## 1 Introduction
They reported a 3.17% increase in pressure for the new design compared to the reference when operated under the same design flow condition. [PERSON] and [PERSON] [12] carried out theoretical and experimental investigations for a regenerative blower used for hydrogen recirculation in an FEM fuel cell system. They proposed a theoretical model based on the momentum exchange theory for a side channel impeller and compared theoretical data to experimental data on blower performance. The pressure was relatively underestimated in the low-flow region compared to the high-flow region, and the results showed a difference of less than 10%. [PERSON] and [PERSON] [13] optimized the two-stage regenerative blower's blade shape using experiments and numerical simulations. They selected two geometric parameters, blade angle and blade hub height, as the design variables for optimization using the response surface method. The optimized impeller showed better performance in terms of higher pressure and lower vorticity. The authors stated that reducing the vortical flow at the outlet and the symmetric flow at the inlet allowed for the increase of pressure, thus enhancing blower efficiency. Similarly, [PERSON] [14] studied the effect of six different geometric parameters on the performance of a regenerative pump. The author tested multiple design combinations of all design variables and reported a 5 per cent increase in efficiency due to lower momentum and energy loss at the pump inlet. The new design was capable of keeping the fluid tangential velocity nearly constant at the inlet and around the blades, which is essential for avoiding vortex formation. As mentioned above, in order to improve pump performance of a regenerative impeller, many researchers performed studies to improve the impeller through the optimization of geometric variables. In other words, there are many results concerning performance improvements and optimization for a regenerative pump impeller in the design flow condition; there are very few investigations of flow characteristics in the off-design flow conditions for regenerative pumps. [PERSON] et al. [15] studied the internal flow characteristics of a regenerative pump impeller in terms of design and off-design flow conditions. They considered four different flow scenarios: i.e., two under design flow conditions, one in the design flow condition, and one over-design flow condition. They found that pressure loss increased as the flowrate decreased because larger vortical flow inside the blade passage was generated. [PERSON] et al. [16] analyzed the internal flow of a regenerative pump in multiple flow conditions using numerical simulation. In lower-flow conditions, larger circulation flow was observed at the exit of the pump, which invoked a rotating stall in the blade passage. They showed that the circulation flow was found to be lower in strength in the design and higher-flow conditions. [PERSON] et al. [17] carried out a study at seven different flow rates to find the BEP for a regenerative pump using experimental measurements and numerical simulations. In the design flow condition, there were no high-pressure fluctuations from the pump. On the other hand, pressure exhibited a non-linear phenomenon at lower-flow conditions, whereas a larger vortex flow was formed at the pump inlet at higher flowrates. Most of the research being conducted on pumps with a regenerative impeller focuses on modifying the geometric parameters of the pump impeller or analyzing the internal flow characteristics in the design flow condition only. It is noted that the performance analysis of the microbubble pumps in the design and off-design flow conditions are rare compared to other fluid machines. In real-world applications, pumps have to operate in a variety of operating conditions other than the design flow condition; therefore, it is crucial to analyze and compare the pump performance along with the internal flow conditions in design and off-design flow conditions.