technical paper hydraulics of stepped spillways with different numbers...
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TECHNICAL PAPER
Hydraulics of stepped spillwayswith different numbers of stepsThis paper describes the study of two physical models that were
built to investigate the energy dissipation and flow regimes for
different discharges over stepped spillways with different numbers
of steps. These physical models had a general slope of 19?2% and
had 12 and 23 steps respectively. Experiments were carried out for
a wide range of discharges. The hydraulic parameters of the flow
over the models were measured and the energy dissipation of flow
was also calculated. Results showed that the 12-step model
dissipated more energy than the 23-step model. However, the flow
regimes that occurred in the 23-step model were considered more
acceptable than in the 12-step model. The experiments showed
that energy dissipation at lower flow rates were similar in both
cases. However, in the skimming flow regime at higher discharges,
energy dissipation was about 12% less in the 23-step model than in
the 12-step model.
IntroductionStepped spillways, in which a series of steps are built
into the sloping floor of the spillway, can be used to
convey flood flows at dams, dissipating some of the
energy of the flow as it passes over the steps.
Depending upon the flow rate for a given stepped
spillway geometry, the flow over a stepped spillway may
be divided into three distinct flow regimes – nappe,
transition and skimming flow – in the order of
increasing flow rates.1 Nappe flow is observed for a
small dimensionless discharge dc/h (where dc is the
critical flow depth and h is the step height) and is
characterised by a succession of free-falling nappes at
each step edge, followed by nappe impact on the
downstream step. The skimming flow regime is
observed for the largest discharges; the water skims
over the pseudo-bottom formed by the step edges as a
coherent stream. Beneath the pseudo-bottom, intense
recirculation vortices fill the cavities between all step
edges.2 These recirculation eddies are maintained by
the transmission of shear stress from the main stream
flow and contribute significantly to the energy
dissipation. Gonzalez1 observed air cavities of different
size, alternating with fluid-filled recirculation vortices,
between step edges below the main stream of the flow.
In the recent past, much research on stepped spillways
has been carried out on different hydraulic parameters
such as flow regimes, inception of air entrainment, air
concentration, velocity distributions and energy
dissipation (examples being Gonzalez,1 Barani et al.3
and Meireles and Matos4).
Experiments on a moderately sized stepped spillway by
Christodoulou5 indicated that the energy loss owing to
the steps depended primarily on dc/h as well as on N
(the number of steps). For values of dc/h near unity, or
near the limit of skimming flow, the stepped surface
was very effective in dissipating energy. For higher
values of dc/h, the effect of N became appreciable at a
certain dc/h, which indicated that the relative energy
loss increased with N.
Pegram et al.6 studied two different physical models of
stepped spillways of slope 60% with the same crest shape,
30 m height and a range of step sizes (0?25 to 2?0 m in a
1:10 scale model and 0?5 to 2?0 m in a 1:20 scale model).
They showed that the residual specific energy was
independent of the step sizes. But this energy at the toe of
a stepped spillway of height 50 m (or higher), within the
range of step heights tested, was less than 60% of the
residual specific energy at the same level on a similar
smooth spillway experiencing flows up to 20 m3/m2.
In the present study, two sets of experiments were
carried out using physical models. In the first set,
experiments were performed to investigate the effects
of different discharges and numbers of steps on the
flow regimes at stepped spillways. In the second set,
energy dissipation on the same flow and geometry
131
Dams and Reservoirs2010 20, No. 3, 131–136DOI: 10.1680/dare.2010.20.3.131
R. RoshanMSc
Hydraulic StructuresDivision, Water ResearchInstitute, Tehran, Iran
A. Ab GhaniMSc, PhD
River Engineering andUrban DrainageResearch Centre(REDAC), Penang,Malaysia
H. Md.AzamathullaME, PhD
River Engineering andUrban DrainageResearch Centre(REDAC), Penang,Malaysia
M. MarosiMSc
Shahid ChamranUniversity of Ahvaz,Ahvaz, Iran
H. PahlavanMSc
Shahrood University ofTechnology, Shahrood,Iran
H. SarkardehMSc
Hydraulic StructuresDivision, Water ResearchInstitute, Tehran, Iran
www.damsandreservoirs.com ISSN 1368-1494 f 2010 ICE Publishing
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conditions was measured to assess the effect of thenumber of steps and of the different step heights.
Experimental set-upThe physical model of the Khansar Dam and Spillway(Yazd-Iran) was built in the hydraulic structureslaboratory of Iran’s Water Research Institute (WRI) tostudy the spillway’s energy losses and flow regimes. The
toe elevation of this dam was 1941?9 m, crest elevation1953?5 m, width of the spillway was 65 m, the maximumflow per unit width of the spillway (q) was 16?15 m3/m2
and the maximum flow passing over the spillway (Q)was 1050 m3/s. The scale of this physical model wasselected as 1:20. The vertical height of the model(difference between crest and toe elevations) was0?78 m. The maximum flow in the modelled spillway
132
Figure 1. Views of the physical models
1957.50
1953.50
1951.5011 1
1
23
Spillw
ay a
xis
Figure 2. A schematic view of ogee spillway of the model
Table 1. Flow regimes of 12-step and 23-step models
qm : m3/m2 dc: m 12-step 23-step
0?026 0?041 NA TRA
0?034 0?049 NA TRA
0?045 0?059 TRA TRA-SK
0?052 0?065 TRA TRA-SK
0?069 0?078 TRA SK
0?086 0?091 TRA SK
0?095 0?097 TRA-SK SK
0?103 0?103 TRA-SK SK
0?120 0?114 TRA-SK SK
0?138 0?125 SK SK
0?155 0?135 SK SK
0?172 0?144 SK SK
0?181 0?149 SK SK
The types of flow regimes in Table 1 are: NA 5 nappe flow, TRA 5 transition flow, SK 5 skimming flow and TRA-SK 5 transitionto skimming flow.
ROSHAN ET AL.
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00 0.60.4
h/l
d c/h
0.2
2.0
1.5
1.0
0.5
2.5
Upper limit of transition flow7
Lower limit of transition flow7
12-step: lower limit
12-step: upper limit23-step: upper limit
Figure 3. Flow observations in comparison with Chanson and Toombes7 equations
Step 3
Step 2Step 1
Nappe flow
Solid flow
Figure 4. Nappe flow at low flow rates
Step 2
Step 3
Step 4
Step 5
Step 6
Figure 5. Skimming flow at high flow rates
HYDRAULICS OF STEPPED SPILLWAYS WITH DIFFERENT NUMBERS OF STEPS
Dams and Reservoirs 2010 20, No. 3, 131–136
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was 0?118 m3/s. The general slope of the model was
19?2%. A rectangular weir, which was installed in the
canal at the downstream end of the model, was used to
measure the flow rate passing the stepped spillway. A
water gauge with 0?1 mm accuracy was used to measure
the depths of flow at the upstream and downstream
ends of the model.
To evaluate the effect of the number of steps, two cases
with 12 and 23 steps were built (by fixing the other
parameters of the Khansar dam model). These two
laboratory cases with the same slope were made of
PerspexR and the step properties were as follows:
length 5 33?7 cm, height 5 6?5 cm for 12-step case and
length 5 16?8 cm, height 5 3?25 cm for 23-step case
(Figures 1 and 2).
Experimental resultsFlow regime observationOn the stepped spillway, the nappe and transition flow
regimes were observed for the low range of water
discharges and skimming flow regime occurred for the
upper range of water discharges. In the 12-step case, for
water discharges less than 0?138 m3/m2, nappe or
transition flows was observed and skimming flow was
observed for discharges of 0?138 m3/m2 and larger. In
the 23-step case, the limit between skimming and
transition flows was 0?069 m3/m2 (Table 1).
134
Figure 6. Strong spray and splashing in transition flows
Figure 7. Strong hydrodynamic fluctuations downstream of the inception point
ROSHAN ET AL.
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Chanson and Toombes7 presented two equations whichshowed the lower and upper limits of transition flows.In this part, experimental observations using the samedefinitions of nappe, transition and skimming flows areplotted in Figure 3. For the lower limit this equation is
1dc
hw0:9174{0:381
h
l0v
h
lv1:7
� �
and for the upper limit is
2dc
hv
0:9821
h=lð Þz0:388½ �0:3840v
h
lv1:5
� �
where l is the step length. Equations 1 and 2 are plottedin Figure 3. The measured data of changes in flowregimes showed good agreement with the findings ofChanson and Toombes7 for the threshold betweennappe flow and transition flow, at a dc/h value ofbetween 0?75 and 0?91 in the 12-step model. However,
there was a rather higher threshold for the boundary
between transition flow and skimming flow, at between
1?75 and 1?92 in the 12-step model and between 2?0
and 2?4 in the 24-step model.
Experimental observations of flow regime for the 12-
step case showed that, for discharges less than 0?045
m3/m2, water cascaded down the spillway as a
succession of free-falling nappes from one step to
another (Figure 4). Flow visualisations permitted clear
and precise views of the intense recirculation taking
place in the cavities between step edges for both
transition and skimming flow regimes. Skimming and
transition flows have distinct appearances. In skimming
flows, the water skimmed smoothly over the pseudo-
bottom formed by the steps (Figure 5).
In transition flows, the water exhibited a chaotic
behaviour associated with the intensive recirculation in
cavities, strong spray and splashing (Figure 6).
Downstream of the inception point, splashing and spray
135
Figure 8. Air entrainment in transition flows
HYDRAULICS OF STEPPED SPILLWAYS WITH DIFFERENT NUMBERS OF STEPS
Dams and Reservoirs 2010 20, No. 3, 131–136
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were observed next to the free surface with waterdroplets that jump out of the flume (Figure 7).
Free-surface aeration was very intense in all transitionflow rates downstream of the inception point of free-surface aeration; rapid free-surface aeration wasobserved. The location of the inception of free-surfaceaeration was clearly defined (Figure 8).
Energy dissipationTo determine the energy dissipation from upstream todownstream, experiments with different flow rates andnumbers of steps (two cases) were carried out. Bymeasuring the hydraulic characteristics of flow upstreamand downstream of the model and based on theBernoulli equation, the total head losses in each casewere calculated. The percentage of dissipated energy ineach case was then determined and plotted (Figure 9).
As can be seen from Figure 9, generally, the energydissipation decreased with increasing dimensionlessdischarge number in both models. This non-dimensional discharge parameter is defined byq� ffiffiffiffiffiffiffi
g hp
P , where P is the height of spillway from crestto toe. Also, the 12-step case results in greater energydissipation than the 23-step case. Thus, it can be statedthat increasing the number of steps in a given height ofthe spillway decreases energy dissipation, because of
the reduced step height. Moreover it should be notedthat flow regimes over a stepped spillway have a greateffect on energy dissipation. For example, a nappe flowregime is more efficient for energy loss than a skimmingflow. This phenomenon could occur in lowerdischarges or higher steps (in the present study, thisoccurred in the 12-step case). Overall it could beconcluded from Figure 9 that the 12-step casedissipated about 12% more energy than the 23-stepcase.
ConclusionsIn this research work, two different models were usedto show the effect of the number of steps on flowregimes and energy dissipation over stepped spillways.Experiments were conducted over a wide range ofdischarges. By observing and measuring the hydraulicparameters, the effect of the number of steps wasevaluated.
Flow regimes visualisation indicated that, in the 12-stepcase, for water discharges less than 0?138 m3/m2, nappeor transition flows were observed and skimming flowsoccurred for discharges larger than 0?138 m3/m2. In the23-step case, the limit between skimming and transitionflows was equal to 0?069 m3/m2. It is interesting to notethat the 12-step case had more effect on energydissipation than the 23-step case.
REFERENCES1. GONZALEZ C. A. An Experimental Study of Free Surface Aeration on Embankment Stepped Chutes. PhD Thesis, Department of Civil
Engineering, University of Queensland, Australia, 2005.2. CHAMANI M. R. and RAJARATNAM N. Characteristics of skimming flow over stepped spillways. Journal of Hydraulic Engineering, ASCE,
1999, 125, No. 4, 361–368.3. BARANI G. A., RAHNAMA M. B. and SOHRABIPOOR N. Investigation of flow energy dissipation over different stepped spillways. Journal of
Applied Science, 2005, 2, No. 6, 1101–1105.4. MEIRELES I. and MATOS J. Skimming flow in the nonaerated region of stepped spillways over embankment dams. Journal of Hydraulic
Engineering, 2009, 135, No. 8, 685–689.5. CHRISTODOULOU C. Energy dissipation on stepped spillways. Journal of Hydraulic Engineering, 1993, 119, No. 5, 644–650.6. PEGRAM G. G. S., OFFICER A. K. and MOTTRAM, S. R. Hydraulics of skimming flow on modeled stepped spillways. Journal of Hydraulic
Engineering, 1999, 125, No. 5, 500–510.7. CHANSON H. and TOOMBES L. Hydraulics of stepped chutes: the transition flow. Journal of Hydraulic Research, 2004, 42, No. 1, 43–54.
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00
23-step model 12-step model NA TRA TRA-SK SK
Ener
gy d
issi
patio
n: %
0.05 0.15
q/(gdc)0.5P
0.10 0.20
90
80
70
60
50
40
30
20
10
100
Figure 9. Energy dissipation for the 12-step and 23-step models
ROSHAN ET AL.
Dams and Reservoirs 2010 20, No. 3, 131–136