Modeling the Mangla Dam Spillway for Cavitation and Aerators Optimization

doi:10.4236/jwarp.2012.412121

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Journal of Water Resource and Protection, 2012, 4, 1051-1060

http://dx.doi.org/10.4236/jwarp.2012.412121 Published Online December 2012 (http://www.SciRP.org/journal/jwarp)

Modeling the Mangla Dam Spillway for Cavitation and

Aerators Optimization*

Mohammad Rafi1, Akhtar Ali2#, Ghulam Qadir3, Rafaquat Ali1

1Water Resources Division, National Engineering Services of Pakistan (NESPAK), Lahore, Pakistan

2Asian Development Bank, Manila, Philippines

3WAPDA Model Study Cell, Irrigation Research Institute, Irrigation Secretariat, Lahore, Pakistan

Email: #[email protected]

Received September 15, 2012; revised October 16, 2012; accepted October 23, 2012

ABSTRACT

This study evaluated the effects of increased reservoir conservation level by 40 ft (12.2 m), on spillway velocities; it’s

discharging capacity and associated cavitation risk. The study optimized the aerators size and shape to avoid cavitations.

The mathematical model was used to estimate the flow velocities and cavitation risk, when scale model study assessed

the spillway discharging capacity and optimized the performance of the aerators for modified conditions. The mathe-

matical model simulations showed increased flow velocities and damage index for modified conditions. The damage

potential was 2 - 3 times higher with modifications and falls within the major to catastrophic region. The scale model

study showed that discharging capacity of the spillway can effectively be restricted to original design by raising spill-

way crest by 5.0 ft (1.52 m). The scale model study also showed that the two aerators near sluice and at the chute with

an air duct pipe of 3.0 ft diameter can improve the free surface flow profile reducing the risks of cavitation. Simulations

for several configurations demonstrated clearer affect of aerators ramps on flow trajectory and gate opening. It also de-

picted that the height of the ramp of sluice aerator has a positive effect on the flow performance to about 7.5 inches (19

cm), when further increase in the ramp height reduced the flow performance.

Keywords: Spillway; Model Studies; Discharging Capacity; Cavitation Risk; Aerators Optimization

1. Introduction

High flow velocities can induce cavitations and cause

serious damages to the spillways of high dams. Forma-

tion of flow bubbles indicates spillway surface deforma-

tion [1]. Increasing flow velocities and as a result de-

creasing pressures may pass through a critical value ini-

tiating cavitation, which is known as incipient cavitation.

Conversely, decreasing velocity resulting in increasing

pressure may arrive to a point to disappear cavitation and

is called desinent cavitation. Surface roughness of spill-

way floor and water impurities aggravate cavitations,

accelerate damages and can result is spillway failure.

Interactions between the flowing water and the at-

mosphere may lead to significant air-water mixing and

complex multiphase flow situation [2,3]. The cavitation

can be prevented either reducing the flow velocity or

increasing the flow pressure or with combination of both.

The studies on the effect of variable spillway width and

invert curvature on the flow pressure for Amaluza dam

spillway in USA indicated that dispersion of a small

amount of air through water prism can significantly re-

duce for the risks of cavitation damage [4]. It was found

that about 7.5% of air by volume was needed to stop

cavitation damages in a 28-day concrete surface with a

compressive strength of 17 mega-Pascals [5]. The re-

quired air quantity to protect a spillway surface from

cavitation increases with decrease in surface strength [6].

Application of aerators to prevent cavitation damage was

successfully tested for Grand Coulee Dam in USA [7].

Bottom aerators are provided when natural aeration of

the high velocity spillway chute does not satisfy the

minimum air concentration requirements to develop posi-

tive pressures. The aerators for the first time were tested

at Yellowtail dam following high discharges in 1967 [8].

The minimum air concentration is function of Froude

Number [9].

0min

90 min0.015 2

C







(1)

*Disclaimer: The ideas and finding presented in this paper are of the

authors and do not necessarily reflect the views and policies of the

organizations, they belong.

#Corresponding author.

where 90 min is minimum air concentration, F0 inflow

Froude number and FCmin is Froude number at the incep-

tion point.

M. RAFI ET AL.

1052

Mangla dam reservoir in Pakistan has a gross storage

capacity of 5.88 millions AF (7.25 km3), it supplies irri-

gation water to over 4 million ha and can generate up to

1000 mega watt of electricity. The dam’s reservoir area

of 100 mi2 (160 km2) creates a live storage capacity of

5.34 millions AF (6.58 km3). Since its inception in 1967,

the reservoir sedimentation has reduced its storage ca-

pacity by 20% or 1.15 MAF (1.42 km3). The reduced

water storage implicated water shortages for irrigation

and hydropower. The studies indicated that increasing

the dam height by 30 ft (9.5 m) and the reservoir conser-

vation level (RCL) by 40 ft from 1202 to 1242 ft is pos-

sible and it can refurbish the lost capacity [10]. Never-

theless, raising the dam height and RCL can increase the

spillway discharge, discharge intensities and flow veloci-

ties, which may cause spillway cavitations and structural

damages. This study 1) checked the effect of raised dam

height and the reservoir conservation level on the spill-

way discharge, discharge intensities and velocities through

hydraulic design computations; 2) tested the effect of

different gate openings and reduced orifice areas on

spillway discharge, discharge intensities and velocities

on a scale model; 3) assessed the cavitation risk due to

increased velocities by using a mathematical model and 4)

optimized the size and shape of the bottom aerator for

reduced cavitation risk by using the scale model.

2. Material and Methods

2.1. Mangla Dam Spillway

The Mangla dam embankment is 380 ft (115.83 m) high

above river bed and 10300 ft long (3140 m) long. It was

proposed to raise the embankment height by 30 ft (9.14

m) and pool conservation level by 40 ft (12.20 m). The

dam spillway is orifice type headworks, two-stage still-

ing basin and sloping side walls. The headworks of the

main spillway are 444 ft (135.33 m) long. It consists of

three monoliths separated by 24 ft (7.3 m) wide piers.

Each monolith comprised three orifices of 36 ft (10.97 m)

width and 40 ft (12.2 m) height, which are equipped with

radial gates. Each orifice within the monoliths is sepa-

rated by 12 ft (3.66 m) wide pier. Parabolic chute follows

the headworks crest. An intermediate weir divides the

chute into two and creates a stilling basin and water pool

at an elevation of 1000 ft (304.8 m). The spillway plan

and the longitudinal sections are in Figure 1.

2.2. Spillway’s Hydraulic Design

In the original design, the probable maximum flood (PMF)

discharge was fixed as 1.01 million ft3·sec–1 (28,600

m3·sec–1) and the discharge intensities over the upper and

lower chutes were fixed as 2275 ft3·sec–1·ft–1 (211.4

m3·sec–1·m–1) and 1443 ft3·sec–1·ft–1 (134 m3·sec–1·m–1),

respectively. The hydraulic design computations showed

that the raised dam height and RCL may increase the

maximum discharge through the existing spillway to 1.31

million ft3·sec–1 (37,095 m3·sec–1)—27% higher than the

original design discharge and corresponding increase in

discharge intensities and flow velocities. The design con-

sidered reducing the orifice area to restrict the spillway

discharge and discharge intensities within the original

design limits. The hydraulic computations showed that

raising the floor level of the spillway crest by 5 ft (1.524

m) from 1086 to 1091 ft can reduce the orifice area to

control the spillway discharge to original design limits.

Therefore, the hydraulic design suggested raising the

invert level by 5 ft to the end of gate piers with 2 ft high

ramp at an angle of 10 degree from end (Figure 2). This

modification1 may have only reduced the spillway dis-

charge to the original design limit, but not the flow ve-

locities, as the velocities are function of total head across.

Hydraulic design computations for the proposed modifi-

cations indicated that the flow velocities are likely to

exceed from original designed velocity of 100 ft·sec–1

(30.48 m·sec–1). This increase in velocity could induce

cavitation risk in the sluice bays and on the parabolic

chute.

2.3. Mathematical Model and Cavitation Risks

The cavitation risk due to increased flow velocities along

the spillway chute were assessed by using a mathematic-

cal model-USBR-EM42 [1]. The cavitation risk to a hy-

draulic structure is function of flow velocities, hydrody-

namic pressures and surface irregularities. Mathemati-

cally, the pressure coefficient (Cp)—basis for the cavita-

tion index, can be derived from the Bernoulli equation

for conditions that reference elevation is equal to the

elevation in question.









DD tt

(2)

where P and P0 pressure intensity and reference pressure

and Vo is reference velocity considering elevation differ-

ence is negligible. The pressure coefficient or pressure

parameter is also referred as Euler number. Damage in-

dex was assumed as a quasi-quantitative measure of the

severity of the cavitation damage as a function of dis-

charge and time. It can be used to differentiate between

minor and major damages. The model computes the cav-

ity damage index from

(3)



tte (4)

where, tc is cumulative time of operation, Di is damage

1The overall modifications include raising the dam height and reservoi

conservation level, raising the spillway invert level by 5 ft and intro-

duction of bottom aerator.

M. RAFI ET AL.

1053

Figure 1. Plan and longitudinal section of Mangla spillway.

M. RAFI ET AL.

1054

Figure 2. Sectional model of modified spillway and sluice and chute ae r ators.

M. RAFI ET AL.

1055

index at end of previous discharge, Dp is damage potential

for next discharge. The integrating constant to allows the

equation to incorporate the cumulative effect of flow at

various discharges. At the start of operation, Di = 0 at tc=

0 and t0 = –1. Damage potential Dp in Equation (2) was

computed from

˗ Discharge for variable gate openings (5, 10, 15, 20, 25

and 30 ft); with reservoir level maintained at 1242 ft.

˗ Discharge for variable gate openings (5, 10, 15, 20, 25

and 30 ft); with reservoir level maintained at 1260 ft.

Francis formula was used to compute discharge from

the observed water levels on the weir.























 (5)

where, σs is cavitation index for initiation of damages, σf

is cavitation index of the flow and V and Vr are flow and

reference velocities, respectively. The model sets cavita-

tion index “σ” equal to pressure coefficient with minus

The spillway chute was divided into 22 sections lon-

gitudinally created by 23 station points to determine the

locations of highest flow velocity and cavitation. Dam-

age potential and damage risks were assessed for incipi-

ent, major and catastrophic damages from the criteria

given in Table 1.

2.4. The Scale Model

The scale model was built and operated at Hydraulic Re-

search Station, Nandi Pur, Pakistan. The scale model was

used to verify the spillway discharge and velocities and

to test the various options of the bottom aerators to re-

duce cavitation risk. A sectional model of the main

spillway was constructed on an undistorted scale of 1:36

(Figure 2). It comprised of 2 bays—one full central bay

and two half bays on either side of the central bay. The

model included a portion of the reservoir, proportionate

central part of the approach channel, headworks, radial

gates, hoisting arrangement, parabolic chute and upper

stilling basin and weir. The model was fabricated in

transparent Perspex in order to minimize the frictions and

facilitate visual observation.

A suppressed sharp-crested rectangular weir of 9 ft

(2.74 m) length and 5 ft (1.52 m) height was constructed

at immediately downstream of the sectional model to

determine the stage-discharge relationship of the modi-

fied spillway (with 5 ft rise in invert level) for the fol-

lowing conditions.

˗ Discharge for different reservoir levels with fully

opened gates (35 ft opening means full open gate).

Table 1. Damage potential and damage index criteria (after

Falvey, 1990).

Damages Damage potential Damage index

Incipient 500 5000

Major 1000 10,000

Catastrophic 2000 20,000

32 32

0.171 aa

QLHhh







(6)





where, Q is discharge in m3·sec–1, L is length of the weir

in m; H is head on weir crest in m and ha is approach

velocity head in m.

A scale of 1:36 was used for geometric similitude be-

tween the model and the prototype. In free surface flows,

most laboratory studies are based on a Froude similitude

since gravity effects are important [11,12]. The same

concept was used in this study, but due to scale effect, it

may not be able to achieve true dynamic similarity. In

fact in geometrical similarity models, it may not be pos-

sible to satisfy simultaneously Froude and Reynolds

similarities unless at full scale [13]. Froudian equations

represented the mathematical relationship between di-

mensional and hydraulic quantities of the model and

prototype.

F (7)





MPP

hgh



 (8)

where Fr is Froude number, V is velocity, g is gravita-

tional force and h is head of water column. Subscripts M

and P represents model and prototype respectively. The

relationships for the transference of model data to proto-

type equivalents are given Table 2.

2.5. Aerators Optimization

The aerators entrained air into the flow through side

ducts due to the pressure difference. This arrangement

generally functions effectively except for submergence

Table 2. Mathematical relationships for dimensional and

hydraulic quantities.

Dimension Ratio

Scale

Relations

Length



1:36

Time 12







1:6

Velocity 12







1:6

Discharge 52





1:7776

Pressure



 1:36

Roughness (Manning’s n) 16







1:1.82

M. RAFI ET AL.

1056

conditions, which may reduce the aerators effectiveness.

The aerators in this study consist of a ramp, circular air

duct under the horizontal floor and an air supply gallery.

The ramp was likely to create sub-pressure region by

lifting up the high velocity water jet above the chute

floor. The scale model study optimized the aerators pa-

rameters, evaluated the air entrainment and checked the

performance of the spillway with modified design. Two

aerators at sluice gate and end of horizontal floor were

tested for several combinations including pipes of 2.25 ft

(0.70 m) and 3 ft (0.91 m) diameters and for different

ramp heights (Table 3). The pipes connected the air duct

with the 5 ft (1.52 m) high vertical step at the raised floor

end. The flow velocity on the model was measured by

using Kempton probes. Graduated staff gauges were used

to measure the water levels at different sections of the

model. Validyne transducers were used to measure the

pressures that recorded magnified signals on strip chart

recorder.

3. Results

3.1. Spillway Discharge Capacity

The spillway stage-discharge relationship at full gate open-

ing and with modifications was superimposed on the

original spillway rating determined in 1967 at the time of

the dam construction (Figure 3). It shows that the stage-

discharge relationship in both the cases with and without

modifications reasonably match and falls on the pro-

jected original rating. Results showed that discharging

capacity of the modified spillway was within the design

limits of its original capacity at maximum pool level of

1260 ft and it was about 0.16% higher at modified reser-

voir conservation level of 1242 ft (Tabl e 4 ). Insignificant

increase in discharging capacity of the modified spillway

at the reservoir conservation level was less likely to

negatively impact the hydraulic performance of the en-

ergy dissipaters. The results based on scale-model study

indicated that the proposed raising of the crest level by 5

ft can effectively curtail the spillway discharging capac-

ity to its original design level.

3.2. Cavitation Risk

Mathematical model study showed that velocities vary

from 100 ft·sec–1 to 125 ft·sec–1 (30.48 to 38.1 m·sec–1)

for different discharges at the lower part of the chute near

the toe under existing conditions. It showed a velocity up

to 138 ft·sec–1 for a discharge of one million ft3·sec–1

with modified conditions. This velocity is most likely to

create cavitation. The logarithmic equations with an r2

value of 0.95 reasonably fit to the discharge velocity re-

lationship for both existing and modified conditions

(Figure 4). However, the trend lines show scatter be-

tween –5% and 18% under existing conditions and be-

tween –5% and 23% for modified conditions. The cavita-

tion risks were estimated by damage potential and dam-

age index under existing and with modifications. It

shows that damage potential for existing spillway were

below 600, which sharply increases up to discharge of

Table 3. Aerators parameters tested on the scale model for gate opening of 5, 10, 15, 20, 25, 30 and 35 ft (gates fully open).

Run no Chute aerator Sluice aerator

Base length = 11.3 ft (3.44 m) Base length = 3.0 ft (0.91 m)

Air duct pipe diameter = 2.25 ft (0.68 m)

Run 1: base case No ramp No ramp

Run 2 Ramp of 2 ft height and 10˚ back slope No ramp

Air duct pipe diameter = 3.0 ft (0.91 m)

Run 3 Ramp of 2 ft height and 10˚ back slope Ramp of 3.6 inches and 5.7˚ back slope

Run 4 Ramp of 2 ft height and 10˚ back slope Ramp of 5.5 inches and 8.68˚ back slope

Run 5 Ramp of 2 ft height and 6˚ back slope Ramp of 5.5 inches and 8.68˚ back slope

Run 6-1 Ramp of 2 ft height and 10˚ back slope Ramp of 6.5 inches and 10.2˚ back slope

Run 6-2 Ramp of 2 ft height and 10˚ back slope Ramp of 7.5 inches and 11.77˚ back slope

Run 6-3 Ramp of 2 ft height and 10˚ back slope Ramp of 8.5 inches and 13.28˚ back slope

Run 6-4 Ramp of 2 ft height and 10˚ back slope Ramp of 10 inches and 15.52˚ back slope

Run 6-5 Ramp of 2 ft height and 10˚ back slope Ramp of 12 inches and 18.43˚ back slope

Run 7 No inverse slope Ramp of 7.5 inches and 11.77˚ back slope

M. RAFI ET AL. 1057

Table 4. Comparison of spillway discharges with and with-

out modifications

200

400

600

800

1000

1200

1400

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

650000

700000

750000

800000

850000

900000

950000

Damage potential (D

)

Discharge (ft3/ s ec)

Reservoir

level

(ft)

Original

discharge

(ft3·sec–1)

Discharge

after

modifications

(ft3·sec–1)

Difference

(%)

1242 936,027 937,513 +0.16

1260 1,010,000 1,009,630 –0.036

Existing DpModified Dp

Poly. (Existing Dp)Poly. (Modified Dp)

The original discharge is based on model study in 1967; and modified on the

basis of model study in 2004.

(ft3/sec)

200000

400000

600000

800000

1000000

1200000

1091

1100

1110

1120

1140

1150

1170

Discharge (ft

sec

-1

)

Reservoir levels (ft)

1200

1242

1260

Original

Modified

Poly. (Original)

(ft

·sec

–1

)

Figure 3. Spillway rating curve with and without modifica-

tions.

100

125

150

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

650000

Velocity (ft/sec)

Discharge (ft3/ sec)

700000

750000

800000

850000

900000

950000

Existing V22Modified V22

Log. (Existing V22)Log. (Modified V22)

(ft

/sec)

Figure 4. Comparison of chute velocities for existing and

modified spillway at 22 ft from crest.

350,000 ft3·sec–1 and flattens down with almost horizon-

tal slope with the further increase in discharge beyond

350,000 ft3·sec–1 (Figure 5). However, the damage po-

tential for modified conditions sharply increases to about

1400 to a discharge of 350,000 ft3·sec–1 and then flattens

down afterwards. It also shows that the damage potential

for modified conditions is more than double the damage

potential under existing condition. Comparing with dif-

ferent cavitation damage levels in Table 1, the damage

potential under modified conditions was between major

Figure 5. Damage potential in relation to spillway dischar-

ges without and with modification scenarios.

and catastrophic levels. Relationship between damage

index and spillway discharge also shows relatively higher

risks of cavitation in case of modifications (Figure 6).

Both analysis for damage potential and damage index

infer that proposed modifications are most likely to cause

cavitation problem. It necessitated for testing the provi-

sion of appropriate aerators to avoid cavitations.

3.3. Optimizing the Aerators

The scale model tested two aerators at sluice gate and

end of parabolic chute for modified pool conservation

level of 1242 ft (378.6 m). The optimization included

two diameters of air supply duct, without ramp and with

different configurations of the ramps.

Run 1: Air duct dia 2.25 ft, both aerator without

ramp (Base trial)

A pipe of 2.25 ft diameter served as air duct. The

model was operated at reservoir conservation level for

gate openings varying from 5 to 35 ft. The results with 5

ft gate opening showed low pressure air pocket under the

flow jet emerging from the gate and the sluice aerator

drew adequate air with hissing noise. Low pressure air

cavity was also noted at the chute aerator. At 10 ft gate

opening, the length of air pocket was reduced and some

back flows were accumulated. Increased flow depth and

back flows caused reduction in air supply to sluice and

chute aerators. At 15 ft gate opening, further increase in

back flows and flow depth reduced the air supply tre-

mendously and the sluice aerator was almost ineffective.

Nevertheless, flow jet drew some air on the spillway

chute showed sign of poor functioning of the chute aera-

tor. At 20 ft gate opening, piling up of back flow at the

tail end of the air duct reduced the air supply to insig-

nificant level and water almost filled the air pocket at the

location of chute aerator. The results showed inefficacy

of the aerators arrangement in supplying the air. Specifi-

cally, the chute aerator was ineffective to supply air to

the duct.

M. RAFI ET AL.

1058

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

550000

600000

650000

700000

D amage in dex (D i)

Discharge (ft3/ sec)

750000

800000

850000

900000

950000

Existing DiModified Di

Log. (Existing Di)Log. (Modified Di)

(ft

/sec)

Figure 6. Damage index in relation to spillway discharges

without and with modification scenarios.

Run 2: Air duct dia 2.25 ft and chute aerator with

ramp of 2.0 ft height &10˚ back slope

The chute aerator was modified to improve the air

supply by providing a ramp of 2 ft height and a back

slope at an angle of 10 degree at the end of raised floor.

The model was run at the pool conservation level and the

gate opening varied from 5 to 35 ft. The results showed

better air flow and longer flow trajectory at the end of

raised floor for 5 ft gate opening. At 10 ft gate opening,

the length of the air cavity on the chute was reduced, but

no back flow was noted. At 15 ft gate opening the size of

the air cavity was further reduced, but the air pocket at

the end of the raised floor was still effective in drawing

the air. At 20 ft gate opening, there was more reduction

in air cavity and accumulation of back flows also started.

At 25 ft gate opening, accumulation of back flow was

increased and the length of flow trajectory tremendously

reduced, but the trajectory was still instrumental to

pushing some air on the top of the parabolic chute. At 30

ft gate opening, the air cavity at the end of raised floor

was almost filled with the back flows. Nevertheless, the

modified ramped aerator was still able to draw some air.

The results from run 2 showed improved air supply to the

parabolic chute as compared with run 1.

Run 3: Air duct dia 3.0 ft and chute aerator with

ramp of 2.0 ft height and 10˚ back slope and sluice

ramp of 3.6 inches and 5.7˚ back slope

In this run, the diameter of the air supply duct was in-

creased from 2.25 ft to 3.0 ft. A ramp of 3.6 inches (back

slope 1:10 or 5.7 degree) in the sluice aerator and 2.0 ft

in the chute aerator with 10 degree back slope were also

provided. The results indicated that the increased pipe

diameter enhanced the air supply to the air duct of the

sluice aerator at all gate openings. The length of flow

trajectory at the end of raised floor was increased from

30 ft with 2.25 ft diameter pipe (run 2) to 33 ft with 3.0 ft

diameter pipe at 5 ft gate opening. Further, air suction

limit of the sluice aerator was increased from 10 ft gate

opening in case of 2.25 diameter pipe to 12 ft gate open-

ing for 3.0 ft diameter air duct. This proved superiority of

3.0 ft diameter air duct over 2.25 ft diameter air duct.

However, it was almost ineffective at gate opening more

than 12 ft.

Run 4: Air duct dia 3.0 ft and chute aerator with

ramp of 2.0 ft height and 10˚ back slope and sluice

ramp of 5.5 inches and back slope of 8.68˚ (1 :1 0)

In this run the ramp height of the sluice aerator was in-

creased from 3.6 inches to 5.5 inches increasing the back

slope of the ramp from 5.7 to 8.69 degree, when all other

features remained same as in case of run 3. The results

showed the length of air cavity as 33 ft, when effective

gate opening increased from 12 to 16 ft. Raising the ramp

height of the sluice gate did not show negative effect on

the discharge rating of the spillway.

Run 5: Air duct dia 3.0 ft and chute aerator with

ramp of 2.0 ft height and 6˚ back slope and sluice

ramp of 5.5 inches and back slope of 8.68˚)

In run 5, the ramp slope of the chute aerator was

changed from 10 to 6 degree with horizontal, when all

other features remained same as in case of run 3. The

results of this run for same set of flow conditions showed

remarked reduction in the length of air cavity as com-

pared with ramp slope of 10 degree (Table 5). The re-

sults showed disadvantages of changing the ramp slope;

therefore, further tests were not conducted with 6 degree

ramp slope and the 10 degree ramp slope was found

more suitable (Run 4). This indicated that the perform-

ance of chute aerator was at maximum for parameters set

in run 4. Therefore, further simulations focused to im-

prove the performance of the sluice aerator, keeping

other parameters constant.

Run 6: O ptimizing the ramp of sluice aerato r, when

keeping the air duct dia 3.0 ft and chute aerator with

ramp of 2. 0 ft h eight and 1 0˚ back slope

The simulation from run 1 to run 5 revealed that in-

crease in ramp height of the sluice aerator from 3.6

inches to 5.5 inches improved the effective gate opening

from 12 to 16 ft. It showed potential to further manure it.

Therefore, a number of simulation runs were made by

increasing the ramp height to 6.5, 7.5, 8.5, 10 and 12

inches without changing the base length of 3.0 ft. The

results of these simulations are given in Table 6. Rela-

tionship between the ramp height, effective gate opening

and discharge is in Figure 7.

Table 5. Comparison of air cavity for different ramp slopes

at the chute.

Gate opening (ft) Length of air cavity (ft)

10 degree slope 6 degree slope

5 131 93

10 143 100

M. RAFI ET AL.

1059

Table 6. Results of optimization of the ramp height of the sluice aerator.

Ramp

height

(inches)

Angle

(Degree) Observations on model

6.5 10.23

˗ Cavity length immediate below the spillway gates was increased from 40 ft for 5.5 inch ramp to 54 ft with 6.5 inch

ramp.

˗ Effective gate opening at which the aerator sucked the air was increased from 16.0 to 19.75 ft.

˗ The aerator submerged and became ineffective at 20 ft gate opening.

˗ The change in ramp height did not affect the maximum discharge outflow at the highest pool level of 1260.

7.5 11.77

˗ Cavity length downstream of spillway gates was increased 62 ft.

˗ Effective gate opening for air sucking increased to 22.75 ft, which can release a discharge of 475,000 ft3·sec–1 at

conservation pool level of 1242 ft.

˗ The change in ramp height did not affect the maximum discharge outflow at the highest pool level of 1260.

8.5 13.28 ˗ No significant improvement noted when effective gate opening changed from 22.75 to 23.25 ft.

10.0 15.52

˗ Cavity length downstream of spillway gates was increased 67 ft.

˗ Effective gate opening for air sucking increased to 24.25 ft, which can release a discharge of 510,000 ft3·sec–1 at

conservation pool level of 1242 ft.

˗ Increased back flow along the bed caused pulsation of the flow jet in the sluice bays. It adversely affected the

discharging capacity of the spillway.

12.0 18.43

˗ The flow jet landed on 2 ft high ramp at the end of the chute aerator resulting in high splashes. Pulsating of the

flow jet was increased. Outflow discharge capacity of the spillway reduced by 7755 ft3·sec–1. Therefore, it was not

acceptable scenario.

ramp was worse in function and reduced the spillway

discharging capacity by 7756 ft3·sec–1 at maximum res-

ervoir level. The above discussion reveals that a sluice

ramp of 7.5 inches with an angle of 11.77˚ performed

better of all the scenarios and appears to be the appropri-

ate ramp height for sluice aerator.

100000

200000

300000

400000

500000

600000

3.6 5.56.5 7.58.510

Discharge (ft

/ sec)

Ramp height (Inches)

Discharge

Effective gate opening

Poly. (Discharge)

Poly. (Effective gate ope

Effective gate open ing (ft)

ning)

Run 7: Sluice aerator with inverse slope eliminated

Elimination of inverse slope (1:20) and provision of

horizontal floor at downstream of sluice aerator at an

elevation of 1091 ft, with all other optimized parameters

resulted in increased cavity length, but decreased cavity

depth, small improvement in effective gate opening and

non-uniform distribution of sucked air along full width of

the bay. It indicates that inverse slope performed better in

cavity depth and is instrumental in uniform air distribu-

tion along the bay width.

Figure 7. Optimization of ramp height of the sluice aerator

in relation to spillway discharge and effective gate opening

(Air duct 3.0 ft diameter). 4. Conclusions

 Five feet rise in the bed of the headworks bay from

1086 to 1091 ft effectively restricted the maximum

spillway discharge to its original design capacity limit

of 1.01 million ft3·sec–1 at the maximum reservoir

level of 1260 ft. This rise did not significantly change

the flow conditions of the spillway.

The observations on the scale model have shown that

an increase in sluice ramp height increased the limit of

effective gate opening. Flow conditions in the sluice bays

within the piers remained smooth and stable to ramp

height of 7.5 inches. Pulsation of flow jet started at ramp

height of 8.5 inches and above. For 5 ft gate opening and

10 inches ramp height, the flow jet landed on the slope of

2.0 ft high ramp at chute aerator and increased splashing.

The ramp height of 10 inches increased the heaving and

pulsating in the headworks bays and reduced the dis-

charging capacity of the spillway. However, 12 inches

 Mathematical model study depicted high cavitation

risks and damage potential for modified spillway and

showed a need for introduction of aerators to avoid

cavitations.

 Scale model study indicated that a chute aerator of 2.0

ft height and an angle of 10˚ was highly effective in

M. RAFI ET AL.

1060

inducing air over the parabolic chute up to gate open-

ings of 25 ft. However, the air suction was reduced at

the gate opening of more than 25 ft.

Among the several ramp heights and slope of the

sluice aerator, an aerator with ramp height of 7.5 inches

performed best of all. It did not negatively affect the

spillway discharging capacity at the conservation level of

1242 ft and maximum reservoir level of 1260 ft. The

sluice aerator with less ramp height (3.6 and 5.5 inches)

failed to lift the flow jet and submerged at 10 ft gate

opening and above. On the other hand high ramp height

for example 10 and 12 inches increased the heaving and

pulsation in the bay and reduced its discharging capacity

significantly. It revealed that 7.5 inches was the optimum

ramp height for the sluice aerator.

5. Acknowledgements

The authors acknowledge the technical support by Mangla

Joint Venture-Mangla Dam Raising Project, Pakistan,

assistance by the technical staff of the Hydraulic Re-

search Station Nandi Pur and financial support by the

Water and Power Development Authority, Pakistan.

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