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

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. *e 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.


Introduction
Vane pump is widely used in mechanical engineering, hydraulic engineering, civil engineering, and military industry. e application of vane pump is affected by its stable and efficient operation. erefore, it is necessary to pay attention to the optimization of the pump [1][2][3][4], and paying attention to the research on pressure pulsation, cavitations, vibration, and noise is also necessary [5][6][7][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. e 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]. e hydraulic performance of guide vane has great influence on the hydraulic performance of axial flow pump and pump system. erefore, 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. e 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 offdesign 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. e abovementioned studies are all about the whole guide vane rotates. us 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. e 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][25][26][27][28][29][30][31] and other aspect [32][33][34][35][36][37][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. e study work has important reference value for the hydraulic design and hydraulic performance improvement of an axial flow pump.

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. e fluid flow in the axial flow pump is considered incompressible. e method of steady flow numerical simulation is used to study the flow and hydraulic performance of the pump. e governing equations that are applied to solve the flow field in the pump include a continuity equation, momentum equations, and k equation and ε equation of the k − ε turbulent model. e Reynolds-averaged Navier-Stokes equations are shown as follows: where ρ is the density; t is the time; u i and u j are the mean velocity components; p is the mean pressure; x i and x j are the coordinate directions; μ is the dynamic viscosity; F i is the body force component; −ρu i ′ u j ′ is the Reynolds stress; and u j ′ and u j ′ are the fluctuating velocity components. e RNG k − 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][43][44][45][46]. e k equation and ε equation of the RNG k − ε turbulent model are shown as follows: where G k is the turbulent kinetic energy production term; C 1ε is an empirical constant; C 2ε is an empirical constant; σ k is the corresponding Prandtl number for turbulent kinetic energy k; and σ ε is the corresponding Prandtl number for the turbulent kinetic energy dissipation rate ε.

Computational Domain and Boundary
Conditions. e 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 ( Figure 1). e inlet boundary for the flow field calculation of an axial flow pump is set at the inlet section of the straight inlet pipe. e discharge rate is known, and the flow velocity distribution is uniform at the inlet section; thus, the velocity inlet boundary condition is adopted [47]. e 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.

2
Shock and Vibration

Numerical Setting and Calculation Accuracy.
e GAMBIT software is used to generate the mesh for the computational domain. e shapes of the straight inlet pipe, conical inlet pipe, bent outlet pipe, and straight outlet pipe are simple; structured hexahedral meshes are applied. e 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. e y+ 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 SIM-PLEC 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. e 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 rate Q is 0.375 m 3 /s for a blade angle of −2°a ccording 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. e calculation formula of pump segment efficiency is as follows: where η b d is the pump segment efficiency; g is the gravitational acceleration; Q is the discharge rate; H b d is the pump segment head; and P bz is the pump shaft power. Table 1 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. e grid generation of the computational domain is shown in Figure 2.
Based on the abovementioned numerical method and setting, the pump efficiency of pump model TJ04-ZL-06 was calculated for a discharge rate between 0.8η b d and 1.2η b d . 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. e comparison of numerical calculation and model test results is shown in Figure 3. e 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.

Research Scheme
To satisfy hydraulic design requirements and structure demands, the guide vane is divided into an inlet segment, middle segment, and outlet segment ( Figure 5). e 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. e middle segment is used to fix the bearing support. e outlet segment, which is used to adjust the circulation of the guide vane outlet, is fixed in this paper.
In Figure 5, 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. erefore, 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.
e inlet angle of the guide vane β 0 for the model pump TJ04-ZL-06 is determined based on the design conditions  Shock and Vibration ( Figure 6). In this paper, the inlet angle of the guide vane β 0 is defined as 0°. Based on β 0 , 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, β 0 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

Calculation Results.
e pump segment energy performance for each calculation scheme was calculated using a 3D turbulent flow numerical simulation. e curves of pump segment efficiency η b d and discharge rate Q for different inlet segment axial chords h and inlet angle adjustments Δβ are shown in Figure 7.

Influence of Inlet Segment Axial Chord on Pump Segment
Efficiency. Based on the calculation results, the pump segment efficiency η b d 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 η b d . When the discharge rate is smaller than the optimum operating discharge rate, if Δβ > 0°, η b d will increase slightly as h increases; if Δβ < 0°, η b d will gradually decrease as h increases. A smaller Δβ corresponds to a greater decrease in η b d . For a discharge rate that is larger than the optimum operating discharge rate, if Δβ > 0°, η b d will decrease as h increases; if Δβ < 0°, η b d gradually increases as h increases. In this case, a smaller Δβ corresponds to a greater increase in η bd . Figure 8 shows that regardless of whether η b d increases or decreases with increasing h, when h > 0.25H, the influence of h on η b d decreases. erefore, considering the support function and hydraulic performance of the guide vane, the inlet segment axial chord h is taken as 0.25H.      When the discharge rate is smaller than the optimum operating discharge rate, a larger Δβ corresponds to a greater η b d ; when the discharge rate is larger than the optimum operating discharge rate, a smaller Δβ corresponds to a greater η b d . Under the condition of h � 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 m 3 /s and 0.40 m 3 /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    Shock and Vibration 5 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).   Shock and Vibration shown in Figure 12(a). In the figure, β 0 is the inlet angle of the guide vane under the design working conditions, v 0 , w 0 , and u are the absolute velocity, relative velocity, and transport velocity, respectively, of the impeller outlet flow under the design working conditions, and α 0 is the angle between v 0 and u.

Matching Relation of the Guide Vane Inlet Angle and the
Obviously, when the axial flow pump operates under the design working conditions, β 0 is equal to α 0 , i.e., the inlet angle of the guide vane matches the flow direction of the impeller outlet.

Smaller Discharge Condition.
e 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 Figure 12(b). When the axial flow pump operates with a smaller discharge rate, the axial velocity at the impeller outlet is v ms , and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are v s and α s , respectively. At this point, because α s less than α 0 and β 0 differs fromα s , 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 β 0 , as shown by the dotted line in Figure 12(b).

Larger Discharge Rate Condition.
e 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 Figure 12(c). When the axial flow pump operates with a larger discharge rate, the axial velocity at the impeller outlet is v mL , and the absolute velocity of the impeller outlet flow and the angle between the absolute velocity and transport velocity are v L and α L , respectively. At this point, because α L larger than α 0 and β 0 differs from α L , 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 β 0 , as shown by the dotted line in Figure 12(c).

Influence of the Inlet Angle on the Guide Vane Flow Field.
For Q � 0.45 m 3 /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). e flow fields of the three tori of the guide vane for Δβ � 0°and Δβ � −10°are shown in Figures 13 and 14, respectively. e 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.
At the same time, the unsteady flow numerical simulation was performed for the axial flow pump with Δβ � 0°and Δβ � −10°when the discharge rate Q is 0.45 m 3 /s. e 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      Table 3. e impeller heads H yl 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°, Δh dy decreases from 0.38 m to 0.17 m because the flow pattern in the guide vane is improved.
According to the calculated impeller head H yl and pump shaft power P bz , the impeller efficiency η yl can be calculated as follows: where g is the gravitational acceleration; Q is the discharge rate; and P bz is the pump shaft power. e η yl values calculated from formula (4) for Δβ � 0°and Δβ � −10°are listed in Table 3.
Using the calculated Δh dy and η yl , the guide vane efficiency η dy can be determined as follows:

Shock and Vibration 13
According to formulas (4) and (5), formula (3) could be transformed as follows: Pump segment efficiency η b d is the product of impeller efficiency η yl and guide vane efficiency η dy . e η dy and η b d values for Δβ � 0°and Δβ � −10°, calculated from formulas (5) and (6), are listed in Table 3.
e abovementioned results indicate that when Δβ is adjusted from 0°to −10°, H yl and η yl 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 Δh dy decreases from 0.38 m to 0.17 m, and then guide vane efficiency η dy increases from 85.7% to 93.4% and pump segment efficiency η b d improves from 73.5% to 80.9% correspondingly. When the inlet angle of the guide vane is rotated counterclockwise with respect to the design condition, η b d increases under the smaller discharge rate condition; when the inlet angle of the guide vane is rotated clockwise with respect to the design condition, η b d increases under the larger discharge rate condition. e greater the deviation from the design condition, the larger the influence of Δβ on η b d . (3) e match between the guide vane inlet angle and the impeller outlet flow direction has a strong influence on the pump segment efficiency η b d 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.

Data Availability
e data used to support the findings of this study are included within the article.