 2]. It employs many empirical correlations and consecutive equations such as bubble and liquid velocity, bubble size distribution, slip ratio, and so on. To provide a reliable database for two-phase flow models, the interaction between two phases and its behavior must be clarified by experimental work, in particular, velocity distribution of liquid and bubble. Hence, it is necessary for the velocity profile of the two-phase bubbly flow to be accurate. Several intrusive measurement techniques have been used to measure the velocity profile in two-phase bubbly flow such as hot-film anemometry [3] and the conductive probe [4; 5]. Intrusive techniques disturb the flow and lead to lifetime distortion. To eliminate these effects, non-intrusive measurement techniques are proposed, such as laser Doppler anemometry (LDA) [6] and Particle Image Velocimetry (PIV) [7; 8]. These techniques are used for measuring the rising velocity of a single bubble or a few bubbles. However, both methods require a transparent test section and obviously fail if the working fluid is opaque. Also, the measurement result is typically obtained from the offline analysis because of the time-consuming image processing. The UVP method is a real-time measurement for obtaining the velocity profile of fluid even though the fluid is opaque. The UVP is a non-intrusive measurement of the velocity profile. It does not require a transparent test section; the probe is installed at the outer wall of a pipe or channel. The UVP uses the pulsed echography of an ultrasonic wave reflected from a moving reflector such as particles dispersed in the fluid to measure the instantaneous velocity profile of fluid along its measurement line. [PERSON] [9] were the first to propose the UVP method for measuring single-phase liquid flow. The advantage of this technique is that it can perform spatial-temporal measurements of the velocity profile. Subsequently, [PERSON] et al. [10; 11; 12] developed a hybrid system, combining the UVP system and video data processing unit to inspect the liquid and bubble velocity distributions, average bubble diameter, and the void fraction in two-phase bubbly flows. The hybrid system applies the statistical method to classify the velocity profile of both phases. However, the limitation in separation occurs when there is not much difference in the velocity of both phases. [PERSON] et al. [13] proposed a phase-separation technique reliant on the UVP method as well. This method applied the pattern recognition of the velocity profile to distinguish a phase of the velocity profile. However, the technique could only be applied in limited flow conditions. [PERSON] et al. [14] proposed a separation technique, using the differences in ultrasonic intensity reflected from particles and bubbles in two-phase bubbly flows. It is clear that the ultrasonic intensity reflected from a bubble's surface is stronger than a particle dispersed in liquid because of the differences in acoustic impedance. [PERSON] et al. [15] employed a multi-wave TDX transducer and the time domain cross-correlation method (UTDC) to measure liquid and bubble velocity profiles with pattern recognition of ultrasonic echo amplitude. Then, [PERSON] et al. [16] employed a multi-wave TDX transducer and the Doppler pulse repetition method to measure and separate liquid and the bubble velocity profile.