Ain Shams Engineering Journal (2014) 5, 1059-1069

Ain Shams University Ain Shams Engineering Journal

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CIVIL ENGINEERING

Minimizing downstream scour due to submerged c^Ma* hydraulic jump using corrugated aprons

Hossam Mohamed Ali a *, Mohamed Mohamed El Gendy b, Ahmed Mohamed Hassan Mirdan c, Abdel Azim Mohamed Ali d, Fahmy Salah Fahmy Abdelhaleem d

a Ministry of Water Recourses and Irrigation, Egypt

b Civil Engineering Department, Faculty of Engineering, Port Said University, Port Said, Egypt c Faculty of Engineering, Port Said University, Port Said, Egypt

d Hydraulic Research Institute (HRI), National Water Research Center, Cairo, Egypt

Received 1 December 2013; revised 2 July 2014; accepted 16 July 2014 Available online 10 August 2014

KEYWORDS

Local scour; Hydraulic structures; Corrugated aprons; Submerged hydraulic jump; Froude numbers

Abstract Local scour downstream of hydraulic structures due to hydraulic jump is considered one of the tedious and complicated problems facing their stability. Throughout this paper, an experimental study was conducted to study the effect of using different spaced corrugated aprons on the downstream local scour due to submerged jump. Sixty runs were carried out in a horizontal rectangular flume to determine the optimal corrugation wavelength which minimizing the scour. A case of flat apron included to estimate the influence of corrugated aprons on scour holes dimensions. Two types of non-cohesive soil were used. Experiments were performed for a range of Froude numbers between 1.68 and 9.29. The results showed that using spaced triangular corrugated aprons minimize the scour depth and length of fine sand by average percentage of 63.4% and 30.2%, respectively and for coarse sand by 44.2% and 20.6% in comparing with classical jump.

© 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

* Corresponding author. Tel.: +20 1006566037.

E-mail addresses: melgendy@elpla.com (M.M. El Gendy), a_mirda-

n@yahoo.com (A.M.H. Mirdan), azim1@hotmail.com (A.A.M. Ali),

fahmyhri@gmail.com (F.S.F. Abdelhaleem).

Peer review under responsibility of Ain Shams University.

1. Introduction

Flow underneath gates has a tremendous amount of potential energy, which is converted into kinetic energy downstream the hydraulic structures. This energy should be dissipated to prevent the possibility of excessive scouring of the downstream river and to minimize erosion and the undermining of the structures which endanger the structure safety. Local scour downstream of hydraulic structures such as low head and high head structures is an important research field due to its significant practical value. Studying the local scour process is a very complex problem given the numerous variables related to both

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Notations

S corrugation wavelength Ls maximum scour length of movable soil

t the height of corrugated apron Fr Froude number at initial water depth

b the base width of corrugated apron g the acceleration of gravity

d50 mean particle diameter of movable soil yi initial water depth of hydraulic jump

d10 percentage of passed particles from 10 mm diameter y 2 sequent water depth of hydraulic jump

d90 percentage of passed particles from 90 mm diameter l viscosity of fluid

d60 percentage of passed particles from 60 mm diameter P density of the fluid

d84 percentage of passed particles from 84 mm diameter Ps density of the movable soil

rg geometric standard deviation L hydraulic jump length

C ^u uniformity coefficient deviation Lr roller hydraulic jump length

ds maximum scour depth of movable soil

the heterogeneity of the eroded soil and the turbulent flow, which produces the erosive action. When jets due to submerged hydraulic structure impinge upon loose beds of granular material downstream of hydraulic structures such as weirs or sluice gates, they can lead to significant local scour and may cause stability problems of the structure which lead to failure. Constructing a rigid apron adjacent to the structure is a typical engineering solution to protect the structure. The safety of an apron downstream of a sluice gate is threatened by the erosive action of the submerged hydraulic jump due to scour downstream of an apron. Because flow conditions around a structure are complex, the design and planning of an apron are typically based on experimental results, modeling and measurements from similar projects. Prediction of local scour holes that develop downstream of hydraulic structures due to submerged jump plays an important role in their design.

Many studies have been conducted with non-cohesive apron materials in this area. But, most of these studies are related to formation of submerged jump upon flat aprons and few studies are carried out in the case of submerged jets on rough apron and the effect of roughness on local scour process. A jump formed in a horizontal, wide rectangular channel with a flat apron is often referred to as the classical hydraulic jump and has been studied extensively by Peterka [1], Rajarat-nam, [2], McCorquodale [3] and Hager [4]. Also, there are many formulae for scour following hydraulic jump in a stilling basin such as developed by Schoklitsch [5], Eggenberger [6], Shalash [7], Novak [8], Catakli [9], Uymaz [10], Pillai [11], Rice and Kadavy [12], Baghdadi [13], Hoffmans [14], El-Abd [15], Dargahi [16], Aytac and Gunal [17], and Oliveto and Victor [18]. Different techniques to reduce local scour have been employed in previous studies by making use of splitter plates or collars. On the other hand, The first study on hydraulic jump over rough apron was carried out by Rajaratnam [19] and this study was showed that, the length of jump upon rough apron is smaller than the length of classical jump, and also Many different corrugated apron shapes have been proposed and studied by Ead and Rajaratnam [20], Izadjoo and Bejestan [21], Ead [22] and Fahmy et al. [23]. When a submerged jet passes over a corrugated apron, the characteristics of velocity and turbulence of flow are different from those of the corresponding jet over a flat apron Hamidifar et al. [24].

Breusers [25] studied the variation time of downstream scour by the flow over and under an estuary closure structure. Scour

created downstream of the apron has been investigated by many researchers like Chatterjee and Ghosh [26], Farhoudi and Smith [27] [28], Hassan and Narayanan [29], and Chatterjee et al. [30] measured the velocity distributions of submerged jets issuing from a sluice opening over an apron followed by a scour holes in non-cohesive aprons; whereas Dey and Westrich [31] detected that the flow characteristics of submerged jets over the apron and in the equilibrium scour holes in cohesive soil.

Balachandar and Kells [32] [33], Balachandaret et al. [34], Kells et al. [35], Lim and Yu [36], Sarkar and Dey [37], Goel and Verma [38] and Dey and Sarkar [39] have studied development of scour holes downstream of an apron for a submerged jet. Downstream scour was studied by many investigators, and a comprehensive state-of-the-art review on the investigations done on scour due to jets was given by Sarkar and Dey [40].

Recently published results indicated that the scour holes develop rapidly in the early stages and progresses toward an asymptotic stage beyond which the scour profile does not change significantly with time and reaches an equilibrium state Alihosseini et al. [41], Oliveto et al. [42], Sarathi et al. [43], Omid et al. [44], and Hamidifar et al. [45,46]. Chen and Siow-Y [47] confirmed that the equilibrium scour state was never reached when jet-flipping occurred during the scouring processes as it consists of two intermittent and cyclical phases: a digging phase with an attached apron-jet scouring the apron to form a deep scour hole and a filling phase where the attached jet flips to become a surface-jet causing sediments to re-fill into the scour hole. Helal et al. [48] confirmed that the case of fully filled floor gave the smaller values of scour parameters. The experimental works were carried out by Blais-dell [49] indicated that the floor blocks should occupy between 40% and 55% of the floor width and the most favorable conditions result when the baffles are placed perpendicular to the incoming flow.

In conclusion, the review of the previous published materials showed that the corrugated aprons can effectively decrease the required conjugate depth and length of the jump; it thus can reduce the cost of energy dissipating aprons. The present study is thus an attempt to extend the previous studies by investigating the effect of strip triangular corrugated apron shapes at downstream heading-up structures. The study reports an experimental investigation, whose findings are used to describe influences of various parameters on scour dimensions.

2. Dimensional analysis

The maximum scour depth downstream of a rigid apron can be expressed as a function of the following independent variables:

dS — f(g, p,ps,yuy2 , V1, S,t,b,d50, Lj, i) (1)

In which dS is the maximum depth of scour, g is the acceleration due to gravity, p is the density of water, pS is the density of movable soil, y1 is the gate opening because lip gate was used to avoid the vena contract a i.e. water entered the flume under a sluice gate with a streamlined lip, thereby producing a uniform supercritical stream with a thickness of y1, Lj is the length of submerged hydraulic jump, d50 is the mean particle diameter of soil, vi is the mean velocity under gate, y2 is the sequent depth of jump, S is the corrugation wavelength between triangular strips corrugated apron, t and b are the height and width of triangular strips corrugated apron respectively, i is the viscosity of water.

Moreover, in turbulent flow, i has a negligible influence on scour and can be neglected. By applying the Buckingham p theorem with p, y1 and v1 as repeating variables, Eq. (1) can be written in dimensionless form as following;

dS — (F pt y2 S L b d50 j (2)

y1 V r ; p ;y1 ;y1 ;y1 ;y1; y1 ;yj

In which Fr — pffi is the Froude number under gate. Because of ps and p are constants so, can be ignored. Height (t) and width (b) of triangle strip corrugated aprons are constant. Hence, Eq. (2) is reduced to Negm et al. [50].

^ —fUA,—,—, —^ (3)

y1 y1 y1 y1 y1

With the same concept, the maximum scour length LS is dependent on the following independent variables

Figure 1 Streamlined lip gate in flume.

3. Experimental setup

In this paper, in order to reach the main purpose of this research, a model of a lip gate with horizontal basin has been constructed, to develop the required supercritical flow and initial depth of the jumps, as shown in Fig. 1. The model is investigated experimentally with flat apron to use its results as a comparison case to the other cases of corrugated aprons. To create the required roughness of the apron, aluminum triangular sheets were installed on the flume apron, and in order to diminish effect of cavitation, the crests of corrugation were set at the same level of upstream apron, as shown in Fig. 2. The corrugations acted as depressions in the apron, to create a system of turbulent eddies which might increase the apron shear stresses.

The dimensions of the corrugated sheet aprons are: triangular corrugated height, t = 40 mm and width b = 40 mm are kept constant and the sections have side slopes length equal to 44.7 mm with side angles 45°. The experiments have been conducted in the laboratory flume of the Hydraulics Research Institute (HRI), National Water Research Center (NWRC). The flume is constructed of bricks sealed with smooth cement mortar except part of Plexiglas sides with length = 2.25 m to facilitate the observation process, as shown in Fig. 3. The flume is 75 cm wide, 70 cm deep and 24.50 m long. A centrifugal pump is used to supply water to the head tank from the storage tank. The head tank has a gravel box which is used to provide an even flow distribution across the flume. The discharges were measured by Ultrasonic-Flow meter which is fixed in the supply lines.

To control the water flow rate, a gate valve is installed on the supply pipe line just before the head tank. The downstream bay is made of wooden with length 2.50 m overlaid on a 0.50 m layer of sand to prevent leakage, this bay is represented the flat apron also, prepared for the corrugated sheets fixation. Water depths and bed levels were measured by a point-gauge, Abde-laziz [51]. The gauge is mounted on carriage moving in the flow and the perpendicular directions. Downstream water depth is controlled by using a tail gate in order to form jumps over the rigid apron, and then, the water flowed to the by-pass channel. The length of floor and dimensions of corrugated sheets is kept constant for all runs. Spacing between corrugated sheets is changed from position to other to specify the optimum location. The rear reach of the channel is filled with a 30 cm layer of sand with d50 = 0.523 mm, d10 = 0.254 mm, d16 = 0.315 mm, d84 = 0.817, d60 = 0.596 and uniformity coefficient Cu = d60/d10 = 2.346 for the first sand sample whereas, d50 = 2.575 mm, d10 = 0.811 mm, d16 = 1.378 mm, d84 = 3.861, d60 = 2.92 and uniformity coefficient Cu = d60/ d10 = 3.6 for the second sample in order to represent the movable apron. The grain size distribution curves for both samples are shown in Figs. 4 and 5.

Generally, bed fluctuations are an interesting feature of the transport of uniform or well sorted sediments, but are essential to the understanding of the transport of sediment mixtures. Sediment mixture grains start to move on the bed when the combined lift and drag forces produced by the fluid become large enough to counteract the gravity and frictional forces that hold the grains in place. An important assumption in most of the existing models is the uniformity of the sand, which means that the sediment mixture is characterized by a single sand size d50.

4 S = 16 cm

Figure 2 Schematic view of scour downstream of an apron due to submerged jump and spaced corrugated aprons.

Figure 3 Plexiglas's wall section.

The gradation of the sediment mixture can be described by geo-

metric standard deviation rg

84/d16) thus, rg = 1.63 and

1.78 for first and second sample respectively. 4. Experimental procedure

To achieve the objective of this research, two discharges were considered (Q = 30 and 45 l/s). Initial water depth (y{) equal

100 90 80 70 60 50 40 30 20 10

0.1 1.0 Sieve opening (mm

Figure 4 Grain size distribution curve for first sand sample.

to 3.86, 2.99 and 2.02 cm were used with discharge 30 l/s whereas, 2.15 and 1.62 cm were used with discharge 45 l/s. All types of submerged hydraulic jumps according to classification of Chow [52] were investigated. Sixty runs had been conducted including 10 runs with flat apron which was taken as a comparison case. For each run, the backwater feeding is started first until its depth reaches higher than the required downstream water depth, and then, the upstream feeding is pumped. To adjust the tail water depth, the tail gate is screwed gradually until the considered depth is adjusted.

100 90

■s 70

Sieve opening (mm)

Figure 5 Grain size distribution curve for second sand sample.

0 60 120 180 240 300 360 420 480 540 600 660 Time (mlri)

Figure 6 Relationship between maximum scour depths and time in case of flat apron.

A precise point gauge was used to adjust the initial depth of jump, (gate opening) and another point gauge was used to measure the sequent depth. The length and the roller length of hydraulic jump were measured by a precise scale. Each test was run for 6 h, which were sufficient for most of the tests to reach a quasi-equilibrium state of scour, as shown in Figs. 6 and 7. The run was stopped and the flume was drained and the expecting scouring area was recorded by a precise point gauge to monitor the apron topography on a grid 2 cm x 2 cm.

5. Results and discussion

5.1. Effect of spaced corrugated aprons on scour depth for fine and coarse sand

Figs. 8 and 9 describe the relation between S/t, and ds/y1 for fine and coarse sand respectively with constant values of Froude number. One can see that, for the considered flow

0 60 120 180 240 300 360 420 480 540 600 660 Time (mlri)

Figure 7 Relationship between maximum scour lengths and time in case of flat apron.

Tin .. . Present Study at Fr= 1.68 ___Present Study at Fr= 2.47 r 1 i i

— . — . Present Study at Fr= 6.08 /

— Present Study at Fr= 9.29 1 1 i i / / i /

> / V i

/ ..--- ! i /

..... * ! /

______________

0 1 2 3 4 5 (

Figure 8 Relationship between ds/y1 and S/t for fine sand.

conditions, the minimum scour dimensions occurred at optimum spacing ratio S/t = 3. For Fr = 1.68, 2.47, 4.45, 6.08 and 9.29 the scour depth decreases by 63.21%, 62.23%, 61.09%, 60.55% and 59.23% respectively, in comparison with the scour depth of flat apron with considering the results presented in the following Section 5.3.

Based on the experimental data and using the statistical method, for different spaced corrugated aprons, several models were proposed and their regression coefficients were estimated. Out of all trials, the average best empirical equation predicting the relative scour depth can be put in the following form:

---------1----------f.

- Present Study at Fr=1.68 . Present Study at Fr=2.47

■ Present Study at Fr=4.45

■ Present Study at Fr=6.08 Present Study at Fr=9.29

Figure 9 Relationship between ds/y1 and S/t for coarse sand.

^ = 0.06

'S' 2 S

- 0.29

+ 0.89 R = 0.90

5.2. Effect of spaced corrugated aprons on scour length for fine and coarse sand

Figs. 10 and 11 describe the relation between S/t, and Ls/y1 for fine and coarse sand respectively with constant values of Fro-ude number. One can see that, for the considered flow conditions, the minimum scour dimensions occurred at optimum spacing ratio S/t = 3. For Fr = 1.68, 2.47, 4.45, 6.08 and 9.29 the scour length decreases by 35.9%, 32.16%, 26.28%, 30.45% and 27.19% respectively, in comparison with the scour

40 36 32 28 24 20 16 12 8 4

- Present Study at Fr=1.68 ' Present Study at Fr=2.47 1 Present Study at Fr*4.45

- Present Study at Fr=6.08 Present Study at Fr=9.29

0 1 2 3 4 5 6

Figure 10 Relationship between Ls/y1 and S/t for fine sand.

24 22 20 18 16 14

— 12 yi

10 8 6 4 2 0

. Present Study at Fr=1.68 . Present Study at Fr=2.47 - Present Study at Fr=4.45 " Present Study at Fr=6.08 ■ Present Study at Fr=9.29

1 2 3 4 5 6

Figure 11 Relationship between Ls/y1 and S/t for coarse sand.

length of flat apron with considering the results presented in the following Section 5.3.

Based on the experimental data and using the statistical method, for different spaced corrugated aprons, several models were proposed and their regression coefficients were estimated. Out of all trials, the average best empirical equation predicting the relative scour length can be put in the following form;

Ls S 2 S

— = 0.45 - 1.94

yi t t

+ 14.51 R2 = 0.92

7.5 6.8 6.0 5.3 4.5 3.8 3.0 2.3 1.5 0.8 0.0

' Present Study for Coarse sand

-------- Present Study for Fine Sand

-----Fahmy S. Abdelhaleem, (2013)

-Fahmy S. Abdelhaleem et al., (2012)

---Dargahi B„ (2003)

Figure 12 Comparison relationship between relative scour depth ds/y1 and Fr for flat apron.

----Present Study for Coarse Sand

------- Present Study for Fine Sand

---Fahmy S. Abdelhaleemf (2013)

- Fahmy S.Abdelhaleemetal., (2012)

I I I I I -----Dargahi B., (2003)

2.7 2.4

— 1.5 Vi

1.2 0.9 0.6 0.3 0.0

— ■ ■ Present Study, S=3t=12 cm

--Present Study, S=t= 4 cm

---Present Study, Smooth Aprons

-------¡.------\-------i------\-------¡..._

Fahmy S. Abdelhaleem et al. (2012) y \ _ /

—I------V/ / "

,-x-/.-.\—I...

i ■■ .„I—

i i ...j—j..._

Figure 13 Comparison relationship between relative scour length Ls/y1 and Fr for flat apron.

Figure 14 Comparison relationship between relative scour depth ds/y1 and Fr in case of spaced corrugated aprons for fine sand.

—T------!------]------1------r..

— ■ ■ Present Study, S=3t=12 cm

5.3. Effect of Froude number on the depth and length of scour for flat aprons

Figs. 12 and 13 illustrate the relation between ds/y1 and Ls/y1 with Fr for present research and compare it with previous studies that were conducted by Fahmy et al. [23], Dargahi [16] and Fahmy [53] on flat apron respectively. One can see that, for the considered flow conditions, generally scour dimensions increase with increasing the Froude number. Figs. 12 and 13 show that, the developed equation of fine sand is approximately closer to Fahmy [53] than both Dargahi [16] and Fahmy et al., [23]. Knowing that, they studied the free jump.

By statistics analysis, average empirical equations predict the relative scour depth and length over smooth can be put as following formulas;

^ = 0.31 [Fr]0'8711 R2 = 0.96 yi

= 3.70[Fr]0'1009 R2 = 0.92

5.4. Effect of Froude number on the depth and length of scour for spaced corrugated aprons

Figure 15 Comparison relationship between relative scour length Ls/y1 and Fr in case of spaced corrugated aprons for fine sand.

Figs. 14 and 15 show the relation between ds/y1 and Ls/y1 with Fr for fine sand in the present research respectively and compare it with previous study on corrugated aprons. Experimental study of Fahmy et al. [23] has been conducted by using three types of corrugated aprons, semicircular, trapezoidal and triangular shapes with no spacing. They concluded that, the triangular corrugated aprons gave the best minimizing of scour dimensions, thus, the results of this case are suitable to compare with the present study. Present study has been conducted on different corrugation wave length S = 4, 8, 12, 16 and 20 cm as mention previously in Fig. 2.

It can be noticed that, there is an acceptable agreement between results of corrugation wavelength (S = 4 cm) in the present study with that of Fahmy et al. [23].

One can see that, for the considered flow conditions, the present study confirmed that, the best minimizing of scour dimensions occurred at spacing ratio S/t = 3. Interpretation that refers to, at this spacing ratio more energy was dissipated between corrugated sheets in comparison with other spacing ratios. At spacing ratio S/t = 3 scour depth decreases by 63.15%, 56.43%, 49.85%, 41.78% and 33.85% and the scour length by 37.24%, 32.75%, 26.64%, 21.35% and 17.95% at

Froude number Fr = 1.86, 2.47, 4.45, 6.08 and 9.29, respectively in comparison with that over flat apron.

In the other hand, Figs. 16 and 17 illustrate the relation between ds/y1 and Ls/y1 with Fr for coarse sand in the present research respectively and compare it with previous study that was conducted by Fahmy et al. [23] on corrugated aprons. For coarse sand at spacing ratio S/t = 3 the scour depth decreases by 42.43%, 36.15%, 29.56%, 25.32% and 21.23% and the scour length by 26.56%, 22.31%, 17.64%, 14.35% and 11.95% at Froude number Fr = 1.86, 2.47, 4.45, 6.08 and 9.29 respectively, in comparison with that over flat apron for coarse sand.

By statistics analysis, average best empirical equations predict the relative scour depth and length at spacing ratio S/t = 3 can be put as following formulas;

— = 0.07[Fr]L3132 R2 = 0.99 (9) y1

— = 3.01 [Fr]0:7683 R2 = 0.98 (10)

5.5. Effect of the relative mean grain size on the scour holes dimensions

Figure 17 Comparison relationship between relative scour length Ls/y1 and Fr in case of corrugated aprons for coarse sand.

Figs. 18 and 19 show the relation between ds/y1 and Ls/y1 with d50/y1 for fine sand in the present research respectively and by comparing it with previous studies in flat apron case. Experimental study of Fahmy [53] has been conducted to analyze effect of semi-circular baffle blocks on local scour downstream clear-over fall weirs by changing the heights and positions of baffles with different flow conditions. As shown in the mentioned figures, there is a relative agreement between the results of present study with that were conducted by Fahmy [53] and Dargahi [16] on flat aprons with taking into consideration that, they studied performance of free hydraulic jump. The results of the present study on corrugated aprons confirm that, the best

1.8 1.6 1.4 1.2 A !0 * 0.8 0.6 0.4 0.2 0.0

-Present Study, S=3t=12 cm

i i I i i --Present Study, S=t=4 cm

-Present Study, Smooth Aprons

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

1 1 n 1 T — ■ ■ Present Study, S= 3t= 12cm -Present Study, Smooth Aprons r

! ! ! ! ! .....i .. .. i.....J......i......i...... L.....

i i i i i Dargahi B., 2003) X A

! ! ! ! ! ! ! ! ! !

"t ■■ J*

Fahmy S. Abdelhaleem, (2013)* \ y' x' ________

It/ ____________ A

/ •

/ / / ____ h ■

—■ ■'

10 0.13 0.16 0.19 0.22 0.25 0.28 0.31 0.34

dso/yi

Figure 18 Comparison relation between relative scour depth ds/ y1 and d50/y1 in case of smooth and corrugated aprons for fine sand.

minimizing of scour hole dimensions occurred at spacing ratio S/t = 3 for all types of jump. Out of all trials, the best empirical equation predicts the relative scour depth over corrugated apron which affected by d50 can be put in the following form;

ds _ 69.14 d50 2 33.97 d50

y1 Ly1 J Ly1 J

4.66 R2 0.90

Figure 16 Comparison relationship between relative scour depth ds/y1 and Fr in case of corrugated aprons for coarse sand.

On the other hand, the best empirical equation predicts the relative scour length over corrugated apron which affected by d50 can be put in the following form;

Ll = 459.98 d50 2 224.57 d50 + 39.39 R2 = 0.90

y1 ,y1. ,y1.

— . Present Study, at S= 3t=12cm -— Present Study, Smooth Aprons

0.10 0.13 0.16 0.19 0.22 0.25 0.28 0.31 0.34 dso/yi

Figure 19 Comparison relation between relative scour length Ls/ y1 and d50/y1 in case of smooth and corrugated aprons for fine sand.

40 36 32 28 24

— 20 Vi

16 12 8 4

— ■ ■ Present Study, S=3t=12 cm - Present Study, Smooth Aprons

Dargahi B., (2003)

Fahmy S.

01— 0.5

0.7 0.8

1.0 1.1 1.3 dso/yi

1.4 1.6

Figure 21 Comparison relation between relative scour length Ls/ y1 and d50/y1 in case of smooth and corrugated aprons for coarse sand.

Figs. 20 and 21 show the relation between ds/y1 and Ls/yx with d50/yi for coarse sand in the present research respectively and compare it with previous studies that were conducted by Fahmy [53] and Dargahi [16] on flat aprons.

The results of the present study for corrugated aprons confirm that, the best minimizing of scour hole dimensions occurs at spacing ratio S/t = 3 for all types of jump. Out of all trials, the average best empirical equation predicts the relative scour depth over corrugated apron which affected by d50 can be put in the following form;

ds = 0.89 d50 2 2.12 d50

y1 ,y1. ,y1.

1.67 R2 0.95

The average best empirical equation predicts the relative scour length over corrugated apron which affected by d50 can be put in the following form;

L = 8.85 d50 2 20.5 d50 + 20.3 R2 = 0.98

y1 ,y1. ,y1.

Figure 20 Comparison relation between relative scour depth ds/ y1 and d50/y1 in case of smooth and corrugated aprons for coarse sand.

6. Conclusions

The results of the experimental and statistical study for the submerged hydraulic jump over smooth and different spaced corrugated aprons and downstream local scour have been presented; the discussion and analysis of the results highlighted the following conclusions:

• The dimensionless interrelationships between different parameters of local scour holes at downstream of a rigid apron are studied experimentally.

• Using corrugated aprons downstream of hydraulic structures is an effective engineering approach to minimize Scour holes dimensions.

• Some experimental equations were presented by using regression analysis.

• At optimal spacing ratio S/t = 3 the minimum dimensions scour occurred and large energy has been dissipated.

• The scour dimensions increase with Froude number increases.

• Scour depth and length are inversely proportional to the mean diameter of grain size particles.

• These proposed criteria can help hydraulic engineers to design structures more safely.

Acknowledgments

This paper is a part of the PhD thesis of the first author under the supervision of the other authors. I would also like to thank the Hydraulics Research Institute (HRI) of National Water Research Center (NCWR) for facilitating the achievement of this research.

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Eng. Hossam has an wide experience in hydraulic applications in the field, covering the different aspects of hydraulic engineering; his good experience in planning and design an irrigation and drainage system, topographic survey, river and hydraulic structures studies, executing pump station, different hydraulic structures such as (bridges, culvert, barrage, etc.), flow in pipes, Holds an international diploma in river basins Sciences.