## 1 Introduction
[20] showed that fluorescent signals from fluorescent particles were weaker than \(320\pm 10\) times Mie scattering on average, but fluorescent PIV could measure surfaces closer than Mie scattering. Fluorescent PIV in this configuration led to velocity vector validation rates of more than 20 times those of Mie scattering in the boundary layer region. Some studies have used external magnetic fields to efficiently control fluid. N\({}_{2}\) gas was injected through vertically placed tubes to measure the flow of nonconductive air under the influence of a magnetic field, and N\({}_{2}\) flow was visualized using PIV techniques. Through magneto-aerodynamics research, [PERSON] et al. [21] showed that PIV techniques are effective tools. [PERSON] et al. [22] measured internal flow using PIV to understand turbulent flow under external magnetic fields. Due to limited internal space, special optical devices have been designed for laser investigation. A magnet is placed outside the horizontal tube and enclosed with a square tube to prevent distortion. Measurement of the internal turbulent flow showed that turbulence was reduced by external magnets. [PERSON] et al. [23] measured the flow around a single particle and compared it with simulation results using a rotating 200 nm magnetic microparticle under low-Reynolds-number flow via uPIV with typical fluorescence. It was also found that the flow produced by two identical particles rotating in one unit was similar to that of a single particle with a twice diameter. [PERSON] et al. [24] showed that the inflation of the magnetic field on the liftoff and blowout properties of a methane/air co-flow diffusion flame is effective. The research used PIV techniques to measure a flame surrounded by magnets on the outside. The results showed that the magnetic gradient minimizes the lift-off head and increases the flow rate emitted. [PERSON] et al. [25] measured the asymmetric gas flow affected by the magnetic file placed around the cylinder and the aerodynamic force acting on the cylinder using the PIV technique. [PERSON] et al. [26] measured the movement of microswimmers affected by an external magnetic field using uPIV techniques. Previous studies showed that external magnetism placed outside of a flow field can effectively control a flow field. The PIV technique allows the measurement of flow fields under this external magnetic field. Table 1 is a summary of previous studies on the effects of external magnetic field. Numerous numerical and experimental studies on ferrofluid in single-phase flow have been performed in previous studies. Very few of them have adopted liquid-gas two-phase flow measurement. In this study, a closed-loop power generation system that uses waste heat, as proposed by [PERSON] et al. [11], was configured. In this system, single- and two-phase flow occur. [PERSON] et al. [11] used experimental and numerical simulation techniques to show that generation is only possible in two-phase flow. If the characteristics of magnetic particles for two-phase flow are known, an efficient nozzle design is possible. The details of this system are described in the next section. Magnetic particle flow without an external magnetic field has the same rotational properties as nonmagnetic particle flow. If it is affected by the external magnetic field, it will be aligned due to the magnetic force, and the degree of rotation is expected to be much lower. The rotationality of the magnetic particle could be determined by observing a single particle alone, but it is realistically impossible to measure a single particle due to its high velocity, small diameter, and complex flow. This study estimates nonrotationality based on vorticity. To verify the effect of the external magnetic force, the two-phase flow is compared to a fully developed theoretical model, nonmagnetic, and magnetic particles in single-phase flow.