Transaction A: Civil EngineeringVol. 17, No. 2, pp. 89{95c Sharif University of Technology, April 2010

E�ect of Anti-Vortex Plates on CriticalSubmergence at a Vertical Intake

S.M. Borghei1;� and A.R. Kabiri-Samani2

Abstract. One of the sources of disturbance at intakes is the occurrence of free-surface vortices withan air core. The most common solution for avoiding air-entrainment is the use of anti-vortex devicesand, especially, plates for large pipe or shaft intakes. If plates are used, then, the geometry and positionof them should be studied experimentally. Since only general guidance for use of plates is available, astudy for the more precise placement of plates is needed. Hence, a comprehensive set of experiments havebeen carried out using rectangular plates with di�erent dimensions and at various positions with respectto the vertical outlet pipe intakes and two di�erent pipe diameters (D = 75 and 100 mm). The resultsof critical submergence with respect to the dimensions and positions of the plates are presented as graphsand equations. Thus, design guides and recommendations are provided.

Keywords: Air entrainment; Experimental data; Intakes; Pipe ow; Plates; Vortices.

INTRODUCTION

Pipe intakes are used to convey water for turbines,pumps, ood routing, irrigation and other demands.When the water level above a pipe intake is low (lessthan critical value), strong vortices may be formed,which may lead to air-entrainment and which maycause loss of e�ciency, cavitation and vibration inpumps, turbines and pipelines. An intake that isprone to vortex formation, results in a considerableentrainment of air and swirl (the conditions for vortexformation is fully discussed in [1]). Intake vortices arethe result of angular momentum conservation at the ow constriction where angular velocity increases witha decrease in the cross sectional area [2]. The commonsolution for avoiding air-entrainment and swirl is toprovide su�cient submergence to the intake. If therequired approach ow conditions cannot be met toavoid swirl and air entrainment, it is economical toconsider other approaches for preventing vortices atwater intakes. While the e�ect of extreme pressure

1. Department of Civil Engineering, Sharif University of Tech-nology, Tehran, P.O. Box 11155-9313, Iran.

2. Department of Civil Engineering, Isfahan University of Tech-nology, Isfahan, P.O. Box 84156, Iran.

*. Corresponding author. E-mail: mahmood@sharif.edu

Received 28 February 2009; received in revised form 24 October2009; accepted 20 February 2010

variation in a pressurized ow due to air entrain-ment is shown by Kabiri-Samani et al. [3], there areseveral means of avoiding air-entrainment where forlarge structures, the most cost-e�ective option is oftendetermined by a physical model study. One of the mostpopular ways is the use of special vortex suppressiondevices [1]. Among the most economical and commonmeasures of reducing the e�ect of air-entrainment andswirl strength, is anti-vortex plates (e.g. for shaftspillways, submerged culverts and gates). These platescan have any geometry and be used singly, in pairsor in other combinations, and perpendicularly or withan angle to the free surface ow. Ample researchwork has been carried out to have a better knowledgeof vortex formation and critical submergence depthsfor vertical pipe intakes. Among the analytical ap-proaches, the works of Odgaard [4] and Hite andMih [5] are more relevant. However, for experimentalpublished work, the studies can be divided into twocategories. First, the understanding of free vortexhydrodynamics [6-11] and second, parameters a�ectingthe critical submergence depth [2,7,12-16]. On theother hand, while many attempts have been madenumerically to analyze the hydrodynamics of vortexand cavity development [17,18], not much publishedwork with a numerical basis exists on air entrainmentdue to shaft intake.

Although much research has been carried out for

90 S.M. Borghei and A.R. Kabiri-Samani

a better understanding of swirl ow and submergencedepth, there is no design criteria for anti vortex plates.Hence, in this paper, the e�ect of using anti-vortexplates as a means of fully reducing critical submergencedepth and air entrainment is studied experimentally.Anti-vortex plates with di�erent dimensions are usedsingly, in pairs and in di�erent combinations andpositions, to study the e�ects on critical submergencedepth.

GOVERNING PARAMETERS

Important dimensionless terms which should be usedfor experimental studies to de�ne the swirling ow ata pipe intake are [1]:

S=D : Relative Submergence; (1a)

�N =�DQ

: Kolf Number; (1b)

FN =4Q

�(gD5)0:5 : Froude Number; (1c)

RN =Q�s

: Reynolds Number; (1d)

WN =(Qr0S)2

�=(�r0): Weber Number; (1e)

or:

S=D = f(�N ;FN;RN;WN); (2)

where S = submergence depth; D = pipe intakediameter; � = circulation intensity; Q = discharge;g = gravitational acceleration; � = kinematic viscosity;ro = pipe intake radius (D=2); � = surface tension;� = density and f = a function. It should be notedthat some of the dimensionless numbers have beenintroduced with di�erent variables as well (Table 1).The e�ects of viscosity or the Reynolds number (RN),and the surface tension or the Weber number (WN),which often occur in model studies, are of majorinterest to many investigators. A summary of the rangeof in uence of the two numbers by some investigatorsis shown in Table 1 (V is the ow velocity in pipe).As seen, di�erent de�nitions and values are suggested.It seems that while the minimum values in the tableshould be satis�ed, it would be better if the results werechecked by a scale e�ect analysis. Also, the SwirlingParameter (SP ) can be used instead of Froude andKolf numbers [1], as:

SP = �NFN =4�

�(gD3)1=2 : (3)

By employing one or a pair of anti-vortex plates forreducing the swirling ow strength, it can be concludedthat critical submergence also depends on normalizedplates dimensions (a=D and b=D) and positions (r=D,z=D and �). Considering that RN and WN are abovethe critical values and not in uential (see Table 2)and that the value of the critical submergence depthis directly represented by (S=D)cr, it can be seen that:�

SD

�cr

= f�SP;

aD;bD;rD;zD; ��: (4)

Table 1. The values for WN and RN to a�ect results.

Reference Weber No. (WN) Reynolds No. (RN)

Daggett and Keulegan [6] V 2�D=� � 120 Q=(�D) � 3� 103

Anwar et al. [7] V 2�D=� � 120,V 2�S=� � 100

Q=(�S) � 104

Jain et al. [8] V 2�D=� � 120 RN=FN = (gD3)0:5=� � 5� 104

Padmanabhan and Hecker [9] V 2�D=� � 600 V D=� � 7:7� 104

Odgaard [4] V 2�D=� � 720 V D=� � 1:1� 105

Table 2. Minimum values of RN and WN for present study.

RN WN

D = 75 mm D = 100 mm D = 75 mm D = 100 mm

Q=(�S) 74322 123869 V 2�D=� 147 169

V D=� 29264 39019 | | |

Q=(�D) 24773 30967 | | |

RN=FN = (gD3)0:5=� 71719 110419 | | |

E�ect of Anti-Vortex Plates on Critical Submergence 91

EXPERIMENTAL EQUIPMENT AND TESTVARIABLES

Tests were conducted in a cylindrical tank, 1.0 m indiameter and 0.8 m in hight. The circulated waterwas pumped from a large sump and the discharge wasmeasured by an electronic owmeter (while passingthrough the pipe) and checked by a rectangular sharpcrested weir at the end of the ume before returningto the sump. Flow enters the tank horizontally anduniformly through a set of vanes. These vanes wereset at speci�c angles to provide the desired entrancecirculation parameters, i.e. the ratio of tangential toaxial velocity. The ow discharges through a verticalshaft or pipe intake, 0.35 m in height, at the centerof the tank. For preventing negative pressure andreducing the suction e�ect at the entrance of the inlet,air vents are used so that the tests are conducted underatmospheric pressure at the inlet. Figure 1 shows theexperimental setup.

The test variables, as shown in Table 3 andFigure 2, were discharge, intake diameter, anti-vortexplate dimensions (rectangular), positions (r = hor-izontal distance from pipecentre to the side of theplate, z = vertical distance from top of the pipe to

the centre of the plate) and the angle between thetwo plates with a plan view (� as in Figure 2). Thedimensions of plates are taken as multiples of the inletpipe diameter (D), and shown as width by height (i.e.,2D�D means a plate which has 2D width or horizontaldimension and D height or vertical dimension). The�rst set of tests were done using one plate placed underdi�erent conditions. Then, the second set of tests weredone for two plates in di�erent positions as well asdi�erent �.

RESULTS

In this study, the discharge was chosen such that thee�ect of viscosity and surface tension would be smalland, thus, RN and WN are omitted (Table 3). Theresults in the table are minimum values. Comparingthese values with the ones in Table 1, minimum valuesare satis�ed and the assumption of not including WNand RN in the results is acceptable. Hence, the mostsigni�cant and relevant parameters involved in thissituation, as discussed previously, are Froude number,circulation number or Kolf number and relative depth(or critical submergence depth). It is not possible to

Figure 1. Schematic of experimental setup.

Table 3. Test variables.

Q D Plates Dimensions a� b Plate Position Plates Angles

(m3/hr) (mm) (Width�Height)� r(From Edge of Plate)

z(From Center of Plate)

��

6-34 75, 100D �D, D � 2D, D � 3D,

2D �D, 2D � 2D, 2D � 3D,3D �D, 3D � 2D

0:5D, D, 1:5D D, 0:5D, 0,�0:5D, �D, �1:5D

180, 135, 120,90, 60, 45

* For 75 mm pipe complete range of plates and for 100 mm pipe only some of the plates have been tested. Overall 12 plates have

been used (8 for 75 mm, and 4 for 100 mm pipe).

92 S.M. Borghei and A.R. Kabiri-Samani

Figure 2. Plates and pipe intake geometry and position.

show the results of all the tests and, hence, samplesrepresenting typical or, sometimes, extreme values arepresented in the graphs and �gures. However, the �nalconclusions include all the measured data. In Figure 3,the results of critical submergence depth, (S=D)cr, ver-sus Swirling Parameter (SP ) is checked with previouspublished works (Table 4). The agreement betweenobserved results and those of previous works [4,5] canbe seen.

On the other hand, to check if the diameter ofthe tank was large enough for avoiding the wall e�ectand the ow �eld representing the swirling vortex, thetheoretical tangential velocity was checked with themeasured, using a pitot tube (Figure 4). The �gureillustrates two important points. First, the velocitypro�le is well matched with theoretical values [1] andexpected ow �eld; second, the tank is large enough forthe ow �eld, and the velocities near the wall, exceptat the vicinity of the entrance, were almost zero witha minimum wall e�ect.

Now, the e�ect of anti-vortex plates is checkedon the critical submergence depth. Thus, the resultsfrom the di�erent sizes and positions of the platesare analyzed. In this case, the non-dimensional factorin Equation 4 should include the plate variables too.With a trial and error methodology and using all theobserved data, the relation for Equation 4 can be found.

Table 4. Critical submergence relations used in Figure 3.

Reference Relation

Jain et al. [8] (S=D)cr = 5:6(�0:84N FN)0:5

Hite and Mih [5] (S=D)cr = 1:65�NFN

Odgaard [4] (S=D)cr = 48�=FN(gD3)0:5

Figure 3. Critical submergence versus SP (equations inTable 4).

Figure 4. Example of tangential velocity versusnondimensional radial distance.

The suggested relation from these results is:�SD

�cr

=1:65(SP )

22:5� ��0:053

aD

+ 1:431�

���0:18

bD

+ 1:445��

0:5� rD

+ 1:67�

��

0:31� zD

�2 � 0:2zD

+ 1:63�

� (�0:07�+ 1:6); (5)

where � is in radian and a and b are the lengthand width of a single plate, respectively. Also, thelimitations to the equation are �=4 � � � �, a=D � 3,b=D � 2, r=D � 5, and jz=Dj � 3. The equation is

E�ect of Anti-Vortex Plates on Critical Submergence 93

Figure 5. Critical submergence (S=D)cr.

veri�ed by observed data in Figure 5. The deviationof �7% between the calculated and observed values of(S=D)cr, R2 = 0:91 and NRMSE = 0.17, for so manyvariables and data points, is acceptable. Although theproposed equation is for a pair of symmetrical plates,it has been checked by the authors that the equationcan also be used for asymmetrical plates. In this case,the position of each plate can be used in the formulaand, then, the average of the two values multipliedby 1.1 should produce the result. Also, for a singleplate, the value from Equation 5 should be dividedby 0.6, while � = �. Another presentation of theresults showing the e�ect of anti-vortex plates withnon-dimensional values of (S=D)cr and FN, is given inFigure 6. In this �gure, the relation between (S=D)crand FN, for the cases of using anti-vortex plates (no-vortex) and no-plate (fully circulating ow condition)is plotted. It can be seen that by using the anti-vortexplates and completely omitting the vortex, the criticalsubmergence of ow is reduced compared with the freevortex ow condition.

Another important result of this study is the val-idation of the model scale and the sensitivity analysis,since two di�erent pipe sizes (75 and 100 mm) and dif-ferent dimensionless parameters were used. The sametrend and the good correlation between the resultshave been observed, which is encouraging for both pipesizes. The results from the two pipe intakes show thatthe smaller pipe diameter is large enough to avoid in-signi�cant forces and, also, that the ow conditions forthe experiments have been suitable. Also, sensitivityanalyses have been done among di�erent important pa-rameters a�ecting critical submergence depths. Afterthe analysis of di�erent parameters, using experimentaldata, the best �t has been resulted as Equation 5.

Figure 6. (S=D)cr versus FN with free vortex, partiallyreduced vortex and without swirling ow from presentstudy.

CONCLUSIONS

For reducing the critical submergence depth at verticalpipe intakes and omitting the swirling ow, anti-vortex plates can be used. Equation 5 can be usedwhile knowing ow conditions (�N and FN), requiredsubmergence depth (Figure 6), pipe diameter andsymmetrically positioned plate positions. Also, fora single plate and for non-symmetrical positions, thesuggestions using the equation are given. It shouldbe noted that the proposed conclusion is made withthe present experimental set-up. There is no doubtthat many more experimental models with di�erent set-ups from di�erent research will be needed, in order to�nalize and achieve a generalized equation.

NOMENCLATURE

Ap area of a single plate (m2)

a� b anti-vortex plates dimensions (m2)D pipe intake diameter (m)FN Froude numberf functiong gravitational acceleration (m/s2)RN Reynolds numberr radial distance (m)r0 pipe intake radius (m)Q discharge of intake pipe (m3/s)Q0 reference discharge (m3/s)V pipe velocity (m/s)V� tangential velocity (m/s)S submergence depth (m)Scr critical submergence (m)

94 S.M. Borghei and A.R. Kabiri-Samani

S1 water depth far from the intake (m)SP swirling parameterWN Weber numberz axial distance (m)� anti-vortex plates angle (rad.)

� circulation intensity (m2/s)�N Kolf number� kinematic viscosity (m2/s)

� water density (kg/m3)� surface tension (N/m)

Subscripts

nv no vortex or ow through pipeswithout any visible vortex or swirling ow when using the anti-vortex plates

np no plate when the ow is natural orhas free swirl

cr critical

REFERENCES

1. Knauss, J. \Swirling ow problems at intakes", Hy-draulic Structures Design Manual 1. A.A., IAHR,Balkema, Rotterdam (1987).

2. Gulliver, J.S., Rindels, A.J. and Lindblom, K.C. \De-signing intakes to avoid free-surface vortices", Journalof Water Power and Dam Construction, 38(9), pp. 24-28 (1986).

3. Kabiri-Samani, A.R., Borghei, S.M. and Saidi, M.H.\Entrapped air in long water tunnels during transitionfrom pressurized to free surface ow regime", ScientiaIranica, 13(2), pp. 174-186 (2006).

4. Odgaard, A.J. \Free-surface air-core vortex", Journalof Hydraulics Engineering, ASCE, 112(7), pp. 610-620(1986).

5. Hite, E.J. Jr., Mih, W.C. \Velocity of air-core vorticesat hydraulic intakes", Journal of Hydraulics Engineer-ing, ASCE, 120(3), pp. 284-297 (1994).

6. Daggett, L.L. and Keulegan, G.H. \Similitude infree surface vortex formations", Journal of HydraulicsDivision, ASCE, 100(11), pp. 1565-1580 (1974).

7. Anwar, H.O., Weller, J. and Amphlet, M.B. \Simi-larity of free-vortex at horizontal intake", Journal ofHydraulic Research, 16(2), pp. 95-105 (1978).

8. Jain, A.K., Ranga Raju, K.G. and Garde, R.J. \Vor-tex formation at vertical pipe intakes", Journal ofHydraulics Division, ASCE, 104(10), pp. 1429-1445(1978).

9. Padmanabhan, M. and Hecker, G.E. \Scale e�ect inpump sump models", Journal of Hydraulics Division,ASCE, 110(10), pp. 1540-1556 (1984).

10. Rocklage-Marliani, G., Schmidts, M. and Ram, V.I.V.\Three-dimensional laser-Doppler velocimeter mea-surements in swirling turbulent pipe ow", AppliedScienti�c Research, Springer Netherlands, 70(1-4), pp.43-67 (2003).

11. Carriveau, R. \The hydraulic vortex - an autocataki-netic system", Intl. Journal of General Systems, 35(6),pp. 707-726 (2006).

12. Reddy, Y.R. and Pickford, J.A. \Vortices at intake inconventional sumps", Water Power, No. 3, pp. 108-109(1972).

13. Yildirim, N. and Kocaba�s, F. \Critical submergencefor intakes in open channel ow", Journal of HydraulicsDivision, ASCE, 121(12), pp. 900-905 (1995).

14. Yildirim, N. and Kocaba�s, F. \Prediction of criticalsubmergence for an intake pipe", Journal of HydraulicResearch, IAHR, 40(4), pp. 507-518 (2002).

15. Borghei, S.M. and Kabiri Samani, A.R. \Critical sub-mergence of vertical intakes using anti-vortex plates",Proc. of 6 Int. Conf. Civil Eng., IUT, Isfahan, Iran, 7,pp. 59-66 (2003).

16. Yildirim, N. \Critical submergence for a rectangularintake", Journal of Engineering Mechanics, 130(10),pp. 1195-1210 (2004).

17. Emdad, H. and Nikseresht, A.H. \Application ofvortex lattice and quasi-vortex lattice method withfree wake in calculation of aerodynamic characteristicsof a hovering helicopter rotor blade in ground e�ect",Scientia Iranica, 10(1), pp. 84-90 (2003).

18. Kazemzade Hannani, S. and Parsinejad, F. \Incom-pressible stokes ow calculation using a �nite pointmethod", Scientia Iranica, 10(1), pp. 44-55 (2003).

BIOGRAPHIES

S.M. Borghei was born in Tehran, Iran on 23 Dec,1954. He received his BS in civil engineering in 1977,and his PhD in hydraulic engineering in 1982 fromNottingham University in the UK. Dr Borghei beganhis academic career at Sharif University of Technology,Iran, in 1983 and became professor in 2006. His mainresearch interests include experimental and physicalmodeling of hydraulic structures, and river engineering.He has published and presented, respectively, morethan 100 papers in scienti�c journals and at conferencesin these areas of interest.

A.R. Kabiri-Samani completed his PhD in civilengineering at Sharif University of Technology in the�eld of hydraulics. He has been faculty a�liate asAssistant Professor in the civil engineering departmentof Isfahan University of Technology since 2006 untilthe present. Since 2008, he is the graduate programcoordinator of the department.

Dr Kabiri received the 2008 \Elite NationalFoundation" for being ranked the highest of all PhD

E�ect of Anti-Vortex Plates on Critical Submergence 95

graduated students in the civil engineering depart-ment of Sharif University of Technology and the 2006\Tavakkoli Award" due to his applicable research intwo-phase ow mechanics. In 2003, he also received anaward for being among the top 10Education at SharifUniversity of Technology.

He has authored more than 40 scienti�c pub-lications, including 10 papers in scienti�c journals,30 conference papers and 4 technical reports. Un-der his guidance, six MS students have also com-

pleted their graduate degrees in hydraulic engineer-ing.

He serves on the review board of the Journal ofFluids Engineering (ASME), the Canadian Journal ofChemical Engineering (CSChE), the National Journalof Hydraulics (Iranian Hydraulic Association) and theNational Journal of Water and Wastewater (IsfahanWater and Wastewater Consulting Engineers Co.).

He is also a member of seven professional societies,including IAHR, EWRI, IHA, etc.