Three-dimensional flow observation on the air entrainment into a vertical-wet-pit pump

The authors consider the air entrainment into a suction pipe which is vertically inserted down into a suction sump across a mean free-water surface. This configuration is often referred to as the “vertical wet-pit pump,” and has many practical advantages in construction, maintenance and operation. Most of the flows appearing in various industrial and environmental problems like the present suction- sump flow become often complicated owing to both of their unsteadiness with poor periodicity and their fully-three-dimensionality. In order to understand the complicated flow inside a suction sump in the vertical-wet-pit-pump configuration, the authors experimentally observe the flow using the three-dimensional particle tracking velocimetry (3D-PTV) technique, which includes more unknown factors in accuracy and reliability than other established measuring techniques. So, the authors examine the simultaneous measurement by the 3D-PTV with another velocimetry the ultrasonic velocity profiler. As a result, under the suitable condition with high accuracy, the authors have revealed the complicated flow.


Introduction
Our aim is to understand the complicated flow inside a suction sump in the vertical-wet-pit-pump configuration. Most of the flows appearing in various industrial and environmental problems like the present suction-sump flow become often complicated owing to both of their unsteadiness with poor periodicity and their fully-three-dimensionality [1][2][3]. So, in instantaneous and three-dimensional observations of such flows could give us useful and effective information.
In this context, a three-dimensional particle tracking velocimetry (hereinafter, referred to as 3D-PTV) is one of the potential solutions against such problems. The 3D-PTV is a technology to specify three-dimensional positions of tracer particles from a couple of stereo images, and to obtain the velocity vectors of tracer particles from their positions at different instants. The 3D-PTV has some advantages. Furthermore, if we record the stereo images using video cameras, we can get a temporally-consecutive series of instantaneous and three-dimensional information of the whole flow. So, various 3D-PTV systems have been developed until now [4][5][6][7][8][9][10][11].
Despite the above advantages, the use of the 3D-PTV has been restricted. One of the main reasons exists in the difficulty to estimate its accuracy. So, at the present stage, it is rational to suppose that all the 3D-PTV measurements should be inevitably accompanied by the other verifying measurements using well-established techniques, to assure the 3D-PTV's accuracy.
In the present study, our concern is the complicated flow inside a suction sump in the vertical-wetpit-pump configuration. To obtain the information of such unsteady and three-dimensional flow, we examine the simultaneous measurement using both of the 3D-PTV and another velocimetry, namely, an ultrasonic velocity profiler (hereinafter, referred to as UVP) with common tracer particles, that is, the simultaneous measurement by the 3D-PTV with the UVP. The UVP has proposed and developed by Takeda [12] and Takeda et al. [13]. This simultaneous measurement is expected to become an effective method to dissolve the above fatal defect of the 3D-PTV. In general, the UVP tends not to be applicable for a small number of large tracer particles. On the other hand, the 3D-PTV tends not to be applicable for a huge number of small tracer particles. -The upper and lower limits concerning both the number and the size of tracer particles are important information from a practical point of view. The number in the present 3D-PTV's measurement volume is in the order of 10 2 to 10 3 , owing to restricted computational time. The size in the present study is in the order of 10 -4 m to 10 -3 m, while the size in the order of 10 -5 m allows detection with a brighter lighting system and with a narrower measurement volume (see [11]). However, in the present study, we do not attempt to exactly specify the limits for the 3D-PTV, as the present purpose is to conduct the simultaneous measurement.-Under the suitable conditions for the simultaneous measurement, we attempt to reveal the time-mean and instantaneous velocity vectors of the unsteady and three-dimensional flow inside the suction sump.
Of course, we may consider alternatives to the UVP as the verification measurements of the 3D-PTV, such as a hot-wire velocimetry (HWV), a laser-Doppler velocimetry (LDV), a two-dimensional or there-dimensional particle-image velocimetry (PIV) and a two-dimensional particle tracking velocimetry (2D-PTV). However, they are not suitable for the verification measurements of the 3D-PTV in the present study. Figure 1 shows the present model, which is a simple system of a suction sump and a suction pipe with the vertical-wet-pit-pump configuration. Geometric parameters D and d are the outer and inner diameters of the suction pipe, respectively. The former is used as a characteristic length scale. The latter is fixed to 0.9D. The suction-pipe intake has a bell-mouth shape. -The diameter of the bell mouth is the same as D, having a simple geometry with less parameters. We should note that the influence of the bell mouth diameter upon the critical condition for the air entrainment is negligible according to Tagomori [14], as D < 1.75d.-The pipe is placed vertically on the centre line of the suction sump. Three geometric parameters B, X and Z denote the breath of the suction sump, the clearance from the suction-pipe centre to the suction-sump back wall and the clearance between the suction-pipe intake and the suction-sump bottom wall, respectively. A geometric parameter H is water level, namely, the height of a mean water-free surface, then the pipe's submergence depth S is equal to (H -Z). A characteristic velocity scale is the mean flow velocity U i at the suction-pipe intake, which is defined by 4 Q / ( D 2 ), where Q is inflow rate, or the flow rate into the suction pipe. We define the Froude number Fr, the Reynolds number Re and the Weber number We by U i /(gD) 1/2 , ρU i D/μ and U i ( D/ ) 1/2 , respectively. Letters g, μ, ρ and T denote the gravitational acceleration, fluid viscosity, fluid density and water-to-air surface tension, respectively. Table 1 summarises chief experimental parameters and their values in the main test of the present study, together with geometric and kinetic parameters in non-dimensional forms. These values are the same as those in one of the two test cases in Funaki et al. [1] where not instantaneous but time-mean flow of the same system of a suction sump and a suction pipe as the present system is revealed by the UVP. Funaki et al. call the test case Case A. -Concerning two kinetic parameters Re and We except for Fr, it might be appropriate to suppose the threshold value above which we ignore the influence of a kinetic parameter [3, 15 & 16]. According to our previous study [3] which concludes that the threshold values of Re and We are 3×10 4 and 12, respectively. Thus, we should account for Re effects, when the present results in Case A are applied to practical aspects with large Re's.- Figure 1 also shows the present coordinate system. The origin O is on the suction-sump bottom    the z axis is vertical. We define three velocity components in the x, y and z directions as v x , v y and v z , respectively.

Experimental apparatus
In the main test of the present study, an experimental apparatus is substantially identical with our previous studies [1][2][3]. A turbopump feeds working fluid (water) to a suction sump from a reservoir. We control the flow rate of the pump by a control valve, and then control the water level H in the suction sump. In the upstream of the suction sump, we put a strainer to make flow uniform. A bendtype jet pump sends water up from the suction sump into the suction pipe, because the jet pump tends to induce less swirling than ordinary pumps. The jet pump itself is driven by another turbopump. Water from the suction pipe falls into the reservoir, then a water-circulation system is closed. Figure 2 shows a schematic view of a close-up experimental apparatus near the suction pipe to explain the simultaneous measurement using both of the 3D-PTV and the UVP. A 3D-PTV system consists of the following: a YAG laser (No. 5 in the figure) with its power supply (No. 6) as a light source, a couple of high-speed video cameras (No. 4) with a frame rate of 1/500 s, and a personal computer (No. 3) on which we conduct 3D-PTV analyses. The 3D-PTV requires more than two cameras which are synchronised with each other to take plural photographs at the same instant. We use a couple of cameras. As shown in Fig. 2, one camera is located outside the back wall of the suction sump, and the other camera is located outside the side wall of the suction sump. A UVP system consists of the following: an ultrasonic transducer (No. 7) as a UVP probe which is placed outside the suction sump, and a UVP monitor (No. 8) for the simultaneous measurement with the 3D-PTV.
The details of the 3D-PTV measurement is as follows (also, see [10,11]). The 3D-PTV system is calibrated in advance, then we take a couple of stereo images of a measurement volume using two high-speed video cameras with a frame rate of 1/500 s as shown in Fig. 2. Total recording time is 0.6 s, which represents 300 frames. This total recording time might not be enough for the flow (see Subsection 4.3), because of the restriction of the 3D-PTV system like the equipped memory size. Each image adequately covers the measurement volume. Next, we calculate the three-dimensional positions of tracer particles from couple of stereo images. The velocity vectors of tracer particles are determined from two consecutive information of the tracer-particle positions. All data processings have been done in a personal computer. Details is as follows.
For the 3D-PTV calibration, first, we fix two cameras so that their fields of view just cover up the whole measurement volume. If possible, two camera centers should cross, and should be right-angled with each other, to attain higher accuracy. Second, we set as many datum points as possible in the measurement volume, and take a couple of stereo photographs. The three-dimensional positions of these datum points are known in advance. In the present study, the number of the datum points is 43. Thirdly, we can determine a coordinate system, by which we construct a virtual space corresponding to the real space in the personal computer.
For the specification of the tracer-particle positions in three dimensions, we use four consecutive series of informations. First, we specify the centre positions of tracer-particles on each twodimensional photograph, through a digital image processing. Namely, after the removal of the background image which is the ensemble mean of stationary pixels during all the measuring time, we consider the maximum luminosity position as the tracer-particle centre. In order to identify each tracer particle from surrounding tracer particles, we suppose two thresholds, that is, the minimum size of the tracer particle and the minimum luminosity for the tracer particle. These thresholds can make the identification more accurate, but we should specify appropriate values depending on experimental conditions. Second, we determine the straight line on which there exist both a tracer-particle centre and a camera's view point. Then, we can see that a tracer-particle position is decided on the coordinate system as an intersection of the two straight lines from a couple of stereo images. Now, we know all the tracer-particle positions in the real 3D space on each time step. For the identification of the same tracer particle on different time steps, a genetic algorithm is used, based on successive four time steps' data. So, we can get tracer-particle velocity vectors which are obtained from successive two time steps' data. The details of the UVP measurement is as follows (also, see [1]). Using the UVP, we can get finetime-resolution informations, which are not merely the time histories of velocity vectors on a few spatially-fixed points like HWV and LDV. That is, we can get instantaneous velocity profiles by the UVP in terms of the Doppler effect of ultrasonic echoes. The UVP has an advantage on accuracy in comparison with the PTV and the PIV, and does not require clearly-visualised photographs. In the present study, we use a UVP of UVP X-2-PS by Met Flow SA with a frequency of 4 MHz. The number of measuring points is 128 in one profile, and then, the space resolution on the profile is 0.75 mm. As the diameter of the ultrasonic beam is 5 mm, one measuring volume is a disc with a diameter of 5 mm and with a thickness of 0.75 mm. We get consecutive 1024 profiles in each measurement with an interval of 32 ms or more.
We should note that the UVP enables us to know only one component of velocity vectors, which is parallel to the axis of the UVP probe an ultrasonic transducer. Moreover, the spatial range for the measurement is restricted. As the position of the UVP probe is outside the suction sump in order to avoid disturbing flow, it is difficult to conduct the measurements far upstream.
To make sure the effectivity of the present measurement further, we conduct another measurement using a still camera with a shutter speed of 1/20 s as a conventional technique with high reliability and low accuracy, in addition to the simultaneous measurement with the UVP. -By the still-camerameasurement technique, we visualise path lines (paths), namely, time integrals with low accuracy and high reliability. Smaller data-process number of this technique than other technique brings us high reliability in addition to the robustness due to the time integrals.- Figure 3 shows an example of the simultaneous measurement using both of the 3D-PTV and the UVP on the complicated flow in the actual suction sump in the main test, together with the measurement using a still camera as a conventional technique with high reliability and low accuracy. More specifically, the figure shows the profile of the x-component of time-mean flow-velocity vector averaging over 0.6 s at y/D = 0.79 and z/D = 1.05. To be exact, the averaging time in the still-camera measurement corresponds to 1/20 s, which is much shorter than the 3D-PTV and the UVP. To conclude, we can see good agreement from a qualitative viewpoint among the 3D-PTV, the UVP and the still-camera measurement despite the complexity of the flow. From a quantitative viewpoint, we can confirm that an average of the relative error to the maximum v x of the 3D-PTV from the UVP is 13 %, although the relative error locally attains 24 % at x/D ≈ -0.5.  Concerning the averaging number and the averaging time to obtain the time-mean velocity vectors, Funaki et al. [1] has shown in the UVP measurement on the same flow as the present study that a 200averaged result is in good agreement with a 500-averaged one, while a 50-averaged one begins to differ from a 500-averaged one especially in the downstream of the suction pipe (at x/D > 0). So, Funaki et al. have concluded that the averaging number of 200 is enough. The averaging time corresponding to this averaging number of 200 is equal to 6.4 s. In the present study, we conduct each 3D-PTV measurement with an averaging number of 300 and an averaging time of 0.6 s, and each UVP measurement with an averaging number of about 10 and an averaging time of 0.6 s corresponding to a measuring interval of 65 ms. In the still-camera measurement, the corresponding averaging number and time are 1 and 1/20 s, respectively. Although the averaging time of the 3D-PTV will be further examined at least, this seems not fatal to discuss the present flow from a qualitative point of view, because the present flow is almost steady without large perturbations (as will be mentioned below) especially in the upstream of the suction pipe (at x/D ≥ 0) where perturbations are much smaller (as will be shown in Figs. 4 and 11). The still-camera measurement is conducted inconsiderably in the upstream of the suction pipe. Now, we have acquired the reliability and the accuracy in measurements by the 3D-PTV in the present suction sump. So, we will reveal the flow next by the 3D-PTV measurement. Figure 4  The present flow is the same as that in one of the two test cases in Funaki et al., which is called Case A. In Case A, we commonly observe the air entrainment from the free surface into the suction pipe. More specifically, there stably exist a pair of symmetric air strings (or string-like air bulks) from the free surface to the suction-pipe intake into the suction sump, whose positions are in the downstream of the suction pipe. Owing to small perturbations, the symmetry is occasionally broken. At such an instant, one or none air string appears instead of the symmetric twin air strings.   figure 5), which represent the time-mean and three-dimensional flow structure near the suction pipe in the same flow as the present study. That is, the flow is symmetric about the vertical centre plane of the suction sump. In the downstream of the suction pipe, there exist two vortex filaments A-3 and A-4 with large-magnitude vorticities. One end of each vortex filament reaches the free surface, and the other end reaches the suction-pipe intake. These vortex filaments usually accompany the air strings, which correspond to the air cores by the air entrainment into the suctionpipe intake. In the upstream of the suction pipe, there exist a pair of vortex filaments A-1 and A-2 with opposite rotations, whose axes are longitudinal.

Time-mean flow
In Fig. 4 Figure 6 shows time-mean velocity vectors by the UVP on the y-z plane at x/D = 0.63 (Funaki et al.). Figure 7 shows the paths of tracer particles by a still camera on the y-z plane at x/D = 0, with a shutter speed of 1/20 s. -Of course, the tracer-particle condition is much different from Condition II.-As these figures well correspond to Fig. 8 in spite of much different averaging times from figs. 6 and 7, we can again confirm the reliability and the accuracy of the present 3D-PTV measurement.
As well, we compare the time-mean flow in the x-z plane, instead of the y-z plane. Figures 8, 9 and 10 show time-mean velocity vectors by the 3D-PTV at y/D = -0.66, time-mean velocity vectors by the UVP at y/D = -0.63 (Funaki et al. [8]), and the paths of tracer particles by a still cameras at y/D = 0.79. We can see that the flows in these figures resemble with one another, that is, there exist (1) a downward streaming at x/D ≈ 0.5 and (2) a clockwise circulating motion with a centre at x/D ≈ 0.5. Then, we can confirm the reliability and the accuracy of the present 3D-PTV measurement, three times.

Instantaneous flow
From such an observation as the air strings in the present flow are stable, we can anticipate that the present flow is stable as well. In fact, the instantaneous flows obtained by the 3D-PTV at most of measuring instants are similar with the time-mean one shown in Fig. 4. On the other hand, we occasionally observe that the symmetry of a pair of the air strings is broken with poor periodicity. At such instants, the instantaneous flow might be different from the time-mean one. Figure 11 is an example at the instants, where only one air string appears at x/D ≈ 0.8 and y/D ≈ 1.      In Figure 11, the flows in the upstream and in the vicinity of the suction pipe at x/D  0.26 (in figures (a)-(d)) resemble one another. Besides, the flow is almost the same as Fig. 4. In other words, we can see (1)  and 4(f). Specifically speaking, in Fig. 11(e), we cannot see neither (1) the symmetric twin circulating motion nor (2) the upward streaming near the suction-sump centre (at y/D ≈ 0). In contrast, in Fig.  11(e), we see a rather downward streaming at y/D ≈ 0 due to a converging point near the bottom centre and ambiguous diverging/saddle points in an area near the surface. This is similar with Figs. 4(a)-(d). But in a strict sense, the downward streaming is not vertical but inclined, since the diverging/saddle area is far from the suction-sump centre. In Fig. 11(f), the flow resembles neither one in Fig. 11(d) nor the others in Figs. 4 and 11. In other words, the flow is governed by a single circulating motion with a centre at y/D ≈ 0 and z/D ≈ 1. In summary, the instantaneous flow in the downstream of the suction pipe tends to fluctuate much more with complicated flow structures than the flow in the upstream and in the vicinity of the suction pipe which is similar with the time-mean flow at any time.

Conclusion
In order to understand the complicated flow inside a suction sump in the vertical-wet-pit-pump configuration, we have conducted the measurement by three-dimensional particle tracking velocimetry (3D-PTV) technique. As the technique includes more unknown factors in reliability and accuracy than other established measuring techniques, we have introduced the simultaneous measurement by the 3D-PTV with another velocimetry. Then, we have revealed the time-mean and instantaneous velocity vectors of the unsteady and three-dimensional flow using the 3D-PTV verified by the UVP in addition to the conventional still-camera measurement. Concerning the time-mean flow, we have confirmed the  reliability and the accuracy of the present 3D-PTV, whose results are consistent with the summary by Funaki et al. (2008) such as four vortex filaments and so on. The instantaneous flow in the downstream of the suction pipe tends to fluctuate much more with complicated flow structures than the flow in the upstream and in the vicinity of the suction pipe which is similar with the time-mean flow at any time. The instantaneous flow in the downstream is closely related with the free-surface behaviour which characterised by symmetry breaking of a pair of the air strings, namely, string-like air bulks in the suction sump.