**1. Introduction**

Low-specific-speed centrifugal pumps have the characteristics of small flow rate, large head, and low efficiency, which are widely used in aerospace, military industry, electric power, water conservancy, chemical industry, and other important fields. After decades of efforts, with the continuous improvement of experimental means and the development of numerical calculation methods for the internal flow of turbo-machinery, more understanding and consensus have been gained on the internal flow characteristics and more achievements have been achieved in hydraulic design optimization methods. Micro internal flow structure controlling has been the method for improving the efficiency of centrifugal pumps with low specific speed.

Karrasik, a well-known pump expert in the United States, pointed out that since flow loss depends on the boundary layer, the efficiency of low-specific-speed centrifugal pumps can be improved by properly controlling the boundary layer of the flow channel [1]. Young-Do et al. studied the internal flow and performance of a centrifugal pump impeller with very low specific speed through an external characteristic test and particle image velocimetry (PIV) internal flow field test. The results show that there is a large recirculation at the outlet of a semi-open impeller, which significantly reduces the absolute tangential velocity and thus reduces the pump's head [2]. Westra et al. simulated the internal flow field of a low-specific-speed centrifugal pump, where Spalart and Allmaras' turbulence model was selected and the near-wall mesh scale was dense, and found that the maximum error of the relative

velocity obtained by PIV was 6%. From the relative velocity distribution, it can be seen that, from the pressure side of the blade to the suction side, when the velocity gradually increases to a certain maximum, the relative velocity on the suction surface of the blade decelerates, and the jet-wake area decreases with the increasing of flow rate. With the spatial change of the flow separation point, the secondary flow structure and intensity also change continuously [3]. Pedersen et al. used PIV and laser Doppler vibrometer to measure the flow inside the impeller of a centrifugal pump. It was found that there were two channels in the impeller under the condition of a small flow rate: the flow in one channel was controlled by the impeller rotation, which was similar to that under the design flow rate, while in the other channel, there was a relatively static stall and the entrance area of the blade was blocked by a cluster, with edthe remaining part of the flow passage being occupied by some vortices [4]. Shao et al. used PIV technology to measure the velocity of the internal flow field of a centrifugal pump impeller with large blade outlet angle, there exists a low energy fluid wake region with relatively low velocity near the suction side of the blade, where there exists a jet region with relatively high velocity while near the pressure side. The flow structure is especially obvious under small flow rates. These flow structures are the result of the interaction between the fluid viscosity, boundary layer, and secondary flow [5]. Tsujita and co-workers' numerical simulation and experiments show that, if the boundary layer thickness of the suction side is larger than that of pressure side at the inflection of the streamline in the impeller inlet area of the centrifugal pump, it will be helpful to restrain the formation of vortices in the internal channel to reduce hydraulic loss [6]. Cui et al.'s numerical simulation of ultra-high speed and low specific speed centrifugal pumps with long and short blades shows that the reflux zone mainly concentrates on the inlet of the long blade on the suction side, the middle of the long blade on the pressure side, and the outlet of the short blade on the suction side; these refluxes have a great influence on the internal and external characteristics of pumps [7]. Limbach et al. simulated the cavitation flow of a low-specific-speed centrifugal pump under different flow rates and different surface roughness conditions, and for non-cavitating flow, the measured and calculated head are in good agreement. According to the measurement, for rough walls, net positive suction head rises slightly higher [8]. Cao et al. studied the influence of the impeller eccentricity on the performance of a low-specific-speed centrifugal pump, and found that with the impeller eccentricity increasing, the head and efficiency become lower and the area of low pressure at the suction side of the short blade inlet becomes gradually smaller; however, the area of low pressure at the suction side of the long blade inlet becomes larger, and the pressure at the impeller inlet and tongue become larger too [9]. Zhang et al. simulated the start–stop process of three kinds of fluids in a low specific speed centrifugal pump, and the effects of viscosity on transient performance, head-flow curve and internal flow structure in impeller and volute were studied. Results show that, the liquid with higher viscosity than water may reduce the operation reliability of low specific speed centrifugal pump during start-up period [10]. Chen et al. explored internal flow and its unsteady characteristics in a low-specific-speed centrifugal pump. There were vortices in various sizes and numbers in flow channels of the impeller under different flow conditions. A high velocity zone was found in two adjacent channels near the tongue. However, the zone disappeared gradually with the increase of flow rate [11]. Dong et. al. studied the effect of the front streamline wrapping angles variation of a low-specific-speed centrifugal impeller on energy performance, the pressure pulsation, interior and exterior noise characteristics, where the front sweep angle variation was found to have an insignificant influence on centrifugal pump performance characteristics; however, it influences fluid hydrodynamics around the volute tongue [12]. The flow field in a low specific speed impeller was reconstructed by Zhang et. al. [13], the root-mean-square error for pressure prediction was 0.84% and the velocity prediction error was within 0.5 m/s, its computation time for the flow field prediction was less than 1/240 of the computational fluid dynamics. Proper orthogonal decomposition (POD) base modal analysis was carried out on the sample set, and the base modal characteristic of the flow field and its energy distribution were analyzed.

The optimization design of low specific speed pumps and the study of large-scale flow characteristics have been carried out, but there are few studies on the flow characteristics near

the blade wall. For this paper, ANSYS CFX 15.0 software used to simulate the unsteady flow of a low specific speed pump by analyzing the near-wall region flow on blades near the tongue and far from the tongue such that the distribution of viscous stress, relative velocity, and static pressure was obtained.
