Investigation of water head variation& relation to empirical Coefficient n of Stepped short Shaft Spill way
محورهای موضوعی : سازه های هیدرولیکی
روزبه آقا مجیدی
1
(گروه آموزشی عمران، دانشگاه آزاد سپیدان ، سپیدان فارس)
محمد نصر اصفهانی
2
(دکتری سازه و رئیس گروه نوآوری و توسعه فناوری سازمان آب و برق خوزستان)
کلید واژه: Shaft Spillway, vortex blades, Submersible ratio, empirical hydraulic Coefficient,
چکیده مقاله :
These spillways (Stepped shaft spillways) pass more flow discharges through themselves in comparison to smooth spillways theoretically. Therefore knowing of flow behavior of these Spillways, help using better and more efficiently. Moreover, using vortex breaker has great effect on passing Flow through Shaft Spillway. For using more efficiently, the risk of flow water head on the crest decreases to less than fluid vapor water head on the crest , called cavitation’s, should be prevented as far as possible. At this research, it has been tried to study different behavior of Stepped chamber and different vortex breaker shapes on spillway flow. From the viewpoint of the effects of flow regime changes on spillway, changes of step dimensions, and the change of type of flow range will Studied Effectively. And finally the best the relation between water head on the crest and Discharge Coefficient are determined.
These spillways (Stepped shaft spillways) pass more flow discharges through themselves in comparison to smooth spillways theoretically. Therefore knowing of flow behavior of these Spillways, help using better and more efficiently. Moreover, using vortex breaker has great effect on passing Flow through Shaft Spillway. For using more efficiently, the risk of flow water head on the crest decreases to less than fluid vapor water head on the crest , called cavitation’s, should be prevented as far as possible. At this research, it has been tried to study different behavior of Stepped chamber and different vortex breaker shapes on spillway flow. From the viewpoint of the effects of flow regime changes on spillway, changes of step dimensions, and the change of type of flow range will Studied Effectively. And finally the best the relation between water head on the crest and Discharge Coefficient are determined.
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Investigation of water head variation& relation to empirical Coefficient n of Stepped short Shaft Spill way
Abstract:
Stepped shaft spillways pass more flow discharges through themselves in comparison to smooth spillways theoretically. Therefore knowing of flow behavior of these Spillways, help using better and more efficiently. Moreover, using vortex breaker has great effect on passing flow through Shaft Spillway. For using more efficiently, the risk of flow water head on the crest decreases to less than fluid vapor water head on the crest , should be prevented as far as possible. At this research, it has been tried to study different behavior of Stepped chamber and different vortex breaker shapes on spillway flow. From the viewpoint of the effects of flow regime changes on spillway, changes of step dimensions, and the change of type of flow range will Studied Effectively. And finally the best the relation between water head on the crest and Discharge Coefficient are determined. Maximum risk of flow rate is magnitude at 1/3 down side of shaft, Magnitude velocity is occurred at the end steps of stepped chamber, and also will take place at ¼ of stepped Shaft spillway.
According to simulation, height and width of each step on stepped chamber has great effect on floe regime , especially when flow regime change from nape to skimming flow
Key words: Shaft Spillway, vortex blades, , Submersible ratio, empirical hydraulic Coefficient.
Introduction:
. The step spillways can significantly decrease the energy loss resulted from chute and eliminate the need to establishment of energy loss system in structure's downstream or decrease it significantly[1]. The flow on stepped spillways occurs in two skimming and napped regime. In high discharges, skimming flow will appeared and in low and intermediate discharges napped flow would occur. [3].
Water flow on a stepped or unsmooth surface in earth dam spillways is completely turbulent and makes small bubbles [2].
Such flow may depreciate a major part of its energy. Therefore, the more is the lost energy the less is the risk of cavitation due to intense fall of velocity [16]. In this study, the Flow and head of water on the crest of morning spillways are measured in regard to many dimensionless parameters of Froude number ,at top of spillway surface, the h/b ratio for each step and number of steps for two different types of spillway, and finally, Cd ( Emptying Coefficient of Shaft Spillway) against Submersible ratio ( H/Rs) for different vortex breaker and 3 different arrangement were studied. For determination the best condition of flow, with using different guide pier and its arrangement, Cd against h/rs are calculated and plotted theoretically. Eventually, some factors which are influenced on emptying Coefficient are present for designing. [17].
Figure (1) a real view of morning glory spillway
The glory spillway is commonly used to deplete the flow along the flood. and this hydraulic structure is capable to switch the free surface flow to fluid flow through the pipeline which is caused that the glory spillway thread by high velocity flow and flow separation. These cases can generate the cavitation bubble through the glory spillway. The cavitation phenomena are commonly happened through the flow with high velocity and minus pressure. The glory spillways included as three main parts as the vertical shaft, bend pipe and horizontal shaft. Some studies were focused on the depletion of the water through the vertical structure such as drop 40 structure which consists of dive flow and vortex drop structures due to free and semi-submerged 41 flow [1,2,3]. Whirling flow is considered as a basic problem in designing of the hydraulic structures with vertical shaft because it can mix the air and water and due to lack of the air above 43 the water surface, the minus static pressure can be generated by circulated currents [4].
There are some researches in the literature which are argued the vortex drop structures and its impacts on the minus pressure at bottom of the hydraulic structure [5,6,7,8]. The morning glory shaft is a type of spiral inlet which including of three main components: an inlet morning glory spillway, a vertical shaft, and an outlet tunnel [11]. Switching the angel of the mounted spoilers at the intake of the morning glory spillway can increase the values of the coefficient discharge. Meanwhile, these spoilers can control the rotation of the vortexed-currents and as a result the flow separation at the crest of the morning glory spillways tends to negligible status [12,13]. Glory spillways are one of the major hydraulic structures in dams, which are appropriately designed to pass the flow properly and effectively. Therefore, for correct and optimal designing, various conditions should be examined to avoid negative pressures at the 58 spillway crest and other parts of the glory spillways which may cause instability in the spillway structure and damage to the concrete surface of the spillway due to cavitation phenomena [14]. Considerable research has been conducted to determine the effect of the shape of the crest of the morning glory on the aeration. Esmailzadeh and Mirzavand indicated that adjusting and mounting the deflector at the crest position of the morning glory spillways can increase the rate This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4329747 Preprint not peer reviewed of the aeration. It was deduced that raising the aeration rate at the crest position of the morning glory spillways can reduce the risk of the cavitation because of removing the minus static pressure induced through the vertical shaft. [15].
Figure (2) A anti vortex blades on crest spillway
Addition of the shape of the morning glory 66 spillway, the upstream slope of the intake is important parameter related to shape to avoid from the minus pressure at crest position and downstream position of the intake such as vertical shaft and bend pipe [16]. Most of available information is include a wide range of data that has been obtained from the results of physical models done by USACE and USBR [17]. Regarding morning glory spillways, the USBR has done valuable research on the shape of the crest and the passing discharge that their results are available in the form of graphs and tables in the Institute's 72 publications. According to available data from USACE and USBR, computational fluid dynamics (CFD) program, Flow-3D, for different levels of flow for modeling of the morning 74 glory spillway were introduced as an acceptable and reliable application to investigate the 75 parameters of the flow due to different submergence ratio To determine to hydraulic characteristic of flow in morning glory shaft spillways, many 77 researchers have tried to solve these issues or problems by using some methods such as 78 prototype measurements, experimental and computational methods [,22,23].
Figure (3) a schematic view of simulation of morning glory spillway in differential situation
The numerical model was first used by Cassidy [24] to determine the water surface level and the static pressure on the glory spillway crest based on a two-dimensional potential flow. Their result illustrated the numerical models are suitable to simulate the flow over the morning glory spillways. The results also indicated that the minimum pressure for a given head depends on the boundary conditions. Ikegawa and Washizu [25] and Betts [26] used the finite element method linearly to solve the equations governing the flow field. The results obtained were compared by Cassidy results. They found the speed of convergence increased in the numerical analysis Savage and Johnson [27] studied the morning glory spillways with ogee crest without the runoff impact using Randomized Group Model (RNG). Their comparison shows the discharge and pressure distribution over the spillway can be accurately predicted by employing numerical models. Olsen and Kjellesvig [28] solved Reynolds averaged Navier-Stokes equations and also analyzed the passing flow over the glory spillway using standard k - ε equations by considering the two and three-dimensional model. Their results indicated that the numerical model can achieve an appropriate solution for calculating the viscosity, kinetic and pressure forces. Fiedler [29] presented the new designs of the Hoover Dam Spillways. He focused on the effective parameters of the morning glory spillway demolition such as spillway capacity/dam overtopping issues; spillway conveyance capacity; gate performance in non-flood situations; and performance of spillway linings under high velocity flow to prevent cavitation. Liu et al. [31] simulated flow in a newly developed vortex drops shaft spillway using experimental and numerical methods. In this study, hydraulic characteristics such as the flow pattern, air core distribution, annular hydraulic jump position, pressure profiles, and water profiles of the outlet tunnel are obtained and agree well with the measured experimental data. Results displayed that the flow around the inlet is apportioned into a free-flow swirling region near the piers and submerged-flow region at the piers. Also, analytic calculations for the resultant velocity and water course thickness of the shaft sections were correlated well with the results of a numerical simulation. Cavitation is defined as the formation of a bubble or void within a liquid. If the void is filled primarily with water vapor, the process is further classified as vaporous cavitation [32]. 1 Aghamajidi et al. [33] studied hydraulic behavior of smooth surface on the performance of the morning glory spillway and compared its results with an experimental type stepped-spillway with and without vortex breakers. To study the risk of the cavitation, the Froude number, index of hb/b (where hb is the height of the step and b is the to width of the step), a number of steps as well as the distance from the beginning of the spillway have been calculated based on the experimental measurements. Results illustrated that the best type of spillway in regard to design and resistance against risk of the cavitation and avoiding from the concrete erosion is the stepped spillway with sixth -stepped spillway. The impacts of dimensions and the number of steps on the flow regime and cavitation in stepped morning glory spillways investigated by Bordbar et al. [34] by using the experimental models. Based on the experimental data of the cavitation phenomena, the eleven-stepped spillway with equal height and width were proposed to avoid from minus static pressure.
Fadaei Kermani et al. [35] investigated two important factors influencing on the cavitation damage risk including flow velocity and cavitation index on the morning glory spillways in Shahid Abbaspour dam spillway in Iran. Results illustrated that based on these factors, the major damage occurs at the end of chute areas. Also, the cavitation index factor provides better predictions for the cavitation damage levels, than the minus pressure. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4329747 Preprint not peer reviewed 5 131 Asadsangabi et al. [36] investigated maximum discharge coefficient and cavitation index in 132 shaft-spillways using Volume of Fluid (VOF) method and flow turbulence is modeled by “k-ε” 133 model. Based on experimental results, models were verified and discharge, velocity, pressure 134 and cavitation index for different inlet shapes were computed. The results showed that the VOF 135 approach can provide the appropriate results for solving the problems related to the cavitation 136 phenomena. 137 Parsaie et al. [23]
Figure (4) piping phenomenon on shaft morning glory spillway
Simulated cavitation phenomenon along spillway's flip bucket of the Balaroud dam using Flow-3D. The results of numerical modeling demonstrated that RNG turbulence model has an appropriate performance for modeling the cavitation. Also, the minimum cavitation index in physical modelling was about 0.85, and minimum cavitation index based on Flow 3D results was about 0.665. It was deduced that due to high values of the water head through the morning glory spillway, the static pressure achieves positive values and as a result, the cavitation index was obtained than 0.45 which were indicated that due to increasing the water depth, the risk of the cavitation is decreased significantly. Morning glory spillway is commonly threated by the cavitation phenomena induced by the high values of the velocity and low static pressure because of the performance of this hydraulic structure. It is supposed that finding the safe zone and threated zone by cavitation due to variating of the flow discharge is important item for avoiding and controlling the cavitation. Present study carried out some experimental tests on the experimental models of the morning glory spillway and validated a numerical model based on the experimental information. It is predicted that the different components of the morning glory spillway such as intake of the spillway, vertical shaft, bend pipe, and horizontal shaft were faced with the cavitation due to achieving the requirements of the cavitation. Proposing the suitable shape of the components of the morning glory spillway could reduce the statistic of the citation to zero. So, the cavitation number of the semi- submerged flow which has the worst impact on the generation of the cavitation with different ratio of D/R (D is the vertical and horizontal shaft diameter size and R is the radius of the pipe bend of the morning glory spillway) were explored numerically and some boundaries were proposed to design of the bend pipe of the morning glory spillway with lower cavitation possibility. salehi etal (2023) tried to study the effect of bend on cavitation number in morning glory spillway.
Figure (5) vortex blade type of morning glory spillway
2- Discharge regulation:
Discharge Coefficient and is empirically a function of Fluid Mechanic dimensionless parameters. Where Discharge Coefficient, fluid water head on the crest enters dimensional analysis calculations, not only they make the results more complicated but also bring far from our main objective. Therefore, the parameters effective in flow regime and energy loss of the step are to be analyzed.
3- Dimensional Analysis
Significant and effective parameters may include the velocity of flow on spillway surface (v), fluid dynamic viscosity (μ), spillway diameter (Ds), the ground gravity acceleration (g), fluid density (ρ), step width(b), height of each step(h), and number of steps(N), S ( number of Vortex Breaker) and (Cd) as Discharge Coefficient, Cv1 is related parameter of vortex breaker and Cv2 is parameter of Stepped chamber It is need to add Cv1 and Cv2 are Dimension less functions of Discharge coefficient. The equation which indicates the mentioned parameters is written as below:
(1)
In accordance with Buckingham method, nine variables with three dimensions M, L and T are available. If the number of variables is deducted from the number of dimensions, the number of dimensionless equations would be achieved. In this article, eight dimensionless equations are developed considering the three variables v, ρ and Ds as repeated variable:
(2)
(3)
(4)
(5)
(6)
(7)
The first and second dimensionless equations are respectively inverses of Froude and Reynolds numbers. Using multiplication or division of the two dimensionless equations a new dimensionless equation can be made; therefore, by division of the third and the 5th dimensionless equations will be as following:
(8)
(9)
There are 5 dimensionless equations (equations 1, 2, 4, 5 and 6). However, since the flow in spillways is free and the shear stress is very small near surface, the effect of dynamic viscosity is very little and ignorable (μ≈0). In this case, the dimensionless equation number 2 is deleted and only the first, fifth and sixth dimensionless equations are used and analyzed. The sixth dimensionless equation indicated the number of steps. Moreover, one Dimensionless Parameter which are symbol of vortex and stepped chamber is define as below:
(10)
5-Materials and Methods:
This study has been inspired by the physical model of San Luis For eBay dam spillway which is located at the central valley of California, America.
This model, the dimensions of which have been presented in figure (1, 2), is constituted of a 2000-liter reservoir in upstream (including the body of dam, spillway and water canal), a tunnel for transferring the spillway's water to downstream, a 2000-liter reservoir in downstream of the water transfer tunnel and a pump for water suction from the downstream reservoir to the upstream one. In this experimental model, the spillway body including two types of spillways with completely different designs is devised in the upstream reservoir (figures 3 to 4). The surface arc on two sides of the body of all spillways follows a same equation.
Besides, dimensions of all spillways are the same but the internal surface of each spillway is different from the other. The first type spillway has a smooth surface, and the spillways of the second type respectively have 6-step, The height of each step is h and the width of each step is b. For the smooth spillway it has been supposed that the height and width of each step is very small and same to each other. For the spillways of the second type, the height of each step is continuously changing, and width of each step is fixed and respectively equal to, two centimeters for each spillway. In the Smooth, six-step spillways, one, two and more holes are made respectively on a specific section on each step for calculating water height equivalent to water head on the crest .
In smooth spillway, location of holes is considered the same as that of the 8 holes of twelve, six, four and two -step spillways; therefore, the sum total of holes in spillways of type one to two is respectively 8, 4 and 9. In this regard. Number of holes indicates the Froude number and h/b ratios we require in order to compare the spillways' surfaces with each other. It is true that the number of holes in all spillways should be equal to each other, but due to long distance of the route, the CNC machine cannot make holes in the ending steps; therefore, only the information related to the available points are compared with each other.
Figure 6: Upper view of the physical model (Dimensions based on millimeter)
To determine the flow regime (Froude number) at surface of each spillway some holes are made in the spillway body with specific distances from the beginning of each spillway. The role of each hole is to measure the water height equivalent to fluid water head on the crest at that specific point using monomeric pipe. (It is to be mentioned that Piezometer pipe is the most accurate fluid water head on the crest measurement instrument). Afterwards, energy equation is established between every two points on spillway surface according to Bernoulli principle regardless of fraction loss.
Figure 7: Physical model of smooth spillway Figure 8: Physical model of six-step spillway
Figure 9: Physical model of other stepped shaft spillway
(Dimensions of all spillways are based on millimeter)
Supposing that the flow velocity on the first step is equal to the velocity of the flow entering the spillway, the flow velocity can be calculated from step two on having available the difference of height equivalent to fluid water head on the crest . If the flow velocity at each point is specified, the Froude number related to that point can be calculated using formula 12. Besides, to measure the velocity and inlet flow discharge for each spillway, Triangular weir has been used:
(11)
(12)
(13)
In order to calculate flow rate, one volumetric cube is used and different flow rate was validate and Height – Discharge formula for Triangular weir was deducted. Water level of Reservoir and head on spillway was measured accurately. Finally different parameter s is calculated.
To govern Vortex creation, in Shaft spillways, always vortex breakers (guide pier) are located at spillway crest, in this situation for studying effect of different shape of vortex breaker, 2 different shape, and 2 different arrangement are used to estimate flow rate for two spillways ( smooth and Stepped Spillways). The figure (5) shows shapes of spillways.
Figure 10 : Different types of vortex breaker of Shaft spillway
6-Discussion and Conclusion:
(Hydraulic behavior of Shaft Stepped Spillway:
In the design of dams, spillways are always necessary as safety structures for conveying flood flows. Among the Various types of spillways, the Shaft is a rare option, which may be adopted if space is limited and other local Conditions do not allow a more conventional design.
The structure normally consists of three main components, namely. The cup shaped overflow inlet, the vertical shaft and a nearly horizontal conduit leading to a dissipation structure.
Ideally the flow over the crest and into the shaft should have a free surface. Then, considering symmetric radial inflow over the circular crest of radius R, the stage – discharge relationship is similar to that of a straight – crested spillway, substituting the circumference of the cycle, 2πR, for the length L. Indeed, according to Vischer and Hager (1998), the discharge is given as:
(14)
In this section for estimation Different Emptying Coefficient of Shaft spillway, some experiments were run as below:
Table 2: Information of experiment which has be done
Type of spillway | Different discharge | Type of vortex breaker | arrangement | Thickness of vortex breaker | Number of Experiments |
4 | 5 | 5 | 3 | 2 | 600 |
For creation wide variety of information different discharge from Q= 1.13 lit/s to Q= 6 lit/s were used. And for determination of Discharge Coefficient, equation (14) is used ideally. As a result, It was revealed that best graph and optimum Cd for smooth Spillway is related to utilize vortex breaker with 6 number as arrangement, and the best vortex breaker is number 3 in figure (5). Figure (8) to Figure (11) shows these results.
Figure 11. Discharge against Head of water on crest of Spillway (Smooth spillway) with different Vortex Breaker
Figure 12. cd against h/rs (Smooth spillway) with low height v. breaker
Figure 13. cd against h/rs (Smooth spillway) with low height v. breaker
Figure 14. Cd against h/rs (Smooth spillway) with low medium v. breaker
According to figure (9) t o figure (9) the best Discharge Coefficient is related to 6 Vortex breakers as Arrangement and the flow rate increase more than 15 % averagely. But it should be add, that height increase of vortex breaker has limitation to influence on flow rate increase. In the other hand, when vortex will appeared through Spillway body, Vortex breaking has limitation to control flow rate and while spill way is completely submerged, the function of vortex controlling is not continued. Moreover, when the thickness of Vortex breaker is bigger than 0.2Rs, the emptying Coefficient is not effective, especially when spillway with 4 Vortex breaker will used.
Picture(15) . Experiment with three vortex breaker shaft spillway
When Stepped Morning Spillway are used the results are completely different, For comparison between two Spillway, all Experiment were Run again, Figure ( 10) to ( 13) show the results of runs with Stepped morning Spillway with 6 Steppes.
Figure16. Discharge against Head of water on crest of Spillway (Stepped spillway) with different Vortex Breaker
Figure 17. cd against h/rs (stepped spillway) high height v. breaker thickness 20mm
Figure 18. cd against h/rs (Smooth spillway) with low height v. breaker thickness 9 mm
As a result, it is revealed that the optimum Discharge Coefficient is related to 6 Vortex breakers series and the flow rate increase more than 13 % averagely. But it should be add, that Thickness increase of vortex breaker has limitation to influence on flow rate increase. In the other hand, when vortex will appeared through Spillway body, Vortex breaking has limitation to control flow rate and while spill way is completely submerged. This phenomenon is because of difference of flow regime, which appeared at Stepped Shaft Spillway. In some cases, using vortex breaker decrease flow rate of discharge (Figure (15)).
Picture (19) . Flow passing through Stepped spillway ( stepped spillway) Picture (3) . Flow passing through Stepped spillway( stepped spillway) with creation vortex at down side of spillway
When two of spillway compared to each other, it would be found out that, totally stepped chamber will increase flow rate, considerably.
Figure20. Cd against h/rs (stepped spillway) and smooth spillway without vortex breaker
According to figure (15), the stepped Shaft spillway has better flow rate range and subsequently it is revealed that flow rate ,at this situation, increase 12 % averagely. For better understanding Effect of Stepped chamber on flow characteristics, some mathematical equation has been developed for smooth and stepped Shaft spillway by using S.P.S.S software as fallowing: (Its need to add for this section equation (2) has developed). For Smooth spillway this equation is as below:
(15)
For stepped spillway the equation is as below:
(16)
These equations show that effect of stepped chamber on Emptying Coefficient is significant and some useful equation can be developed for designing more efficient spillway.
For studying effect of different shapes of vortex breaker and different arrangement of guide pier on crest of spillway, some different experiments were done. According to these runs, the best efficiency of discharge coefficient is related to ogee shape as vortex breaker with sixth number on crest. Table (2) shows the result of different discharge coefficient:
Table (2) . Effect of vortex breaker on increasing Discharge Coefficient ( with Using 6 vortex breaker)
EFFICIENCY increasing rate | Shape of spillway | Q(L/s) |
| Cd | Shape of vortex breaker |
1 | smooth | 2.25 | 0.09 | 0.41 | Without vortex breaker |
1.18 | stepped | 2.26 | 0.092 | 0.81 | Triangular long |
1.07 | stepped | 2.26 | 0.172 | 0.44 | Triangular short |
1.14 | stepped | 2.27 | 0.141 | 0.62 | Triangular middle |
1.22 | stepped | 2.26 | 0.12 | 0.69 | ogee shape |
1.09 | stepped | 2.26 | 0.096 | 0.605 | rectangular |
Due to table (2), the best result of utilizing vortex breaker is related to ogee shape vortex breaker which has better effect on passing stream lines through spillway. In the other words, minimum eddies will occur when stream line move smoothly near Shaft spillway body and one boundary line with lower friction will appeared subsequently .
For better understanding and applicability of Experiments, According to number (10) , some coefficient were developed which are present as table(3).
Table (3) . Effect of vortex breaker on increasing Discharge Coefficient ( with Using 6 vortex breaker) and coefficients of steps& vortex breaker
Discharge (lit/s) |
| Cd |
|
|
|
|
|
|
2 | 0.08 | 0.87 | 0 | 0 | 0 | 0 | 1 | 1 |
1.98 | .073 | 1.38 | 6 | 0.2 | 0.025 | 0 | 1.62 | 1 |
2.03 | 0.17 | 0.59 | 0 | 0 | 0 | 0 | 1 | 0.69 |
1.97 | 0.13 | 0.63 | 3 | 0.2 | 0.025 | 0.06 | 1.62 | 0.28 |
2.05 | 0.08 | 0.79 | 0 | 0 | 0 | 0.086 | 1 | 0.929 |
2.04 | 0.079 | 0.81 | 3 | 0.2 | 0.025 | 0.086 | 1.32 | 0.543 |
2.05 | 0.102 | 0.69 | 0 | 0 | 0 | 0.11 | 1 | 0.81 |
2.06 | 0.12 | 0.67 | 3 | 0.2 | 0.025 | 0.11 | 1.32 | 0.449 |
2.01 | 0.08 | 0.86 | 0 | 0 | 0 | 0.028 | 1 | 1.02 |
2.03 | 0.098 | 0.89 | /6 | 0.2 | 0.025 | 0.028 | 1.62 | 0.398 |
In this table Lc is number of steps in spillway barrel, Tv is thickness of vortex breaker, Lv is length of vortex breaker , d is structure diameter and H/Rs is submersible ratio.
According to table (3), the best discharge coefficient is related to smooth spillway with 6 vortex breaker (Cd= 1.38) and second better Cd is stepped spillway, with 12 steps, and 6 vortex breaker.
As a result, It is revealed that when steps chamber will be used emptying parameter decrease averagely about 30 % , but when vortex breaker with 6 arrangement and ogee shape will be utilized , suitable condition for passing flow will be appeared. In the other words, using steps chamber has very good efficiency, especially when cavitations risk should be considered
In order to use these result for using vortex breaker, some equation for calculating Cd based on Submersible ration have been developed. These formulas are estimate for twelve steps spillway with different vortex breaker:
Table (4) . Design formula for Stepped morning spillway
Descriptions | Equations | no | ||
Cd for spillway with 4th Vortex breaker ( with ogee shape ) |
| 1 | ||
Cd for spillway with 3 Vortex breaker ( with ogee shape ) |
| 2 | ||
Cd for spillway with 6 Vortex breaker ( with ogee shape ) |
| 3 |
Maximum H/re ratio for cavitations risk probability | Minimum H/re ratio for cavitations risk probability | Vortex breaker arrangement | Spillway type | no |
Less than 0.37 | More than 0.45 | 6 vortex breaker on crest | smooth | 1 |
Less than 0.34 | More than 0.38 | 6 vortex breaker on crest | 6 STEPS | 2 |
Less than 0.28 | More than 0.36 | 6 vortex breaker on crest | 4 STEPS | 3 |
According to table (5) ,when submersible ratio is less than 0.37 ,then cavitations Index will be more probably increased . But while steps chamber is utilized the story is going to be changed and submersible ration would be changed dramatically. Besides, shape of steps has great effect on flow variation regime. Some normal equation could not be achieved and strongly recommend that for each type of steps some experiment should be run.
Figure (21) water head on the crest ( on manometer) on crest of spillway to body of shaft
7-CONCLUSIONS:
Based on the present experimental investigation, the following main conclusions may be drawn:
Maximum risk of flow rate is magnitude at 1/3 down side of shaft, Magnitude velocity is occurred at the end steps of stepped chamber, and also will take place at ¼ of stepped Shaft spillway.
According to simulation, height and width of each step on stepped chamber has great effect on floe regime , especially when flow regime change from nape to skimming flow
-A morning – glory spillway should be placed as far as possible from reservoir boundaries to ensure radial flow
Over the crest. Then, the discharge calculation is straight forward, with negligible influence of the presence of Piers. Boundary proximity may induce vortex flow and significantly reduce the capacity of the spillway. Therefore, if Vortex development is anticipated, a larger structure (inlet/ shaft/ outlet conduit) would be needed, implying Higher construction costs.
Placement of piers on the crest is an efficient way of coping with the negative effects of the vortex. The
Significance of piers is evident mainly for high discharges, as they can limit the stage increase to about half the
Value observed without piers, and also suppresses water level oscillations.
Using Stepped Shaft spillway has effect on flow rate and in some cases, may caused flow rate increase while using stepped chamber, the cavitation risk should be considered. . According to the runs, although, stepped chamber on spillway decrease flow rate, and also stepped chamber deduce cavitations risk, using vortex breaker with ogee shape increase flow rate till 22%.
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