Inﬂuence of Blade Leading-Edge Shape on Rotating-Stalled Flow Characteristics in a Centrifugal Pump Impeller

Featured Application: This study can be applied to turbomachinery ﬂow cases for energy loss study and ﬂow-induced noise evaluation. Abstract: Rotating stall, which is a common phenomenon in turbomachinery, strongly relates to the ﬂow rate condition. In centrifugal impellers, rotating stall was induced by the incidence angle on blade leading-edge at partial-load. The blade leading-edge shape also inﬂuences the rotating stall because of the subtle change of local ﬂow-ﬁeld. In this study, the inﬂuence of blade leading-edge shape on rotating-stalled ﬂow characteristics was studied in a six-blade centrifugal pump impeller. The stall pattern was “alternating”: Three passages were stalled, three passages were well-behaved, and the stalled and well-behaved passages occurred alternately. The stalled ﬂow characteristics can be studied without the interruption of stall cell movement. Four types of blade leading-edge (blunt, sharp, ellipse, and round) were numerically compared based on the initial typical impeller and the numerical–experimental veriﬁcation. The numerical comparison shows that the leading-edge shape has a strong inﬂuence on the stalled ﬂow pattern, velocity, pressure, turbulence kinetic energy, and ﬂow-induced noise inside impellers. The blunt and sharp leading-edge impellers had a similar internal pattern; the ellipse and round leading-edge impellers were also similar in the internal ﬂow-ﬁeld. Pressure pulsation analysis showed more obvious di ﬀ erences among these impellers. The main frequency and the pulsation peak–peak values were completely di ﬀ erent because of the slight leading-edge shape di ﬀ erences. It revealed the impact of leading-edge geometry on the transient ﬂow-ﬁeld change under the same incidence angle conditions. It also provided reference for inﬂuencing or controlling the rotating stall by blade proﬁle design.


Introduction
When designing a pump impeller, two main targets need special considerations. Firstly, operation efficiency at design load is important. Secondly, reliability at off-design load is also crucial, because the pump usually operates off from the design condition [1]. The puzzle of how to improve the pump efficiency at design load has been solved with many typical methods in the past decades [2]. The current works are applying these methods for specific cases [3][4][5]. On the contrary, flow inside pump impeller under off-design conditions are treated as uncontrollable. The internal flow becomes complex at inside pump impeller under off-design conditions are treated as uncontrollable. The internal flow becomes complex at off-design load, especially at partial-load, with noise, vibration, and other undesirable phenomena [6,7]. These phenomena would affect the stability and security of the pump unit, and even cause faults.
Under the design flow rate condition Q = Qd, flow is along the impeller blade geometry with high efficiency. From design load to partial load, the incidence angle becomes higher and higher and causes undesirable flow on the blade suction side [8]. Typically, the undesirable flow develops in three steps. Firstly, small-scale flow separation occurs on the blade suction side [9]. Secondly, backflow occurs at both the inlet and outlet of the impeller. Passage blockage happens and brings vibration and efficiency drop [10]. Thirdly, the inlet and outlet backflow structures expand and block the entire passage [11]. Among them, the second stage, which may cover the flow rate from 0.3 to 0.8 Qd, is complex and important, because pumps usually operate in this flow rate range with partial passage blockage. Emmons [12] used "rotating stall" to describe this complex changing blockage and distinguish it against "surge". In actual pumps and compressors, impeller eccentricity or asymmetricity may exist due to installation, manufacturing, and instantaneous flow destabilization [13]. Affected by the eccentricity or asymmetricity, the blocked flow turns into neighboring passages, as shown in Figure 1a. In the neighboring passage rotational, turned flow strikes the suction surface and diminishes part of the stall cell. In the neighboring passage, counter-rotational, turned flow strikes the pressure surface and increases the scale of the stall cell. The asymmetric distribution of stall cell moves counter-rotationally during impeller rotation. It makes the flow regime more complicated. Many researchers studied the rotation stall mechanism and influences [14][15][16][17]. Because of the compressibility of the fluid medium, people mainly focused on the rotating stall in aerodynamic turbomachines like compressors. Cumpsty [18] studied the mechanism of rotating stall and explained the partial passage blockage as an adaptability of small flow rate. Cossar et al. [19] experimentally tested the rotating stall in axial-flow compressors. The stall cell was found starting from the trailingedge and developing to the leading-edge. Experiences show that the rotating stall is relative to the incidence angle at the leading-edge and the flow distortion at inlet [20,21]. The counter-rotational movement of the stall cell [12] is found relative to the impeller rotation. The stall frequency will be 1/5~1/2 impeller rotating frequency in different cases [19]. Based on the mechanism studies, Weigl [22], Day [23], Behnken et al. [24], and Suder et al. [25] investigated the controlling method of rotating stall, using different methods in the past. The sound generated by the rotating stall was also studied by Mongeau et al. [26]. Low-frequency noise from the impeller was found to be relative to the rotating stall. Currently, researchers still focus on the rotating stall phenomenon in turbomachinery, which has complicated flow characteristics [27][28][29]. In pumps which usually transport incompressible Many researchers studied the rotation stall mechanism and influences [14][15][16][17]. Because of the compressibility of the fluid medium, people mainly focused on the rotating stall in aerodynamic turbomachines like compressors. Cumpsty [18] studied the mechanism of rotating stall and explained the partial passage blockage as an adaptability of small flow rate. Cossar et al. [19] experimentally tested the rotating stall in axial-flow compressors. The stall cell was found starting from the trailing-edge and developing to the leading-edge. Experiences show that the rotating stall is relative to the incidence angle at the leading-edge and the flow distortion at inlet [20,21]. The counter-rotational movement of the stall cell [12] is found relative to the impeller rotation. The stall frequency will be 1/5~1/2 impeller rotating frequency in different cases [19]. Based on the mechanism studies, Weigl [22], Day [23], Behnken et al. [24], and Suder et al. [25] investigated the controlling method of rotating stall, using different methods in the past. The sound generated by the rotating stall was also studied by Mongeau et al. [26]. Low-frequency noise from the impeller was found to be relative to the rotating stall. Currently, researchers still focus on the rotating stall phenomenon in turbomachinery, which has complicated flow characteristics [27][28][29]. In pumps which usually transport incompressible fluids, researchers have also studied the rotating stall characteristics. Krause et al. [30] studied the rotating stall in a radial pump and provided time-resolved particle image velocimetry (PIV) measurements in the impeller passages. A spatially stable stall cell was found in the passage and analyzed on its frequency. Sinha [17] studied the flow structure during onset and developed states of rotating stall in centrifugal pump's guide vane. The movement and frequency of rotating stall was discussed. Takamine et al. [31] discussed the diffuser rotating stall in a three-stage centrifugal pump, and the mechanism of the widen onset range of rotating stall was well explained. Pedersen et al. [32] showed a static alternating stall pattern in a centrifugal pump by PIV and laser Doppler velocimetry (LDV) measurements. In the six-blade impeller, three stalled and three un-stalled passages were observed, as shown in Figure 1b. The well-behaved passages and stalled passages occurred alternately and were cite-fixed without periodically moving.
Above all, the rotating stall in pumps were also strongly related to the local flow around the blade leading-edge, which was mainly the incidence angle. The leading-edge shape also influences the local flow field [33,34]. However, there is a lack of discussion on the influence of leading-edge shape on rotating stall. Thus, in this study, numerical simulation was conducted to compare the rotating stall characteristics for different leading-edge geometries, based on the experimental measurement by Pedersen et al. [32], at partial-load of a centrifugal pump impeller. The velocity, turbulence kinetic energy, pressure pulsation, and noise are discussed in detail.

Pump Impeller Object
In this study, the impeller investigated by Pedersen et al. [32] was used as the studied object. Its design flow rate, Q d , is 3.06 kg/s, and its angular rotating speed is ω = 725 r/min (revolution per minute). This is a typical pump impeller with six untwisted blades (blade number Z = 6) and widely studied by researchers [35,36]. In this case, the quarter partial-load condition Q = 0.25 Q d , which is about 0.76 kg/s, was analyzed. As shown in Figure 2, the impeller inlet radius is R 1 = 35.5 mm, the impeller outlet radius is R 2 = 95 mm, the impeller leading-edge width is b 1 = 13.8 mm, and the impeller trailing-edge width is b 2 = 5.8 mm. For single stage simulation, the impeller domain was modeled with inlet and outlet extension. The inlet extension is e 1 = 0.5 R 2 , and the outlet extension is e 2 = 0.125 R 2 .
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 21 fluids, researchers have also studied the rotating stall characteristics. Krause et al. [30] studied the rotating stall in a radial pump and provided time-resolved particle image velocimetry (PIV) measurements in the impeller passages. A spatially stable stall cell was found in the passage and analyzed on its frequency. Sinha [17] studied the flow structure during onset and developed states of rotating stall in centrifugal pump's guide vane. The movement and frequency of rotating stall was discussed. Takamine et al. [31] discussed the diffuser rotating stall in a three-stage centrifugal pump, and the mechanism of the widen onset range of rotating stall was well explained. Pedersen et al. [32] showed a static alternating stall pattern in a centrifugal pump by PIV and laser Doppler velocimetry (LDV) measurements. In the six-blade impeller, three stalled and three un-stalled passages were observed, as shown in Figure 1b. The well-behaved passages and stalled passages occurred alternately and were cite-fixed without periodically moving. Above all, the rotating stall in pumps were also strongly related to the local flow around the blade leading-edge, which was mainly the incidence angle. The leading-edge shape also influences the local flow field [33,34]. However, there is a lack of discussion on the influence of leading-edge shape on rotating stall. Thus, in this study, numerical simulation was conducted to compare the rotating stall characteristics for different leading-edge geometries, based on the experimental measurement by Pedersen et al. [32], at partial-load of a centrifugal pump impeller. The velocity, turbulence kinetic energy, pressure pulsation, and noise are discussed in detail.

Pump Impeller Object
In this study, the impeller investigated by Pedersen et al. [32] was used as the studied object. Its design flow rate, Qd, is 3.06 kg/s, and its angular rotating speed is ω = 725 r/min (revolution per minute). This is a typical pump impeller with six untwisted blades (blade number Z = 6) and widely studied by researchers [35,36]. In this case, the quarter partial-load condition Q = 0.25 Qd, which is about 0.76 kg/s, was analyzed. As shown in Figure 2, the impeller inlet radius is R1 = 35.5 mm, the impeller outlet radius is R2 = 95 mm, the impeller leading-edge width is b1 = 13.8 mm, and the impeller trailing-edge width is b2 = 5.8 mm. For single stage simulation, the impeller domain was modeled with inlet and outlet extension. The inlet extension is e1 = 0.5 R2, and the outlet extension is e2 = 0.125 R2.

Turbulence and Acoustic Modeling
In this case, the Reynolds-Averaged Navier-Stokes (RANS) equations were used for turbulence flow. The zonal-mixed turbulence model SST (Shear Stress Transport) k-ω model [37] was applied. Its k equation and ω equation can be expressed as follows: where t denotes the time, ρ the density, u the velocity, and x the coordinate. P is the production term, µ is the dynamic viscosity, µ t is the turbulent eddy viscosity, σ is the model constants, C ω is the coefficient of the production term, and l k-ω is the turbulence scale. F 1 is the zonal mixture function, which is used to combine the standard k-ε model and Wilcox's k-ω model. To improve the sensitivity of streamline curvature and system rotation, the Spalart-Shur correction [38] was also applied, accompanied by the SST k-ω turbulence model. It adds the correction term f r1 as a multiplier on the production term P k . Moreover, f r1 has its specific limiters: where C s is the correction scaling factor. The constants C r1 , C r2 , and C r3 are equal to 1.0, 2.0, and 1.0. The remaining functions are defined as follows: where Ω rot is the rotation rate of the reference frame, and DS ij /D t is the Lagrangian derivative of the strain rate tensor. In this study, the Lighthill acoustic analogy method was used to analyze the near-field of noise in the pump impellers. Proudman [39] introduced a sound power calculation method for the flow-induced noise: where α ε is a constant which can be valued as 0.1, ρ is the density, ε is the eddy dissipation rate, and M t can be expressed as follows: where c is the sound speed, which is 1500 m/s in water. Thus, the sound power level, L sp , can be calculated as follows: L sp = 10 log 10 W A W re f (12) where W ref is the reference sound power in water, which is about 6.7 × 10 −19 W/m 3 .

Computational Fluid Dynamics Setup
Computational fluid dynamics (CFD) method was used for flow simulation. The impeller domain shown in Figure 3a was discretized by tetrahedral unstructured mesh elements. The mesh number was checked to balance the simulation accuracy and the time-cost. The residual of the hydraulic efficiency was checked for determining the final mesh scheme. The mesh schemes with about 0.16, 0.32, 0.60, 1.5, and 3.1 million nodes (different leading-edge shape has similar but different mesh node number) are checked by monitoring the residual of the hydraulic efficiency for less than 1%. As an example, the mesh check detail of the initial leading-edge impeller is shown in Figure 3b and Table 1. After checking, we see the meshes for different leading-edge impellers have about 1.5 million nodes and 6.0 million elements. Figure 3 shows the schematic map of mesh.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 21 10 10 log where Wref is the reference sound power in water, which is about 6.7 × 10 −19 W/m 3 .

Computational Fluid Dynamics Setup
Computational fluid dynamics (CFD) method was used for flow simulation. The impeller domain shown in Figure 3a was discretized by tetrahedral unstructured mesh elements. The mesh number was checked to balance the simulation accuracy and the time-cost. The residual of the hydraulic efficiency was checked for determining the final mesh scheme. The mesh schemes with about 0.16, 0.32, 0.60, 1.5, and 3.1 million nodes (different leading-edge shape has similar but different mesh node number) are checked by monitoring the residual of the hydraulic efficiency for less than 1%. As an example, the mesh check detail of the initial leading-edge impeller is shown in Figure 3b and Table 1. After checking, we see the meshes for different leading-edge impellers have about 1.5 million nodes and 6.0 million elements. Figure 3 shows the schematic map of mesh.    Based on the domain, three types of boundaries are given: (a) Velocity inlet was given on the inlet boundary. The velocity value depends on the flow rate Q = 0.25 Q d . On this boundary, pressure followed the Neumann condition; (b) Pressure outlet was given on the outlet boundary. The average static pressure was 0 Pa, based on the environment pressure of 1 Atm. On this boundary, velocity followed the Neumann condition; (c) No-slip walls were set on the solid walls, including the blade, hub, and shroud.
The fluid medium is set as water at 20 • C. Steady state simulation was conducted before transient simulation. The maximum iteration number was 1000 for steady state, with convergence criteria of RMS (root mean square) value less than 1 × 10 −5 . The transient simulation was conducted because the flow was continually changing during rotation. A total of 360 time-steps were set for each revolution. The maximum iteration number for each time-step was 10 for transient state with convergence criteria of RMS value less than 1 × 10 −5 .

Computational-Experimental Result Verification
Computational fluid dynamics (CFD) method was used for predicting the flow field in centrifugal pump impellers with different leading-edge shapes. To have an accurate computational result, a computational-experimental result verification was conducted at first. The relative velocity, V, vectors on the spanwise 50% surface, the contour of turbulence kinetic energy (k 2D ) on the spanwise 50% surface, and the relative radial velocity (V r /U 2 ) distribution on the spanwise 50% surface at R = 0.9 R 2 were compared. U 2 denotes the rotational linear velocity at R = R 2 . Figure 4 shows the CFD predicted relative velocity (V) vectors on the spanwise 50% surface. It can be compared with the experimental data by Pederson et al. in Ref. [32]. The alternate stall pattern, which includes three well-behaved and three stalled passages, can be observed in the impeller. The symbols "A" and "B"-"A" denotes the well-behaved passage, and "B" denotes the stalled passage-were drawn on this figure. CFD simulation captured the flow separation at leading-edge on the blade suction side and the backflow near the outlet in the B passage. The large-scale "vortex" flow was also found in the middle of the B passage. These undesirable flow structures were also measured in the experiment. Figure 5 shows the CFD-predicted contour of turbulence kinetic energy (k 2D ) on the spanwise 50% surface, compared with the experimental data in Ref. [32]. There were three high k 2D cites captured. Firstly, a high k 2D cite occurred at the leading-edge flow separation region in the B passage. Secondly, a high k 2D cite occurred on the blade suction side in the middle of the A passage. Thirdly, a high k 2D cite generated at the impeller outlet in the B passage. These three high k 2D cites were also captured in the experiment, which proved the CFD simulation to be relatively accurate. However, there is a deviation that shows the experimental k 2D value at the impeller outlet was stronger than CFD simulation. In this computational case, only the impeller domain was considered. In the experimental study of Reference [32], a vaned-diffuser was set downstream to the impeller. The intensity of k 2D would be influenced by the vaned-diffuser. In this study, the main target was to compare the internal flow among different leading-edge impellers. Thus, the CFD simulation can be considered correct and accurate.
can be compared with the experimental data by Pederson et al. in Ref. [32]. The alternate stall pattern, which includes three well-behaved and three stalled passages, can be observed in the impeller. The symbols "A" and "B"-"A" denotes the well-behaved passage, and "B" denotes the stalled passagewere drawn on this figure. CFD simulation captured the flow separation at leading-edge on the blade suction side and the backflow near the outlet in the B passage. The large-scale "vortex" flow was also found in the middle of the B passage. These undesirable flow structures were also measured in the experiment.  . Relative velocity (V) vectors on the spanwise 50% surface by CFD, the experimental pattern can be found in Reference [32]. Figure 5 shows the CFD-predicted contour of turbulence kinetic energy (k2D) on the spanwise 50% surface, compared with the experimental data in Ref. [32]. There were three high k2D cites captured. Firstly, a high k2D cite occurred at the leading-edge flow separation region in the B passage. Secondly, a high k2D cite occurred on the blade suction side in the middle of the A passage. Thirdly, a high k2D cite generated at the impeller outlet in the B passage. These three high k2D cites were also captured in the experiment, which proved the CFD simulation to be relatively accurate. However, there is a deviation that shows the experimental k2D value at the impeller outlet was stronger than CFD simulation. In this computational case, only the impeller domain was considered. In the experimental study of Reference [32], a vaned-diffuser was set downstream to the impeller. The intensity of k2D would be influenced by the vaned-diffuser. In this study, the main target was to compare the internal flow among different leading-edge impellers. Thus, the CFD simulation can be considered correct and accurate. To have a better comparison near impeller outlet, the radial velocity, which represents the flow direction, was compared at R = 0.9 R2. Figure 6 compares the relative radial velocity, Vr/U2, distribution on the spanwise 50% surface at R = 0.9 R2. Generally, the distribution laws were similar between the CFD data and the experimental data. In detail, in the A passages, the radial velocity from the CFD simulation was larger than that from by experimental test. In the middle of the B passages, the CFD-predicted radial velocity was higher than that of the experimental data. These two differences might also be influenced by the downstream vaned-diffuser and may have changed the local velocity intensity.

Figure 5.
Contour of turbulence kinetic energy k 2D on the spanwise 50% surface by CFD, the experimental pattern can be found in Reference [32]. A: well-behaved passage, B: stalled passage.
To have a better comparison near impeller outlet, the radial velocity, which represents the flow direction, was compared at R = 0.9 R 2 . Figure 6 compares the relative radial velocity, V r /U 2 , distribution on the spanwise 50% surface at R = 0.9 R 2 . Generally, the distribution laws were similar between the CFD data and the experimental data. In detail, in the A passages, the radial velocity from the CFD simulation was larger than that from by experimental test. In the middle of the B passages, the CFD-predicted radial velocity was higher than that of the experimental data. These two differences might also be influenced by the downstream vaned-diffuser and may have changed the local velocity intensity. Above all, the CFD simulation in this study correctly predicted the internal flow in the centrifugal pump impeller. The predictions of velocity and turbulence kinetic energy were reasonable and reliable. Thus, the CFD simulations can be used for further comparisons among different leadingedge impellers. Above all, the CFD simulation in this study correctly predicted the internal flow in the centrifugal pump impeller. The predictions of velocity and turbulence kinetic energy were reasonable and reliable. Thus, the CFD simulations can be used for further comparisons among different leading-edge impellers.

Leading-Edge Reshaping
To compare the influence of different leading-edge shapes, the initial impeller [32] was reshaped on the leading-edge, as shown in Figure 7. The blunt, sharp, round, and ellipse leading-edges were created step by step. Firstly, the initial leading-edge geometry was extended along the meanline and its perpendicular direction. The blunt leading-edge was created, and its width was L LE . Secondly, we cut the two sides off by S LE = 0.5 L LE , to create the sharp leading-edge. Thirdly, the leading-edge geometry was changed to be an arc and generated the round leading-edge, whose radius was R LE = 0.5 L LE . Finally, the arc of the round leading-edge was changed to an elliptical arc and generated the ellipse leading-edge, whose long axis is a LE = 2 L LE , and short axis b LE = L LE . Above all, the CFD simulation in this study correctly predicted the internal flow in the centrifugal pump impeller. The predictions of velocity and turbulence kinetic energy were reasonable and reliable. Thus, the CFD simulations can be used for further comparisons among different leadingedge impellers.

Leading-Edge Reshaping
To compare the influence of different leading-edge shapes, the initial impeller [32] was reshaped on the leading-edge, as shown in Figure 7. The blunt, sharp, round, and ellipse leading-edges were created step by step. Firstly, the initial leading-edge geometry was extended along the meanline and its perpendicular direction. The blunt leading-edge was created, and its width was LLE. Secondly, we cut the two sides off by SLE = 0.5 LLE, to create the sharp leading-edge. Thirdly, the leading-edge geometry was changed to be an arc and generated the round leading-edge, whose radius was RLE = 0.5 LLE. Finally, the arc of the round leading-edge was changed to an elliptical arc and generated the ellipse leading-edge, whose long axis is aLE = 2 LLE, and short axis bLE = LLE.

Alternating Stall Patterns
The internal flow patterns were predicted by CFD simulation. Figure 8 indicates the streamlines in the impellers with different leading-edge shape on the spanwise 50% plane. As in the situation in the initial impeller, the alternating stall patterns were observed in the blunt, sharp, ellipse, and round impellers. As indicated by "A", there were three well-behaved passages in each impeller. As indicated by "B", three stalled passages also existed in each impeller. The A and B passages distributed alternately. The backflow regions in the blade passages, which are indicated by red-dash circles, had relative fixed cites during impeller rotation.
Differences were found when comparing the pattern in different impellers. In the blunt and sharp leading-edge impellers, the B passages were completely blocked by undesirable flow characters. Two backflow regions were generated in the B passages. The smaller one was located between two blades' leading-edge, and the larger one blocked the passage from the middle passage to the trailing-edge. The A passages were smooth, without obvious blockage. In the ellipse and round impellers, the B passages were almost blocked by undesirable flow characters with two equal-scale backflow regions. One was located from the leading-edge to middle passage, and the other was located from the middle passage to trailing-edge. The A passages were also slightly blocked with a small backflow region near the blade suction side in the middle passage.

Impeller Performances
Considering the difference of streamline patterns in different impellers, it is necessary to compare the impeller performance based on the initial impeller [32]. Figure 9 compares the difference in pump head, as an example of the performance. The pump impeller head, H, can be calculated as follows: where ∆p total is the difference of total pressure in stationary frame between the impeller outlet and inlet, ρ is the density of fluid medium, and g is the acceleration of gravity. As shown in Figure 9, H ini is the CFD-predicted head of the initial impeller. The H values of the blunt and sharp impellers were lower than the initial impeller by 0.21% and 0.33%, respectively. The H values of the ellipse and round impellers were higher than those of the initial impeller by 1.31% and 1.54%, respectively.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 21 The internal flow patterns were predicted by CFD simulation. Figure 8 indicates the streamlines in the impellers with different leading-edge shape on the spanwise 50% plane. As in the situation in the initial impeller, the alternating stall patterns were observed in the blunt, sharp, ellipse, and round impellers. As indicated by "A", there were three well-behaved passages in each impeller. As indicated by "B", three stalled passages also existed in each impeller. The A and B passages distributed alternately. The backflow regions in the blade passages, which are indicated by red-dash circles, had relative fixed cites during impeller rotation.
Differences were found when comparing the pattern in different impellers. In the blunt and sharp leading-edge impellers, the B passages were completely blocked by undesirable flow characters. Two backflow regions were generated in the B passages. The smaller one was located between two blades' leading-edge, and the larger one blocked the passage from the middle passage to the trailing-edge. The A passages were smooth, without obvious blockage. In the ellipse and round impellers, the B passages were almost blocked by undesirable flow characters with two equal-scale backflow regions. One was located from the leading-edge to middle passage, and the other was located from the middle passage to trailing-edge. The A passages were also slightly blocked with a small backflow region near the blade suction side in the middle passage.   where Δptotal is the difference of total pressure in stationary frame between the impeller outlet and inlet, ρ is the density of fluid medium, and g is the acceleration of gravity. As shown in Figure 9, Hini is the CFD-predicted head of the initial impeller. The H values of the blunt and sharp impellers were lower than the initial impeller by 0.21% and 0.33%, respectively. The H values of the ellipse and round impellers were higher than those of the initial impeller by 1.31% and 1.54%, respectively.  where Q is the flow rate; M is the total torque on blades, impeller hub, and shroud; and ω is the rotational angular speed of impeller. The η values were between 0.901 and 0.905. The differences were very slight. The ellipse impeller has the highest value, η = 0.905, which is also higher than the initial impeller (η = 0.904). Generally, the hydraulic efficiency has no obvious law among these impellers.
where Q is the flow rate; M is the total torque on blades, impeller hub, and shroud; and ω is the rotational angular speed of impeller. The η values were between 0.901 and 0.905. The differences were very slight. The ellipse impeller has the highest value, η = 0.905, which is also higher than the initial impeller (η = 0.904). Generally, the hydraulic efficiency has no obvious law among these impellers.

Pressure Coefficient Cp
Based on the alternating stall pattern and the differences among different impellers, the flowfield was also compared by plotting relevance parameters in contours. Firstly, the pressure distributions in the impellers were important. The dimensionless pressure coefficient, Cp, was used: where p is pressure, p∞ is the reference pressure on the impeller inlet boundary, and V∞ is the reference Figure 10. Comparison of the impeller hydraulic efficiency, η, among different impellers.

Pressure Coefficient C p
Based on the alternating stall pattern and the differences among different impellers, the flow-field was also compared by plotting relevance parameters in contours. Firstly, the pressure distributions in the impellers were important. The dimensionless pressure coefficient, C p , was used: where p is pressure, p ∞ is the reference pressure on the impeller inlet boundary, and V ∞ is the reference velocity on the impeller inlet boundary. Figure 11 shows the contour of the pressure coefficient, C p , on the spanwise 50% surface. Caused by the backflow region near leading-edge, the wide low-pressure region occurred at the inlet of B passages in the blunt and sharp impellers. The pressure value near the leading-edge in the A passages was at a relative high level, because all of the fluid smoothly flowed into A passages. Differently, the low-pressure region near the leading-edge is much narrower in the ellipse and round impellers. However, local pressure-drop can be found on the suction side of every blade's leading-edge. It means that leading-edge flow separation also happened in the A passages in the ellipse and round impellers. This is why backflow "vortex" also exists in the A passages. 6.3.2. Turbulence Kinetic Energy (k2D) Figure 12 shows the contour of turbulence kinetic energy, k2D, on the spanwise 50% surface in these impellers. It is found that high k2D region covered the B passages' inlet in all the impellers. In the blunt and sharp impellers, the k2D values at the A passages' inlet were small. In the ellipse and  Figure 12 shows the contour of turbulence kinetic energy, k 2D , on the spanwise 50% surface in these impellers. It is found that high k 2D region covered the B passages' inlet in all the impellers. In the blunt and sharp impellers, the k 2D values at the A passages' inlet were small. In the ellipse and round impellers, a high k 2D region can be observed at the A passages' inlet, near the suction surface. The high k 2D region covered nearly half of the A passages' inlet. Thus, it can be recognized that high k 2D region and flow blockage were relative to the backflow characteristics.  Figure 13 shows the contour of the flow-induced sound power level, Lsp, on the spanwise 50% surface in these impellers. According to Equation (10) to Equation (12), the sound power level was dominated by the turbulence kinetic energy when sound speed was a constant. Comparing Figure 13 to Figure 12, we see that the high noise was induced by high turbulence kinetic energy. In the blunt and sharp impellers, the Lsp value near the blade leading-edge was higher than that in the ellipse and round impellers. However, high Lsp regions can be found in the A passages in the ellipse and round impellers, due to the high k2D regions' existence.  Figure 13 shows the contour of the flow-induced sound power level, L sp , on the spanwise 50% surface in these impellers. According to Equation (10) to Equation (12), the sound power level was dominated by the turbulence kinetic energy when sound speed was a constant. Comparing Figure 13 to Figure 12, we see that the high noise was induced by high turbulence kinetic energy. In the blunt and sharp impellers, the L sp value near the blade leading-edge was higher than that in the ellipse and round impellers. However, high L sp regions can be found in the A passages in the ellipse and round impellers, due to the high k 2D regions' existence. Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 21

Pressure Pulsations
Considering the cite-fixed alternating stall and its different performances in different blade passages of these different impellers, the pressure pulsations were monitored and analyzed. As shown in Figure 14, three monitoring points were set in an A passage: PAin, PAmid, and PAout. At the same time, three monitoring points were set in the neighbor B passage: PBin, PBmid, and PBout. The pressure pulsations were monitored for more than 10 revolutions, as they became stable or rotating-periodic in changing.

Pressure Pulsations
Considering the cite-fixed alternating stall and its different performances in different blade passages of these different impellers, the pressure pulsations were monitored and analyzed. As shown in Figure 14, three monitoring points were set in an A passage: P Ain , P Amid , and P Aout . At the same time, three monitoring points were set in the neighbor B passage: P Bin , P Bmid , and P Bout . The pressure pulsations were monitored for more than 10 revolutions, as they became stable or rotating-periodic in changing. The time-domain data were handled by the fast Fourier transform (FFT) method with Hanning window. The time-domain and frequency-domain plots are shown below. Figure 15 shows the pressure pulsations in the blunt leading-edge impeller. Periodic variation was obvious on the time-domain plot. In the A passage, the pressure pulsation amplitude is relatively high, with peak-peak values of about 5 × 10 −6 Pa, on P Ain and P Amid . On P Aout , the pressure pulsation amplitude decreased to a lower level. In the B passage, the pressure pulsation amplitude is relatively high, with peak-peak values larger than 6 × 10 −6 Pa, on P Bin . Because of the blockage and strong backflow, the pressure pulsation amplitude on P Bmid and P Bout became much lower.
passages of these different impellers, the pressure pulsations were monitored and analyzed. As shown in Figure 14, three monitoring points were set in an A passage: PAin, PAmid, and PAout. At the same time, three monitoring points were set in the neighbor B passage: PBin, PBmid, and PBout. The pressure pulsations were monitored for more than 10 revolutions, as they became stable or rotating-periodic in changing. The time-domain data were handled by the fast Fourier transform (FFT) method with Hanning window. The time-domain and frequency-domain plots are shown below.  Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 21 Figure 15 shows the pressure pulsations in the blunt leading-edge impeller. Periodic variation was obvious on the time-domain plot. In the A passage, the pressure pulsation amplitude is relatively high, with peak-peak values of about 5 × 10 −6 Pa, on PAin and PAmid. On PAout, the pressure pulsation amplitude decreased to a lower level. In the B passage, the pressure pulsation amplitude is relatively high, with peak-peak values larger than 6 × 10 −6 Pa, on PBin. Because of the blockage and strong backflow, the pressure pulsation amplitude on PBmid and PBout became much lower.
The frequency-domain plot shows the frequencies on each point. These points were all dominated by frequency fmb, which is 9.67 Hz. This frequency was about 4/5 rotating frequency. Frequency 5 fmb can be found in the A passage. Another frequency of 370 Hz was obvious on PAmid and was widened to a band of 350~380 Hz. Frequencies 3 and 5 fmb can be found in the B passage. On PBin and PBmid, 3 and 5 fmb frequencies were both obvious. On PBout, 5 fmb was obvious. Another frequency band of 140~200 Hz was found on PBin. It disappeared on PBmid and PBout.  Figure 16 shows the pressure pulsations in the sharp leading-edge impeller. The waveform of the pressure pulsations was also periodic. The peak-peak value on PBin was the largest among the six monitoring points. It was about 1.2 × 10 −3 Pa. The peak-peak values on the other five points were about The frequency-domain plot shows the frequencies on each point. These points were all dominated by frequency f mb , which is 9.67 Hz. This frequency was about 4/5 rotating frequency. Frequency 5 f mb can be found in the A passage. Another frequency of 370 Hz was obvious on P Amid and was widened to a band of 350~380 Hz. Frequencies 3 and 5 f mb can be found in the B passage. On P Bin and P Bmid , 3 and 5 f mb frequencies were both obvious. On P Bout , 5 f mb was obvious. Another frequency band of 140~200 Hz was found on P Bin . It disappeared on P Bmid and P Bout . Figure 16 shows the pressure pulsations in the sharp leading-edge impeller. The waveform of the pressure pulsations was also periodic. The peak-peak value on P Bin was the largest among the six monitoring points. It was about 1.2 × 10 −3 Pa. The peak-peak values on the other five points were about 4 × 10 −4 Pa~5 × 10 −4 Pa. Generally, the pressure pulsation intensity in the sharp leading-edge impeller was approximately 100 times that of the blunt leading-edge impeller.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21 4 × 10 −4 Pa~5 × 10 −4 Pa. Generally, the pressure pulsation intensity in the sharp leading-edge impeller was approximately 100 times that of the blunt leading-edge impeller. As shown in Figure 16b, the frequency of pressure pulsation in the sharp leading-edge impeller was dominated by three frequencies. Firstly, the main frequency (with the highest amplitude) was fms = 0.81 Hz on all six points. Moreover, fms is about 0.067 rotating frequency. Secondly, there was a vice frequency of about 2 fms. Thirdly, the frequency of about 3 fms was also obvious in the A passage. The frequency of about 3 fms was widened to a band of 3.2 ~4.9 Hz, which was about 4~6 fms in the B passage.
When comparing the pressure pulsation characteristics between the blunt impeller and sharp impeller, we can find differences on both the peak-peak values and the frequency values. Even though the instantaneous flow patterns in the blunt and sharp impellers were similar, the slight change of leading-edge shape can strongly influence the pressure pulsation that represented the subtle change of flow field.  Figure 17 shows the pressure pulsations in the ellipse leading-edge impeller. Based on the waveform, it was observed that the pressure pulsation peak-peak values became much higher than in the blunt and sharp impellers. The peak-peak values were especially high on PBin and PBmid, as they As shown in Figure 16b, the frequency of pressure pulsation in the sharp leading-edge impeller was dominated by three frequencies. Firstly, the main frequency (with the highest amplitude) was f ms = 0.81 Hz on all six points. Moreover, f ms is about 0.067 rotating frequency. Secondly, there was a vice frequency of about 2 f ms . Thirdly, the frequency of about 3 f ms was also obvious in the A passage. The frequency of about 3 f ms was widened to a band of 3.2~4.9 Hz, which was about 4~6 f ms in the B passage.
When comparing the pressure pulsation characteristics between the blunt impeller and sharp impeller, we can find differences on both the peak-peak values and the frequency values. Even though the instantaneous flow patterns in the blunt and sharp impellers were similar, the slight change of leading-edge shape can strongly influence the pressure pulsation that represented the subtle change of flow field. Figure 17 shows the pressure pulsations in the ellipse leading-edge impeller. Based on the waveform, it was observed that the pressure pulsation peak-peak values became much higher than in the blunt and sharp impellers. The peak-peak values were especially high on P Bin and P Bmid , as they were about 1.2 × 10 −2 Pa and 1.0 × 10 −2 Pa, respectively. The peak-peak values on the other points were about 3 × 10 −3 Pa~5 × 10 −3 Pa, which were also higher than in the blunt and sharp impellers. were about 1.2 × 10 −2 Pa and 1.0 × 10 −2 Pa, respectively. The peak-peak values on the other points were about 3 × 10 −3 Pa~5 × 10 −3 Pa, which were also higher than in the blunt and sharp impellers. As in the sharp leading-edge impeller, there were also three obvious frequencies. Firstly, the main frequency was fme = 2.41 Hz, which was approximately 1/5 rotating frequency. The second and third dominant frequencies were 2 and 3 fme, which are also indicated on Figure 17. Another low-frequency band can be observed on all the points, especially on PAmid, PBin, and PBmid. This low-frequency band covered about 0.2~1.4 Hz.  Figure 18 shows the pressure pulsations in the round leading-edge impeller. The peak-peak value on PAmid was around 1.8 × 10 −2 Pa, which was the highest among the six points. The peak-peak value was around 1.0 × 10 −2 Pa on PBin and much smaller on the other four points. Generally, in the A passage, pressure pulsation was high in the middle of the passage. In the B passage, pressure pulsation was high Pressure pulsation in the ellipse leading-edge impeller: (a) time-domain plot (three revolutions); (b) frequency-domain plot, monitor points (1) P Ain , (2) P Amid , (3) P Aout , (4) P Bin , (5) P Bmid , and (6) P Bout.
As in the sharp leading-edge impeller, there were also three obvious frequencies. Firstly, the main frequency was f me = 2.41 Hz, which was approximately 1/5 rotating frequency. The second and third dominant frequencies were 2 and 3 f me , which are also indicated on Figure 17. Another low-frequency band can be observed on all the points, especially on P Amid , P Bin , and P Bmid . This low-frequency band covered about 0.2~1.4 Hz. Figure 18 shows the pressure pulsations in the round leading-edge impeller. The peak-peak value on P Amid was around 1.8 × 10 −2 Pa, which was the highest among the six points. The peak-peak value was around 1.0 × 10 −2 Pa on P Bin and much smaller on the other four points. Generally, in the A passage, pressure pulsation was high in the middle of the passage. In the B passage, pressure pulsation was high in the inlet and decreased gradually from the inlet to middle-passage to outlet. The instantaneous flow patterns in the ellipse and round leading-edge impellers were similar. However, the frequency of pressure pulsation characteristics was different. The main frequencies were also different, as listed in Table 2. Comparing among all the four types of impellers, the blunt leadingedge impeller had the smallest amplitude of pressure pulsation but a noisier frequency pattern. On the contrary, the ellipse and round had the strongest pulsation amplitudes, but the frequency pattern is relatively pure. Table 3 shows the obvious frequencies or frequency bands on the frequency-domain plots of all the four leading-edge types of impellers. These obvious frequencies and frequency bands are denoted by their main frequency values: fmb, fms, fme, and fmr. As shown in Table 3, the obvious frequencies or bands are complex, with five parts in the blunt leading-edge impeller. The 5 parts are fmb, Figure 18.
According to the frequency-domain plot, the main frequency on all six points was f mr = 1.00 Hz, which was 0.083 rotating frequency. However, a wide frequency band covered around the main frequency. The band was approximately from 0.33 to 1.35 Hz. Another peak, 3.33 Hz, can be found on the frequency-domain plot.
The instantaneous flow patterns in the ellipse and round leading-edge impellers were similar. However, the frequency of pressure pulsation characteristics was different. The main frequencies were also different, as listed in Table 2. Comparing among all the four types of impellers, the blunt leading-edge impeller had the smallest amplitude of pressure pulsation but a noisier frequency pattern. On the contrary, the ellipse and round had the strongest pulsation amplitudes, but the frequency pattern is relatively pure. Table 3 shows the obvious frequencies or frequency bands on the frequency-domain plots of all the four leading-edge types of impellers. These obvious frequencies and frequency bands are denoted by their main frequency values: f mb , f ms , f me , and f mr . As shown in Table 3, the obvious frequencies or bands are complex, with five parts in the blunt leading-edge impeller. The 5 parts are f mb , 3 f mb , 5 f mb , 14.5~20.7 f mb and 36.2~39.3 f mb . In the sharp leading-edge impeller, it is also complex with 4 obvious frequencies or bands that f ms , 2 f ms , 3 f ms and 4~6 f ms which are relatively ordered. In the ellipse leading-edge impeller, the obvious frequencies or bands becomes purer with only 3 very ordered parts that f me , 2 f me , 3 f me . In the round leading-edge impeller which is the most hydrodynamic, there is only one obvious frequency band that 0.33~1.35 f mr which includes the main frequency of 1.0 f mr . Generally, Tables 2 and 3 reveal the difference of the subtle transient change of flow field induced by different leading-edge shapes.  Table 3. Obviously seen frequencies and frequency bands in different leading-edge shape impellers.

Conclusions
By comparing the flow pattern, impeller performance, internal flow field distribution, and pressure pulsation, the following conclusions can be drawn: (1) At partial-load (0.25 Q d in this study), incoming flow struck on the blade leading-edge on the pressure surface. Flow separation happened on the blade suction surface and induced the passage blockage. In this case, an alternating stall pattern was found in the impellers. In the six blade passages, three passages were well-behaved, and three passages were stalled (flow-blockage caused by backflow structures). The well-behaved and stalled passages distributed alternately and cite-fixed during rotation. (2) Leading-edge shape strongly influenced the alternating stall pattern and showed differences.
In the blunt and sharp leading-edge impellers, the leading-edge geometry had sudden turned corners. Flow direction suddenly changed at the corner with large-scale separation. The stalled passages were completely blocked. Fluid went into the well-behaved passages. The flow pattern in the well-behaved passages was very smooth, without undesired flow structures, meaning that only three passages were accessible. In the ellipse and round leading-edge impellers, the geometry continually changed on the arc or elliptical-arc without sudden turning. The backflow scale in the stalled passages was smaller with slight accessibility because the leading-edge separation was