Last updated: August 11, 2019
Topic: ArtDesign
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1- Introduction:

The addition of H2O demand needs for human multi-purposes and the environmental betterment facets have necessitated the building of new dikes and their related constructions, particularly spillways. Spillwaies frequently are run over moderate to immerse incline channel ranges to convey extra H2O from higher to take down lifts. The flow over such channels is characterized with high speed and kinetic energy. Therefore, excess H2O should be released every bit safely as possible ; otherwise it would do a series harm of cavitation and eroding to the construction itself and the environing country. This could be achieved by protecting the surface of the construction in such a manner that provides a hydro-dynamically unsmooth surface with highly high turbulency which has the ability to decelerate down the rapid flow and disperse a important part of the overruning energy. In order to heighten their effectivity, many techniques have been investigated by hydraulic research workers such as stepped wasteweirs riprap, rock pitching, gabions, stepped wasteweirs… etc.

Stepped channels and wasteweirs have been used for more than 3500 old ages. The easiness of building and the design simpleness have led this construction to be more popular since 1980 ( Chanson, 2002 ) . A stepped wasteweir can be defined as that hydraulic construction in which a series of stairss of different forms, dimensions, and agreements is built into the spillway surface at some distance from the wasteweir crest and extended to the toe and the dissipation of the overruning energy would take topographic point on the construction. Chanson ( 2002 ) points out that energy dissipation is caused by stairss on the wasteweir. These stairss could bring forth high turbulency and aeration due to the strong interaction between the afloat H2O and the environing atmospheric air. Although, the energy dissipation efficiency would be significantly enhanced by stepped wasteweirs, the demand for a big size of the energy dissipator construction at the downstream of the wasteweir could be greatly reduced as good ( Chanson, 2002 ) . The development of new building engineering has regained the design of such construction. Consequently, an intensive probe on stepped wasteweirs has been conducted to find the flow behavior and to supply standardised design standards, particularly associated with roller compacted concrete ( RCC ) for both embankment and gravitation dikes.

2- Literature Review:

Stepped wasteweirs have become popular in recent old ages due to the development of new building engineering. A series of stairss is introduced into the wasteweir profile by which a important part of the overruning energy may be dissipated. High turbulency could be created by the stairss which can be considered as the cardinal point of the energy dissipation procedure. The flow over stepped wasteweirs are characterized with high speed, high turbulency and self-aerated. Assorted measure geometries have been tried to heighten the turbulency and accordingly the public presentation of the construction to disperse the flow energy every bit much as possible. The stairss might be horizontal, pooled, inclined upward and inclined downward.

A brief comprehensive reappraisal of commendations in the literature sing the assorted elements associated with the definition of the fluid mechanicss of stepped wasteweirs is explained in this subdivision. In add-on, due to the limited figure of probes conducted on the inclined stairss, the fluid mechanicss of flow over stepped wasteweirs is concentrated on the flow features over horizontal stairss.

2-1 flow governments and conditions over stepped wasteweirs.

Depending on the discharge and measure geometry, three different flow governments could be distinguished over a stepped wasteweir of any incline. Nappe flow government with little flow rates, planing flow government corresponds with high overruning discharges and the passage flow government between the first two governments with intermediate discharges. Although, each government has its ain flow features, the flow behavior is characterized with extremely disruptive and self-aerated. A item feature of the flow regimes is discussed in the undermentioned subdivision.

2-1.1 Nappe flow government:

By and large, with little flow rates and comparatively big measure highs, a series of over-falls comprises the wasteweir profile. The free falling nappe at the upstream terminal of each measure, an air pit, a pool of recalculating H2O, and with or without a hydraulic leap on the stairss are the flow features of this government. The formation of a hydraulic leap downstream the nappe impact depends on the measure geometry and the flow conditions. Fig ( 1 ) shows a nappe flow government on a single-step theoretical account.

The design of a wasteweir to run specifically for this government is limited for low dikes with larger stairss and flatter inclines. Nappe flow will non be investigated in this survey. More inside informations for this flow government can be found in Horner ( 1969 ) , Chamani and Rajaratnam ( 1994 ) , Chanson ( 1996 ) , Toombes and Chanson ( 2002 ) and Toombes ( 2002 ) , Andre` ( 2004 ) , El-Kamash et Al ( 2005 ) and Toombes and Chanson ( 2008 ) .

Fig ( 1 ) Photograph of nappe flow government on a single-step theoretical account ( from Toombes, 2002 ) .

2-1.2 Skimming flow government:

For comparatively high discharges, the afloat H2O skims over the pseudo underside as a coherent watercourse and cushioned by intense re-circulating pits underneath which are trapped inside the stairss and revolving in a rounded triangular whirl ( Diez-Cascon, Blanko, Revilla and Garcia 1991 ; Chanson 1994 ; Chamani and Rajaratnam 1999 ; Pegram, Officer and Mottram 1999 ) . Pseudo bottom refers to a conjectural line analogue to the chute incline and formed by go throughing through the stairss outer borders. Filled pool with H2O inside the stairss re-circulating whirls are the chief features of this flow government. Fig ( 2 ) presents a planing flow government over a stepped wasteweir. The transmittal of shear emphasis from the fluid fluxing sustains the whirls. This mechanism is considered to be the overriding part of the energy dissipation in this government. In the present survey the flow behavior under planing flow government will be investigated extensively over upward inclined stepped chutes with moderate inclines.

In planing flow government and based on the whirls features and the chute incline, Chanson ( 2002 ) proposed three sub-regimes as follows:

SK1- Wake-step intervention sub-regime. This might be occurred in level chutes ( ? & A ; lt ; 12 ) and can be discriminated by the formation of a wake part downstream the measure border which does non widen over the full measure length and skin clash retarding force could be occurred on the measure downstream of the aftermath.

SK2- Wake-wake measure intervention sub-regime. For inclines ( 12 & A ; lt ; ? & A ; lt ; 25 ) the retarding force tegument fraction is little which could be due to the extension of the aftermath part about over the full length of the measure and the intervention with the aftermath of the consecutive measure.

SK3- Re-circulating pit flow sub-regime. For steep inclines ( ? & A ; gt ; 25 ) a quasi-stable re-circulation may be occurred in the measure corners and the re-circulating Eddies in the pit are large-scale whirls.

Fig ( 2 ) Photograph of planing flow government over a stepped wasteweir ( from Gonzalez 2005 ) .

2.1-3 Transition flow government:

This government would be appeared with moderate discharges. The flow in this government has non been investigated extensively ; hence the current cognition about this government is limited. Basically, the flow is helter-skelter and important figure of H2O droplets would be ejected for highs about 3 to 8 times the measure tallness ( Chanson and Toombes 2004 ) . For this government, nappe flow associated with the presence of air pits can be observed on some stairss and planing flow with re-circulating whirls on the other stairss. Fig ( 3 ) displays the passage flow government over a stepped chute. Passage flow government will non be investigated in this survey. More item on the passage flow government can be found on ( Chanson, 2002 ) , Toombes and Chanson ( 2002 ) and Gonzales ( 2005 ) .

Fig ( 3 ) Photograph of passage flow government over a stepped chute ( from Gonzalez 2005 ) .

2.1-4 Onset of planing flow government:

The complexness of the flow construction, due to high turbulent and air entrainment, has led the analytical solution sing the clear definition of boundaries between the flow regimes to be hard. The ocular reading based on the visual aspect of smooth and glassy H2O surface and measure pits filled with H2O matching for planing flow government and a series of free-falling nappe and air pocket within measure pits for nappe flow government would be greatly subjective. Hence many empirical equations have been proposed based on the ocular reading. Dimensional analysis showed that the flow government anticipation depends on the discharge defined by the dimensionless parametric quantity ( dc/h ) and the wasteweir incline defined by the dimensionless measure geometry ( h/l ) , where, District of Columbia is the critical deepness and H and cubic decimeter are the tallness and length of the measure ( Essery and Horner 1978, Peyras et al 1992 ) .

Rajaratnam ( 1990 ) proposed the first standard to specify the oncoming of planing flow in footings of the ratio between the ( dc/h ) to be greater than o.8 for values of ( h/l ) between 0.4 and 0.9. While, Chanson ( 1994 ) suggested the undermentioned equation to foretell the oncoming of planing flow for 0.2 & A ; lt ; h/l & A ; lt ; 1.25 based on suiting the experimental informations:

… … … … … … … … … … … … … … … ( 1 )

On the other manus, Yasuda and Ohtsu ( 1999 ) proposed the undermentioned equation for the anticipation of the lower bound of planing flow government for stepped wasteweirs of inclines lower than 55:

… … … … … … … … … … … … … … . ( 2 )

… … … … … … … … … … … … … … . ( 3 )

Furthermore, Chamani and Rajaratnam ( 1999 ) presented the undermentioned equation to find the oncoming of planing flow government based on the observation that in planing flux the jet and the wasteweir incline are parallel:

-1… … … … … … … … … … . ( 4 )

While, Chanson ( 2002 ) stated that the oncoming of planing flow government can be predicted from the undermentioned equation:

… … … … … … … … … … … … … … … . ( 5 )

The derivation of the above equation is based on the re-analysis of a big of experimental observation of alteration in flow governments.

Finally, the experimental consequences of Boes and Hager ( 2003a ) on stepped wasteweirs of inclines 30, 40, and 50 showed that the undermentioned equation can be used to foretell the oncoming of planing flows which was in understanding with informations of others.

It should be noted that the above empirical equations were derived for horizontal stairss. In the present survey upward inclined stairss will be investigated and may ensue in the derivation of different empirical equations.

2.2 flow parts over steeped wasteweirs in planing flow government:

In the undermentioned subdivision, the description of natural air entrainment mechanism is merely related to planing flow government. For a skimming flow regime down a besotted stepped wasteweir, four distinguishable parts can be observed as follows:

As H2O flows down a stepped wasteweir, the flow is accelerated and the boundary bed develops and grows quickly following to the crest which has no a important consequence on the H2O surface. This part is known as non-aerated flow and the flow deepness is known as the clear H2O deepness because air is non entrained yet and the flow is seemed to be smooth and glassy.

Natural air entrainment or self-aeration mechanism initiates as the outer border of the disruptive boundary bed reaches the H2O surface and this point is called origin point and white H2O appears clearly. In add-on, the disruptive energy of the whirls moving following to the free surface becomes big plenty to get the better of both the surface tenseness and perkiness effects. Downstream this point a bed incorporating air and H2O extends the flowing fluid which increases the air concentration and the free surface becomes wavy. Further downstream and near the downstream stop the quasi-uniform flow may be achieved, peculiarly in comparatively long incline chutes, where the flow parametric quantities are about changeless on each measure. Fig. ( 4 ) illustrates typical flow parts and air entrainment down a stepped wasteweir under planing flow government. Indeed, Felder, S. And Chanson ( 2009 ) observed seesaw form for the air-water flow belongingss at the to the full developed aerated part downstream a 21.6 steeped wasteweir. They believed that the interaction of consecutive measure pits and their intervention with the free surface cause this form to take topographic point. Therefore, they stated that the construct of unvarying flow on wasteweirs may be restricted to smooth wasteweirs and farther probes needed for the proof of unvarying flow for planing flow on stepped wasteweirs.

2.3- Inception point of air entrainment:

As mentioned above, the intersection point of disruptive boundary bed with the H2O surface is known as the point of origin. Based on ocular reading, it corresponds to the point of the phantom of white H2O ( Chanson, 1994 ; Chamani, 2000 ; Matos, 2000 ) . The exact location of this point is necessary for the interior decorator, because the upstream range of this point is subjected to cavitation hazard. Different empirical equations have been proposed by research workers sing the length to and the flow deepness at this point. Their chief decisions are: the stairss lead the boundary bed to turn faster and hence switching up the origin point farther upstream ; the discharge is the dominate parametric quantity impacting the origin point with a little consequence of the chute incline.

Fig. ( 1 ) Typical flow parts and natural air entrainment down a stepped wasteweir under planing flow part.

The re-analysis for a broad scope theoretical account informations of ( Beitz and Lawless1992 ; Bindo et Al 1993 ; Frizell and Mefford 1991 ; Sorenso 1985 ; and Tozzi 1992 ) , Chanson ( 1996 ) proposed the following two equations to foretell the length to, and the deepness at, the point of origin for spillway inclines from 6.8 & A ; lt ; & A ; lt ; 59:

… … … … … … … … … … … … … … … … … … … .. ( 6 )

… … … … … … … … … … … … … … … … … … … .. ( 7 )

Where, Li, di are the length to, and the deepness at, the origin point severally ; , is the chute incline ; ks is roughness tallness measured perpendicular to the flow way: Kansas = H cos, ; H is the measure height ; and F* is the Froude figure defined in footings of the raggedness tallness deduced from:

… … … … … … … … … … … … … … … … … … . ( 8 )

Where, q is unit discharge, and g as the gravitative acceleration.

Uniting equation ( 11 ) and equation ( 12 ) outputs:

… … … … … … … … … … … … … … … … … … … .. ( 9 )

While, Chamani ( 2000 ) obtained the undermentioned equation to gauge the length from an ogee crest form to the point of origin and the chute incline scope ( 50 & A ; lt ; & A ; lt ; 60:

… … … … … … … … … … … … … … … … ( 10 )

Where Fi is the Froude figure defined in footings of origin point calculated from:

… … … … … … … … … … … … … … … … ( 11 )

In which, cubic decimeter is the measure length.

Matos ( 2000 ) conducted experiments on 53 incline of crested stepped gulch and found the undermentioned equations:

… … … … … … … … … … … … … … … … ( 12 )

… … … … … … … … … … … … … … … … . ( 13 )

… … … … … … … … … … … … … … … … .. ( 14 )

In which, dw and Ci are the clear H2O deepness and the average air concentration at the point of origin severally.

On the other manus, the experimental probe by Boes and Hager ( 2003 ) on gated stepped gulchs with the extension consequences for 26 & A ; lt ; & A ; lt ; 55 crested stepped spillways outputs:

… … … … … … … … … … … … … … … … .. ( 15 )

… … … … … … … … … … … … … … … … .. ( 16 )

… … … … … … … … … … … … … … … … … ( 17 )

Where, Fs is the measure Froude figure defined as:

… … … … … … … … … … … … … … … … … ( 18 )

Additionally, Meireles and Matos ( 2009 ) studied the skimming flow government in the non-aerated part down a 26.6 stepped wasteweir and obtained the undermentioned two equations which about best fit the information of some other research workers:

… … … … … … … … … … … … … … … … . ( 19 )

… … … … … … … … … … … … … … … … . ( 20 )

Although, different empirical expressions have been acquired by different research workers and the subjective standard is still missing, it can be concluded that the flow prosperities at this point depends on the measure geometry and the discharge. The same decision was made by LANE ( 1939 ) on smooth inclines.

In the present survey the point of origin is thought to be shifted farther upstream when compared with horizontal stairss which may be due to decrease of the disruptive boundary bed thickness produced by upward inclined stairss. This could be considered as another advantage of these stairss which shorten the length subjected to the cavitation hazard.

2-4 flow over stepped wasteweirs with upward inclined stairss:

Few experimental probes have been performed on stepped wasteweirs with upward inclined stairss. Research workers studied the efficiency of inclined stairss in footings of energy dissipation or the residuary energy at the downstream terminal of the wasteweir without inside informations of air-water flow prosperities. The cardinal characteristic of upward inclined stairss is to heighten the turbulency and accordingly the energy dissipation.

Horner ( 1969 ) classified the flow over upward inclined stairss into three classs: subcritical with comparatively low discharges, supercritical with higher discharges, and a passage class in which a mix of subcritical and supercritical flow may happen. With subcritical class, the flow leaves the stairss would go through from subcritical to supercritical through a critical deepness and the may return to subcritical by agencies of a hydraulic leap. Furthermore, he considered the full cascade to be acted as a unvarying zone. While, the flow features in the supercritical class were thought to act similar to that on horizontal stairss. However, with passage class he observed subcritical flow in the transitory zone and supercritical flow in the unvarying zone.

Essery and Horner ( 1978 ) stated that with the same incline and measure size and at any discharge, lesser figure of stairss on Cascadess with inclined stairss is required than on Cascadess with horizontal stairss.

Chinnarasri and Wongwises ( 2004 ) investigated the flow over stepped wasteweirs with upward inclined stairss. The chute inclines were 30, 45, and 60 whilst the measure dispositions were 10, 20, and 30 Twenty indistinguishable stairss with measure highs 7.5cm, 10.6cm, and 13.0cm severally were tested with a discharge ranged from 0.01 to 0.17 m2/s. A pitot tubing was used for the mercantile establishment speed measuring at a subdivision which was located downstream to the lowest measure face about 3 to 4 times the measure length where it was thought that the air entrainment was lessened significantly.

Three flow governments were observed ; nappe, passage, and planing flow as the same on the horizontal stairss. In nappe flow, at little sum of discharges, they observed free falling nappe at the measure threshold of the inclined measure and the development of hydraulic leap on the measure face. While the free jet was vanished in the passage flow government, with intermediate discharges, and the free surface became wavy with spray. On the other manus, smooth H2O surface with little air entrainment were the features of planing flow with big discharges. Furthermore, they studied the consequence of measure disposition on the upper bound of nappe flow and the lower bound of planing flow in order to specify the passage government. They observed that the upper bound of nappe flow is non influenced by the measure disposition. While they observed a little addition of the lower bound of planing flow as the measure disposition is increased. This was attributed to the fact that the addition of the measure disposition increases the comparative tallness of the outer border and accordingly both the pool tallness and air pocket under the falling jet of the nappe flow are increased every bit good. However, the undermentioned equation was presented to foretell the minimal critical deepness required for the oncoming of planing flow on chutes with inclined stairss for ( :

… … … … … … … … … … … … … … … … ( 21 )

With as the measure upward inclined angle.

Their experimental consequences demonstrated that, for the same flow conditions, a higher energy dissipation of approximately 6 % of the entire bead height HT was presented by upward inclined stairss, peculiarly in planing flow government, compared with horizontal stairss. They besides concluded that the energy loss is increased by the addition of the measure inclined angle which may be due to the production of more spray caused by the stairss obstructor to the flow way. On the other manus, in nappe flow government, they observed a rapid lessening of energy loss as the bead figure additions. While, in planing flow government, this lessening of energy loss was lessened and approached a changeless value. Furthermore, in footings of speed ratio defined as, this ratio was increased as the bead figure additions for the chute inclines and measure angles tested and the undermentioned empirical equation was proposed to gauge the kinetic ratio:

… … … … … … … … … … … … … . ( 22 )

Finally, they stated that the little difference in the building cost would take the upward inclined stairss to be considered as a more effectual option to horizontal stairss. However, Chanson ( 2002 ) argued that such technique may exercise more hydraulic tonss and increase the cost of the wasteweir and more researches are needed for this intent.

Chinnarasri and Wongwises ( 2006 ) studied the public presentation of stepped chutes holding steep inclines 30, 45, and 60, in footings of energy dissipation, with different measure geometries: horizontal stairss, endsills, and upward inclined 10, 20, and 30 stairss. They introduced the characteristic tallness ( m ) defined as the tallness of the endsill and the incremental tallness due to the upward inclined measure above the horizontal measure. In nappe flow, important energy dissipation was caused by the formation of the hydraulic leap and impact of jet on the measure face connoting a little consequence of the characteristic tallness ( m ) on the comparative energy loss. While, the addition of the characteristic tallness ( m ) increases the comparative energy loss in both passage flow and planing flow governments. However, the consequences demonstrated that stairss with terminal Sillss produced higher comparative energy loss than stairss with upward inclined stairss. This is because the flow is disturbed and obstructed by the terminal sills more than that by the inclined stairss and ensuing in the development of smaller re-circulating whirls in the latter.

In contrast, the experimental consequences of Barani et Al ( 2005 ) showed that the more energy dissipation was produced by stairss with upward inclined than stairss with terminal Sillss in 41.41 stepped wasteweirs with 21 indistinguishable stairss of 4cm tallness and four inclined inclines 15, 26, 36, and 45. Furthermore, the undermentioned empirical equations were proposed to gauge the comparative energy loss as a map of the comparative critical deepness ( ) :

… … … … … … … … … … … … … … … … … . ( 23 )

Where, EL is the energy loss of flow, Eo is the entire caput of flow, , and are coefficients defined as follows:

For inclined stairss:

… … … … … … … … … … … ( 24 )

… … … … … … … … … … … … … . ( 25 )

While, for stairss with terminal Sillss:

… … … … … … … … … … … … … .. ( 26 )

… … … … … … … … … … … … … … ( 27 )

Barani et Al ( 2005 ) stated that for little dikes with low flow rates matching to nappe flow government, most of the energy can be dissipated with inclined stairss and the demand for calming basin at the downstream terminal of the wasteweir can be neglected. For big dikes and high discharges, stepped wasteweirs with inclined stairss can bring forth higher energy loss than stairss equipped with terminal Sillss. They besides concluded that the loss of energy is increased as the angle of measure disposition additions. The same decisions were made by Karim El-Jumaily and Mariam Al-Lami ( 2009 ) when used graduated table 1:20 to analyze Bastora stepped spillway research lab. The stepped wasteweir incline was 42 and three upward slopes 14, 28, and 42 for the stairss were tested with 92 indistinguishable stairss of 4.5cm tallness and 5cm length.

It can be observed that few experiments have been performed on the fluid mechanicss of flow over stepped wasteweirs with inclined stairss. These surveies are restricted to immerse inclines and experiments on moderate inclines are still missing. On the other manus, the fluid mechanicss of flow in footings of the force per unit area on the stairss, the location of the origin point where the self-aeration procedure novices and the part where the boundary bed develops, upstream the origin point, that is capable to the cavitation hazard have non been investigated yet.

In the present survey the hydraulic features of the flow over moderate sloped stepped wasteweirs with upward inclined topography underside are investigated by taking into consideration assorted elements regulating the phenomenon.

3- Numerical simulation and its function in work outing technology jobs:

Recent progresss in computing machines, hardware engineering and the development of robust computational fluid kineticss ( CFD ) package have led the numerical simulation, for work outing practical scientific jobs, to be used widely and be considered as a more powerful alternate tool. Despite the expensive cost and clip consuming of experiments, the direct measurings needed in some of such experiments are frequently, even with high accurate and developed instruments, could non be acquired easy and becomes debatable. Two cardinal attacks have been used to accomplish this end are ; Grid-based methods and Particle-based methods.

Assorted computational fluid dynamic theoretical accounts have been utilized by hydraulic research workers and applied scientists to look into the hydraulic features of flow over stepped wasteweirs based on Grid-based methods. In the present survey this job is investigated exhaustively utilizing Particle-based method for the first clip. Therefore, a comprehensive reappraisal related to Particle-based methods is presented in more inside informations.

3-1 Grid-based methods for imitating flow over stepped wasteweirs:

This method requires pre-defined grid to descretize the job sphere. The complexness of the hydraulic behavior of the flow over stepped wasteweirs, as described in the literature which is characterized by the wavy free surface, high turbulency, self-aerated due to the air entrainment procedure, and droplets ejected into the atmospheric air environing the flow, might do the realistic numerical modeling of such flows be slightly hard. A few numerical simulation of flow over stepped wasteweirs has been investigated utilizing assorted techniques such as Finite difference method, Finite Volume method, Finite Element method, Volume of Flow method ( VOF ) , FLUENT, … … etc. this subdivision illustrates some of import research conducted in this field.

Mehdi, A. ( 1997 ) developed the SPIL-FLOW programme for a 2D finite component method algorithm to happen the location of the free H2O surface profile over an ogee type stepped spillway. In this survey the test and mistake process based on Bernoulli ‘s equation was used. The well-known and by and large accepted U.S Army Corps of Eng. expression was applied to present the effects of the air entrainment on the flow features. It was observed that the theoretical account can be applicable for the day of the month set where the unvarying flow status over the theoretical account was achieved. Furthermore, it was besides found that the numerical consequences of the H2O surface profiles were ever underestimated the experimental consequences by a upper limit of 10 % . It was thought that this could be due to the unsatisfactory application of the air entrainment equation in this survey.

Chen et Al ( 2002 ) investigated flow, including free surface profile, speed profile, force per unit area on the stairss and energy dissipation rates, over an ogee type stepped spillway by experimentation and numerically. In this survey VOF with unstructured grid is used to track the free surface composed of H2O and air. While, the k-e turbulency theoretical account was used to imitate Eddies organizing at the measure corners by which a important part of the overruning energy can be dissipated. The hydrostatic force per unit area distribution was modelled by utilizing a modified resulting force per unit area term. The experimental and numerical consequences were about the same, except in tracking the H2O surface profile where a small disagreement was observed particularly at the terminal of the wasteweir. This was attributed to the fact that in this part the air concentration is comparatively high and the free surface is fluctuated strongly taking the accurate measurings be hard to carry on. On the other manus, the fluid is considered as a single-phase mixture and the impulse and continuity equations are solved based on this premise. Therefore, the cogency of the consequences is still needed to take into consideration the effects of the air entrainment on the flow.

Andre` , S. ( 2004 ) developed a quasi-2D numerical theoretical account of two stage flow over stepped wasteweirs of moderate and steep inclines based on the finite volume attack by using the classical depth-averaged simplified Navier-Stokes equations with the consideration of the stepped underside. A transport equation of depth-averaged air concentration was used to pattern the procedure of air entrainment. While, Bossinesq rectification coefficient was applied to accomplish turbulent flow constructions such as internal jets and recirculating cells for passage and planing flow governments over stepped wasteweirs. Although the comparing of the numerical and experimental consequences were promising and encouraging and demonstrated that the theoretical account is adequately simulated the flow, the theoretical account is still needed to be improved in footings of the disruptive constructions in the perpendicular plane and moving ridges on the free surface.

Chatila and Tabbara ( 2004 ) and Tabbara et Al ( 2005 ) studied the flow behavior, over smooth an ogee wasteweir and a stepped wasteweir severally, by experimentation and numerically. ADINA-F package was used in both surveies by using the finite component attack. The consequences of the physical and numerical theoretical accounts, for tracking the H2O surface profile, of both theoretical accounts were in good understanding particularly for the stepped wasteweir instance. The skip of the air entrainment effects at the mid-section of the smooth ogee type wasteweir led some disagreements to be noticed.

The flow features, in footings of the interaction between entrained air bubbles and pit recirculation in the skimming flow government, speed distribution and force per unit area profiles on the measure surface, over stepped wasteweirs were simulated by CHENG Xiangju et Al ( 2006 ) by using the combined mixture theoretical account of air-water two-phase flow and RNG k-e turbulency theoretical account utilizing the finite volume CFD faculty of the FLUENT package with unstructured grids. The experimental consequences of Chen ( 2002 ) were used in this survey. Promising consequences were achieved in this survey and considered to be the cardinal tool for measuring the cavitation hazard which might take topographic point at the upstream to the origin point.

Zong Dong, Q. et Al ( 2006 ) applied four different turbulency theoretical accounts, viz. : realizable k-e theoretical account, SST k-w theoretical account, V2-f theoretical account and LES theoretical account, to imitate the flow over a steep incline stepped spillway theoretical account. The simulation included the comparing between the experimental and numerical consequences in footings of the growing of disruptive boundary bed, the mean flow speed and the spanwise vorticity behavior. It was noticed that more sensible consequences can be obtained with realizable k-e turbulent theoretical account for simulation flow over stepped wasteweirs. This was attributed to the fact that the rotary motion tensor, which is involved in the flow over stepped wasteweirs, is represented by this theoretical account, but is ignored in the subgrid-scale emphasis in the Smagorinsky-Lilly of LES turbulency theoretical account. Indeed, other theoretical accounts provided inaccurate appraisals. This is because higher turbulency degrees were produced with SST k-w theoretical account particularly in stagnancy parts and parts with strong acceleration. Furthermore, the flow could non be good predicted in the recirculation part near the wall with the v2-w turbulency theoretical account.

The experimental and computational consequences of the speed and force per unit area field flow were besides compared based on the realizable k-e theoretical account. The comparing shows this theoretical account can foretell the flow field adequately. It should be noted that in this survey the writer simulated the flow features in the non-aerated part where the air entrainment is non initiated. However, more probes would be needed to include the consequence of self-aeration on the flow over stepped wasteweirs in the aerated part.

Amarin, T. et Al ( 2009 ) assessed assorted turbulency theoretical accounts, Large Eddy Simulation with Smagorinsky-Lilly subgrid graduated table theoretical account, the non-linear turbulency theoretical account of Craft et Al. ( 1996 ) and the modified non-linear turbulency theoretical account, to foretell multiphase recirculating disruptive free-surface flows over the chute wasteweir with air entrainment. It was observed that higher accurate consequences can be predicted with non-linear turbulency theoretical accounts than with additive 1s. Furthermore, it was concluded that although the consequences of both LES and modified non-linear turbulency theoretical accounts were near, the latter can be run with faster computational clip up to four times than the former. Finally, for wasteweirs wither higher inclines and measure highs, it was found that higher accurate consequences can be predicted with modified non-linear turbulency theoretical accounts than LES.

Fabian, B. et Al ( 2010 ) studied the flow behavior, by experimentation and numerically, in the non-aerated part of the planing flow government in a comparatively big graduated table stepped spillway theoretical account. The air-water flow belongingss, the boundary bed development and the free surface and speed profiles were the chief facets involved in their survey. The finite volume technique of the FLOW-3D package with multi-block grids is applied. Furthermore, k-e and TruVOF methods were utilized to present the effects of the turbulency and air entrainment in the flow over stepped wasteweirs severally. The numerical consequences demonstrated a really good satisfactory to the corresponding experimental consequences. However, some differences were observed with regard to the boundary bed growing with the experimental informations and looks presented by Chanson ( 2006 ) and Amador A. ( 2005 ) , particularly near the wasteweir crest.

3-3 Particle-based methods for imitating flow over stepped wasteweirs:

It is common to work out unstable dynamic jobs, particularly free surface flows, by utilizing grid-based methods as described in the old subdivision. Hydraulic applied scientists frequently encounter jobs from these methods refering to the deficiency of making synergistic fluid simulations together with elaborate flow surfaces. Presents, the equations of gesture of synergistic fluids are solved more efficaciously by utilizing assorted techniques of particle-based methods known as Smoothed Particle Hydrodynamics ( SPH ) . This method is characterized with a meshfree and 3D Lagrangian attack.

Basically, in ( SPH ) the physical belongingss of a unstable component can be represented by smoothened atoms. The physical measures of the fluid elements are averaged over an drawn-out volume utilizing Kernel map to make the smoothened atoms ( Cha, S.-H. et Al 2003 ) .

Originally, this method was presented by Lucy ( 1977 ) and Gingold and Monaghan ( 1977 ) to work out the tree dimensional astrophysical jobs. It has been developed extensively to suit with other physical applications, for illustration free surface flows. Free surface flow and flow over hydraulic constructions, such as weirs ; have been simulated by this method, but up to now this method has non been applied to imitate the flow belongingss over stepped wasteweirs.

Initially, Monaghan ( 1994 ) studied the free surface flow by discretizing the continuum into a finite set of atoms distributed randomly. Each atom carries the physical belongingss, including denseness, force per unit area and speed, of the fluid and moves along the streamline in the infinite and at a certain clip. Problems affecting big distortions can be successfully simulated by this without any mesh polish like other classical grid-based methods.

Ferrari, A. ( 2010 ) developed a new ( SPH ) strategy to imitate the overtopping flow over a sharp-crested weir. The mathematical theoretical account of this survey was based on the decrepit compressible Navier-Stokes equations with the Tait equation of province. The theoretical account was solved by utilizing the 3D parallel SPH strategy, to accurately accomplish both tracking the free surface profile and calculating the force per unit area field, proposed by the same writer ( 2009 ) for free surface flows. The numerical consequences were compared with the experimental information of Scimemi ( 1930 ) in which a really good quantitative understanding was obtained.

4- Problem Statement:

In position of above, it can be noticed that the fluid mechanicss of stepped wasteweirs with upward inclined stairss has non been understood good, peculiarly with moderate and level inclines, sing to upstream range of the origin point where the cavitation might be taken topographic point, the growing of boundary bed and the flow opposition of such stairss to gauge the energy dissipation/ residuary energy accurately.

In the present survey the features of planing flow on stepped wasteweirs of moderate inclines, typical to embankment dikes, with upward inclined stairss will be studied by experimentation and numerically.

5- The purpose of the present survey:

The aim of this research is to:

Conduct an experimental probe on stepped wasteweirs of moderate inclines typical to embankment dikes with upward inclined stairss for a broad scope of flow rate sing to planing flow government.

Analyze the flow belongingss upstream of the origin point which is prone to the potency of cavitation hazard and the development of boundary bed.

Investigate the flow opposition of upward inclined stairss.

Analyze the public presentation of such stairss on the energy dissipation.

To compare the consequences of this probe with others using other measure geometries.

Develop a numerical theoretical account utilizing smoothened atom hydrokineticss ( SPH ) as a new technique for imitating the flow over stepped wasteweir.