# Experimental study of environmental effect of installing deflector on energy dissipation and dynamic pressure fluctuations on stepped spillways.

INTRODUCTION

Increasingly growth of population, as well as improvement of technology are elements for loss of water in world and it causes about third of world population live with anxiety of crisis of drought and pollution. This crisis has created economical depression in many regions of world. Nowadays developing in industrial and agricultural fields, as well as increasingly growth of population in cities, make it essential to maintain and protect available limited resources of underground and surface water. If we add gradual warming of air in the earth into above problems, that leads into lack of raining in dry and semi-dry regions, we findout that making new designs to use and maintain existing water, is important. Building dams and spillway on them, is one of the methods of managing water resources. In recent years and thanks to technology improvement of builing dams by R.C.C method, applying stepped spillway has considered much attention [2, 3]. In this method, thickness of concrete layer is between 0.3 to 1 meter[11, 14].

The most important advanteges of stepped spillway includes: a) easy of build and economical, b)risk of cavitation on steps decreases because of entering air into flow, c)dimensions of stilling basin in toe of dam decrease because of increase in flow energy loss by steps of spillway [2, 3]. Most studies related to condition of flow in stepped spillway, have done in recent years [4, 5, 6, 7, 8, 9, 10, 13].

Much of studies are related to case experiment in a special structure and obtaining results related to general condition of flow in stepped spillway. Other studies are related to following cases: a) condition of flow related to passing water discharge per unit width; b) different regimes of flow and range of discharge making these regimes; c) energy loss and flow velocity in downsteam of chute [14]. d) amount of air concentration in flow passing spillway and its effect on energy dissipation. One of the characteristics of stepped spillway is limitation in ((water discharge per unit width)) of flow passing over it which have been stated (25-30[m.sup.3]/s/m) by researchers that has significantly more limited application, in comparision with smooth spillway that passes q=100 [m.sup.3]/s/m [11, 14].

Reason of this limitation, is generating skimming flow over spillway and making non-aeration zone(black water) in distance of spillway crest to inception point of aeration. This phenomenom leads to decrase of pressure on steps and creating cavitation on them. Because of entering natural air into flow and increase in air concentration near bed of downstream steps, risk of creating cavitation will be reduced effectively[2, 3, 5, 6]. stated that one way to reduce cavitation risk in upper part of spillway--before inception point--is installing deflector and aerator in first steps of spillway and air entrance through it into flow. This has much influence on increasing pressure on steps and decreasing cavitation risk and finally increases the ability of spillway to pass water discharge higher than (25-30[m.sup.3]/s/m) [15].

Boes et al., [2, 3] stated that installing deflector decrease black water length and causes that inception point occure in shorter length of spillway. They stated that by installing deflector , energy dissipation increases on the spillway and residual energy at the toe of spillway decreases significantly.

The hydrodinamic pressure field on the channel steps is an important factor affecting the design and safety of stepped spillway. Amador et al., [1] stated that the zone near the inception point of air entrainment will be critical in terms of the risk of cavitation damage. They studied characterizing the developing flow region and examined the pressure fluctuation on the steps induced by the skimming flow. They stated that the largest dynamic pressure are present on the horizontal face near the step edge where pressure are governed by the impact of the overlying flow. On the vertical faces, the pressure are affected by flow separation from steps face [1].

In this study, effect of installing different types of deflectors has been studied on: a) energy loss on stepped spillway; b) distribution of dynamic pressure on vertical and horizontal surface of steps; c) created jet length over deflector; d) volume of air entering into flow.

MATERIALS AND METHODS

Experimental facilities:

In this study effect of installing types of deflector have been studied on replacement of inception point, as well as increase in passing water discharge. Experiments have been done on two models of stepped spillways of plexiglass material which their characteristics have been written in Table 1.

In this table: N=number of step; b=width of spillway; 1=horizontal step length; h= step height and [THETA]= slope of stepped channel. Water flow has been entered to a tank in dimensions of (11x11x5) through pumps of existing channel in lab and entered to a spillway by two guide walls and after passing stepped chute and stilling basin of downstream, entered wooden flume and again retured to channel. In order to water discharge measure gauge available beside spillway, as well as sharpe edge rectancular spillway in downstream chute has been used, by which rating curve has been prepared for these stepped spillways. Measuring depth of flow has been done by a Point gauge with accuracy of 1mm and measuring flow velocity by Pitot-static tube.According to condition of each experiment,10 to 15 cross-sections have been considered and in each cross-section, in three points (b/4,b/2,3b/4), depth and flow velocity have been measured. In order to measure accurate pressure fluctuations, a pressure transducer with six sensors has been used. Experiment time in each point is determined 30 seconds and recieved data rate is determined 200 data per second. Totally 6000 data in each point is acceptable data to analyze pressure fluctuation. In order to inject air into passing water flow over deflector, an aerator with dimensions of 5.5x6cm was installed on model no.1 and an aeraor with dimensions of 4x4cm was installed on model no.2. these aerators have suitable cabs and a hole by diameter of 1cm to enter ((hot-wire)) device that computed velocity of passing air inside aerator in m/s. Measuring partial negative pressure obtained of installing deflector and closing aerator, is computed by a U-tube manometer.

Characteristics of deflectors:

In experiments done on model no.1, four types of deflector--types 1, 2 and 4 with triangular cross-section and type 3 with trapezoidal cross-section. on model no.2, deflector type 1 has been installed in end of ogee spillway and before first step and has L--6cm and angles of [phi] 4,9,14 5,18,22(deg). Deflector type 2 has been installed on upper part of vertical face of first step and above pseudobottom and has two slopes [phi] = 5,10(deg). Deflector type 3 has been installed on upper part of vertival face of first step and under pseudobottom and has characteristics that have been written in Table 2. Deflector type 4 has characteristics as type1 but has been applied as jagged in width of spillway(Fig. 1).

Dimensional Analysis:

In order to dimentional analysis to determine energy dissipation in condition of not installing deflector that is necessary to determine parameters which have influence on amount of energy loss, according to previous studies[5, 6, 9, 10], energy loss in stepped spillway depends on, [H.sub.0]: total energy in upstream of spillway, q: wate discharge per unit width of spillway, h :height of step, l :length of step, [[rho].sub.w] :density of water, [sigma] :surface tension between water and air, [f.sub.e] :coefficient of roughness of spillway bed, N :number of steps, [mu] : dynamic viscosity of water and g :gravity accelaration. Thus relation between these quantities is as follow:

F([DELTA]H, [H.sub.0], q, h, l, [[rho].sub.w], [sigma], [f.sub.e], N, [mu], g) = 0 (1)

number of variables aqualn -11 and number of basic dimensions equal m--3. According to Buckingham Pi method, n - m = 11 - 3 = 8 dimensionless parameters can be defined that final resuls are as follow:

f([DELTA]H/h, [H.sub.0]/h, [y.sub.c]/h, h/l, [sigma]/[[rho].sub.w]g[h.sup.2], [f.sub.e], [mu]/[[rho].sub.w]g[h.sup.2], [f.sub.e], [mu]/[[rho].sub.w] [square root of (g[h.sup.2])], N) = 0 (2)

[FIGURE 1 OMITTED]

by ignoring the effect of fluid viscosity [mu] and surface tension [sigma] and by few operations on stated parameters effected on energy loss in stepped spillway in condition of not installing deflector as follow:

[DELTA]H/[H.sub.0] = f([y.sub.c]/h, h/l, N. [f.sub.e]), (3)

Dimensional Analysis to determine energy dissipation in condition of installing deflector:

Effective parameters in this condition can be stated as follow:

F([DELTA]H, [H.sub.0], q, h, l, [[rho].sub.w], [sigma], [f.sub.e], N, [mu], g, tan [phi]) = 0 (4)

Where: tan [phi] : slope of deflector installed over spillway. Finally it can be stated, dimensionless parameters effective on energy loss in stepped spillway in condition of installing deflector as follow:

[DELTA]H/[H.sub.0] = f([y.sub.c]/h, h/l, N, [f.sub.e] tan[phi]) (5)

Results:

Hydraulic jump sequent depth in stilling basin:

Computing energy loss in downstream of stepped spillway is very difficult through direct measuring of depth and velocity of flow, because of foamy flow and high turbulance waves. So in this paper, reverse computing method has been used in which at first sequent depth([y.sub.2])of hydraulic jump in stilling basin is measured- where the oscillation of water surface and number of bubble in flow is few- and then initial depth([y.sub.1]) is calculated using standard hydraulic jamp equations. With water discharge and initial depth([y.sub.1]), quantity of specific energy ([E.sub.1]) existing in spillway toe can be determined with desirable accuracy[14].

Energy loss:

Fig. 2 presents energy loss of flow in condition: 1) not installing deflector and 2) installing deflector and closing aerator in defferent models.

Table 3 shows value of difference average in energy loss, in condition of installing deflector and closing aerator relative to not installing deflector condition in pecent.

Results obtained of experiments state that: a) in stepped spillway when flow discharge increases, remained energy increases in toe of spillway. In other words, energy loss decrease as water discharge increase. b) in a constant flow discharge, the value of energy loss increases as dimensions of deflector enlarge which its reason is shortening length of black water zone and faster formation of inception point of aeration. As a result, the number of vortex increases in stepped spillway and existance of such vortex lead to make energy loss. c) for a deflector with constant dimensions, energy loss decreases as flow discharge increases. d) installing deflector causes increase in energy loss in stepped spillway.

Fig. 3 presents energy loss of flow, in condition of installing deflector and opening aerator in different models. Table 4 shows value of difference average in energy loss, in condition of installing deflector and openin aerator relative to condition of not installing deflector in pecent.

Deflector type 1:

in condition of open aerator and air entrance into passing flow, below results are obtained: a) in a constant flow discharge, the value of energy loss increase as dimensions of deflector increases that as noted befor, shorten length of black water zone, more air enters flow through aerator and more vortices forms in stepped spillway, energy loss increases.

b) for a deflector with constant dimensions, energy loss decreases as flow discharge increases. a)in open aerator and entering air into flow, enrgy loss is more than closed aerator condition.

Deflector type 2:

in condition that deflector is installed on vertical face of first step above pseudobottom bottom, similar to type 1, energy loss decreases when flow discharge increases for a deflector with certain dimensions, and in a constant flow discharge, energy loss increases as dimensions of deflector increase.

In experiments related to deflector type 2, ultimate deflector angle is 10 degree and by increase in angle, severe contact of flow are seen with deflector and producing turbulance and forming irregular waves in flow surface.

Deflector type 3:

in condition that deflector is installed on vertical face of first step below pseudobottom, it is seen that in a constant flow discharge with replacement of deflector in different points, although overlap is seen between results but energy loss increases than condition of not installing deflector, but have less efficacy on energy loss than deflectors type1 and type 2 -without comparision between different types of deflectors because of their different shapes.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Deflector type 4:

in this condition, jagginess of deflector shortens the width of spillway. So flow passes a smaller crosssection. Observations show that flow comes into contact with downstream steps as falling jet and severe waves and oscillations are formed in passing flow. By examining the results obtained of experiment, following equations can be stated to anticipate enrgy loss in stepped spillways:

a) not installing deflector condition:

[DELTA]H/[H.sub.max] = 1 -[[([f.sub.e]/8 sin [theta]).sup.0.347] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.697]/1.5 + [H.sub.dam]/[d.sub.c]]

b) installing deflector and close aerator condition:

[DELTA]H/[H.sub.max] = 1 -[[([f.sub.e]/8 sin [theta]).sup.0.345] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.697]/1.5 + [H.sub.dam]/[d.sub.c] [(tan [phi]).sup.-0.081]] (7)

c) installing deflector and open aerator condition:

[DELTA]H/[H.sub.max] = 1 - [[([f.sub.e]/8 sin [theta]).sup.0.346] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.628]/1.5 + [H.sub.dam]/[d.sub.c] [(tan [phi]).sup.-0.077]] (8)

Negative partial pressure resulted from instating deflector:

In condition of installing deflector and closed aeraor, negative partial pressure is produced in the distance between deflector and first step surfaces because of the separation of stream lines from steps surface and this negative pressure causes air entrance and forming outlet jet from deflector in an open aerator condition. Fig. 4 shows negative partial pressure of flow, in condition of installing deflector and closed aerator in different models.

Table 5 shows the value of difference average of negative partial pressure of flow-in condition of installing deflector and closed aerator-relative to deflector with angle [phi] = 9 deg in percent.

The results obtained of experiment state that:

Deflector type 1:

a) with increase in water discharge, negative pressure of flow increases due to increase in existing energy in flow and tendency to seperate from surface of spillway. b) in a constant flow discharge, negative pressure increases as the dimensions of deflector increase that is because of contact of flow with greater obstacle and seperation of stream lines from surface of steps. c) for a deflector with constant dimensions, increase in flow discharge lead to increase in negative partial pressure of flow.

Deflector type 2:

similar to type 1, for a deflector with constant dimensions, negative partial pressure increases as flow discharge increases. Totally, deflector type 2 has less efficacy on negative partial pressure than type 1. In this case, it is observed that in a constant flow discharge in different points, overlap is seen between observed data but negative partial pressure increases relative to condition of not installing deflector. Overall, deflector type 3 has less efficacy than tow other types of deflector. With examining the results obtained of experiments following equations can be stated to anticipate the negative partial pressure in stepped spillway in condition of installing deflector and closed aerator in which [DELTA]p is negative partial pressure:

[DELTA]p = [alpha][([y.sub.c]/h).sup.[beta]] (9)

[alpha] = 1.8e [0.99.sup.(tan[phi].tan[theta])] (10)

P = 1.47 [e.sup.0.29(tan[phi].tan[theta])] (11)

Discharge of air entering from aerator:

As stated before, installing deflector and closing aerator causes negative pressure in the space under deflector, and if the aerator would be opened in this condition, this negative pressure sucks air into the space under deflector. Fig. 5 shows discharge of air entering from aerator in condition of installing deflector and open aerator in different models. In these figures, vertical axis is values of air discharge relative to flow discharge passing deflector.

Table 6 shows values of difference average of air entering from aerator-in condition of installing deflector and open aerator-relative to deflector [phi] = 9 deg in percent.

[FIGURE 4 OMITTED]

The experiment results state that: a) in proportion to negative pressure, air discharge entering flow increases as flow discharge increases. b) in a constant flow discharge, discharge of inlet air increases as the dimensions of deflector increases. c) for a deflector with constant dimensions, air discharge increases as flow discharge increases.

By examining the results obtained of experiments, following equations can be stated to anticipate air discharge entering aerator in stepped spillway in condition of installing deflector and open aerator in which [Q.sub.a]: air discharge and [Q.sub.w]: water discharge:

[Q.sub.a]/[Q.sub.w] = [alpha][([y.sub.c]/h).sup.[beta]] (12)

[alpha] = 0.022[e.sup.0.9] (13)

[beta] = -0.99[e.sup.0.499] (tan[phi].tan[theta]) (14)

[FIGURE 5 OMITTED]

Length of outlet jet from deflector:

In condition of installing deflector and open aerator, the flow passes over deflector goes out as falling jet and in this case, a vacant place is prodused under this outlet jet. Fig. 6 presents the curve of jet length goes out deflector, in condition of installing deflector and open aerator in different models. Table 7 shows the values of difference average of jet length-in condition of installing deflector and open aerator- relative to deflector [phi] = 9 deg in percent.

The results of experiments state that: a) for a deflector with constant dimensions, the length of jet increases as flow discharge increases. b) in a constant flow discharge, the length of jet increases as dimensions of deflector enlarge. According to place of installing different types of deflectors, it is observed that deflector type 1 has the most influence on the length of outlet jet from deflector, for the way of contact with flow and after that deflector type 2 and 3 have less effect.

By examining the results obtained of experiments following equations can be stated to anticipate length of outlet jet from deflector in stepped spillway, in condition of installing deflector and open aerator in which L. is length of outlet jet passing over deflector:

[L.sub.j]/h = [alpha][([y.sub.c]/h).sup.[beta]] (15)

[alpha] = -0.743 ln(tan[theta].tan[phi]) + 1.485 (16)

[beta] - 0.781 ln(tan[theta].tan[phi]) + 1.284 (17)

[FIGURE 6 OMITTED]

Dynamic pressure fluctuations:

In order to study the condition of flow over stepped spillway, several Piezometer was installed on steps but the results obtained from them(static pressure), did not have enough accuracy because of the oscillating nature of flow on steps. So by applying the pressure transducer device with speed of collecting 200 data per second and in time of 30 seconds-about 6000 data for each point- condition of pressure fluctuations over steps have been studied. After collecting data, this data has been analyzed by spss software and show obtained results have normal curve distribution (Fig. 7). After that, values P 0.1%, P 1%, P 5%, P 95%, P 99%, P 99.99% that P * % --number that * % of data are smaller than it- are determined. Then for each point p99% is selected as Pmax-maximum pressure- and value P 0.1% as Pmin-minimum pressure. according to Amador et al., [1] critical point in stepped spillway are points placed on vertical face of stepped and specially on sub-upper part near edge of each step, in relation to reduce pressure on steps and generating cavitation phenomanon.

Fig. 8 presents pressure fluctuations in condition of not installing deflector in different models and on horizontal face of steps. These experiment have been done for condition of: 1) installing deflector and closed aerator, 2) installing deflector and open aerator. Table 8 shows the values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on internal part of steps horizontal face, in percent. Table 9 shows the values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on external part of steps horizontal face, in percent.

The results of experiments state that: a) by examining pressure fluctuation, the horizontal face of step can be divided into two parts (internal:between previous step and external part, and external: near to sharp edge of step); b) maximum pressure are seen in external part of horizontal face of step. The reason is contact and direct descent of flow passing over this part. c) value of pressure in internal part is less than external part. d) the reason of pressure oscillation in internal part is the seperation of flow from the surface of step. e) in external part, by increase in flow discharge, the average pressure increases and minimum pressure decreases.

Table 10 shows values of difference average of dynamic pressure fluctuations-in condition of not installing deflector on internal part of vertical face of steps in percent. Table 11 shows values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on external part of vertical face of steps in percent.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

The results of experiments state that: a) by studying fluctuations of pressure, the vertical face of step can be divided into two part(internal and external). b) in external part, by the increase in flow discharge, maximum pressure increases. c) in internal part, by increase in flow discharge, maximum pressure increases, average pressure increases with great oscillations and minimum pressure increases too.

By examining the results related to condition of installing deflector and closed aerator, it can be stated that: a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. B)in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on horizontal surfaces of steps increases because by increase in dimentions of deflector, flow depth increases and flow velocity decreases and as result, the pressure enforced from flow on steps increases.

The results related to pressure fluctuations on vertical faces of steps in condition of installing deflector and closed aerator state that:

a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. b) in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on vertical surfaces of steps increases. Similar experiments were done in condition of installing deflector and open aerator that results of pressure on horizontal faces state that: a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase.

b) in internal part, by increase in flow discharge, all these pressures, increase. c) overall, by enlarging the dimentions of deflector, pressure enforced on horizontal surfaces of steps increases. d) air entrance causes increase in pressure fluctuation on steps.

By examining the results related to pressure oscillations on vertical and horizontal faces of steps in condition of installing deflector and opening aerator, it can be stated that: a)in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. b) in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on vertical surfaces of steps increases. The reason of this phenomenon is that with increase in dimentions of deflector, volume of air entering the flow increases, flow depth increases and the pressure enforced on step increases. d) air entrance causes increase in pressure fluctuation on vertival and horizontal faces of steps.

Coefficient of cavitation:

By using values of minimum pressure computed in previous section, cavitation index of flow passing stepped spillway is computed from following equation:

[[sigma].sub.i] = ([h.sub.pi] - [h.sub.v] + [h.sub.a]/([V.sub.2]/2g) (18)

Where: [[sigma].sub.i]:cavitation index, [h.sub.pi]:height equals pressure on surface, [h.sub.v]:height equals vapour pressure [h.sub.a]: height equals atmosphere pressure V : average velocity of cross-section. Fig. 9 presents cavitation index in different models-in condition of no t installing deflector- and on vertical and horizontal face of steps.

Results present that: a) cavitation index decreases, as flow discharge increases because of decrease in pressure enforced on step surface. b) cavitation index decreases, with increase in distance from crest of spillway, because of increase in flow velocity and decrease in pressure. c) cavitation index in internal part of horizontal face and in external part of vertical face is less than other parts. d)totally, cavitation index in vertical face of steps is less than horizontal face and it means that possibility of occuring cavitation, in external zone on vertical face is more than other parts. Fig. 10 presents cavitation index--in condition of installing deflector and opening aerator- in different models and on vertical and horozontal face of steps.

Results of experiments in condition of entering air into flow passing from spillway present that: a) cavitation index decreases as distance from crest of spilway indreases because of increase in velocity and reduce in pressure. b) cavitation index in horizontal internal part and vertical external part is less than other parts. c)by installing deflector and opening aerator -enterance of air- generally, cavitation index has been increased in step surface that means risk of creating cavitation on steps decreases. d)increasing in deflector dimensions has a positive effect on increasing cavitation index in stepped spilways.

[FIGURE 9 OMITTED]

Conclusion:

By examining results obtained of experiments on model no.1 with slope of 40 degree, according to critical cavitation index [sigma] = 0.2 and scale factor [[lambda].sub.l] = 20, the ultimate water discharge in unit width is about q = 36.5 [m.sup.3]/s/m. installing deflector and entrance of air into flow, reduces risk of cavitation, and cavitation index for a certain water discharge increases relative to not installing deflector condition and ultimate water discharge in unit width can be increased about q = 50.6 [m.sup.3]/s/m that presents increasing 38.6%.

But in model no.2 with slope of 51 degree, according to critical cavitation index of a = 0.2 ultimate water discharge in unit width is about q = 30.9 [m.sup.3]/5/ m. By installing deflector and air entrance to flow, water discharge in unit width can be increased about q = 40.1 [m.sup.3]/5/m that presents increasing 29.3% (Fig. 11).

The following findings of the installing deflector and aerator on upper part of stepped spillway apply: A)decreasing in black water length. B) increasing in boundary layer turbulence and rapid growth. C) occurring inception point in short distance of spillway. D) energy losing increases on stepped spillway more than smooth wear and standard stepped spillway. E) pressure on step face increases significantly and causes F) increasing in cavitation index. Finally, by these advantages, it is possible to improve stepped spillway design and that due to increase passing water discharge per unit width significantly more than (25-30[m.sup.3]/s/m).

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

ACKNOWLEDGEMENT

Authors wish to thank Eng. Hasan Roshan and Eng. Khorasinizade (member of water research institute of Energy Ministry, iran); experimental facilities of this study is provided by water research institute of Energy Ministry of iran.

ARTICLE INFO

Article history:

Received 25 September 2014

Received in revised form 26 October 2014

Accepted 25 November 2014

Available online 31 December 2014

REFERENCES

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[5] Chanson, H., 1994. Hydraulics of Skimming Flows Over Stepped Channels and Spillways. Journal of Hydraulic Research 32(3): 66-75.

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[7] Chinnarasri, C., S. Wongwises, 2006. Flow Patterns and Energy Dissipation Over Various Stepped Chutes. Journal of Irrigation and Drainage Engineering 32(1): 99-108.

[8] Essery, I.T.S., M.W., Horner, 1978. The Hydraulic Design of Stepped Spillways. Journal of Hydraulic Engineering 125(5): 453-461.

[9] Ohatsu, I., Y. Yasuda, 1997. Characteristics of Flow Conditions on Stepped Channels. Journal of Hydraulic Engineering 110(5), 583-588.

[10] Ohatsu, I., Y. Yasuda and M. Takahashi, 2004. Flow Characteristics of Skimming Flow in Stepped Channels. Journal of Hydraulic Engineering 130(9): 223-230.

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(1) Safarpour Mojtaba, (2) Mousavi jahromi Habib, (3) Shafaei bajestan Mahmood, (4) Masjedi Alireza, (5) Kashkouli Heidar Ali

(1) Department Water Science and Engineering, Khuzestan Science and Reaserch Branch, Islamic Azad University, Ahvaz, Iran.

(2) Department Water Science and Engineering, Tehran Science and Reaserch Branch, Islamic Azad University, Tehran, Iran.

(3) Department Water Science and Engineering, Shahid Chamran University, Ahvaz, Iran.

(4) Department Water Science and Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

(5) Department Water Science and Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

Corresponding Author: Safarpour Mojtaba, Department Water Science and Engineering, Khuzestan Science and Reaserch Branch, Islamic Azad University, Ahvaz, Iran.

Increasingly growth of population, as well as improvement of technology are elements for loss of water in world and it causes about third of world population live with anxiety of crisis of drought and pollution. This crisis has created economical depression in many regions of world. Nowadays developing in industrial and agricultural fields, as well as increasingly growth of population in cities, make it essential to maintain and protect available limited resources of underground and surface water. If we add gradual warming of air in the earth into above problems, that leads into lack of raining in dry and semi-dry regions, we findout that making new designs to use and maintain existing water, is important. Building dams and spillway on them, is one of the methods of managing water resources. In recent years and thanks to technology improvement of builing dams by R.C.C method, applying stepped spillway has considered much attention [2, 3]. In this method, thickness of concrete layer is between 0.3 to 1 meter[11, 14].

The most important advanteges of stepped spillway includes: a) easy of build and economical, b)risk of cavitation on steps decreases because of entering air into flow, c)dimensions of stilling basin in toe of dam decrease because of increase in flow energy loss by steps of spillway [2, 3]. Most studies related to condition of flow in stepped spillway, have done in recent years [4, 5, 6, 7, 8, 9, 10, 13].

Much of studies are related to case experiment in a special structure and obtaining results related to general condition of flow in stepped spillway. Other studies are related to following cases: a) condition of flow related to passing water discharge per unit width; b) different regimes of flow and range of discharge making these regimes; c) energy loss and flow velocity in downsteam of chute [14]. d) amount of air concentration in flow passing spillway and its effect on energy dissipation. One of the characteristics of stepped spillway is limitation in ((water discharge per unit width)) of flow passing over it which have been stated (25-30[m.sup.3]/s/m) by researchers that has significantly more limited application, in comparision with smooth spillway that passes q=100 [m.sup.3]/s/m [11, 14].

Reason of this limitation, is generating skimming flow over spillway and making non-aeration zone(black water) in distance of spillway crest to inception point of aeration. This phenomenom leads to decrase of pressure on steps and creating cavitation on them. Because of entering natural air into flow and increase in air concentration near bed of downstream steps, risk of creating cavitation will be reduced effectively[2, 3, 5, 6]. stated that one way to reduce cavitation risk in upper part of spillway--before inception point--is installing deflector and aerator in first steps of spillway and air entrance through it into flow. This has much influence on increasing pressure on steps and decreasing cavitation risk and finally increases the ability of spillway to pass water discharge higher than (25-30[m.sup.3]/s/m) [15].

Boes et al., [2, 3] stated that installing deflector decrease black water length and causes that inception point occure in shorter length of spillway. They stated that by installing deflector , energy dissipation increases on the spillway and residual energy at the toe of spillway decreases significantly.

The hydrodinamic pressure field on the channel steps is an important factor affecting the design and safety of stepped spillway. Amador et al., [1] stated that the zone near the inception point of air entrainment will be critical in terms of the risk of cavitation damage. They studied characterizing the developing flow region and examined the pressure fluctuation on the steps induced by the skimming flow. They stated that the largest dynamic pressure are present on the horizontal face near the step edge where pressure are governed by the impact of the overlying flow. On the vertical faces, the pressure are affected by flow separation from steps face [1].

In this study, effect of installing different types of deflectors has been studied on: a) energy loss on stepped spillway; b) distribution of dynamic pressure on vertical and horizontal surface of steps; c) created jet length over deflector; d) volume of air entering into flow.

MATERIALS AND METHODS

Experimental facilities:

In this study effect of installing types of deflector have been studied on replacement of inception point, as well as increase in passing water discharge. Experiments have been done on two models of stepped spillways of plexiglass material which their characteristics have been written in Table 1.

In this table: N=number of step; b=width of spillway; 1=horizontal step length; h= step height and [THETA]= slope of stepped channel. Water flow has been entered to a tank in dimensions of (11x11x5) through pumps of existing channel in lab and entered to a spillway by two guide walls and after passing stepped chute and stilling basin of downstream, entered wooden flume and again retured to channel. In order to water discharge measure gauge available beside spillway, as well as sharpe edge rectancular spillway in downstream chute has been used, by which rating curve has been prepared for these stepped spillways. Measuring depth of flow has been done by a Point gauge with accuracy of 1mm and measuring flow velocity by Pitot-static tube.According to condition of each experiment,10 to 15 cross-sections have been considered and in each cross-section, in three points (b/4,b/2,3b/4), depth and flow velocity have been measured. In order to measure accurate pressure fluctuations, a pressure transducer with six sensors has been used. Experiment time in each point is determined 30 seconds and recieved data rate is determined 200 data per second. Totally 6000 data in each point is acceptable data to analyze pressure fluctuation. In order to inject air into passing water flow over deflector, an aerator with dimensions of 5.5x6cm was installed on model no.1 and an aeraor with dimensions of 4x4cm was installed on model no.2. these aerators have suitable cabs and a hole by diameter of 1cm to enter ((hot-wire)) device that computed velocity of passing air inside aerator in m/s. Measuring partial negative pressure obtained of installing deflector and closing aerator, is computed by a U-tube manometer.

Characteristics of deflectors:

In experiments done on model no.1, four types of deflector--types 1, 2 and 4 with triangular cross-section and type 3 with trapezoidal cross-section. on model no.2, deflector type 1 has been installed in end of ogee spillway and before first step and has L--6cm and angles of [phi] 4,9,14 5,18,22(deg). Deflector type 2 has been installed on upper part of vertical face of first step and above pseudobottom and has two slopes [phi] = 5,10(deg). Deflector type 3 has been installed on upper part of vertival face of first step and under pseudobottom and has characteristics that have been written in Table 2. Deflector type 4 has characteristics as type1 but has been applied as jagged in width of spillway(Fig. 1).

Dimensional Analysis:

In order to dimentional analysis to determine energy dissipation in condition of not installing deflector that is necessary to determine parameters which have influence on amount of energy loss, according to previous studies[5, 6, 9, 10], energy loss in stepped spillway depends on, [H.sub.0]: total energy in upstream of spillway, q: wate discharge per unit width of spillway, h :height of step, l :length of step, [[rho].sub.w] :density of water, [sigma] :surface tension between water and air, [f.sub.e] :coefficient of roughness of spillway bed, N :number of steps, [mu] : dynamic viscosity of water and g :gravity accelaration. Thus relation between these quantities is as follow:

F([DELTA]H, [H.sub.0], q, h, l, [[rho].sub.w], [sigma], [f.sub.e], N, [mu], g) = 0 (1)

number of variables aqualn -11 and number of basic dimensions equal m--3. According to Buckingham Pi method, n - m = 11 - 3 = 8 dimensionless parameters can be defined that final resuls are as follow:

f([DELTA]H/h, [H.sub.0]/h, [y.sub.c]/h, h/l, [sigma]/[[rho].sub.w]g[h.sup.2], [f.sub.e], [mu]/[[rho].sub.w]g[h.sup.2], [f.sub.e], [mu]/[[rho].sub.w] [square root of (g[h.sup.2])], N) = 0 (2)

[FIGURE 1 OMITTED]

by ignoring the effect of fluid viscosity [mu] and surface tension [sigma] and by few operations on stated parameters effected on energy loss in stepped spillway in condition of not installing deflector as follow:

[DELTA]H/[H.sub.0] = f([y.sub.c]/h, h/l, N. [f.sub.e]), (3)

Dimensional Analysis to determine energy dissipation in condition of installing deflector:

Effective parameters in this condition can be stated as follow:

F([DELTA]H, [H.sub.0], q, h, l, [[rho].sub.w], [sigma], [f.sub.e], N, [mu], g, tan [phi]) = 0 (4)

Where: tan [phi] : slope of deflector installed over spillway. Finally it can be stated, dimensionless parameters effective on energy loss in stepped spillway in condition of installing deflector as follow:

[DELTA]H/[H.sub.0] = f([y.sub.c]/h, h/l, N, [f.sub.e] tan[phi]) (5)

Results:

Hydraulic jump sequent depth in stilling basin:

Computing energy loss in downstream of stepped spillway is very difficult through direct measuring of depth and velocity of flow, because of foamy flow and high turbulance waves. So in this paper, reverse computing method has been used in which at first sequent depth([y.sub.2])of hydraulic jump in stilling basin is measured- where the oscillation of water surface and number of bubble in flow is few- and then initial depth([y.sub.1]) is calculated using standard hydraulic jamp equations. With water discharge and initial depth([y.sub.1]), quantity of specific energy ([E.sub.1]) existing in spillway toe can be determined with desirable accuracy[14].

Energy loss:

Fig. 2 presents energy loss of flow in condition: 1) not installing deflector and 2) installing deflector and closing aerator in defferent models.

Table 3 shows value of difference average in energy loss, in condition of installing deflector and closing aerator relative to not installing deflector condition in pecent.

Results obtained of experiments state that: a) in stepped spillway when flow discharge increases, remained energy increases in toe of spillway. In other words, energy loss decrease as water discharge increase. b) in a constant flow discharge, the value of energy loss increases as dimensions of deflector enlarge which its reason is shortening length of black water zone and faster formation of inception point of aeration. As a result, the number of vortex increases in stepped spillway and existance of such vortex lead to make energy loss. c) for a deflector with constant dimensions, energy loss decreases as flow discharge increases. d) installing deflector causes increase in energy loss in stepped spillway.

Fig. 3 presents energy loss of flow, in condition of installing deflector and opening aerator in different models. Table 4 shows value of difference average in energy loss, in condition of installing deflector and openin aerator relative to condition of not installing deflector in pecent.

Deflector type 1:

in condition of open aerator and air entrance into passing flow, below results are obtained: a) in a constant flow discharge, the value of energy loss increase as dimensions of deflector increases that as noted befor, shorten length of black water zone, more air enters flow through aerator and more vortices forms in stepped spillway, energy loss increases.

b) for a deflector with constant dimensions, energy loss decreases as flow discharge increases. a)in open aerator and entering air into flow, enrgy loss is more than closed aerator condition.

Deflector type 2:

in condition that deflector is installed on vertical face of first step above pseudobottom bottom, similar to type 1, energy loss decreases when flow discharge increases for a deflector with certain dimensions, and in a constant flow discharge, energy loss increases as dimensions of deflector increase.

In experiments related to deflector type 2, ultimate deflector angle is 10 degree and by increase in angle, severe contact of flow are seen with deflector and producing turbulance and forming irregular waves in flow surface.

Deflector type 3:

in condition that deflector is installed on vertical face of first step below pseudobottom, it is seen that in a constant flow discharge with replacement of deflector in different points, although overlap is seen between results but energy loss increases than condition of not installing deflector, but have less efficacy on energy loss than deflectors type1 and type 2 -without comparision between different types of deflectors because of their different shapes.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Deflector type 4:

in this condition, jagginess of deflector shortens the width of spillway. So flow passes a smaller crosssection. Observations show that flow comes into contact with downstream steps as falling jet and severe waves and oscillations are formed in passing flow. By examining the results obtained of experiment, following equations can be stated to anticipate enrgy loss in stepped spillways:

a) not installing deflector condition:

[DELTA]H/[H.sub.max] = 1 -[[([f.sub.e]/8 sin [theta]).sup.0.347] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.697]/1.5 + [H.sub.dam]/[d.sub.c]]

b) installing deflector and close aerator condition:

[DELTA]H/[H.sub.max] = 1 -[[([f.sub.e]/8 sin [theta]).sup.0.345] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.697]/1.5 + [H.sub.dam]/[d.sub.c] [(tan [phi]).sup.-0.081]] (7)

c) installing deflector and open aerator condition:

[DELTA]H/[H.sub.max] = 1 - [[([f.sub.e]/8 sin [theta]).sup.0.346] cos[theta] + 0.5[([f.sub.e]/8 sin [theta]).sup.- 0.628]/1.5 + [H.sub.dam]/[d.sub.c] [(tan [phi]).sup.-0.077]] (8)

Negative partial pressure resulted from instating deflector:

In condition of installing deflector and closed aeraor, negative partial pressure is produced in the distance between deflector and first step surfaces because of the separation of stream lines from steps surface and this negative pressure causes air entrance and forming outlet jet from deflector in an open aerator condition. Fig. 4 shows negative partial pressure of flow, in condition of installing deflector and closed aerator in different models.

Table 5 shows the value of difference average of negative partial pressure of flow-in condition of installing deflector and closed aerator-relative to deflector with angle [phi] = 9 deg in percent.

The results obtained of experiment state that:

Deflector type 1:

a) with increase in water discharge, negative pressure of flow increases due to increase in existing energy in flow and tendency to seperate from surface of spillway. b) in a constant flow discharge, negative pressure increases as the dimensions of deflector increase that is because of contact of flow with greater obstacle and seperation of stream lines from surface of steps. c) for a deflector with constant dimensions, increase in flow discharge lead to increase in negative partial pressure of flow.

Deflector type 2:

similar to type 1, for a deflector with constant dimensions, negative partial pressure increases as flow discharge increases. Totally, deflector type 2 has less efficacy on negative partial pressure than type 1. In this case, it is observed that in a constant flow discharge in different points, overlap is seen between observed data but negative partial pressure increases relative to condition of not installing deflector. Overall, deflector type 3 has less efficacy than tow other types of deflector. With examining the results obtained of experiments following equations can be stated to anticipate the negative partial pressure in stepped spillway in condition of installing deflector and closed aerator in which [DELTA]p is negative partial pressure:

[DELTA]p = [alpha][([y.sub.c]/h).sup.[beta]] (9)

[alpha] = 1.8e [0.99.sup.(tan[phi].tan[theta])] (10)

P = 1.47 [e.sup.0.29(tan[phi].tan[theta])] (11)

Discharge of air entering from aerator:

As stated before, installing deflector and closing aerator causes negative pressure in the space under deflector, and if the aerator would be opened in this condition, this negative pressure sucks air into the space under deflector. Fig. 5 shows discharge of air entering from aerator in condition of installing deflector and open aerator in different models. In these figures, vertical axis is values of air discharge relative to flow discharge passing deflector.

Table 6 shows values of difference average of air entering from aerator-in condition of installing deflector and open aerator-relative to deflector [phi] = 9 deg in percent.

[FIGURE 4 OMITTED]

The experiment results state that: a) in proportion to negative pressure, air discharge entering flow increases as flow discharge increases. b) in a constant flow discharge, discharge of inlet air increases as the dimensions of deflector increases. c) for a deflector with constant dimensions, air discharge increases as flow discharge increases.

By examining the results obtained of experiments, following equations can be stated to anticipate air discharge entering aerator in stepped spillway in condition of installing deflector and open aerator in which [Q.sub.a]: air discharge and [Q.sub.w]: water discharge:

[Q.sub.a]/[Q.sub.w] = [alpha][([y.sub.c]/h).sup.[beta]] (12)

[alpha] = 0.022[e.sup.0.9] (13)

[beta] = -0.99[e.sup.0.499] (tan[phi].tan[theta]) (14)

[FIGURE 5 OMITTED]

Length of outlet jet from deflector:

In condition of installing deflector and open aerator, the flow passes over deflector goes out as falling jet and in this case, a vacant place is prodused under this outlet jet. Fig. 6 presents the curve of jet length goes out deflector, in condition of installing deflector and open aerator in different models. Table 7 shows the values of difference average of jet length-in condition of installing deflector and open aerator- relative to deflector [phi] = 9 deg in percent.

The results of experiments state that: a) for a deflector with constant dimensions, the length of jet increases as flow discharge increases. b) in a constant flow discharge, the length of jet increases as dimensions of deflector enlarge. According to place of installing different types of deflectors, it is observed that deflector type 1 has the most influence on the length of outlet jet from deflector, for the way of contact with flow and after that deflector type 2 and 3 have less effect.

By examining the results obtained of experiments following equations can be stated to anticipate length of outlet jet from deflector in stepped spillway, in condition of installing deflector and open aerator in which L. is length of outlet jet passing over deflector:

[L.sub.j]/h = [alpha][([y.sub.c]/h).sup.[beta]] (15)

[alpha] = -0.743 ln(tan[theta].tan[phi]) + 1.485 (16)

[beta] - 0.781 ln(tan[theta].tan[phi]) + 1.284 (17)

[FIGURE 6 OMITTED]

Dynamic pressure fluctuations:

In order to study the condition of flow over stepped spillway, several Piezometer was installed on steps but the results obtained from them(static pressure), did not have enough accuracy because of the oscillating nature of flow on steps. So by applying the pressure transducer device with speed of collecting 200 data per second and in time of 30 seconds-about 6000 data for each point- condition of pressure fluctuations over steps have been studied. After collecting data, this data has been analyzed by spss software and show obtained results have normal curve distribution (Fig. 7). After that, values P 0.1%, P 1%, P 5%, P 95%, P 99%, P 99.99% that P * % --number that * % of data are smaller than it- are determined. Then for each point p99% is selected as Pmax-maximum pressure- and value P 0.1% as Pmin-minimum pressure. according to Amador et al., [1] critical point in stepped spillway are points placed on vertical face of stepped and specially on sub-upper part near edge of each step, in relation to reduce pressure on steps and generating cavitation phenomanon.

Fig. 8 presents pressure fluctuations in condition of not installing deflector in different models and on horizontal face of steps. These experiment have been done for condition of: 1) installing deflector and closed aerator, 2) installing deflector and open aerator. Table 8 shows the values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on internal part of steps horizontal face, in percent. Table 9 shows the values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on external part of steps horizontal face, in percent.

The results of experiments state that: a) by examining pressure fluctuation, the horizontal face of step can be divided into two parts (internal:between previous step and external part, and external: near to sharp edge of step); b) maximum pressure are seen in external part of horizontal face of step. The reason is contact and direct descent of flow passing over this part. c) value of pressure in internal part is less than external part. d) the reason of pressure oscillation in internal part is the seperation of flow from the surface of step. e) in external part, by increase in flow discharge, the average pressure increases and minimum pressure decreases.

Table 10 shows values of difference average of dynamic pressure fluctuations-in condition of not installing deflector on internal part of vertical face of steps in percent. Table 11 shows values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on external part of vertical face of steps in percent.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

The results of experiments state that: a) by studying fluctuations of pressure, the vertical face of step can be divided into two part(internal and external). b) in external part, by the increase in flow discharge, maximum pressure increases. c) in internal part, by increase in flow discharge, maximum pressure increases, average pressure increases with great oscillations and minimum pressure increases too.

By examining the results related to condition of installing deflector and closed aerator, it can be stated that: a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. B)in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on horizontal surfaces of steps increases because by increase in dimentions of deflector, flow depth increases and flow velocity decreases and as result, the pressure enforced from flow on steps increases.

The results related to pressure fluctuations on vertical faces of steps in condition of installing deflector and closed aerator state that:

a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. b) in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on vertical surfaces of steps increases. Similar experiments were done in condition of installing deflector and open aerator that results of pressure on horizontal faces state that: a) in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase.

b) in internal part, by increase in flow discharge, all these pressures, increase. c) overall, by enlarging the dimentions of deflector, pressure enforced on horizontal surfaces of steps increases. d) air entrance causes increase in pressure fluctuation on steps.

By examining the results related to pressure oscillations on vertical and horizontal faces of steps in condition of installing deflector and opening aerator, it can be stated that: a)in external part, by increase in discharge, maximum pressure, average pressure and minimum pressure, increase. b) in internal part, by increase in flow discharge, all these pressures, increase. c)by enlarging the dimentions of deflector, pressure enforced on vertical surfaces of steps increases. The reason of this phenomenon is that with increase in dimentions of deflector, volume of air entering the flow increases, flow depth increases and the pressure enforced on step increases. d) air entrance causes increase in pressure fluctuation on vertival and horizontal faces of steps.

Coefficient of cavitation:

By using values of minimum pressure computed in previous section, cavitation index of flow passing stepped spillway is computed from following equation:

[[sigma].sub.i] = ([h.sub.pi] - [h.sub.v] + [h.sub.a]/([V.sub.2]/2g) (18)

Where: [[sigma].sub.i]:cavitation index, [h.sub.pi]:height equals pressure on surface, [h.sub.v]:height equals vapour pressure [h.sub.a]: height equals atmosphere pressure V : average velocity of cross-section. Fig. 9 presents cavitation index in different models-in condition of no t installing deflector- and on vertical and horizontal face of steps.

Results present that: a) cavitation index decreases, as flow discharge increases because of decrease in pressure enforced on step surface. b) cavitation index decreases, with increase in distance from crest of spillway, because of increase in flow velocity and decrease in pressure. c) cavitation index in internal part of horizontal face and in external part of vertical face is less than other parts. d)totally, cavitation index in vertical face of steps is less than horizontal face and it means that possibility of occuring cavitation, in external zone on vertical face is more than other parts. Fig. 10 presents cavitation index--in condition of installing deflector and opening aerator- in different models and on vertical and horozontal face of steps.

Results of experiments in condition of entering air into flow passing from spillway present that: a) cavitation index decreases as distance from crest of spilway indreases because of increase in velocity and reduce in pressure. b) cavitation index in horizontal internal part and vertical external part is less than other parts. c)by installing deflector and opening aerator -enterance of air- generally, cavitation index has been increased in step surface that means risk of creating cavitation on steps decreases. d)increasing in deflector dimensions has a positive effect on increasing cavitation index in stepped spilways.

[FIGURE 9 OMITTED]

Conclusion:

By examining results obtained of experiments on model no.1 with slope of 40 degree, according to critical cavitation index [sigma] = 0.2 and scale factor [[lambda].sub.l] = 20, the ultimate water discharge in unit width is about q = 36.5 [m.sup.3]/s/m. installing deflector and entrance of air into flow, reduces risk of cavitation, and cavitation index for a certain water discharge increases relative to not installing deflector condition and ultimate water discharge in unit width can be increased about q = 50.6 [m.sup.3]/s/m that presents increasing 38.6%.

But in model no.2 with slope of 51 degree, according to critical cavitation index of a = 0.2 ultimate water discharge in unit width is about q = 30.9 [m.sup.3]/5/ m. By installing deflector and air entrance to flow, water discharge in unit width can be increased about q = 40.1 [m.sup.3]/5/m that presents increasing 29.3% (Fig. 11).

The following findings of the installing deflector and aerator on upper part of stepped spillway apply: A)decreasing in black water length. B) increasing in boundary layer turbulence and rapid growth. C) occurring inception point in short distance of spillway. D) energy losing increases on stepped spillway more than smooth wear and standard stepped spillway. E) pressure on step face increases significantly and causes F) increasing in cavitation index. Finally, by these advantages, it is possible to improve stepped spillway design and that due to increase passing water discharge per unit width significantly more than (25-30[m.sup.3]/s/m).

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

ACKNOWLEDGEMENT

Authors wish to thank Eng. Hasan Roshan and Eng. Khorasinizade (member of water research institute of Energy Ministry, iran); experimental facilities of this study is provided by water research institute of Energy Ministry of iran.

ARTICLE INFO

Article history:

Received 25 September 2014

Received in revised form 26 October 2014

Accepted 25 November 2014

Available online 31 December 2014

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(1) Safarpour Mojtaba, (2) Mousavi jahromi Habib, (3) Shafaei bajestan Mahmood, (4) Masjedi Alireza, (5) Kashkouli Heidar Ali

(1) Department Water Science and Engineering, Khuzestan Science and Reaserch Branch, Islamic Azad University, Ahvaz, Iran.

(2) Department Water Science and Engineering, Tehran Science and Reaserch Branch, Islamic Azad University, Tehran, Iran.

(3) Department Water Science and Engineering, Shahid Chamran University, Ahvaz, Iran.

(4) Department Water Science and Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

(5) Department Water Science and Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.

Corresponding Author: Safarpour Mojtaba, Department Water Science and Engineering, Khuzestan Science and Reaserch Branch, Islamic Azad University, Ahvaz, Iran.

Table 1: Characteristics of stepped spillways applied in experiments Model [theta] h l b N Q no. (deg) (cm) (cm) (cm) (lit/s) 1 40 6 7.2 75 84 220-240- 270-290- 310 2 50 4.8 4 72 64 126-137- 155-166- 178-192 -209 Table 2: characteristics of deflector type 3 Deflector L C Cd c/cd [gamma] location (cm) (cm) (cm) (deg) Zone 1 2.5 2.3-2.6-2.9 2.9 0.8-0.9-1 20-30-40 Zone 2 3.5 3.2-3.6-4 4 0.8-0.9-1 20-30-40 Zone 3 4.5 4.1-4.7-5.2 5.2 0.8-0.9-1 20-30-40 Table 3: value of difference average in energy loss, in condition of installing deflector and closing aerator relative to condition of not installing deflector (in percent). [theta]:Deflector slope(degree) [y.sup.c]/h 22 18 14 9 4 7.5 6.4 5.2 3.1 1.1 3.3 7.8 6.7 5.5 3.6 1.3 3.6 8.0 7.0 6.0 4.0 1.5 3.9 8.3 7.3 6.4 4.5 1.6 4.1 8.3 7.7 6.8 4.9 1.8 4.3 8.1 7.1 5.9 4.1 1.4 ave Table 4: value of difference average in energy loss, in condition of installing deflector and opening aerator relative to condition of not installing deflector(in percent) [theta]:Deflector slope(degree) [y.sub.c]/h 22 18 14 9 4 8.5 7.5 6.3 4.0 1.8 3.3 8.9 7.8 6.6 4.5 2.0 3.6 9.1 7.8 7.1 5.0 2.3 3.9 9.4 8.5 7.3 5.5 2.3 4.1 9.7 8.9 7.9 5.8 2.5 4.3 9.1 8.2 7.1 4.9 2.2 ave Table 5: value of difference average of negative partial pressure of flow-in condition of installing deflector and closed aerator- relative to deflector with angle [phi] = 9 deg (in percent) [theta]:Deflector [y.sub.c]/h slope(degree) 22 18 14 123.5 67.1 24.2 3.3 136.3 68.7 25.9 3.6 152.1 81.5 30.7 3.9 163.8 87.9 47.4 4.1 166.1 88.5 35.8 4.3 148.4 78.7 30.6 Ave Table 6: values of difference average of air entering from aerator- in condition of installing deflector and open aerator-relative to deflector [phi] = 9 deg (in percent) [theta]:Deflector [y.sub.c]/h slope(degree) 22 18 14 48.5 28.7 11.2 3.3 52.7 29.3 11.9 3.6 57.7 34.1 14.1 3.9 61.3 36.5 16.6 4.1 61.2 36.6 16.3 4.3 56.4 33.1 14.1 Ave Table 7: values of difference average of jet length-in condition of installing deflector and open aerator-relative to deflector 9deg (in percent) [theta]:Deflector [y.sub.c]/h slope(degree) 22 18 314.4 208.6 105.8 3.3 211.6 143.6 68.9 3.6 174.5 118.8 57.3 3.9 149.6 100.1 50.3 4.1 119.2 80.7 40.6 4.3 193.9 130.4 64.6 Ave Table 8: values of difference average of dynamic pressure fluctuations--in condition of not installing deflector on internal part of horizontal face of steps (in percent) Min Avr Max [y.sub.c]/h -- -- -- 3.3 -1.7 10.4 2.9 3.6 -8.1 11.5 3.2 3.9 -10.8 11.4 4.2 4.1 -16.7 20.5 7.8 4.3 Table 9: values of difference average of dynamic pressure fluctuations-in condition of not installing deflector on external part of horizontal face of steps (in percent) Min Avr Max [y.sub.c]/h -- -- -- 3.3 -0.9 6.5 7.3 3.6 -1.2 6.8 7.4 3.9 -3.7 9.9 10.1 4.1 -4.3 14.5 16.6 4.3 Table 10: values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on internal part of vertical face of steps (in percent) Min Avr Max [y.sub.c]/h -- -- -- 3.3 -22.6 23.1 6.1 3.6 -11.8 32.5 6.3 3.9 -24.3 50.9 13.1 4.1 -33.3 59.5 20.3 4.3 Table 11: values of difference average of dynamic pressure fluctuations -in condition of not installing deflector on external part of vertical face of steps (in percent) Min Avr Max [y.sub.c]/h -- -- -- 3.3 -19.4 8.6 4.7 3.6 -14.6 14.1 4.8 3.9 -19.2 16.9 7.3 4.1 -26.5 23.8 14.2 4.3

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Author: | Mojtaba, Safarpour; Habib, Mousavi jahromi; Mahmood, Shafaei bajestan; Alireza, Masjedi; Ali, Kashko |
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Publication: | Advances in Environmental Biology |

Article Type: | Report |

Date: | Nov 1, 2014 |

Words: | 5939 |

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