## 1 Introduction  
The economic and industrial high-speed development has led to remarkable changes to people's daily lives and the environment. Therefore, reducing the environmental pollution caused by resource exploitation and improving production efficiency has become a momentous subject. Marine oil resources are abundant and exploration is urgently needed. The multiphase pump has become an important piece of production equipment for the efficient transportation of non-renewable resources in the energy industry. The application of oil-gas mixed-transportation technology can considerably simplify the marine treatment process, reduce the platform area, and reduce the cost of construction investment by 40% [1]. The flow inside a multiphase mixed-transport pump is complicated, and the performance of the pump is affected by many factors, such as loss of friction, erosive environment, divulgation loss, and different inlet gas contents [2,3]. The prediction of the performance and dependability can be validated by analyzing the lift and efficiency of a mixed-transport pump under different inlet-gas-volume fraction (IGVF) conditions [4]. [PERSON] et al. [5] adopted a new type of underwater gas-liquid mixer to reduce the fluctuation range under the gas content condition and improve the boosting capacity of the mixed transfer pump. [PERSON] et al. [6] studied the turbulence intensity and turbulence dissipation law within the compression stage of the mixed-transport pump under the air and water two-phase flow condition. [PERSON] et al. [7] showed that the forces between the air and water in the gas and liquid flow include a lift force, a turbulent dissipation force, resistance, and a virtual mass force. Under transient conditions, the pump head decreases and instantaneous fluctuation occurs, given the effect of a virtual mass force. Therefore, studying the pressure pulsation and internal flow field of the multistage mixed-transport pump under different gas content conditions is necessary. Pressure pulsation exists in various types of pumps as a universal phenomenon. Studies on the mixed-transport pump were conducted through experiments and numerical calculations. [PERSON] et al. [8] used pressure sensors to measure transient pressure signals under 90% and 98% IGVF condition for analysis, as well as pressure fluctuation. [PERSON] et al. [9] found that the pressure fluctuation in the inlet area was intense by exploring the transfer process of the mixed-transport pump. [PERSON] et al. [9] also discovered that under different IGVFs, the head of the multistage mixed-transport pump decreased first and then fluctuated periodically. [PERSON] et al. [10] studied the transient phenomenon of a mixed-transport pump through experiments; their findings showed that the pressure pulsation amplitude was higher and the frequency was lower when the flow rate was small. [PERSON] et al. [11] studied gas aggregation, gas-liquid separation, and pressure fluctuation at different positions in the mixed-transport pump under a gas-liquid two-phase flow. They showed that axial power, pressure, and liquid phase volume fractions fluctuated during the experiment. [PERSON] et al. [12] studied the T-shaped blade pressure pulsation under mixed flow and discovered that the pressure fluctuation amplitude was the largest at the blade head. Moreover, the effects of the blade setting angle and tip clearance on pressure fluctuation and flow law were studied. In recent years, many investigations have been carried out on the internal flow mechanism and flow pattern of the mixed-transport pump. [PERSON] et al. [13] revealed the internal stream field specifics of a vane-type gas and liquid mixed-transport pump. [PERSON] et al. [14] improved the gas-volume fraction (GVF) distribution at the hub by optimizing the shape of the multiphase pump; their findings suggest that with an increased gas-liquid separation, the liquid-phase medium in the impeller flows near the blade pressure surface and the gas phase gathers at the low-pressure surface side of the blade. [PERSON] et al.