Helical axial-flow multiphase pumps are core devices for developing deep-sea oil and gas, but the complex two-phase flow inside such pumps affects their transport stability. As reported here, for enhanced flow characteristics, splitter blades were added at the noncoincidence area of the impeller tail by using a multi-objective optimization method, and their impact on the pump performance was explored in comparison with the original model. The results indicate that Gaussian process regression combined with particle swarm optimization accurately predicts the pump external characteristics. Under an inlet gas volume fraction of 30%, the optimized model increases the head coefficient by 22.2% without reducing efficiency. Although splitter blades enhance the impeller tail, they intensify gas-phase accumulation at the tail. The optimized model promotes more-uniform two-phase flow in the channels, with the axial velocity uniformity of the gas phase and liquid phase improving by 15.1% and 9.5% and the average velocity angle increasing by 12.3° and 8.3° under an inlet gas volume fraction of 30%.

With rapid socioeconomic development, the average annual consumption rate of oil and gas resources has reached 3% of the total resource consumption.1 The extraction rate of onshore oil and gas resources cannot keep up with consumption, prompting attention to submarine reserves as vital future sources. As crucial devices for developing deep-sea oil and gas fields, helical axial-flow multiphase pumps can adapt to complex conditions in oil fields.2 However, the intricate interactions among different phases inside such pumps result in complex and variable internal flows that impact the transport performance. Therefore, further research is necessary to ensure the efficient and stable operation of multiphase pumps.

Research on helical axial-flow multiphase pumps has spanned many years. Among the earliest initiatives, the Poseidon Project investigated blade operation principles in transporting mixed media and the impacts of different operational conditions on internal flow states.3 Over years of study, scholars have summarized design methods for multiphase pumps and developed pumps with significantly improved efficiency, nearly doubling oil and gas production.4 Subsequently, researchers proposed new designs. Zhang et al.5 suggested a scheme based on the velocity gradient equation and conducted experimental research, developing an impeller suitable for high-flow conditions. Cao et al.6 proposed a combined forward and reverse problem approach, validating its effectiveness through comparative experiments. Because of the complexity of two-phase flow, scholars have applied optimization methods such as orthogonal experimental design,7 response surface methodology,8 and intelligent algorithms9 to enhance existing pump performance and verify reliability. Zhang et al.10 proposed three modification schemes to improve gas entrapment within blade-type multiphase pumps, i.e., adding splitter blades, blade perforation, and T-shaped blades, and numerical calculations confirmed that each method enhances the pressure boosting capabilities compared to the original impeller. Xu et al.11 added splitter blades to the impeller tail of multiphase pumps, monitoring the internal pressures to reveal the transient pressure characteristics of such pumps. Via numerical calculations, Xiao et al.12 showed that splitter blades offer enhanced impeller control over the flow dynamics at the trailing edge.

However, although the performance of multiphase pumps has been improved significantly via modifications, their internal mechanisms have not been fully revealed. To gain a deeper understanding of these internal flow mechanisms, Zhang et al.13 used an improved Eulerian two-fluid model to simulate a two-stage multiphase pump numerically, comparing different conditions for the inlet gas volume fraction (GVF) and liquid media; they found that resistance is relatively sensitive to inlet GVF. Yuan et al.14 analyzed the gas-phase distribution in the flow field, identifying differing centrifugal forces on the gas and liquid phases as the primary cause of phase separation. Via separation coefficients, Li et al.15 explained that gas–liquid separation is less likely to occur in the flow direction, with significantly higher coefficients on the blade suction side than on the pressure side in the blade height direction. Using dynamic mode decomposition, Liu et al.16 analyzed the transient characteristics in a multiphase pump at 20% inlet GVF; they observed jet impacts at the impeller exit, leading to the formation of air pockets in the guide vanes, and dynamic modal analysis indicated that radial nonuniformities near the impeller pressure side and recirculation near the guide-vane suction side are major features of the pump flow field.

The performance of multiphase pumps deteriorates with increasing GVF, and the noncoincidence area of the impeller lacks control over the fluid dynamics. Therefore, the aim herein is to improve the transportation performance by adding splitter blades in the noncoincidence area at the impeller outlet. First, a multiphase pump with splitter blades is constructed based on multi-objective optimization. Second, an analysis of the internal flow field elucidates the mechanisms through which splitter blades influence the performance of the multiphase pump. Finally, the axial velocity uniformity and average velocity angle are introduced to quantify the flow uniformity state at the impeller cross section. This study provides a reference for enhancing the performance of multiphase pumps by adding splitter blades.

1. Original model

As shown schematically in Fig. 1, the focus here in on the developed single-stage helical axial-flow multiphase pump model. Figure 1 shows the main geometric parameters, and Table I lists the primary design parameters.

FIG. 1.

Meridional plane of multiphase pump.

FIG. 1.

Meridional plane of multiphase pump.

Close modal
TABLE I.

Design parameters of multiphase pump.

ItemValue
Rotational speed 4500 rpm 
Rated flow rate 100 m3/h 
Number of impeller blades 
Number of diffuser blades 17 
ItemValue
Rotational speed 4500 rpm 
Rated flow rate 100 m3/h 
Number of impeller blades 
Number of diffuser blades 17 

2. Splitter-blade structural parameters

Figure 2 shows the blade spacing at the impeller shroud. Introducing splitter blades in the noncoincidence area of the outlet causes the channel to separate into three sections: region A transitions into a new coincidence area, while regions B and C transform into new noncoincidence areas. The primary parameters influencing the splitter-blade geometry are the offset angle (S), which is the deflection angle of the main blade’s pressure side in the circumferential direction, the inlet installation angle of the splitter blade (βin,splitter), and the outlet installation angle of the splitter blade (βout,splitter). The splitter blades adopt the 791-airfoil profile and maintain consistency in camber ratio with the original model. To ensure that the splitter blades fill the entire noncoincidence areas, their chord length is set to 40% of the main blade’s chord length.

FIG. 2.

Geometric parameters of splitter blades.

FIG. 2.

Geometric parameters of splitter blades.

Close modal

The single-stage helical axial-flow multiphase pump comprises one impeller and one guide vane. In the numerical calculations, polyhedral meshing was used to divide the computational domain. The mesh was refined locally around the impeller and guide-vane blades to balance computational accuracy with reduced mesh size. Figure 3 shows the mesh distribution across the fluid computational domain, highlighting compressed cells.

FIG. 3.

Computational domain and mesh distribution.

FIG. 3.

Computational domain and mesh distribution.

Close modal

To ensure that the computational results were unaffected by mesh density, five different meshes were designed to verify mesh independence, with the total number of mesh points ranging from 2.64 × 106 to 4.26 × 106. Numerical calculations were conducted under the conditions of pure liquid (GVF = 0) and gas–liquid two-phase flow (GVF = 30%). Given the impeller and guide vane’s critical role in pressurization, mesh independence was verified by varying the mesh density around these components while maintaining consistent meshes for the inlet and outlet extensions. Table II details the meshes and the corresponding numerical calculation results for the head and efficiency. Beyond 3.53 × 106 mesh points, both the head and efficiency stabilized, so mesh 3 was selected for the subsequent modeling.

TABLE II.

Settings and results of independence test of mesh elements.

ItemMesh 1Mesh 2Mesh 3Mesh 4Mesh 5
Inlet pipe 372 107 372 107 372 107 372 107 372 107 
Impeller 1 023 872 1 248 359 1 486 256 1 684 528 1 835 647 
Diffuser 872 648 1 018 790 1 298 237 1 510 506 1 675 238 
Outlet pipe 372 107 372 107 372 107 372 107 372 107 
Total 2.64 × 106 3.01 × 106 3.53 × 106 3.94 × 106 4.26 × 106 
GVF = 0 Head (m) 34.74 35.48 35.97 36.16 35.99 
Efficiency (%) 74.18 74.21 74.56 74.61 74.52 
GVF = 30% Head (m) 21.15 22.34 23.06 22.98 23.04 
Efficiency (%) 65.97 66.54 66.94 67.08 67.01 
ItemMesh 1Mesh 2Mesh 3Mesh 4Mesh 5
Inlet pipe 372 107 372 107 372 107 372 107 372 107 
Impeller 1 023 872 1 248 359 1 486 256 1 684 528 1 835 647 
Diffuser 872 648 1 018 790 1 298 237 1 510 506 1 675 238 
Outlet pipe 372 107 372 107 372 107 372 107 372 107 
Total 2.64 × 106 3.01 × 106 3.53 × 106 3.94 × 106 4.26 × 106 
GVF = 0 Head (m) 34.74 35.48 35.97 36.16 35.99 
Efficiency (%) 74.18 74.21 74.56 74.61 74.52 
GVF = 30% Head (m) 21.15 22.34 23.06 22.98 23.04 
Efficiency (%) 65.97 66.54 66.94 67.08 67.01 
The software FLUENT was used for the numerical calculations, with the Euler–Euler method used to calculate the flow field.17 In this model, different phases are treated mathematically as interpenetrating continuous phases. The equations for the conservation of mass and momentum are
(1)
(2)
where i represents either the liquid phase (l) or the gas phase (g); ρi and αi are the density and volume fraction of phase i, respectively; vector ui is the Cartesian velocity; Si and SMi respectively represent the transfer of gas-phase mass and momentum during bubble rupture and coalescence; Mi is the total force acting between the gas and liquid phases; τ is the stress tensor.

The impeller blades of the multiphase pump have significant curvature and operate at high speeds. To calculate the complex flow in the multiphase pump accurately, this study used the kω shear stress transport model,18 which not only enhances the accuracy of fluid calculation near walls but also effectively predicts flow separation induced by adverse pressure gradients.19 

During the operation of the multiphase pump, various interactions occur between the fluid and particle phases, primarily involving drag and lift forces. Herein, these forces are used to describe the momentum transfer between the continuous and particle phases. The drag model is the Schiller–Naumann model, and the lift model is the Tomiyama model.20 

As bubbles move in the multiphase pump, they continuously aggregate and rupture; the population balance model is used to calculate bubble rupture and aggregation and to determine the number and size distribution of bubbles in the flow field.21 The mass transfer of bubbles is determined by Eq. (3). Based on previous experimental studies where the bubble diameters inside the pump were 0.1–10 mm,22 this paper selects ten different bubble sizes. The formulas for bubble-size calculation are Eqs. (4) and (5), and the computed results are presented in Table III. The aforementioned equations are
(3)
(4)
(5)
where BB is the production rate of bubbles from the fragmentation of larger particles, DB is the mortality rate of bubbles from the fragmentation of larger particles, BC is the production rate of bubbles from the aggregation of smaller particles, and DC is the mortality rate of bubbles from the aggregation of smaller particles; VN and dN are the bubble volume and diameter, respectively, with N = 0–9 denoting the bubble group.
TABLE III.

Diameters of bubble groups.

Bubble groupd0d1d2d3d4d5d6d7d8d9
Value (mm) 0.10 0.17 0.28 0.46 0.76 1.27 2.11 3.51 5.84 9.70 
Bubble groupd0d1d2d3d4d5d6d7d8d9
Value (mm) 0.10 0.17 0.28 0.46 0.76 1.27 2.11 3.51 5.84 9.70 
We assume that the inlet gas–liquid mixture is bubbly flow with equal velocities for both phases, where the liquid phase is incompressible and the gas phase is an ideal gas that is insoluble in the liquid phase. The inlet bubble diameter is calculated according to23 
(6)
where ωn is the angular velocity, λ is the GVF, representing the ratio of gas volume flow rate to mixture volume flow rate, σ is the measured surface tension, and r1 is the hub radius of the impeller. The inlet is set as a velocity inlet with its value determined to be 3.43 m/s based on the design flow rate; the outlet is set as a pressure outlet. The interface between moving and stationary parts adopts the frozen rotor method, and all walls are specified as no-slip walls. Convergence is achieved when residuals are less than 10−5.

To validate the accuracy of the numerical calculations, experiments were conducted on a single-stage helical axial-flow multiphase pump, as shown in Fig. 4. The experimental setup comprised a gas–liquid mixer, a multiphase pump, a piping system, and various measuring instruments. During an experiment, the rotation speed of the pump was regulated by an electromotor, and an air compressor was used to pressurize the gas. The flow rate of liquid was regulated by the liquid inlet valve and the flowmeter, and the gas flow rate into the pipeline was regulated by the air flowmeter and air inlet valve. The gas and liquid were mixed in the mixer to form a homogeneous two-phase flow that was then pressurized by a multiphase pump before entering the tank.

FIG. 4.

Test bench: 1—water tank; 2—air tank; 3—gas–liquid mixer; 4—multiphase pump; 5—console; 6—electromotor; 7—air compressor; 8—flowmeter.

FIG. 4.

Test bench: 1—water tank; 2—air tank; 3—gas–liquid mixer; 4—multiphase pump; 5—console; 6—electromotor; 7—air compressor; 8—flowmeter.

Close modal
Under a rotational speed of 4500 rpm and a volumetric flow rate of 100 m3/h, experiments were conducted by controlling the inlet GVF at a gas content of zero, 10%, 20%, and 30%. After obtaining the corresponding data using pressure gauges and flow meters, the head and efficiency of the multiphase pump were calculated using Eqs. (7)(9), and numerical calculations were performed under the respective operating conditions. The numerical results are compared with the experimental data for performance characteristics, as shown in Fig. 5. As can be seen, the numerical results tend to exceed the experimental results, primarily because of neglecting volumetric losses. Moreover, the errors increase with higher GVF as the bubbly flow transitioned to churn flow, amplifying the discrepancies between the interphase force models and actual conditions. The largest errors occurred under 30% GVF, with the head and efficiency errors reaching 9.86% and 4.58%, respectively. Overall, the discrepancies in the performance characteristics are within 10%, meeting engineering standards. The aforementioned equations are
(7)
(8)
(9)
where pin and pout are the inlet and outlet pressures of the compression unit; vin and vout are the inlet and outlet velocities of the compression unit; ρmix is the density of the gas–liquid mixture; M is the torque of the multiphase pump impeller; ω is the rotational angular velocity; η is the efficiency; H is the head.
FIG. 5.

Comparison of experimental and numerical results.

FIG. 5.

Comparison of experimental and numerical results.

Close modal

Here, we establish the relationship between the parameters of the multiphase pump and the head coefficient and efficiency via Gaussian process regression (GPR), and from multi-objective optimization we obtain a multiphase pump with splitter blades that exhibits superior external characteristics compared to the original model. First, we use theoretical analysis to determine which geometric parameters to optimize: we use a Plackett–Burman design to select the parameters that most affect the external characteristics of the multiphase pump, then we subject them to Latin hypercube sampling (LHS). Second, we subject the sample data to three-dimensional modeling and numerical calculations to build a database, then we use GPR to predict the transport performance of the multiphase pump and particle swarm optimization (PSO) to optimize its structural parameters, obtaining the Pareto front. Finally, the optimized model is evaluated numerically to obtain the errors between the computational fluid dynamics (CFD) results and the GPR predictions, thereby verifying the accuracy of GPR. The surrogate model and the optimization experiments were implemented using Python, and the primary optimization process is shown in Fig. 6.

FIG. 6.

Flow chart of splitter-blade design.

FIG. 6.

Flow chart of splitter-blade design.

Close modal
Adding splitter blades increases the exclusion coefficient Φ, which affects the inlet axial velocity vm, thereby increasing the flow coefficient Θ. The corresponding formulas are
(10)
(11)
(12)
where f is the wing area; δmax is the maximum blade thickness; t is the pitch; βL is the blade installation angle; Dt and Dh are the rim diameter and hub diameter, respectively; vm and u are the inlet axial velocity and circumferential velocity, respectively.

To ensure miniaturization of the multiphase pump, we do not discuss changes in rotational speed and rim diameter. Equation (12) shows that changing the axial velocity can reduce the flow coefficient, and Eq. (11) shows that the main factors affecting the axial velocity are the flow area and the exclusion coefficient. Starting from the perspective of flow area, changing the hub half-cone angle can alter the impeller outlet flow area and thus adjust the flow coefficient. From the perspective of the exclusion coefficient, reducing the blade area can be achieved by changing the inlet and outlet installation angles, the number of blades, and the blade thickness. To ensure the reliability of the impeller structure, only the installation angles at the inlet and outlet of the main blades are considered. For the inlet installation angle of the splitter blades, the initial value is set to be the same as that of the main blades at the corresponding axial position. For the guide vanes, because the outlet installation angle determines the inflow conditions of the next impeller stage, no changes are made, and only the inlet installation angle and number of guide-vane blades are considered. The range of parameters is determined based on a 20% upstream and downstream variation from the initial value, while also satisfying the design requirements for the impeller, as shown in Table IV.

TABLE IV.

Preliminarily selected parameters.

ParameterOriginal valueRange
Inlet placement angle of main blade, βin,main (deg) 10 8–12 
Outlet placement angle of main blade, βout,main (deg) 14 13–17 
Inlet placement angle of guide vane, βin,g (deg) 38 35–45 
Number of guide vanes, Z2 17 11–17 
Inlet placement angle of splitter blade, βin,splitter (deg) 13 8–16 
Outlet placement angle of splitter blade, βout,splitter (deg) 22 17–25 
Offset angle, S (deg) 35 20–55 
Hub half-cone angle, γ (deg) 4–8 
ParameterOriginal valueRange
Inlet placement angle of main blade, βin,main (deg) 10 8–12 
Outlet placement angle of main blade, βout,main (deg) 14 13–17 
Inlet placement angle of guide vane, βin,g (deg) 38 35–45 
Number of guide vanes, Z2 17 11–17 
Inlet placement angle of splitter blade, βin,splitter (deg) 13 8–16 
Outlet placement angle of splitter blade, βout,splitter (deg) 22 17–25 
Offset angle, S (deg) 35 20–55 
Hub half-cone angle, γ (deg) 4–8 
Optimizing multiple parameters simultaneously increases the workload significantly and can be time-consuming. Therefore, the first step is to identify the parameters that affect the performance of the multiphase pump most significantly. In 1964, Plackett and Burman proposed a two-level screening experiment (Plackett–Burman design method) that can reduce the number of experiments while rapidly and effectively determining the significance and sensitivity of factors.24 Herein, the eight aforementioned design parameters are used as control variables, resulting in the design of 20 experiments for CFD calculations. To better describe the variation of the external characteristics of the multiphase pump, the head coefficient ψ is introduced to describe the variation of head, as shown in Eq. (13). A reliability analysis of the numerical calculation results was performed via hypothesis testing, where if P < 0.1 (T > 1.812), then the parameter is considered significant.25 As Fig. 7 shows, four parameters were identified as significant parameters and are considered to have the same sensitivity. The optimization region for each parameter is as follows: βin,main ∈ (7, 13), βout,main ∈ (14, 18), βout,splitter ∈ (17, 25), γ ∈ (3, 7); the remaining parameters are set according to βin,g = 40°, Z2 = 11, βin,splitter = 16°, and S = 35°. The aforementioned equation is
(13)
where g is the local gravitational acceleration and u2 is the circumferential velocity at the impeller outlet.
FIG. 7.

Pareto chart of Plackett–Burman design.

FIG. 7.

Pareto chart of Plackett–Burman design.

Close modal

Before establishing the surrogate model, it is necessary to build a database, and LHS can adequately reflect the basic characteristics of the sample space with fewer sample points.26 In this study, 41 sample points were selected, and the data were normalized to [−1, 1] to standardize the magnitude.27 Modeling and CFD were performed on these 41 samples, and the results were used as the database.

GPR is a powerful nonparametric Bayesian regression method that can model the relationship between inputs and outputs with an infinite number of parameters. GPR is commonly used for complex nonlinear predictions in various scenarios and is particularly suitable for small datasets. In this study, we used GPR to establish the mapping relationship between four factors and the head coefficient as well as efficiency. The GPR model comprises a mean function, a covariance function, and a likelihood function. As reported in this section, the mean function was a constant, the covariance function was the radial basis function kernel, and the likelihood function was based on Gaussian likelihood.25 To improve the predictive accuracy of the model, the Broyden–Fletcher–Goldfarb–Shanno algorithm was used to optimize the hyperparameters when establishing the model. The iteration was stopped when the gradient of the logarithmic marginal likelihood function fell below 105, resulting in the optimal model. Also, to eliminate the impact of dataset partitioning on the prediction results and enhance the robustness of the model evaluation, ten random partition experiments were conducted, where the dataset was divided randomly into a 70% training set and a 30% testing set for each experiment; the training set was used for model training, and the testing set was used for model evaluation. The mean values of RMSE and R2 from the ten experiments were taken as the final performance metrics of the model.

For the head coefficient, R2 was 0.981 and RMSE was 0.0009, indicating high accuracy. For the efficiency, R2 was 0.994 and RMSE was 0.0007, showing excellent predictive capability. Figure 8 shows the errors between the predicted and actual values in the validation set, showing predictions generally within the 95% confidence interval of the actual values. This indicates that the model can effectively predict the performance of the multiphase pump.

FIG. 8.

Prediction errors.

FIG. 8.

Prediction errors.

Close modal
The purpose of the optimization is to enhance the external characteristics over those with the original model. The optimization problem is defined as follows:
(14)

Here, the objective functions f1 and f2 are abstract functions of the head coefficient ψ and efficiency η, respectively, and the inequalities represent the constraints of this problem.

We use the Pareto method to form a Pareto front consisting of a series of nondominated solutions without compromising other objectives, thereby identifying solutions that meet the target requirements.28 PSO is commonly used for multi-objective optimization problems because of its excellent convergence and robustness.29 Therefore, PSO is chosen to obtain the Pareto boundary and select designs with better external characteristics than those with the original model, specifically those with a head coefficient ψ greater than 0.36 and an efficiency η greater than 67%, as shown in Fig. 9. The design parameters for this solution are βin,main = 11.2°, βout,main = 17.4°, βout,splitter = 17.7°, and γ = 5.1°. This design is modeled and then analyzed using CFD and compared with the GPR prediction results. The head-coefficient error is 0.9%, and the efficiency error is 0.7%, both within 1%, indicating high reliability of the predictive model.

FIG. 9.

Pareto front of ψ and η.

FIG. 9.

Pareto front of ψ and η.

Close modal

After optimizing with GPR–PSO, an optimized model was obtained, and to assess whether it outperforms the original model under various conditions, numerical calculations were conducted under different GVFs. Figure 10 shows the computed results of the optimized model and the original model under the same conditions. As can be seen, the optimized model consistently outperforms the original model in terms of head coefficient and efficiency across all conditions.

FIG. 10.

Comparison of external characteristics between optimized and original models.

FIG. 10.

Comparison of external characteristics between optimized and original models.

Close modal

With increasing GVF, the reduction in the head coefficient is more pronounced than the decrease in efficiency. As the gas content increases to 30%, the head coefficient of the original model decreases by 0.152 and the efficiency drops by 3.7%; in contrast, the head coefficient with the optimized model decreases by 0.117, with a corresponding efficiency reduction of 4.18%.

The optimized model outperforms the original model and maintains efficiency while enhancing the head coefficient of the multiphase pump, especially under high GVF.

As mentioned earlier, adding splitter blades increases the head of the multiphase pump significantly, with gas accumulation occurring at the impeller hub of the multiphase pump. Therefore, under 30% GVF, the static pressure distributions of blades at 0.1 times the blade height for both models are analyzed, as shown in Fig. 11. The centrifugal force due to streamline curvature causes an increase in static pressure on the pressure side and a decrease on the suction side.30 

FIG. 11.

Distributions of static pressure.

FIG. 11.

Distributions of static pressure.

Close modal

Comparing the static pressure distributions of the original and optimized models, the optimized model exhibits a greater pressure difference between the pressure and suction sides of the main blades. This is primarily because the optimized model has a smaller hub half-cone angle, resulting in greater curvature of the blade profile compared to the original model, thereby increasing the pressure differential. At 0.5 times the axial distance, the pressure difference across the main blade approaches zero. This phenomenon is attributed to the addition of splitter blades, which induce turbulence in the upstream fluid and result in insufficient lift on the airfoil. Subsequently, the pressure difference continues to increase, ultimately satisfying the Kutta condition at the trailing edge.

Bonaiuti et al. defined the static pressure difference between the pressure and suction sides of the blades as the pressure load.31 This leads to the blade load, which is the partial derivative of velocity with respect to the streamwise direction. Typically, dividing the blade load by ωr32 and then nondimensionalizing yields the blade load coefficient CL. The pressure load is given by
(15)
the blade load is given by
(16)
and the blade load coefficient is given by
(17)
where ps,PS and ps,SS are the static pressure values on the pressure and suction sides of the blade; Z is the number of blades; r is the radius; v̄m is the circumferential average axial velocity; vu is the circumferential component of absolute velocity; m is the flow coefficient; r3 is the radius at the pump inlet.

The distribution of the blade load coefficient is plotted separately for both models at 0.1 times the blade height. Figure 12 shows the integral value of that distribution, which is related to the blade circulation, indicating the blade’s work capacity. This shows that in the noncoincidence area at the leading edge of the impeller, the optimized model exhibits higher blade load coefficients compared to the original model. However, because of the presence of the splitter blades, the load coefficients decrease continuously at the leading edge of the coincidence area, reaching a minimum when the flow coefficient is 0.5 and increasing sharply thereafter. This results in weaker blade work capacity in the coincidence area compared to the original model.

FIG. 12.

Distributions of load factor.

FIG. 12.

Distributions of load factor.

Close modal

At the impeller trailing edge, the presence of both splitter and main blades performing work simultaneously results in a greater increase in work area compared to the area of loss in the coincidence area. Overall, the optimized model demonstrates stronger capability compared to the original model.

To investigate the gas-phase accumulation characteristics in the flow passage of the multiphase pump, the plane of 0.1 times the blade height was selected for analysis. Figure 13 shows the pressure contour map, GVF contour map, two-phase volumetric flow rate, and axial velocity contour map for both models. These show that the optimized model gives significantly higher pressure in the flow passage compared to the original model, and the degree of gas-phase accumulation is also markedly intensified.

FIG. 13.

S1 flow surface cloud map.

FIG. 13.

S1 flow surface cloud map.

Close modal

The contour map for the volumetric flow rate shows that both the gas and liquid phases exhibit backflow near the inlet of the main blades. The gas phase shows a much larger area of backflow compared to the liquid phase at this location, primarily because of the lower density of the gas phase compared to the liquid phase. This results in a higher backflow velocity for the gas phase under the same momentum, thereby expanding the backflow area and causing gas–liquid separation.

Near the inlet of the main blades, the volumetric flow rate of the liquid phase is higher than that of the gas phase, and the liquid-phase volumetric flow rate on the pressure side is greater than that on the suction side. In the flow direction, because of centrifugal forces, the liquid phase decreases near the hub while the gas phase increases. This leads to a continuous increase in gas-phase volumetric flow rate and tends toward stability in the noncoincidence area of the outlet. Excessive gas on the suction side blocks flow, causing diffusion to the adjacent pressure side.

By changing the inlet placement angle of the main blades, the optimized model reduces inlet impact and suppresses flow separation before the coincidence area. At the impeller outlet, both phases exhibit backflow, but the gas-phase backflow rate is much higher than that of the liquid phase. This is because the circumferential pressure gradient between the pressure and suction sides at the blade outlet (as shown in Fig. 11) is greater than the axial pressure gradient, causing the liquid to migrate from the pressure side to the suction side. Gas migrates more than does liquid because of the lower inertia of the former. The reverse pressure gradient in the passage causes gas to block the suction-side outlet channel, exacerbating its tendency to diffuse toward the adjacent pressure side, forming a vicious cycle and ultimately achieving balance.

The optimized model increases the number of backflow areas induced by circumferential reverse pressure gradients at the outlet; these result in severe passage blockage and increased losses and so make efficiency improvement difficult.

To describe clearly the flow state in the passage, the axial velocity uniformity δ and average velocity angle θ̄ are introduced to quantify the fluid distribution uniformity.32 As defined in Eq. (18), the axial velocity uniformity indicates the degree of uniformity of fluid in the flow direction. As defined in Eq. (19), the average velocity angle reflects the angle between the actual water flow and the centerline of the passage, with a value closer to 90° indicating a more ideal flow state. The aforementioned equations are
(18)
(19)
where δ is the uniformity of axial velocity on the cross section; uai is the axial velocity of a certain unit; uā is the average axial velocity; n is the total number of units; uti is the radial velocity of a certain unit.

The impeller is divided evenly into ten equal parts in the axial direction, and the axial velocity uniformity and average velocity angle of the liquid and gas phases on each cross section are calculated separately. Figure 14(a) shows that the axial velocity uniformity of the liquid and gas phases exhibits an initial increase followed by a decrease in the streamline direction, with the liquid-phase uniformity greater than that of the gas phase. Analysis of the uniformity variations in the two models reveals that at the impeller inlet, because of impact reflux and blade rectification, the flow uniformity increases rapidly from low to high. Compared with the original model, the optimized model adjusts the placement angle of the main blade at the inlet, resulting in similar gas–liquid uniformity at the inlet. After blade rectification, the uniformity begins to decrease because of the combined effects of gas–liquid separation and reflux. In the noncoincidence area at the outlet, the presence of splitter blades again enhances uniformity and slows down the decreasing trend of axial velocity uniformity, making the gas–liquid axial velocity more uniform at the outlet of the optimized model impeller. Figure 14(b) shows that the trends of the average velocity angles for the gas and liquid phases in both models are nearly identical, showing an overall decreasing trend, with the average velocity angle of the optimized model significantly better than that of the original model. Because of blade rectification, the average velocity angle at the noncoincidence area of the impeller leading edge increases. Subsequently, the centrifugal force causes an increase in radial velocity, which in turn results in a gradual decrease in the average velocity angle. In the noncoincidence area at the outlet of the impeller, intensified reflux and gas accumulation cause a decrease in axial velocity, leading to a sharp decrease in the average velocity angle.

FIG. 14.

Changes in flow velocity distribution.

FIG. 14.

Changes in flow velocity distribution.

Close modal

In summary, the fluid uniformity inside the optimized model’s flow passage is much better than that of the original model. At the impeller outlet, compared to the original model, the optimized model improves the axial velocity uniformity of the gas and liquid phases by 15.1% and 9.5%, respectively, and increases the average velocity angle by 12.3° and 12.1°, respectively.

Proposed herein was a design method for a multiphase pump with splitter blades, combined with intelligent optimization algorithms, and this method predicts the external characteristics accurately. At a GVF of 30%, the optimized model not only maintains an efficiency comparable to that of the original model but also achieves an increase of 22.2% in the head coefficient.

Adding splitter blades increases the loading coefficient at the impeller trailing edge, thereby enhancing flow rectification. The circumferential pressure gradient at the blade outlet is larger than the axial pressure gradient, leading to more gas accumulation zones, which exacerbates gas stagnation.

Adding splitter blades results in a more uniform distribution of the fluid at the impeller outlet cross section. Under 30% GVF, the axial velocity uniformity of both the gas and liquid phases improves by 15.1% and 9.5%, respectively, while the average velocity angle increases by 12.3° and 8.3°, respectively.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52179086 and 52269022) and the Central Government Guides’ Local Science and Technology Development Funding Project (Grant No. 23ZYQA0320).

The authors have no conflicts to disclose.

Chunpei He: Data curation (equal); Methodology (equal); Software (equal); Writing – original draft (equal). Wei Han: Conceptualization (equal); Resources (equal); Supervision (equal). Rennian Li: Supervision (equal); Validation (equal); Writing – review & editing (equal). Yifan Dong: Methodology (supporting); Writing – original draft (supporting). Yukun Zhang: Data curation (supporting); Software (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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