Similarity of scour evolution downstream of stilling basin with an end sill

EHSAN ZAHED**, JAVAD FARHOUDI

**, and MAHMOOD JAVAN

***

** Department of Irrigation, Faculty of Agriculture Engineering and Technology,

University of Tehran,

Karaj,

Iran

** zahed@ut.ac.ir

** jfarhoudi@ut.ac.ir

*** Department of Water Science Engineering, Faculty of Agriculture,

Shiraz University,

Shiraz,

Iran

Javan@shirazu.ac.ir

Abstract: - The results of an experimental study on scour phenomenon downstream of a rigid apron, equipped with an

end sill, downstream a sluice gate are reported. The objective of the present paper is to examine the similarity of scour

hole profiles downstream of hydraulic jump formed in a stilling basin with an end sill. Experiments were conducted

under various gradations of non-cohesive sediments, flow rates and end sill heights. A total of 65 tests were carried

out, and the scour profiles were collected in geometrical time progression for a period of 24 hours. The profiles were

traced using a digital photography technique. Although, an equilibrium scour condition was not attained over this time

period, the analysis showed that the scour profiles at different times follow a particular geometrical similarity, even in

presence of end sill. A new mathematical approach was achieved to predict the non-dimensional scour profile under

the defined circumstances.

Key-Words: - scour, stilling basin, end sill, geometrical similarity, hydraulic jump

1 Introduction Local scour caused by flow in the vicinity of hydraulic

structures is a problem of considerable importance in

river engineering practice. Local scour downstream of

aprons due to wall jets caused by issuing water through a

sluice opening or flowing over grade control structures

can endanger the safety of these structures.

Remarkable studies on erosion downstream of hydraulic

structures, especially grade control structures, have been

carried out in the past century. For example, Breusers

[5] has done a wide range of study by using various bed

materials of different densities and a variety of

geometric arrangements. He suggested an equation for

temporal scour evolution and also reported that for a

given geometry, the scour profiles were similar, at all

times. Larsen [14] was the first who reported the

similarity of scour profiles developed by a horizontal jet,

without any theoretical implications. Altinbelick [2]

presented a volumetric approach to local scour progress

by determining certain assumptions.

Numerous tests were carried out by Farhoudi and Smith

[10, 11] who used six different materials (Sand and

Bakelite) and three physical models. They applied the

findings of Breusers [5] to determine the time scale of

scour downstream of a spillway apron due to hydraulic

jump, and the results were in considerable agreement

with the study of Breusers [5]. Hassan and Narayanan

[12] studied the flow characteristics and the similarity of

scour profiles downstream of an apron due to a

submerged jet issuing from a sluice opening. They used

the mean velocity distribution in rigid model to develop

a semi-empirical theory to estimate the temporal rate of

scour depth. Farhoudi and Smith [11] studied the scour

process downstream of hydraulic jumps featuring the

characteristic parameters defining the scour hole. They

demonstrated that the development of local scour hole

downstream of apron in the passage of time shows a

certain geometrical similarities and non-dimensional

scour profiles can be presented by a unified equation.

Moreover, they studied the effects of the sediment size

and tailwater depth on the asymptotic scour depth

downstream of a spillway. Breusers and Raudkivi [6]

provided an interesting and useful mixture of much of

the work done on scour below various types of hydraulic

structure, including those similar to the flow under a

sluice gate. They deduced the similarity of scour profiles

in various time values and reported the attainment of an

equilibrium state of scour for different sediment sizes

and velocity conditions. Balachandar and Kells [3, 4]

investigated the time variation of scour depth with

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

ISSN: 1792-4596 45 ISBN: 978-960-474-215-8

uniform bed materials downstream of a relatively short

apron under a submerged jet to analyze the

instantaneous water surface and scour profiles by

applying the technique of video image analysis.

Chatterjee et al. [7] studied the local scour downstream

of an apron due to a submerged jet issuing from a sluice

opening and developed an empirical equation for the

time variation of scour depth and the time to reach

asymptotic scour depth. Kells et al. [13] investigated the

effect of sediment size on the depth and area of

equilibrium scour profiles that developed downstream a

short apron due to a submerged jet flowing off a sluice

opening. Moreover, they studied the effect of discharge

and tailwater depth on length and dept of scour hole.

Dargahi [8] presented an experimental study to examine

the similarity of scour profiles and the scour geometry.

No experimental evidence was found in support of the

similarity assumption for temporal development of the

scouring process. Power-law type equations were

introduced to predict the scour geometry, mainly in

terms of controlling scour parameters (the head above

the spillway crest and the grain size of the sediment

bed). Dey and Sarkar [9] carried out an experimental

investigation on the effects of different parameters on

scour depth due to submerged horizontal jets. A

particular geometrical similarity of scour profiles at

different times have been exhibited and expressed by a

combination of two polynomials. A detailed analysis on

the hydraulic and structural behavior of block ramps was

proposed in Whittaker and Jaggi [19], Robinson et al.

[18], Pagliara [15] and Pagliara and Palermo [16].

Previous studies on local scour downstream of a rigid

apron due to wall jets almost have shown a geometrical

similarity in scour profiles at different values of time.

The scope of the present paper is to investigate the

similarity of scour hole profiles downstream of

hydraulic jump formed in a stilling basin with an end

sill. In addition, attempts made to derive a new

mathematical approach to predict the non-dimensional

scour profile under the defined circumstances.

2 Experiments The experiments were conducted in a rectangular

Plexiglas-walled flume of 4.9-m length, 0.40-m width

and 0.6-m-depth, having a reticulating flow system. A

sluice gate with an opening (b), of 15 mm followed by a

stilling basin was installed in the flume. The 1.1-m long

apron was made of Plexiglas. Four wooden End sills

with different height of hs= 0.5, 1, 1.5 and 2-cm were

installed at the end of the stilling basin. Fig. 1 provides a

Fig.1. Definition sketch for Scour downstream of stilling

basin

definition sketch for the model. A sediment reservoir of

0.25-m depth and 1.7-m length was constructed across

the whole width of the flume. As indicated in Table 1,

three uniformly graded sand were used.

Table 1. Characteristics of the bed material.

Materials

(-) 16D

(mm)

50D

(mm)

60D

(mm)

84D

(mm)

gσ

(-)

sρ

(Kg/m3)

S1 0.38 0.54 0.57 0.66 1.31 2,650

S2 0.74 1.12 1.17 1.39 1.37 2,650

S3 1.17 1.53 1.6 1.84 1.25 2,650

A sieve analysis was carried out to determine the grain

size distribution for each type of sand and the median

grain size (D50) and coefficient of uniformity (Cu = (D84

– D16)/D50) were then obtained as indicated in Table and

Fig. 2. Downstream of the sediment box was equipped

with a sad trap to prevent any incidental transport of the

fine sand into the flow system. An adjustable tailgate at

the downstream end of the flume was used to control the

tailwater depth insuring a free hydraulic jump on stilling

basin. A calibrated V-notch weir was used to measure

the water discharge at inlet, and the discharge was

controlled by a valve. The Froude number was ranged

from 3.3 to 9.3. In order to avoid the undesirable erosion

of the sediment bed, the flume was initially filled with

water. Once the water level reached the desired depth,

the sediment surface was graded and tests were

commenced by adjusting the discharge to desired

magnitude.

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10

Percentage of finer

Grane size (mm)

S3

S2

S1

Fig.2. Grain size distribution curves.

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

ISSN: 1792-4596 46 ISBN: 978-960-474-215-8

50

63 6.44

1.53 2

Run Fr

D mm hs cm

=

= =

24t hr=

12t hr=

8t hr=15mint =

30mint =

1t hr=

4t hr=8mint =

2t hr=4mint =

Fig.3. Temporal development of scour profiles for test

R65.

On the basis of previous studies conducted by Farhoudi

and Smith [10, 11], each test was carried out over a

period of 24 hours. Although, equilibrium scour

condition was not attained over this time period, it was

sufficient for most of the tests to reach a quasi

equilibrium state of scouring. The two-dimensional local

scour profiles were obtained in geometrical time

progression for a period of 24 hours by applying the

technique of digital photography analysis. A total of 65

tests were performed and near 645 scour profiles were

collected. Fig.3 shows the time evolution of scour holes

for test R63.

3 Scour profiles The observed profiles of scour holes were plotted by

digitizing the photos taken by a digital camera. Fig.4 (a)

and (b) illustrates the typical time evolution of scour

profiles for tests R18 and R40 as an example.

Although the scour profiles vary by time, change in bed

material size and different sill heights, it is quite evident

Fig.4. Temporal scour profiles superimposed in one plot

for test (a) R18 and (b) R40.

That a similarity exists among scour profiles at different

times. This similarity implies that, the scour profiles

could be presented by a single curve using appropriate

variables to normalize the profiles. Temporal maximum

scour length (Xm) and depth (Ym) were used respectively

to normalize the length and depth of scour holes at

different time intervals. Fig.4 (a) and (b), illustrate non-

dimensional scour profiles for tests R18 and R40,

respectively.

Plotting non-dimensional scour profiles for different

runs at various times emphasized the existence of

similarity between non dimensional scour profiles in

different conditions and presence of end sill. In other

word, the existence of end sill will not disturb the

geometrical similarity of scour holes. Fig. 5 displays the

non-dimensional scour profiles for all tests.

There are lots of scour profile equations presented by

different scientists and researchers in literature, such as

equations obtained by Rajaratnam [17], Farhoudi and

Smith [15], Ali and Lim [1], and Dey and Sarkar [9].

Attempts were made to develop a single relation for the

non-dimensional profile. Finally, in order of best

precision, it was revealed that a combination of tow

equations to present the non-dimensional scour hole

would be utilized with significant accuracy.

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

ISSN: 1792-4596 47 ISBN: 978-960-474-215-8

Fig.5. Non-dimensional scour profiles for test (a) R18

and (b) R40.

A parabolic equation was best fitted for upstream limb

of scour hole (Eq. 1) while a rational equation of second

order of was determined to define the downstream limb

(Eq.2).

21 0.889( 1)Y X− = − for 1X ≤ (1)

2

( 0.65 0.11 )

(1 0.8 0.34 )

XY

X X

− +=

− + for 1X ≥ (2)

The derived equations are plotted in Fig. 6 against the

observed data which shows a very good agreement with

observed data depicted from scour profiles.

21 0.889( 1)Y X− = −

2

( 0.65 0.11 )

(1 0.8 0.34 )

XY

X X

− +=

− +

Fig.6. Non-dimensional scour profiles for test (a) R18

and (b) R40.

Fig. 7(a) and (b), depicts the comparison of experimental

Y with computed Y from Eq. 1 and 2 respectively. The

correlation coefficient (r) between the experimentally

obtained and computed scour depths from Eq. 1 for

upstream limb was 0.98 (Standard error = 0.06), and

from Eq. 2. for downstream limb was 0.95 (Standard

error = 0.096). These results indicate a very good

conformity between computed and observed scour

depths with high accuracies.

Fig.7. Comparison of observed and computed Y (a) for

upstream limb ,equation (Eq.1) and (b) downstream

limb, equation (Eq.2).

4 Conclusion The primary purpose of this study was to examine

the similarity of scour hole profiles downstream of

hydraulic jump formed in a stilling basin with an

end sill. Some experiments were conducted using

three types of uniformly graded sands, as bed

materials, and five end sill height. In brief, it was

found that the scour profiles at different times

follow a particular geometrical similarity, even in

presence of end sill. Finally, a new mathematical

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.5 1 1.5 2 2.5 3 3.5

Y

X

50

18

7.5

1.5

0.52

s

Run

Fr

h cm

D mm

=

=

=

(a)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.5 1 1.5 2 2.5 3 3.5

Y

X

50

40

8.1

1

1.12

s

Run

Fr

h cm

D mm

=

=

=

(b)

(a)

(b)

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

ISSN: 1792-4596 48 ISBN: 978-960-474-215-8

relationship was derived to predict the non-

dimensional scour profile under the defined

circumstances which shows a very good conformity

between computed and observed scour depths with high

accuracies.

References:

[1] Ali, K. H. M., and Lim, S. Y., Local scour caused by

submerged wall jets. Proc. Inst. of Civ. Eng., London,

81(Dec.), 1986, pp.607–645.

[2] Altinbelick, H.,Localized Scour at the Downstream

of Outlet Structures., International Commission on

Large Dams, Congress, Madrid, 1973, pp105-122.

[3] Balachandar, R., and Kells, J. A., Local channel

scour in uniformly graded sediments: The time-scale

problem., Can. J. Civ. Eng., 24(5), 1997, pp. 799–807.

[4] Balachandar, R., and Kells, J. A., Instantaneous

water surface and bed scour profiles using video image

analysis., Can. J. Civ. Eng., 25(4), 1998, pp.662–667.

[5] Breusers, H. N. C., Time scale of two-dimensional

local scour., Proc., 12th IAHR Congress, Vol. 3, IAHR,

Delft, The Netherlands, 1967, pp.275–282.

[6] Breusers, H.N.C. and Raudkivi, A.J., Scouring,

Hydraulic Structures Design Manual 2, International

Association for Hydraulic Research, A.A. Balkema,

Rotterdam, The Netherlands, 1991.

[7] Chatterjee, S. S., Ghosh, S. N., and Chatterjee, M.,

Local scour due to submerged horizontal jet., J.

Hydraul. Eng., 120(8), 1994, pp.973–992.

[8] Dargahi, B. ,Scour Development Downstream of a

Spillway, Journal of Hydraulic Research. IAHR, 41(4),

2003, pp.417-426.

[9] Dey, S. and Sarkar, A., Scour Downstream of and

Apron Due to Submerged Horizental Jets, J. Hydraul.

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[10] Farhoudi, J., and Smith, K. V. H., Time scale for

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[11] Farhoudi, J., and Smith, K. V. H., Local scour

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[12] Hassan, N. M. K. N., and Narayanan, R., Local

scour downstream of an apron., J. Hydraul. Eng.,

111(11), 1985, pp.1371–1385.

[13] Kells, J. A., Balachandar, R., and Hagel, K. P.

Effect of grain size on local channel scour below a sluice

gate., Can. J. Civ. Eng., 28(3), 2001, pp.440–451.

[14] Larsen, E. M., Observation on the nature of scour.

In: Proc. 5th Hydraulic Conference. University of Iowa,

Iowa City, USA.,1952, pp.79–197.

[15] Pagliara, S., Influence of sediment gradation on

scour downstream of block ramps., J. Hydraul. Eng.,

133(11),2007 ,pp.1241–1248.

[16] Pagliara, S., Plermo, M., Influence of tailwater

depth and pile position on scour downstream of block

ramps., J. Hydraul. Eng., 136(2), 2010, pp.120–130.

[17] Rajaratnam, N., Erosion by plane turbulent jets., J.

Hydraul. Res., 19(4),1981 ,pp.339–358.

[18] Robinson, K. M., Rice, C. E., and Kadavy, K. C.,

Design of rock chutes., ASAE Paper No. 972062, St.

Joseph, Mich, 1997.

[19] Whittaker, W., and Jaggi, M., Blockshwellen.,

Mitteilungen 91, Versuchsanstalt fur Wasserbrau,

Hydrologie und Glaziologie, ETH, Zurich, Switzerland,

1996.

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

ISSN: 1792-4596 49 ISBN: 978-960-474-215-8