# Improvement of the Efficiency of the Axial-Flow Pump at Part Loads due to Installing Outlet Guide Vanes Mechanism

Authors: Fan Yang; Hao-ru Zhao; Chao Liu
Journal: Mathematical Problems in Engineering
 (2016)

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## Abstract

In order to investigate the influence of adjustable outlet guide vane on the hydraulic performance of axial-flow pump at part loads, the axial-flow pump with 7 different outlet guide vane adjustable angles was simulated based on the RNGk-ε turbulent model and Reynolds time-averaged equations. The Vector graphs of airfoil flow were analyzed in the different operating conditions for different adjustable angles of guide vane. BP-ANN prediction model was established about the effect of adjustable outlet guide vane on the hydraulic performance of axial-flow pump based on the numerical results. The effectiveness of prediction model was verified by theoretical analysis and numerical simulation. The results show that, with the adjustable angle of guide vane increasing along clockwise, the high efficiency area moves to the large flow rate direction; otherwise, that moves to the small flow rate direction. The internal flow field of guide vane is improved by adjusting angle, and the flow separation of tail and guide vane inlet ledge are decreased or eliminated, so that the hydraulic efficiency of pumping system will be improved. The prediction accuracy of BP-ANN model is 1%, which can meet the requirement of practical engineering.


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## Body

## 1. Introduction

With the increasing application of an axial-flow pump, the improvement of its efficiency continues to become more and more important. One of the most useful methods to increase its efficiency is the installation of a guide vane behind the pump impeller [1]. Out guide vane (OGV) can improve the head and the efficiency of the pump by transforming the kinetic energy of the rotating flow, which has a tangential velocity component, into pressure energy. When the axial-flow pump is working under off-design condition, the attack angle, which causes hydraulic loss, will always exist at the leading edge of the guide vane. This is because the traditional guide vane is fixed on the guide vane hub with a fixed angle for the design condition and cannot be adjustable with the change in working conditions. The literature on OGV investigations for aircraft engine mainly falls into the following categories: effects of OGV on aircraft engine’s noise [2–4], unsteady interaction between the stationary OGVs and the rotor [5], and flow characteristics of OGVs [6–9]. The flow in a compressor OGV blade row downstream of a single-state rotor was carried out by Carrotte et al. [10]. Many researchers studied the internal flow characteristics of OGV based on the whole passage of pump [11–14]. Compared with aircraft engine and compressor, the usage of adjustable OGVs is extremely rare for axial-flow pump. The paper investigates the influence of OGVs setting angles on the hydraulic performance of axial-flow pump by CFD. The internal flow of OGVs is analyzed in different setting angles. The BP-ANN prediction model will be built about the influence of OGVs setting angles on the pump performance based on the resulting data.


## 2. Numerical Calculations

### 2.1. Numerical Model and Calculation Method

The numerical model and method for simulating the flow field in the axial-flow pump can be found in previous work by Yang and Liu [15] and Jafarzadeh et al. [16]. The governing equations for the turbulent incompressible flow encountered in this research are the steady-state RANS equations for the conservation of mass and momentum, given as(1)∂∂xiρu-i=0,(2)∂∂xiρu-iu-j=-∂p-∂xi+∂∂xiμ∂u-i∂xj-ρui′uj′¯,where p- is the averaged pressure, μ is the molecular viscosity, and -ρui′uj′¯ is the Reynolds stress. To correctly account for turbulence, the Reynolds stresses are modeled in order to achieve the closure of (2). The modeling is based on the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients within the flow. The Reynolds stresses are given by(3)-ρui′uj′¯=μt∂u-i∂xj+∂u-j∂xi-23δij·ρk+μt∂u-i∂xi,where μt is the turbulent viscosity and k is the turbulent kinetic energy.The renormalization group (RNG)k-ε turbulent model is widely applied in turbo machines, which is suitable for simulating the complex flow in rotating and high curvature computational domain. A more comprehensive description of RNG theory and its applications to turbulence computation can be found in [17].The turbulence kinetic energyk and its rate dissipation ε are obtained from the following transport equations:(4)∂ρku-i∂xi=∂∂xjαkμeff∂k∂xj+Gk-ρε,(5)∂ρεu-i∂xi=∂∂xjαεμeff∂ε∂xj+C1ε∗kGk-C2ερε2k.The production term in (4) is given by(6)Gk=μtS2,where S is the modulus of the mean rate-of-strain tensor, defined by(7)S=2SijSij,Sij=12∂u-i∂xj+∂u-j∂xi.The effective viscosity is calculated by(8)μeff=μ+μt,μt=ρCμk2ε,withCμ=0.0845, αk=αε=1.39, C1ε=1.42, and(9)C1ε∗=C1ε-η1-η/η01+βη3,η=2Sij·Sij0.5kε,η0=4.377,β=0.012,C2ε=1.68.In the present calculation work, the commercial CFD code ANSYS CFX14.0 is employed. ANSYS CFX uses the element based finite volume method and an algebraic multigrid approach. The equations solved in the calculation are the Navier-Stokes equations coupled with the RNGk-ε turbulence model. A uniform axial velocity based on the mass-flow rate is specified at the inlet for each computation run, and the static pressure at the outlet is set to 1.2 atm. The turbulence intensity at the inlet totally depends on the upstream history of flow. Since the fluid in the suction tank is undisturbed, the turbulence intensity for all conditions is considered 1%. Scalable wall functions are used to simulate the boundary layers. Adiabatic and hydraulically smooth walls with no slip condition were considered at solid boundaries. Periodic boundaries are set at the blade passage interfaces. Water was used as a working fluid in ambient condition.


### 2.2. Computational Domain and Mesh

Figure1 shows 3D geometry of axial-flow pump model, with the specific speed ns of 1200 and impeller diameter of 300 mm, which is used to simulate and measure its entire flow field. The specific speed ns is defined below:(10)ns=3.65nQH3/4=3.65r/min⁡·m3/s1/2m3/4.Figure 1
The whole flow passage axial-flow pump model.The impeller has 3 blades and the outlet guide vane has 5 blades. The rotating speedn is 1450 r/min. The average tip clearance of impeller is 0.2 mm at blade angle φ=0°, which are the same as those of the experimental model. The computational domain is the flow passage from the inlet to outlet, including the inlet passage, outlet passage, impeller, and guide vane.The grid quality in the impeller and guide vane will affect the accuracy of axial-flow pump simulation. Accordingly, H/J/L-type topology structure is applied to the impeller, and H-type topology structure is applied to the outlet guide vane. O-type grid is used at the blade surface region to control boundary layer distribution. Prior to step for analysis of axial-flow pump, in order to determine the optimal number of grids, a preliminary grid dependency test with numbers of nodes ranging from 500000 to 1600000 is carried out. The computations have shown that grid convergence has been obtained for the performance of the axial-flow pump atKQ=0.521, as shown in Figure 2. With the increase of grid numbers, the head coefficient KH and efficiency change greatly at first and then change very little gradually. Finally, the appropriate grid number for the simulation was determined by the preliminary simulation results. In the present study, grid number 1272707 was selected for the final simulation.Figure 2
Verification of grid independence to prediction of performances.The nondimensional head and power coefficients are defined as follows.Head coefficient is as follows:(11)KH=gHn2D2,where KH is head coefficient, H is the head of the axial-flow pump, n is rotation speed, and D is the impeller diameter.Flow coefficient is as follows:(12)KQ=QnD3,where the efficiency of the pump is defined as follows:(13)η=30ρgQHπnM×100,where Q is volume flow rate and M is the measured torque.


## 2.1. Numerical Model and Calculation Method

The numerical model and method for simulating the flow field in the axial-flow pump can be found in previous work by Yang and Liu [15] and Jafarzadeh et al. [16]. The governing equations for the turbulent incompressible flow encountered in this research are the steady-state RANS equations for the conservation of mass and momentum, given as(1)∂∂xiρu-i=0,(2)∂∂xiρu-iu-j=-∂p-∂xi+∂∂xiμ∂u-i∂xj-ρui′uj′¯,where p- is the averaged pressure, μ is the molecular viscosity, and -ρui′uj′¯ is the Reynolds stress. To correctly account for turbulence, the Reynolds stresses are modeled in order to achieve the closure of (2). The modeling is based on the Boussinesq hypothesis to relate the Reynolds stresses to the mean velocity gradients within the flow. The Reynolds stresses are given by(3)-ρui′uj′¯=μt∂u-i∂xj+∂u-j∂xi-23δij·ρk+μt∂u-i∂xi,where μt is the turbulent viscosity and k is the turbulent kinetic energy.The renormalization group (RNG)k-ε turbulent model is widely applied in turbo machines, which is suitable for simulating the complex flow in rotating and high curvature computational domain. A more comprehensive description of RNG theory and its applications to turbulence computation can be found in [17].The turbulence kinetic energyk and its rate dissipation ε are obtained from the following transport equations:(4)∂ρku-i∂xi=∂∂xjαkμeff∂k∂xj+Gk-ρε,(5)∂ρεu-i∂xi=∂∂xjαεμeff∂ε∂xj+C1ε∗kGk-C2ερε2k.The production term in (4) is given by(6)Gk=μtS2,where S is the modulus of the mean rate-of-strain tensor, defined by(7)S=2SijSij,Sij=12∂u-i∂xj+∂u-j∂xi.The effective viscosity is calculated by(8)μeff=μ+μt,μt=ρCμk2ε,withCμ=0.0845, αk=αε=1.39, C1ε=1.42, and(9)C1ε∗=C1ε-η1-η/η01+βη3,η=2Sij·Sij0.5kε,η0=4.377,β=0.012,C2ε=1.68.In the present calculation work, the commercial CFD code ANSYS CFX14.0 is employed. ANSYS CFX uses the element based finite volume method and an algebraic multigrid approach. The equations solved in the calculation are the Navier-Stokes equations coupled with the RNGk-ε turbulence model. A uniform axial velocity based on the mass-flow rate is specified at the inlet for each computation run, and the static pressure at the outlet is set to 1.2 atm. The turbulence intensity at the inlet totally depends on the upstream history of flow. Since the fluid in the suction tank is undisturbed, the turbulence intensity for all conditions is considered 1%. Scalable wall functions are used to simulate the boundary layers. Adiabatic and hydraulically smooth walls with no slip condition were considered at solid boundaries. Periodic boundaries are set at the blade passage interfaces. Water was used as a working fluid in ambient condition.


## 2.2. Computational Domain and Mesh

Figure1 shows 3D geometry of axial-flow pump model, with the specific speed ns of 1200 and impeller diameter of 300 mm, which is used to simulate and measure its entire flow field. The specific speed ns is defined below:(10)ns=3.65nQH3/4=3.65r/min⁡·m3/s1/2m3/4.Figure 1
The whole flow passage axial-flow pump model.The impeller has 3 blades and the outlet guide vane has 5 blades. The rotating speedn is 1450 r/min. The average tip clearance of impeller is 0.2 mm at blade angle φ=0°, which are the same as those of the experimental model. The computational domain is the flow passage from the inlet to outlet, including the inlet passage, outlet passage, impeller, and guide vane.The grid quality in the impeller and guide vane will affect the accuracy of axial-flow pump simulation. Accordingly, H/J/L-type topology structure is applied to the impeller, and H-type topology structure is applied to the outlet guide vane. O-type grid is used at the blade surface region to control boundary layer distribution. Prior to step for analysis of axial-flow pump, in order to determine the optimal number of grids, a preliminary grid dependency test with numbers of nodes ranging from 500000 to 1600000 is carried out. The computations have shown that grid convergence has been obtained for the performance of the axial-flow pump atKQ=0.521, as shown in Figure 2. With the increase of grid numbers, the head coefficient KH and efficiency change greatly at first and then change very little gradually. Finally, the appropriate grid number for the simulation was determined by the preliminary simulation results. In the present study, grid number 1272707 was selected for the final simulation.Figure 2
Verification of grid independence to prediction of performances.The nondimensional head and power coefficients are defined as follows.Head coefficient is as follows:(11)KH=gHn2D2,where KH is head coefficient, H is the head of the axial-flow pump, n is rotation speed, and D is the impeller diameter.Flow coefficient is as follows:(12)KQ=QnD3,where the efficiency of the pump is defined as follows:(13)η=30ρgQHπnM×100,where Q is volume flow rate and M is the measured torque.


## 3. Performance Prediction Results and Experimental Validation

### 3.1. Test Device and Method

Physical model of axial-flow pump was tested in the Hydrodynamic Engineering Laboratory of Jiangsu Province. Figure3 shows the rig for the experimental measurements. The test apparatus consists of three sections: ① water supply section: the inlet water tank, the outlet water tank, the surge water tank, mixed-flow pump, and regulating value; ② outlet section: pressure gauge, electromagnetic flowmeter, and regulating value; and ③ pump section: axial-flow pump, composite torque detector, and motor. Axial-flow pump head is measured by differential pressure transmitter EJA110A with ±0.113%, and measuring sections are closed in the tanks with the inlet and outlet passages for concluding hydraulic loss of inlet and outlet sections. Torque is measured by TS-3100B digital torque and speed sensor with ±0.0203%, which is transmitted by pump shaft. Flow rate is measured by E-mag DN400 electromagnetic flowmeter with ±0.197%.Figure 3
Schematic diagram of the experimental rig:(1) axial-flow pump, (2) inlet water tank, (3) outlet water tank, (4) surge water tank, (5) electromagnetic flowmeter, (6) regulating valve, and (7) mixed-flow pump.


### 3.2. Results Comparison

According to test data, the highest efficiency of axial-flow pump is 80.39% at blade angleφ=0°, with flow rate coefficient KQ of 0.511 and head coefficient KH of 0.604. The prediction data agree with the experimental head and efficiency, as shown in Figure 4. There is a good quantitative agreement at the flow rate coefficient KQ of 0.36~0.60, with the maximum relative errors smaller than 4.0%, which demonstrates that numerical calculations simulate the pump performance accurately.Figure 4
Experimental and calculated results.


## 3.1. Test Device and Method

Physical model of axial-flow pump was tested in the Hydrodynamic Engineering Laboratory of Jiangsu Province. Figure3 shows the rig for the experimental measurements. The test apparatus consists of three sections: ① water supply section: the inlet water tank, the outlet water tank, the surge water tank, mixed-flow pump, and regulating value; ② outlet section: pressure gauge, electromagnetic flowmeter, and regulating value; and ③ pump section: axial-flow pump, composite torque detector, and motor. Axial-flow pump head is measured by differential pressure transmitter EJA110A with ±0.113%, and measuring sections are closed in the tanks with the inlet and outlet passages for concluding hydraulic loss of inlet and outlet sections. Torque is measured by TS-3100B digital torque and speed sensor with ±0.0203%, which is transmitted by pump shaft. Flow rate is measured by E-mag DN400 electromagnetic flowmeter with ±0.197%.Figure 3
Schematic diagram of the experimental rig:(1) axial-flow pump, (2) inlet water tank, (3) outlet water tank, (4) surge water tank, (5) electromagnetic flowmeter, (6) regulating valve, and (7) mixed-flow pump.


## 3.2. Results Comparison

According to test data, the highest efficiency of axial-flow pump is 80.39% at blade angleφ=0°, with flow rate coefficient KQ of 0.511 and head coefficient KH of 0.604. The prediction data agree with the experimental head and efficiency, as shown in Figure 4. There is a good quantitative agreement at the flow rate coefficient KQ of 0.36~0.60, with the maximum relative errors smaller than 4.0%, which demonstrates that numerical calculations simulate the pump performance accurately.Figure 4
Experimental and calculated results.


## 4. Results and Discussion

### 4.1. Influence of OGV on the Hydraulic Performance of Axial-Flow Pump

The hydraulic performances of axial-flow pump with seven different OGV setting angles were predicted. The OGV setting angle is in the range of −10°~+10°. The 3D models of OGV with three different setting angles are shown in Figure5.Figure 5
Schematic diagram of (a) OGV adjustment and different OGV setting angles: (b) OGV-5°, (c) OGV 0°, and (d) OGV 5°.The hydraulic performances of axial-flow pump with seven different OGV setting angles were predicted. The OGV setting angle is in the range of −10°~+10°. Figure6 shows the numerical results of pump head coefficient KH and efficiency for different flow rates. The change law of pump efficiency, head coefficient KH, and OGV setting angle is not the same in the same flow rate coefficient KQ. The OGV setting angle has great influence on the inner flow pattern of OGV and hydraulic performance of pump, and the rotor-stator interaction is complex. The OGV setting angle has great influence on the hydraulic performance of outlet passage. When the OGVs are regulated to the positive angle, the hydraulic performance will be improved in the large flow rate condition. When the OGVs are regulated to the negative angle, the hydraulic performance will be improved in the small flow rate condition. If the OGVs are regulated to the positive angle, the high efficiency area will be closed to the large flow rate condition; otherwise, the high efficiency area will be closed to the small flow rate condition. In order to eliminate the inlet incidence angle and tail flow separation of blade, the OGV setting angle should be regulated according to axial-flow pump operating conditions.Figure 6
Performance curves of (a) pump head coefficientKH and (b) efficiency for different flow rate coefficient KQ and OGVs setting angles θ.
(a)
(b)


### 4.2. Internal Flow Pattern of Axial-Flow Pump

The flow patterns in the OGV channel at low flow rate condition (KQ=0.398), high efficiency flow rate condition (KQ=0.521), and large flow rate condition (KQ=0.644) are shown in Figures 7–9. These figures show the flow patterns of OGV channel in different OGV setting angles.Figure 7
Flow pattern of OGV channel at low flow rate conditionKQ=0.398: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)Figure 8
Flow pattern of OGV channel at high efficiency flow rate conditionKQ=0.521: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)Figure 9
Flow pattern of OGV channel at large flow rate conditionKQ=0.644: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)In the low flow rate condition (KQ=0.398), the vortices appeared in the OGV suction surface from the 1/4 length of inlet edge, the backflow is in the inlet edge of blade, but the flow pattern of trailing edge is good for OGV. The hydraulic loss increases because of vortices appearing, and it is 21.41% of the pump head in KQ=0.398. With the increase of OGV setting angles to positive, the hydraulic loss increases gradually. Compared with the OGV setting angle θ=0°, the hydraulic loss increases by 38.66% and the hydraulic efficiency dropped by 3.93% in the OGV setting angle θ=10°. From Figure 7, flow separation occurs in the trailing edge of OGV blade, and it influences the flow field of the inlet region of OGV blade. The hydraulic loss increases because the flow hits the pressure surface of OGV blades. With the increase of OGV setting angles to negative, the hydraulic loss decreases firstly and then increases. Compared with the OGV setting angle θ=-2.5°, the hydraulic loss decreases by 6.41% and the hydraulic efficiency improves by 0.74%. With the increase of OGV setting angles to negative from θ=-2.5°, the area of vortex region increases gradually in the OGV suction surface, and the hydraulic loss increases and the hydraulic efficiency decreases gradually. The vortex region accounts approximately for 33.3% of the OGV suction surface area at OGV setting angle θ=-2.5°.In the high efficiency flow rate condition (KQ=0.521), the vortices appeared in the OGV suction surface from the 1/2 length of inlet edge, and the hydraulic loss of OGV accounts for 8.22% of axial-flow pump head. Compared with the OGV setting angle θ=0°, the hydraulic loss of OGV increases approximately by 55%, the hydraulic efficiency of pump decreases approximately by 1% at θ=2.5° and θ=5°, and the hydraulic loss of OGV increases by 118.55%, and the hydraulic efficiency of pump decreases by 4.86% at θ=10°. The vortex region is in the middle of OGV suction surface at θ=2.5° and θ=5°, and the vortex region extends to the inlet region of OGV blade at θ=10° from Figure 8. With the increase of OGV setting angle to negative, the hydraulic loss decreases firstly and then increases. Compared with the OGV setting angle θ=0°, the hydraulic loss decreases by 14.55% and the hydraulic efficiency improved by 1.59% at θ=-5°. With the increase of OGV setting angle to negative from θ=-5°, the hydraulic loss increases and the hydraulic efficiency decreases gradually. The vortex is in the trailing edge of OGV blade suction surface at θ=-10°. The hydraulic loss increases because flow separation is in the trailing edge of OGV blade.In the large flow rate condition (KQ=0.644), with the increase of OGV setting angles to negative, the vortex region increases gradually in the OGV pressure surface. The hydraulic loss of OGV increases gradually. Compared with the OGV setting angle θ=0°, the hydraulic loss increases by 297%, and the hydraulic efficiency of pump decreases by 17.87%. From Figure 9, the vortex region is in the OGV pressure surface from the 1/4 and the 3/4 length of inlet edge. The vortex causes the hydraulic efficiency to drop significantly. There are no vortex and flow separation around the airfoil of OGV blades at the OGV setting angles θ=0°, θ=2.5°, and θ=5°. The flow separation is in the trailing edge of OGV blade, so the hydraulic loss increases at θ=10°. The coupling effects of impeller, OGV, and outlet passage are considered in the numerical simulation of axial-flow pump. Compared with the OGV setting angle θ=0°, the hydraulic loss decreases by 14.65%, and the hydraulic efficiency of pump improved by 5.29% at the OGV setting angle θ=5°.


### 4.3. Artificial Neural Networks

In this paper, a computational tool, known as back propagation artificial neural networks (BP-ANN), is used to predict the hydraulic performance of axial-flow pump with OGVs. The network usually consists of input layer, hidden layer, and output layer. A schematic diagram of the typical three-layer feed-forward neural network architecture is shown in Figure10. The prediction mathematical model is constructed based on the modified BP-ANN. The modified BP-ANN consists of two layers of back propagation network structure. The hyperbolic tangent S-type function tansig( ) is used in the input layer and hidden layer. The pure linear function purelin( ) is used in the output layer. The neurons numbers of input layer are assumed as the samples index Ai. The repeated training of node number was carried out in the hidden layer [18], and the node numbers are assumed as Ay. The neurons numbers of output layer are assumed as Ao, so the network structure model is Ai×Ay×Ao. The BP elastic algorithm trainrp( ) was adopted for training function, and it can be used in the bulk mode training. It has fast convergence speed and calculation with small storage space. The topology structure of BP-ANN network is shown in Figure 10.Figure 10
Topology structure of BP-ANN network.The impeller torqueTp, the pump flow rate coefficient KQ, the pump head coefficient KH, and the OGVs setting angle Δθ are assumed as input variables, the neurons number of input layer is 4 and the neurons number of output layer is 1 for BP-ANN network. The neurons number of hidden layer is calculated by(14)Ay=Ai+Ao+a,where 1<a<10. The neurons number of hidden layer is 1 by using the comparative method and cut-and-try method. The network structure model is 4×9×1.The seven groups of OGVs setting angles were used to train and test the BP-ANN prediction model, and each group includes seven pump operating conditions and 49 groups of pump performance data. The 49 groups were divided into two parts: one part was used as training samples, and the other part was used to exam the BP-ANN prediction model. In order to ensure the learning precision of BP-ANN prediction model, more training samples were needed, 42 groups were chosen randomly, and the rest of data were used to test the prediction model. Normalization processing was carried out for samples firstly, and then the prediction model was trained. Function premnmx( ) was used to recode the normalization processing of input value and output value in Matlab software, so that training samples were in the range of −1 to 1.The function newff( ) was used to construct the BP-ANN prediction model by using the commercial mathematical software Matrix & Laboratory; it can be expressed by(15)net=newffP,T,S,TF,BTF,BLF,PF,IPF,OPF,DDF,where net is mesh object of BP-ANN, P is the number of input groups, T is the number of output groups, S is unit number of hidden layers, TF is the transfer function of each layer, BTF is the training function of BP-ANN, BLF is learning function of weight, PF is objective performance function, IPF is row unit array of input proceeding function, OPF is row unit array of output proceeding function, and DDF is data decomposition function.The prediction model was trained by using 42 groups of pump performances data. The trained prediction model has a good stability and satisfies the precision demands for prediction assessment. The error curve is shown in Figure11.Figure 11
Mean squared error curve of the network.In order to validate the effectiveness of prediction model, numerical results of 7 operating conditions were assumed as testing sample at the OGVs setting angleθ=5°. The comparison of predicted results and simulated results is shown in Table 1. The maximum deviation is 0.98%, the minimum deviation is 0.03%, and the average deviation is 0.35%. The prediction accuracy of BP-ANN model is below 1%, which can meet the requirement of practical engineering.Table 1
Parameters of test samples.
Input samples
Simulated results (CFD)
Predicted results (BP-ANN)
Deviation/%
Flow rate coefficientKQ
Head coefficientKH
TorqueTp
The OGVssetting angles(°)
0.337
1.005
119.942
5
65.053
65.255
0.31
0.398
0.824
105.162
5
71.913
71.892
0.03
0.460
0.671
92.795
5
76.527
76.497
0.04
0.521
0.539
80.752
5
80.076
80.043
0.04
0.582
0.365
64.514
5
75.890
76.630
0.98
0.613
0.288
54.436
5
74.546
74.478
0.09
0.644
0.175
41.081
5
63.268
62.661
0.96The pump performance is predicted by using BP-ANN model, which needs to give 4 parameters, including setting angle, flow rate coefficient, torque, and head coefficient. The functional relation surface of flow rate coefficientKQ, head coefficient KH, and the OGVs setting angles θ with a determination coefficient of 0.997, and the functional relation surface of flow rate coefficient KQ, the OGVs setting angles θ, and torque Tp with a determination coefficient of 0.998 are shown in Figure 12 by using binary nonlinear regression analysis method.Figure 12
Fitting surface of binary nonlinear functions.
(a)
θ
-
K
Q
-
K
H
(b)
θ
-
K
Q
-
T
pThe suitable OGVs setting angle can be predicted firstly according to flow rate coefficient and head coefficient based on the fitting surface of binary nonlinear function aboutKQ-KH-θ; then, the torque can be predicted according to flow rate coefficient and OGVs setting angle based on the fitting surface of binary nonlinear function about KQ-KH-Tp, and the pump hydraulic efficiency can be predicted by using BP-ANN model according to different OGVs setting angles.As shown in Figure13, if the guide vane inlet attack angle αj=0, the OGVs suitable angle β will be calculated by(16)v1a=QπRs2-Rh2,β=arctan⁡v1ak0v1u,k0=1-ZS1uπDc,where k0 is the crowding coefficient at the entrance of OGVs, v1a is the axial velocity at the entrance of OGVs, v1u is the circumferential component of absolute velocity at the entrance of OGVs, and S1u is the circulation thickness of blade at the OGVs inlet.Figure 13
Schematic diagram of OGV adjustment.The OGVs suitable angles are intended to maintain the shock free flow pattern. The schematic diagram of OGV is shown in Figure13. The basic idea of the OGV is that the guide vane inlet flow angle αj should be adjusted according to the impeller outlet flow angle βc to reduce hydraulic loss. The impeller outlet flow angle βc can be derived from the velocity triangle when the blade angle and flow rate are known, as shown in Figure 13. According to theorem of moment of momentum about impeller outlet flow and guide vane inlet flow v1uRd=v0uRy, if the radius of OGV calculation flow surface is relative to impeller calculation flow surface, v1u will be equal to v0u. The formula of αc can be derived from the velocity triangle and discharge as follows [19]:(17)αc=arctan⁡60Q2π2Rc2-rc2Rcn-60Qcotβc,where Rc is the radius of pump case at the impeller outlet, rc is the radius of hub at the impeller outlet, and n is the impeller rotation speed.If the hydraulic loss is minimum, the OGVs suitable angleβ will be equal to αj and αc. The OGVs suitable angle β can be written as follows:(18)β=arctan⁡πDctan⁡αcπDc-ZS1u;S1u=S1sin⁡β,where S1 is the blade thickness at the impeller inlet.The OGVs setting angleθ is calculated by (19)θ=β-βd,where β is the OGVs suitable angle and βd is OGVs fixed angle.The OGVs setting angleθ can be calculated based on the flow rate coefficient KQ and head coefficient KH; then, the torque Tp is calculated based on the OGVs setting angle θ and the flow rate coefficient KQ. The three operating conditions (KQ=0.521, 0.552, and 0.664) were chosen for verifying the BP-ANN model. The calculation results are shown in Table 2 based on the OGV fixed angle formula given in [19] and binary nonlinear function.Table 2
Adjustable angles of outlet guide vane and performance of pumping system.
Flow rate coefficientKQ
Head coefficientKH
OGV
Setting anglesθ/(°)
Torque (N·m)
Efficiency/(%)
Suitable angleβ/(°)
Fixed angleβ/(°)
0.521
0.541
59.64
64.8
−5.16
77.825
83.55
0.552
0.458
63.31
64.8
1.49
72.081
80.79
0.664
0.171
68.53
64.8
3.73
40.360
60.96The predicted efficiency is closer to calculated efficiencyη=82.67% by CFD at the OGV setting angle θ=-5°, and the absolute deviation is less than 1%. The difference is because the rotor-stator interaction is not considered in the OGV setting angle formulae (17)–(19).In order to verify the feasibility of predication method, the internal flow of axial-flow pump was simulated by ANSYS CFX atKQ=0.552 for the OGV setting angle θ=1.49°. The Vector graph of airfoil flow of OGV is shown in Figure 14. There are no vortex and flow separation around the airfoil. The pump efficiency is 81.12% based on the simulated results; the difference value is 0.41%, compared with predicted results η=80.79% in Table 2. The pump efficiency η=83.55%, and the OGV setting angle θ=-5.16° in the flow rate coefficient KQ=0.521.Figure 14
Vector graph of airfoil flow (KQ=0.552).


## 4.1. Influence of OGV on the Hydraulic Performance of Axial-Flow Pump

The hydraulic performances of axial-flow pump with seven different OGV setting angles were predicted. The OGV setting angle is in the range of −10°~+10°. The 3D models of OGV with three different setting angles are shown in Figure5.Figure 5
Schematic diagram of (a) OGV adjustment and different OGV setting angles: (b) OGV-5°, (c) OGV 0°, and (d) OGV 5°.The hydraulic performances of axial-flow pump with seven different OGV setting angles were predicted. The OGV setting angle is in the range of −10°~+10°. Figure6 shows the numerical results of pump head coefficient KH and efficiency for different flow rates. The change law of pump efficiency, head coefficient KH, and OGV setting angle is not the same in the same flow rate coefficient KQ. The OGV setting angle has great influence on the inner flow pattern of OGV and hydraulic performance of pump, and the rotor-stator interaction is complex. The OGV setting angle has great influence on the hydraulic performance of outlet passage. When the OGVs are regulated to the positive angle, the hydraulic performance will be improved in the large flow rate condition. When the OGVs are regulated to the negative angle, the hydraulic performance will be improved in the small flow rate condition. If the OGVs are regulated to the positive angle, the high efficiency area will be closed to the large flow rate condition; otherwise, the high efficiency area will be closed to the small flow rate condition. In order to eliminate the inlet incidence angle and tail flow separation of blade, the OGV setting angle should be regulated according to axial-flow pump operating conditions.Figure 6
Performance curves of (a) pump head coefficientKH and (b) efficiency for different flow rate coefficient KQ and OGVs setting angles θ.
(a)
(b)


## 4.2. Internal Flow Pattern of Axial-Flow Pump

The flow patterns in the OGV channel at low flow rate condition (KQ=0.398), high efficiency flow rate condition (KQ=0.521), and large flow rate condition (KQ=0.644) are shown in Figures 7–9. These figures show the flow patterns of OGV channel in different OGV setting angles.Figure 7
Flow pattern of OGV channel at low flow rate conditionKQ=0.398: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)Figure 8
Flow pattern of OGV channel at high efficiency flow rate conditionKQ=0.521: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)Figure 9
Flow pattern of OGV channel at large flow rate conditionKQ=0.644: (a) OGV -10°, (b) OGV -5°, (c) OGV -2.5°, (d) OGV 0°, (e) OGV 2.5°, (f) OGV 5°, and (g) OGV 10°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)In the low flow rate condition (KQ=0.398), the vortices appeared in the OGV suction surface from the 1/4 length of inlet edge, the backflow is in the inlet edge of blade, but the flow pattern of trailing edge is good for OGV. The hydraulic loss increases because of vortices appearing, and it is 21.41% of the pump head in KQ=0.398. With the increase of OGV setting angles to positive, the hydraulic loss increases gradually. Compared with the OGV setting angle θ=0°, the hydraulic loss increases by 38.66% and the hydraulic efficiency dropped by 3.93% in the OGV setting angle θ=10°. From Figure 7, flow separation occurs in the trailing edge of OGV blade, and it influences the flow field of the inlet region of OGV blade. The hydraulic loss increases because the flow hits the pressure surface of OGV blades. With the increase of OGV setting angles to negative, the hydraulic loss decreases firstly and then increases. Compared with the OGV setting angle θ=-2.5°, the hydraulic loss decreases by 6.41% and the hydraulic efficiency improves by 0.74%. With the increase of OGV setting angles to negative from θ=-2.5°, the area of vortex region increases gradually in the OGV suction surface, and the hydraulic loss increases and the hydraulic efficiency decreases gradually. The vortex region accounts approximately for 33.3% of the OGV suction surface area at OGV setting angle θ=-2.5°.In the high efficiency flow rate condition (KQ=0.521), the vortices appeared in the OGV suction surface from the 1/2 length of inlet edge, and the hydraulic loss of OGV accounts for 8.22% of axial-flow pump head. Compared with the OGV setting angle θ=0°, the hydraulic loss of OGV increases approximately by 55%, the hydraulic efficiency of pump decreases approximately by 1% at θ=2.5° and θ=5°, and the hydraulic loss of OGV increases by 118.55%, and the hydraulic efficiency of pump decreases by 4.86% at θ=10°. The vortex region is in the middle of OGV suction surface at θ=2.5° and θ=5°, and the vortex region extends to the inlet region of OGV blade at θ=10° from Figure 8. With the increase of OGV setting angle to negative, the hydraulic loss decreases firstly and then increases. Compared with the OGV setting angle θ=0°, the hydraulic loss decreases by 14.55% and the hydraulic efficiency improved by 1.59% at θ=-5°. With the increase of OGV setting angle to negative from θ=-5°, the hydraulic loss increases and the hydraulic efficiency decreases gradually. The vortex is in the trailing edge of OGV blade suction surface at θ=-10°. The hydraulic loss increases because flow separation is in the trailing edge of OGV blade.In the large flow rate condition (KQ=0.644), with the increase of OGV setting angles to negative, the vortex region increases gradually in the OGV pressure surface. The hydraulic loss of OGV increases gradually. Compared with the OGV setting angle θ=0°, the hydraulic loss increases by 297%, and the hydraulic efficiency of pump decreases by 17.87%. From Figure 9, the vortex region is in the OGV pressure surface from the 1/4 and the 3/4 length of inlet edge. The vortex causes the hydraulic efficiency to drop significantly. There are no vortex and flow separation around the airfoil of OGV blades at the OGV setting angles θ=0°, θ=2.5°, and θ=5°. The flow separation is in the trailing edge of OGV blade, so the hydraulic loss increases at θ=10°. The coupling effects of impeller, OGV, and outlet passage are considered in the numerical simulation of axial-flow pump. Compared with the OGV setting angle θ=0°, the hydraulic loss decreases by 14.65%, and the hydraulic efficiency of pump improved by 5.29% at the OGV setting angle θ=5°.


## 4.3. Artificial Neural Networks

In this paper, a computational tool, known as back propagation artificial neural networks (BP-ANN), is used to predict the hydraulic performance of axial-flow pump with OGVs. The network usually consists of input layer, hidden layer, and output layer. A schematic diagram of the typical three-layer feed-forward neural network architecture is shown in Figure10. The prediction mathematical model is constructed based on the modified BP-ANN. The modified BP-ANN consists of two layers of back propagation network structure. The hyperbolic tangent S-type function tansig( ) is used in the input layer and hidden layer. The pure linear function purelin( ) is used in the output layer. The neurons numbers of input layer are assumed as the samples index Ai. The repeated training of node number was carried out in the hidden layer [18], and the node numbers are assumed as Ay. The neurons numbers of output layer are assumed as Ao, so the network structure model is Ai×Ay×Ao. The BP elastic algorithm trainrp( ) was adopted for training function, and it can be used in the bulk mode training. It has fast convergence speed and calculation with small storage space. The topology structure of BP-ANN network is shown in Figure 10.Figure 10
Topology structure of BP-ANN network.The impeller torqueTp, the pump flow rate coefficient KQ, the pump head coefficient KH, and the OGVs setting angle Δθ are assumed as input variables, the neurons number of input layer is 4 and the neurons number of output layer is 1 for BP-ANN network. The neurons number of hidden layer is calculated by(14)Ay=Ai+Ao+a,where 1<a<10. The neurons number of hidden layer is 1 by using the comparative method and cut-and-try method. The network structure model is 4×9×1.The seven groups of OGVs setting angles were used to train and test the BP-ANN prediction model, and each group includes seven pump operating conditions and 49 groups of pump performance data. The 49 groups were divided into two parts: one part was used as training samples, and the other part was used to exam the BP-ANN prediction model. In order to ensure the learning precision of BP-ANN prediction model, more training samples were needed, 42 groups were chosen randomly, and the rest of data were used to test the prediction model. Normalization processing was carried out for samples firstly, and then the prediction model was trained. Function premnmx( ) was used to recode the normalization processing of input value and output value in Matlab software, so that training samples were in the range of −1 to 1.The function newff( ) was used to construct the BP-ANN prediction model by using the commercial mathematical software Matrix & Laboratory; it can be expressed by(15)net=newffP,T,S,TF,BTF,BLF,PF,IPF,OPF,DDF,where net is mesh object of BP-ANN, P is the number of input groups, T is the number of output groups, S is unit number of hidden layers, TF is the transfer function of each layer, BTF is the training function of BP-ANN, BLF is learning function of weight, PF is objective performance function, IPF is row unit array of input proceeding function, OPF is row unit array of output proceeding function, and DDF is data decomposition function.The prediction model was trained by using 42 groups of pump performances data. The trained prediction model has a good stability and satisfies the precision demands for prediction assessment. The error curve is shown in Figure11.Figure 11
Mean squared error curve of the network.In order to validate the effectiveness of prediction model, numerical results of 7 operating conditions were assumed as testing sample at the OGVs setting angleθ=5°. The comparison of predicted results and simulated results is shown in Table 1. The maximum deviation is 0.98%, the minimum deviation is 0.03%, and the average deviation is 0.35%. The prediction accuracy of BP-ANN model is below 1%, which can meet the requirement of practical engineering.Table 1
Parameters of test samples.
Input samples
Simulated results (CFD)
Predicted results (BP-ANN)
Deviation/%
Flow rate coefficientKQ
Head coefficientKH
TorqueTp
The OGVssetting angles(°)
0.337
1.005
119.942
5
65.053
65.255
0.31
0.398
0.824
105.162
5
71.913
71.892
0.03
0.460
0.671
92.795
5
76.527
76.497
0.04
0.521
0.539
80.752
5
80.076
80.043
0.04
0.582
0.365
64.514
5
75.890
76.630
0.98
0.613
0.288
54.436
5
74.546
74.478
0.09
0.644
0.175
41.081
5
63.268
62.661
0.96The pump performance is predicted by using BP-ANN model, which needs to give 4 parameters, including setting angle, flow rate coefficient, torque, and head coefficient. The functional relation surface of flow rate coefficientKQ, head coefficient KH, and the OGVs setting angles θ with a determination coefficient of 0.997, and the functional relation surface of flow rate coefficient KQ, the OGVs setting angles θ, and torque Tp with a determination coefficient of 0.998 are shown in Figure 12 by using binary nonlinear regression analysis method.Figure 12
Fitting surface of binary nonlinear functions.
(a)
θ
-
K
Q
-
K
H
(b)
θ
-
K
Q
-
T
pThe suitable OGVs setting angle can be predicted firstly according to flow rate coefficient and head coefficient based on the fitting surface of binary nonlinear function aboutKQ-KH-θ; then, the torque can be predicted according to flow rate coefficient and OGVs setting angle based on the fitting surface of binary nonlinear function about KQ-KH-Tp, and the pump hydraulic efficiency can be predicted by using BP-ANN model according to different OGVs setting angles.As shown in Figure13, if the guide vane inlet attack angle αj=0, the OGVs suitable angle β will be calculated by(16)v1a=QπRs2-Rh2,β=arctan⁡v1ak0v1u,k0=1-ZS1uπDc,where k0 is the crowding coefficient at the entrance of OGVs, v1a is the axial velocity at the entrance of OGVs, v1u is the circumferential component of absolute velocity at the entrance of OGVs, and S1u is the circulation thickness of blade at the OGVs inlet.Figure 13
Schematic diagram of OGV adjustment.The OGVs suitable angles are intended to maintain the shock free flow pattern. The schematic diagram of OGV is shown in Figure13. The basic idea of the OGV is that the guide vane inlet flow angle αj should be adjusted according to the impeller outlet flow angle βc to reduce hydraulic loss. The impeller outlet flow angle βc can be derived from the velocity triangle when the blade angle and flow rate are known, as shown in Figure 13. According to theorem of moment of momentum about impeller outlet flow and guide vane inlet flow v1uRd=v0uRy, if the radius of OGV calculation flow surface is relative to impeller calculation flow surface, v1u will be equal to v0u. The formula of αc can be derived from the velocity triangle and discharge as follows [19]:(17)αc=arctan⁡60Q2π2Rc2-rc2Rcn-60Qcotβc,where Rc is the radius of pump case at the impeller outlet, rc is the radius of hub at the impeller outlet, and n is the impeller rotation speed.If the hydraulic loss is minimum, the OGVs suitable angleβ will be equal to αj and αc. The OGVs suitable angle β can be written as follows:(18)β=arctan⁡πDctan⁡αcπDc-ZS1u;S1u=S1sin⁡β,where S1 is the blade thickness at the impeller inlet.The OGVs setting angleθ is calculated by (19)θ=β-βd,where β is the OGVs suitable angle and βd is OGVs fixed angle.The OGVs setting angleθ can be calculated based on the flow rate coefficient KQ and head coefficient KH; then, the torque Tp is calculated based on the OGVs setting angle θ and the flow rate coefficient KQ. The three operating conditions (KQ=0.521, 0.552, and 0.664) were chosen for verifying the BP-ANN model. The calculation results are shown in Table 2 based on the OGV fixed angle formula given in [19] and binary nonlinear function.Table 2
Adjustable angles of outlet guide vane and performance of pumping system.
Flow rate coefficientKQ
Head coefficientKH
OGV
Setting anglesθ/(°)
Torque (N·m)
Efficiency/(%)
Suitable angleβ/(°)
Fixed angleβ/(°)
0.521
0.541
59.64
64.8
−5.16
77.825
83.55
0.552
0.458
63.31
64.8
1.49
72.081
80.79
0.664
0.171
68.53
64.8
3.73
40.360
60.96The predicted efficiency is closer to calculated efficiencyη=82.67% by CFD at the OGV setting angle θ=-5°, and the absolute deviation is less than 1%. The difference is because the rotor-stator interaction is not considered in the OGV setting angle formulae (17)–(19).In order to verify the feasibility of predication method, the internal flow of axial-flow pump was simulated by ANSYS CFX atKQ=0.552 for the OGV setting angle θ=1.49°. The Vector graph of airfoil flow of OGV is shown in Figure 14. There are no vortex and flow separation around the airfoil. The pump efficiency is 81.12% based on the simulated results; the difference value is 0.41%, compared with predicted results η=80.79% in Table 2. The pump efficiency η=83.55%, and the OGV setting angle θ=-5.16° in the flow rate coefficient KQ=0.521.Figure 14
Vector graph of airfoil flow (KQ=0.552).


## 5. Conclusion

Simulations of the three-dimensional steady flow in an axial-flow pump with OGV were conducted using the commercial CFD software ANSYS CFX, and the BP-ANN prediction model was established firstly about the effect of adjustable outlet guide vane on the hydraulic performance of axial-flow pump. The results show the following:(1)
The mathematical model used in this paper can accurately simulate the flow field inside the axial-flow pump. The computationalKQ-KH curves agree well with the experimental ones.(2)
The internal flow field of guide vane is improved by adjusting angle, and the flow separation of tail and guide vane inlet ledge are decreased or eliminated, so that the hydraulic efficiency of pumping system will be improved.(3)
The adjustable outlet guide vane can significantly improve the head and efficiency of the pump at off-design conditions. If the OGVs are regulated to the positive angle, the high efficiency area will be closed to the large flow rate condition; otherwise, the high efficiency area will be closed to the small flow rate condition.(4)
BP-ANN prediction model is established firstly about the effect of adjustable outlet guide vane on the hydraulic performance of axial-flow pump. The prediction accuracy of BP-ANN model is 1%, which can meet the requirement of practical engineering.



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*Source: 6375314-2016-02-04.xml*