Performance improvement of a double-suction centrifugal pump for water supply system based on energy loss analysis and cavitation behaviour prediction

B_im

impeller outlet width (mm)

D_im

impeller diameter (mm)

D_imn

impeller inlet diameter (mm)

D_in

pump inlet diameter (mm)

D_out

pump outlet diameter (mm)

approximate relative error (%)

extrapolated relative error (%)

F_cond

empirical calibration parameters of condensation

F_vap

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)

n_s

specific speed

N

total number of cells used for the simulation

p

pressure (Pa)

p_{im_in}

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

p_{im_out}

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

p_in

total pressure at the inlet of the pump (Pa)

p_out

total pressure at the outlet of the pump (Pa)

p_{su_in}

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

p_{su_out}

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

p_v

vapour pressure (Pa)

p_{vo_in}

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

p_{vo_out}

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

Q

flow rate (m³·h⁻¹)

Q_d

design flow rate (m³·h⁻¹)

R_B

radius of a nucleation site (m)

u

velocity (m·s⁻¹)

u_in

inlet velocity of pump (m·s⁻¹)

ΔV_i

volume of the i-th cell

Z

blade number

α_nuc

nucleation site volume fraction

α_v

vapour volume fraction

μ_l

liquid dynamic viscosity (Ns·m⁻²)

μ_m

mixture of dynamic viscosity (Ns·m⁻²)

μ_t

turbulent viscosity (Ns·m⁻²)

μ_v

vapour dynamic viscosity (Ns·m⁻²)

ρ_l

liquid density (kg·m⁻³)

ρ_m

mixture of density (kg·m⁻³)

ρ_v

vapour density (kg·m⁻³)

ω

angular velocity (rad·s⁻¹)

η

efficiency

η_im

impeller loss efficiency

η_su

suction casing loss efficiency

η_vo

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 k–ε (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 k–ω (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 k–ε and k–ω 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.

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.

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 Q_d. 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.

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.

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

Parameters .	φ = static pressure of P1/Pa .	φ = 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%

Parameters .	φ = static pressure of P1/Pa .	φ = 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%

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The findings demonstrate that the error of the k–ω model was higher than that of the RNG k–ε 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.

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.

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.

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.

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 Q_d.

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.