# Influence of Inlet Angle of Guide Vane on Hydraulic Performance of an Axial Flow Pump Based on CFD

Authors: Lei Xu; Dongtao Ji; Wei Shi; Bo Xu; Weigang Lu; Linguang Lu
Journal: Shock and Vibration
 (2020)

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## Abstract

Axial flow pump has been widely used in hydraulic engineering, agriculture engineering, water supply and sewerage works, and shipbuilding industry. In order to improve the hydraulic performance of pump under off-design working conditions, the influence of the inlet segment axial chord and inlet angle adjustment of the guide vane on the pump segment efficiency and flow filed was simulated by using the renormalization group (RNG)k−ε turbulent model based on the Reynolds-averaged Navier–Stokes equations. The results indicate that the inlet segment axial chord and inlet angle adjustment of guide vane have a strong influence on the pump segment efficiency. Considering the support function and hydraulic loss of the guide vane, the inlet segment axial chord is set to 0.25 times the axial chord of guide vane. On the basis of the inlet angle of the guide vane under design conditions, when the inlet segment angle is turned counterclockwise, the pump segment efficiency is improved in the lower flow rate region; moreover, the pump segment efficiency is improved in the larger flow rate region when the inlet segment angle is turned clockwise. As the conditions deviate from the design working conditions, the influence of the guide vane inlet angle on the pump segment efficiency increases. If the inlet segment angle is properly adjusted under off-design working conditions, the flow pattern in the guide vane is improved and the hydraulic loss is decreased, because the inlet segment angle matches with the flow direction of impeller outlet; consequently, the pump segment efficiency is increased.


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## Body

## 1. Introduction

Vane pump is widely used in mechanical engineering, hydraulic engineering, civil engineering, and military industry. The application of vane pump is affected by its stable and efficient operation. Therefore, it is necessary to pay attention to the optimization of the pump [1–4], and paying attention to the research on pressure pulsation, cavitations, vibration, and noise is also necessary [5–8]. Axial flow pump is a kind of vane pump with high specific speed, which is characterized by low head and large discharge rate. Due to the characteristics, axial flow pump is widely applied to low head pumping stations in the fields of water resource allocation, water environment improvement, urban flood control, irrigation, and drainage. The guide vane is an important part of the axial flow pump that is used to recover the kinetic energy of the flow at the impeller outlet [9, 10]. The hydraulic performance of guide vane has great influence on the hydraulic performance of axial flow pump and pump system. Therefore, it is of great significance to study the matching of guide vane and impeller to improve the hydraulic performance of axial flow pump.At present, studies on the effect of the guide vane on the hydraulic performance of an axial flow pump can be summarized as follows. Li et al. [11] studied the ability of the guide vane to recover rotational kinetic energy, and Hu et al. [12] and Durmus Kaya [13] studied the influence of the guide vane on the pump efficiency for cases with and without a guide vane. Zhou et al. [14] studied the pump efficiency for different guide vanes, and Shi et al. [15] studied the hydraulic characteristics of axial flow pumps with different guide vane sweep angles. Liu et al. [16] studied the hydraulic characteristics of an axial flow pump with different numbers of guide vane panels, and Luo et al. [17] and Feng et al. [18] studied the influence of the guide vane on the hydraulic performance of the pump system.The guide vane is used to undertake the flow from the impeller outlet and recycle tangential energy. For the design working conditions, the guide vane inlet angle matches the flow direction of the impeller outlet. For off-design working conditions, the inlet angle of the guide vane is inconsistent with the flow direction of the impeller outlet, which leads to an increased hydraulic loss of the guide vane and a reduced axial flow pump efficiency. In recent years, some studies have explored adjusting the guide vane angle and its effect on the hydraulic performance of an axial flow pump under off-design working conditions; the results indicate that a complete adjustment of the guide vane angle improves the flow pattern in the guide vane and reduces the hydraulic loss, with a head improvement of 0.4964 m and a pump efficiency improvement of 2.1648% measured in [19]. Yang et al. [20, 21] studied a complete adjustment of the guide vane angle and its effect on the hydraulic performance of an axial flow pump system; the results indicate that the high efficiency area moves to a large discharge rate when the angle is rotated clockwise and to a small discharge rate when the angle is rotated counterclockwise. Qian et al. [22] found that when the whole angle of the guide vane is adjusted in the saddle zone, the head increases by 0.15 m, the efficiency increases by 1.93%, and the flow pattern in the axial flow pump is substantially improved. The abovementioned studies are all about the whole guide vane rotates. Thus far, no studies on matching the inlet angle of the guide vane with the flow direction of the impeller outlet for an axial flow pump have been reported.On the one hand, the guide vane of an axial flow pump takes the flow from the impeller outlet; on the other hand, the guide vane needs to support the guide-bearing seat [23]. To avoid affecting the support function of the guide vane, in this work, the guide vane is divided into inlet segment, middle segment, and outlet segment. The inlet segment angle is adjustable, while the middle and outlet segments are fixed and used to support the guide-bearing seat. CFD method has been widely used in the studies of pump [24–31] and other aspect [32–38]. In this paper, based on the TJ04-ZL-06 pump model, which has 3 impeller blade components and 5 guide vane components [39], influence of inlet angle of guide vane on hydraulic performance was studied using a 3D turbulent flow numerical simulation. According to the numerical simulation results, the reason of the influence of inlet angle of guide vane on the hydraulic performance was analyzed. The study work has important reference value for the hydraulic design and hydraulic performance improvement of an axial flow pump.


## 2. Mathematical Model and Numerical Setting

### 2.1. Governing Equations and Turbulent Model

A 3D turbulent flow numerical simulation for an axial flow pump is established by solving the Reynolds-averaged Navier–Stokes equations [40, 41] using FLUENT software.The fluid flow in the axial flow pump is considered incompressible. The method of steady flow numerical simulation is used to study the flow and hydraulic performance of the pump. The governing equations that are applied to solve the flow field in the pump include a continuity equation, momentum equations, andk equation and ε equation of the k−ε turbulent model. The Reynolds-averaged Navier–Stokes equations are shown as follows:(1)∂ρ∂t+ρ∂ui¯∂xi=0,ρ∂ui¯∂t+ρ∂ui¯uj¯∂xj=−∂p¯∂xi+∂∂xjμ∂ui¯∂xj+∂uj¯∂xi−ρui′uj′¯+Fi,where ρ is the density; t is the time; ui¯ and uj¯ are the mean velocity components; p¯ is the mean pressure; xi and xj are the coordinate directions; μ is the dynamic viscosity; Fi is the body force component; −ρui′uj′¯ is the Reynolds stress; and uj′ and uj′ are the fluctuating velocity components.The RNGk−ε turbulent model is chosen to solve the flow in the pump because this model is suitable for solving complicated flows such as rotating flows, separated flows, and vortex flows [42–46]. The k equation and ε equation of the RNG k−ε turbulent model are shown as follows:(2)ρ∂k∂t+ρ∂kui¯∂xi=∂∂xjμ+μtσk∂k∂xj+Gk−ρε,ρ∂ε∂t+ρ∂εui¯∂xi=∂∂xjμ+μtσε∂ε∂xj+C1εεkGk−C2ερε2k,where Gk is the turbulent kinetic energy production term; C1ε is an empirical constant; C2ε is an empirical constant; σk is the corresponding Prandtl number for turbulent kinetic energy k; and σε is the corresponding Prandtl number for the turbulent kinetic energy dissipation rate ε.


### 2.2. Computational Domain and Boundary Conditions

The computational domain of the flow field in an axial flow pump is composed of a straight inlet pipe, conical inlet pipe, impeller and impeller chamber, guide vane, bent outlet pipe, and straight outlet pipe (Figure1). The inlet boundary for the flow field calculation of an axial flow pump is set at the inlet section of the straight inlet pipe. The discharge rate is known, and the flow velocity distribution is uniform at the inlet section; thus, the velocity inlet boundary condition is adopted [47]. The outlet boundary for the flow field calculation of the axial flow pump is set at the outlet section of the straight outlet pipe, where the flow is fully developed; thus, the outflow boundary condition is adopted. In the flow field calculation, the sidewalls of the pipes, impeller chamber, guide vane, pump shaft, fair water caps at the impeller inlet, and the guide vane outlet are solid and are treated according to the conditions for a solid wall [48]. Since the axial flow pump impeller rotates periodically, the rotating walls such as the impeller blade and hub adopt the moving wall boundary condition, and the rotation speed and direction are the same as those of the impeller.Figure 1
Computational domain for an axial flow pump.


### 2.3. Numerical Setting and Calculation Accuracy

The GAMBIT software is used to generate the mesh for the computational domain. The shapes of the straight inlet pipe, conical inlet pipe, bent outlet pipe, and straight outlet pipe are simple; structured hexahedral meshes are applied. The shapes of the impeller and guide vane are complicated; unstructured meshes are applied. Moreover, since the flows in the impeller and guide vane are very complicated, the meshes are subject to local refinement. They+ value of the near-wall mesh scale is in the range of 20–70, which meets the requirement of numerical simulation. During the numerical simulation, a first-order upwind difference scheme is used to solve the convection-diffusion equation, the SIMPLEC algorithm is used to solve the pressure-velocity coupling equations, and the convergence precision is set to 1 × 10−7.A mesh independence verification was performed to ensure the calculation accuracy and computation efficiency. The calculation parameters for the TJ04-ZL-06 pump model are as follows: the diameter and rated speed of the pump impeller are 0.3 m and 1450 r/min, respectively, and the design discharge rateQ is 0.375 m3/s for a blade angle of −2° according to model test results obtained for the test bed of Beifang Investigation, Design and Research Co., Ltd., Tianjing, China [39].Pump segment efficiency is an important energy performance index of pump, which is used as the judgment basis for mesh independence analysis. The calculation formula of pump segment efficiency is as follows:(3)ηbd=ρgQHbdPbz×100%,where ηbd is the pump segment efficiency; g is the gravitational acceleration; Q is the discharge rate; Hbd is the pump segment head; and Pbz is the pump shaft power.Table1 shows the relationship between the pump segment efficiency and grid number under the abovementioned conditions. When the grid number of computational domain exceeds 1,863,552, the pump segment efficiency changes only slightly. Based on the verification results, the grid number of the entire calculation domain is set to approximately 1,860,000 in the calculations; the grid numbers of each component are shown in Table 2. The grid generation of the computational domain is shown in Figure 2.Table 1
Relationship between outlet conduit hydraulic loss and grid number.
Grid number788,332967,8061,262,5191,516,0221,863,5521,966,5852,256,251Pump segment efficiency (%)85.7385.6785.2484.5184.1684.1284.12Table 2
Detailed mesh information of computational domain.
DomainStraight inlet pipeConical inlet pipeImpeller and impeller chamberGuide vaneBent outlet pipeStraight outlet pipeGrid number (×103)203252317392495201Figure 2
Grid generation of the computational domain.Based on the abovementioned numerical method and setting, the pump efficiency of pump model TJ04-ZL-06 was calculated for a discharge rate between0.8ηbd and 1.2ηbd. Based on the calculated results, the relationship between the discharge rate and pump segment efficiency is shown in Figure 3; the flow fields in the pump are shown in Figure 4. It could be seen that the pump segment efficiency increases firstly and then decreases as the discharge rate increases. Because the inlet angle of guide vane does not match with the flow direction from the impeller outlet under the off-design conditions, there will be vortex on the back of guide vane under the condition of small discharge rate, and there will be vortex on the front of guide vane under the condition of large discharge rate. The comparison of numerical calculation and model test results is shown in Figure 3. The test data of TJ04-ZL-06 pump model is from the model pump test on the same test bed for the south-to-north water diversion [39]. Clearly, the trends observed for the numerical simulation are consistent with those for the model test, and the two curves are similar, indicating that the numerical results are reliable.Figure 3
Comparison of the numerical simulation and model test results.Figure 4
Flow fields in the pump segment under different conditions of discharge rates. (a)Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)


## 2.1. Governing Equations and Turbulent Model

A 3D turbulent flow numerical simulation for an axial flow pump is established by solving the Reynolds-averaged Navier–Stokes equations [40, 41] using FLUENT software.The fluid flow in the axial flow pump is considered incompressible. The method of steady flow numerical simulation is used to study the flow and hydraulic performance of the pump. The governing equations that are applied to solve the flow field in the pump include a continuity equation, momentum equations, andk equation and ε equation of the k−ε turbulent model. The Reynolds-averaged Navier–Stokes equations are shown as follows:(1)∂ρ∂t+ρ∂ui¯∂xi=0,ρ∂ui¯∂t+ρ∂ui¯uj¯∂xj=−∂p¯∂xi+∂∂xjμ∂ui¯∂xj+∂uj¯∂xi−ρui′uj′¯+Fi,where ρ is the density; t is the time; ui¯ and uj¯ are the mean velocity components; p¯ is the mean pressure; xi and xj are the coordinate directions; μ is the dynamic viscosity; Fi is the body force component; −ρui′uj′¯ is the Reynolds stress; and uj′ and uj′ are the fluctuating velocity components.The RNGk−ε turbulent model is chosen to solve the flow in the pump because this model is suitable for solving complicated flows such as rotating flows, separated flows, and vortex flows [42–46]. The k equation and ε equation of the RNG k−ε turbulent model are shown as follows:(2)ρ∂k∂t+ρ∂kui¯∂xi=∂∂xjμ+μtσk∂k∂xj+Gk−ρε,ρ∂ε∂t+ρ∂εui¯∂xi=∂∂xjμ+μtσε∂ε∂xj+C1εεkGk−C2ερε2k,where Gk is the turbulent kinetic energy production term; C1ε is an empirical constant; C2ε is an empirical constant; σk is the corresponding Prandtl number for turbulent kinetic energy k; and σε is the corresponding Prandtl number for the turbulent kinetic energy dissipation rate ε.


## 2.2. Computational Domain and Boundary Conditions

The computational domain of the flow field in an axial flow pump is composed of a straight inlet pipe, conical inlet pipe, impeller and impeller chamber, guide vane, bent outlet pipe, and straight outlet pipe (Figure1). The inlet boundary for the flow field calculation of an axial flow pump is set at the inlet section of the straight inlet pipe. The discharge rate is known, and the flow velocity distribution is uniform at the inlet section; thus, the velocity inlet boundary condition is adopted [47]. The outlet boundary for the flow field calculation of the axial flow pump is set at the outlet section of the straight outlet pipe, where the flow is fully developed; thus, the outflow boundary condition is adopted. In the flow field calculation, the sidewalls of the pipes, impeller chamber, guide vane, pump shaft, fair water caps at the impeller inlet, and the guide vane outlet are solid and are treated according to the conditions for a solid wall [48]. Since the axial flow pump impeller rotates periodically, the rotating walls such as the impeller blade and hub adopt the moving wall boundary condition, and the rotation speed and direction are the same as those of the impeller.Figure 1
Computational domain for an axial flow pump.


## 2.3. Numerical Setting and Calculation Accuracy

The GAMBIT software is used to generate the mesh for the computational domain. The shapes of the straight inlet pipe, conical inlet pipe, bent outlet pipe, and straight outlet pipe are simple; structured hexahedral meshes are applied. The shapes of the impeller and guide vane are complicated; unstructured meshes are applied. Moreover, since the flows in the impeller and guide vane are very complicated, the meshes are subject to local refinement. They+ value of the near-wall mesh scale is in the range of 20–70, which meets the requirement of numerical simulation. During the numerical simulation, a first-order upwind difference scheme is used to solve the convection-diffusion equation, the SIMPLEC algorithm is used to solve the pressure-velocity coupling equations, and the convergence precision is set to 1 × 10−7.A mesh independence verification was performed to ensure the calculation accuracy and computation efficiency. The calculation parameters for the TJ04-ZL-06 pump model are as follows: the diameter and rated speed of the pump impeller are 0.3 m and 1450 r/min, respectively, and the design discharge rateQ is 0.375 m3/s for a blade angle of −2° according to model test results obtained for the test bed of Beifang Investigation, Design and Research Co., Ltd., Tianjing, China [39].Pump segment efficiency is an important energy performance index of pump, which is used as the judgment basis for mesh independence analysis. The calculation formula of pump segment efficiency is as follows:(3)ηbd=ρgQHbdPbz×100%,where ηbd is the pump segment efficiency; g is the gravitational acceleration; Q is the discharge rate; Hbd is the pump segment head; and Pbz is the pump shaft power.Table1 shows the relationship between the pump segment efficiency and grid number under the abovementioned conditions. When the grid number of computational domain exceeds 1,863,552, the pump segment efficiency changes only slightly. Based on the verification results, the grid number of the entire calculation domain is set to approximately 1,860,000 in the calculations; the grid numbers of each component are shown in Table 2. The grid generation of the computational domain is shown in Figure 2.Table 1
Relationship between outlet conduit hydraulic loss and grid number.
Grid number788,332967,8061,262,5191,516,0221,863,5521,966,5852,256,251Pump segment efficiency (%)85.7385.6785.2484.5184.1684.1284.12Table 2
Detailed mesh information of computational domain.
DomainStraight inlet pipeConical inlet pipeImpeller and impeller chamberGuide vaneBent outlet pipeStraight outlet pipeGrid number (×103)203252317392495201Figure 2
Grid generation of the computational domain.Based on the abovementioned numerical method and setting, the pump efficiency of pump model TJ04-ZL-06 was calculated for a discharge rate between0.8ηbd and 1.2ηbd. Based on the calculated results, the relationship between the discharge rate and pump segment efficiency is shown in Figure 3; the flow fields in the pump are shown in Figure 4. It could be seen that the pump segment efficiency increases firstly and then decreases as the discharge rate increases. Because the inlet angle of guide vane does not match with the flow direction from the impeller outlet under the off-design conditions, there will be vortex on the back of guide vane under the condition of small discharge rate, and there will be vortex on the front of guide vane under the condition of large discharge rate. The comparison of numerical calculation and model test results is shown in Figure 3. The test data of TJ04-ZL-06 pump model is from the model pump test on the same test bed for the south-to-north water diversion [39]. Clearly, the trends observed for the numerical simulation are consistent with those for the model test, and the two curves are similar, indicating that the numerical results are reliable.Figure 3
Comparison of the numerical simulation and model test results.Figure 4
Flow fields in the pump segment under different conditions of discharge rates. (a)Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)


## 3. Research Scheme

To satisfy hydraulic design requirements and structure demands, the guide vane is divided into an inlet segment, middle segment, and outlet segment (Figure5). The inlet segment is used to adjust the inlet angle of the guide vane in order to match the flow direction of the impeller outlet under off-design conditions. The middle segment is used to fix the bearing support. The outlet segment, which is used to adjust the circulation of the guide vane outlet, is fixed in this paper.Figure 5
Segmentation of the guide vane.In Figure5, the axial chord of the guide vane is H, and the inlet segment axial chord of the guide vane is h (Figure 4). For a given H, a larger h corresponds to a shorter fixed region (middle and outlet segments), and the support function of the guide vane will be negatively affected. However, a smaller h corresponds to a weaker adjustment effect for the inlet angle of the guide vane. Therefore, h values of 0.1H, 0.2H, 0.25H, and 0.33H were employed to study the influence of h on the hydraulic performance of the axial flow pump.The inlet angle of the guide vaneβ0 for the model pump TJ04-ZL-06 is determined based on the design conditions (Figure 6). In this paper, the inlet angle of the guide vane β0 is defined as 0°. Based on β0, if the inlet segment of the guide vane is rotated counterclockwise (Figure 6(b)), the inlet angle adjustment Δβ is positive; if the inlet segment of the guide vane is rotated clockwise (Figure 6(c)), the angle adjustment Δβ is negative. According to the velocity triangle at the impeller outlet, when the pump operates under a flow that is larger than the design condition, β0 does not match the absolute velocity of the flow at the impeller outlet, and the inlet segment needs to rotate clockwise. By contrast, when the pump operates under smaller flow conditions, the inlet segment needs to rotate counterclockwise. In an actual system, the pump at a low head pumping station usually operates under a large flow; thus, the pump system efficiency is low [49, 50]. To improve the efficiency, the study in this paper places an additional emphasis on the influence of Δβ on the pump segment efficiency under large flow conditions; therefore, Δβ is taken as −15°, −10°, −5°, 0°, and +5°.Figure 6
The datum and turn direction for adjusting the guide vane inlet angle. (a) Inlet angle of the guide vane. (b) Counterclockwise rotation. (c) Clockwise rotation.
(a)(b)(c)The inlet segment of the guide vane is based on two geometrical parameters: the inlet segment axial chordh and the inlet angle adjustment Δβ. The calculation schemes are determined by h and Δβ, the h is selected as 0.1H, 0.2H, 0.25H, and 0.33H, and the Δβ is selected as +5°, 0°, −5°, −10°, and −15°. The combination of the two factors forms a total of 20 calculation schemes. Based on the model pump TJ04-ZL-06 for a blade angle of −2°, the calculation discharge rates for the schemes are taken as 0.30 m3/s, 0.325 m3/s, 0.35 m3/s, 0.375 m3/s, 0.40 m3/s, 0.425 m3/s, and 0.45 m3/s. Note that when Δβ = 0°, the scheme is the same as the original guide vane.


## 4. Results and Analysis

### 4.1. Calculation Results

The pump segment energy performance for each calculation scheme was calculated using a 3D turbulent flow numerical simulation. The curves of pump segment efficiencyηbd and discharge rate Q for different inlet segment axial chords h and inlet angle adjustments Δβ are shown in Figure 7.Figure 7
Q∼ηbd curves for the different calculation schemes. (a) h = 0.10H. (b) h = 0.20H. (c) h = 0.25H. (d) h = 0.33H.
(a)(b)(c)(d)


### 4.2. Influence of Inlet Segment Axial Chord on Pump Segment Efficiency

Based on the calculation results, the pump segment efficiencyηbd and inlet segment axial chord h for different values of discharge rate Q are shown in Figure 8. It can be seen that h has a strong effect on ηbd. When the discharge rate is smaller than the optimum operating discharge rate, if Δβ>0°, ηbd will increase slightly as h increases; if Δβ<0°, ηbd will gradually decrease as h increases. A smaller Δβ corresponds to a greater decrease in ηbd. For a discharge rate that is larger than the optimum operating discharge rate, if Δβ>0°, ηbd will decrease as h increases; if Δβ<0°, ηbd gradually increases as h increases. In this case, a smaller Δβ corresponds to a greater increase in ηbd. Figure 8 shows that regardless of whether ηbd increases or decreases with increasing h, when h>0.25H, the influence of h on ηbd decreases. Therefore, considering the support function and hydraulic performance of the guide vane, the inlet segment axial chord h is taken as 0.25H.Figure 8
ηbd∼h curves for each calculation scheme. (a) Q = 0.30 m3/s, (b) Q = 0.325 m3/s, (c) Q = 0.35 m3/s, (d) Q = 0.375 m3/s, (e) Q = 0.40 m3/s, (f) Q = 0.425 m3/s, and (g) Q = 0.45 m3/s.
(a)(b)(c)(d)(e)(f)(g)


### 4.3. Influence of Inlet Angle Adjustment on Pump Segment Efficiency

Based on the calculation results, the pump segment efficiencyηbd and inlet angle adjustment Δβ for different discharge rate Q values with h = 0.25H are shown in Figure 9. It could be seen as follows: as the inlet angle adjustment Δβ increases, the pump segment efficiencies ηbd increase when the discharge rates Q are 0.30 m3/s, 0.325 m3/s, and 0.35 m3/s, the pump segment efficiencies ηbd are basically constant when the discharge rates Q are 0.375 m3/s and 0.40 m3/s, and the pump segment efficiencies ηbd decrease when the discharge rates Q are 0.425 m3/s and 0.45 m3/s. When the discharge rate is smaller than the optimum operating discharge rate, a larger Δβ corresponds to a greater ηbd; when the discharge rate is larger than the optimum operating discharge rate, a smaller Δβ corresponds to a greater ηbd.Figure 9
ηbd∼Δβ curves for different discharge rates when h=0.25H.Under the condition ofh = 0.25H, the flow fields in the pump at different discharge rates when the inlet angle adjustments Δβ are +5° and −10° are shown in Figures 10 and 11, respectively. Comparing the flow fields in Figures 4, 10, and 11, it could be seen as follows: under the same discharge rate condition, the flow fields in the impeller are the same for different inlet angle adjustments; when the discharge rates are 0.35 m3/s and 0.40 m3/s, the flow pattern in the guide vane is all good for different inlet angle adjustments, so the pump segment efficiency changes little as the inlet angle adjustment increases (Figure 9); when the discharge rate is 0.30 m3/s, there is flow separation on the back of the guide vane, and there is a big range of vortex when the inlet angle adjustment is −10°; the smaller the inlet angle adjustment, the worse the flow separation and the bigger the energy loss, therefore the pump segment efficiency decreases as the inlet angle adjustment decreases at the small discharge rate (Figure 9); when the discharge rate is 0.45 m3/s, there is flow separation on the front of the guide vane; there is a big range of vortex when the inlet angle adjustment is +5°; the pump segment efficiency decreases dramatically; the bigger the inlet angle adjustment, the worse the flow separation and the bigger the energy loss, so the pump segment efficiency decreases as the inlet angle adjustment increases at the large discharge rate (Figure 9).Figure 10
Flow fields in the pump segment under different conditions of discharge rates (Δβ = +5°, h=0.25H). (a) Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)Figure 11
Flow fields in the pump segment under different conditions of discharge rates (Δβ = −10°, h=0.25H). (a) Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)


### 4.4. Matching Relation of the Guide Vane Inlet Angle and the Impeller Outlet Flow Direction

#### 4.4.1. Design Working Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump under optimum operating conditions is shown in Figure12(a). In the figure, β0 is the inlet angle of the guide vane under the design working conditions, v0, w0, and u are the absolute velocity, relative velocity, and transport velocity, respectively, of the impeller outlet flow under the design working conditions, and α0 is the angle between v0 and u. Obviously, when the axial flow pump operates under the design working conditions, β0 is equal to α0, i.e., the inlet angle of the guide vane matches the flow direction of the impeller outlet.Figure 12
Matching relationships between the guide vane inlet angle and the impeller outlet flow direction. (a) Design discharge rate condition. (b) Smaller discharge rate condition (αs<α0). (c) Larger discharge rate condition (αL>α0).
(a)(b)(c)


#### 4.4.2. Smaller Discharge Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a smaller discharge rate is shown in Figure12(b). When the axial flow pump operates with a smaller discharge rate, the axial velocity at the impeller outlet is vms, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vs and αs, respectively. At this point, because αs less than α0and β0 differs fromαs, the flow strikes the pressure side of the guide vane. Flow separation and vortices will simultaneously occur on the vacuum side of the guide vane, resulting in an additional hydraulic loss for the guide vane. To ensure that the inlet angle of the guide vane matches the flow direction of the impeller outlet for a smaller discharge rate, the inlet angle must be changed by a certain angle counterclockwise based on β0, as shown by the dotted line in Figure 12(b).


#### 4.4.3. Larger Discharge Rate Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a larger discharge rate is shown in Figure12(c). When the axial flow pump operates with a larger discharge rate, the axial velocity at the impeller outlet is vmL, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vL and αL, respectively. At this point, because αL larger than α0 and β0 differs from αL, the flow strikes the vacuum side of the guide vane. Flow separation and vortices will simultaneously arise on the pressure side of the guide vane, resulting in additional hydraulic loss for the guide vane. To match the guide vane inlet angle with the impeller outlet flow direction for a large discharge rate, the inlet angle must change by a certain angle clockwise based on β0, as shown by the dotted line in Figure 12(c).


### 4.5. Influence of the Inlet Angle on the Guide Vane Flow Field

ForQ = 0.45 m3/s, a 3D steady turbulent flow numerical simulation was performed for the axial flow pump with Δβ = 0° and Δβ = −10°. For ease of analysis, three tori are chosen between the hub and the rim of the guide vane as follows: inner torus (near the hub), middle torus (between the hub and rim), and outer torus (near the rim).The flow fields of the three tori of the guide vane forΔβ = 0° and Δβ = −10° are shown in Figures 13 and 14, respectively. The figures show that for the larger discharge rate condition, when Δβ = 0°, the inlet angle of the guide vane does not match the flow direction of the impeller outlet; thus, the vacuum side of the guide vane is struck by the flow. Flow separation and vortices occur simultaneously on the pressure side of the guide vane; therefore, the hydraulic loss of the guide vane is increased. For Δβ = −10°, the inlet angle of the guide vane matches the flow direction of the impeller outlet, and the flow to the adjacent guide vane is smooth. Essentially, no collisions or vortices occur, the flow pattern in the guide vane is substantially improved, and the hydraulic loss of the guide vane is reduced.Figure 13
Flow fields of the three tori of the guide vane (Δβ = 0°). (a) Inner torus. (b) Middle torus. (c) Outer torus.
(a)(b)(c)Figure 14
Flow fields of the three tori of the guide vane (Δβ = −10°). (a) Inner torus. (b) Middle torus. (c) Outer torus.
(a)(b)(c)At the same time, the unsteady flow numerical simulation was performed for the axial flow pump withΔβ = 0° and Δβ = −10° when the discharge rate Q is 0.45 m3/s. The total calculation time was set to 8 times the rotation period of the impeller, the total time T is 0.33103448 s, and the time step t was set as 3.448275833 × 10–4 which is the time required for the impeller to rotate 3°. In consideration of the stability of the flow field calculation, the internal flow field was analyzed after 4 rotation periods. The flow fields of middle tori of pump segment at different time in one period T are respectively shown in Figures 15 and 16 for Δβ = 0° and Δβ = −10° by unsteady flow numerical simulation. When the inlet angle adjustment Δβ is 0°, there is a tendency of vortexes on the front of the guide vane at 1/4 T, and the vortex is appeared on the front of the guide vane at 3/4 T; it is basically consistent with the results of steady flow numerical simulation. When the inlet angle adjustment Δβ is −10°, there is no vortex on the front of the guide vane during the full period; it is the same with the results of steady flow numerical simulation.Figure 15
Flow fields of middle tori of the pump segment at different time in one periodT (Δβ = 0°). (a) t = 1/4 T, (b) t = 2/4 T, (c) t = 3/4 T, and (d) t = T.
(a)(b)(c)(d)Figure 16
Flow fields of middle tori of the pump segment at different time in one periodT (Δβ = −10°). (a) t = 1/4 T, (b) t = 2/4 T, (c) t = 3/4 T, and (d) t = T.
(a)(b)(c)(d)


### 4.6. Influence of the Guide Vane Inlet Angle on Hydraulic Loss and Efficiency

#### 4.6.1. Influence ofΔβ on the Hydraulic Loss of the Guide Vane Δhdy

In the range of considered working conditions, whenQ = 0.45 m3/s, the inlet angle adjustment Δβ has a strong effect on pump segment efficiency ηbd. Therefore, this working condition is chosen for analysis. The curves of ηbd∼Δβ and Δhdy∼Δβ for different h values under the chosen working condition are shown in Figure 17. Over the range of −15° to +5° for Δβ, the hydraulic loss of the guide vane Δhdy increases substantially as Δβ increases, while ηbd decreases dramatically. Δhdy increases under the larger discharge rate condition because as Δβ increases, the mismatch between the inlet angle of the guide vane and the flow direction of the impeller outlet increases, the flow impact and vortex in the guide vane become greater (Figure 13), and thus, Δhdy increases.Figure 17
ηbd∼Δβ and Δhdy∼Δβ curves for different h values. (a) h = 0.10H, (b) h = 0.20H. (c) h = 0.25H, and (d) h = 0.33H.
(a)(b)(c)(d)


#### 4.6.2. Influence ofΔhdy on the Guide Vane Efficiency ηdy and ηbd

Forh = 0.25H, curves of ηyl∼Q, ηbd∼Q, and Δhdy∼Q for each calculation scheme are shown in Figure 18. The main energy performance parameters for Δβ = 0° and Δβ = −10° for the pump segment with Q = 0.45 m3/s are listed in Table 3. The impeller heads Hyl for Δβ = 0° and Δβ = −10° are approximately equal at 2.66 m and 2.69 m, respectively; when Δβ is adjusted from 0° to −10°, Δhdy decreases from 0.38 m to 0.17 m because the flow pattern in the guide vane is improved.Figure 18
Influence ofΔhdy on ηdy and ηbd for different values of Δβ. (a) ηyl = +5°, (b) ηdy = 0°, (c) Δβ = −5°, (d) ηdy=Hbd/Hyl=Hyl−Δhdy/Hyl×100% = −10°, and (e) Δβ = −15°.
(a)(b)(c)(d)(e)Table 3
Comparison of energy performance for the pump withΔβ = 0° and Δβ = −10°.
Inlet angle adjustment,Δβ (°)Impeller head,Hyl (m)Shaft power,Pbz (kW)Hydraulic loss of guide vane,Δhdy (m)Impeller efficiency,ηyl (%)Pump segment head,Hbd (m)Guide vane efficiency,ηdy (%)Pump segment efficiency,ηbd (%)0°2.6613.670.3885.82.2885.773.5−10°2.6913.760.1786.22.5293.780.9According to the calculated impeller headHyl and pump shaft power Pbz, the impeller efficiency ηyl can be calculated as follows:(4)ηyl=ρgQHylPbz×100%,where g is the gravitational acceleration; Q is the discharge rate; and Pbz is the pump shaft power. The ηyl values calculated from formula (4) for Δβ = 0° and Δβ = −10° are listed in Table 3.Using the calculatedΔhdy and ηyl, the guide vane efficiency ηdy can be determined as follows:(5)ηdy=HbdHyl=Hyl−ΔhdyHyl×100%.According to formulas (4) and (5), formula (3) could be transformed as follows:(6)ηbd=ρgQHbdPbz=ρgQHylPbz×HbdHyl=ηyl×ηdy.Pump segment efficiencyηbd is the product of impeller efficiency ηyl and guide vane efficiency ηdy.Theηdy and ηbd values for Δβ = 0° and Δβ = −10°, calculated from formulas (5) and (6), are listed in Table 3.The abovementioned results indicate that whenΔβ is adjusted from 0° to −10°, Hyl and ηyl are basically unchanged, and the hydraulic performance of impeller is not affected by the inlet segment adjustment of the guide vane. However, when the inlet segment angle is −10°, the inlet angle of guide vane is matched with flow direction at the impeller outlet well, the flow pattern in the guide vane becomes better, and the vortex is eliminated, so the Δhdy decreases from 0.38 m to 0.17 m, and then guide vane efficiency ηdy increases from 85.7% to 93.4% and pump segment efficiency ηbd improves from 73.5% to 80.9% correspondingly.


## 4.1. Calculation Results

The pump segment energy performance for each calculation scheme was calculated using a 3D turbulent flow numerical simulation. The curves of pump segment efficiencyηbd and discharge rate Q for different inlet segment axial chords h and inlet angle adjustments Δβ are shown in Figure 7.Figure 7
Q∼ηbd curves for the different calculation schemes. (a) h = 0.10H. (b) h = 0.20H. (c) h = 0.25H. (d) h = 0.33H.
(a)(b)(c)(d)


## 4.2. Influence of Inlet Segment Axial Chord on Pump Segment Efficiency

Based on the calculation results, the pump segment efficiencyηbd and inlet segment axial chord h for different values of discharge rate Q are shown in Figure 8. It can be seen that h has a strong effect on ηbd. When the discharge rate is smaller than the optimum operating discharge rate, if Δβ>0°, ηbd will increase slightly as h increases; if Δβ<0°, ηbd will gradually decrease as h increases. A smaller Δβ corresponds to a greater decrease in ηbd. For a discharge rate that is larger than the optimum operating discharge rate, if Δβ>0°, ηbd will decrease as h increases; if Δβ<0°, ηbd gradually increases as h increases. In this case, a smaller Δβ corresponds to a greater increase in ηbd. Figure 8 shows that regardless of whether ηbd increases or decreases with increasing h, when h>0.25H, the influence of h on ηbd decreases. Therefore, considering the support function and hydraulic performance of the guide vane, the inlet segment axial chord h is taken as 0.25H.Figure 8
ηbd∼h curves for each calculation scheme. (a) Q = 0.30 m3/s, (b) Q = 0.325 m3/s, (c) Q = 0.35 m3/s, (d) Q = 0.375 m3/s, (e) Q = 0.40 m3/s, (f) Q = 0.425 m3/s, and (g) Q = 0.45 m3/s.
(a)(b)(c)(d)(e)(f)(g)


## 4.3. Influence of Inlet Angle Adjustment on Pump Segment Efficiency

Based on the calculation results, the pump segment efficiencyηbd and inlet angle adjustment Δβ for different discharge rate Q values with h = 0.25H are shown in Figure 9. It could be seen as follows: as the inlet angle adjustment Δβ increases, the pump segment efficiencies ηbd increase when the discharge rates Q are 0.30 m3/s, 0.325 m3/s, and 0.35 m3/s, the pump segment efficiencies ηbd are basically constant when the discharge rates Q are 0.375 m3/s and 0.40 m3/s, and the pump segment efficiencies ηbd decrease when the discharge rates Q are 0.425 m3/s and 0.45 m3/s. When the discharge rate is smaller than the optimum operating discharge rate, a larger Δβ corresponds to a greater ηbd; when the discharge rate is larger than the optimum operating discharge rate, a smaller Δβ corresponds to a greater ηbd.Figure 9
ηbd∼Δβ curves for different discharge rates when h=0.25H.Under the condition ofh = 0.25H, the flow fields in the pump at different discharge rates when the inlet angle adjustments Δβ are +5° and −10° are shown in Figures 10 and 11, respectively. Comparing the flow fields in Figures 4, 10, and 11, it could be seen as follows: under the same discharge rate condition, the flow fields in the impeller are the same for different inlet angle adjustments; when the discharge rates are 0.35 m3/s and 0.40 m3/s, the flow pattern in the guide vane is all good for different inlet angle adjustments, so the pump segment efficiency changes little as the inlet angle adjustment increases (Figure 9); when the discharge rate is 0.30 m3/s, there is flow separation on the back of the guide vane, and there is a big range of vortex when the inlet angle adjustment is −10°; the smaller the inlet angle adjustment, the worse the flow separation and the bigger the energy loss, therefore the pump segment efficiency decreases as the inlet angle adjustment decreases at the small discharge rate (Figure 9); when the discharge rate is 0.45 m3/s, there is flow separation on the front of the guide vane; there is a big range of vortex when the inlet angle adjustment is +5°; the pump segment efficiency decreases dramatically; the bigger the inlet angle adjustment, the worse the flow separation and the bigger the energy loss, so the pump segment efficiency decreases as the inlet angle adjustment increases at the large discharge rate (Figure 9).Figure 10
Flow fields in the pump segment under different conditions of discharge rates (Δβ = +5°, h=0.25H). (a) Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)Figure 11
Flow fields in the pump segment under different conditions of discharge rates (Δβ = −10°, h=0.25H). (a) Q = 0.30 m3/s, (b) Q = 0.35 m3/s, (c) Q = 0.40 m3/s, and (d) Q = 0.45 m3/s.
(a)(b)(c)(d)


## 4.4. Matching Relation of the Guide Vane Inlet Angle and the Impeller Outlet Flow Direction

### 4.4.1. Design Working Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump under optimum operating conditions is shown in Figure12(a). In the figure, β0 is the inlet angle of the guide vane under the design working conditions, v0, w0, and u are the absolute velocity, relative velocity, and transport velocity, respectively, of the impeller outlet flow under the design working conditions, and α0 is the angle between v0 and u. Obviously, when the axial flow pump operates under the design working conditions, β0 is equal to α0, i.e., the inlet angle of the guide vane matches the flow direction of the impeller outlet.Figure 12
Matching relationships between the guide vane inlet angle and the impeller outlet flow direction. (a) Design discharge rate condition. (b) Smaller discharge rate condition (αs<α0). (c) Larger discharge rate condition (αL>α0).
(a)(b)(c)


### 4.4.2. Smaller Discharge Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a smaller discharge rate is shown in Figure12(b). When the axial flow pump operates with a smaller discharge rate, the axial velocity at the impeller outlet is vms, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vs and αs, respectively. At this point, because αs less than α0and β0 differs fromαs, the flow strikes the pressure side of the guide vane. Flow separation and vortices will simultaneously occur on the vacuum side of the guide vane, resulting in an additional hydraulic loss for the guide vane. To ensure that the inlet angle of the guide vane matches the flow direction of the impeller outlet for a smaller discharge rate, the inlet angle must be changed by a certain angle counterclockwise based on β0, as shown by the dotted line in Figure 12(b).


### 4.4.3. Larger Discharge Rate Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a larger discharge rate is shown in Figure12(c). When the axial flow pump operates with a larger discharge rate, the axial velocity at the impeller outlet is vmL, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vL and αL, respectively. At this point, because αL larger than α0 and β0 differs from αL, the flow strikes the vacuum side of the guide vane. Flow separation and vortices will simultaneously arise on the pressure side of the guide vane, resulting in additional hydraulic loss for the guide vane. To match the guide vane inlet angle with the impeller outlet flow direction for a large discharge rate, the inlet angle must change by a certain angle clockwise based on β0, as shown by the dotted line in Figure 12(c).


## 4.4.1. Design Working Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump under optimum operating conditions is shown in Figure12(a). In the figure, β0 is the inlet angle of the guide vane under the design working conditions, v0, w0, and u are the absolute velocity, relative velocity, and transport velocity, respectively, of the impeller outlet flow under the design working conditions, and α0 is the angle between v0 and u. Obviously, when the axial flow pump operates under the design working conditions, β0 is equal to α0, i.e., the inlet angle of the guide vane matches the flow direction of the impeller outlet.Figure 12
Matching relationships between the guide vane inlet angle and the impeller outlet flow direction. (a) Design discharge rate condition. (b) Smaller discharge rate condition (αs<α0). (c) Larger discharge rate condition (αL>α0).
(a)(b)(c)


## 4.4.2. Smaller Discharge Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a smaller discharge rate is shown in Figure12(b). When the axial flow pump operates with a smaller discharge rate, the axial velocity at the impeller outlet is vms, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vs and αs, respectively. At this point, because αs less than α0and β0 differs fromαs, the flow strikes the pressure side of the guide vane. Flow separation and vortices will simultaneously occur on the vacuum side of the guide vane, resulting in an additional hydraulic loss for the guide vane. To ensure that the inlet angle of the guide vane matches the flow direction of the impeller outlet for a smaller discharge rate, the inlet angle must be changed by a certain angle counterclockwise based on β0, as shown by the dotted line in Figure 12(b).


## 4.4.3. Larger Discharge Rate Condition

The relationship between the guide vane inlet angle and the impeller outlet flow direction for an axial flow pump with a larger discharge rate is shown in Figure12(c). When the axial flow pump operates with a larger discharge rate, the axial velocity at the impeller outlet is vmL, and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are vL and αL, respectively. At this point, because αL larger than α0 and β0 differs from αL, the flow strikes the vacuum side of the guide vane. Flow separation and vortices will simultaneously arise on the pressure side of the guide vane, resulting in additional hydraulic loss for the guide vane. To match the guide vane inlet angle with the impeller outlet flow direction for a large discharge rate, the inlet angle must change by a certain angle clockwise based on β0, as shown by the dotted line in Figure 12(c).


## 4.5. Influence of the Inlet Angle on the Guide Vane Flow Field

ForQ = 0.45 m3/s, a 3D steady turbulent flow numerical simulation was performed for the axial flow pump with Δβ = 0° and Δβ = −10°. For ease of analysis, three tori are chosen between the hub and the rim of the guide vane as follows: inner torus (near the hub), middle torus (between the hub and rim), and outer torus (near the rim).The flow fields of the three tori of the guide vane forΔβ = 0° and Δβ = −10° are shown in Figures 13 and 14, respectively. The figures show that for the larger discharge rate condition, when Δβ = 0°, the inlet angle of the guide vane does not match the flow direction of the impeller outlet; thus, the vacuum side of the guide vane is struck by the flow. Flow separation and vortices occur simultaneously on the pressure side of the guide vane; therefore, the hydraulic loss of the guide vane is increased. For Δβ = −10°, the inlet angle of the guide vane matches the flow direction of the impeller outlet, and the flow to the adjacent guide vane is smooth. Essentially, no collisions or vortices occur, the flow pattern in the guide vane is substantially improved, and the hydraulic loss of the guide vane is reduced.Figure 13
Flow fields of the three tori of the guide vane (Δβ = 0°). (a) Inner torus. (b) Middle torus. (c) Outer torus.
(a)(b)(c)Figure 14
Flow fields of the three tori of the guide vane (Δβ = −10°). (a) Inner torus. (b) Middle torus. (c) Outer torus.
(a)(b)(c)At the same time, the unsteady flow numerical simulation was performed for the axial flow pump withΔβ = 0° and Δβ = −10° when the discharge rate Q is 0.45 m3/s. The total calculation time was set to 8 times the rotation period of the impeller, the total time T is 0.33103448 s, and the time step t was set as 3.448275833 × 10–4 which is the time required for the impeller to rotate 3°. In consideration of the stability of the flow field calculation, the internal flow field was analyzed after 4 rotation periods. The flow fields of middle tori of pump segment at different time in one period T are respectively shown in Figures 15 and 16 for Δβ = 0° and Δβ = −10° by unsteady flow numerical simulation. When the inlet angle adjustment Δβ is 0°, there is a tendency of vortexes on the front of the guide vane at 1/4 T, and the vortex is appeared on the front of the guide vane at 3/4 T; it is basically consistent with the results of steady flow numerical simulation. When the inlet angle adjustment Δβ is −10°, there is no vortex on the front of the guide vane during the full period; it is the same with the results of steady flow numerical simulation.Figure 15
Flow fields of middle tori of the pump segment at different time in one periodT (Δβ = 0°). (a) t = 1/4 T, (b) t = 2/4 T, (c) t = 3/4 T, and (d) t = T.
(a)(b)(c)(d)Figure 16
Flow fields of middle tori of the pump segment at different time in one periodT (Δβ = −10°). (a) t = 1/4 T, (b) t = 2/4 T, (c) t = 3/4 T, and (d) t = T.
(a)(b)(c)(d)


## 4.6. Influence of the Guide Vane Inlet Angle on Hydraulic Loss and Efficiency

### 4.6.1. Influence ofΔβ on the Hydraulic Loss of the Guide Vane Δhdy

In the range of considered working conditions, whenQ = 0.45 m3/s, the inlet angle adjustment Δβ has a strong effect on pump segment efficiency ηbd. Therefore, this working condition is chosen for analysis. The curves of ηbd∼Δβ and Δhdy∼Δβ for different h values under the chosen working condition are shown in Figure 17. Over the range of −15° to +5° for Δβ, the hydraulic loss of the guide vane Δhdy increases substantially as Δβ increases, while ηbd decreases dramatically. Δhdy increases under the larger discharge rate condition because as Δβ increases, the mismatch between the inlet angle of the guide vane and the flow direction of the impeller outlet increases, the flow impact and vortex in the guide vane become greater (Figure 13), and thus, Δhdy increases.Figure 17
ηbd∼Δβ and Δhdy∼Δβ curves for different h values. (a) h = 0.10H, (b) h = 0.20H. (c) h = 0.25H, and (d) h = 0.33H.
(a)(b)(c)(d)


### 4.6.2. Influence ofΔhdy on the Guide Vane Efficiency ηdy and ηbd

Forh = 0.25H, curves of ηyl∼Q, ηbd∼Q, and Δhdy∼Q for each calculation scheme are shown in Figure 18. The main energy performance parameters for Δβ = 0° and Δβ = −10° for the pump segment with Q = 0.45 m3/s are listed in Table 3. The impeller heads Hyl for Δβ = 0° and Δβ = −10° are approximately equal at 2.66 m and 2.69 m, respectively; when Δβ is adjusted from 0° to −10°, Δhdy decreases from 0.38 m to 0.17 m because the flow pattern in the guide vane is improved.Figure 18
Influence ofΔhdy on ηdy and ηbd for different values of Δβ. (a) ηyl = +5°, (b) ηdy = 0°, (c) Δβ = −5°, (d) ηdy=Hbd/Hyl=Hyl−Δhdy/Hyl×100% = −10°, and (e) Δβ = −15°.
(a)(b)(c)(d)(e)Table 3
Comparison of energy performance for the pump withΔβ = 0° and Δβ = −10°.
Inlet angle adjustment,Δβ (°)Impeller head,Hyl (m)Shaft power,Pbz (kW)Hydraulic loss of guide vane,Δhdy (m)Impeller efficiency,ηyl (%)Pump segment head,Hbd (m)Guide vane efficiency,ηdy (%)Pump segment efficiency,ηbd (%)0°2.6613.670.3885.82.2885.773.5−10°2.6913.760.1786.22.5293.780.9According to the calculated impeller headHyl and pump shaft power Pbz, the impeller efficiency ηyl can be calculated as follows:(4)ηyl=ρgQHylPbz×100%,where g is the gravitational acceleration; Q is the discharge rate; and Pbz is the pump shaft power. The ηyl values calculated from formula (4) for Δβ = 0° and Δβ = −10° are listed in Table 3.Using the calculatedΔhdy and ηyl, the guide vane efficiency ηdy can be determined as follows:(5)ηdy=HbdHyl=Hyl−ΔhdyHyl×100%.According to formulas (4) and (5), formula (3) could be transformed as follows:(6)ηbd=ρgQHbdPbz=ρgQHylPbz×HbdHyl=ηyl×ηdy.Pump segment efficiencyηbd is the product of impeller efficiency ηyl and guide vane efficiency ηdy.Theηdy and ηbd values for Δβ = 0° and Δβ = −10°, calculated from formulas (5) and (6), are listed in Table 3.The abovementioned results indicate that whenΔβ is adjusted from 0° to −10°, Hyl and ηyl are basically unchanged, and the hydraulic performance of impeller is not affected by the inlet segment adjustment of the guide vane. However, when the inlet segment angle is −10°, the inlet angle of guide vane is matched with flow direction at the impeller outlet well, the flow pattern in the guide vane becomes better, and the vortex is eliminated, so the Δhdy decreases from 0.38 m to 0.17 m, and then guide vane efficiency ηdy increases from 85.7% to 93.4% and pump segment efficiency ηbd improves from 73.5% to 80.9% correspondingly.


## 4.6.1. Influence ofΔβ on the Hydraulic Loss of the Guide Vane Δhdy

In the range of considered working conditions, whenQ = 0.45 m3/s, the inlet angle adjustment Δβ has a strong effect on pump segment efficiency ηbd. Therefore, this working condition is chosen for analysis. The curves of ηbd∼Δβ and Δhdy∼Δβ for different h values under the chosen working condition are shown in Figure 17. Over the range of −15° to +5° for Δβ, the hydraulic loss of the guide vane Δhdy increases substantially as Δβ increases, while ηbd decreases dramatically. Δhdy increases under the larger discharge rate condition because as Δβ increases, the mismatch between the inlet angle of the guide vane and the flow direction of the impeller outlet increases, the flow impact and vortex in the guide vane become greater (Figure 13), and thus, Δhdy increases.Figure 17
ηbd∼Δβ and Δhdy∼Δβ curves for different h values. (a) h = 0.10H, (b) h = 0.20H. (c) h = 0.25H, and (d) h = 0.33H.
(a)(b)(c)(d)


## 4.6.2. Influence ofΔhdy on the Guide Vane Efficiency ηdy and ηbd

Forh = 0.25H, curves of ηyl∼Q, ηbd∼Q, and Δhdy∼Q for each calculation scheme are shown in Figure 18. The main energy performance parameters for Δβ = 0° and Δβ = −10° for the pump segment with Q = 0.45 m3/s are listed in Table 3. The impeller heads Hyl for Δβ = 0° and Δβ = −10° are approximately equal at 2.66 m and 2.69 m, respectively; when Δβ is adjusted from 0° to −10°, Δhdy decreases from 0.38 m to 0.17 m because the flow pattern in the guide vane is improved.Figure 18
Influence ofΔhdy on ηdy and ηbd for different values of Δβ. (a) ηyl = +5°, (b) ηdy = 0°, (c) Δβ = −5°, (d) ηdy=Hbd/Hyl=Hyl−Δhdy/Hyl×100% = −10°, and (e) Δβ = −15°.
(a)(b)(c)(d)(e)Table 3
Comparison of energy performance for the pump withΔβ = 0° and Δβ = −10°.
Inlet angle adjustment,Δβ (°)Impeller head,Hyl (m)Shaft power,Pbz (kW)Hydraulic loss of guide vane,Δhdy (m)Impeller efficiency,ηyl (%)Pump segment head,Hbd (m)Guide vane efficiency,ηdy (%)Pump segment efficiency,ηbd (%)0°2.6613.670.3885.82.2885.773.5−10°2.6913.760.1786.22.5293.780.9According to the calculated impeller headHyl and pump shaft power Pbz, the impeller efficiency ηyl can be calculated as follows:(4)ηyl=ρgQHylPbz×100%,where g is the gravitational acceleration; Q is the discharge rate; and Pbz is the pump shaft power. The ηyl values calculated from formula (4) for Δβ = 0° and Δβ = −10° are listed in Table 3.Using the calculatedΔhdy and ηyl, the guide vane efficiency ηdy can be determined as follows:(5)ηdy=HbdHyl=Hyl−ΔhdyHyl×100%.According to formulas (4) and (5), formula (3) could be transformed as follows:(6)ηbd=ρgQHbdPbz=ρgQHylPbz×HbdHyl=ηyl×ηdy.Pump segment efficiencyηbd is the product of impeller efficiency ηyl and guide vane efficiency ηdy.Theηdy and ηbd values for Δβ = 0° and Δβ = −10°, calculated from formulas (5) and (6), are listed in Table 3.The abovementioned results indicate that whenΔβ is adjusted from 0° to −10°, Hyl and ηyl are basically unchanged, and the hydraulic performance of impeller is not affected by the inlet segment adjustment of the guide vane. However, when the inlet segment angle is −10°, the inlet angle of guide vane is matched with flow direction at the impeller outlet well, the flow pattern in the guide vane becomes better, and the vortex is eliminated, so the Δhdy decreases from 0.38 m to 0.17 m, and then guide vane efficiency ηdy increases from 85.7% to 93.4% and pump segment efficiency ηbd improves from 73.5% to 80.9% correspondingly.


## 5. Conclusions

(1)
The inlet segment axial chordh of the guide vane influences the pump segment efficiency ηbd. As h increases, ηbd increases under smaller discharge rate conditions and decreases under larger discharge rate conditions for Δβ>0°; in contrast, ηbd decreases under smaller discharge rate conditions and increases under larger discharge rate conditions when Δβ<0°. When h>0.25H, the influence of h on ηbd weakens.(2)
The inlet angle adjustmentΔβ of the guide vane has a strong effect on the pump segment efficiency ηbd. When the inlet angle of the guide vane is rotated counterclockwise with respect to the design condition, ηbd increases under the smaller discharge rate condition; when the inlet angle of the guide vane is rotated clockwise with respect to the design condition, ηbd increases under the larger discharge rate condition. The greater the deviation from the design condition, the larger the influence of Δβ on ηbd.(3)
The match between the guide vane inlet angle and the impeller outlet flow direction has a strong influence on the pump segment efficiencyηbd because the flow pattern is highly sensitive to deviations in the inlet angle of the guide vane; this change in the flow pattern will directly influence the hydraulic loss of the guide vane.



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*Source: 8880789-2020-12-19.xml*