35.2 Stepped or Cascade Spillways (Fig. 35.4) - nptel - Indian ...

Hydraulics Prof. B.S. Thandaveswara 

35.2 Stepped or Cascade Spillways (Fig. 35.4) 

Recent advances in technology have led to the construction of large dams, reservoirs 

and channels. This progress has necessitated the provision of adequate flood disposal 

facilities and safe dissipation of the energy of the flow, which may be achieved by 

providing steps on the spillway face. Stepped channels and Spillways are used since 

more than 3000 years. Stepped spillway is generally a modification on the downstream 

face of a standard profile for an uncontrolled ogee spillway. At some distance in the 

downstream of the spillway crest, steps are fitted into the spillway profile such that the 

envelope of their tips follows the standard profile down to the toe of the spillway. A 

stepped chute design increases higher energy dissipation and thus reduces greatly the 

need for a large energy dissipator at the toe of the spillway or chute. 

Spillway 

Indian Institute of Technology Madras 

Stepped Spillway 

Step height Sh 

Length of the step ls 

Figure 35.4 - Definition Sketch of a Stepped Spillway 

Stepped spillway was quite common in the 19th century and present practice is 

confined to simple geometries ( e.g. flat horizontal steps in prismatic chutes). Generally, 

a stepped channel geometry is used in channels with small - slope: for river training, in 

sewers and storm waterways and channels downstream of bottom outlets, launder of 

chemical processing plants, waste waterways of treatment plants and step -pool 

streams.


Detailed investigation into its various elements started only about 1978 with the 

comprehensive laboratory tests by Essery and Horner (1978). 

During the 19th century and early 20 th century, Stepped waste - waterways ( also 

called ' byewash' ) were commonly used to assist with energy dissipation of the flow 

(CHANSON 1995, "Hydraulic design of stepped Cascade channels, Weirs and 

Spillway", pergamon UK, 292 pages Jan 1995). Now a days stepped spillways are often 

associated with roller compacted concrete ( RCC ) dams. 

The stepped geometry is appropriate to the RCC placement techniques and enhances 

the rate of energy dissipation compared to a smooth chute design. A related application 

is the overtopping protection of embankments with RCC overlays ( e.g. ASCE Task 

Force Report, 1994. 

Alternatives for over topping protection of Dam - Task force Commitee on over topping 

protection, 139 pages). 

35.2.1 Suitability 

Energy dissipation below hydraulic structures is accomplished generally by single -fall 

hydraulic jump type stilling basins, roller buckets or trajectory buckets. However, when 

the kinetic energy at the toe of the spillway would be high. The tail water depths in the 

river are often inadequate. Then first two devices, cannot be used as in the case of high 

head dams. 

In narrow curved gorges consisting of fractured rocks, buckets cannot be used. In such 

situations, a system of cascading falls down the side of a valley, with a stilling basin in 

the downstream, can be used as an alternative spillway. Cascade spillways can be 

used for any type of dam irrespective of the material of construction. 

The only disadvantage with stepped spillway is that at large discharges, as the jet is not 

aerated for some distance downstream of the spillway, low pressure may occur and 

lead to cavitation damage. 

Indian Institute of Technology Madras


35.2.2 Physical Modelling of Stepped Spillway 

Free surface flows are commonly modelled using Froude similitude. The various flow 

elements, 

(1) the role of the steps in enhancing turbulent dissipation as well as their interaction 

with other adjacent steps and, 

(ii ) the effect of aerated flow make it difficult to model. 

35.2.3 Classification of Flow 

The concept of stepped spillway was used as early as 1892 - 1906 in New Croton dam. 

Lombardi and Marquenent were first to consider stepped spillway consisting of concrete 

drop spillway and intermediate erodible river reaches. The slopes of these reaches were 

such that a hydraulic jump occurred at the base of each drop. However, the 

experimental studies revealed three types of flows over a stepped spillway, namely, 

nappe flow, partial nappe flow (intermediate(transition)) and skimming flow. 

A stepped chute consists of a open channel with a series of drops in the invert. For a 

given chute profile, the flow patten may be either nappe flow at low flow rates, transition 

flow for intermediate discharges or skimming flow at larger flow rates. 

Nappe Flow 

This type of flow occurs for small discharges. The flow cascades over the steps, falls in 

a series of plunges from one step to another in a thin layer that clings to the face of 

each step, with the energy dissipation occurring by breaking of the jet in the air, impact 

of jet on the step, mixing on the step, with or without the formation of a partial hydraulic 

jump on the step. The step height sh must be relatively large for nappe flow. This 

situation may apply to relatively flat stepped channels or at low flow rates. 

The depths can be determined from the expressions, 

Following equations to be checked for notations: 




0.425 

y ⎛ 2 

1 q ⎞ 

= 0.54 ⎜ ⎟ 

(35.1) 

S 3 

h ⎜ gS 

⎟ 

1 ⎝ h1 

⎠ 

0.27 

y ⎛ 2 

1 q ⎞ 

= 1.66 ⎜ ⎟ 

(35.2) 

S 3 

h ⎜ gS 

⎟ 

1 ⎝ h1 

⎠ 

0.22 

yc 

⎛ q 

2 ⎞ 

= ⎜ ⎟ 

(35.3) 

S 3 

h ⎜ gS 

⎟ 

1 ⎝ h1 

⎠ 

However, the steps for a nappe flow or plunge pool type of flow need to be relatively 

large. In otherwords, tread requires to be larger than the depth of flow. This requires 

downstream slope of dam face to be relatively flatter. Chanson observes that if slope of 

downstream face is greater than 1 : 5, the nappe flow system becomes uneconomical 

except in case of embankment type structure or steep rivers. 

Partial Nappe Flow (Fig.35.5) 

In this type of flow, the nappe does not fully impinge on the step surface and it 

disperses with considerable turbulence. Flow is super - critical down the length of the 

spillway. 

yc 

yp 

yp 

Figure 35.5 - Partial nappe flow


For a given step geometry, an increase in flow rate may lead to intermediate flow patten 

between nappe and skimming flow - the transition flow regime also called a partial 

nappe flow. The transition flow is characterised by a pool of circulating water and often 

accompanied by a very small air bubble (cavity), and significant water spray and the 

deflection of water jet immediately downstream of the stagnation point. Downstream of 

the spray region, the supercritical flow decelerates upto the downstream step edge. The 

transition flow pattern exhibits significant longitudinal variations of the flow properties on 

each step. It does not present the coherent appearance of skimming flows. 

Skimming Flow (Fig. 35.6) 

In skimming flow regimes, the water flows down the stepped face as a coherent stream, 

skimming over the steps and cushioned by the recirculating fluid trapped between them. 

The external edges of the steps form a pseudobottom over which the flow skims. 

Beneath this, recirculating vortices form and are sustained through the transmission of 

shear stress from the water flowing past the edge of the steps. At the upstream end, the 

flow is transparent and has glossy appearance and no air entrainment takes place. After 

a few steps the flow is characterised by air entrainment similar to a self -aerated flow 

down a smooth invert spillway. In case of the skimming flow, at each step, whether air 

entrainment occurs or otherwise, a stable vortex develops and the overlying flow moves 

down the spillway supported by these vortices, which behave as solid boundary for the 

skimming flow, and the tips of the steps. There is a continous exchange of flow between 

top layer and vortices formed on steps. The flow rotates in the vortex for a brief period 

and then returns to the main flow to proceed on down the spillway face. Similarly, air 

bubbles penetrate and rotate with the vortex flow, when aeration takes place. 

Transition from one type of flow to another is gradual and continuous, as a result both 

the nappe flow and the skimming flow, appear simultaneously in a certain range, one of 

them on some steps and other on the remaining, both changing spatially and 

temporarily. 




sh 

Recirculating 

flow 

l 

yc 

V0 

Figure 35.6 - Fully developed skimming flow 

35.2.4 Transition from Crest to Initial Steps 

Sorensen found the free surface jet to be smooth down to the point of inception of air 

entrainment. This point of inception moves progressively upstream as the discharge 

decreases. However, for very small discharge, the jet after striking the first step was 

redirected outward and skips several steps before it strikes the spillway face again 

several steps further down. This could be overcome by introducing few smaller steps on 

upper reaches of the spillway.


35.2.5 Basic Equation for Skimming Flow 

Consider a skimming flow in which dominant feature is the momentum exchange 

between the free stream and the cavity flow within the steps. Basic dimensional analysis 

yields ( Figure 35.6 ), 


f 1 ( V ο, y ο, S h , ls 

, k s , g, θ ο, 

µ , ρ )= 0 (35.4) 

1 

for horizontal steps, θ = tan 

-1 

ο (S h / ls). 

1 

Using Buckingum pi- theorem equation can be written as 

⎡ V ρV 

y Sh 

1 ks 

⎤ 

f 2 

⎢ ο , ο ο , , , θο ⎥ = 0 (35.5) 

⎢ gyο µ ls 

S 

⎣ h ⎥ 

1 ⎦ 

Mixing layer 

__ 

V0 

δ 

sh 

y0 

Velocity Distribution 

Shear layer edges 

Cavity (bubble) 

Figure 35.7 - Hydrodynamic feature of a skimming flow 

While deriving the above equation the interaction of adjacent steps and the effect of air 

entrainment has not been taken into account. Hence, Froude number similitude alone 

cannot describe the complexity of stepped spillway flows completely. 

Chanson showed that Froude number has no effect on flow resistance and that 

Reynolds number might not have a substantial effect and that the form drag was related 

primarily to step cavity geometry. It was also reported that in case of small scale models 

the developing flow regimes and flow resistance were not correctly reproduced. 

ls


35.2.6 Onset of Skimming Flow 

Onset of skimming flow occurs when the space between the water surface at the two 

consecutive edges of the steps is filled up with water, there by, creating a smooth 

surface of water parallel to the average slope of the spillway face - the condition very 

difficult to establish analytically. Therefore, empirical equations have been proposed by 

many investigators for the delineation of the skimming flow from nappe flow over 

stepped spillway. 

Essery and Horner reported that it is very difficult to distinguish between nappe and 

skimming flow for flatter slopes having S /l < 04 . . 


h1s Based on available data Rajaratnam found the skimming flow to occur for 

On the other hand, Stephenson introduced a term called Drop number, 

to distinguish between nappeflow [ D< 0.6 ] and skimming flow [ D > 0.6] 

y / S > 08 . . 

c h1 

⎡ 2 3 

D= q / gS ⎤ 

⎣ h1 

⎦ 

Peyras, et al. studied gabion dams consisting of four step element each 0.2 m high. 

It was found that the transition from nappe to skimming flow occurs for a discharge of 

approximately 1.5 m3 / s /m or at y/ S < 05 . while Degoutte found the onset of 

c h1 

skimming flow on gabion steps to occur at y/ S = 074 . for S /l = 033 . and at 0.62 for 

c h1 

h1s S /l = 10 . . Based on the available data, Chanson developed a regression equation 

h1s for the onset of skimming flow, namely. 

In which k1 1 , F 

2 b 

Fb 

yc 

> 

s 

h 

2/3 

b 1 

F k 

⎛ 2 3/2 cos α ⎞ 

1+ 2F b 

b(k 1) 

⎜1− ⎜ 

⎟ 

k ⎟ 

⎝ 1 ⎠ 

1 

= + is the Froude number at the brink of the step and α b is the 

streamline angle with the horizontal. This equation is applicable to the accelerated flow 

and may predict jet deflection at the first step of the cascade.


yc / sh 

1.40 

1.20 

1.00 

0.80 

0.60 

0.40 

0.20 


Skimming Flow 

Nappe Flow 

0.00 

0 0.2 0.4 0.6 0.8 1 1.2 

Figure 35.8 - Onset of skimming / Nappe flow 

sh / ls 

35.2.7 Prediction of the flow regime 

Essery and Horner 

PEYRAS et al. 

STEPHENSON 

BEITZ and LAWLESS 

MONTES 

KELLS 

RU et al. (1994) 

HORNER (1969) 

ELVIRO and MATEOS 

-20% Band 

+20% Band 

Transition fully / partially developed jump 

HORNER [NA1/NA2] 

The type of stepped flow regime is a function of the discharge and step geometry. 

Chanson has reanalysed a large number of experimental data related to change in flow 

regimes. Most of the data were obtained with flat horizontal steps . 

Overall the result suggest that the upper limit of nappe flow may be approximated as: 

y 

c Sh 

=0.89 - 0.4 (35.6) 

Sh 

ls 

in which y c is the critical depth, S h is the step height, and 

ls 

is the step length. The above equation indicates the transition 

of flow from nappe to transition flow regime. 

While the lower limits of skimming flow may be estimated as. 

y 

c Sh 

= 1.2 −0.325 

(35.7) 

Sh 

ls 

on set of skimming flow is given 

by 

y 

c Sh 

> 1.057 −0.465 

Sh 

ls 

Further the equation 2 indicates the change of flow from 

transition flow to skimming flow region. 

Two issues must be clearly under stood.


Eqations 35.6 and 35.7 were fitted for flat horizontal steps with Sh/ls ranging from 0.05 to 

1.7 ( i.e 3.4°



0.9 

0.8 

0.7 

35.2.8 Coefficient of Friction 

Rajaratnam 

Tatewar and Ingle 

Chanson 

0.6 

0.4 0.5 0.6 0.7 0.8 0.9 

sh1/l 

Figure 35.9 - Onset of skimming flow 

Noori studied in detail stepped steep open channel flows and reported a drag coefficient 

of 0.19 for ( S /l = 0.2 and 

h1s M = 62 [ { y + ( S / 2 ) for S > 6 ] and, 0.17 for ( S /l ) = 0.1 and M= 100 [ { y + ( S / 

2 ) for 

S h > 10 ]. 

1 

h1 

h1 

h1s In this, the value of y can be estimated at any point on the spillway as, 

y = 

φ 

q 

[ 2g(z -H) ] 

in which z is the vertical distance below the crest measured to the water surface at the 

point where y is to be determined. 

The value of φ for a stepped block was found to be considerably smaller than that for 

smooth spillway for large value of (ls/ yc); 

0.5 

h1


S h is the length of the step) and slope of the spillway, and hence, a considerable 

1 

energy loss at the toe of the stepped spillway. 

Based on the avilable data, Rajaratnam suggested the following equation for the 

variation of coefficient of friction, c f , for aerated skimming flow. 


3 

2y0gs0 f 2 

c = q 

The value of c f was found to be 0.18 as compared to 0.0065 for smooth spillway, while 

Christodoulou (1993) found c f to vary from 0.076 to 0.89 and , c f being higher down 

the steps. 

Tozzi evaluated the friction factor on stepped chutes of slope 1:2 ( V: H ) by analysing 

the energy loss of air flowing in a closed conduit with roughness elements designed to 

simulate the slope, 

The value of is found to be f = 0.09. It was noted that the value is overestimated if 

uniformly aerated flow conditions are not attained. Matos and Quentela concluded that a 

value of f = 0.1 can be safely considered for the preliminary hydraulic design of stepped 

spillway for slopes around 1 : 0.75 ( V: H ), typical of concrete gravity dams. 

35.2.9 Energy Loss on Stepped Spillway 

When an overflow is smoothly directed to an outlet structure by the chute where a 

concentrated energy dissipation takes place, the cascade corresponds to a distributed 

dissipator. Hence, the terminal structure has only smaller area of energy to dissipate, 

and would be significantly smaller. A quantitative comparison between the conventional 

system chute - stilling basin and the spillway cascade is shown in figures. The latter 

type is suited for small and medium discharges and has recently gained some 

popularity with Roller Compacted Concrete dams.


RVF 


GVF 

boundary layer 

Point of 

inception 

Growth of boundary layer 

Energy Line 

PI 

DZ 

UAF 

T 

PHJ 

PI = Point of Inception 

RVF = Rapidly Varied Flow 

GVF = Gradually Varied Flow 

DZ = Developing Zone 

UAF = Uniformily Aerated Flow Region 

PHJ = Pre-entrained Hydraulic Jump 

Skimming Flow 

A


The typical geometry of the stepped spillway with the standard crest geometry and 

increasing step height up to the point of tangency T are shown in the above figure. 

The free surface profile is smooth upto crest inspite of the development of vortex in 

each step. The transition to rough surface flow occurs beyond point A where the air 

entrainment is initiated. The hydraulic features of the cascade spillway as compared to 

chute flow are: 


• the flow depth is much larger than in a chute due to the highly turbulent cascade 

flow, and higher sidewalls are required, 

• more air is entrained and the spray action may become an important issue. 

• abrasion can be a serious problem for flows with sediment or with floating debris. 

In cascade spillways two flow types may occur as shown in Figure. 

• Nappe flow: is the flow from each step hits the next step as a falling jet; 

• Skimming flow: the flow remains coherent over the individual steps. 

• The onset of skimming flow occurs for yc /sh > 0.8, where yc is the critical depth 

and sh is the height of the step. When uniform cascade flow occurs in long 

channels, skimming flow dissipates more energy than nappeflow. However, 

nappe flow is more efficient for a short cascade than skimming flow (Chanson, 

1994) the energy dissipated hf relative to the drop height Hodepends on the drop 

Froude number and the slope of the spillway. 

Stephenson ( 1991 ) expressed the relative energy loss as 

∆H ⎛ 0.84 ⎞ 

= F 

-1/3 

⎜ ο 

(1) 

H 0.25 ⎟ 

0 ⎝θ⎠ in which ∆H is the energy loss over a height H0, F0 is the 

⎡ q ⎤ 

Froude Number = ⎢ 3 ⎥ 

⎣gH0 ⎦ 

0.5 

, and θ is expressed in degrees in the above equation. 

The energy dissipated ∆H relative to the drop height H0 depends on the drop Froude 

3 

number Fo q ( gHo) 

= and θ slope of the spillway.


Accordingly, the effect of slope is small, where as the dam height has considerable 

influence on the head loss. Christodoulou (1993) studied the effect of number of steps N 

on the energy dissipation ∆ H / H0. He introduced the parameter hc= yc / ( Nsh ) with yc = 

(q 2 /g) 1 / 3 as critical depth sh as the step height and found for hc < 0.25 

∆ H 

= exp( − 30 h 

2 

c ) (2) 

Hο 

By Increasing the number of steps the energy dissipation can be increased and hence 

the performance of the stepped spillway. 

For a long cascade, above 90% of mechanical energy is dissipated along the cascade 

and only a small Portion of energy must be dissipated in the stilling basin. 

According to Stephenson ( 1991 ) the efficiency of the cascade spillway depends mainly 

on its height and the specific discharge and marginally on the slope. 

The cascade flow may reach a state of nearly uniform flow (subscript n) which may be 

approximated with ls , as step length ( Vischer and Hager. 1995). 


h 

4 6 3 1/2 

n = 0.23 [ l s q / ( shg 

)] (3) 

Diez-Cascon et al. (1991) conducted experimental investigation on a cascade spillway 

of step size ls / sh = 0.75 and slope θ = 53°, followed by a horizontal stilling basin . The 

sequent depth ratio varied with the approach Froude number F1 as 

Y r = 2.9 F 

1 

The resulting tailwater depth is higher than for the classical hydraulic jump, however, 

the value F 1 for cascade flow is much smaller. The above equation is valid for uniform 

approach flow. One may derive the following equation. 

2 /3 

F 

2 / 3 1/ 3 

n = 7. 3 ( h n / l s ) 

and Y 

1 / 3 

r = 21.1 ( h n / l s ) (4) 

The sequent depth ratio varies slightly with the uniform flow depth relative to the step 

height.


* 

According to Chanson ( 1994) the onset of nappe flow occurs for yc > yc 

where 

y 

* 

c 

sh 

= 1.057 − 0.465 

sh ls In the transitional regime between nappe and skimming flow hydraulic instability occurs 

which should be avoided to prevent the problems with vibration of structures. 

For skimming flow, the resistance characteristics are governed by the distance between 

two adjacent step edges, protruding into the flow. Even though Chanson (1994) 

analysed the hydraulics of skimming flow, there is inadequate data to describe uniform 

cascade flow. A basic investigation is needed to obtain further information. 

Though, it was clearly stated as early as 1970 that the adavantage of steps is to 

dissipate energy a little at a time but this is true only at low flow rates. 

Where as, the energy dissipation occurs due to jet breakup in the air, jet mixing on the 

step, with or with out the formation of a partial hydraulic jump on the steps in case of 

nappe flow; the energy dissipation in skimming flow occurs due to the momentum 

transfer to the recirculating fluid. Hence, the methods required for estimation of the 

energy loss need to be different for the two types. In general, about 88% to 94 % 

reduction in kinetic energy was noted from the velocity measurements at the spillway 

toe without and with steps. For isolated nappe flow, Peyras et al., presented an 

equation (see table) for determining the energy loss below the stepped gabion 



Authors Remarks Energy loss equation 

Peyras et al. 

(1992) 

Isolated 

nappe 

⎛ 2 

q ⎞ 

∆E = Ns h + 1.5 y c - ⎜ 2 ⎟ 

2gy ⎟ 

⎝ 1 ⎠ 

Rajarathnam, skimming 88.89 % of self aerated flow 

1990 flow 

Tatewar and 

Ingle (1999) 

Relative 

loss (upper 

limit of 

energy 

loss) 

∆ E 1 

= 

E0 2 ⎡ y 

1 1.25 C c 

⎤ 

+ d ⎢ ⎥ 

⎣H dam + Head over spillway ⎦ 

Chamani and 

Rajarathnam 

Relative 

loss 

⎡ N−1 ⎡ yc 

⎤ 

⎤ 

⎢( 1− αf ) ⎢1+ 1.5 ( 1 αfi) 

E s 

⎥+ 

∑ − ⎥ 

∆ h i= 1 

= 1−⎢ 

⎣ ⎦ 

⎥ 

E ⎢ 

0 ⎡ y 

N 1.5 c ⎤ ⎥ 

⎢ ⎢ + 

s 

⎥ ⎥ 

⎢⎣ ⎣ h ⎦ ⎥⎦ 

in which α is the proportion of energy loss per step a function 

Tatewar and 

Ingle (1966) 


Regression 

analysis for 

α 

Chanson in terms of 

friction 

factor f 

f 

⎛y⎞ ⎛s⎞ of and 

f 

c h 

⎜ ⎟ ⎜ ⎟ 

⎝sh ⎠ ⎝ ls 

⎠ 

y s 

α f = -0.1169 - 0.8221 log + 0.0675 log θ - 0.5481 log 

s l 

E0E = 1 - 

E0 

c h 

h s 

1/3 − 2/3 

− 

⎛ f ⎞ 

⎜ ⎟ 

⎝8sin θ ⎠ 

⎛ f ⎞ 

cos θ + 0.5 ⎜ ⎟ 

⎝8sin θ ⎠ 

H 

15 + dam 

y 

It was found that actual dissipation could be 10 % more in case of gabions as compared 

to concrete steps due to factors like infiltration in to the gabions, difference in surface 

roughness and spillway slope. It was also found that their equation is valid within 10% in 

case of partial nappe flow. 

Rajaratnam, found the ratio of energy dissipation by skimming flow to the energy 

contained in the flow down a smooth spillway is about 89%. He has assumed that the 

flow is uniform skimming flow which implies a high spillway, 

with many steps. The residual energy varies from 9 % to 12 % depending on the 

discharge. Christodoulou in 1993 studied the effect of number of steps on energy 

dissipation in case of skimming flow. 

c


Using his own data for 


S h /l 

1 s = 0.7 and for N = 15 (number of steps) as well as the 

avilable data for hc < 25, where hc = ( yc / NSh ), he showed for the same discharge the 

energy dissipation increases with the increase in the number of steps. The dissipation 

may be significantly less on moderately stepped spillway when compared to the uniform 

flow on high spillway. As he has not consider the effect of 

l s / S h and, the energy loss 

1 

by the steps in the curved portion is likely to be more, the results of Christodoulou is not 

applicable to prototype. Using the weir formula to express discharge over the spillway in 

terms of head over the spillway including velocity of approach head, Tatewar and Ingle 

derived a simplified expression for energy loss (upper limit of energy dissipation) using 

the equation for the discharge over the weir and is given by 

∆ E 

1 

= 

E0 9 2⎛ 

y ⎞ 

1+ C c 

d ⎜ ⎟ 

8 ⎝Hdam + H ⎠ 

Chamani and Rajaratnam established a relation for the energy dissipation in jet flow. 

Tatewar and Ingle based on regression analysis fitted an equation for the proportion of 

energy per step for the range of θ from 5° to 20° S 

h 

/ l 

1 

y 

( c ) from 0.05 to 0.833. 

S 

h 

1 

s 

from 0.421 to 0.842 and 

They concluded that energy dissipation is more in case of inclined steps and α f 

increases marginally for steeper slope and that the increase of α 

f 

is comparatively 

larger for flatter slopes.


X 


1.00 

0.90 

0.80 

0.70 

0.60 

0.50 

0.40 

0.30 

θ = 0 0 

Horizontal steps 

θ = 10 0 θ = 5 0 

θ = 20 0 

θ = 15 0 }Inclined steps 

0.20 

0.15 

0.05 0.1 

yc/sh1 

0.5 

35.2.10 Effect of Air Entrainment 

Variation of X with yc/sh1 

For higher discharges the point of inception of air entrainment occurs past the end of 

the spillway section and move progressively up as the discharge decreases. 

Typically, the depth decreases from the crest inception point, beyond which, owing to 

the bulking of the flow, the depth continuously 

increases towards the spillway toe. At very low Reynolds number, the nappe does not 

break and energy loss is affected. 

Aeration of cascades 

The Quality of waters of rivers, streams, creeks etc is often expressed in terms of the 

dissolved oxygen content ( DOC). Low dissolved oxygen value often does not allow the 

development as well may cause the death of aquatic life forms and indicates some form 

of pollution associated with excessive waste water inflows. In natural streams, obtain 

the DOC from the aeration of the free surface.


Stepped cascades are characterised by a large amount of self aeration and it may be 

used to reoxygenate depleted waters. In rivers, artificial stepped cascades and weirs 

have been built to enhance the DOC of polluted or eutrophic streams. 

Stepped cascades are also built in the downstream reach of large dams to re-oxygenate 

water. 

Example: Labyrinth weir crest length of 640 m, single drop 2.3 m, design discharge 14 

to 68 m 3 /s at South Houlston weir, USA and the two-step labyrinth drop structure (2 

drops of 2 m height and design discharge of 110 m 3 /s) of 640 m buit by the French 

Electricity Commission downstream of the Petit -Saut Dam ( the Petit-Saut Dam is a 

RCC construction) installed with an overflow stepped spillway. The downstream 

stepped cascade is designed to re- oxygenete the tailrace waters of power station ( 

depleted in oxygen ). Further, there is a series of five aeration cascades built along the 

Calumet waterway in Chicago. The waterfalls are designed to re-oxygenate the polluted 

canal and combine flow aeration and aesthetics to create recreation parks. 

Stepped cascades could be used to reduce the dissolved nitrogen content also. 

In the treatment of drinking water, cascade aeration is used to remove dissolved gases ( 

e.g. chlorine). 

35.2.11 Air entrainment in Nappe Flow Regime 

Typical air concentration profiles based on the experimental investigation by Chanson 

and Toombes are shown in the figure. 



Air Cavity 


Impact Point 

Spray Rebound Reattachment 

90 % 50 % 

Longitudinal Variation of Air Concentration (isocons) along the nappe 

Centre line of Step 2 qw = 0.150 m 2 /s after Chanson and Toombes, 

June - 1997 

The un-ventilated air cavity, the impact point and the spray region are also indicated. 

The main features of the air - water flow on step for q = 0.15 m 2 s -1 are: 

• the large air-cavity beneath the nappe, 

• the sidewall standing waves and the spray ( i.e. rebounding waters ), 

• the large amount of flow aeration in the spary region, 

• the de- trainment at the spray re-attachment, and 

• the substantial free-surface aeration at the end of the step ( i.e. C = 19% ) 

The flow patterns of the air - water flow on a down stream step : for the same flow rate 

at the cascade ( step No.9). (Sh = 0.143, ls = 2.4 m, θ = 3.4°, 10 steps over 25 m long 

flume of 0.5 m width. In the absence of steps θ = 4.0 °). 

• in the absence of ventilation the air cavity had disappeared completely and 

recirculating water occupies the space beneath the nappe, 

• the introduction of a splitter ( into the nappe ) ventilates the nappe and induces 

the formation of a sizeable air cavity; as a result the nappe trajectory increases, 

• the spray region is important, 

• the amount of entrained air is basically identical at the upstream and downstream 

ends of the step ( i.e. C = 17% to 19%); the mean air content is maximum at the 

downstream of the nappe impact ( in the spray region ) and minimum at the 

downstream end of the step . An interesting difference is the presence of a small 

bubble (cavity) between the nappe and the re - circulating water . The



introduction of a splitter helps in occurance of larger air cavity and enlarges the 

nappe trajectory. 

In comparison the mean air content at the downstream end of the smooth chute was 

about 0.08 and the maximum mean air concentration was about 0.12 at a section 

located 4 m downstream. 

Overall the stepped chute flow is significantly has higher aeration than the smooth chute 

flow for the same flow rate. The air - water flow with the stepped channel is three - 

dimensional in nature unlike the smooth chute flow which is two - dimensional. 

35.2.12 Air Entrainment in Skimming Flows 

Modern concrete stepped spillways operate in a skimming flow regime. at the upstream 

end, the free surface is clear and transparent. 

However, a turbulent boundary layer develops along the chute invert. 

When the outer edge of the boundary layer emerges to the free surface, air entrainment 

commences. 

The distance to the inception point of air entrainment and the flow depth at inception are 

correlated by : 

The location where free surface aeration occurs is called the inception point of air 

entrainment. Its characteristics are the distance Li from the crest 

(measured along the invert) and the flow depth yi measured normal to the channel 

invert. 

Model and prototype data were re - analysed by Chanson in 1994. 

The dimensionless distance Li/ ks and depth yi /ks are plotted as functions of the 

dimensionless discharge.


k s is the step depth per unit width ( normal to the flow direction ), s h is the step height. 

empirical correlations for stepped chutes: 

- The dimensionless distance from crest L 

i 

/ Ks and flow depth 

y I 

( ) 


I 

s 

s 

/ k s increase with increasing dimensionless discharge F * = 

( ) 

k s can be written as s h cos θ 

Thus F * = 

qw 

g sin θ k 

3 

L 

k 

( ) 

0.0796 

( ) ( ) 

= 9.719 sin θ F 

yI 0.4034 

= 

k sin θ 

0.04 

( F ) 

* 

0.592 

s 

* 

0.713 

q 

w 

( ) 

g sin θ s cos θ 

h 

3


LI / ks 


y 

___ I 

ks 

1000 

500 

100 

50 

20 

10 

5 

2 

1 

10.00 

1.00 

0.10 

Trigomil dam 

___ LI 

ks = 9.719(sin ) 0.0796 (F*) 0.713 

θ 

Inception on smaller steps 

1.00 10.00 100.00 

1.00 10.00 100.00 

F 

* 

BaCaRa [1:10] (53 deg.) 

BEITZ and LAWLESS (50 deg.) 

BINDO (51 deg.) 

FRIZELL (27 deg.) 

HORNER (36.4 deg.) 

SORENSEN (52 deg.) 

TOZZI (53.1 deg.) 

ZHOU (51.3 deg.) 

Given equation for 52 deg. 

Trigomil (51.3 deg.) 

PROTOTYPE 

Normalised Inception length as a function of dimensionless discharge 

after (Chanson and Toombes) 

___ yI 

ks = _______ 0.4034 

0.04 (sin θ) 

(F*) 0.592 

BaCaRa [1/10 \ 53 deg. ] 

BINDO (51 deg.) 

FRIZELL (27 deg.) 

SORENSEN (52 deg.) 

HORNER (36.4 deg.) 

TOZZI (53.1 deg.) 

ZHOU (51.3 deg.) 

Given equation (52 deg.) 

Normalised Inception depth (y ) as a function of dimensionless discharge 

after (Chanson and Toombes) I 

F * 

boundary layer growth rate is grater on stepped channels than on smooth chutes. 

Chanson in 1995 based on the reanalysed data, concluded that the experimental results 

are basically independent of the type of crest profile. 

The reanalysed data included the types of crest profile were included smooth ogee 

crest profiles follows by stepped chute ( with or without smaller first steps) and broad - 

crests followed by stepped chute.


Above Equations may be used for estimating Li and yi. It may be noted that one 

prototype observation (Trigomil dam) fills the equation 1. 

35.2.13 Aeration in Fully - Developed Skimming Flow 

Downstream of the inception point of air entrainment, the flow becomes fully -developed 

and a layer containing a mixture of both air and water extends gradually through the 

fluid. Far downstream the flow becomes uniformly aerated. This region is defined as the 

uniform equilibrium flow region. The air concentration profiles are compared with a 

simple diffusion model by CHANSON 1995 and validated with prototype and model 

smooth - chute data . The following equation describes the air concentration distribution. 

2 ⎛ y ⎞ 

C= 1−tanh ⎜K′ − 

⎜ 

⎟ 

2 D ′ y90 ⎟ 

⎝ ⎠ 

in which C is the air concentration, D' is a dimensionless turbulent diffusivity and K ' is 

constant of integration. D' and K' are functions of the mean air concentration C , y90 is 

the distance from bed at which 90% air concentration occurs. 

y 

__ 

y90 

0.8 

0.6 

0.4 

0.2 


1 

Measurements at Brushes Clough dam spillway (BAKER 1994) - 

Inclined downward steps (Sh = 0.19 m, is δ = - 5.6 deg.), θ = 18.4 degrees 

after BAKER (1994) 

Brushes Clough dam spillway 

0 

0 0.2 0.4 0.6 0.8 1 

Air concentration 'C' 

__ 

C = 0.235 - Step 50 

__ 

C = 0.178 - Step 30 

__ 

C = 0.15 - Step 10 

__ 

C = 0.20 - Step 73 

__ 

Theory: C = 0.15 

__ 

Theory: C = 0.235


y 

__ 

y90 

0.8 

0.6 

0.4 

0.2 


1 

0 

0 0.2 0.4 0.6 0.8 1 

Air concentration 'C' 

after RUFF AND FRIZELL (1994) 

(qw = 2.6 m 2 /s, θ =26.6 , inclined downward steps, Sh = 0.154 m ) 

x is the distance 

__ 

x = 14.8 m - C = 0.25 

__ 

x = 13.8 m - C = 0.31 

__ 

x = 26.8 m - C = 0.33 

__ 


__ 


Air concentration distribution in prototype observation after Baker and Ruff and Frizell (Chanson 1994) 

Table: Variation of the turbulent diffusivity and constant of integration with C . 

C 

( 1 ) 

D' 

( 2 ) 

K' 

( 3 ) 

0.01 0.007 68.70 

0.05 0.037 14.00 

0.10 0.073 7.16 

0.15 0.110 4.88 

0.20 0.146 3.74 

0.30 0.223 2.57 

0.40 0.311 1.93 

0.50 0.423 1.51 

0.60 0.587 1.18 

0.70 0.878 0.90 

y90 

1 

C = ∫ C dy 

y90 0 

The analysis of model and prototype data showed that the air concentration profiles in 

skimming flows down a stepped chute have similar shape as those in smooth chute 

flows. Further the observed values of mean air concentration over stepped chute flow 

are very nearly same as the mean air concentration of the fully developed flow over 

smooth chutes : i.e., ( C) = 27% and 36% respectively for = 18.4 

e o and 26.6 o . 

The data of Baker (1994) yielded C ranging between 15% and 23% with 18.4o slope 

and the data of Ruff and Frizell indicate C of 33% at the end of the 26.6 o slope channel. 

0


Free-surface aeration causes the bulkage of the flow and thus reducing the risks of 

cavitation damage and enhanaces the air -water gas transfer (e.g. re- oxygenation of 

the water). Futher, the presence of air nearer to the bed induces a reduction of drag and 

results in decrease in friction factor . The drag reduction effect and the associated 

reduction in flow resistance may have a significant impact on the rate of energy 

dissipation on stepped spillway. The above analysis [ of energy dissipation ] by chanson 

neglects the effects of air entrainment. The friction factor and the energy dissipation are 

affected significantly by the rate of free- surface aeration. The effects of air entrainment 

on the residual energy cannot be neglected for [ channel ] slope larger than 30 degrees 

" and " the residual energy is strongly underestimated if the effect of air entrainment is 

neglected. It is most important that design engineers to take into account aeration of 

flow to estimate the residual enegy and to dimension stilling basins downstream of 

stepped chutes". 

35.2.14 Rapidly Varied Flow at the Inception Point 

The flow properties rapidly vary next to and immediately downstream of the inception 

point obervations suggest that some air is entrapped in the step cavity (ies). 

Immediately upstream the flow is extremely turbulent and the free surface is oscillating. 

At irregular time intervals, a water jet impinges on the horizontal step face and air is 

trapped in the step cavity. An instant later, a rapid unsteady flow bulking is observed 

downstream. Velocity measurements indicate that, immediately upstream of the 

inception point, the turbulent velocity fluctuations are large, with dimensionless 

fluctuations u' / V of about 15 - 18 % and normal longitudinal and lateral components of 

turbulent velocity, respectively. Observed values of u' = 0.14 m /s next to the free 

surface are large enough to initate air bubble entraiment. Immediately downstream of 

the inception point, time-averaged air concentration data showed an increased aeration. 

For example, increase in mean air concentration ∆ C = 25% along a distance ∆ x = 6.5 yc 

down a 30 o slope for yc / sh = 5.2 ; an increase in mean air concentration ∆ C = 55 % in 

18 step heights down a 53 o slope for yc / sh < 2 ; an increase in mean air concentration 



∆ C = 32% in 2 step heights down a 22 o slope for yc / sh = 1.1, (where ∆ C is the mean 

air concentration). 


Table : Increase in Mean Air Concentration Over Stepped Spillway 

Increase in 

concentration 

∆ I Bed slope S0 

(in degree) 

c 

Remarks 

∆ C% 

h 

25 6.5 yc 30 5.2 

55 * 53 < 2.0 * Over 18 steps 

32 * 22 1.1 Over 2 steps 

heights 

Reference 

1. BaCaRa, "Etude de la dissipation d' energie sur les evacuateurs a marches", (study 

of the energy dissipation on stepped spillways) Rapport d' Essais, Project National 

BaCaRa, CEMAGREF-SCP, Aix -en-provence, France, October 1991, 111 pages. 

2. BaCaRa. "Roller compacted concrete: RCC for dams. "Presses de l' Ecole Nationale 

des Ponts et Chausse'es, Paris, 1997. 

3. Baker, R. "Brushes clough wedge block spillway - progress report no. 3" SCEL Proj. 

Rewp. No. SJ542-4, University of Saford, U.K, 1994. 

4. Boes R.M, "Physical model study on two - phase cascade flow" , Proc 28th IAHR 

Congress, Graz, Austria, Session S1, 6 pages, 1991. 

5. Chamani, M.R., and Rajaratnam N. "characteristics of skimming flow over stepped 

spillways". J. Hydraulic Engineering, ASCE, 125 (5), 1999, 500 - 510. Discussion by 

Robert M. Boes; Chanson H; Jorge Matos; Ohtsu I, Yasuda Y and Takahashi; Tatewar 

S.P, Ingle R.N, Porey P.D and closure, ibid, November 2000, page 860 - 873. 

6. Chanson H and Toombes Luke "Flow aeration at stepped cascades", Research 

report number CE155, Department of Civil Engineering, Research Report series, 

University of Queensland, June 1997. 

7. Chanson, H. "stepped spillway flows and air entrainment" Can. J. Civil Engineering, 

Ottawa, 20 (3), 1993, 422 - 435. 

y 

s


8. Chanson, H. "Discussion of model study of a roller compacted concrete spillway", J. 

Hydraulic Enginnering, ASCE, 123 (10), 1997b, 931 - 933. 

9. Chanson, H. "Hydraulics of Nappe flow regime above Stepped chutes and Spillways", 

Aust. Civil Engineering Trans., I.E. Aust., Vol. CE36, No. 1, Jan., 1994, pp.69-76. 

10. Chanson, H. "Hydraulic Design of Stepped cascades, Channels, Weirs and 

Spillways", Pergamon, Oxford, UK, Jan., 292 pages, 1995 . 

11. Chanson, H. "Air Bubble Diffusion in super critical open channel flow, Proc. 12th 

Australasian Fluid Mechanics Conference AFMC, Sydney Australia, R.W. Bilger Ed., 

Vol. 2, 1995 , pp. 707 - 710. 

12. Chanson, H. " Prediction of the transition nappe / skimming flow on a stepped 

channel", Jl of Hydraulic Res., IAHR, Vol. 34, No. 3, 1996, pp. 421 - 429. 

13. Chanson, H. "Air bubble entrainment in free surface turbulent shear flows", 

Academic Press, London, UK, 1997, 401 pages. 

14. Chanson, H., and Whitmore, R.L. "Investigation of the gold creek dam spillway, 

Australia. "Research Report No. CE153, Department of Civil Engineering, University of 

Queensland, Australia, 1996, 60 pages. 

15. Chanson H. "Stepped Spillways Parts 1 and 2", Journal of Physcial Science and 

Engineering Periodical, TA1 17526, Volume 5, No. 4, December 1997, Engineering 

update, technical paper number 10, page no. 7 to 12 and Journal of Physcial Science 

and Engineering Periodical, TA1 17256, Volume 6, No. 1, January - March 1998, 

Engineering update, Technical paper No. 2, page no. 9 to 14. 

16. Geoffrey G.S. Pegram, Andrew K. Officer and Samule R. Mottram, "Hydraulics of 

skimming flow on Modeled Stepped Spillways", Journal of Hydraulic Engineering, May 

1999, Volume 125, No. 5, Paper 3557, Discussion by Robert M. Boes; Jorge Matos; 

Ohtsu I, Yasuda Y and Takahashi M; Tatewar S.P, Ingle R.N, Porey P.D; ibid, and 

closure December 2000, page 947 - 953. 

17. Goubet, A. "Evacuateurs de Crues en Marches d' Escalier" (stepped spillways) La 

Houille Blanche, No. 2/3, pp. 247 - 248 , 1992. 

18. Hans - Erwin Minor and Willi Hager editors "Hydraulic of Stepped Spillways", 

Balkema, Rotterdam, The Netherlands, 2000; 201 pages. 



19. Houston, K.L. "Hydraulic Model Studies of Upper Stillwater Dam stepped Spillway 

and Outlet works". Report No. REC - ERC - 87 - 6, US Bureau of Reclamation, Denver 

Co, USA, 1987. 

20. Ruff. J.F. and Frizell, K.H, "Air concentration measurements in highly turbulent flow 

on a steeply sloping chute", Proceeding Hydraulic Engineering Conference, ASCE, New 

York, Vol. 2, 999 - 1003. 

21. Stephenson, D. "Energy dissipation down stepped spillways" Water Power and Dam 

construction, September, 27 - 30, 1991. 

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Institution of Engineers (India), Volume - 79, Page- 175 - 179, Feb. 1999. 

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Proceeding International Seminar on Civil Engineering Practices in 21st Century, 

Roorkee, India, 1039 - 1048. 

24. Tozzi, M.J. "Residual energy in stepped spillways. "International water Power and 

Dam construction, 1994, 46 (5), 32 - 34. 

25. Virender Kumar, Stepped Spillway - a State of the art, Journal of The Institution of 

Engineers (India), Volume - 82, Page- 217 - 223, Feb. 2002. 

26. Vischer D.L. and Hager W.H. "Dam Hydraulics", John Wiley and Sons, 1997. 

27. Yildiz, D., and Kas, I, "Hydraulic performance of stepped chute spillways", 

Hydropower and Dams, 1998, 5 (4), 64 - 70.

35.2 Stepped or Cascade Spillways (Fig. 35.4) - nptel - Indian ...

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