Transactions of JSCES, Paper No.20180010

Numerical Study of Effect of Flow Rate on Free Surface Vortex in Suction Sump*

B. Shin

Department of Mechanical Design Systems Engineering, University of Miyazaki (Gakuen Kibanadai Nishi 1-1, Miyazaki 889-2192, Japan)

1. Introduction

In the designs of pump sumps in power generation plants

and urban drainage pump stations, it is continuously required to consider lower construction costs and more compact size(1),(2). In these situations, however, it is easy to cause undesirable vortices such as air-entrained free surface and subsurface vortices in the sump. When a vortex enters a pump, the impeller blade encounters the abnormal fluctuating pressure and load, resulting in mechanical unbalance, vibration, noises and acceleration of mechanical wear(3). Consequentially, it leads to a clear reduction in pump performance, loss of efficiency, and increased operating costs. These problems are related to certain undesirable flow characteristics in the pump sump, and are caused mainly by poor design of the intake structure layout or insufficient water levels.

In order to make sure of the expected pump performance and durability, it is important to design the pump sump so that it prevents adverse flow conditions. Detailed flow information in such flow conditions is also necessary for the advanced design. Therefore, a great deal of experimental work for the flow phenomena that happen in the pump sumps of water intake structures has been carried out by many researchers. The usual approach to assess the performance of sumps as well as to solve the possible problems in sump flow is to construct a scaled model in the laboratory and conduct the experiments on the physical model(4)~(8). Such physical model tests, however, involve high costs and consume a lot of time. There are many limitations on the modification of the geometry and the variation of test options. Therefore, alternative methods to solve those drawbacks are required. Fortunately, with the progress in computational environment and rapid propagation of computational fluid dynamics (CFD), numerical simulation is being regarded recently as a suitable

alternative for evaluating sump performance and solving fluid flow problems. So there have been many attempts to determine flow conditions and to make numerical prediction of the flow in the sumps.

Rajendran et al.(9), developed a CFD model to simulate three-dimensional (3-D) single-phase flow field in the pump station with single intake. This model is solved by using the Raynolds-averaged Navier-Stokes (RANS) equations and the two-layer k-ε model, a fully implicit and fractional-step method based on ADI approximate factorization in curvilinear coordinates. Predicted properties of the vortices were compared those of experiments, but they were relatively larger and weaker than the measured ones due to the application of inadequate turbulence model and the flow unsteadiness. To tackle these problems, succeeding studies were made by Constantinescu and Patel(10) with regard to the role of eddy viscosity turbulence model in prediction of pump-bay vortices. They calculated the vortices using a k-ε and a k-ω model, and presented that these models were found to predict vortices of similar shape and size, but their locations and strength depended on the turbulence model and treatment of the near-wall flow. Desmukh and Gahlot(11) analyzed flow conditions in the sump using commercially available CFX software and studied the effect of horizontal angle of forebay on the flow conditions. The results showed that reducing the angle of expansion in the horizontal plane improves the flow conditions considerably. Also, Abir et al.(12) presented a CFD application to investigate the submergence effect in pump intakes by using the Fluent code and showed that the CFD could be employed in preliminary design to determine the geometric configurations. In the sensitivity test of the application of turbulence models with the k-ε model and k-ω model, they reported that the k-ω model seems to be the most appropriate one to be able to fit the real flow field.

On the other hand, Okamura, et al.(1) conducted a CFD benchmark test to examine the characteristics of various CFD codes. The computation was performed by using five commercial codes with some turbulence models such as Shear Stress Transport (SST) turbulence model. Even though the flow and the free surface were treated as a single phase flow

The effect of the flow rate and water level on free surface vortices in a suction sump was studied by using numerical simulation. Free surface flow in an intake channel was solved by using finite volume method for RANS equations with k-ω SST turbulence model. A VOF multiphase model and the open channel model were used to solve the multiphase flow in the sump. Minimum position of air-water interface, air-entrained vortex length, air volume fraction contours and iso-surfaces were used to identify visually the location and shape of the free surface as well as surface vortices. From the numerical investigation with varying flow rate and water level, it was found that when the water level decreased or the flow rate increased, more free surface vortices appeared. The predicted velocity distributions at the entrance of bell mouth and the location of the center core of air-entrained vortices on the free surface were in good agreement with experimental results. Key Words: Free surface flow, Air-water interface, Surface vortex, Vortex length, Suction sump

* 原稿受付2018年01月05日, 改訂年月日2018年06月16日, 発行年月日 2018年08月02日, © 2018年日本計算工学会． Manuscript received, January 05, 2018; final revision, June 16, 2018; published, August 02, 2018. Copyright© 2018 by the Japan Society for Computational Engineering and Science.

and a fixed slip wall without friction, they showed that some CFD codes could predict the visible vortex occurrence and its location with enough accuracy for industrial use. Like this, CFD becomes a useful engineering tool for evaluating sump performance and contributes to improve the flow condition for the optimum design of pump suction sump. However, the behavior of free surface vortices still has not been satisfactorily clarified in most CFD studies because they computed the free surface flow, which strongly influences on surface vortices, under the assumptions such as the flat free surface or fixed slip wall without friction and a single phase problem.

In this paper, a numerical simulation of 3-D free surface flows in suction sump is conducted to investigate the effect of the flow rate and water level on free surface vortices. A finite volume method is used to solve RANS equations with k-ω SST turbulence model. A volume of fluid (VOF) multiphase model and an open channel model are applied to analyze the free surface flow problem. By using the iso-surface contour of air-water interfaces and air-entrained vortices, velocity profiles and pressure distributions, the behavior of the free surface and surface vortices is identified and investigated.

2. Suction Sump Model

The suction sump model for computation is a single pump-intake configuration as shown in Fig.1. It was designed based on the recommendation of HI-Standard(13) for a single rectangular intake channel. In this figure, the inlet bell mouth diameter D of 250mm was used as the basic design parameter. The intake pipe with the inside diameter of 0.6D is located in the middle of intake channel width W (=2D) at a distance of 0.75D from the back wall to the pump inlet bell center. Thickness of the intake pipe and bell was taken by 0.04D. E denotes intake channel height adjustable according to the water level H. A fixed value of the bottom clearance from floor is equal to 0.4D. The length L of rectangular intake channel is 7.32D. The origin of coordinates was located at the center of the bell mouth on the floor.

Computation was carried out under several operating conditions with variation of flow rates and water levels through the bell entrance D as listed in Table 1.

3. Computational Method

3.1 Fundamental Equation and Boundary Conditions Numerical analysis of 3-D multiphase flow in a pump suction sump was done by using the finite volume method incorporated in a CFD code Fluent(14). k-ω SST turbulence model which seems to be an appropriate model to compute the real flow field(12),(15), and VOF multiphase model were used to solve the problem of multiphase turbulence flow in the open channel. The fundamental equations are the continuity equation and the RANS equations expressed as

)3,2,1( 0

juxt j

j

(1)

v

i

b

i

i

j

j

i

eff

ji

ji

j

i ffx

u

x

u

xx

puu

xt

u

)3,2,1,( ji (2)

where , and refer to fluid density, velocity and static pressure, respectively. is the time and is the effective viscosity considered molecular viscosity and turbulent viscosity. is the body force (gravity in this case), and is the volumetric tension force formulated by using continuum surface force model(16) to consider the effects of surface tension at fluid-fluid interface. A conservation equation of air volume fraction is solved to capture the air-water interface, and the second order discretization was used in all derivatives.

In this computation, the Dirichlet boundary condition of pressure was imposed on the inlet boundary with the law of hydrostatics. The boundary condition of mass flow rate was used for the outlet with its respective values referred to Table 1. The top plane of air phase was set to a pressure boundary condition with zero atmospheric gauge pressure. On the boundary between the air and water interface, an open channel model which is combined with the VOF model in the Fluent and suitable for the free surface flow problem was applied so that it can accurately capture the air-water interface and flow interactions between phases. The remaining parts of the present sump model were set to no-slip walls in the turbulent flow problem. The working liquid is city water at 20C. 3.2 Computational Grid The computational grid was generated by ICEM CFD(17). A multi-block structured hexahedral grid with high density at the free surface region

Fig.1 Schematic illustration of sump model and dimensions.

Table 1 Flow conditions of flow rates and water levels.

Flow rate

Q (m3/h)

Water level, H

1.0D 1.2D 1.6D

126.90 ○ ○ ○

190.35 ○ ○ ○

237.94 ○ ○ ○

253.80 - ○ -

285.53 ○ - -

(a) High density mesh near free surface (side view)

(b) O-grid structure around bell mouth and intake pipe (bottom view)

Fig.2 Computational grid near intake pipe.

was generated to capture the sensitive behaviors of the fluid-fluid interface as shown in Fig.2(a). An O-type structured fine mesh near bell mouth and intake pipe (Fig.2(b)) was used to capture the boundary layer with accurate.

In order to confirm the grid dependency, the grid convergence and uncertainty on the numerical result was investigated by using the Grid Convergence Index (GCI)(18). For the GCI evaluation, three structured hexagonal grids, such as coarse grid (having 301,000 cells), intermediate grid (407,000 cells) and fine grid (851,000 cells), were generated and applied to solving a free surface flow with the water level of 1.2D and the flow rate of 126.9m3/h. As a result of the GCI estimation for the pressure monitored at the center of bell mouth entrance, the GCI values were decreased with grid refinements and an asymptotic range of 1.00024 was obtained, indicating that the fine grid solutions are well within the asymptotic range of convergence and nearly grid independent. From these results, the grid with 851,000 hexahedral elements was, therefore, used in all simulations of this study.

4. Numerical Results

4.1 Effect of Flow Rate and Water Level Figure 3 shows an instantaneous elevation of the air-water interfaces near the intake pipe at different flow rates and water level of H=1.0D. It is a view from the back wall. In this figure, the position of free surface and free surface vortices were specified by the elevation of the z-coordinate, so that the scale, distribution and overall shape of free surface vortices and the wavy pattern of the

interface are easy to understand. The minimum position of the interface around intake pipe was decreased with flow rates. Since the water level is lower than the recommended value by the HI-standard(13), free surface vortices appear at all flow rates even if a symmetric type of surface swirl (similar to the Type A1 vortex in the HI-Standard) occurred at small flow rate in Fig.3(a). The scale of free surface vortices and their depth are proportional to the flow rate. At relatively low flow rates, the vortex depth and variation is shallow and stable. However at the higher flow rates, the shape of vortices was changed from almost symmetric pattern to an asymmetric one due to the flow instability and mutual interaction of two vortices. The vortex greater in depth and strength moved gradually to the right hand side of the channel in Figs.3(b) and (c). When the flow rate is up to 285.53m3/h in Fig.4, for instance, a full air core vortex like Type A6(13) was obtained. The air-entrained surface vortices were strongly pulled down and moved toward the bell mouth. This investigation well simulated and reproduced a typical free surface flow pattern with wavy flow motion and concave shape of free surface vortices as well as counter rotating swirling flow behind the intake pipe in suction sump by using a volume rendering technique and streamlines. Swellings and dimples of free surface around the intake pipe were clearly simulated. This flow pattern agrees well with that of experiments in Fig.4(b)(19) and could be obtained by solving the free surface flow problem with a suitable method, such as the multiphase open channel flow model(14), to deal with the problem.

Figure 5 shows a time averaged air-entrained vortex length (h/D) with different flow rates. h/D is defined by h=H-zmin with the minimum z-position (zmin) of air-water interface of the

Fig.3 Instantaneous air-water interfaces indicated by

z-elevation at H=1.0D and (a) Q = 126.90m3/h, (b) Q = 190.35m3/h, (c) Q = 237.94m3/h.

(a)

(b)

(c)

Fig.4 Free surface and free surface vortices around intake pipe and streamlines at H=1.0D and Q= 285.53m3/h.

(a) Present and (b) Experiment

(a)

(b)

Fig.5 Time averaged air-entrained vortex length.

[m]

air-entrained vortex. As investigated above, when flow rate was increased gradually from 126.9m3/h to 237.94m3/h, the vortex length increased correspondingly at the same water level. But, it was decreased with the water level. Figure 6 shows another time averaged minimum position of the air-water interface around the intake pipe with different water levels. When the water level decreased, the minimum position of the air-water interface lowered for all flow rates tested in this study because of the potential for more appearance of air-entrained vortices as deduced from Fig.5. Also it was found that the minimum position became lower with flow rates at the same water level as mentioned in Fig.3 due to the increment of hydrodynamic suction forces. The slope of the minimum position was increased with the flow rate and low water level.

Figure 7 shows predicted velocity profiles along the y direction at the bell mouth center and z of 0.38D from the sump floor (just below the bell mouth) at the water level of 1.2D. u, v and w represent the velocity components in the x, y, and z direction respectively as shown in Fig.1. Vm denotes the mean velocity at the bell mouth for given flow rates. It can be observed that with the flow rate the amplitude of u-velocity fluctuation is decreased due to the suction velocity corresponding to the flow rate, and from the change of the velocity direction of u, v, the existence of vortices and their strength is figured out. In the vicinity of the bell mouth, axial velocity, w was predominant compared with the other velocities and formed a small velocity valley between two vortices which originated from the free surface vortices. The overall tendency of the predicted velocity distributions qualitatively agreed well with the PIV measurements(1).

Figure 8 shows the computational results of instantaneous velocity vectors and pressure contours at z =1.0D cross section of intake pipe at the water level of 1.2D. It can be seen that the intake flow entered through the bell mouth is discharged accompanying secondary flows with several vortices, and a pair of counter rotating vortices caused by the free surface vortex is significantly stronger than the others. In general, the

Fig.6 Time averaged minimum position of the air-water interface in free surface and free surface vortices.

Fig.7 Instantaneous velocity u, v and w profiles along

the y direction at bell mouth center and H=1.2D.

Fig.8 Instantaneous velocity vectors and pressure contoursat z=1.0D and H=1.2D (top view).

(a) Q=126.90m3/h

(b) Q=190.35m3/h

(c) Q=237.94m3/h

pressure is decreased with the flow rate(20) due to increment of the suction velocity, and it is relatively high at impinging area of velocity, especially near the back wall. In addition, it indicated that larger flow rate made stronger vortices with low pressure. 4.2 Free Surface Vortex behind Intake Pipe Figure 9(a) shows an instantaneous location of air-water interface with free surface vortices near intake pipe at the water level of 1.2D and flow rate of 126.90m3/h. At relatively low flow rates, two nearly symmetrical free surface vortices appeared and the time variation of the vortices was rather stable and symmetric pattern remained for a long time. The vortex core of the vortices was mostly located at around Dy /2.0 behind the intake pipe as illustrated in Fig.9(b) by red symbols (o), and the location was quite similar to the experimental results(1) (symbol ●) and other numerical results(21) (▲) even the present flow condition is somewhat different from the experimental ones. Figure 10 shows another computational result at flow rate of 190.35m3/h. Since the flow rate has increased, the intensity of swirl flow as well as suction pressure acting on the free surface is increased accordingly. In this flow condition, almost symmetric vortices occurred in the early stage of computation like Figs.3(a) and 9(a). With time, however, the symmetric pattern of these vortices was gradually changed to the asymmetric pattern mainly due to the flow instability derived from the water intake structures. That is, because the narrow space between the intake pipe and the back wall influences the normal development of these vortices as shown in Fig.10(b), the shape of vortex is shown somewhat differently from the conventional vortex occurring behind the cylinder. The depth of large vortex on the left hand side (Fig.10(a)) is greater than the other side and shows a coherent swirl. Figure 10(c) shows an iso-surface contour of vorticity for the free- and sub-surface vortices and velocity vectors. The coherent swirls formed by the free surface vortices are merged with sub-surface vortices under the bell mouth and discharge through the intake pipe(22). At a larger flow rate of 253.8m3/h in Fig.11, a pair of vortices pulling air bubbles (Type A5(13)) appeared since the intensity of swirl flow as well as suction pressure acting on the free surface was increased accordingly due to increased flow rate. When the air-entrained vortices are pulled down enough and

consequently break off, the air bubble appears. When these bubbles enter a pump, it can adversely affect pump performance and raise many problems faced by the pumping system. The mechanism of formation of pulling air bubbles can be seen clearly in this figure illustrated by the air volume fraction distribution (Fig.11(a)) and the air-water interface presented by z-elevation (Fig.11(b)).

5. Conclusions

A numerical simulation of 3-D free surface flow with surface vortices occurred around the intake pipe in suction sump was conducted to investigate the effect of the flow rate and water level on the vortices. A finite volume method with a RANS turbulence model and a VOF multiphase model was applied to solve the free surface flow in the sump with a single intake channel. The open channel boundary conditions were imposed with a multi-blocked structured grid to capture the behavior and interaction of flow between two fluid phases with higher accuracy.

From the observation of the minimum position of air-water interface and the length of air-entrained surface vortex, the behavior and shape of free surface vortex corresponding to each case of given flow rates and water levels were clearly identified. By visualizing the air-water interfaces with an air volume fraction distribution and volume

 

Fig.9 Instantaneous location of (a) free surface, free surface vortex and (b) vortex core at H=1.2D and Q = 126.90m3/h.

(a)

(b)

Fig.10 Computational results of surface vortices at H=1.2D and Q = 190.35m3/h.

(a)

(b)

(c)

[m]

[m]

rendering, the mechanism of formation of free surface vortices and the pulling air bubbles, and their development process were well explained. By monitoring the air-water interface with variation of flow rates and water levels, it was confirmed that the flow rate and water level have a significant effect on the occurrence of free surface vortex. It showed that the larger flow rate increased the appearance of the surface vortices, and the lower water level induced the generation of the surface vortices more. The predicted location of the air-entrained vortex core on the free surface behind the intake pipe qualitatively agreed well with experimental and numerical results.

Acknowledgements

The author thanks Mr. I. Ngo for his assistance in preparing this manuscript.

References

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(2) Funaki, J., Neya, M., Hattori, M., Tanigawa, H. and Hirata, K., Flow Measurements in a Suction Sump by UVP, JSME J. Fluid Sci. and Tech., 3-1, pp.68-79, 2008.

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Vorticity Interactions in an Open Channel Flow, J. Hydraul. Eng., 130-4, pp.313-323, 2004.

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(10) Constantinescu, G.S. and Patel, V.C., Role of Turbulence Model in Prediction of Pump-Bay Vortices, J. Hydraul. Eng., 126-5, pp. 387-391, 2000.

(11) Desmukh, T.S. and Gahlot, V.K., Numerical Study of Flow Behavior in a Multiple Intake Pump Sump, Int. J. Advanced Eng. Tech., 2-2, pp.118-128, 2011.

(12) Abir Issa, Annie-Claude Bayeul-Laine Geard Bois, Numerical Simulation of Flow Field Formed in Water Pump-Sump, Proc. 24th IAHR Symp. on Hydraulic Machinery and Systems, Iguassu, 2008, pp.1-11.

(13) ANSI, American National Standard for Pump Intakes Design, Hydraulic Institute, ANSI/HI 9.8, 1998.

(14) ANSYS group, FLUENT User’s Manual, Ver. 13, 2010. (15) Issa, A., Bayeul-Laine, A.C. and Bois, G., Numerical

Simulation of Flow Field Formed in Water Pump-Sump, Proc. 24th IAHR Symp. on Hydraul. Machinery Systems, Iguassu, 2008.

(16) Brackbill, J., Kothe, D. and Zemach, C., A continuum method for modeling surface tension, J. of Comput. Phys., 100-2, pp.335-354, 1992.

(17) ANSYS group, ICEM CFD User’s Manual, Ver. 13, 2010. (18) Roache, P.J., Perspective: A Method for Uniform

Reporting of Grid Refinement Studies, ASME J. Fluids Eng., 116-3, pp. 405-413,1994.

(19) Kang, W.T., Yu, K.H., Lee, S.Y. and Shin, B.R., An Investigations of Cavitation and Suction Vortices Behavior in Pump Sump, Proc. ASME-JSME-KSME Joint Fluids Eng. Conf., AJK2011-33020, 2011, pp.257-262.

(20) TSJ, Standard Method for Model Testing the Performance of a Pump Sump, TSJ S002, Turbomachinery Society of Japan, 2005.

(21) Zhao, L.J. and Nohmi, M., Numerical simulation of free water surface in pump intake, Proc. 26th IAHR Symp. on Hydraul. Machinery Systems, Beijing, 2012.

(22) Iwano, R., Shibata, T., Nagahara, T. and Okamura, T., Numerical Prediction Method of a Submerged Vortex and Its Application to the Flow in Pump Sump with and without a Baffle Plate, Proc. 9th Int. Symp. of Transport Phenomena and Dyn. of Rotating Machinery, Hawaii, 2002.

      

Fig.11 Computational results of (a) air-volume fraction contours and (b) elevation of air-water interface at H=1.2D

and Q = 253.80m3/h.

(a)

(b)

[m]