## 1 Introduction
[PERSON] and [PERSON] [11] used PIV to study the wake of a model impeller in a rotating machine and its interaction with fixed diffuser blades. They used instantaneous streamline patterns and vortex contours to describe flow separation. The observed phenomena are further elaborated through numerical simulation. The unstable flow phenomena such as rotating stall and surge are also studied for centrifugal compressors with air as the working fluid [12]. Due to the different working fluid and mechanics, the developmental mechanism of stall is studied accordingly for a compressor with a vaneless or vaned diffuser [13; 14; 15]. Some other types of pumps such as radial flow pumps, radial diffusion pumps, and mixed flow pumps working at low flow rate conditions would produce unstable vortices due to flow instability as the flow experiences deceleration in a diverging section [16; 17; 18; 19; 20]. [PERSON] et al. [21] numerically and experimentally investigated the stall inception mechanisms in a centrifugal compressor with volute. The results indicate that the stall inception onset is determined by the impeller leading edge (LE) spillage flow, and the occurrence time of trailing edge (TE) back flow is prior to the LE spillage. The nonuniform static pressure circumferential distribution at the impeller outlet induced by the volute tongue caused two stall inception regions located at certain circumferential positions, which are 120 deg and 300 deg circumferential positions at impeller LE, corresponding to the circumferential static pressure peak (PP) and bulge regions at impeller outlet, respectively. [PERSON] et al. [22; 23; 24] mainly investigated one large external volute configured for different diffuser ratios and blade exit angles and coupled with different impellers by means of CFD to understand the relationship between volute matching and pressure distortion. It was found that pressure distortion is directly related to the volute's pressure recovery coefficient, and how the resulting pressure distortion evolves towards the impeller was analyzed. The physics of unsteady flow in the impeller and volute of centrifugal turbo-machineries have been extensively studied, as reviewed above. The flow characteristics, such as the evolution of vortices and turbulent statistics, were presented and analyzed to reveal their influences on the performance of the impeller. We understand that the flow in a rotating centrifugal impeller experiences the effect of pressure gradient on the surface of the blade passage, which is essential in triggering the initial separation and the confinement from walls which strongly induce the three-dimensional patterns of the flow; thus, the three-dimensional patterns of the flow have to be revealed, which may help in the redesign of the impeller and may improve the performance of the whole machine. In this paper, we performed a numerical simulation investigation on the internal flow in a shrouded centrifugal impeller under the off-designed flow rate condition. The motivation is to explore the three-dimensional characteristics of the flow in the impeller as presented and analyzed by the distributions of the pressure coefficient and skin friction coefficient on both the pressure and suction surfaces in the stalled and unstalled passages, which reveal the characteristics of near-wall flow behaviors. The formation and evolution of the separated vortices are discussed on various cross sections in the axial direction. The paper is organized as follows. Section 2 gives the physical model of the impeller, the details of the numerical simulation, and the validation and grid independence study. Section 3 presents and discusses the flow characteristics. Some conclusions are given in Section 4.