Transient characteristics during start-up of dual pumps in the prefabricated pumping station

The prefabricated pumping station featuring a relatively new structure plays an essential role in constructing new rural drainage facilities and managing waterlogging in urban areas (Hsu et al. 2013; Zeferino et al. 2017). The prefabricated pumping station comprises a storage tank, single or multiple pumps, pipes, and various fittings. Typically, two identical pumps will be installed in the prefabricated pumping station. The prefabricated pump station's diameter and height are generally less than 4 m and 12 m due to the limitation of transportation conditions, respectively. The restricted space of the tank constrains the internal flow of the prefabricated pump station. A disturbance between neighboring components is inevitable (Olszewski 2016; Li et al. 2019).

In recent years, with the continuous expansion of the application scope of the prefabricated pump station, the internal flow characteristics have been concerned extraordinarily. Based on the CFD results, Zhang et al. (2021) found that the geometric installation parameters of pumps had an impact on the hydraulic performance of the prefabricated pump stations. Wang et al. (2020) used the discrete phase model (DPM) to study the influence of the suspension height and interval of the pumps on the deposition performance of a prefabricated pump station and proposed the deposition rate and area ratio of the easy deposition region to evaluate the anti-deposition performance. But so far, the existing research literature has been focused on revealing the hydraulic performance of a prefabricated pumping station under steady operation. The liquid level in the prefabricated pumping station constantly fluctuates, resulting in the frequent start and stop of the transport pump. Enough consideration should be paid to the transient start-up process in the prefabricated pumping station. The complex operation mode of the prefabricated pump station is the main factor affecting the performance of the transfer pump. During the start-up of the pump, the drastic variation of the external characteristic parameters of the pump, such as flow rate and head, may cause unstable flow. The internal flow in the prefabricated pumping station responds rapidly to the pump rotational speed due to the effect of flow involvement. Remarkably, one pump is started during the operation of the other pump. The intricate flow structures in the prefabricated pump station are of high possibility.

However, it is not easy to detect the internal flow field with optical flow measurement technology, given the complex structure of the prefabricated pump station. Nevertheless, the experimental research on the pump, especially the research on the starting characteristics of the pump, can provide a reference for this study. Fu et al. (2020) investigated the axial flow pump's flow behaviors and transient characteristics during start-up. They found the unstable flow in the impeller and guide vane area and the instantaneous impact characteristics remarkable. This unsteady flow may also arise during the start-up of the prefabricated pump station. Transient behaviors of a centrifugal pump during rapid start-up was experimentally investigated by Tanaka et al. (2021) and illustrated that the time-dependent flow field change in several stages. Alternatively, the CFD technique could reveal the evolution process of internal flow structure and the variation of external characteristic parameters (Li et al. 2018; Barrios et al. 2019; Liu et al. 2021). The VLES model was used to simulate the dominant vortex structure (horn-like vortex) in an axial flow pump by Zhao et al. (2021). Wang et al. (2022) simulated gas-liquid two-phase flow using a volume of fluid (VOF) mathematical model. Li et al. (2020) obtained the effect of the distorted inflow condition on the performance of a reactor coolant pump numerically. They experimentally verified that the computational fluid dynamics (CFD) technique could be employed in performance predictions. Furthermore, the coupling of the discrete element method (DEM) and the CFD technique has been attempted to multiphase fluid flow.

Moreover, different from the study of the transient characteristics of an impeller pump independently starting, interaction mechanisms of the internal flow field of multi-flow passage components in a prefabricated pumping station have rarely been reported. The prefabricated pumping station is a drainage system comprised of multiple components, among which imparity in flow characteristics is remarkable. It may cause mutual interference between the operation of the two pumps. Especially in the transportation of sewage, sedimentation may occur in the prefabricated pumping station. The instantaneous impact characteristics during start-up may affect the stability of the pump station operation.

The emphasis of the presented work is concerned with the complex flows in a prefabricated pumping station that allows transporting the solid-liquid two-phase medium. Unsteady numerical simulations were performed for the start-up of the prefabricated pumping station under two different start-up conditions, namely the start-up of the pump P_A and the start-up of the pump P_B during the operation of the pump P_A. Time-dependent variation of the pump performance and instantaneous flow characteristics of the prefabricated pumping station during the start-up of the two pumps were described. Solid-liquid two-phase medium parameter distributions, and interference between two pumps, were investigated comprehensively. Instantaneous flow features during the start-up of the two pumps in the prefabricated pumping station were analyzed. The present study aims to reveal transient characteristics in a prefabricated pumping station during start-up.

where the subscript l represents liquid phase and s solid phase; φ is the volume fraction; ρ is the density; is the velocity.

The standard k–ε turbulence model was selected for turbulence modeling to accomplish the closure of RANS equations, and standard wall functions were used to treat near-wall flows (Balakin et al. 2011). The standard k–ε turbulence model can accurately predict the complex flow patterns inside the prefabricated pumping station. The Eulerian-Eulerian model was employed as the multiphase flow model (Shi et al. 2010; Ahmadkermaj et al. 2020). Such a multiphase flow model has been widely used to simulate solid-liquid two-phase flows. The Eulerian-Eulerian model can fully simulate the turbulent transport of solid particles and obtain the detailed spatial distribution of solid particles (Kaushal et al. 2012). The Eulerian-Eulerian model can describe the influence of particle inertia on particle gravity flow, including the flow structure and dynamic characteristics of particle gravity flow. This model also applies to the sedimentation of a non-Brown sphere with uniform size in a viscous fluid. A good agreement of computed results with this model and experimental data is observed (Messa et al. 2015).

Based on practical requirements, the mixture of water and sand particles with a mean diameter of 0.5 mm was selected as the solid-liquid two-phase medium to be transported. The density of sand particles was 2,300 kg/m³. The volume fraction possessed by the solid phase in the mixture was set as 3%. At the inlet of the prefabricated pumping station, the velocity inlet boundary conditions were imposed. Liquid velocity magnitude was calculated with the designated flow rate and the inlet area. Velocities of the two phases were set as equivalent and uniformly distributed over the inlet section. For the two start-up modes, the inflow rate of 1,940 m³/h was selected for the start-up of the pump P_A, and the inflow rate of 3,880 m³/h was selected for the start-up of the pump P_B during the operation of the pump P_A. At the outlet of the prefabricated pumping station, constant static pressure at local atmospheric pressure was defined, and the flow direction was perpendicular to the outlet section (Kang et al. 2020). The time step of the unsteady numerical simulation was set to 0.0022 s, which was demonstrated to sufficiently capture the flow process in such pump arrangements.

To eliminate the uncertainty possibly caused by insufficient grid numbers on the numerical simulation results, seven sets of grids with numbers ranging from about 4.75 to 8.19 million were selected to evaluate the dependence of the pump head on the pump P_A, and the solid-phase concentration averaged over the inlet section of the pump P_A on the grid resolution. The corresponding results are listed in Table 1 (Kang et al. 2020). As the grid number exceeded 724 million, the gap between adjacent pump heads or solid-phase concentrations is below 2%. Therefore, Grid scheme E was adopted in the current simulations.

As for the start-up of the pump P_B during the operation of the pump P_A, as shown in Figure 6(b). It is noticeable that the pump head changes irregularly during the first 0.22 seconds of the pump P_B start-up, as shown in Figure 6(c). As the rotational speed of the pump P_B increases, the pump head changes to a more regular increase. It is apparent that the pump P_B is susceptible to interference from the operation of the pump P_A when the speed is low. The head change during the start-up process of the pump P_B is gentler, and there is no apparent mutation, so the instantaneous impact on the head is weak. However, the pump P_B starts with a maximum head of 13 m, nearly 18% higher than the design head. It can be clearly reflected in Figure 6 that at the initial start-up stage, the growth rate of the pump head growth rate is less than that of impeller rotation speed. Therefore, it can be concluded that the pump head's response velocity lags behind the impeller rotation acceleration.

As for the start-up of the pump P_B during the operation of the pump P_A, the velocity of the liquid phase near the pump P_A inlet is exceptionally high overall. In the pump P_B start-up process, the liquid phase's velocity near the pump suction gradually increases, and the flow velocity presents the same rule as that of pump P_A start-up. However, the velocity uniformity on the section near the inlet of the pump P_A is destroyed. It is further revealed that there is mutual interference between the two pumps. In the first 0.55 s of the pump P_B start-up, the flow of the section is featured by uniform distribution, demonstrated by the streamlines. On the one hand, due to the more substantial suction capacity of the pump P_A, the medium mainly flows to the pump P_A at this moment. On the other hand, with the gravity effect, pump P_B's rotational speed is insufficient to disturb the flow. The two factors jointly contribute to the uniform flow distribution in the section. Nevertheless, with the increased rotation speed of the pump P_B, the mutual interference between the pump P_B and the pump P_A enhances, thereby destroying the uniform flow. The mutual interference between pumps is the main reason that causes the pump performance to deviate from the design condition and unstable operation.

In Figure 8(b), the axial velocity distribution at the pump inlet section during the start-up of the pump P_B is exhibited. The axial suction velocity of the solid particles at the pump inlet is relatively smaller, mainly due to the combined influence of the impeller rotation of the pump P_A and gravity. However, due to the disturbance and dispersion of the solid particles in the storage tank by the pump P_A, when the rotational speed of the pump P_B reaches the nominal rotational speed, the axial velocity of the solid particles at the inlet of the pump P_B is greater than that of the pump P_A. Such a flow pattern mitigates the deposition in the storage tank, which is beneficial for the pump P_B to transport solid particles.

The two different start-up conditions exhibit the same changing tendency, i.e., the radial force exerted on the fluctuating impeller grows with the pump rotational speed increase. On the one hand, the medium's suction volume increases with the pump's acceleration. On the other hand, the unsteady start-up process of the pump results in an unstable internal flow field. The two factors jointly contribute to the various characteristics of the radial force exerted on the impeller during the start-up process. The difference in the highest radial force exerted on the impeller is significant for two different start-up conditions. At the end of the start-up process, the radial force exerted on the impeller of the pump P_B is reduced by nearly 200 N compared with that on the impeller of the pump P_A.

In this work, unsteady numerical simulations were performed to investigate the start-up process of the prefabricated pumping station under two different start-up conditions. Time-dependent variation of the pump performance and instantaneous flow characteristics of the prefabricated pumping station during the pump start-up were identified.

At the initial start-up stage of two pumps, the response velocity of the increase of the pump head lags behind the acceleration of impeller rotation. There is a transient impact on the head of the pump P_A. The pump P_A head increases sharply by nearly 73% relative to the maximum head from 1.8 s to 2.2 s. The maximum starting head of the pump P_B is 13 m, which exceeds the design head by 18%. The transient impact of the head and the deviation of the maximum head from the design head during start-up may cause damage to the pumps, valves, and pipes, especially when transporting solid-liquid two-phase media. Therefore, the reliability of components should be fully considered in the design of a prefabricated pump station.

Intense disturbance stemming from the pump P_A and the pump P_B operation to the tank's medium is demonstrated. Although the two pumps are symmetrically arranged in the storage tank of the prefabricated pump station, the flow fields formed by the start-up of the pump P_A and the pump P_B are not identical. The pump P_A and pump P_B also have different suction capacities for solid particles during start-up. Meanwhile, the difference in radial force exerted on the two pumps is evident during start-up. The radial force exerted on the impeller of the pump P_B is reduced by nearly 40% compared with that on the impeller of the pump P_A at the end of the start-up process. It indicates that there is apparent interference between the two pumps. Therefore, the inter-pump distance of the two pumps should be reasonably designed to mitigate the interference characteristic.

In this paper, limited by the experimental conditions and methods, only the numerical simulation method is used to qualitatively study the transient flow characteristics during the start-up of dual pumps in prefabricated pump stations. In the follow-up research, on the premise of improving the flow measurement and visualization methods, model experiments can be used to visualize the complex flow in the prefabricated pump station and obtain quantitative research results.

This study was supported by the National Natural Science Foundation of China (Grant No.51809081), the Natural Science Foundation of Jiangsu Province (Grant No. BK20201315), the China Postdoctoral Science Foundation (Grant No.2019M661707), the Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No.2019K095), and the Science and Technology Plan Project of State Administration for Market Regulation of China (Grant No. 2021MK060).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.