Downpull force gates

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Prediction of downpull on closing high head gatesIsmail Aydin

a , Ilker T. Telci

a & Onur Dundar

a

a Civil Engineering Department , METU , 06531, Ankara, Turkey Fax:

Published online: 26 Apr 2010.

To cite this article: Ismail Aydin , Ilker T. Telci & Onur Dundar (2006) Prediction of downpull on closing high head gates,Journal of Hydraulic Research, 44:6, 822-831, DOI: 10.1080/00221686.2006.9521733

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Journal of Hydraulic Research Vol. 44, No. 6 (2006), pp. 822–831

© 2006 International Association of Hydraulic Engineering and Research

Prediction of downpull on closing high head gatesCalculs de l’abaissement de fermeture de vannes sous fortes charges

ISMAIL AYDIN, Associate Professor, Civil Engineering Department, METU, 06531 Ankara, Turkey. Tel.: + 90 (312) 210 54 55;

fax: + 90 (312) 210 24 38; e-mail: [email protected] (author for correspondence)

ILKER T. TELCI, Graduate Student, Civil Engineering Department, METU, 06531 Ankara, Turkey. Tel.: + 90 (312) 210 24 19;

fax: + 90 (312) 210 24 38; e-mail: [email protected]

ONUR DUNDAR, Graduate Student, Civil Engineering Department, METU, 06531 Ankara, Turkey. Tel.: + 90 (312) 210 24 76;

fax: 90 (312) 210 24 38; e-mail: [email protected]

ABSTRACTDownpull on tunnel gates installed in the intake structure of a hydroelectric power plant was studied experimentally using a hydraulic model. Thepressure distribution on the gate lip surface was measured, and the lip downpull was evaluated by surface-area integration of the measured pressuredistribution. An easy to use lip downpull coefficient was defined as a function of the lip angle and gate opening. The lip downpull coefficient functionis linked to a one-dimensional mathematical model of unsteady flow in the intake-penstock system. The model is based on the integral energy andcontinuity equations. Overflow through the gate spacings is also included in the model to compute the water level in the gate shaft and to evaluate thedownpull component on the top face of the gate. Time-dependent calculation of the total downpull force acting on a closing gate is exemplified. Thetotal downpull is also measured by the direct weighing method for fixed and closing gates. Predictions of the mathematical model compare favorablywith the downpull obtained from the direct weighing method.

RÉSUMÉL’abaissement des vannes de tunnel installées dans la structure de prise d’eau d’une usine hydroélectrique est étudié expérimentalement sur un modèlehydraulique. La distribution de pression sur la surface de la tranche de la vanne a été mesurée, et l’effort a été évalué par l’intégration de la pressionmesurée sur la surface. Un coefficient, facile d’emploi, de l’effort sur la tranche a été défini en fonction de l’angle de la tranche et de l’ouverturede la vanne. La fonction donnant ce coefficient est liée à un modèle mathématique unidimensionnel de écoulement instationnaire du système de

prise-conduite forcée. Le modèle est basé sur l’intégrale des équations d’énergie et de continuité. Le débordement dans l’espace interne de la vanneest également inclus dans le modèle pour calculer le niveau d’eau dans la vanne et évaluer l’effort sur la face supérieure de la vanne. Le calcul enfonction du temps des efforts agissant sur la vanne en fermeture est illustré. L’effort total de fermeture est également mesuré par la méthode de peséedirecte pour les vannes fixes et en fermeture. Les prévisions du modèle mathématique donnent de bonnes comparaisons.

Keywords: Pressure distribution, downpull, hydraulic gate, dams, hydropower.

1 Introduction

Vertical leaf gates are widely used high head gates for discharge

control and emergency closure in large cross-sectional conduits

since they provide many advantages in construction and main-

tenance. However, leaf gates may cause problems in certain

circumstances due to large downpull or uplift.

The hydrodynamic downpull can be defined as the total force

induced by the flowing water on the gate surfaces acting in the

closing direction. Hydrodynamic downpull results mainly from

the difference between pressure forces acting on the top and lip

surfaces of the gate. The pressure on the top surface depends

on the gate position (opening) and water level in the gate cham-

ber. The water level in the gate chamber is affected by overflow

Revision received January 9, 2006/Open for discussion until June 30, 2007.

822

through the spacings between the gate faces and walls of the gate

chamber. The spacings around the gate can be adjusted to con-

trol overflow and therefore the water level in the gate chamber.

Pressure on the lip surface mainly depends on the lip geometry,

flow rate under the gate and the streamline pattern around the lip.

Gate geometry is characterized by the lip angle, corner round-

ings and the end plate. The flow rate is usually characterized by

the average velocity in the flow section under the gate lip. The

streamline pattern of the gate region is characterized by the gate

opening.

For opening a gate, the hoist mechanism should resist the

weight of the gate, the downpull and the frictional resistance.

When the gate is closing, hydrodynamic downpull added to the

dead weight of the gate minus the frictional resistance determines


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Prediction of downpull on closing high head gates 823

the hoist capacity required. In some cases, negative downpull

resulting in an uplift force may prevent safe closure of the gate.

Downpull force prediction methods were developed by hydro-

dynamic analysis of high head gates (Colgate, 1959; Naudascher

et al., 1964; Murray and Simmons, 1966; Naudascher, 1986,

1991) and have been validated by simultaneous model studies.

Naudascher et al. (1964) and Naudascher (1986) presented aone-dimensional analysis of the discharge passing under a tunnel

gate and of the hydraulic downpull acting on it. The studies of

Naudascher showed that the downpull is significantly affected

not only by the geometry of the gate bottom but also by the rate

of flow passing over the top of the gate through the gate chamber.

Sagar (1977) andSagar andTullis(1979)indicated that impor-

tant factors such as geometry, boundary layers and turbulence

influence the downpull on a gate and discussed various forces

which play important roles during opening and closing. Sagar

developed non-dimensionalformulae to illustrate the dependence

of downpull on these factors and also outlined the limitations on

the prediction capability.

The accurate prediction of the downpull force acting on a gate

is important to the designer to determine the capacity of the lift-

ing system and to ensure safe closure in adverse circumstances.

Available methods for determination of hydrodynamic downpull

are based on steady-state measurements obtained for fixed posi-

tions of themodelgatesand arenot verified for moving conditions

(Naudascher, 1991). When the gate moves fast, as in the case of

emergency closure, pressures on the gate faces can be different

than the corresponding steady-state values.

A mathematical model for the determination of air demand

during gate closure was presented by Aydin (2002). The modelwas based on the numerical solution of the continuity and inte-

gral form of the one-dimensional unsteady energy equations. The

time-dependent piezometric line along the intake-penstock struc-

ture and pressures on the upstream and downstream faces of the

gate were computed. Later (Aydin et al., 2003), the mathemat-

ical model was improved to include the overflow for accurate

determination of air demand.

Experimental work on downpull including lip pressure dis-

tribution measurements and direct weighing of downpull are

Figure 1 Experimental set-up.

presented in this paper. The time-dependent calculation of the

total downpull force acting on a closing gate is illustrated through

the numerical solution of the one-dimensional energy equation.

2 Experimental facilities

2.1 Hydraulic model

The hydraulic model (Figs 1 and 2) consists of a streamlining

pool to represent the reservoir, entrance details of the intake,

0.30 × 0.24 m rectangular discharge control (gate) region (sec-

tion 2), ventilation shaft (section 3), transition from a rectangular

to a circular cross-section, the penstock represented by a 0.30 m

diameter circular plexiglass pipe, end valve to represent the tur-

bine, and the discharge measuring channel. H 1 is the reservoir

water surface level, h2 is the water level in the gate chamber, h3

is the piezometric head at the contracted section (section 3), and

H 4 is the tail water level. For partial openings of the gate, h2 isaffected by the overflow through the spacings between the walls

of the gatechamber and the gate(Fig. 2). The gate opening isindi-

cated by e, which isequalto e0, the tunnel height, when the gate is

fully open. Discharge through the intake (upstream of section 2)

is indicated by QI, and discharge in the penstock (downstream of

the gate) is indicated by QP. Water discharge in the experimental

set-up is measured from a sharp-crested weir located at the end

of the prismatic measuring channel. Water levels (H 1, h2, h3, H 4)

are measured by manometer tubes for steady-state cases and by

electronic transducers for unsteady cases.

2.2 Gate design

Two model gates are constructed to perform pressure and down-

pull measurements alternately. One of the gates is equipped with

piezometer connections for measurement of the pressures on

the gate lip (Fig. 3). The second gate (without piezometer con-

nections) is used for direct measurement of the downpull using

force transducers connected to the lift mechanism. Both gates are

wheeled to move up and down in the gate chamber. Four vertical


4/11

824 Aydin et al.

Figure 2 Gate region parameters.

θ

s

r = 0.01 m

n

0.04 m

r

Piezometer tubes

Figure 3 Gate lip details.

faces of the gates are wheeled to minimize friction and to ease

motion of the gate in the gate chamber.

In the pressure measurements, four different lip angles are

considered. The gate is designed such that the lip section on it

can be de-mounted and another one can be plugged in. On the

lips there are five piezometer tappings (Fig. 3), each of which is

connected to a vertical copper pipe in the gate chamber. Plasticmanometer tubes are used to connect the copper pipes to elec-

tronic pressure transducers. The piezometertappings were shifted

in the transverse direction to avoid any streamwise interaction at

Table 1 Gate lip parameters.

Lip symbol n (m) Lip angle θ (◦)

A 0.02 26.5

B 0.03 36.7

C 0.04 44.7

D 0.05 51.6

the measuring points and to help the arrangement of copper pipes

along the gate width.

The gate lip angles used in the present study (Table 1) are

selected to cover the complete practical range. Corner roundings

and end plate variations are not considered in the experimental

program. The gate slot spacings are minimized to reduce leakage

from the sides and subsequent vortex formations. Overflow is

also prevented in the pressure measurements.

2.3 Data acquisition system

An electronic data acquisition system is used to measure the

instantaneous pressures at five measuring points on the gate lip

and the water level in the reservoir simultaneously. Electronic

pressure transducers (HBM type PD1) are capable of sensing

time-wise fluctuations accurately. Transducers are connected to

HBM MC55 amplifier system for electronic amplification. Ana-

log signals obtained from the amplifier system are directed to

a computer equipped with an analog-to-digital converter for

digitization.

3 Measurements and analysis

3.1 Experimental procedure

Pressure recordings from the gate lip surface contain time-

dependent fluctuations due to vortex structures and turbulence

around the gate lip. Record duration and data sampling rate are

determined from power density spectrum analysis of the pres-

sure records. The upper and lower limits on the frequency axis of

the spectrum are determined as 2 Hz and 0.01 Hz, respectively.

The digital data sampling rate is fixed as 20 Hz, which provides

10 discrete data points for a fluctuation component at the high-

est frequency level. The record duration is decided as 10 mins,

which enables recording six consecutive fluctuations from the

lowest frequency band.

To start a pressure recording, the gate is positioned at a desired

opening and the discharge is adjusted by the end valve. When the

discharge in the system is high, the piezometric line may fall

below the tunnel ceiling, which causes the entrance of air into

the gate region from the ventilation shaft. Air in the gate region

is entrapped into the measuring tubes due to the strong mixingaction of the vortices around the gate lip, which prevents accurate

measurement. Discharges causing low piezometric levels are not

considered to avoid any air entrainment into the measuring tubes.


5/11


3.2 Pressure distributions on the gate lip

Piezometric levels from five points arranged on the gate lip are

measured to obtain pressure head distributions and to evaluate the

lip downpull coefficients. Three parameters, i.e., the lip angle (θ ),

dimensionless gate opening (y = e/e0), and the discharge under

the gate (Qg), are considered as variables of the experimental

investigation. The discharge is replaced by the Reynolds number,

Rg, defined by using the hydraulic radius of the cross-sectional

area and the average velocity under the gate lip, U g. Thus, all

variables are made dimensionless.

To observe variations of the pressure distributions, five gate

openings (y = 0.1, 0.2, 0.4, 0.6, and 0.8) and (for each opening)

fivedifferent dischargevalues areconsidered for thefour gate lips

described in section 2.2. Pressure head distributions as a function

of the inclined distance, s, in the streamwise direction along the

gate lip are shown in Fig. 4 for y = 0.4. The pressure on the

upstream edge is lower than the pressure on the downstream edge

for lipA, which has a lip angle of26.5◦

. As the lip angle increases(lip B and lip C), pressure on the upstream edge increases. At

high Reynolds numbers, the downstream edge pressure is lower

than the upstream edge pressure for large lip angles (lip D). To

visualize the flow pattern around the gate lip, color photographs

and video records were taken by dye injection from the most

upstream piezometer tapping. It was not easy to identify any

separation vortices in the photographs. However, video records

showed that large separation vortices are formed spontaneously

for very short duration causing intermittent spikes in the pressure

records.

s (m)

p / γ

w

( m )

0 0.01 0.02 0.03 0.04-0.5

0

0.5

1

1.5

100694

190873

320387

358681

470089

Lip A

Rg

s (m)

p / γ

w

( m )

0 0.01 0.02 0.03 0.04 0.05-0.5

0

0.5

1

1.5

141915

256994

352679

449653

494544

Lip B

Rg

s (m)

p / γ

w

( m )

0 0.01 0.02 0.03 0.04 0.05-0.5

0

0.5

1

1.5

140724

264983

342956

409177

474008

Lip C

Rg

s (m)

p / γ

w

( m )

0 0.02 0.04 0.06-0.5

0

0.5

1

1.5

161458

241071

328423

399702

472867

Lip D

Rg

Figure 4 Gate lip pressure distributions at y = 0.4.

3.3 Definition of lip downpull coefficient

The measured piezometric head distributions are used to evalu-

ate the dimensionless downpull coefficient for the gate lip. The

piezometric head, hp, is integrated over the horizontally projected

area, AhL, of the gate lip and divided by the same area to obtain

the average piezometric head, h, acting on the gate lip.

h =

hp dAhL

AhL(1)

In the literature (Naudascher, 1991), the downpull coefficient for

a gate lip is defined as

KB =h − h3

U 2c /2g. (2)

where U c is the average velocity at section 3. The reference

piezometric head h3 and the reference velocity U c, are both

dependent on the gate region and gate design details. There-

fore, the downpull coefficient given by Eq. (2) is dependent on

the characteristics of the model on which the measurements areperformed. To reduce the influences of the specific experimen-

tal set-up on the lip downpull coefficient, a new definition is

introduced:

KL =h∗2 − h

U 2g /2g(3)

where h∗2 (= H 1 − (1 + Ke)U 2t /2g) is the piezometric head

just upstream from the gate, Ke is the head loss coefficient for

the intake section (excluding the conversion of potential energy

to velocity head) and U t is the average velocity in the tunnel


6/11

826 Aydin et al.

Rg x 10

-5

K L

0 1 2 3 4 5-1

0

1

2

3

Lip A

Lip B

Lip C

Lip D

y = 0.8

Rg x 10

-5

K L

0 0.5 1 1.5 2-1

0

1

2

3

Lip A

Lip B

Lip C

Lip D

y = 0.1

Figure 5 Downpull coefficient—Reynolds number relationship.

cross-section when the gate is open. In the present study, both

definitions of the lip downpull coefficient are evaluated.

3.4 Lip downpull coefficient—Reynolds number relationship

Thedownpull on thegate lipis assumed to dependon thelip angle,

dimensionless gate opening and the Reynolds number Rg. It is

expected that the downpull coefficient becomes independent of

the Reynolds number for sufficiently high values of Rg. However,

in model studies, high Reynolds numbers may not be reached,

due to the limitations on the size of the hydraulic model and the

model discharge. Before conducting the detailed downpull exper-

iments, the relationship between the lip downpull coefficient and

the Reynolds number was studied.

Naudascher (1991) reported that lip downpull coefficient

becomes independent of the Reynoldsnumber whenthe Reynolds

number exceeds 165,000. In the present study, the values of KL

independent of the Reynolds number are easily achieved at about

Rg = 150,000 for small gate openings (Fig. 5).

As the gate opening increases, an asymptotic approach to a

constant KL value is observed at a Reynolds number of approx-

imately 400,000 for lip A. The lip downpull coefficient, KL, is

shown in Fig. 5 as function of the Reynolds number for the gateat y = 0.1 and y = 0.8. Downpull coefficients presented in the

following sections are measured at the highest Reynolds num-

ber that can be achieved for a given gate opening. The highest

Reynolds number is obtained at the highest discharge, which is

defined as the discharge that maintains pressurized flow behind

the gate without any air volume. This restriction on the discharge

is required to avoid any air bubbles in the pressure measuring

tubes.

3.5 Comparison of lip downpull coefficientsThe lip downpull coefficient, KB, defined by Eq. (2), is evaluated

from the measured pressure data. The results are shown in Fig. 6

together with the measurements of Naudascher (1991) for com-

parison purposes. Since the lip angles are not identical in both

data sets, it is not possible to give a measure of agreement. How-

ever, for close lip angles, similar KB distributions are obtained.

The present data provides a complete description of the lip down-

pull coefficient near full openings of the gate that was not shown

before.

3.6 Lip downpull coefficient as a function of the gate

opening and the lip angle

The complete data set for the lip downpull coefficient, KL, eval-

uated according to the new definition, Eq. (3), using measured

pressure data of this study is shown in Fig. 7 as a function of y

and the lip angle. At both ends of the graph, for a fully open gate

(y = 1) and completely closed gate (y = 0), KL is zero since

the average pressure on the gate lip is equal to the local static

pressure. The maximum downpull on the lip is observed at about

y = 0.4. The lip downpull increases with decreasing lip angle for

a given y value. The lip downpull coefficient is negative for gate

openings around y = 0.9, indicating that the average pressure

on the gate lip is greater than the static component due to the

stagnation pressure that result from the constriction of the flow

section by the gate. The scatter of data near the fully open gate

cases is increased due to the pressure fluctuations induced by the

vortices created around the corners of the gate chamber. That is

also the reason why the measured data of KL is not exactly zero

at y = 1.

Finally, a functional representation of KL dependent on y and

θ can be given. The general form of the fitting function is assumed

y

K B

0 0.2 0.4 0.6 0.8 1-0.2

0

0.2

0.4

0.6

0.8

1

Lip A (θ=26.5o)

Lip B (θ=36.7o

)Lip C (θ=44.7

o)

Lip D (θ=51.6o)

θ=20o

(Naudascher, 1991)

θ=30o

(Naudascher, 1991)

θ=45o

(Naudascher, 1991)

Figure 6 Comparison of downpull coefficients.


7/11


y

K L

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

1.5

Lip ALip B

Lip C

Lip D

Eq. 5

Figure 7 Downpull coefficient as a function of the gate lip angle and

the gate opening.

to be:

KL = c1 + c2y + c3y2+ · · · + cny

n−1 (4)

where ci are considered as functions of θ . The curvature of

KL over y changes sign at about y = 0.8 as shown in Fig. 7.

Therefore, the curve fitting is accomplished in two steps:

For 0 ≤ y


8/11

828 Aydin et al.

of Qo, H u, h2 and H d for various spacings on the upstream and

downstream faces of the gate for no underflow (Qg = 0). The

correction coefficients are obtained from Eqs (10) and (11) by

utilizing the experimental data:

αu = 3.893aum

max(au)− 0.189, 1 ≤ αu ≤ 3.7 (12a)

αd = 10.32 admmax(ad)

− 0.42, 1 ≤ αd ≤ 9.9 (12b)

Equations(10)–(12)give a closed formsolution for overflowfrom

known values of H u and H d. The water level in the gate chamber

is determined from the unsteady continuity equation written for

the gate chamber:

∂h2

∂t =

Qod − Qou

Agc(13)

where Agc is the cross-sectional area of the gate chamber. The

upstream piezometric head at the top corner of the tunnel is

obtained from:

H u = H 1 − (1 + Ke)U 2t

2g+

U 2stg

2g(14)

where U stg is the stagnation velocity such that, in dynamic head

form, it represents the head converted into pressure near the

tunnel ceiling due to blockage of the partially closed gate. Mea-

surements of H u as function of Qg were performed for variable

gate openings to determine the stagnation velocity from Eq. (14).

Thestagnation velocityis assumed to be proportionalto thetunnel

velocity through a function of the gate opening:

U stg = f s(y)U t (15)

The function f s is obtained as a polynomial fitted to theexperimental data:

f s = 1−2.985y+13.73y2−30.05y3+31.45y4−13.14y5 (16)

The piezometric head on the downstream side of the gate, H d, is

taken as the elevation of the tunnel ceiling plus the pressure head

at the ventilation shaft exit on the tunnel ceiling.

4.2 Unsteady flow due to closing gate

The volume of the structure between the reservoir and section 3

is called the intake region (I), and the volume between section 3

and the end valve is called the penstock region (p). The integralform of the modified energy equation is applied to the intake and

penstock regions to compute the time-dependent volume flow

rates of water and air:

∂

∂t

I

U 2

2g+ z

γ wd ∀ = H 1QIγ w − heQIγ w − hgQgγ w

− H uQouγ w − H cgQgγ w (17)

∂

∂t

p

U 2

2g+ z

γ wd ∀ = H cgQgγ w + H dQodγ w + H sQsγ s

− h jQgγ w − hdQpγ w

− H 4Qpγ w (18)

where H cg is the total head of the underflow fluid in the con-

tracted section, the subscript s indicates the ventilation shaft,

H s is the total head at the exit from the shaft into the penstock,

and he, hg, h j,and hd are head losses at the intake sec-

tion, in the gate region, dueto hydraulicjump, andin thepenstock

region, respectively. Thelink between theintake andthe penstock

is completed by the continuity equation written at the interface

of the two volumes:

Qs = Qp − Qg − Qod (19)

The model equations are solved iteratively starting from full gate

opening to complete closure. In this iteration cycle, when the

ventilation shaft discharge is evaluated, the pressure at the bot-

tom end of the ventilation shaft can be obtained by writing the

unsteady energy equation for the flow in the shaft. Detailed

description of the mathematical model, evaluation of model

parameters and the solution method were presented in Aydin

(2002).

The one-dimensional formulation of unsteady flow in the

intake–penstock system, together with the lip downpull coeffi-

cient given by Eq. (5), provide a complete mathematical model

for determination of total downpull on the gate. Some example

calculations as functions of lip angle θ (a), initial discharge Qm

(b), gate spacing adm (c) and closure time T c (d) are shown in

Fig. 8. For lip A (θ = 26◦), the net hydrodynamic force is pos-

itive (downpull) for 0.1 < y < 0.5 and negative (uplift) for the

other gate openings (Fig. 8a). For lip C (θ = 44.7◦), positive

downpull is observed only around y = 0.25 for small down-

stream spacings. For lip D (θ = 51.6◦), the hydrodynamic force

is always negative (uplift) for all gate openings. Increased initial

discharge produces larger downpull and shifts the occurrence of the maximum downpull to larger gate openings (Fig. 8b). Larger

downstream spacings cause larger uplift forces (Fig. 8c). The

gate closure time has a significant influence on the downpull only

when the upstream spacing is small and downstream spacing is

relatively larger (Fig. 8d).

5 Direct measurement of total downpull

5.1 Measuring system

The gate was hung on a chain-gear system actuated by a variable

speed electric motor, which is controlled by the computer of the

data acquisition system. Tension on the lift chain was measured

by electronic force transducers, and digitized data was recorded.

Before the downpull measurements, the gate was moved in the

gate chamber with no water in the intake, and the dry weight

of the gate-chain system was measured as a function of the gate

opening. The total hydrodynamic downpull is evaluated as the

force measured during the experiments minus the dry weight

measured at the same gate opening. The friction force from the

gate wheels for both fixed and moving gate cases is small and

neglected. When there is no flow, the total downpull is equalto the negative of the lifting force due to water, which is the

buoyancy for a totally submerged gate. Downpull weighing was

performed with lip C only.


9/11


y

F d

( N )

0 0.2 0.4 0.6 0.8 1-60

-40

-20

0

20

40

60

Lip A

Lip B

Lip CLip D

aum

= 0.005 m

adm

= 0.001 m

αu = 2.0

αd = 1.0

Qm

= 0.090 m3/s

(a)

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-160

-140

-120

-100

-80

-60

-40

-20

0

20

5

10

20

∞

Lip A

aum

= 0.001 m

adm

= 0.004 m

αu = 1.00

αd = 3.51

Qm

= 0.090 m3/s

Tc (s)

(d)

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-60

-40

-20

0

20

40

60

0.030

0.060

0.090

0.120

Lip A

aum

= 0.005 m

adm

= 0.001 m

αu = 2.0

αd = 1.0

Qm

(m3/s)

(b)

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-100

-80

-60

-40

-20

0

20

0.001 1.00

0.002 1.55

0.003 2.53

0.004 3.51

Lip C

aum

= 0.004 m

αu = 1.58

Qm

= 0.090 m3/s

adm

(m)

(c)

αd

Figure 8 Downpull obtained from the mathematical model. (a) Variations with the lip angle, (b) variations with initial discharge, (c) variations with

downstream spacing and (d) variations with closure time.

5.2 Measurement of downpull on fixed gate

The measurement of total downpull at static positions of the

gate is important to compare with the results of the pressure-

area integration. Different overflow spacing configurations are

studied for different initial discharges by measuring the total

downpull at six gate openings. Measured and computed down-

pull data for aum = 0.0088 m and adm = 0.0032 m are shown

in Fig. 9. Computed and measured values are in satisfactory

agreement.

5.3 Measurement of downpull on closing gate

Downpull measurements for the closing gate were performed

for different closure speeds. In total, 45 test cases were con-

sidered. Example records of measured and computed downpull

are presented in Fig. 10. In general, test cases with large

initial discharges and smaller downstream spacings (small over-

flow discharge and higher water levels in the gate chamber)

show better agreement between the model predictions and

measurements.

It must be noted that the most difficult component to model

is overflow in the unsteady cases. A fast closing gate cre-ates secondary currents in the gate chamber that interact with

the overflow and affect the resultant downpull on the gate.

The one-dimensional mathematical model, based on averaged

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-60

-50

-40

-30

-20

-10

0

10

0.050

0.074

0.119

Qm

(m3/s)

θ = 44.70

aum

= 0.0088 m

adm

= 0.0032 m

αu = 3.70

αd = 2.73

Figure 9 Comparison of measured (symbols) and predicted (lines)

downpull on fixed gate.

experimental data obtained at the steady-state conditions, is not

expected to reproduce the complex unsteady flow characteristics

around the gate. However, comparisons of model predictionsand measured quantities for both steady and unsteady cases give

confidence for use of the model results when detailed downpull

measurements are not available.


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830 Aydin et al.

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

Measured

Computed

Lip C

aum

= 0.0088 m

adm

= 0.0042 m

Qm

= 0.119 m3/s

Tc = 34 s

y

F d

( N )

0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

Measured

Computed

Lip C

aum

= 0.0088 m

adm

= 0.0042 m

Qm

= 0.074 m3/s

Tc = 34 s

y

F d ( N )

0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

Measured

Computed

Lip C

aum

= 0.0088 m

adm

= 0.0028 m

Qm

= 0.075 m3/s

Tc = 7 s

y

F d ( N )

0 0.2 0.4 0.6 0.8 1-80

-60

-40

-20

0

20

Measured

Computed

Lip C

aum

= 0.0088 m

adm

= 0.0028 m

Qm

= 0.120 m3/s

Tc = 7 s

Figure 10 Comparison of measured and predicted downpull on closing gate.

6 Conclusions

The hydrodynamic downpull acting on a vertical tunnel gate

has two main components on the top and bottom faces of the

gate. Both components are dependent on numerous geometrical

parameters of the gate and its surroundings. It is not practical to

develop a downpull prediction formula covering the full range of

all variables due to the large number of parameters encountered.

Measurement of the total downpull either by direct weighing or

by pressure integration may not be convenient in model stud-

ies for each specific application. Experimental data summarized

by Eq. (5) as a function of the two most significant variables

(the gate opening and the lip angle) is used in the prediction

of the lip downpull. The force on the gate top requires moredetailed modeling of the flow around the gate. The mathemat-

ical model developed for this purpose requires the energy loss

coefficients of the intake–penstock system, which can easily be

determined from steady-state measurements of piezometric line

on a hydraulic model. It is then possible to run the computer code

to investigate the downpull for varying gate lip geometry, gate

spacings in the gate chamber and operational conditions.

The methodology described above can be efficiently used

to predict downpull from hydraulic models for variable design

considerations from easy to measure experimental data such as

discharge and piezometric levels.All loss coefficients and expres-sions based on the experimental data are specific to the physical

model used in this study. Therefore, they can not be directly used

for any other intake structure.

Acknowledgments

This study was supported financially by the Scientific and Tech-

nical Research Council of Turkey (TUBITAK), contract no.

INTAG-831.

Notation

A = Cross-sectional area

a = Spacing between the gate and walls of the gate chamber

e = Gate opening

e0 = Tunnel height

f = Functions of gate opening

g = Gravitational acceleration

H = Total head

h = Piezometric head (water surface elevation)

K = Head loss coefficient

L = Lengths

p = Pressure

Q = Discharge

R = Reynolds number

t = Time

T c = Closure time

U =Average velocityw = Tunnel width

x =Axial distance

y = Dimensionless gate opening (e/e0)


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z = Elevation

α = Overflow correction coefficient

ν = Kinematic viscosity

γ = Specific weight

h = Head loss

∀ = Volume

Subscriptsc = Vena contracta

d = Downstream side

e = Entrance

g = Gate

I = Intake

o = Overflow

p = Penstock

s = Quantities in the ventilation shaft

t = Tunnel

u = Upstream side

w = Water

1 = Reservoir

2 = Gate section

3 = Ventilation shaft

4 = Tail water

References

1. Aydin, I. (2002). “Air Demand Behind High Head Gates

During Emergency Closure”. J. Hydraul. Res. IAHR 40(1),

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2. Aydin, I. , Dundar, O. and Telci, I.T. (2003). Hydrody-

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