## 1 Introduction  
Control valves that provide precise flow control would be a major component in fluid transportation. Precise flow control plays an important role in process industries such as nuclear power plants, petrochemical plants, and thermal power plants [1]. Among them, ball valves are widely used as flow control devices. The conventional ball valve design involves a hollow, perforated, or pivoting ball to control the flow of working fluids [2]. Due to a simple structure that requires only a quarter-turn of the stem for a fully open or fully closed state, ball valves are known for their durability and excellent shut-off properties. This design, however, does not always allow for precise flow control as a result of unique flow characteristics [3]. Reports from related studies have described the phenomenon of these flow characteristics. [PERSON] [4] conducted a study focused on improving the flow characteristics of the ball valve. The study showed that irregular flow occurred due to changes in the flow path caused by the opening rate. The irregular flow rate was influenced by the shape and size of the opening hole in the ball. Those factors were improved by altering the placement of the existing hole to prevent complications with the flow path. [PERSON] et al. [5] carried out computational fluid dynamic and experimental analysis to investigate the flow characteristics of the ball valve that were due to changes in the opening rate. As the opening rates became smaller, complicated flow paths gradually increased the presence of vortices in the valve trim. The vortex-induced cavities were found to be a major hindrance to precise flow control. [PERSON] et al. [6] experimentally studied the flow coefficients and cavitation in ball valves. The pressure loss coefficient, K, and the flow coefficient, \(CV\), were estimated by measuring the pressure and flow rate via steady-flow testing. Cavitation was evaluated via a cavitation index that was determined through pressure data measurements. The authors found that vortices in the valve trim were the main cause of the cavitation that was significantly influencing the flow characteristics. The studies mentioned above have shown that significant vortices occur with small opening rates, which result in irregular flow characteristics. Vortices complicate precise flow control in the ball valve. They are a major contributor to cavitation and, in addition, exacerbate safety problems in piping systems, so that the application of a flow control valve to the ball valve has limitations. To overcome these limitations, researchers have improved the shape of the opening hole in the ball and given it a V-shaped geometry, which is the so-called V-port ball valve. [PERSON] et al. [7] proposed a V-port ball valve with V-shaped angles of 30, 60, and 90 degrees and investigated the resulting flow characteristics. The results showed that the V-port ball valve improved the irregular flow characteristics of the conventional ball valve. Decreases in the V-shaped angles, however, resulted in a loss of pressure and a remarkable occurrence of the cavitation phenomenon. With a V-shaped angle of 30 degrees, cavitation occurred even when the valve was fully opened. In a similar study, [PERSON] et al. [8] proposed an improved V-port ball valve with two types of ports, i.e., approximately triangular and rectangular ports, and investigated the flow characteristics for each port type. The \(CV\) values for both types increased as the opening rates of the valve increased. Under the same opening rate, however, the V-port ball valve with an approximately rectangular port showed higher \(CV\) values. [PERSON] et al. [9] used Strouhal and Reynolds numbers to study the flow characteristics of the V-port ball valve. These numbers helped to construct a five-dimensional polynomial relationship that explained the occurrence of a dominant vortex at the end of the valve trim.