The effects of balancing holes on the axial force of a centrifugal pump in the reverse mode

Centrifugal pumps can feasibly act as turbines in small hydropower plants. However, prediction and reduction methods of axial force is still challenging. A proposed method to this goal is the use of balancing holes. Accordingly, this paper investigates the effect of balancing holes diameter on the hydraulic performance and the axial force of a centrifugal pump as turbine (PAT). In this study, modeling of the fluid flow within the pump was carried out by using the commercial software of Ansys CFX R19.0 and the SST turbulence model. The numerical results showed that by working in the reverse mode, the operating flowrate, head and the axial force of the pump are increased remarkably. This study proved that drilling balancing holes in the impeller, despite being simple, is a useful method in reducing the axial force and has minor effects of the output power. Results showed that by drilling a hole of diameter 2 mm, the axial force is approximately decreased by 60 % in almost all flowrates. Finally, it is observed that increasing holes diameter is mostly influential at high flowrates, and with diameter of 6.5 mm, the axial force is reduced about 90%.


Introduction
Centrifugal pumps can be used for converting the energy of water flows to electrical energy.To achieve this goal, pumps act as turbines which are called pump-as-turbine (PAT).Due to mass production, availability and low operational costs, pumps in the reverse mode (PATs) can be alternatives to small hydropower plants in the remote areas [1,2,3,4].Since the hydraulic characteristics of pumps in the turbine mode are not provided by the suppliers, selection of the most appropriate turbine meeting the requirements of a defined hydropower plant has been an issue [5].A solution to this problem is predicting the performance curves of a pump in the reverse mode by its hydraulic characteristics in the direct mode.Accordingly, correction factors for discharge, head and efficiency are developed [6,7,8].For instance, researchers such as Stepanoff [6], Childs [7], and Sharma [8] developed correlations for prediction of the pump performance in the reverse mode based on the pump hydraulic characteristics at best efficiency point (BEP).In our research group, Derakhshan and Nourbakhsh [9] proposed correlations for prediction of turbine mode characteristic curves of the pumps with specifics speeds of 14.6 to 55. 6.In a similar research, an experimental investigation to obtain predictive models of PAT performance curves was performed by Barbarelli et al .[10].In a spite of being straight forward, their proposed model does not present generality.Moreover, several researchers attempted to improve the accuracy of the prediction methods by proposing novel methods.For example, Novara et al. [11] proposed a model based on the performance curves of more than 113 PATs and found that the given model can accurately predict the turbine operation of pumps with specific speeds below 100.
In addition to experimental and theoretical studies, Computational Fluid Dynamics (CFD) methods have also been reliable tools for predicting the performance of centrifugal pumps and PATs [12,13,14,15,16].By using CFD methods, the details of the flow field of the PAT are accessible, and thus the time and the cost of the design process are effectively reduced.Jovanocić et al. [16] predicted the performance of a centrifugal pump in the reverse mode using numerical methods.Simulation was accomplished through commercial software of Ansys-CFX and the k− turbulence model.They reported that numerical results were consistent with experiments by small discrepancies (below 4%).Numerical investigation of a centrifugal pump with specific speed of 70 at rotational speed of 1450 rpm in both direct and reverse modes was carried out by Ismail et al. [15].For obtaining the numerical data, the Ansys-CFX with the k − model were utilized and measurements were conducted for the normalized flowrates ranging from 0.7 to 1.3 of BEP.They claimed that CFD tools can appropriately predict the pump performance in both operating modes.
Along with hydraulic characteristics of the PATs, achieving a deep understanding of the mechanical forces exerted on the turbine is also crucial as they affect the life and durability of the machine.However, few researchers have focused on studying the behavior of the mechanical forces.For instance, the mechanical forces of an axial pump was studied experimentally by Gantar [17].Their results showed that in the reverse operation of the pump, the axial force became about 2-2.5 times greater than the direct mode.In another investigation, Bario et al. [18], numerically investigated the transient radial force of a PAT.They reported that during direct operation, radial force takes its minimum at the pump's best efficiency point, while it follows an increasing trend with the flowrate in the reverse mode.Another research on steady-state and transient radial force in a reverse pump was performed by Fernandez et al. [13].This study disclosed that the averaged radial force rises by flowrate and its direction alters with the impeller rotation.
In our research group, attempts have been made to improve the hydraulics of PATs along with reduction of the mechanical forces.Through experiments conducted by Alemi et al. [19], the effects of volute tongue geometry on the performance and radial force of a pump in reverse operation was studied.This research showed that the tongue with medium stretching reduced the radial force, while more stretching did not return smaller radial force.Also, we showed that the tongue angle could substantially affect both hydraulic performance and radial force.In a follow up research, Alemi et al. [20] improved the hydraulic and mechanical forces of a PAT by introducing a new volute.Results showed that, for a given impeller, the PAT efficiency in high flowrates is increased by using a volute with a larger cross section, and the radial force noticeably dropped in comparison to the main geometry.
As discussed above, researchers have proposed several predictive models enabling the users to opt the most appropriate pump for working in the reverse mode for a given power plant.However, a few number of studies have been devoted to mechanical.Meanwhile, these limited studies mainly focus on radial force and the axial force has not been studied in details yet.Therefore, this paper numerically studies the axial force generated in the reverse operation of a centrifugal pump.In addition, effects of drilling balancing holes, as a practical and fiscally reasonable solution, on hydraulics and axial forces are investigated.
The current paper is organized as follows.In Section 2, the test case and computational details are presented.In Section 3, the numerical results for pump mode are validated against experiments.Next, the results for hydraulics and axial force in PAT mode are reported.Thereafter, the effects of balancing holes on the hydraulic and axial force of pump in reverse mode are discussed.Finally, the main achievements of this research are summarized.

Test case
The present numerical study is conducted on the test case presented in [21] wherein experimental data for hydraulic characteristics of a centrifugal pump are reported.Current pump is a single suction with

Governing equations
In order to simulate the fluid flow of the pump, the governing equations of continuity and 3D steady-state incompressible Reynolds Averaged Navier-Stokes are employed as: where ρ, ν, and −ρu i u j are density, kinematic viscosity and Reynolds stress tensor.To close the above equations, the k − ω SST turbulence model, proposed by Menter [22], is used.This model takes advantage of the k − ε model in capturing the bulk flow with the capability of the k − ω model for resolving the near-wall region.
In this model, the Reynolds stress is obtained using Boussinesq eddy viscosity hypothesis (3) as: where δ ij is the Kronecker delta.

Computational grid
The computational domain is composed of five regions namely, impeller, volute, rear chamber, inlet and outlet.Inlet and outlet pipes are sufficiently extended to have fully-developed condition at the impeller inlet and pump outlet.The computational grid for each domain is generated separately by ANSYS-Meshing.Figures 3 and 4 show the mesh grid generated for impeller and volute.Due to complexity of the geometry, hybrid meshing is used so that adjacent to the wall regions, the clustered boundary layer mesh was used, while far from solid walls, the tetrahedral cells were utilized.
A sensitivity study has been conducted to assure the results are independent of computational grid size.Therefore, three grids were generated and the corresponding results are compared.The simulation was performed at the design flow of the pump mode with no balancing hole.Figure 5 depicts the variation of head coefficient (ψ = gH/(ω 2 d 2 2 )) at BEP with respect to the grid size.As it is shown, by increasing the elements number from 3 × 10 6 to 3.4 × 10 6 , the head coefficient varies below 0.3%.Therefore, the computational grid with 3 × 10 6 elements was selected for the simulations in both direct and reverse modes.

Numerical simulation
In order to simulate the flow in the pump, the commercial software of ANSYS CFX R16.0 was used.Frozen rotor type interface was chosen for inlet-impeller and impeller-volute domains.The boundary condition of inlet, outlet and walls are set to total head, mass flow and no-slip respectively.The high resolution advection scheme is used for discretization of the convective terms.This transient scheme uses second order scheme whenever and wherever possible, and returns to first order when required Computational grid for impeller domain.to achieve a bounded solution.Finally, the maximum residual criterion for all variables were set to 1.0 × 10 −5 .

Result and discussion
To facilitate the analysis, dimensionless flowrate, head and power are respectively defined as: where φ, ψ and π are flow, head and power coefficients respectively.Ω is the rotational speed and Q, H, T represent the volumetric flowrate, head and hydraulic torque respectively.g and ρ are the gravitational acceleration and water density.b 2 and d 2 stand for the impeller width and diameter at trailing edge.Accordingly, the hydraulic pump efficiency is obtained as:

Validation of numerical results
In order to validate the result given by numerical methods, a comparison between the numerical data and experiments reported in the literature [21] is made.Figure 6 displays the pump hydraulic performance of in the direct mode returned by numerical simulation.As displayed in Figure 6, good agreement between numerical results and experimental data is found.In the regions close to BEP, results are accurate, but by moving from the BEP toward low flowrates, the difference between numerical results of and experiments for head and power increases.This can be explained by the fact that in low flowrates, the presence of vortices and other transient phenomenon makes the flow field complex, and thus it is hard to obtain very accurate results.However, the efficiency obtained from numerical simulation is in a very good agreement with experiments all over the working range.Figure 6 shows that pump head follows a descending trend and by increasing flowrate from φ/φ n = 25% to φ/φ n = 150%, head is decreased from ψ = 0.09 to ψ = 0.04.However, power and efficiency follow increasing and decreasing trends with flowrate.It can be seen that the power commencing from π = 0.015, reaches π = 0.021 at φ/φ n = 100% and thereafter drops to π = 0.019.Next, efficiency increases from η = 27% to η = 63% and then drops to η = 56%. .Grid sensitivity analysis.Figure 6.Pump performance curves.

Effects of balancing holes
In the following sections, the results for pump performance in the reverse mode are presented, and the effects of balancing holes on hydraulic characteristics, axial force and internal leakage are presented.It should be noticed that as the pump changes its operation to turbine mode, the nominal mass flowrate changes from 2.42 to 6.40 kg/s.
3.2.1.PAT hydraulic characteristics.Figure 7 displays the returned head coefficient of the pump running in the turbine mode.D h is the balancing hole diameter and D h = 0 represents the impeller with no balancing hole.As shown in Figure 7, head increases sharply by the flowrate for all cases.Moreover, it can be seen that hole diameter has negligible effects on head at low flowrates, but is influential at high flowrates.As the flowrate increases, the effects of balancing holes become more pronounced so that at φ/φ n = 140%, by drilling the balancing holes with diameter of D h = 6.5 mm, the head is dropped about 8 %.The power generated by the pump in the reverse mode is shown in Figure 8.It shows that the power in the PAT is monotonically increasing with the flowrate.Moreover, the values of power production in the PAT mode are considerably higher than the power consumption in pump mode.For instance, by changing to turbine mode, the power coefficient at BEP increase form π = 0.21 to π = 0.35.Also, the power takes maximum values of π = 0.97 which is about five times greater than that of pump mode.In addition, similar to the head, the power of PAT is also affected by the balancing holes only at high flowrates.As it can be seen, at the flowrates below φ/φ n = 100%, the power varies slightly by the balancing holes.Meanwhile, at flowrate of φ/φ n = 140%, by increasing the balancing hole diameter to D h = 6.5 mm, the power is dropped about 7%.
The effects of the balancing holes on the PAT efficiency are displayed in the Figure 9.It shows that the maximum efficiency of pump and PAT are very close to each other (about 63%).It can also be understood from Figure 9 that at the high flowrates, balancing holes are negligibly influential, while at the low flowrates, they can reduce the efficiency.Similar to the pump mode, the efficiency curve is more steep at low flowrates, meaning that by deviating from BEP toward low flowrates, the efficiency reduces more quickly than shifting to higher flowrates.However, a comparison between the efficiency curves of pump (Figure 6) and PAT (Figure 9) reveals that at low flowrates, PAT efficiency is noticeably lower than that of pump mode so that at φ/φ n = 60%, the efficiency drops from η = 51% to η = 35%.
/ n (%) / n (%) 3.2.2.Axial Force.In practice, the pressure distributions on the sides of the impeller are not the same, and thus a net force parallel to the rotation axis is generated.The axial force coefficient of the PAT is defined as: where F axial is the summation of the axial force on hub and shroud sides which are obtained by integrating static pressure over impeller sides.Figure 10 depicts the axial force exerted on the impeller in the turbine mode.As it is shown, for the impeller without any balancing hole, the axial force remarkably increases by flow so that by increasing flow from φ/φ n = 60% to φ/φ n = 140%, the axial force becomes about 9 times greater (from F * a = 7 to F * a = 63).Moreover, previous research published by the authors [21] reported maximum axial force of F * a = 11.6 in the pump mode which is considerably lower than the values obtained for the turbine / n (%) mode.This finding urges the users to consider precautions for endurance of hydro-power plants utilizing PATs for electricity generation.Figure 10 also displays the effect of balancing holes on the axial force generated during reverse operation.It shows that balancing holes can reduce the axial force in all working ranges, more specifically at high flowrates where the maximum axial force occurs.As depicted in Figure 10, by drilling holes with diameters of D h = 2 mm and D h = 3.5 mm, the maximum axial force drops from F * a = 63 to F * a = 40 and F * a = 20 respectively.These findings also disclose that by drilling larger holes, the axial force becomes relatively flat, with maximum forces about F * a = 8.Interestingly, by using large holes such as D h = 5 mm and D h = 6.5 mm, zero axial force is experienced with negative axial force in the part-load operation.This implies that in the low flowrates, the direction of the axial force is reversed and by increasing the flowrates, it becomes zero and changes its direction.

Internal leakage.
The balancing hole is a parameter affecting the internal leakage of the PAT.As a balance hole is drilled in the impeller, a new passage for the leakage of the fluid from the back side of the impeller to its front side is created.These new passages reduces the hydraulic resistant between two sides and consequently more flow is circulated between the sides.Figure 11 represents the internal leakage to nominal flowrate ratio against operating flowrates.The internal leakage is introduced by considering only the flow passing through the balancing holes.As shown in this figure, the internal leakage varies slightly with balancing hole diameter of D h = 2 mm.However, by increasing the balancing hole, internal leakage becomes more affected by the flowrate so that the leakage increase from 2% to 8% in the range of φ/φ n = 60% to φ/φ n = 140%.This finding is consistent with results obtained for power and head since higher values of internal leakage are considered as the main reason for the reduction of power and head in the high flowrates.

Conclusion
This paper presents a numerical study on the effects of balancing holes on hydraulics, axial force and internal leakage of a centrifugal pump in the reverse mode.Verification of the numerical simulation is performed by comparing the results of direct mode against the experiments in the literature, and good agreements are observed.The findings of turbine operation reveal that balancing holes reduces PAT's head and power only at high flowrate and has negligible effects at low flowrate.Moreover, it is observed that the balancing holes efficiently reduce the axial force.By drilling holes of D h = 5 mm, the maximum axial force is reduced about 80%.Interestingly, using larger hole makes the axial force alters its direction with experiencing zero value.Finally, it can be concluded that balancing holes can be a practical solution to provide favorable conditions for endurance of the pumps in the turbine mode, although the output power is slightly reduced.

Figure 2 .
Figure 2. Components for simulation of the pump operation in direct and reverse modes.

Figure 7 .
Figure 7.The effects of balancing holes on PAT's head.

Figure 8 .Figure 9 .
Figure 8.The effects of balancing holes on PAT's power.

Figure 10 .
Figure 10.The effects of balancing holes on PAT's axial force.

Figure 11 .
Figure 11.The effects of balancing holes on PAT's leakage.