Investigation on subsurface vortices within a closed pump intake under different pressure conditions ＊

Miao Guo , Xue-lin Tang , Xiao-qin Li , Fu-jun Wang , Xiao-yan Shi

1. College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China

2. Beijing Engineering Research Centre of Safety and Energy Saving Technology for Water Supply Network System, China Agricultural University, Beijing 100083, China

Abstract: An experimental study to investigate various features of subsurface vortices and their evolutions inside a closed pump intake under different pressure conditions at free surface, and to analyze the influence of a pipe bell with different mean axial velocities at the same water level on flow patterns is presented. For all cases, three different flow regimes are closely observed: various side-wall attached, back-wall attached and submerged vortices structures, and their evolutions are subject to the free-surface pressure for a critical flow rate, the number and strength of all these vortex rise as the absolute value of the pressure increases for a higher flow rate,for a lower flow rate, whether the side-wall vortices occur or not is related closely to the pressure magnitude, and there are no vortices for lower absolute pressure values, the number and the strength of the side-wall vortices increase as the absolute pressure values increase. Besides, based on statistical analyses, the side-wall vortex probability on the right side along the stream-wise direction is much higher than that on the opposite side for all operation cases, particularly single vortex probability, and the back-wall vortex probabilities are quite higher with values of more than 90%, meanwhile, the multi-vortices probability is much higher than that of the single-vortex. The captured vortices have been qualitatively classified into different “vortex zones”: no vortex zones and vortex zones including transition, single- and multi-vortex. The Reynolds number and the absolute value pressure are the most important parameters which influence the existence and the number of these vortices, and the increase of the two parameters reduces the no vortex transition zone and causes bigger difference in the back-wall and side-wall vortex zones.

Key words: Evolution of subsurface vortices, particle-image velocimetry (PIV), vortex probability, closed pump intake

Introduction

Closed pump intakes are widely used in various industrial fields like the cooling water systems of nuclear power stations, sodium-cooled fast reactors,pumping stations with great variations in water level,and so on. The very complex flows inside pump intakes commonly contain many coherent structures[1-2], especially near the surrounding area of the pump bell. The subsurface vortices[3-5]influence safe and steady operation of pump stations, which causes noise and vibrations, impeller damage due to cavitation[5], and uneven impeller loadings[6-7]. This not only results in severe deterioration of flow patterns inside closed pump intakes, and even influences pump performances, but it also leads to a significant increase in operational and maintenance costs[8].

It is often very useful and important to understand the various complex vortices inside pump intakes by means of observations and measurements of physical models. Generally, visual observation technologies,such as the acoustic Doppler velocimeter (ADV)technique, particle-image velocimetry (PIV), high-speed video, and laser Doppler velocimetry (LDV) techniques,are applied in test models to study subsurface vortices and the flow in pump intakes. Sch?fer et al. observed the flow and subsurface vortices in the front of open and covered intake systems by model testing, and the optimization schemes were used for the devices guiding the cost-effective flows in open and covered intake systems and to improve pump performance[9]. Choi et al.[10]examined flow uniformity in a pump model with a single intake and seven intakes to find out the detailed cause of vortex occurrence, and found that the submerged vortex intensity in the vicinity of side walls was higher than those both near back wall and near the upstream region of the bell mouth, and also that the vorticity around the bell-mouth was higher value in the multi-intake model than that in the single-intake. Ahmad et al. obtained the velocity distribution at nine points with the help of an ADV probe in a scaled pump-intake model. Type-2 (dye core) subsurface vortices were noticed and the swirl angle was high in most of the tests without vortex breakers, and the axial velocities at the throat of the bell mouth of four test pumps were almost uniform[11]. Ansar obtained the mean velocity distribution in a pump intake model with and without a cross-flow device using an ADV probe. The results showed that there were nearly symmetric flows with respect to the longitudinal axis of the intake and no reverse flow for the no cross-flow case. However, the reverse flow concentrated at lower depths and close to the right intake sidewall for the cross-flow case.Simultaneously, a large recirculation region existed in the upstream of the suction pipe at higher depths and near the left intake side wall[12]. Rajendran and Patel[13]used PIV to obtain the vortices in a laboratory simple intake model under conditions of small surface tension and negligible free-surface elevation effects. They found that some vortices had relatively-fixed mean positions while others were intermittent or meandering and the subsurface vortex strength depended on the distance between the wall or floor to which the vortex was attached and the intake pipe, and smaller distance promoted stronger vortices. Nagahara et al.[14]studied the effect of submerged vortices on hydraulic forces of a mixed flow pump impeller in a model pump intake, and obtained the strength of the submerged vortex, the tangential velocities, and the diameter of the cavitation area by using a high-speed video camera and a digital image processing system. It was found that the strength of submerged vortices was in the control of the upper stream velocity distortion and the diameter of the cavitation area of the submerged vortex correlated with the circulation of the vortex. Besides, Tahershamsi et al.[15]used a submerged water jet to alleviate or even eliminate the vortices, and verified it by experiments.

All the above experimental investigations of subsurface vortices focus on the open channel pump intakes,and pay less attention to the flow pattern and subsurface vortices in closed pump intakes. Besides, for the same cases, the evolution of the vortex probabilities and geometric scale of these vortices are not clear, which are significantly affect safe and steady operation in pump stations. It is not conducive to design the appropriate geometry of the closed pump intake, nor can it provide good inflow conditions for the inlet of pump. Therefore,it is worthwhile to investigate such subsurface vortices in closed pump intake including the related kinematic and dynamic mechanism.

The stereo PIV technique is used to measure the complicated flow patterns for more accurately analyzing in the closed pump intake model. The specific impacts of both vortex evolution and pressure variation on velocity distribution under the pipe bell were investigated in a closed pump intake. This paper also systematically analyzed the various subsurface vortices and the relative vorticity distribution on different selected sections, and the time-dependent evolution inside the closed pump intake under different free-surface pressures. The locations and the strength of different subsurface vortices, the occurrence probability, and the statistical characteristics of various subsurface vortices, as well as vortex probability distribution of various subsurface vortices in the closed pump intake, were also comprehensively analyzed.

The remaining parts of the present paper are organized as follows. In section of experimental system, the apparatus of the closed pump intake model and the experimental procedure adopted in this study are described. The experimental study focuses three different kinds of flow rates and five pressure conditions in the closed pump intake. In section of results and discussion, the various subsurface vortices and the vorticity distribution on two side walls and back wall, and the related evolution with different pressures of the closed pump intake are analyzed in detail. In section of experimental statistics and vortex probability, the occurrence probability and statistics of various subsurface vortices on selected sections were also carried out. Finally, in section of conclusions, the summary and conclusions of this experimental study of closed pump intake are provided.

1. Experimental system

The experimental tests have been carried out in a pump intake facility[16]. The main component of the experimental facility is a parallelepiped shaped intake and pipe bell in polymethyl methacrylate (PMMA).Other components of the experimental facility (i.e.,pump, regulation valve, pressure/vacuum pump, surge tank, flow meter, data processor, synchronizer, data acquisition system, charge-coupled device (CCD)cameras, Lasers and Diversion barriers et al.)complete the loop in a closed circuit.

1.1 Experimental facility

Geometrical and physical similarity are basic principles to allow a definite transfer of model test results to a prototype structure. By these means, the Froude number (Fr) of the physical and prototype model is equal to 1 in order to achieve similar flow conditions in the model and the prototype structure[17].

In Fig. 1 the closed pump intake experimental facility is shown. The test rig is characterized by a closed loop and pump intake with different pressure conditions to obtain a steady state test flow pattern. The four main operational functions, which can be controlled in the experimental loop are: (1) draining and refilling the closed pump intake, (2) controlling the water flow rate, (3) controlling and steadying the pressure inside of the closed pump intake, (4) PIV operations and taking pictures.

The pressure inside of the closed pump intake can be obtained by vacuum pump (in this experiment,controlled by the motor control system) connected with the closed pump intake and the valve installed under the surge tank. The state of the valve (open/closed position)and the motor control system allows the investigation of several pressure conditions in the closed pump intake. In the present work, five different pressure conditions are considered. The fluid from the pipe bell discharge flows through the flow meter, then is pumped by the pump system, and is controlled by the regulation valve, and finally into the test section. The measurement devices used in this experiment and its accuracy are given in Table 1.

The closed PMMA intake channel is 800 mm×450 mm×450 mm (Lx×Ly×H) with walls 20 mm thick. The parameters of the single closed pump intake and various subsurface vortices sketch are exhibited in Fig. 2. The details of the geometry of the closed pump intake are list in Table 2.

1.2 Experimental procedure

The initial conditions for each case strongly affect the vortices formation. For this reason, the experimentally captured procedure took an initial waiting time to reach a better condition within the closed circuit and pump intake. According to the first experimental campaign, 20 min has been recommended as the minimum waiting time. This particular procedure has been applied by the need to compare consistent experimental data, avoiding initial conditions affecting the results. Flow patterns and various subsurface vortices formation are certainly affected by non-uniform boundary conditions or by geometry shapes; however, these instabilities are unavoidable in any experimental campaign and are not related to the particular geometry. It is need to highlight that the repeatability of the different experimental cases was verified concerning the general validity of the test,replicating each observation with the aim of eliminating statistical errors due to these instabilities as much as possible.

Fig. 1 (Color online) A schematic description of the present experimental system. The numbers marked in the figure represent(1-Pump system, 2-Regulation valve, 3-Vacuum pump system, 4-Surge tank, 5-Magnetic flow meter, 6-Data processor,7-Synchronizer, 8-Data acquisition system, 9-CCD cameras, 10-Lasers, 11-Test pump intake, 12-Diversion barriers,13-Controlling valve, 14-Pressure sensor, 15-Motor control system)

Table 1 A list of details of the experimental instrument employed in the present experiment

Fig. 2 (Color online) The details of closed pump intake

Table 2 Geometry parameters of closed pump intake

Particles in the fluid are illuminated by a sheet of light that is pulsed, which are the 8 μm-12 μm diameter glass balloons with good optical capabilities.The size of the interrogation area is 64×64 pixels in the experiment, with a pixel being approximately 0.15 mm. The parameters of PIV such as exposure timetδ, the time step of system ΔT, the number of framesNpic[18]and the number of the total picturesNtalare listed in Table 3. In order to capture the evolutionary process of various vortices in a closed pump intake accurately and comprehensively, 90 images in each successful experimental step were considered sufficient to obtain the properties of the subsurface vortices. The PIV system is combined in the experimental facility shown as Fig. 1.

Table 3 The paramount parameters of PIV. The given parameter refers to the case 1

1.3 Experimental conditions

Three different flow regimes have been investigated: a “l(fā)ower flow rate” (case 1), a “critical flow rate” (case 2), and a “higher flow rate” (case 3).Referencing to Denny’s definition[19], the critical submergence is 260 mm in this experiment, within the flow rate in case 2. Three different conditions with different flow rates,Q, and same submergence water depth,Hf, of the pump bell listed in Table 4 are considered. The detailed pump intake non-dimensional parameters are listed in Table 5. Additionally,the pressure conditions performed in the present experiment are given in Table 6. Two parameters have been changed within the following ranges: the flow rate between 19.78 m3/h to 25.43 m3/h and the pressure between -0.07 MPa to 0 MPa.

Table 4 The definition of the operating conditions in terms of three cases

Table 5 Pump intake dimensionless parameters

Table 6 The pressure conditions of the present experiments

2. Results and discussion

2.1 Velocity and vorticity analysis and discussion

When the local pressure in the closed pump intake was lower than the vapor pressure of the fluid,cavitation occurred and the vortices attached to side walls or back wall of the closed pump intake would be suctioned in the pump and decreased the efficiency of the system. Hence, 3 selected sections (two side walls and the back wall) around the pipe bell were chosen to reproduce the real flow in relative planes through the PIV technique. Figure 3 shows the measurement section of the side walls 0.35Dfrom the physical side wall 1 and the same distance from the real side wall 2.The domain of two side sections presented by the coordinates inxandydirections are [5.45,7.45]and [0,2].

Fig. 3 (Color online) PIV measurement section of side walls

The combination of streamline and vorticity is used to identify the vortices in the present experiment.The evolution of the velocity and vorticity on the side walls section from 0 MPa to -0.07 MPa for case 1 is displayed in Fig. 4. Obviously, the number and scale of the vortices on the side wall 1 were almost increasing with the absolute value of the pressure.There were only one or two small scale vortices formed on side wall 1 at the first three pressure conditions, but two bigger scale vortices at least were captured on the same section at higher absolute value of the pressure conditions (p=-0.06 MPa, -0.07 MPa).Inverse, the velocity and vorticity on the side wall 2 were different to those on the side wall 1. No vortex was found on this section at the lower absolute value of pressure conditions (p=0 MPa, -0.02 MPa,-0.04 MPa and -0.06 MPa), and a vortex with weak strength was formed on the side wall 2 at highest absolute value of pressure condition (p=-0.07 Μ Pa) of this experiment.

Fig. 4 (Color online) The velocity and vorticity in y-direction (ω y) on the side walls section for case 1. (a1)-(e1), (a2)-(e2) refer to the velocity distributions under the conditions with p=0 MPa, -0.02 MPa, -0.04 MPa, -0.06 MPa and -0.07 MPa on the section of side walls 1 and 2, respectively. (f1)-(j1), (f2)-(j2) refer to the ωy distributions under the conditions with p =0 MPa, -0.02 MPa, -0.04 MPa, -0.06 MPa and -0.07 MPa on the section of side wall 1 and 2, respectively

The evolution of the velocity and vorticity on the side walls section for case 2 at all pressure conditions is shown in Fig. 5. With the constant tendency of case 1, the number and scale of the vortices on side wall 1 were slightly increasing with the increase of the absolute value of the pressure. Compared with case 1,only one distinct vortex was captured on side wall 1 at the first three pressure conditions, and at least two vortices were captured on the same section at higher absolute pressure value conditions (p=-0.06 MPa,-0.07 MPa), which was the common point of velocity evolution between cases 1 and 2 on side wall 1.However, the velocity and vorticity on side wall 2 have different tendencies with those on side wall 1.There was not any distinct vortex that could be found until the absolute value of the pressure was elevated to 0.06 MPa or higher. Between the evolution of velocity and vorticity in case 1 and 2, the remarkable progress is the absolute pressure value of a distinct vortex formed on side wall 2, which dropped from 0.07 MPa to 0.06 MPa. This development was attributed to the higher mean velocity for case 2.

When the mean axial velocity in the intake pipe rose to 0.9 m/s, the Reynold numberRe=9× 105, the more turbulent flow was performed in the closed pump intake. For case 3, velocity and vorticity on the side walls section evolved from 0 MPa to -0.07 MPa is indicated in Fig. 6. A distinct vortex with increasing strength located in the same domain was captured on side wall 1 at the first three pressure conditions, then,more vortices meandered on this section with fluctuating vorticities at higher absolute pressure values. It is noted that an obvious vortex located at the same domain on side wall 2 was found at all of the pressure conditions.

Fig. 6 (Color online) The velocity and vorticity in y-direction (ω y) on the side walls section for case 3. (a1)-(e1), (a2)-(e2) refer to the velocity distributions under the conditions with p=0 MPa, -0.02 MPa, -0.04 MPa, -0.06 MPa and -0.07 MPa on the section of side walls 1 and 2, respectively. (f1)-(j1), (f2)-(j2) refer to the ωy distributions under the conditions with p =0 MPa, -0.02 MPa, -0.04 MPa, -0.06 MPa and -0.07 MPa on the section of side wall 1 and 2, respectively

After analyzing and comparing the velocity and vorticity evolution on the side walls sections for cases 1, 2 and 3, it was concluded that the flow on section of side wall 1 was more turbulent than that of side wall 2,and the vortex/vortices were progressing with the rising of the absolute value of the pressure conditions on section of side wall 2, which became more and more unsteady and meandering.

The back-wall section was chosen to study the real flow on the back wall of the closed pump intake.Figure 7 shows the measurement section of the back wall 0.35Dfrom the physical one. The domain of selected sections located by theyandzcoordinates directions are [1.25,3.25] and [0,2].

Fig. 7 (Color online) PIV Measurement section of back wall

The velocity and vorticity evolution on the back-wall section from 0 MPa to -0.07 MPa for Case 1 is displayed in Fig. 8. Clearly, the number and scale of the vortices on the back wall were almost increasing along with the increase of the absolute pressure value. Specifically, only one distinct vortex on the back wall could be captured at the first two pressure conditions, then, more vortices were found on the same section with the rising of the absolute value of the pressure. It should be noted that the core of the vortex on this section was unsteady and meandered.

Fig. 8 (Color online) The velocity and vorticity in x-direction(ω x) on the back-wall section for case 1. (a)-(e) refer to the velocity distributions under the conditions with p=0 MPa,-0.02MPa,-0.04MPa,-0.06MPa and-0.07 MPa respectively. (f)-(j) refer to the ωx distributions under the conditions with p=0 MPa, -0.02 MPa,-0.04 MPa, -0.06 MPa and -0.07 MPa respectively

The velocity and vorticity evolution on the section of the back wall from 0 MPa to -0.07 MPa for case 2 is illustrated in Fig. 9. Similarly, the number of the vortices on the back wall was increasing with the increase of the absolute pressure value for case 2.Specifically, only one distinct vortex on the back wall formed at the first pressure conditions (i.e.,p= 0 MPa ),then more vortices were found on the same section with the rising absolute pressure value. Additionally,the core of the vortex was unsteady and meandered on this section. Remarkably, comparing the velocity and vorticity evolution between cases 1 and 2, the absolute pressure value conditions of multiple vortices formed on the back wall dropped from 0.04 MPa to 0.02 MPa.This change was contributed by the higher mean velocity for case 2.

Fig. 9 (Color online) The velocity and vorticity in x-direction(ω x) on the back-wall section for case 2. (a)-(e) refer to the velocity distributions under the conditions with p=0MPa,-0.02MPa,-0.04MPa,-0.06MPaand-0.07 MPa respectively. (f)-(j) refer to the ωx distributions under the conditions with p=0 MPa, -0.02 MPa,-0.04 MPa, -0.06 MPa and -0.07 MPa respectively

When the mean axial velocity in the intake pipe rose to 0.9 m/s, the velocity and vorticity evolution on the section of the back wall from 0 MPa to -0.07 MPa is indicated in Fig. 10 for case 3. The dramatic progress is that multiple vortices were captured on the back wall for case 3 at all pressure conditions, which was distinctly different from the previous cases.Moreover, the core of the vortex was unsteady and meandered on this section.

Fig. 10 (Color online) The velocity and vorticity in x-direction (ω x) on the back-wall section for case 3. (a)-(e)refer to the velocity distributions under the conditions with p=0 MPa,-0.02 MPa,-0.04 MPa,-0.06 MPa and -0.07 MPa respectively. (f)-( j) refer to the ωx distributions under the conditions with p=0 MPa,-0.02MPa,-0.04MPa,-0.06MPa and-0.07 MPa respectively

Based on the results provided by this paper on the side walls and back wall sections for all cases under all pressure conditions, it can conclude that the flow patterns on the back wall were more turbulent than those on the sections of the side wall, and the core of the vortex was more unsteady and flexible on the section of back wall and the number of these vortices was more than that on side walls, which was difficult to predict.

2.2 Experimental statistics and vortex probability

The vortices were unsteady and meandered in pump intake[20-22]. After examining the PIV experimental results attentively and comprehensively, it was revealed that the various subsurface vortices were developing with the condition in the closed pump intake and they showed some trends in probability and statistics. Hence, it is necessary and meaningful to statistically analyze and correlate the probability of the subsurface vortices in the closed pump intake through experiments, which are contributing to a better understanding and explaining the formation and development of the various subsurface vortices in the closed pump intake.

Four vortex probability bar graphs are shown in Figs. 11-14 which include experimental results obtained with 90 groups of continuous experimental images. The vortex probability on different measured sections (side-wall 1 and 2, back-wall) was computed and displayed for each case and different pressure conditions.

Fig. 11 (Color online) Vortex probability on the section of two side walls for case 1 at different pressure condition. (a),(b) refer to the vortex probability on the section of side walls 1 and 2 respectively

Fig. 12 (Color online) Vortex probability on the section of two side walls for case 2 at different pressure condition. (a),(b) refer to the vortex probability on the section of side walls 1 and 2 respectively

Fig. 13 (Color online) Vortex probability on the section of two side walls for case 3 at different pressure condition. (a),(b) refer to the vortex probability on the section of side walls 1 and 2 respectively

Fig. 14 (Color online) Vortex probability on the section of the back wall for all cases at different pressure condition.(a), (b) and (c) refer to the vortex probability on the section of the back wall for case 1, 2 and 3 respectively

During the tests, all the four vortex probabilities have been computed, merging PIV experimental data obtained with the different sections and cases. The letterη(light color bars) stands for that there was vortex captured on the selected sections for each cases at different pressure conditions, on the other side, the value of 1-ηmeans that there was not any vortex existing on the measured sections (not displayed in Figs. 11-14). The dark color bars ()θare used to represent the probability of a single vortex forming on the PIV captured domain, similarly, at least two different vortices are observed on the selected sections and can be calculated throughη-θ(not displayed in Figs. 11-14). The relative definitions are

whereNTis the total number of the successful PIV images of each test,NA,NBare the number of the PIV images of the existing vortices in the PIV results,and only one vortex on the selected section at least in each test, respectively.

The vortex probabilities on the two side wall sections for case 1 and different pressure conditions are illustrated in Fig. 11. On the section of side wall 1,the value of throughηis rising with the increase of the absolute value of the pressure, and reached the maximum value of 88.33% at -0.07 MPa. Inversely,the probability of only one vortex is down to the minimum value of 15% at -0.07 MPa. On the section of side wall 2, the vortex probabilities are lower than the corresponding value on the side wall 1. The value ofηis increasing with the increase of the absolute pressure value, and reached the maximum value of 80%at -0.07MPa. The variation ofθis small on this section, whose value is maintained around 15%.

The probabilities on the two side wall sections for case 2 and different pressure conditions are illustrated in Fig. 12. On the section of side wall 1, the value ofηis increasing with the increase of the absolute pressure value, reaching the maximum value 98.33% at -0.07 MPa. In the other side, the value ofθis lowest at 5% at -0.07 MPa. It is evident that the probabilities ofη,η-θand 1-η,θhave a clearly inversed tendency in side wall 1. On the section of side wall 2, the vortex probabilities are lower than the corresponding value on the section of side wall 1. The value ofηis increasing with the increase of the absolute pressure value, and reached the maximum value of 68.33% at -0.07MPa.Compared to case 1, the variation ofθis small too,whose value is maintained around 30%.

The vortex probabilities on the two side wall sections for case 3 and different pressure conditions are shown in Fig. 13. On the section of side wall 1, the value ofηis maintained a high level with small variation. The maximum and minimum ofηare 90%and 61.67% at 0 MPa and -0.04 MPa or 0.07 MPa,respectively. The probability of only one vortexθis down to the minimum value at -0.07 MPa, which is 16.67%. On the section of side wall 2, compared with the previous conditions, the value ofηshowed an obvious trend of rising. The maximum and minimum values ofηwere 93.33% and 28.33%, respectively.Compared to the previous cases, the variation ofθis small as well, whose value is maintained around 28.33%.

The vortex probabilities on the back wall for all cases and different pressure conditions are shown in Fig. 14. Clearly, the value ofηis quite high compared with its value on the side walls, reaching the maximum value of 100%. These flow patterns indicated that vortices are easily formed and developed on the back wall for all cases. Contrarily,the probability of only one vortexθis relatively small for all cases, especially at pressured conditions,and its minimum value wasθ=5% for case 2 at-0.07 MPa.

2.3 Experimental statistics and vortex probability distribution

The vortex probability distribution and merging experimental data obtained with the different pressure conditions have been charted dramatically as well.According to the statistical results of the above relative parts, the core of the vortices is unsteady and meandering, which is driven by the instantaneous conditions of the flow. Moreover, the vorticities of the vortices changed during the test running. It is not clear if this instability is a peculiar characteristic of the vortex phenomena, or if it is only caused by the closed pump intake geometry and flow perturbations introduced by the pump or other elements. Either way,each experimental condition has been classified considering the worst vortex phenomena observed during the experiment.

A dimensional analysis was performed in order to identify the dimensionless parameters that influence the various subsurface vortices formation and the number of various subsurface vortices in the closed pump intake.

Taking the mean axial velocity in the pipeup,the streamwise mean velocity in the channeluc,density of fluidρ, the interior diameter of the pipeD, the dynamic viscosity of waterμ(at 20°C), the angular velocity of rotation of the systemΩ(the angular velocity of rotation of the earth in the present paper) and the width of the intakeLyas the repeating variables:

Different selected sections in the closed pump intake of experiments have been grouped according to the observed subsurface vortex phenomena, different pressure conditions, and the dimensionless parameters.The subsurface vortex probability distribution are built according to the relative experimental results. A preliminary evaluation of the different subsurface vortex phenomena zone boundaries has been done.However, this must be considered only a preliminary and rough estimation of the transition boundaries,resulting from the qualitative classification criteria adopted in the present paper.

In detail, the relative zones are partitioned according to the following: No vortex zone means the Vortex probabilityα=[0%,30%), transition zone present the vortex probabilityα=[30%,60%)α=[30%, 60%), and the vortex probability of vortex zone is between 60% and 100%. Furthermore, the vortex zone is separated into single and multi-vortices zones, and the vortex probability of the single vortex zone isβ=(50%,100%], the multi-vortices zone equals that of the vortex probabilityβ=[0%,50%).

On the basis of a large number of experimental data, combined with dimensionless analysis, the vortex probability distribution is obtained, furthermore, which is also based on rich experimental experience accumulated during the experiment. The vortex probability distribution of the side wall 1 section is illustrated in Fig. 15. The transition zone includes only one case: The Reynolds number is 7×104and the corresponding pressure is 0 MPa. The single vortex zone contains three cases: The Reynolds number is 7×104and the corresponding pressure is-0.02 MPa and -0.04 MPa, the Reynolds number is 9×104and the corresponding pressure is 0 MPa. The rest of the cases in the present experiments are all classified in the multi-vortices zone. Moreover, in this map, a general agreement of the experimental results considering the influence of the variation of the pressure and dimensionless number can still be noticed. The no vortex transition zones are located the area with low pressure, along with the values of the dimensionless number. At first, with the raising of theReand pressure values, the no vortex zone turns into the transition zone, then, the vortex zone is divided into single and multi-vortices zones, and they even appeared in the high pressure and the dimensionless number domains. For the single vortex zone on the side wall 1 for largeRecase, the possible explanation is that the flow near the side wall 1 to gather and then turn back to form a single vortex with clear flow pattern after the impact on the back wall.The same mechanism can also explain the related flow patterns on the section of back wall.

The vortex probability distribution of the side wall 2 section is demonstrated in Fig. 16. The no vortex zone includes four cases: The Reynolds number is 7×104and the corresponding pressure is 0 MPa, -0.02 MPa and -0.04 MPa, the Reynolds number is 9×104and the corresponding pressure is 0 MPa. The transition zone contains four cases else:the Reynolds number is 7×104and the corresponding pressure is -0.06 MPa, the Reynolds number is 8×104and the corresponding pressure is 0 MPa, -0.02 MPa and -0.04 MPa. The rest of the cases in this section are all classified in the multi-vortices zone. The relative high area of no vortex zone and transition zone indicate that vortex is not a common phenomenon in this section. Moreover, it is need to high-light that there is no unambiguous single vortex zone on the measurement section, which means that there is multi- or no distinct vortex on this measurement section, and the flow patterns on the same section is quite complicated.

Fig. 15 (Color online) P- Re vortex probability distribution on the section of side wall 1

Fig. 16 (Color online) P- Re vortex probability distribution on the section of side wall 2

The vortex probability distribution of the back-wall section is demonstrated in Fig. 17. The no vortex zone and transition zone on this section are not included in any case in the present experiments, which are charted qualitatively by experience and the related fluid mechanics principle. Then, the single vortex zone includes only one case: The Reynolds number is 9×104, the corresponding pressure is 0 MPa, and this vortex pattern may result from the strong circulation and the flow impacting on this wall. The rest of the cases in the present section are all classified in the multi-vortices zone, which intimates that the multi-vortices structures on the back-wall section are very common.

Fig. 17 (Color online) P- Re vortex probability distribution on the section of back wall

3. Conclusions

An experimental study was undertaken in order to investigate the working conditions of a closed pump intake, with the same water level, made up of a vertical intake pipe with variable flow rates and pressure conditions.

For different cases and pressure conditions, the number of vortices on the side wall sections were almost increasing with the increase of the absolute pressure value and the strength of the vortex fluctuated from 0 MPa to -0.07 MPa. Additionally, the scale of the vortices on the side wall 1 were almost increasing with the increase of the absolute pressure value. The remarkable progress in the evolution of vortices on the side wall sections is the pressure condition of a distinct vortex formed on side wall 2, which dropped with the rising of the absolute pressure value. This progress is attributed to the higher mean velocity for case 2 and indicated that the vortices were formed more easily on side wall 1 than 2 at the same time. Moreover, the evolution of the velocity and vorticity on the back-wall section from 0 MPa to -0.07 MPa for all cases had a similar and stronger tendency compared to the selected vertical planes sections under the pipe bell and side walls.

The vortex probability on different measured sections were presented for all cases and pressure conditions. The variation ofθwas small in all cases,whose value maintained around 15%, 30% and 28.33%for cases 1, 2 and 3, respectively. On the back-wall section, the value ofηwas quite high compared with that of the side wall sections, and reached the maximum value of 100%. This indicated that vortices are formed and developed on the back wall easily for all cases. The probability of only one vortexθwas relatively small for all cases.

The captured vortices have been qualitatively classified in different “vortex zones”, and the most important parameters that influenced the physical phenomenon were identified through a dimensionless analysis. The results showed that the no vortex transition zone was expanding with the rising of theReand the absolute pressure value, following the order of the back wall, and side walls 1 and 2, which were quite well distinguished. Moreover, the single vortex transition zone was expanding with the rising ofReand the absolute pressure value, following the order of the back wall, and side walls 1 and 2, but was not recognized as easily as it was in the previous zones. Finally, multiple vortices zones were divided after being analyzed and counted in the experimental results. It was found that the no vortex transition zone is located in the area with low pressure and values of the dimensionless number. Then, with the rising of theReand the absolute pressure value, the single vortex transition zones were separated, and they even appeared in the high pressure and the dimensionless number domains.

Experiments showed that the vortical features and their evolution in a closed pump intake are quite complicated, but follow some regularity. Therefore,the present paper suggested that the key sections and regions for the suppression of subsurface vortices should be carried out according to the vortex probability distribution. The results of the paper are of guiding significance for optimizing geometry of the closed pumping stations and designing inlet flow conditions of the next installations. The rest of the results of closed pump intakes at pressured conditions will be shown in future work.