Analysis of internal flow characteristics of a multistage pump during start-up

In order to study the transient characteristics during the startup process of a multi-stage pump, the Flowmaster software was used to obtain the rotating speed and flow characteristic curves of the pump under different valve openings, and analyze its internal flow and structural characteristics based on numerical simulation. The study results indicate that the time required for the flow to reach a steady state lags significantly behind the time required for the rotational speed to reach a stable state during the initial stage of pump start-up. By comparing the pressure distributions of a multistage pump under quasi-steady state and transient conditions, it can be seen that the internal flow field evolution of the pump under transient condition during the startup process lagged behind that under quasi-steady state condition, which makes using quasi-steady state laws were not suitable for describing the changes in transient flow field. The deformation law of the first-stage impeller under stable and start-up conditions was similar. The impact of increased flow rate on deformation was relatively weak and the difference in deformation values under different flow rates was relatively small under transient condition.


Introduction
The fire pump is an important component of the fire protection system, its extinguishing principle is based on water as the material physical characteristic: spray water onto the fire site to extinguish fire quickly and effectively, minimize the harm which caused by the fire.Fire pumps are widely used due to their low cost, flexibility, and high efficiency, making them the main force in firefighting equipment in various countries.When a fire occurs, the required water needs to be pressurized by the pump.Multistage centrifugal pumps have rapidly developed and become irreplaceable in fire-fighting [1].Whether the pump can be started smoothly will have a significant impact on the fire operation process [2][3].As a result, higher requirements have been placed on their stability and durability [4].
During the start-up/shut-down process of the centrifugal pump, the rapid changes in rotating speed and flow rate cause significant variations in the parameters within the flow field within a short period of time, which may lead to the inability of the pump to operate properly.Elaoud et al. [5] conducted numerical simulations of transient flow in a cylindrical pipe induced by the start-up of a centrifugal pump.It was found that there were significant variations in hydraulic parameters as the start-up time increased.The three factors causing the dynamic stability deviation of the pump during the transient process were: the mass of water in the pipeline, the percentage of valve opening, and the start-up time.Chalghoum et al. [6] conducted theoretical analysis on the transient flow inside the centrifugal pump and studied the transient behavior during the initial stage of start-up.Numerical simulations of a centrifugal pump with different start-up time and varying valve openings were conducted to reveal changes in its transient characteristics.
During the start-up of a centrifugal pump, the rotor components experience stress responses over time, which impacts fatigue damage to impeller hub and pump shaft [7].Li W [8] studied the stress and deformation of the impeller under steady state, transient conditions for an axial flow pump based on a two-way altering fluid-structure interaction method.It was found that under the combined effect of the changing internal flow field and centrifugal force during start-up, the deformation had increased by 68.7% compared to the steady state condition, making it more prone to fatigue damage.
The main purpose of this study is to explore the variation of performance parameters of a multistage pump during the start-up process and to obtain the transient flow field distribution at different valve opening percentages.Due to the short duration of the start-up process and the rapid changes in rotating speed and flow rate, the components in contact with the internal fluid are subjected to fluid pressure.Therefore, the structural strength of the pump is analyzed to understand its variation.This research has practical significance in improving the stability and reliability of multistage pumps.

Pump model
The computational model in this study is a multistage fire pump which composed of 7 impellers and 6 guide vanes.The shape of the water body of the pump is shown in Figure 1.The detailed information is listed in Table 1.

Grid description and validation
The mesh partitioning of the model was used by ANSYS ICEM, where the mesh for the computational domain is shown in Figure 2. The impeller section used a structured hexahedral mesh, while other parts of the computational domain used tetrahedral mesh.Since this study focused on a 7-stage centrifugal pump, directly performing grid independence analysis on a multistage pump will result in a large number of grids and low computational efficiency.Therefore, a single-stage pump was used for validation.When the number of grid for the single-stage impeller was about 1.7 million and the number of grid for the guide vanes was about 1.1 million, the total 7-stage centrifugal pump computational domain was set to about 21.2 million.As the number increased, the head change decreased and gradually stabilized.Figure 3 displays the grid independence verification results of a single-stage pump under design condition.Consequently, these grid partitioning results were selected for subsequent analysis of multistage pump.

Boundary condition settings
This study used ANSYS CFX to perform the steady simulation of flow field calculation of the model pump.Pure water was used as the working medium.Compared to the k-model, RNG k-model is better at handling strong streamline curvature, vortex, and rotation.It solves the problem of unknown variables exceeding the number of equations caused by the reynolds stress term [9].Therefore, this model was selected for the further research.The inlet boundary condition was set to total pressure, and the reference pressure was set to 1 atm, the outlet boundary condition was set as a mass flow rate boundary condition.The convergence criterion for residual calculation was set to be 10 -5 .Load the relationship between rotating speed and time during transient calculation by writing a user-defined function, the rotating speed variation during the start-up process usually follows an exponential form.Based on previous research [10], the start-up process rotating speed variation is usually exponential: where f is the stable rotating speed after start-up, in this case, 3500 r/min, T na is the nominal acceleration time, which is the time it takes for the stable rotating speed to rise to 63.2% of final rotating speed, in this case, 0.367 s.
Centrifugal pumps are commonly started with closed valve to prevent damage to the motor from power overload during the start-up process, which can affect its stable operation.During the closed valve start-up, the pump operates at the closure exit point, the flow rate can be considered as 0 m 3 /h.Once the closed valve start-up is completed, the outlet valve opening percentage will be adjusted to increase the flow rate to the desired value.To analyze the variation characteristics of various performance parameters of the centrifugal pump during the transient process and reveal its transient characteristics, the relationship between flow rate and time during the open valve start-up is obtained by using Flowmaster.As shown in Figure 4, the operating model was built by Flowmaster.To make the simulation results much closer to the actual results, the parameters used in this simulation of the multistage pump are set according to actual experimental measurement.The total time for numerical simulation of the open valve start-up process was 3.0s.
Figure 5 shows the characteristic curves of the rotating speed and flow rate obtained when the gate valve was adjusted to different valve openings.According to previous studies [11][12], when the rotating speed remained constant, the shaft power increased significantly with the increase of the valve opening or flow rate.Consequently, the torque output by the motor also increased.
Compared to the rotating speed, the increase of flow rate was noticeably lagging.In the early stage of pump start-up, the flow rate increased slowly, with the increase of time, the rotating speed increment gradually accelerated until the flow rate stabilized.

Experimental methods
This study conducted an experiment on the external characteristics of the multistage pump on an enclosed test bench at the Wenling Institute of Product Quality Inspection, Zhejiang Province.The schematic figure of the external characteristic test device for the pump is shown in Figure 6.A high torque motor was used in the experiment, after the start-up process was completed, the motor output shaft and the pump input shaft were quickly connected using an electromagnetic clutch, the rotating speed reached the rated rotating speed within 3.0 s.A pressure sensor was installed at the inlet and outlet of the test pump to measure the pressure, make it easy to measure head.

Comparison of numerical calculation and experimental results
To verify the accuracy of the established model, a comparative analysis was conducted between the experimental data and the simulated data of the pump model in this study.The dimensionless volumetric flow rate and dimensionless head were used for description, the definition of both were as follow.Figure 7 shows the comparison between the experimental and simulated head.The trend of both were consistent with an error within 5%, validating the accuracy and reliability of the established model.

Analysis of internal flow characteristics during steady state process
Figure 8 shows the pressure distribution results of the first, second, and last stage impeller under different operating conditions.Due to the high speed rotation of the impeller and its worked on the fluid, a low pressure area was formed at the leading edge of the blade and the pressure reached its maximum at the blade outlet.The pressure of impeller in different stages continuously increased from inlet to outlet.As the flow rate increased, the pressure of impeller in the same stage gradually decreased.
In Figure 8 (a), as the flow rate gradually increased, the pressure on the pressure side of the blade at the same radius was greater than the value on the suction side, the pressure value near the impeller hub gradually decreased with the increase of flow rate.In Figure 8 (b), the fluid flowed from the first-stage impeller to the next stage, and the second-stage impeller further worked on the incoming flow of the first-stage impeller.The overall pressure was higher than the previous stage.Under high flow rate condition, the pressure gradient distribution was uniform, the low pressure area increased.In Figure 8 (c), the pressure distributions inside the last-stage impeller were similar to that of the first two stages.

Analysis of internal flow characteristics during transient process
Quasi-steady state refers to the absence of significant changes in the flow state within a short period of time, while transient state is the result of continuous changes over a period of time, the definition of the two do not match.In the subsequent transient analysis, the quasi-steady state results will be used as the initial condition for transient calculation.Figure 9 clearly shows the pressure distributions of the first-stage impeller under quasi-steady and transient calculation.
Figure 9(a) shows the temporal variation of pressure distribution inside the first-stage impeller of a centrifugal pump under quasi-steady state condition.As the rotating speed increased, the pressure significantly increased.At t=0.42 s, the low pressure region was concentrated at the suction side of the blade leading edge, the high pressure region near the outlet was still unstable and distributed in a relatively disordered manner.At t=0.69 s, the area of the high pressure region increased and reached a stable value as the rotating speed increased.At t=2.2 s, the pressure gradient distribution in the impeller channel was uniform, but the low pressure area near the leading edge of the blade increased.As the impeller rotating speed increased from 0 r/min to 3500 r/min, the inlet pressure of the impeller gradually decreased.At t=0.42 s, the pressure under quasi-steady state condition was slightly higher than the pressure value under transient condition.
As the flow rate continued to increase, at t=0.69 s, there was an expansion of the low pressure area near the leading edge of the blade.When the time was t=2.2 s and the rotating speed reached a stable value, the low pressure area occupied most of the impeller flow channel, which was significantly different from the pressure distribution under quasi-steady state condition at the same time.
By comparing the pressure distributions of quasi-steady state and transient at different rotating speeds, it could be found that the flow field evolution lagged behind the change rate of quasi-steady state in a short period of time during start-up.The pressure distribution trends under quasi-steady state condition were the same, while the pressure changes under transient condition were more obvious.The pressure distributions of the two were not the same, which made using quasi-steady state distributions not suitable for describing the changes in transient flow field.

Analysis of flow field during valve opening and transient process
To analyze the impact of transient effect on the external characteristics of a multistage pump when the valve opening changes.Figure 10 shows the external characteristic change curves at different time.In Figure 11, it could be clearly observed that when the rotating speed was 2400 r/min, the flow rate and rotating speed had not yet reached stability.At this moment, a large number of vortices appeared in the impeller and guide vane flow passages, occupying almost the entire flow passages near the impeller outlet in a long strip shape.As the start-up time reached t=0.69 s, the streamline distribution within the impeller became more uniform, only a small range of vortices existed at the tail of the guide vane.As the speed increased to the rated rotating speed, the operating condition was relatively stable.At this moment, the vortex clusters appeared in the impeller and guide vane flow passages were broken, the distribution of vortices significantly reduced, which compared to the initial stage of start-up.As the flow rate increases, the relative velocity in the flow channel also gradually increases.The original vortices occupying the impeller and guide vane flow passages gradually broke down into smaller vortices, resulting in a more uniform flow distribution.

Analysis of structural dynamics during valve opening and transient process
Steady state conditions refer to both idle condition and stable operating condition at various flow rate.Mode shapes of the rotor structure were extracted for the idle operating condition and design condition, the deformations of the first-stage impeller during the idle condition and design condition are shown in Figure 12.
In Figure 12(a) and (b), the impeller only experienced rotational centrifugal force without any pressure under idle condition.The deformation gradually increased along the radial direction.Under design condition, the deformation of the impeller was calculated based on the principle of fluid structure coupling.The maximum deformation of the impeller was concentrated in the outlet area of the impeller shroud and hub.Compared to the idle operating condition depicted in Figure 12(a), the rotor components were affected not only by the rotating centrifugal force, but also by the liquid pressure difference in the internal flow field.During the short start-up period of a multistage pump, the impeller interacts with the fluid during high-speed rotation, causing vibration and potentially affecting the safe and stable operation of the pump [13].Figure 12(c) shows the deformation situations of the impeller when the valve opening was 0.4 and the flow rate were 0.42 m 3 /h, 4.2 m 3 /h, and 15.5 m 3 /h respectively.Before reaching the rated rotating speed, the total deformation of the impeller gradually increased radially, following the same deformation pattern as under stable condition in Figure 12(b).The deformation pattern of the first-stage impeller was similar, the maximum shape variable of the impeller was located near the impeller outlet.However, the impact of increased flow rate on deformation was relatively weak and the difference in deformation values under different flow rates was relatively small.But the impact of increased flow rate on deformation was relatively weak and the difference in deformation values under different flow rates was relatively small under transient condition.

Figure 4 .
Operation model of multistage fire pump.

Figure 6 .
Figure 6.External characteristic testing device.A high torque motor was used in the experiment, after the start-up process was completed, the motor output shaft and the pump input shaft were quickly connected using an electromagnetic clutch, the rotating speed reached the rated rotating speed within 3.0 s.A pressure sensor was installed at the inlet and outlet of the test pump to measure the pressure, make it easy to measure head.

Figure 8 .
Figure 8. Pressure distribution under different operating conditions.

Figure 9 (
Figure 9(b) shows the temporal variation of pressure distribution inside the first stage impeller of a centrifugal pump under transient operating condition.As the impeller rotating speed increased from 0 r/min to 3500 r/min, the inlet pressure of the impeller gradually decreased.At t=0.42 s, the pressure under quasi-steady state condition was slightly higher than the pressure value under transient condition.As the flow rate continued to increase, at t=0.69 s, there was an expansion of the low pressure area near the leading edge of the blade.When the time was t=2.2 s and the rotating speed reached a stable value, the low pressure area occupied most of the impeller flow channel, which was significantly different from the pressure distribution under quasi-steady state condition at the same time.By comparing the pressure distributions of quasi-steady state and transient at different rotating speeds, it could be found that the flow field evolution lagged behind the change rate of quasi-steady state in a short period of time during start-up.The pressure distribution trends under quasi-steady state condition were the same, while the pressure changes under transient condition were more obvious.The pressure distributions of the two were not the same, which made using quasi-steady state distributions not suitable for describing the changes in transient flow field.

Figure 9 .
Figure 9.Comparison of quasi-steady state and transient flow field evolution of the first-stage impeller during transient process.

Figure 10 .Figure 11 .
Figure 10.Transient external characteristic change curves during the valve opening process.During the initial stage of valve opening and start-up, the flow suddenly changed and head underwent a significant change with a significant decrease.As the flow rate gradually increased, head gradually increased.At t=1.4 s, the head reached the first local peak.After this period of time, the head showed a gradual downward trend.When the flow rate gradually increases to close to the design operating condition, the head value and efficiency value on the transient characteristic curves gradually approach those on the steady state characteristic curves, as shown in Figure7and Figure10.The efficiency of the multistage fire pump still fluctuated in a small range during the initial start-up stage, but as the flow rate increased, it reached the optimal design point in about t=1.72 s.
(a) Idle operating condition.(b) Design condition.Q=0.42 m 3 /h 2400 r/min Q=4.2 m 3 /h 2950 r/min Q=15.5 m 3 /h 3500 r/min (c) Deformation distribution of the first-stage impeller at different flow rate with a valve opening of 0.4.

Figure 12 .
Figure 12.Comparison of deformation distribution of impeller under stable and transient operating conditions.During the short start-up period of a multistage pump, the impeller interacts with the fluid during high-speed rotation, causing vibration and potentially affecting the safe and stable operation of the pump[13].Figure12(c)shows the deformation situations of the impeller when the valve opening was 0.4 and the flow rate were 0.42 m 3 /h, 4.2 m 3 /h, and 15.5 m 3 /h respectively.Before reaching the rated rotating speed, the total deformation of the impeller gradually increased radially, following the same deformation pattern as under stable condition in Figure12(b).The deformation pattern of the (a) In the early stage of start-up, the flow rate increased relatively slowly with a significant lag behind the rotating speed of increase.(b) Comparing the pressure distribution patterns of quasi-steady state and transient at different rotating speed, the evolution of the flow field in the transient process lags behind the evolution of the flow field in the quasi-steady state process.The pressure distribution trends under quasi-steady state condition were similar, the pressure distribution trends under transient condition were more significant.(c) The deformation laws of the first-stage impeller under stable and start-up conditions were similar.