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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),

ISSN 0976 – 6316(Online), Volume 5, Issue 4, April (2014), pp. 82-90 © IAEME

82

LOCATION OF AIR INCEPTION POINT FOR DIFFERENT

CONFIGURATIONS OF STEPPED SPILLWAYS

Najm Obaid Salim Alghazali1, Salam M. Jasim

2

(1)

Corresponding author, Asst. Prof. Doctor, Civil Engineering Department, Babylon

University, Iraq (2)

M.Sc. Student, Civil Engineering Department, Babylon University, Iraq

ABSTRACT

Twelve stepped spillway models have been manufactured with three downstream slope

angles: 25, 35 and 45°, and four numbers of steps: 5, 10, 15 and 20. The results of experimental work

emphasize that for the same model air inception point location moved downstream as the discharge

increased. For the same discharge, the location of air inception point was closer to the crest for larger

step heights and lesser slope angle. The location of air inception point was closer to the crest in

pooled steps compared with flat steps; this location was farther than flat steps when the gaps between

end sills and step rises were filled with gabions. Twelve empirical equations for air inception point

distance on stepped spillways were suggested based on the experimental results. The experimental

results for flat steps were compared with the results of three relationships: Matos et al. (2000),

Chanson (2001) and Boes and Hager (2003) for the prediction of the location of air inception point in

the limits of this study. The comparison showed that Boes and Hager relationship results (2003) were

the closest to the experimental results.

Keywords: Air Entrainment, Gabions Steps, Inception Point, Pooled Steps, Stepped Spillway.

1. INTRODUCTION

The stepped spillway is a spillway whose face is provided with a series of steps from near the

crest to the toe, they have gained popularity with modern construction techniques including roller

compacted concrete (RCC) and gabions [1], [2], [3], [4].

A peculiar aspect of the flow on a stepped spillway is the large aeration occurs at all nappe,

transition and skimming flow regimes. Modern stepped spillways are designed to operate with a

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING

AND TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 4, April (2014), pp. 82-90

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skimming flow regime [5].In the skimming flow regime, the determination of the exact location at

which air entrainment starts on stepped spillway is very important due to its significant effect on

energy dissipation rate, cavitation risk and training wall height [6], [7]. Air entrainment starts at the

location where the turbulent boundary layer reaches the free surface [1].

The presence of air within high-velocity flows may prevent or reduce cavitation damage. On

stepped spillway with skimming flow regime, the reduction of flow velocity and the resulting

increase of flow depth reduce also the risks of cavitation [8]. Uncertainty in this notion has

perpetuated conservative design practices [9].

The zone near the inception point of air entrainment is critical in terms of the risk of

cavitation damage. For increasing flow rates, the non-aerated region of the spillway will increase and

larger velocities will be reached that could cause unacceptable pressure fluctuations. Downstream the

inception point, the presence of an adequate percentage of air in the mixture near the solid surfaces is

expected to prevent cavitation damage [10].

In the last two decades, there has been an increasing interest in the stepped spillways in

various laboratories around the world [11]. The stepped spillway design is not limited to flat uniform

steps, some prototype stepped chutes were designed with pooled steps (e.g. Sorpe dam, Germany),

alternate sills (e.g. Neil Turner stepped weir, Australia), and weir structures designed with gabion

steps, etc.[3], [12]. Alternative stepped designs are poorly understood [3].In the recent years, the air-

water flows on pooled stepped spillways were researched in a few studies[13].Also, the hydraulics of

gabions stepped spillway has received less attention due to the complexity to evaluate the flow

patterns and flow resistance [14]. The advantages of gabions are: low cost, ease of installation,

flexibility, and ease of maintenance [15]. With proper construction practice, spillways having a

stepped downstream face built of gabions can withstand floods of up to 3 m2/s without damage

[16].Stone size and shape have little influence on the energy loss and flow velocity as compared to

the increasing effect of the weir slope [14].

Many relationships have been developed to predict the location of air inception point for

conventional flat stepped spillway. The estimation of this point in other configurations is not yet well

understood. The objective of this study is to suggest new empirical equations for three configurations

(flat steps, pooled steps, pooled with gabions steps).

2. EXPERIMENTAL WORK

Twelve stepped spillway models were made from wood and coated with varnish to avoid

wood swelling of water and to increase its smoothness. The models have vertical upstream face with

three downstream slope angles (25°, 35° and 45°). For each slope, four models were designed as

ogee stepped spillway with 5, 10, 15 and 20 steps. All models have 0.3 m width and 0.3 m height

(from the base to the upper point in the crest).

The tests were carried out in a recirculating flume located at the fluid laboratory of

Engineering College, Babylon University, Iraq (Photo 1). The flume is 10 m length and 0.3m width.

It has transparent side walls with height of 45 cm. The flume has a pump with a discharge capacity of

30 l/s, a flow meter is installed on its pipeline for measuring the discharge of the passing flow. Two

movable carriages with point gauges were mounted on brass rail at the top of flume sides, which

have an accuracy of 0.1 mm.

The experiments were conducted for fifteen discharges runs ranging from 0.9 to 9.3 l/s

(Table 1). This range was satisfying the need of this study. Photo 2 shows a sample of the observed

locations of air inception points. Figure 1 explains the distance to the air inception point (Li) and the

step roughness height (Ks).

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

ISSN 0976 – 6316(Online), Volume 5, Issue 4, April (2014), pp.

The used end sills are of height equals to half step height i.e.,

height and h is the step height. Four thicknesses of end sills are used: 0.5, 1, 3 and 5 mm for the

models having number of steps: 5, 10, 15 and

Photo 1: The used flume (Civil Engineering Department, Engineering College,

Table 1:

Run No. Q (l/s)

1 0.90

2 1.50

3 2.10

4 2.70

5 3.30

6 2.90

7 4.50

8 5.10


6316(Online), Volume 5, Issue 4, April (2014), pp. 82-90 © IAEME

84

The used end sills are of height equals to half step height i.e., he = 0.5h; h


models having number of steps: 5, 10, 15 and 20 steps respectively.

The used flume (Civil Engineering Department, Engineering College,

Babylon University, Iraq)

Table 1: Discharges used in the 15 runs

q (l/s.m) Run No. Q (l/s)

3.00 9 5.70

5.00 10 6.30

7.00 11 6.90

9.00 12 7.50

11.00 13 8.10

13.00 14 8.70

15.00 15 9.30

17.00


= 0.5h; he is the end sill


The used flume (Civil Engineering Department, Engineering College,

q (l/s.m)

19.00

21.00

23.00

25.00

27.00

29.00

31.00



Photo 2a Photo 2: Sample of the observed locations of air inception points

Figure 1: Schematic representation of the measured L

The gabion dimensions are

length and t is the end sill thickness. During testing runs, the gabions were placed into the steps and

removed alternately. Wire mesh of rhombus shape with side length of 0.68 cm and diagonals of 0.65

and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95

porosity of 41%. These types of wire mesh and gravel were selec

filled material should be larger than 1.5 times the wire mesh opening and the porosity values

between 38 and 42 are preferable as suggested by previous studies (such as

Kells (1993) cited in [17]).

3. DATA ANALYSIS

3.1 Suggested Relationships

The suggested empirical equations for the location of air inception point for flat steps, pooled

steps and pooled with gabions steps for all the slope angles 25°, 35° and 45° are presented in

Table 2. All symbols are defined in appendix 1.



85

Photo 2b

Sample of the observed locations of air inception points

a) Side view. b) Top view.

Schematic representation of the measured Li

he × (l-t) 0.3 × m, where he is the end sill height,



and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95

porosity of 41%. These types of wire mesh and gravel were selected taking into account that the


between 38 and 42 are preferable as suggested by previous studies (such as Stephenson (1979) and



All symbols are defined in appendix 1.


is the end sill height, l is the step



and 1.2 cm has been used. The wire mesh boxes were filled with gravel of size 0.95-1.27 cm and

ted taking into account that the


Stephenson (1979) and





86

Table 2: Suggested empirical equations.

θ Equation R2 Case

45° Li

Ks

= 5.1083Fr*1.1731

0.7621

Flat steps

35° Li

Ks

= 5.4641Fr*1.2130 0.9239

25° Li

Ks

= 6.6039Fr*1.0395 0.8449

For all slopes Li

Ks

= 5.8851 �sin θ�-0.09572Fr*

1.0800 0.8604

45° Li

Kt

= 6.0784 Fr*1.0353

0.8621

Pooled steps

35° Li

Kt

= 7.2552Fr*0.9515 0.9267

25° Li

Kt

= 7.7555 Fr*0.8830 0.8556

For all slopes Li

Kt

= 7.6019 �sin θ�-0.1023Fr*

0.8088 0.8777

θ Equation R2 Case

45° Li

Kt

= 9.5795 Fr*1.0122

0.7816

Pooled steps with

gabions

35° Li

Kt

= 10.4540Fr*0.9880 0.8057

25° Li

Kt

= 9.9647 Fr*1.0149 0.7171

For all slopes Li

Kt

= 10.4367 �sin θ�-0.0999Fr*

0.8501 0.8171



3.2 Comparison with Previous RelationshipsFor flat stepped spillways, the selected

present study are presented in Table 3

ones for the three slope angles (45°, 35° and 25°) are shown in the

Table 3:

Researcher

Chanson (2001)[1]

Matos et al. (2000)

(cited in [18])

Boes and Hager (2003)

Figure 2: Li/Ks and Fr



87

3.2 Comparison with Previous Relationships For flat stepped spillways, the selected equations to be compared with the results of the

Table 3. Comparisons between the obtained data and the calculated

ones for the three slope angles (45°, 35° and 25°) are shown in the Figs. 2, 3 and 4.

Table 3: The studied relationships

Equation

Matos et al. (2000)

Boes and Hager (2003)[19]

and Fr* scatter on 45° slope angle flat models


equations to be compared with the results of the

. Comparisons between the obtained data and the calculated



Figure 3: Li/Kt and Fr

Figure 4: Li/Ks and Fr

4. CONCLUSIONS

It can be concluded that for the same model

moves downstream as the discharge increases. For the same discharge, the location of air inception

point is closer to the crest for larger step heights and lesser slope angle. The location of inception



88



or the same model the location of inception point of air entrainment




the location of inception point of air entrainment





89

point of air entrainment is closer to the crest in pooled steps compared with flat steps; this location is

farther than flat steps when the gaps between end sills and step rises are filled with gabions.

The comparison of experimental results for flat steps with the results of three relationships:

Matos et al. (2000), Chanson (2001) and Boes and Hager (2003) for the prediction of the location of

air inception point in the limits of this study showed that Boes and Hager relationship results (2003)

were the closest to the experimental results.

REFERENCES

[01] Chanson, H., The Hydraulics of Stepped Chutes and Spillways, Balkema, Lisse, the

Netherlands, 2001.

[02] Gonzalez, C. A., An Experimental Study of Free-Surface Aeration on Embankment Stepped

Chutes, Ph.D. Thesis, University of Queensland, Australia, 2005.

[03] Felder, S. and Chanson, H., Air Entrainment and Energy Dissipation on Porous Pooled

Stepped Spillways, International Workshop on Hydraulic Design of Low-Head Structures

(IWLHS), Aachen, Germany, (87-97), 2013.

[04] Guenther, P., Felder, S. and Chanson, H., Flat and Pooled Stepped Spillways for Overflow

Weirs and Embankments: Cavity Flow Processes, Flow Aeration and Energy Dissipation,

IWLHS, 2013.

[05] Gonzalez, C.A. and Chanson, H., Experimental Study of Turbulence Manipulation in Stepped

Spillways. Implications on Flow Resistance in Skimming Flows, Proceeding of the 31st IAHR

CONGRESS, Soul, Korea, 2005.

[06] Hunt, S. L. and Kadavy K.C., Inception Point Relationship for Flat-Sloped Stepped

Spillways, J. Hydr. Eng., ASCE, 137(2): 262-266, 2011.

[07] Jian-hua, W., Bin, Z. and Fei, M., Inception point of air entrainment over stepped spillways,

ScienceDirect J. hydrodynamics 25(1):91-96, 2013.

[08] Chanson, H., Hydraulics of Stepped Spillways and Cascades, International Conference on

Hydraulics in Civil Engineering, University of Queensland, Brisbane, Australia: 217-222,

1994.

[09] Frizell, K.W., Renna, F.M. and Matos, J., Cavitation Potential of Flow on Stepped Spillways,

J. Hydr. Eng., ASCE, 139(6): 630-636, 2013.

[10] Amador, A., Sanchez-Juny, M., and Dolz, J., Developing Flow Region and Pressure

Fluctuations on Steeply Sloping Stepped Spillways, J. Hydr. Eng., ASCE, 135(12):

1092-1100, 2009.

[11] Khatsuria, R.M., Hydraulics of Spillways and Energy Dissipators, Marcel Dekker, New

York, U.S.A., pp. 95-127, 2005.

[12] Chanson, H. and Gonzalez, C.A., Stepped Spillways for Embankment Dams: Review,

Progress, and Development in Overflow Hydraulics, Proc. Intl Conf. on Hydraulics of Dams

and River Structures, Tehran, Iran, Balkema Publ., The Netherlands, pp. 287-294, 2004.

[13] Felder, S., Guenther, P. and Chanson, H., Air-Water Flow Properties and Energy Dissipation

on Stepped Spillways: A Physical Study of Several Pooled Stepped Configurations, Research

Report No. CH87, School of Civil Engineering, the University of Queensland, Brisbane,

Australia, 2012.

[14] Chinnaarasri, C., Donjadee, S. and Israngkura, U., Hydraulic Characteristics of Gabion-

Stepped Weirs, J. Hydr. Eng., ASCE, 134(8): 1147-1152, 2008.

[15] USACE, Use of Gabions in the Coastal Environment." CETN-III-31, 12/86, 1986.

[16] Peyras, L., Royet, P. and Degoutte, G., Flow and Energy Dissipation over Stepped Gabion

Weirs, J. Hydr. Eng., ASCE, 118(5): 707-717, 1992.



90

[17] Salmasi, F., Sattar, M. and Pal, M., Application of data mining on Evaluation of Energy

Dissipation over Low Gabion-Stepped Weir, Turkish Journal of Agriculture and Forestry

No. 36: 95-106,2012.

[18] Sarfaraz, M. and Attari,J., Selection of Empirical Formulae for Design of Stepped

Spillways on RCC Dams, World Environmental and Water Resources Congress, ASCE:

2508-2517,2011.

[19] Boes, R. and Hager, W., Two-Phase Flow Characteristics of Stepped Spillways, J. Hydr.

Eng., ASCE, 129 (9): 661-670, 2003.

Appendix 1: Symbols

Symbol Unit Definition

Fr* [‒‒‒‒] Roughness Froude number =q /�g (sin θ)(h cos θ)3

g [m/s2] Gravity acceleration

h [m] Step height

he [m] End sill height

Ks [m] Step roughness height perpendicular to the pseudo bottom

Kt [m] Equivalent roughness height perpendicular to the pseudo bottom

Li [m] Distance from the upper point on the spillway crest to the inception point

q [m2/s] Discharge per unit width

R2 [‒‒‒‒] Coefficient of determination

yc [m] Critical flow depth above spillway crest

θ Degree Downstream slope angle

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