Effect of valve opening on starting performance of pump as turbine

doi:10.21203/rs.3.rs-1992736/v1

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Effect of valve opening on starting performance of pump as turbine

https://doi.org/10.21203/rs.3.rs-1992736/v1

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The study on transient characteristics of pump as turbines during atypical startup has not been deeply explored yet. In order to reveal the transient characteristics of a small centrifugal pump reversing as turbine during startup process in this paper, the transient hydraulic performance experiments are conducted for three steady rotational speed cases. Under the condition of each case, three, five and, three valve opening scenarios are completed to measure the performance. The dimensionless analysis are also employed so as to better reveal transient behavior of the pump as turbine during atypical startup. The results show that the rise rate of each performance parameter is different, wherein the shaft power and rotational speed have the fastest rising rate, followed by the flow rate, and the head rise is the slowest. It is clearly seen that the shock phenomenon in static pressure easily occurs at the outlet of pump as turbine. With the increase of valve opening, the dimensionless flow rate, head and, power coefficient all show the evolution trend of gradually increasing.

pump as turbine

valve opening

startup

transient characteristics

dimensionless

In the petrochemical, refining, and, desalination industries, there is a large amount of high-pressure fluid that is depressurized to low pressure or discharged directly through pressure reducing valves. In seawater desalination systems, the pressure of waste concentrated brine discharged from membrane vessels is as high as 5.5 to 6.0 MPa [1]. If it is discharged directly without energy recovery, it will cause serious energy waste. At present, the use of centrifugal pump reversal as a hydraulic turbine (pump as turbine, abbreviated PAT) is a very important means to achieve the recovery of liquid pressure energy.

It is found from the published literatures that most of scholars obtain the hydraulic performance of PATs based on their hydraulic performance under pump operating conditions. Williams et al. conducted a forward and reverse performance comparison experiments on 35 pumps so as to compare the accuracy of eight prediction methods [2]. It was found that none of the eight prediction methods was completely accurate. Singh et al. proposed a unified prediction model to describe the performance of PATs based on the basic flow theory of pumps [3]. The model is able to clearly display the prediction error, wherein the specific speed is thought as variable. Huang et al. theoretically derived the performance equation of turbine impeller based on the effect of vane outlet slip and finite vane number, and proposed a prediction equation for the optimal operating point of PAT, which pointed out the matching range of optimal parameter of PAT and external load [4]. The essence of this study is to apply the area ratio principle of pump to the optimal design of the PAT, which has a good practical value.

Derakhshan et al. theoretically derived a method for calculating the optimal efficiency point of PATs, and the results confirmed that the predicted value based on this method is slightly lower than the experimental value [5]. Shi et al. proposed three methods for calculating the slip coefficient of impeller outlet of PAT based on different assumptions [6]. It was found that the ratio of the induced velocity on the blade pressure side over the slip velocity on the impeller outlet was equal to the ratio of the areas of two triangles with the pressure side and impeller outlet as one curved edge respectively, the slip factor is subject to a very good accuracy. This literature can be beneficial to improve the prediction accuracy of theoretical performance of PAT. Li conducted a detailed theoretical study on the relationship between the performance curves of pump and PAT when conveying viscous oil, and proposed multiple expressions for correction factors describing the performance correlation between them [7]. This literature provides an important reference for the selection of PAT products with viscous oil as the working medium, and the delivering medium in the study is a high-viscosity viscous oil, which is different from the previous clear water medium. Tan et al. proposed a performance prediction method with high accuracy [8]. The specific speed and impeller diameter characteristics are found to be approximately linear between the pump operating conditions and the turbine operating conditions.

Wang et al. designed four forward-curved impellers with different blade inlet and outlet angles and found that the efficiency curve of the forward-curved impeller became flatter and the optimal efficiency increases significantly compared with the backward-curved impeller [9]. Doshi et al. chamfered the inner side of the hub and shroud [10]. Moreover the blade inlet of the PAT impeller is also chamfered. It is found that the hydraulic loss could be effectively reduced and the conveying efficiency could be improved. What is more, modifying backward-curved blade angle could cause hydraulic loss to reduce to 5–10%. Li et al. found that the flow rate and the energy head consumed under the optimal working condition of the turbine increased with the increase of viscosity, while the hydraulic efficiency showed a decreasing trend, and the output shaft power was mainly determined by the liquid density [11, 12]. It is also pointed out that viscosity has a more serious impact on turbine performance than pumps. The net positive suction head (NPSH) of the PAT increases with the increase of liquid viscosity, but the magnitude is relatively small.

CFD (computational fluid dynamics) has become one of the important methods for studying PATs [13, 14, 15]. The authors' preliminary numerical calculations found that as the liquid viscosity increased, the morphology and size of the lobe cavities at the outlet side of the vane under each operating condition did not change significantly, but the length of the cavity at the tip of the drain cone gradually became shorter [12].

To sum up, it can be found that the scholars have carried out lots of studies to predict hydraulic performance of PAT from various aspects, however, these studies aim to the stable working condition, i.e., the performance prediction study under the steady rotational speed condition, while the study on starting characteristics of the PAT has rarely been involved. In this paper, the performance experiments would be conducted on the external characteristics of a small centrifugal pump reversing as turbine during an atypical startup process, and the transient characteristics of the PAT during this atypical startup process are further revealed with the help of dimensionless analysis.

2.1 Test rig

The test rig of PAT in this paper is shown in Fig. 1. The test rig is mainly composed of booster pump unit, PAT unit, tank, piping system and, test system, etc. The drive source of the booster pump is a three-phase asynchronous motor, and its rotational speed is controlled by a frequency converter. The PAT unit mainly consists of PAT, dynamic torque sensor and, special three-phase asynchronous motor for frequency control. The dynamic torque sensor is a strain gauge torque sensor model NH-901 with a range of 0ཞ100 N.m. The speed measurement is done by an optical encoder mounted on the dynamic torque sensor with a range of 0ཞ9999 r/min. The special three-phase induction motor is used to absorb the shaft power generated by the PAT. The test system mainly includes electromagnetic flowmeter, import and export pressure sensors, and speed-torque sensor, etc. The type of electromagnetic flowmeter is ZHLDG-40, the range is 0ཞ70.65 m³/h. The import and export pressure sensors are WIKA type, the range of import and export pressure sensors are 0ཞ1.6 MPa and − 0.1ཞ0.5 MPa respectively.

2.2 Physical model

The booster pump is a direct-connected pipeline centrifugal pump, the type is ISW-65-160(1). Its rated parameters are: flow rate (Q_r) 50 m³/h, head (H_r) 32 m, rotational speed (n_r) 2900 r/min. The prototype pump reversing for turbine is a centrifugal clear water pump, as shown in Fig. 2, the type is IS80-50-200J. Its rated parameters are: flow rate (Q_r) 25 m³/h, head (H_r) 12.5 m, rotational speed (n_r) 1450 r/min.

2.3 Experimental methods and scheme

The testing process is as follows. Open each valve, and then start the booster pump. Part of the booster water flows back to the tank, another part flow into the PAT, and then flow back to the tank. The pump turbine is driven by the pressurized water flow, it starts to rotate and drive the torque sensor and the special three-phase asynchronous motor with frequency regulation. The frequency-controlled three-phase asynchronous motor consumes the power generated by the PAT and controls the magnitude of its rotational speed.

In this paper, the experiments on different valve openings under the stable speed of 400r/min are firstly conducted, then the stable speed of the PAT increases to 600r/min, and finally to 800r/min, which are called as low, medium, and high speed, respectively. The corresponding starting process are also called as low-speed start, medium-speed start, and high-speed start, respectively. The detailed testing scheme is shown in Table 1.

Table 1

Testing scheme
startup status	targeted stable speed n_f(r/min)	targeted stable flowrate Q_f(m³/h)
startup status	targeted stable speed n_f(r/min)	20	25	30	35	40	45
low-speed start	400	Π		Π		Π
medium-speed start	600		Π	Π	Π	Π	Π
high-speed start	800		Π		Π		Π

3.1 Low-speed start

The stable flowrate after startup is controlled by adjusting the opening of the outlet valve. The speed rise curve during low-speed atypical startup for the three valve openings is shown in Fig. 3. Three stable flowrate are respectively 20m³/h, 30m³/h, and 40m³/h, which corresponding to small, medium, and large valve openings. Obviously, the speed curves under different valve openings have similar evolutionary characteristics, namely that a slow rise, then a rapid rise, and then a slow rise to the final stable value.

The rotational speed rise is extremely slow before 1.20s. This is because the rotating parts of PAT are stationary at the beginning of the startup process, the torque generated by the pressurized fluid firstly overcomes the frictional resistance of the rotating parts. After overcoming the frictional resistance, the rotational speed begins to rapidly rise. Among them, the rise rate of rotational speed is significantly higher in the medium and large opening cases than in the small opening case. The main reason for this phenomenon is that because the rotational speed more rapidly rises, the torque generated by the larger flowrate is also greater.

At about 8.1s, the rotational speed in the medium opening case exceeds the speed in the large opening case for the first time, and completely exceeds the other two opening cases after that. At about 16.0s, the rotational speed almost stops rising and reaches a stable value. The stabilization values for the small, medium and large openings are about 353.3 r/min, 425.5 r/min, and 388.5 r/min, respectively, and the stabilization rotational speed value for the medium opening case (i.e., stable flow rate of 30 m³/h) is significantly higher than the other two cases. The difference between the experimental speed and the targeted speed for the three valve opening cases may be related to the unstable voltage in the process of testing.

The instantaneous flow curves measured during the low-speed atypical startup are shown in Fig. 4. The actual measured steady flow values for the three valve opening scenarios in this paper were 19.989 m³/h, 30.176 m³/h and 39.881 m³/h. The differences from the targeted values of 20.0 m³/h, 30.0 m³/h and 40.0 m³/h are very slight. This is due to the fact that the stable working flowrate after startup is achieved by adjusting the outlet valve opening in present experiments, which is an active adjustment, so the measured values do not differ much from the targeted solutions. Also in the atypical startup process, the three flowrate curves generally show similar evolutionary characteristics, all of which are characterized by a slow rise, then a rapid rise, and then a slow rise to a steady flow. The actual measured flowrate are 0.363 m³/h, 0.364 m³/h, and 1.545 m³/h for the small, medium and large open cases before about 3.5 s. The time required for the three flowrate curves to rise to their respective stable values is about 27.0 s, 26.5 s and 27.0 s, respectively. It is obvious that the flowrate rise obviously lags behind the rotational speed rise. The three flowrate curves still have extremely slight fluctuations after reaching stability, which is due to the rotor-stator interaction of PAT, and its analysis will not cause significant impact.

Under the low-speed startup situation, the transient static pressure curves measured at the inlet and outlet of the PAT are shown in Fig. 5. It is seen from Fig. 5(a) that the static pressures at the initial moment of atypical startup are about 13.0 kPa. With the rapid increase of rotational speed of the booster pump, the static pressure at the inlet of the PAT also shows a rising trend. It can be found that the rise of the static pressure at PAT inlet is basically the same before 20.0s under the condition of three valve opening, the differences among them are small. After 20.0s, with the increase of valve opening of PAT, the rise rate of the inlet static pressure decreases and the pressure rises slowly. In the case of small, medium and large valve openings, the stable static pressures at PAT inlet after startup are about 339.636 kPa, 306.594 kPa, and 270.088 kPa, respectively, and the corresponding rise times are about 24.6 s, 23.6 s, and 22.5 s. It can be found that as the valve opening increases, the time required for the inlet static pressure to rise to a stable value shows a slight tendency to advance during atypical startup.

Figure 5(b) shows that in the case of small, medium and large three valve opening, the outlet static pressure curves of PAT as a whole show a slow rise, then a rapid rise, and then down to a stable value, i.e., the outlet static pressure of PAT generally has the shocked phenomenon during the atypical startup process. It can be found that the outlet static pressure rises extremely slowly before 5.0 s, and then the rise rate is gradually accelerated. The maximum instantaneous static pressure values are 263.572 kPa and 198.176 kPa for the medium and large valve openings, which correspond to about 24.5 s and 23.4 s. It can be found that the larger the valve opening, the earlier the shock phenomenon of outlet static pressure occurred. The final stable static pressures after atypical startup are about 317.828 kPa, 258.964 kPa, and 192. 806 kPa, respectively. The shock static pressures (the difference between the maximum value and the stable value) are 4.086 kPa and 5.370 kPa for the two valve opening cases of medium and large, respectively. This indicates that the shock phenomenon of outlet static pressure is the most intense in the case of large valve opening.

Figure 6 shows that the evolution curve of the instantaneous head fluctuates very sharply. In the case of small valve opening, there are two local maxima and two local minima in the rising stage of the head curve. For medium valve opening, there are one local maxima and two local minima in the corresponding head curve. For large valve opening, there is one local minima. It can be seen that compared with the two valve opening cases of medium and large, the head rise curve in the small valve opening case fluctuates most dramatically.

The average heads after startup are 2.29 m, 4.92 m, and 7.62 m for the small, medium and large valve opening cases, respectively. The instantaneous head curves do not rise after about 28.0 s, after which each head curve fluctuates within a certain range. With the increase of outlet valve opening of PAT, the head showed a trend of increasing.

Figure 7 shows that the overall shaft power curves show an evolutionary process of slow rise, then fast rise, then slow rise again at all three valve openings, i.e., there are two slow and one fast rising evolutionary feature. The shaft power rises extremely slowly before 1.0 s. In the rapid rise phase, the rise rate is different for each valve opening case. At 5.0 s, the corresponding instantaneous shaft powers are 0.028 kW, 0.080 kW, and 0.153 kW for small, medium and large valve openings, respectively, and the ratios of transient shaft power to their final steady values are about 0.667, 0.630 and 0.754, respectively. Obviously, the shaft power rises is the fastest in the large valve opening case, followed by the small valve opening, and the slowest is the medium valve opening. Then the shaft power curve enters the slow growth stage and reaches their stable values at about 14.5 s, 17.7 s, and 16.6 s, corresponding to the stable values of 0.042 kW, 0.127 kW, and 0.203 kW, respectively, which fully shows that as the valve opening increases, the shaft power of PAT is also larger.

3.2 medium-speed Start

Figure 8 shows the measured rotational speed curves during the medium-speed startup process. The stable flow values are respectively adjusted as 25 m³/h, 30 m³/h, 35 m³/h, 40 m³/h, and 45 m³/h in this case, which corresponding to the five valve openings of small, lower middle, middle, upper middle, and large, respectively. The five rotational speed rise curves have a similar evolutionary history, which shows a slow rise, then a rapid rise, and then a slow rise to the final stable value.

The rotational speed rise is extremely slow until about 1.0s. The rise rate of instantaneous rotational speed in the lower middle valve case (30 m³/h) is faster than the other four cases. After 1.0 s, the rotational speed enters a rapid increase phase. In this phase, the rise rate is more rapid in the lower medium valve opening. Consistent with the low-speed startup process, the instantaneous speed at the small and medium valve opening (i.e., steady flow rate of 30 m³/h) is significantly larger than the other four valve openings, while the instantaneous speed at the upper middle valve opening is the smallest among the five valve openings. At about 7.0 s, the speed rise becomes slow again, and the instantaneous speed in the case of the upper middle valve opening exceeds that of the large valve opening, and the speed values in the large valve opening are the minimum thereafter. After about 16.0 s, the rotational speed rises gradually to the stable values, which are about 609.132 r/min, 613.971 r/min, 592.316 r/min, 593.121 r/min, and 570.300 r/min, respectively. The steady speed achieved at each valve opening is still different from the targeted rotational speed. Moreover at a steady flow rate of 30 m³/h, the corresponding speed rises is the fastest and has the highest steady speed value.

The instantaneous measured flowrate curves during the medium-speed startup are shown in Fig. 9. Again, since the flowrate regulation is an active control, the five measured steady flowrates are 24.966 m³/h, 30.084 m³/h, 35.038 m³/h, 40.197 m³/h and 44.968 m³/h, and the difference from the targeted values is very small. The all flowrate curves show an evolutionary characteristic of slow increasing, then rapidly rising to a maximum value, and then slowly decreasing to a stable value. There is no obvious correspondence between the valve opening and the rise rate of flowrate at the medium-speed start compared to the low-speed start. In the five valve opening cases, except for the two flowrate curves of 30.0 m³/h and 40.0 m³/h, the other three flowrate curves rise rapidly to a maximum value and then fall slowly until they drop to their respective stable values. Unlike the low-speed start, there is a flowrate shock phenomenon during the medium-speed start, with the maximum values of 25.846 m³/h, 36.273 m³/h and 45.488 m³/h for small, medium and large valve openings, respectively, and the ratios of the maximum values to the final stable values are 1.035, 1.035 and 1.012 after startup. In the case of three valve openings, the shock flowrates (defined as the difference between the maximum value and the stable value) are 0.880 m³/h, 1.232 m³/h and 0.520 m³/h, respectively. This indicates that the flowrate shock phenomenon is the strongest in the middle valve opening case and relatively insignificant in the rest of the valve opening cases.

Figure 10(a) shows that at the beginning of the startup period, each static pressure curve rises slowly, and it displays a fluctuating upward trend. Thereafter, the inlet static pressure of the PAT shows a rapid growth. For five valve openings, the stable inlet static pressure after startup are respectively 323.888 kPa, 307.197 kPa, 287.696 kPa, 269.576 kPa, and 242.806 kPa, corresponding to a rise time of 24.7 s, 25.6 s, 25.7 s, 25.6 s, and 25.9 s. Unlike low-speed startup, the time required for the inlet static pressure of PAT to rises to the steady value during medium-speed shows a slight trend of delay with the increase of valve opening. In addition, the stable inlet static pressure decreases as the steady flow rate increases.

Figure 10(b) show that the outlet static pressure of PAT as a whole shows a slow rise, then a rapid rise, and then down to a stable value of the evolution characteristics, that is, the outlet static pressure of PAT in the atypical startup process has generally shock phenomenon. The outlet static pressure rises very slowly before 6.0 s, and then the rise rate is gradually accelerated. In the five valve opening cases, the maximum instantaneous static pressures are 292.784 kPa, 262.256 kPa, 227.502 kPa, 190.527 kPa, and 146.911 kPa, and the corresponding moments are about 23.8 s, 24.1 s, 23.0 s, 23.0 s, and 24.1 s. It can be found that the time of shock static pressure did not change with the change of the valve opening, that is, the shock phenomena of outlet static pressure and the valve opening is not related. The stable outlet static pressures are about 281.48 2 kPa, 254.021 kPa, 218.745 kPa, 182.744 kPa, and 140.104 kPa after startup, the shock static pressure (the difference between the maximum value and the stable value) are 11.302 kPa, 8.235 kPa, 8.757 kPa, 7.783 kPa, and 6.807 kPa. In the process of medium-speed start, the shock phenomenon of static pressure is the most intense in the case of small valve opening, and it also shows a trend of weakening with the increase of valve opening. In addition, the outlet static pressure also shows a certain degree of fluctuation due to rotor-stator interaction.

Figure 11 shows that the evolution curve of the instantaneous head fluctuates sharply especially before 10.0s. There are several extreme points in this phase, and there is no obvious rule for the instantaneous head under each valve opening. Taking the upper middle valve opening as an example, the instantaneous heads reach local extreme values of 1.93 m, 0.74 m, 1.47 m, and 0.64 m at 3.5 s, 4.6 s, 5.7 s, and 7.6s. And then the instantaneous head curve rises to a stable value. In addition, the final average heads after startup are 3.94 m, 5.17 m, 6.68 m, 8.30 m, and 10.04 m for the five valve openings, and there are still small fluctuations after the rising to the stable value. It can be found that the head fluctuation is reduced and the stable head is increased compared with the low-speed start.

The shaft power curve also shows a general evolution of a slow rise, then a fast rise, and then a slow rise in Fig. 12. The shaft power rises more significantly after about 1.0 s, while it rises extremely slowly before 1.0 s. In the fast rise phase, the rise rate is different for each valve opening case. At 5.0 s, the corresponding instantaneous shaft power are 0.074 kW, 0.119 kW, 0.157 kW, 0.205 kW, and 0.274 kW for the five valve openings, and the ratios of instantaneous shaft powers to their final steady values are 0.685, 0.726, 0.677, 0.670, and 0.719, respectively. It is seen that the rise rate is fastest in the lower middle opening and is slowest in the middle opening. After that, the shaft power curve begins to slowly rise, and the final steady values are about 0.108 kW, 0.164 kW, 0.232 kW, 0.306 kW, and 0.381 kW, respectively. The higher the valve opening is, the greater the shaft power is. By comparing with the low-speed start, it is found that the higher the stable speed after start, the higher the stable shaft power. However, the effect of valve opening on shaft power is more significant compared with the effect of rotational speed on shaft power.

3.3 High-speed Start

Figure 13 shows the rotational speed rise during high-speed start, corresponding to 25 m³/h, 35 m³/h and 45 m³/h for the small, medium and large valve opening cases. The three curves still have similar evolutionary characteristics compared to the low and medium-speed start. The rise rate of rational speed is highest in the medium opening, followed by the large opening, and is slowest in the small opening case. It can be found that the speed rise in the case of medium and large valve openings is significantly higher than that in the case of small valve opening. The main reason for this phenomenon is that because the speed rises more rapidly, the larger flowrate causing torque is also greater. After about 20.0 s, the rotational speeds of the three valve open cases gradually reach the stable values of 755.836 r/min, 801.768 r/min, and 778.912 r/min respectively. The measured stable rotational speeds still have a difference with the targeted values because of the unstable voltage during the experiment. The steady rotational speed value is maximum in the medium opening case and is minimum in the small opening case.

Figure 14 shows that the measured steady flowrates for the three valve opening scenarios are 25.115 m³/h, 35.558 m³/h, and 44.836 m³/h, respectively, with very small differences from the targeted values, this feature is consistent with the low and medium-speed startup. At 10.0 s, the flowrates are 8.589 m³/h, 11.123 m³/h, and 15.453 m³/h for the three openings, with ratios of 0.342, 0.313 and 0.345 respectively to the steady flow rate after startup. At 20.0 s, the flowrates are 21.857 m³/h, 29.831 m³/h, and 38.874 m³/h, whose ratios to the steady flow rate after startup are 0.871, 0.839, and 0.867, respectively. It can be seen that the individual flowrate is increased by 49.7%, 52.6%, and 52.2%, respectively in 10.0 s, which rise by nearly half during the 10.0 s time. At about 26.0 s, the instantaneous flowrate gradually increases to the steady value.

Figure 15(a) shows that in the case of three valve openings, the corresponding stable static pressure at PAT inlet after startup are 322.4 kPa, 285.6 kPa, and 243.7 kPa, respectively, and the corresponding rise time is 23.6 s, 24.6 s, and 29.9 s. With the valve openings increases, the atypical startup process shows a slight trend of delay in the time required for inlet static pressure to rise to stable value during the medium and high-speed start. Figure 15(b) shows that the outlet static pressure still has a shock phenomenon during atypical startup. In the small, medium and large valve opening cases, the measured maximum instantaneous static pressures are 284.821 kPa, 218.774 kPa, and 135.575 kPa, corresponding to the time of about 23.0 s, 23.4 s and 22.8 s. In is found that the required time of shock static pressure is not very different. Thus, it can be seen that the required time of shock phenomenon at the outlet static pressure is not much related to the valve opening. The final static pressures after start are about 270.162 kPa, 205.882 kPa, and 128.728 kPa, the shock static pressure are 14.659 kPa, 12.892 kPa, and 6.847 kPa, respectively, which shows that the static pressure shock phenomenon is the most intense in the case of small valve opening. With the increase of valve opening, the impact phenomenon of the outlet static pressure also shows a trend of weakening. Through the comparison of the three starting processes, it is found that the strength of the static pressure shock is related to the start acceleration. The faster the start speed, the more intense the static pressure shock.

Figure 16 shows the average head after startup for the three valve openings of 4.95 m, 7.82 m and 11.23 m. The comparative analysis o shows that as the steady rotational speed of PAT increases, the head also tends to increase, and its fluctuation is slowed down to some extent.

Figure 17 shows that the shaft powers rise by 0.105 kW, 0.260 kW, and 0.478 kW from 2.0 s to 8.0 s after start, which account for 82.7%, 87.2% and 93.5% of the overall rise, respectively. The final stable values are 0.127kW、0.298kW, and 0.511kW at about 12.0 s. It can be found that the effect of valve opening on shaft power is more significant compared to the effect of rotational speed value on shaft power.

3.4 Dimensionless analysis

The dimensionless volumetric flowrate, dimensionless head and dimensionless shaft power are now used to further reveal the transient characteristics of PAT during atypical startup [16]. It is seen from Fig. 18 that the trends of the dimensionless flow coefficients during atypical startup are generally similar for any steady rotational speed and valve opening. At the beginning of startup, the dimensionless flow coefficients all have extreme values, then drop rapidly to a minimum value, and then rise slowly to a final stable value. However, the time required to decrease from the extreme value to the minimum value varies under different startup conditions. Figure 18(a) shows that the dimensionless flow coefficient drops to a very small value at 2.3 s, 2.3 s and 1.8 s, respectively. Subsequently, the three curves rise again to stable values at 27.1 s, 26.5 s and 25.8 s. The corresponding stable values of the dimensionless flow coefficients are 0.260, 0.328 and 0.474, respectively. It can be seen that during the low-speed startup process, the dimensionless flow coefficient increases as the valve opening increases, and the time to reach the stable value shifts forward. Figure 18(b) shows that the extremely large values at the beginning of the startup decrease to the very small values at 2.2 s, 2.3 s, 2.5 s, 3.3 s and 2.9 s, respectively, and then they rise to stable values at about 34.5 s, 27.8 s, 31.4 s, 24.7 s, and 27.1 s.

Figure 18(c) shows that the minimum values are very close to the emergence times for the small and medium valve openings, reaching the minimum values at 2.5 s and 2.7 s, respectively, while the time to reach the minimum values for the large valve opening is first delayed compared to the first two valve openings, reaching the minimum values at 3.3 s. Then the three curves start to rise slowly and reach the stable values at 24.0 s, 27.0 s and 31.7 s, respectively. It can be seen that the required time to reach the stable value lags as the valve opening increases during the high-speed startup.

Combining the above three startup statuses, it can be found that both valve opening and steady rotational speed are important factors in determining the variation characteristics of the dimensionless flow coefficient. The steady rotational speed variation has a certain influence on the dimensionless flow coefficient. The corresponding dimensionless flow coefficients are about 0.272 and 0.201 when the startup finally ends into the normal operation and steady state, respectively. It can be seen that the dimensionless flow coefficient shows a gradually decreasing trend with the increase of the steady rotational speed after the startup, and the dimensionless flow coefficient shows a gradually increasing trend with the increase of the steady flowrate.

Comparing Fig. 18 and Fig. 19, it can be found that the dimensionless head and flowrate coefficients generally have an approximately consistent evolutionary trend during the atypical startup. However, there are still some differences between them, the dimensionless head coefficient changes more drastically compared with the dimensionless flowrate coefficient in the same situation. It can be seen that the dimensionless head coefficient also shows a gradually decreasing trend with the increase of the stable rotational speed after starting, while it also shows a gradually increasing trend with the increase of the stable flow rate after starting.

It is seen from Fig. 20 that during the atypical startup of PAT, the dimensionless power coefficient has a very different evolution trend from the dimensionless flowarate and head coefficient, namely that the dimensionless power coefficient has a great value at the beginning of the atypical startup, and then decreases rapidly to the final stable value. With the increase of stable flowrate after startup, the dimensionless power coefficient also shows a gradual increase, but its increase is negligible compared with the other two dimensionless coefficients.

3.5 Nominal Acceleration Time

The valve opening has an effect not only on the final stabilization value, but also on the acceleration time of the entire startup process during the atypical startup. It is seen that the time required for each performance parameter to reach stability is different during the startup process. To better analyze the effect of valve opening on the startup process, a nominal acceleration time is introduced [17], which was defined as the time required for each performance parameter to reach its stable value of 63.2%. By comparing the nominal acceleration time for each parameter at different valve openings, the influence degree of the valve opening on each parameter can be more intuitively reflected.

Figure 21 shows that the nominal acceleration time of the shaft power and the rotational speed is much smaller than the other performance parameters, i.e., the rise rate of the shaft power and the rotational speed is much faster than the rest of the performance parameters during the startup process. In the process of low-speed start, the curves of shaft power and rotational speed both show a rising and then decreasing trend with the increase of valve opening. The nominal acceleration times of shaft power at the three valve openings were 4.6, 4.9 and 4.0 s, with growth rates of 6.52% and − 18.37%, respectively. Meanwhile, the nominal acceleration times of rotational speed are 4.3 s, 4.4 s, and 3.5 s, with growth rates of 2.32% and − 20.45%, respectively. In the process of medium-speed start, the shaft power and rotational speed curves still show similar trends, both of which are decreasing, then increasing and then decreasing. As can be seen from the Fig. 21, the two curves show a high degree of overlap. The nominal acceleration times for shaft power at the five valve openings is 4.6 s, 4.2 s, 4.7 s, 4.7 s, and 4.3 s, with growth rates of -8.69%, 11.91%, 0% and − 8.51%, respectively, while the nominal acceleration times for rotational speed are 4.8 s, 4.5 s, 4.8 s, 4.9 s, and 4.5 s, with growth rates of -6.25%, 6.67%, 2.08%, and − 0.082%, respectively. In the process of high-speed start, the shaft power shows a rising trend, while the rotational speed shows a falling and then rising trend, and the change of rotational speed is obviously much more drastic than the change of shaft power. The nominal acceleration times for shaft power are 3.9 s, 3.9 s, and 4.1s with 0% and 5.13% growth rate respectively for the three valve openings, while the nominal acceleration times for speed are 4.8 s, 4.3 s, and 4.4 s with − 10.42% and 2.33% growth rate respectively. It can be seen that both shaft power and rotational speed show highly similar characteristics in terms of growth trend and nominal acceleration time, and the size of the valve opening has a certain influence on the acceleration time. In addition, the rise rate of shaft power is relatively fastest at high-speed start, while the rotational speed is relatively fastest at low speed start-up.

Similarly, the nominal acceleration time of the pressures at inlet and outlet has highly similar characteristics. For low-speed start, the nominal acceleration time all shows a decreasing trend with increasing valve opening. At the three valve openings, the nominal acceleration times for inlet pressure are 19.8 s, 18.9 s, and 18.1 s with growth rates of -4.54% and − 4.23%, respectively, while the nominal acceleration times for outlet pressure are 19.4 s, 18.6 s, and 17.6 s with growth rates of -4.12% and − 5.38%, respectively. For medium-speed start, both the pressure curves at inlet and outlet show a trend of rising, then falling, then rising. The nominal acceleration times of inlet pressure at five valve openings are 18.4, 18.7, 18.2, 18.3 and 18.9 s, with growth rates of 1.63%, -2.67%, 0.55%, and 3.28%, respectively, while the nominal acceleration times of outlet pressure are 18.1 s, 18.4 s, 17.9 s, 17.6 s, and 18.5 s, with growth rates of 1.66%, -2.72%, -1.68%, and 5.11%. For high-speed start, the inlet pressure curve shows a decreasing trend followed by an increasing trend, while the outlet pressure curve shows the exact opposite trend. The nominal acceleration times of inlet pressure at the three valve openings are 15.2 s, 14.3 s, and 15.6 s, with growth rates of -5.92% and 9.01%, respectively, while those at the outlet are 15.2 s, 14.3 s, and 15.6 s, with growth rates of 1.32% and − 3.92%, respectively. It can be found that the nominal acceleration time changes with the change of valve opening under the same starting condition, and the trend of change is not the same under different acceleration conditions. Unlike the shaft power and rotational speed curves, the difference in nominal acceleration time between medium-speed and high-speed is more obvious. As can be seen, the rise rate at which the inlet and outlet pressures reach stable values is much faster for high-speed start than for medium-speed start.

The nominal acceleration time curve corresponding to the flow rate is relatively most stable at different valve openings, and the nominal acceleration time does not vary much between different valve openings at each startup condition. Consistent with the pressures at inlet and outlet, the nominal acceleration time of the flowrate decreases significantly during the high-speed start. For example, in the targeted stable flowrate of 35 m³/h, the nominal acceleration time of the flowrate in the medium-speed start condition is 15.8 s, while it in the high-speed start condition drops to 12.7 s, with a difference of 3.1 s. It can be seen that the flowrate in the medium and high-speed start conditions, the acceleration difference is larger, that is, the high-speed start than the medium-speed start acceleration to the stable flow rate is much faster. Unlike other performance parameter curves, the head curve shows different trends under different starting conditions. For low-speed start, the head curve increases and then decreases as the valve opening increases. The nominal acceleration time of heads are 14.7 s, 19.9 s, and 18.8 s, respectively. The nominal acceleration time from small valve to medium valve opening is extremely large, with a growth rate of 35.37%. During the medium-speed startup, the nominal acceleration curves of head show a trend of decreasing and then increasing, with nominal acceleration times of 23.8 s, 21.9 s, 20.8 s, 19.8 s, and 20.7 s at the five valve openings, with growth rates of -7.98%, -5.02%, -4.81%, and 4.54%, respectively. During the high-speed start, the nominal acceleration curves of head show a trend of decreasing all the time with nominal acceleration times of 23.3 s, 22.1 s, and 20.4 s, and its growth rates are − 5.15% and − 7.69%, respectively.

In summary, the rise rate of the shaft power and rotational speed is not much different, and the rise rate of rising to stable conditions is also significantly faster than the other parameters. The nominal acceleration time of flowrate is less obvious with the change of valve opening. In contrast, the nominal acceleration time of head changes drastically with the change of valve opening, and the maximum difference between adjacent valve openings reaches 5.2 s.

In order to better understand the rise rate of performance parameter at different startup process, a dimensionless time (λ) is introduced, which is defined as the ratio of the nominal acceleration time (T_na) to the total time (T₀) required for the parameter itself to reach stability. The ratio fully reflects the rise rate of each parameter in the first half of the startup process, and a smaller ratio means that each performance parameter rises faster in the first half of the startup process and slower in the second half, and vice versa.

$$\lambda ={T_{\text{n}\text{a}}}/{T_0}$$

Figure 22 shows that the dimensionless time can fully reflect the rising speed in the first half of the starting process, and the smaller its value, the faster the rising speed in the first half. It can be found that the dimensionless time corresponding to shaft power and rotational speed fluctuates around 0.3, i.e., the rise rate of shaft power and rotational speed in the first half of the starting process is much larger than that in the second half. Unlike the nominal acceleration time, the inlet static pressure and outlet static pressure curves are not so similar in terms of dimensionless time. For example, at low-speed start, the dimensionless times of inlet static pressure are 0.805, 0.801 and 0.804, which are extremely small, while in contrast, the dimensionless times for the outlet static pressure were 0.785, 0.667 and 0.642, respectively, with a difference of 0.118 between the small and medium valves. The reason for this difference may be that the pressure shock phenomenon of the outlet static pressure during the startup. Since the oscillation change of the head is extremely obvious during the startup process, the dimensionless time changes extremely drastically at different valve openings. For low-speed start, the dimensionless time firstly rises and then drop with the rising of valve opening. The dimensionless time is 0.525, 0.522, and 0.644 at three valve openings. The large valve opening firstly decreases by 0.003 and then increases by 0.122, i.e., the head starts fastest in the first half of the process at the medium valve opening. During the medium-speed startup, the dimensionless time of the flow rate at the upper middle valve opening (40 m³/h) is very special, its value increases abruptly from 0.454 to 0.625 from the middle valve opening and finally decreases gradually to 0.5. The reason for this situation is that, unlike the flow rate values at other valve openings, the shock phenomenon of flowrate does not occur at the upper middle valve opening, which leads to its time to reach the stable working condition earlier, which in turn leads to an increase in the dimensionless time.

In summary, the shaft power and the rotational speed rise very fast in the first half of the startup process, while the inlet pressure rises is the slowest in the first half, and the difference between them is several times. In the low-speed start process, the valve opening has a very obvious effect on the dimensionless time of the head, and the larger the valve opening, the slower the rise in the first half of the start-up process. In the medium-speed start process, the dimensionless time of the head decreases with the increase of the valve opening. It can be seen that the dimensionless time of head is not directly related to the valve opening. Unlike the nominal acceleration time, the valve opening has an effect on the dimensionless time of flowrate, and it is most obvious in the low-speed start process.

3.6 Discussion

In this experiment, three to five flowrate conditions are selected for comparative analysis at each steady rotational speed by changing the outlet valve opening of PAT at three steady rotational speeds (400 r/min, 600 r/min, 800 r/min) to investigate the effect of flowrate and rotational speed on the transient hydraulic performance of PAT during atypical start-up process. It can be seen that the differences among steady rotational speeds and steady flow rates are small, especially the latter. Therefore, it is the next work to systematically explore the effect of more significant rotational speed differences and flowrate differences on transient hydraulic performance in the future work.

In this paper, experimental tests and analyses are conducted for PAT during the atypical startup process, and the following conclusions are obtained. the rise rate of the shaft power and the rotational speed of PAT is the highest, followed by flow rate and inlet and outlet pressure, and finally head. The shaft power and rotational speed rise extremely fast in the first half of the start-up process, while the rises of inlet pressure is the slowest in the first half of the startup process. The evolution trends of dimensionless flow coefficient and dimensionless head coefficient are similar, while the evolution trends of both of them are very different from dimensionless power coefficient. As the valve opening increases, the dimensionless flowrate, head and power coefficients all show a gradual increase in evolution. The outlet static pressure of PAT generally has a shock phenomenon.

Acknowledgement

The research was financially supported by the "Pioneer" and "Leading Goose" R&D Program of Zhejiang (Grant No. 2022C03170), National Natural Science Foundation of China (Grant No. 51876103), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LZY21E060001).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Accessibility

The data used to support the findings of this study are available from the corresponding author upon request.

ORCID iD

Yu-Liang Zhang: https://orcid.org/0000-0003-3249-5629.

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Effect of valve opening on starting performance of pump as turbine

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Abstract

Figures

1 Introduction

2 Test Rig And Physical Model

2.1 Test rig

2.2 Physical model

2.3 Experimental methods and scheme

3 Results Analysis

3.1 Low-speed start

3.2 medium-speed Start

3.3 High-speed Start

3.4 Dimensionless analysis

3.5 Nominal Acceleration Time

3.6 Discussion

4 Conclusion

Declarations

References

Additional Declarations

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