To gain a comprehensive understanding of the energy dissipation of a double-suction pump, analysing the energy loss of its various components is necessary. However, the liquid temperature in the double-suction pump remains almost constant, using the entropy production or dissipation method to evaluate energy loss is difficult. The traditional analysis method based on pressure drop cannot quantify the internal energy changes in each component. To solve this problem, a pressure energy loss evaluation approach is developed on the basis of the pressure drop theoretical analysis and numerical prediction, and the effects of cavitation on the energy loss are investigated. The structure of the volute casing is improved to enhance the performance based on energy loss analysis and cavitation behaviour prediction. The results show that the energy loss efficiencies for the suction casing, impeller, and volute casing are 0.55, 4.6, and 5%, respectively, at the design flow rate. The proportion of energy loss in the impeller and volute casing increased with a decrease in NPSHa. The RNG kε and kω turbulence models are chosen for the numerical simulation, and the numerically predicted results are verified experimentally.

  • A pressure energy loss evaluation approach for a double-suction pump is developed.

  • The effects of cavitation on energy consumption are analysed.

  • Two turbulence models of RNG kε and kω are used for numerical simulation.

  • Energy changes within the component for double-suction pump are revealed.

  • Experiments are performed to verify the accuracy of the numerical model.

Bim

impeller outlet width (mm)

Dim

impeller diameter (mm)

Dimn

impeller inlet diameter (mm)

Din

pump inlet diameter (mm)

Dout

pump outlet diameter (mm)

approximate relative error (%)

extrapolated relative error (%)

Fcond

empirical calibration parameters of condensation

Fvap

empirical calibration parameters of evaporation

H

head (m)

g

gravitational acceleration (m·s−1)

fine-grid convergence index (%)

m+

mass transfer source terms of evaporation

m

mass transfer source terms of condensation

M

torque (N·m)

n

speed (r·min−1)

ns

specific speed

N

total number of cells used for the simulation

p

pressure (Pa)

pim_in

total pressure at the inlet section of the impeller (Pa)

pim_out

total pressure at the outlet section of the impeller (Pa)

pin

total pressure at the inlet of the pump (Pa)

pout

total pressure at the outlet of the pump (Pa)

psu_in

total pressure at the inlet section of the suction casing (Pa)

psu_out

total pressure at outlet section of the suction casing (Pa)

pv

vapour pressure (Pa)

pvo_in

total pressure at the inlet section of the volute casing (Pa)

pvo_out

total pressure at outlet section of the volute casing (Pa)

Q

flow rate (m3·h−1)

Qd

design flow rate (m3·h−1)

RB

radius of a nucleation site (m)

u

velocity (m·s−1)

uin

inlet velocity of pump (m·s−1)

ΔVi

volume of the i-th cell

Z

blade number

Greek Letters

αnuc

nucleation site volume fraction

αv

vapour volume fraction

μl

liquid dynamic viscosity (Ns·m−2)

μm

mixture of dynamic viscosity (Ns·m−2)

μt

turbulent viscosity (Ns·m−2)

μv

vapour dynamic viscosity (Ns·m−2)

ρl

liquid density (kg·m−3)

ρm

mixture of density (kg·m−3)

ρv

vapour density (kg·m−3)

ω

angular velocity (rad·s−1)

η

efficiency

ηim

impeller loss efficiency

ηsu

suction casing loss efficiency

ηvo

volute casing loss efficiency

Double-suction centrifugal pumps have a high flow rate and are utilised extensively in various areas such as water supply systems, the energy industry, and agriculture. The energy used by pumps accounts for nearly 22% of the total energy consumed by electric motors worldwide (Kalaiselvan et al. 2016; Wang et al. 2017; Gan et al. 2022; Wang et al. 2023), which means that pumps have great potential for energy savings. The structure of a double-suction pump is more complex than that of a single-stage centrifugal pump and usually has a semi-spiral-type suction casing. To gain a comprehensive understanding of the energy dissipation of a double-suction pump, analysing the energy loss of its various components is necessary.

Numerous analytical and experimental studies have been conducted to analyse the energy losses of pumps or pumps operating in turbine modes. Zhang et al. (2018), Li et al. (2020), and Chen et al. (2022) used the particle image velocimetry (PIV) technique to explain the flow pattern in pumps, described the velocity evolution for different flow rates in the impeller, and analysed the energy conversion characteristics. Huan et al. (2021) conducted a visual experiment using a high-speed camera to investigate the progression of cavitation in an inducer-equipped high-speed centrifugal pump and performed a numerical simulation to analyse the alterations in flow patterns caused by cavitation. However, the PIV measurement technique requires certain parts of the pump to be transparently visible and then combined with a high-speed camera for experiments, which limits its application.

Entropy production or dissipation is commonly used to assess the energy loss of a pump. For instance, Hou et al. (2016a) and Wang et al. (2019) adopted an entropy production method to analyse the energy loss of a cryogenic submerged pump for liquefied natural gas (LNG) and investigated the internal flow conditions and distribution of the entropy production rate. Lin et al. (2021) adopted the entropy dissipation method to assess the energy loss of a centrifugal pump used as a turbine and studied the entropy dissipation component under variable working conditions. Li et al. (2018) analysed the cavitation head-drop characteristics of a centrifugal pump using the entropy generation method and described the vapour distribution and entropy generation rate. However, double-suction centrifugal pumps are typically used as front pumps for high-pressure boiler water supply systems, and the temperature in the pump remains almost constant. Therefore, using the entropy production or dissipation method to evaluate energy loss is difficult.

Previous studies used pressure energy dissipation to predict the loss of each component of a centrifugal pump. Hou et al. (2016b) examined the effects of a radial diffuser while analysing the energy loss of a double-suction centrifugal pump. Hou et al. (2017) and Wang et al. (2019) compared the values of the entropy production energy loss and pressure energy loss of pumps and observed little difference between the two methods. However, these studies focused on the total energy loss in the pump component and did not analyse the energy changes within each component. In addition, the turbulence model is critical in the energy loss simulation of a pump, and a reasonable turbulence model can improve the calculation accuracy. Moreover, RNG kε (Xu et al. 2016; Tang et al. 2017; Song et al. 2018; Quan et al. 2020; Yan et al. 2020; Zhang et al. 2023) and kω (Li et al. 2019, 2021; Wang et al. 2020) are commonly used turbulence models, but few studies have focused on the differences between the two models.

Cavitation may lead to the degradation of pump performance, vibration, noise, and erosion (Al-Obaidi 2020a, 2020b; Al-Obaidi & Mishra 2020), which often occurs with a vapour region attached to the impeller blades, where the region grows as the pump inlet pressure decreases. Several studies have been conducted to understand and explain the cavitation characteristics. Tao et al. (2018) examined the cavitation behaviour of a reversible pump turbine in pump mode along with the characteristics of critical and inception cavitation. Zhu et al. (2021) examined the effects of leading-edge cavitation on the axial force of an impeller blade in the pump of a reversible pump turbine and found that the axial force first increased and then decreased. Fan et al. (2022) studied the cavitation behaviour of liquid nitrogen inducers at various rotating speeds and inlet temperatures and developed a theoretical prediction method to predict cavitation performance. Cavitation characteristics have been extensively studied by previous investigators. However, studies on the effects of cavitation on the energy loss of pumps are rare. Although Shi et al. (2021) revealed the effects of cavitation evolution on the energy conversion characteristics of a multiphase pump, no energy loss analysis has been conducted for each component of the pump.

In this study, a pressure energy loss evaluation approach for a double-suction pump is proposed that is easier to implement and has a wider range of applications. The RNG kε and kω turbulence models are used to predict the pump performance, and the differences between the two models are investigated. The energy loss and internal changes in each component at different flow rates are analysed numerically, and the effects of cavitation on energy consumption are investigated. The numerically predicted results are verified experimentally. In addition, the structure of the volute casing is improved to enhance the performance based on energy loss analysis and cavitation behaviour prediction.

The tested double-suction pump is a front pump for high-pressure feed-water systems, which is a centrifugal pump with a single and six inline vane blades. Figure 1 shows the cross-section of the pump, which has a double-suction impeller, one suction casing with two outlets, and a spiral volute casing. Table 1 lists the primary design criteria of the pump.
Table 1

Basic design parameters of the test pump

ParametersValuesParametersValues
Flow rate Qd (m3·h−11,300 Pump outlet diameter Dout (mm) 375 
Head H (m) 14 Blade number Z 
Speed n (r·min−1970 Impeller diameter Dim (mm) 380 
Specific speed ns 293.96 Impeller inlet diameter Dimn (mm) 262 
Pump inlet diameter Din (mm) 450 Impeller outlet width Bin (mm) 101.25 
ParametersValuesParametersValues
Flow rate Qd (m3·h−11,300 Pump outlet diameter Dout (mm) 375 
Head H (m) 14 Blade number Z 
Speed n (r·min−1970 Impeller diameter Dim (mm) 380 
Specific speed ns 293.96 Impeller inlet diameter Dimn (mm) 262 
Pump inlet diameter Din (mm) 450 Impeller outlet width Bin (mm) 101.25 
Figure 1

Cross-section view of the tested double-suction pump.

Figure 1

Cross-section view of the tested double-suction pump.

Close modal
Figure 2 illustrates the open-type test rig, which mainly consists of a pump, motor, pool, flowmeter, two pressure gauges, and a control valve. An electromagnetic flowmeter (IFM4080F, China) was employed to measure the flow rate, and its precision was ±0.3% of the measured value. Two pressure gauges (accuracy of ±0.25% of the full scale) were used to measure the inlet and outlet pressures, where the inlet gauge was in the range of −0.1 to 0 MPa and the outlet gauge range from 0 to 0.6 MPa. The pump speed was measured by a digital tachometer (DM6234P, China) with a precision of ±(0.05% + 1) of the measured value. The pump power was measured by an intelligence power meter (ZW5433B, China) with a precision of ±0.5% of the measured value. In addition, vibration and noise were measured using a vibration meter (Vm-63A, Japan) and sound level meter (DT-805, China), respectively.
Figure 2

Schematic diagram of the test rig.

Figure 2

Schematic diagram of the test rig.

Close modal

Steady simulations were carried out utilising the ANSYS CFX 18.0 flow solver, and both RNG k–ε and k–ω turbulence models were used for numerical simulation. Since the k–ω and RNG k–ε turbulence models are widely used in the low specific speed centrifugal pumps, and RNG k–ε turbulence model can accurately predict the rotating and curvature flow in the flow passage components. Moreover, two models are verified by a large amount of previous work (see Section 1). The effects of cavitation can be disregarded because the total pressure at the pump inlet throughout the test was at atmospheric pressure.

Performing a steady calculation without cavitation was necessary, where the result was then used as the initial condition, and the inlet pressure was gradually reduced for the cavitation calculation. During the numerical simulation, the following equations were used to monitor the double-suction pump's head H and efficiency η.
formula
(1)
formula
(2)
where pin and pout are the total pressure at the pump's inlet and outlet, g is the gravitational acceleration, Q is the flow rate, M is the torque, and ω is the angular velocity.

Physical model and setting up

Physical model and mesh

As Figure 3 shows, the entire computational flow domain included the volute casing, shroud chamber, impeller, suction casing, and outlet and inlet extensions. To reduce the number of interfaces, the inlet and outlet extensions were generated together with the suction and volute casings, and their lengths were 4Din and 6Dout, respectively.
Figure 3

Physical model of the double-suction pump.

Figure 3

Physical model of the double-suction pump.

Close modal
The suction casing consisted of inlet, transition, and semi-spiral parts. This casing was more complex than the volute casing and impeller, and the modelling approach is depicted in Figure 4. For convenience, the study used half of the suction casing for modelling. Sections of the inlet part (red line), transition part (red line), and semi-spiral part (blue line) were drawn first. Surfaces were generated from the drawn sections, and smooth surfaces were constructed to make connections between the transition and semi-spiral surfaces. A solid body was created and the excess of the transition was cut off according to the volute casing. Finally, mirroring was performed to generate a complete suction casing.
Figure 4

Modelling approach of the suction casing.

Figure 4

Modelling approach of the suction casing.

Close modal
The fluid domains of the double-suction pump were meshed and integrated using ANSYS ICEM, where the local prism, pyramid, and tetrahedral meshes were produced together with a hexahedral element mesh, as shown in Figure 5. The impeller adopted a hexahedral mesh structure, whereas the other fluid domains were unstructured meshes. In the close-to-wall regions, such as the blade surface and volute tongue, local mesh refinement was performed to increase the accuracy of the numerical prediction. For the unstructured mesh, the Robust (Octree) method of tetra/mixed meshing was used to generate the volume mesh. Prism layers were adopted for the boundary layer, and the maximum number of layers was five. The minimum mesh quality for volute casing, suction casing and shroud chamber was 0.23, 0.12, and 0.1, respectively. For the structured mesh, the BiGeometric mesh law was used to control the node distribution on the boundary layer, and the minimum mesh quality for the impeller was 0.14.
Figure 5

Meshes of the double-suction pump.

Figure 5

Meshes of the double-suction pump.

Close modal

Numerical setup

At the inlet section of the suction casing, the total pressure was given, whereas for the outlet section of the volute casing, the mass flow rate was in the range of 0.2–1.4 Qd. The reference pressure was set to 0 atm. For a proper connection, the interface was adopted in the fluid–fluid domain, and the interfaces between the impeller and stationary components were taken as a frozen rotor. The rotational speed of the impeller was specified in a rotating frame of reference, whilst the suction and volute regions were set as stationary. The boundary walls were modelled using a non-slip smooth wall condition. The maximum number of iterations was set as 3,500 and the residual value of the convergence criteria was 1 × 10−4.

Mesh-independence study and uncertainty analysis

The inlet and outlet extensions were modelled together with the suction and volute casings, respectively; therefore, they were also meshed together. As listed in Table 2, Case A was used as the initial mesh for the mesh-independence study under a total mesh size of 2,810,586. The mesh was further improved to investigate its effect on the numerical results. The mesh numbers for Cases B–E were 1.16, 1.31, 1.58, and 1.83 times that of Case A, respectively. The predicted head H changed significantly from Case A to D as the mesh size increased, and slightly from Case D to E. Therefore, mesh D was deemed appropriate and utilised throughout the study.

Table 2

Different mesh sizes

CaseMesh elements
H (m)Error (%)
Suction casing and inlet extendImpellerVolute casing and outlet extendShroud chamber
815,520 1,091,304 670,854 232,908 13.85 – 
886,145 1,255,612 839,344 279,489 14.21 2.53 
998,756 1,411,855 959,645 299,553 14.59 2.6 
1,009,962 1,988,820 1,123,522 329,508 14.8 1.42 
1,278,797 2,187,709 1,280,815 395,417 14.73 0.47 
CaseMesh elements
H (m)Error (%)
Suction casing and inlet extendImpellerVolute casing and outlet extendShroud chamber
815,520 1,091,304 670,854 232,908 13.85 – 
886,145 1,255,612 839,344 279,489 14.21 2.53 
998,756 1,411,855 959,645 299,553 14.59 2.6 
1,009,962 1,988,820 1,123,522 329,508 14.8 1.42 
1,278,797 2,187,709 1,280,815 395,417 14.73 0.47 

Different turbulence models have different y+ requirements for accurate predictions of the near-wall flow. In general, the maximum value of the y+ in the water pump is less than 300 for a two-equation turbulence model, such as the k-epsilon or k-omega model (Wei et al. 2019; Wang 2020). The y+ of the impeller is displayed in Figure 6. The largest value of y+ was below 150, which satisfies the minimum requirement of the wall function used in the simulation.
Figure 6

y+distribution on the impeller and suction & volute casing.

Figure 6

y+distribution on the impeller and suction & volute casing.

Close modal
Mesh-independence study has no theoretical basis, but great randomness. A more reasonable procedure for the estimation of the discretisation error is based on the Richardson extrapolation and the recommendation by Journal of Fluids Engineering (Bai et al. 2013; Zhao et al. 2020). Three sets of mesh sizes with A (2,810,586), C (3,669,809), and D (4,451,812) elements were chosen for the numerical accuracy analysis. The static pressure of two monitor points in the volute casing was selected as the ‘variable φ’ at a flow rate of 1.1Qd (see Figure 7). The mesh size h is defined as
formula
(3)
where ΔVi is the volume of the i-th cell and N is the total number of cells used for the simulation. The apparent order pao of the estimation method can be written as
formula
(4)
Figure 7

Pressure monitor points in the volute casing.

Figure 7

Pressure monitor points in the volute casing.

Close modal
and
formula
(5)
where rCD = hC/hD, rAC = hC/hD, εAC = φAφC, εCD = φCφD.
The extrapolated value is given by
formula
(6)
Approximate relative error, extrapolated relative error, and the fine-grid convergence index are defined as
formula
(7)

The errors for monitor points 1 and 2 can be obtained by the above equations, and the results are shown in Table 3. Hence, the numerical uncertainty in the fine-grid solution for the reattachment length should be reported as 2.095%.

Table 3

The uncertainty analysis based on Richardson extrapolation

Parametersφ = static pressure of P1/Paφ = static pressure of P2/Pa
ND, NC, NA ND = 4,451,812, NC = 3,669,809, NA = 2,810,586 
rCD 1.0665 
rAC 1.0930 
φD 233,696 213,102 
φC 232,823 212,361 
φA 231,154 211,078 
pao 4.2047 2.9306 
 236,504.05 216,670.46 
 0.374% 0.348% 
 1.187% 1.647% 
 1.504% 2.095% 
Parametersφ = static pressure of P1/Paφ = static pressure of P2/Pa
ND, NC, NA ND = 4,451,812, NC = 3,669,809, NA = 2,810,586 
rCD 1.0665 
rAC 1.0930 
φD 233,696 213,102 
φC 232,823 212,361 
φA 231,154 211,078 
pao 4.2047 2.9306 
 236,504.05 216,670.46 
 0.374% 0.348% 
 1.187% 1.647% 
 1.504% 2.095% 

Numerical accuracy validation

Figure 8 shows the head H and efficiency η at the design speed of 970 r·min−1. To consider the uncertainty of sensors, the pump outlet pressure pout = (pout m ± 0.0015) MPa, inlet pressure pin = (pin m ± 0.00025) MPa, flow rate Q = Qm(1 ± 0.003), and power P = Pm (1 ± 0.005). Hence, the head H and efficiency η can be written as
formula
(8)
and
formula
(9)
Figure 8

Numerical and experimental results of the head and efficiency.

Figure 8

Numerical and experimental results of the head and efficiency.

Close modal

The findings demonstrate that the error of the k–ω model was higher than that of the RNG kε model, particularly under small flow conditions. Thus, for this investigation, the RNG k–ε model was used. At various flow rates, the H and η predicted by the RNG k–ε model agreed well with the experimental findings. As the flow rate increased, the head decreased, and the numerical results were larger than the experimental results at high flow rates. However, the experimental values were greater at low flow rates. As the flow rate increased, the efficiency first increased and then decreased, and the optimal efficiency point was at the design flow rate for both the test and simulation results. The discrepancies between the test and numerical values were within 5% at each flow rate, thereby validating the numerical method.

Energy loss analysis

In general, the pressure drop for each component of a double-suction centrifugal pump can be transformed into energy loss. For the double-suction impeller, the entire input shaft power should be subtracted from the total pressure rise for the working fluid to determine the energy loss. Thus, the loss efficiency of the impeller can be defined as
formula
(10)
where pim_in and pim_out represent the total pressure at the inlet and outlet sections of the impeller. The pressure can be obtained by the function calculator in the CFX-Post, and the ‘Total Pressure in Stn Frame’ was used for this study.
Similarly, for the suction casing and volute casing, the energy loss efficiency is given by
formula
(11)
formula
(12)
where psu_out and psu_in are the total pressure at the outlet and inlet sections of the suction casing, pvo_out and pvo_in represent the total pressure at the outlet and inlet sections of the volute casing.
The working flow rate for the double-suction pump was 1,200–1,400 m3·h−1, and this study used a flow rate in the range of 780–1,820 m3·h−1 (0. 6–1.4 Qd) as the study object. According to Equations (3)–(5), the energy loss of each component can be obtained (see Figure 9). Excluding the design flow rate, the energy loss of the impeller was greater than that of the suction and volute casings, whereas the energy loss of the suction casing was the lowest. The energy loss of each component was the lowest at the design flow rate and increased as the flow rate increased/decreased, particularly for the impeller.
Figure 9

Energy loss of each component at different flow rates.

Figure 9

Energy loss of each component at different flow rates.

Close modal

The total energy loss of each component can be obtained through Equations (10)–(12). However, studying the energy changes within each component is also important, and the sections that follow introduce them in order.

Suction casing and volute casing

As Figure 10 shows, according to the geometric shape of the suction casing, it can be divided into inlet, transition, and semi-spiral parts. Similarly, the volute casing can be divided into spiral and outlet parts. Table 4 lists the corresponding energy loss efficiencies for the different parts under different flow rates. For the suction casing, the energy losses in the inlet and transition parts increased as the flow rate increased, which accounted for a small proportion of the total loss. The semi-spiral part contributed most of the energy loss to the suction casing, which had minimal energy loss at the design flow rate. For the volute casing, the energy loss in the spiral part was significantly greater than that in the outlet part at a low flow rate. However, the energy losses in the spiral and outlet parts were nearly identical at the design/large flow rates, indicating that vortices or flow separations were present in the outlet part at design/large flow rates.
Table 4

Energy loss efficiency for each part under different flow rate

ItemsInlet (%)Transition (%)Semi-spiral (%)Spiral (%)Outlet (%)
0.6Qd 0.009 0.044 3.985 5.855 0.331 
0.8Qd 0.02 0.078 1.4 5.004 0.544 
Qd 0.036 0.119 0.398 3.473 1.523 
1.2Qd 0.059 0.197 0.692 2.496 2.365 
1.4Qd 0.1 0.332 1.128 4.873 3.012 
ItemsInlet (%)Transition (%)Semi-spiral (%)Spiral (%)Outlet (%)
0.6Qd 0.009 0.044 3.985 5.855 0.331 
0.8Qd 0.02 0.078 1.4 5.004 0.544 
Qd 0.036 0.119 0.398 3.473 1.523 
1.2Qd 0.059 0.197 0.692 2.496 2.365 
1.4Qd 0.1 0.332 1.128 4.873 3.012 
Figure 10

Sections in the suction casing and volute casing.

Figure 10

Sections in the suction casing and volute casing.

Close modal
To confirm the validity of the energy analysis approach, the flow field and pressure distribution of the suction and volute casings are described as follows. Figure 11 shows the streamlines in the suction casing at the design flow rate. Compared with the transition and semi-spiral parts, the inlet part had a more uniform streamline distribution. The maximum velocity occurred at S4 and S5 discharge sections, which also indicated that the minimum total pressure occurred at Sections S4 and S5.
Figure 11

Streamlines in the suction casing at the design flow rate.

Figure 11

Streamlines in the suction casing at the design flow rate.

Close modal
Figure 12 shows the total pressure contour of the S1–S5 sections in the suction casing at the design flow rate. The average total pressure on the S1–S5 sections decreased gradually, which was due to flow loss. The loss in the inlet part was relatively small and that in the semi-spiral part was the largest, which was consistent with the previous energy loss analysis. In addition, the total pressure near the casing wall was relatively low, indicating that flow losses mainly occurred in the near-wall region. A baffle plate was at the position with the smallest flow area in the semi-spiral part of the suction casing, which can effectively prevent fluid rotation or vortex generation.
Figure 12

Total pressure contour of the S1–S5 sections in the suction casing at design flow rate.

Figure 12

Total pressure contour of the S1–S5 sections in the suction casing at design flow rate.

Close modal
As Figure 13 shows, the streamline was relatively smooth at a low flow rate of 0.8 Qd for the entire volute casing. However, vortices were present at the outlet under Qd and 1.2Qd flow rate conditions. This also explains why the energy loss increased in the outlet at high flow rates. As the flow rate increased, the total pressure distribution in the volute casing tended to fall in the symmetry plane, as shown in Figure 13(b). The results indicated that the design of the volute casing deviated slightly from the flow condition of Qd, which could be corrected by adjusting the angle of the volute outlet.
Figure 13

Streamlines and total pressure contour in the volute casing at different flow rates. (a) Streamlines and (b) total pressure contour in the symmetry plane.

Figure 13

Streamlines and total pressure contour in the volute casing at different flow rates. (a) Streamlines and (b) total pressure contour in the symmetry plane.

Close modal

For the suction casing and volute casing, the energy loss caused by flow mainly occurred in the near-wall region, indicating that energy loss is closely related to the shape of the casing when there is no vortex exists. However, the energy loss has increased significantly with the generation of vortex. Hence, the design principle of the suction casing and volute casing is to reduce the generation of vortex.

Impeller

As Figure 14 shows, circular sections of S9–S15 were established within the double-suction impeller based on the ratio of the section radius to the impeller radius. S16 and S17 are the axial plane sections, and their distances from the symmetry plane were 25 and 50 mm, respectively.
Figure 14

Sections in the double-suction impeller.

Figure 14

Sections in the double-suction impeller.

Close modal
Figure 15 shows the average total pressure in each section at different flow rates. In Sections S9–S12, the average total pressure increased almost uniformly, and the growth rate decreased for Sections S12–S14. The average total pressure of Sections S14–S15 decreased slightly. This means that the blade contributed the most to the fluid in Sections S9–S12, and the profiles of Sections S12–S15 could be improved by optimising the performance of the impeller. In addition, the average total pressure first decreased and then increased as the flow rate decreased.
Figure 15

Average total pressure in each section at different flow rates.

Figure 15

Average total pressure in each section at different flow rates.

Close modal
Figure 16 shows the streamlines and total pressures in Sections S16 and S17 at different flow rates. Vortices occurred on the back of the blade at a low flow rate of 0.8 Qd, which explains the impeller's significantly increased energy loss at low rates. The streamline was relatively smooth at the intended flow rate Qd and at a higher flow rate of 1.2 Qd. With an increase in the flow rate, the impeller flow velocity increased gradually from the impeller's inlet to its outlet, as shown in Figure 16(a). As the flow rate increased, the impeller's total pressure decreased and then increased from the impeller inlet to its outlet, as shown in Figure 16(b).
Figure 16

Streamlines and total pressure in Sections S16 and S17 at different flow rates. (a) Streamlines and velocity and (b) total pressure.

Figure 16

Streamlines and total pressure in Sections S16 and S17 at different flow rates. (a) Streamlines and velocity and (b) total pressure.

Close modal

Cavitation performance analysis

The cavitation characteristics of a double-suction centrifugal pump are crucial indicators, which are usually evaluated by the available net positive suction head (NPSHa) and are written as
formula
(13)
where uin and pv represent the inlet velocity of pump and vapour pressure.
To further investigate the effects of inlet pressure, a two-phase mixture model and a cavitation model were adopted and described in Section 4.3, and a Zwart–Gerber–Belamri cavitation model (Zwart et al. 2004) was selected, which considers the effects of bubble dynamics. The cavitation behaviour is more serious at a low flow rate for the double-suction pump for water supply systems. Therefore, a cavitation investigation for the double-suction pump at a flow rate of 0.772 Qd was conducted, as shown in Figure 17. NPSH3% denotes a head drop of 3%, which is indicative of cavitation behaviour. The results of the numerical prediction were in good agreement with the data that have been measured, where the maximum error for the head was within 4% and was equal to 0.45 m for NPSH3%.
Figure 17

Measured and predicted cavitation characteristics at a flow rate of 0.772Qd.

Figure 17

Measured and predicted cavitation characteristics at a flow rate of 0.772Qd.

Close modal
Figure 18 shows the changes in energy loss of each component of the double-suction pump with and without cavitation. The energy loss efficiencies of the suction casing, impeller, and volute casing without cavitation were 1.48, 11.37, and 5.11%, respectively. The energy loss proportion in the suction casing changed slightly before and after cavitation, indicating that the effect of cavitation on this part was negligible. With decreasing NPSHa, the energy loss proportions of the impeller and volute casing increased. In addition, the energy loss of the impeller increased at a rate faster than that of the volute casing.
Figure 18

Energy loss of each component at a flow rate of 0.772Qd for different NPSHa.

Figure 18

Energy loss of each component at a flow rate of 0.772Qd for different NPSHa.

Close modal
Figure 19 shows the distribution of the impeller vapour volume fraction for different NPSHa. The cavitation region gradually migrated from the inlet edge of the blade to the middle area as NPSHa decreased, and the vapour volume fraction increased. Due to the low pressure on the suction surfaces of the blade, the bubbles were mainly concentrated on these surfaces. However, the pressure surfaces did not experience cavitation. The overall cavitation region and squeeze effect were both relatively small when NPSHa = 5.24 m. As NPSHa decreased to 3.2 m, numerous bubbles developed in the double-suction impeller, and the squeeze effect was more obvious.
Figure 19

Vapour volume fraction distribution in the impeller for different NPSHa.

Figure 19

Vapour volume fraction distribution in the impeller for different NPSHa.

Close modal

Energy loss optimisation

A previous energy loss and cavitation performance analysis revealed that the volute casing accounts for too much of the energy loss. The volute casing loss is greater than that of the impeller, which is unreasonable. Vortices at the outlet of the volute casing contribute considerably to the energy loss. To mitigate the effects of these vortices, the inclination angle of the volute outlet was optimised, and the best inclination value was 8° away from the volute tongue.

Figure 20 shows the results of the head H and efficiency η before and after optimisation. The figure shows that H and η increased under each flow rate after optimisation, particularly at high flow rates. At a flow rate of 1.4 Qd, the values of H and η exhibited the largest increases of 0.89 m and 3.36%, respectively. Prior to optimisation, H and η experienced rapid drops at flow rates of 1.2 and 1.4 Qd, as the energy loss of each component increased dramatically at high flow rates.
Figure 20

Head H and efficiency η before and after optimisation.

Figure 20

Head H and efficiency η before and after optimisation.

Close modal
Figure 21 shows the energy losses of the different components at various flow rates before and after optimisation. The energy loss of each component was reduced after optimisation, initially decreasing and then increasing as the flow rate increased. The energy loss of the suction casing showed little change before and after optimisation, and the maximum value was 0.12% at a flow rate of 0.6 Qd. The changes in energy losses for the impeller and volute casing were much greater than that for the suction casing, and the maximum values were 0.98 and 2.03%, respectively, at a flow rate of 1.4 Qd.
Figure 21

Energy losses of the different components at various flow rates before and after optimisation. (a) Suction casing, (b) impeller, and (c) volute casing.

Figure 21

Energy losses of the different components at various flow rates before and after optimisation. (a) Suction casing, (b) impeller, and (c) volute casing.

Close modal

In this study, the performance of a double-suction pump was investigated using theoretical, numerical, and experimental methods to obtain a more accurate energy loss prediction method. The conclusions are summarized as follows.

  • (1)

    The energy loss in the impeller was greater than those in the suction and volute casings, and the value in the suction casing was the lowest. Each component had a minimal energy loss at the intended flow rate, which increased as the flow rate increased/decreased, particularly for the impeller.

  • (2)

    For the suction casing, the energy losses in the inlet and transition parts increased as the flow rate increased, accounting for a small proportion of the total loss. For the volute casing, the energy loss in the spiral part was significantly greater than that in the outlet part at a low flow rate. However, the energy losses in the spiral and outlet parts were nearly identical at the design/high flow rate, indicating that vortices or flow separation occurred in the outlet part. For the impeller, the average total pressure increased uniformly for Sections S9–S12, and the growth rate decreased for Sections S12–S14. The average total pressure of Sections S14–S15 decreased slightly.

  • (3)

    The proportion of energy loss in the suction casing changed slightly before and after cavitation. However, the proportion of the impeller and volute casing increased with a decrease in NPSHa, and the loss in the impeller increased at a faster rate than that in the volute casing. The cavitation region gradually migrated from the inlet edge of the blade to the middle area as NPSHa decreased and the vapour volume fraction increased. Due to the low pressure of the suction surfaces of the blade, the bubbles were mainly concentrated on these surfaces, and the pressure surfaces did not experience cavitation.

  • (4)

    With the angle of the volute outlet part inclined 8° away from the volute tongue, H and η increased, and each component's energy loss decreased. The changes in the energy losses for the impeller and volute casing were much greater than that for the suction casing, and the maximum values were 0.98 and 2.03%, respectively, at a flow rate of 1.4 Qd.

This work was supported by National Key Research and Development Program of China (Grant No. 2022YFB4003404).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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