INTRODUCTION
Dissipation of kinetic energy generated at the base of a spillway is essential for bringing the flow into the downstream river to the normal condition in as short of a distance as possible. This is necessary not only to protect the riverbed and banks from erosion but also to ensure that the dam itself and adjoining structures like powerhouse, canal, etc. are not undermined by the high velocity turbulent flow.
Stilling basins include horizontal or sloping aprons equipped with chute blocks,
baffle piers and end sills are the most common type of energy dissipaters. These
structures affects up to 60% dissipation of the energy entering the basin depending
of the Froude Number of the flow. Different type of basins have been studied
by USBR and its performance has been classified (Peterka,
1983). But in large dams because of special conditions, these mentioned
samples for stilling basins were not secure. For example according to the studies
carried out in water research institute, in Masjed Soleiman dam, the stilling
basin was adjacent to powerhouse outlet so the stilling basin walls were not
continued to the end and have been performed in overflow condition. Furthermore
the velocity and Froude Number were widely larger than global recommended values.
By construction and study of physical models we can optimize the length, dimensions,
location of baffle piers and chute blocks in stilling basin and degree of protection
needed for tail water in different flood passages and then select the optimized
arrangements of these elements in design. Extensive works on different parameters
in physical models of stilling basin has been done. Some of these relevant experiences
are implied in the following:
Posey and Hsing (1938) studied the effect of lateral
slope on hydraulic jump length in trapezoidal basins. This experiment was conducted
in a model with variable slope between 0.5:12:1 and stated that, when lateral
slope decreased, the length of the jump increased compared with rectangular
channel. Wanoschek and Hager (1989) by experimental
investigation implied that for trapezoidal channel with 1:1 lateral slope in
comparison with rectangular channel, depth ratio decreased and the length of
jump increased. Omid (1996) studied hydraulic jumps
in trapezoidal stilling basins and showed that compared with rectangular basins
for decreasing lateral slope, relative length of jump and dissipated energy
increases.
Complication of converged or diverged hydraulic jump relations compared with
normal jump is a result of existing lateral force in momentum equation. Arbhabhirama
and Albella (1971) investigated hydraulic jump in diverged rectangular channel
in 0 to 13 degrees of diversion and showed that diversion causes increasing
in relative energy dissipation and decreasing in depth ratio and jump length.
Esmaeeli varaki (2003) investigated diverged hydraulic
jump in rectangular channel with 0.5x9x0.6 meter (widthxlengthxdepth) dimensions
for 0.5:1, 1:1, 1.5:1 lateral slope, 5 and 7 degrees of divergence and 3 to
9 Froude number. According to the results in this trapezoidal sections decreasing
in degree of diversion for each lateral slope compared with direct trapezoidal
section(i.e., lateral slope = 0), decreases depth ratio and jump length and
increases the percent of relative energy dissipation.
Experimental studies shows that using the new roughened bed, the length of
the basin can be decrease as low as 40% of the regular basins (Bejestan
and Neisi, 2009).
Ezizah et al. (2012) have performed to investigate
the effect of change of intensity and roughness length parameters on the hydraulic
jump length.
Analysis of experimental data shows that the Froude number in smooth bed hydraulic
jump decreases the conjugate depth 20% and the hydraulic jump length 50% (Izadjoo
and ShafaiBejestan, 2007).
Rizi et al. (2006) said that the discharge variation
as a boundary condition for moving hydraulic jump parameter could reliably be
determined based on time independent relationships.
According to performed researches, there is no systematic experimental study for investigate the effect of convergence on hydraulic jump operation and because of complication in flow pattern in this cases, this research investigated the effect of convergence of stilling basin walls on energy dissipation condition and jump formation in stilling basin.
MODEL AND TEST EQUIPMENT
Nazloochay earthfill dam with 100 m high is constructing in northwest of Orumieh.
The designed stilling basin for dam was a II type of USBR for probable maximum
flood of 2270 cm. Thus with these conditions (i.e., height of dam and type of
stilling basin), this case selected for experiments and hydraulic model was
constructed. The following model includes three linked parts:
• 
Flood discharge system: 

• 
Approach canal 

• 
Free ogee spillway 

• 
Converged chute 

• 
Stilling basin 
• 
Downstream tank with (6.1x7.65x1.25 m, heightxlengthxwidth)
dimensions 
With respect to thickness of water layer on spillway for preventing viscose effects and surface tension and laboratory limitations, 1:40 model scale was selected. Regulated amount of water pumped into model and its discharge measured with rectangular weir setup downstream. For regulating water level the sluice gate used at the end of canal in model.
The length and width of stilling basin in prototype are 43 and 30 m. Stilling basin model and other parts of it such as chute constructed of transparent plexiglas and baffle piers was made of wood covered with oily color. The inception of canal (i.e., after spillway) with 21 m length in prototype connected from stilling basin bed to river bed with 3:1 (horizontal: vertical) adverse slope. Bed level of basin is 1396 masl and river bed level is 1403 masl. Topographic surface constructed up to 1415 masl level based on map. The upper level of stilling basin walls is 1411 masl (Fig. 13).

Fig. 1: 
Physical model layout 

Fig. 2: 
Schematic plan of model 

Fig. 3: 
Stilling basin cross section 
Test procedure: According to project hydrologic studies, design flood
of stilling basin is 500 cm with return period of 1000 year. Experiments were
done for six discharges as summarized in Table 1 for surveying
the effect of discharge. For each discharge, the values of depth, velocity and
static pressure in basin sections were measured as defined in Table
2 and 3 and Fig. 4. Depth measured with
Eshel. Because of flow fluctuation in basin measuring accuracy in model was
±5 mm. Velocity measured with micro mulline with ±1 m sec^{1}
accuracy in model. Also hydraulic jump type and location, situation of return
flow and submergence of basin walls were investigated in each discharge for
study the effect of variety of discharge on hydraulic parameters.
RESULT ANALYSIS
Nazloochay dam stilling basin had been designed as a II type USBR standard
model according to project condition (Fig. 5a).
Table 1: 
Range of discharges 

Table 2: 
Location of sections in stilling basin 

Table 3: 
Location of bed piezometers 


Fig. 4: 
Stilling basin sections for depth, velocity and static pressure
measuring 
Construction of physical model and perform experiments showed that this stilling
basin cannot dissipate the energy safe and sufficiently, in some points the
static pressure were negative, so in first change in basin design, the inclined
end sill removed by three steps (Fig. 5b) for increasing tail
water depth.
Although, this change had been done for stabilizing jump in basin but there are serious problems in basin operation especially in large discharges, yet. In such condition hydraulic jump move downstream and the flow left basin with high velocity, so caused erosion downstream of stilling basin like a ski jump bucket.
Thus for increasing depth ratio and stabilize jump in basin we need other preparation,
so in this research the effect of the convergence of stilling basin walls and
submergence caused by it, on hydraulic jump properties, energy dissipation and
tail water condition has been investigated. Experiment has been done for 5,
7.5, 10, 12.5 degree of convergence of stilling basin walls. The converged walls
were installed symmetrically in stilling basin as shown in Fig.
5c and 6.
Depth: The effect of convergence of walls on depth variation for 82
L sec^{1} discharge in various sections has been showed in Fig.
7. According to diagram with converged walls has been increased in all sections
compared with parallel walls.

Fig. 5(ac): 
Stilling basin arrangements 

Fig. 6: 
Converged walls stilling basin (schematic plan and cross
section) 
For each degree of convergence by increasing discharge, minimum depth decreases
in measuring section and maximum depth increases, because by increasing discharge,
hydraulic jump moves downstream relative to initial measuring section (Fig.
8).

Fig. 7: 
Depth variation for 82 L sec^{1} discharge in various
sections and degrees 

Fig. 8: 
Depth variation for 7.5 degree of convergence and various
discharges 

Fig. 9: 
Surface profile in 82 L sec^{1} discharge in parallel
walls stilling basin 
Figure 9 and 10 which show the water surface
profile in 82 L sec^{1} discharge in parallel and converged walls condition,
certify this result also. While it is observed that for parallel walls condition
the water surface profile is concave which is showing free hydraulic jump and
for parallel walls condition, the water surface profile is convex and hydraulic
jump is submerged (Fig. 9 and 10). In this
case no negative static pressure was observed.

Fig. 10: 
Surface profile in 82 L sec^{1} discharge in converged
walls stilling basin 

Fig. 11: 
Flow condition for 178 L sec^{1} discharge (parallel
walls) 

Fig. 12: 
Flow condition for 178 L sec^{1} discharge (converged
walls, 10 degree of convergence) 
Velocity: The velocity was measured in four sections (N,O,P,Q) as described
above in 20 and 80 percent of depth from surface. Therefore the mean velocity
was calculated by averaging two measurements. The velocity variation for 82
L sec^{1} discharge has been showed in Fig. 13 by
the effect of converged walls in stilling basin on water flow (Fig.
12), the velocity quantity in ending section (x = 7.88 m), has been decreased
compared with parallel walls condition (Fig. 11).
Table 4: 
Calculated efficiency in various conditions 


Fig. 13: 
Velocity variation for 82 L sec^{1} discharge in
sections 

Fig. 14: 
Location of measuring y1, y2 
So in this case, stilling basin has been transformed shallow depth flow with
high velocity of entrance (at x = 7.13 m), to a deep low velocity flow in the
ending section(at x = 7.88 m). Therefore, stilling basin has good operation
in energy dissipation and causes less erosion downstream.
Efficiency: Hydraulic jump operation efficiency were calculated by equations 13 in all experiment conditions (parallel and converged walls) and has been shown in Table 4. Initial depth of jump (y1) has been measured on sections while surface roller is formed and conjugate depth (y2) has been measured at the end of surface roller as shown in Fig. 14. According to results, hydraulic jump operation in converged wall stilling basin is better than parallel wall basins and the effect of convergence increases by increasing discharge. The variation of efficiency (especially in 82 L sec^{1} discharge) is not affected by variation of degree of convergence and so 5 degree of convergence has the best operation.
CONCLUSION
For large dams according to special conditions, we cannot design standard stilling basins without physical modeling.
Nazloochay dam stilling basin was a II type USBR standard basin that had not good performance. So its arrangement was changed by physical modeling and its end sill removed by three steps. Application of three steps instead of end sill blocks at the end of stilling basin was not successful on stabilize the hydraulic jump in the basin specially in large discharges thus converged walls were installed in basin that leads to below results:
• 
For each degree of convergence by increasing discharge, minimum
depth decreases in measuring section and maximum depth increases, because
by increasing discharge, hydraulic jump moves downstream relative to initial
measuring section in all experimented degrees, submerged hydraulic jump
formed, so downstream erosion will be decreased 
• 
Convergence has positive effect on energy dissipation and
efficiency of hydraulic jump and 5 degree of convergence has the best operation 