Literature Review and Objectives of Study

Transcription

1 Chapter 2 Literature Review and Objectives of Study 2.1 Introduction Chapter 1 briefly introduces problem statement and need to address the issue of energy dissipation. Statistics and studies made by International Commission on Large Dams (ICOLD) show that more than 20% of dam accidents occurred due to poor provision of energy dissipation arrangements (Chaudhry 2008). Energy dissipators are one of the most important parts of dams. Stilling basins are widely used as energy dissipators depending upon their suitability. Many stilling basins are of hydraulic jump type with jump occurring either on horizontal or sloping apron (Bhowmik 1975). According to USBR classification, stilling basins are conventionally designed for a single discharge which is usually the design discharge and their performance at other discharges is tested in a hydraulic model (Vittal and Al-Garni 1992). While the conventional design ensures non-occurance of tail water deficit and hence eliminates repelled (i.e. swept up) jumps, it results in severe submerged or drowned jumps at lower discharges. The deleterious effects of drowned jumps are well known (Chow 1959). Therefore it is necessary to contain clear hydraulic jump (i.e. non-swept and non-submerged) within stilling basin. According to USBR Monograph 25 (page 76), the Bureau of Reclamation has constructed very few stilling basins with horizontal aprons for its larger dams. It has been the consensus that the hydraulic jump on a horizontal apron is very sensitive to slight changes in tail water depth. The horizontal apron tests demonstrate this to be true for the larger values of the Froude number, but this characteristic can be remedied. If a horizontal apron is designed for a Froude number of 10, for example, the basin will operate satisfactorily for conjugate tail water depth, but as the tail water is lowered to 98%, the front of the jump will begin to move. By the time the tail water is dropped to 96%, the jump will probably be completely out of the basin. Thus, to design a stilling basin in this range, the tail water depth must be known with certainty or a factor of safety provided in the design (Peterka 1984). Thus location of hydraulic jump (i.e. toe or front of jump) should be maintained near toe of spillway at all discharges to ensure clear hydraulic jumps. 4

2 2.2 Scope of the Chapter This chapter gives a brief introduction of energy dissipators, their types and factors affecting their design. It includes effects of inadequate energy dissipation and importance of hydraulic energy dissipation. It gives an overview of hydraulic jump including classical and forced hydraulic jumps. Further it discusses use of hydraulic jump as energy dissipator in which an emphasis is given on location of jump and methods to control it. A brief account of hydraulic jumps on sloping apron is given with respect to their types and characteristics. Apart from energy dissipation, other applications of hydraulic jump are also stated. Finally the focus is made on location of hydraulic jump. The factors affecting location of hydraulic jump and their contribution in location control are discussed in detail. The objectives of present study are set based on the limitations of the conventional designs. 2.3 Energy Dissipators When spillway flows fall from reservoir pool level to downstream river level, a large part of static head (total head reduces by losses) is converted into kinetic energy. This energy manifests itself in the form of high velocities which if impeded, results in large pressures. On the other hand, if the high energy of flow is not dissipated, serious erosion to stream bed and damage to hydraulic structures may be caused. The device used to protect the river or tail channel and the hydraulic structures on downstream, is called as energy dissipator. The function of energy dissipator is to absorb high energy of spillway flows and discharge these flows to the downstream water course, without causing serious scour or erosion of the toe of the dam/spillway or damage to adjacent structures (IS ). In hydraulic engineering numerous devices like stilling basins, baffled aprons & vortex shafts are known under the collective term of energy dissipators. Their purpose is to dissipate hydraulic energy. Dissipators are used to dissipate hydraulic energy which may cause damages like erosion of tail water channels, abrasion of hydraulic structures, generation of tail water waves, or scouring Types of energy dissipators IS 4997 (1968) gives classification of different types of energy dissipators. Normally hydraulic jump type stilling basins and bucket type energy dissipators are used depending upon conditions of downstream tail water. Although in case of projects 5

3 where fall is greater than 15 m or discharge intensity is more than 30 m 3 /s/m or for possible asymmetry of flow, it is recommended that performance of energy dissipation arrangement shall be tested on model. The classical hydraulic jump is the best known phenomenon related to energy dissipation. It can be compared with sudden expansion in a pipe and works somehow in a similar manner. It is a free surface phenomenon characterized by a transition from supercritical to subcritical flow. If the tail water level is too low for a classical jump to be generated, the jump can be provoked by various appurtenances. Such a dissipater is called a forced hydraulic jump type stilling basin and it occupies a vital preference among other types Factors affecting design of energy dissipators i) Nature of foundations (geological conditions) ii) Magnitude of floods and their recurrence iii) Velocity of flow iv) Orientation of flow v) Tail water rating curve (i.e. depth-discharge relationship of the downstream water course at the site of the structure). Present study considers two of the above factors that are velocity of flow and tail water rating curve. Rests of the factors are beyond the scope of present study. A brief introduction of these factors is given below. i) Nature of Foundation The foundation of dam, spillway and that of tail channel should be of sound rock and should be watertight. The cracks and interconnected passages present in the rock may lead to uplift pressures. The static and dynamic uplift due to tail water may cause damage to stilling basin floor (Khatsuria 2005). ii) Magnitude of floods and their recurrence The estimation of spillway design flood or the inflow design flood is an exercise involving diverse disciplines of hydrology, meteorology, statistics and probability. 6

4 Several countries have formed their own guidelines or regulations for determination of spillway design flood. In India mostly US guidelines are followed. Generally large dams (storage capacity > 51.7 MCM) are designed for PMF, intermediate dams/barrages (storage capacity < 51.7 MCM) for SPF/PMF and small dams for floods of return period of 100 years to SPF (Khatsuria 2005). Once the spillway design flood is finalized, accordingly spillways are designed. During operations, depending upon the situation, spillways have to pass discharges lower than the design discharge. It may vary from 20% to 100% of design discharge. It should be noted that the damage to Karnafuli dam s spillway and stilling basin occurred at 20% of design discharge of spillway (Bowers and Toso 1988). iii) Velocity of flow The velocity of flow depends on head or energy on upstream. In other words it is the elevation difference between the head race and the top of apron (H). Higher the energy on upstream, at toe of spillway, higher will be the supercritical velocity of flow and lower will be the depth of flow. This means the Froude number F r1 will also be higher. Now higher the inflow Froude number, higher will be the length of hydraulic jump and larger will be the length of stilling basin. Hence on the grounds of economy, instead of hydraulic jump type one may go in for other types of energy dissipator which are comparatively economical (provided the foundation conditions are suitable). Secondly higher velocity may lead to cavitation and the subsequent damage to stilling basin, appurtenances, tail channel and ultimately the spillway or the dam as a whole. Not only high velocities, but low velocities with lot of fluctuations give birth to fluctuating pressures and prove to be dangerous. The floor blocks of Pit 7 dam in Northern California were damaged on account of the swept up hydraulic jump and exposure of blocks to supercritical velocities (Cassidy 1990). USBR Monograph 25 gives formula to calculate supercritical velocities at the foot of spillway (Peterka 1984). The computation of supercritical velocity is discussed in detail in chapter 3. iv) Orientation of flow The orientation of flow also affects the type of energy dissipator. If immediately after energy dissipating arrangement, the channel has curvature in plan, then there 7

5 might be an increase in the tail water depth before the curvature. In case of hydraulic jump type energy dissipator, this may prove to be an important parameter which may strongly govern the design of energy dissipator. In case of ski jump bucket, there are chances that the jet of water, instead of falling into the water cushion, it may directly hit the banks of channel and may severely damage them. v) Tail water rating curve (i.e. depth-discharge relationship of the downstream water course at the site of the structure) The last factor, i.e. tail water rating curve, is the most important of all the factors. A thorough knowledge of its implications on the design of energy dissipation arrangements is a pre-requisite for the design of the most efficient and at the same time cheapest type of structure to serve the purpose. The accuracy of prediction of the prototype performance from the model studies or from theoretical calculations leading to the design of energy dissipator, depends entirely on the accuracy of the data related to depth-discharge relationship at the particular site, where the structure is proposed to be constructed. The simplest kind of device to dissipate energy of the high velocity flow is to enable the formation of hydraulic jump. If the conditions are such that the jump would form for all discharges on a horizontal floor at the stream bed level, then a simple paving on the stream bed extending from the dam to the downstream end of the jump would serve the purpose. A tail water rating curve, for the regime of the river below spillway is fixed by the natural conditions along the stream and is generally not changed by the spillway design or by release characteristics. However retrogression / aggradation of the river below the dam which will affect the ultimate stage discharge conditions must be taken into account while selecting the type of energy dissipating arrangements. Usually where river flows which approach the maximum design discharge have never occurred, an estimate of the tail water rating curve must either be extrapolated from known conditions or computed on the basis of assumed or empirical criteria. Thus usually the tail water rating curve is only approximate and the design of energy 8

6 dissipating arrangements should therefore be slightly on the conservative side, to account for the inevitable deficiencies or inaccuracies in tail water rating curve (Garud 1984). The effect of tail water submergence is discussed in detail in chapter Effects of inadequate energy dissipation It is already mentioned that more than 20% of dam accidents occurred due to poor provision of energy dissipation arrangements (Chaudhry 2008). Various case studies related to damages of spillways and stilling basins and tail channel erosion are reported all over the world. These studies have revealed the importance of adequate energy dissipating arrangements. Following are some of the illustrations of damages due to inadequate energy dissipation Sardar Sarovar Project Sardar Sarovar Project (SSP) is one of the major projects in India. In the year 1999 it is reported that during a flood in monsoon season, 10,000 m 3 of concrete was washed out due to flood flows. The design discharge of spillway is 87,000 m 3 /s. The flood was even lesser than 50% of the design discharge. The approximate cost of concrete that washed out was Rs. 3 crore. Also it was mentioned that the damage of varying magnitude occurs almost every year. The technical analysis of the damage is given by Khatsuria (2005) and is briefly discussed below. Flow conditions downstream of partly constructed spillway are often unsatisfactory and conducive to damage. When different monoliths are kept at different elevations instead of at uniform level for the entire spillway, unequal discharge distribution occurs. Floors of hydraulic jump stilling basins are particularly vulnerable to damage due to horizontal eddies forming in the downstream. Such eddies pickup loose material from downstream, bring it inside the basin, and cause abrasion damage to the concrete floor, commonly known as roll-mill action. The damage sometimes is so extensive as to expose the reinforcement steel of the apron floor. Fig. 2.1 shows view of damaged stilling basin floor of a dam as a result of the abrasion caused due to material that was brought in by the return eddies during a construction stage. This, perhaps, cannot be prevented in ordinary situations. A remedy adopted at the Sardar Sarovar Dam, was to provide a number of low height divide walls in the basin. 9

7 Fig. 2.1 Damage to stilling basin floor of SSP Report of World Commission on Dams The report of world commission on dams includes research papers on Dams and Development. It is expected that the literature would be helpful towards developing a new framework for decision making. The case study included hereunder is one of 126 contributing papers to the World Commission on Dams. Excessive scour downstream of spillway When a high velocity jet or sheet of water flows downstream from the spillway, it may erode the bed material and carry it either in suspension or as bed load farther downstream. Serious scour immediately below the spillway may endanger its foundation. Several Dams with flip buckets, founded on stratified rocks are experiencing scour downstream. Ukai Dam in Gujarat is such example. Ukai Dam (Guiarat) The spillway of Ukai dam is designed for the discharge of 45,300 m 3 /s. Ukai dam spillway with 22 gates for catering to an outflow of 39,330 m 3 /s was operated as an ungated structure in the year The floods were released over the crest without gates and later gates were erected in A deep scour hole was noticed 100 m downstream indicating a 29m deep scour in dolerite dyke. In 1978 the spillway 10

8 discharged 12,750 m 3 /sec only through 11 gates. The trajectory of the ski jump had caused scour below the foundation level of the dam. As a measure of rehabilitation among other items, anchoring of rock foundations by steel grip rods embedded in M20 concrete was undertaken Pit River Spillways (Northern California) Pit 7 Dam on Pit River in Northern California is a hydroelectric facility with only a moderate amount of reservoir storage. The dam was completed in After peak spills of m 3 /s in 1969 and a flood with an estimated peak flow of m 3 /s in 1970 (design flow was 2267 m 3 /s), the reinforced concrete stilling basin, chute blocks and floor blocks severely damaged due to sweep out of hydraulic jump (Cassidy 1990). Six of the ten floor blocks had been broken off and carried downstream of the stilling basin. The remaining four floor blocks and the chute blocks had been severely damaged by cavitation. The blocks were then reconstructed and covered with 2 inch thick steel plates. In 1974, after another large flood of 850 m 3 /s, the floor and chute blocks were again badly damaged; two of the floor blocks were again broken off and carried out of the basin. Analysis showed that velocities entering the basin probably exceeded 30 m/s, well beyond the limit of 15 m/s for such basins recommended as a maximum by the U.S. Bureau of Reclamation (Peterka 1984). A model study subsequently showed that the hydraulic jump was located too far downstream in the basin to keep the blocks from being impacted by the very high velocity flow. Thus, both the floor and chute blocks were subject to velocities of approximately 30 m/s, which made the possibility of cavitation damage a certainty. Examination of the failed blocks indicated that the floor blocks that had been broken off probably failed by fatigue. Fatigue had to be caused by fluctuating forces on the blocks caused by the flow oscillations created by flow around the blocks. In this case, it was possible to change the design from a hydraulic-jump type stilling basin to a flip bucket. A similar hydraulic-jump basin had been constructed at Pit 6 dam that was nearly identical to Pit 7 in hydraulic design and had also been completed in Similar damage had been experienced at this basin. However, for that dam, it was impossible to modify the design to a ski jump because of a cliff and a bend in the river immediately downstream from the dam. A roller bucket energy dissipater would have been a logical modification. 11

9 Karnafuli Dam (Bangladesh) The Karnafuli Hydroelectric Project is located in Bangladesh. It consists of an earth fill dam 41.2 m high, a spillway 227 m wide, and hydropower facilities. The project was largely complete by June 1961, when the spillway was placed in operation to pass the monsoon floods. On August 13, 1961, "distress was noted in the spillway flow". The gates were closed on August 20. Inspection of the spillway revealed extensive damage to the chute floor over an area about 180 m wide and 23 m long. Fig. 2.2 shows the damages to the spillway chute and Fig. 2.3 (a) shows the damaged chute blocks (Bowers and Toso 1988). According to Bowers and Toso, the model studies indicated that fluctuating pressures in the drowned hydraulic jump, with magnitude upto 11m of head could have entered the 0.3m drain lines in the chute blocks and caused uplift of the chute blocks. Fig. 2.3 (b) shows typical profiles of clear (profile-1) and drowned (profile-2) hydraulic jump. Discharges up to 3,480 m 3 /s had occurred at Karnafuli Dam during the 1961 season. This was about 20% of the design discharge of 18,000 m 3 /s. A special board of consultants considered possible causes of the chute damage, such as: (1) Uplift pressure from seepage; (2) uplift pressure under the pavement having origin in the difference in head over the drainage ejectors in the dentates and on the surface of the pavement, i.e., tailwater uplift and (3) impact of logs. On the basis of site inspection, it was concluded that seepage uplift was not the cause of the damage. There was a difference of opinion on the other two possible causes. Inspection of the site after dewatering of the stilling basin revealed only a small amount of seepage. 12

10 Fig. 2.2 View of one-half of Karnafuli dam spillway showing damage Fig. 2.3 (a) View of chute blocks, drain openings and damaged chute slabs 13

11 Fig. 2.3 (b) Typical Stilling basin profile, showing flow profile curve 1 (frequently assumed in spillway design), and profile curve 2 which may actually occur Bhama Askhed Dam (India) At Bhama Askhed Dam EDA (India), in the year 2005, flood damages have occurred. 12 out of 35 RCC panels (of size 11m x 7m x 0.3m thick and weighing 55 Tons each and with 5-anchor bars of 25mm diameter) were dislodged from their location and few of them were thrown away outside the basin. It will be clear from photographs shown in Fig 2.4, Fig. 2.5 and Fig Fig. 2.4 View of dislodged RCC panels in Bhama Askhed dam EDA 14

12 Fig. 2.5 Close view of twisted reinforcement of RCC panel Fig. 2.6 Close view of damaged RCC panels Importance of Hydraulic Energy Dissipation Stilling basins including baffles, flip buckets or other energy dissipators should be examined for any conditions which may pose constraints on the ability of the stilling basin to prevent downstream scour or erosion which may create or present a potential 15

13 hazard to the safety of the dam. The existing condition of the channel downstream of the stilling basin should be determined. Therefore it is necessary to understand following parameters. The Mechanism of Energy Dissipation Every moving fluid particle or drop of water loses some of its hydraulic energy along its trajectory. This loss is a result of friction or drag forces that are closely related to turbulence production in hydraulic energy dissipators. The process of energy dissipation can be usefully divided into two cases: 1. A particle of water within a water current, and 2. A drop of water in an air current. In the first case, the energy dissipation is related to energy consuming eddies. Such eddies are mainly generated in shear zones, i.e. in zones of large velocity gradients. To induce a considerable loss of energy, the creation of high turbulence zones is therefore important. In the second case, the energy dissipation results from the air resistance exerted to the drop of water. It is large if the drop is small and the relative velocity between the drop & the ambient air is high. Efficient energy dissipation is a matter of disturbing the water current either by increasing its turbulence or by diffusing it into spray. An economical energy dissipator design is the one which affects such an impact within a comparatively small region. The Methods Various methods are available for the concentrated dissipation of energy. According to two mechanisms mentioned above, they can be divided into two process categories characterized by the following group of phenomena: 1. Provoking large velocity gradients and thus increasing turbulence in the current with devices like sudden expansions, sharp deflections, throttles, sills & end sills, chute blocks, baffle piers and beams, counter flows, vortex chambers. 2. Creating extended and turbulent interfaces between the water and the surrounding air by devices that create free jets and split free jets. 16

14 Out of various mechanisms given above, attention is focused on end sills. The other mechanisms are beyond the scope of the present study. Limitations Energy dissipation is achieved either by strong disturbance or by an effective diffusion of the flow. Therefore the designs of energy dissipator and of a hydrodynamic element are opposed; the latter tends to produce a smooth current with only small disturbances. The large disturbances have strong consequences. The energy dissipators can induce forces like Uplift (static + dynamic), Pulsation, Vibration, Erosion, Abrasion and Cavitation. Energy dissipators must have the structural stability to resist these stresses. Unfortunately, hardly any material can endure strong & permanent cavitation and can withstand abrasion by flow that is heavily laden with silt or gravel. Thus there are limits pertaining to the hydrodynamic designs. Most energy dissipaters are built of concrete and steel, hence the properties of common building materials set the limit. Thus, it becomes important to address suitable methods of energy dissipation, which are practically feasible and at the same time are not prohibitively expensive. Generally the dissipation devices are designed to give very good results, for the given design conditions but they fail when the operation condition differ from the design condition or give less than satisfactory results. In the present research work efforts are made to overcome this limitation by designing a suitable energy dissipator which performs satisfactorily over wide range of operational condition. Guidelines of USBR Monograph 25 USBR Monograph-25 Hydraulic Design of Stilling Basins and Energy Dissipators, by A. J. Peterka, generalizes the designs of stilling basins, energy dissipators of several kinds and associated appurtenances. General design rules are presented so that the necessary dimensions for a particular structure may be easily and quickly determined and the values can be selected (checked by others) without the need for exceptional judgment or extensive previous experience. It deals with the hydraulic phenomena of energy dissipation in hydraulic structures. As already mentioned, the focus is on currents with comparatively high rate of energy dissipation, i.e. flows in which significant energy is dissipated in a limited amount of space. 17

15 Energy dissipaters are used in pressurized flows as well as in open channel flows. They provide a transition between high and low hydraulic energy. Three such transitions can be distinguished: One pressure conduit to another, A pressure conduit to a channel, One channel to another channel. This monograph includes primarily those energy dissipators that think either pressure conduits to channels or one channel to another. The other types comprise the rich variety represented by throttles, pressure valves, mixing tubes, etc which are not dealt in monograph. 2.4 Hydraulic Jump as an Energy Dissipator An Overview Hydraulic jump in open channel is an abrupt transition from supercritical depth to subcritical depth. The hydraulic jump forms when two jets of water, moving in same direction override each other. At the common plane of interaction, the force due to rate of change of momentum is balanced by the pressure force. The phenomenon of formation of hydraulic jump is associated with formation of eddies and turbulence which ultimately lead to dissipation of energy. Chow (1959) has given a chronological development of hydraulic jump theory. The theory of jump developed in early days is for horizontal or slightly inclined channels in which the weight of water in the jump has little effect upon the jump behavior and hence is ignored in the analysis. The results thus obtained, however, can be applied to most channels encountered in engineering problems. For channels of large slope, the weight effect of water in the jump become pronounced and needs to be included in the analysis. The hydraulic jump is also known as standing wave. In French, it is called le ressaut hydraulique. In German, it is der wassersprung. In honor of Bidone, the hydraulic jump in Italian is named il salto di Bidone (the jump of Bidone). 18

16 2.4.1 Hydraulic Jump in General When supercritical flow with small depth meets the flow in subcritical region with large depth, the high velocity flow tries to penetrate through the low velocity flow. Rollers (stagnant eddies) are generated with high turbulence releasing energy. Thus energy of the high velocity flow is dissipated in short distance and the flow stabilizes in subcritical zone. This principle is considered in hydraulic jump type energy dissipators. The pre jump depth y 1 in the supercritical zone and the post jump depth y 2 in the subcritical zone, generally known as conjugate depths or sequent depths, are design parameters for such energy dissipators. A jump can occur below spillway or sluice gate. The high head on upstream of spillway or sluice gate give rise to supercritical flow near toe of spillway or sluice gate. The flow in the channel downstream would be subcritical due to mild slope. Thus the change of flow from supercritical stage to subcritical stage results in formation of hydraulic jump. A hydraulic jump also forms at the junction of steep slope and the mild or horizontal slope Classical Hydraulic Jump Hydraulic jump formed under laboratory conditions in rectangular prismatic channel with horizontal slope is known classical hydraulic jump. Assumptions in the Theory of Classical Hydraulic Jump 1. The Channel is rectangular and prismatic. 2. The slope of the channel is horizontal or very mild so that the component of the weight of liquid in the direction of flow is negligible. 3. The hydraulic jump takes place in a very short distance of the channel so that the frictional losses are negligible. 4. The flow before the jump and after the jump is uniform and one dimensional. 5. The pressure distribution before the jump and after the jump is hydrostatic. 6. The velocity distribution before the jump and after the jump is uniform so that α = β =

17 2.4.3 Forced Hydraulic Jump In overflow structures water is released to downstream side from high head. In such situation the high velocity flow needs to be controlled and released with non eroding velocity. This is attained by introduction of different artificial roughnesses, such as chute blocks, baffle blocks and end sill in a stilling basin to control formation of a hydraulic jump at various locations on the apron depending upon the tail water depth (Bhowmik 1975). These artificial roughnesses can forcibly form the jump at the entrance section of the stilling basin and thus confine the jump within a specified limit making it practical to predict the location of jump. Such a jump is termed as forced hydraulic jump. Since a forced hydraulic jump is the basic design element for the hydraulic jump type stilling basin, a considerable amount of experimental, theoretical and field work has been performed on these types of basins. Blaisdell, Forster and Skrinde, Harleman, Rajaratnam, Peterka, Rand and other investigators have made extensive laboratory experiments, in some instances with field follow-up, on the design and performance of forced hydraulic jump type stilling basins (Chow 1959). The simplest of the appurtenances is a vertical rectangular end sill occupying the whole width of the basin. The vertical sill is ineffective if the sill height is too small or the front of the jump is too far upstream from the end sill. As the Froude number increases, the front of the jump travels downstream, forms a boil above the end sill, and returns to a stage less than critical after the boil; a secondary hydraulic jump may then develop in the downstream reach of the basin. With further increase in upstream Froude number, the supercritical flow passes over the sill and continues downstream. But for any one of the above cases, adjustment of tail-water depth can substantially alter the location and formation of the jump. The most common type of stilling basin on a horizontal floor is a rectangular basin supplied with an end sill and one or two rows of baffle blocks controlling the tail water depth, the hydraulic jump can be stabilized within the basin Hydraulic Jump as Energy Dissipator As the water flows over spillway or under sluice gate, the potential energy possessed by water gets converted into kinetic energy. In case of spillway, by the time water reaches the toe of spillway, it takes the form of high velocity jet. This high velocity jet has lot of scouring potential. When this supercritical flow passes through the solid 20

18 boundary it leads to cavitation. But, when hydraulic jump forms, the supercritical flow converts into subcritical flow with the rise in depth of water and there is reduction in velocity of water. The subcritical water depth can be as high as 10 times that of supercritical depth for F r1 =7.4. Conversely the subcritical velocity can be as low as 1/10 th of the supercritical velocity. More the reduction in velocity more will be the energy dissipation. Hence all that is expected in energy dissipation is the reduction of incoming supercritical velocity. And it can be best achieved within limited space and at reasonable cost with the help of hydraulic jump type energy dissipator. The hydraulic jump used for energy dissipation is usually confined partly or entirely to a downstream channel reach that is known as stilling basin. The bottom of the basin is paved to resist scouring. In practice, the stilling basin is seldom designed to confine the entire length of a free hydraulic jump on the paved apron, because such a basin would be too expensive. Consequently, accessories to control the jump are usually installed in the basin. The main purpose of such control is to shorten the range within which the jump will take place and thus to reduce the size and cost of the stilling basin (Moharami et al 2000). The control has additional advantages, like; it improves the dissipation function of the basin, stabilizes the jump action and in some cases increases the factor of safety. In designing a stilling basin using hydraulic jump as energy dissipator, following practical features should be considered Jump position There are three alternative patterns that allow a hydraulic jump to form on downstream from the source (such as an overflow spillway, a chute, or a sluice). The most important parameter that influences the position / location of hydraulic jump is the tail water depth. The relative magnitudes of post jump depth and tail water depth decide whether the jump would form or not (Chow 1959). If at all it forms, it may be partially swept up or drowned or with proper location. There are six cases which demonstrate different possibilities discussed above. First three cases will demonstrate the process of natural jump formation on horizontal apron without any appurtenances. Thus in all these cases y 2 = y t and y 2 ' = y t. Remaining three cases will demonstrate the process of forced jump formation on horizontal apron with a rectangular broad crested weir at its end. Brief description of these cases is as follows. 21

19 Case I It represents the pattern under design discharge condition in which the tail water depth y t is equal to post jump depth y 2 which is sequent to pre jump depth y 1. In this case, the values of F r1, y 1 and y 2 (= y t ) will satisfy Belanger equation, and a free jump will occur on a solid apron immediately ahead of depth y 1 as shown in Fig For scour protection purposes, this is an ideal case. One big objection to this pattern however, is that, a little difference between the actual and assumed values of the relevant hydraulic coefficients may cause the jump to move downstream from its estimated position. Consequently, some device to control the position of the jump is always necessary, Design discharge condition (y t = y 2 ), y 2 is sequent to y 1 Hence jump formed at y 1 y 2 y t y 1 Fig. 2.7 Location of hydraulic jump at exact tail water condition Case II It represents the pattern under design discharge condition in which the tail water depth y t is less than y 2. As a result of this, the jump will recede downstream as shown in Fig. 2.8 and form at a point where Belanger equation is satisfied. If possible, this case must be avoided in design. Because in this case the jump may partially or fully sweep out of the basin and a high velocity supercritical flow may directly come in contact with the basin floor and the tail channel. This may further lead to cavitation and subsequent damages. Also if the jump is swept partially as shown in Fig. 2.8, apart from the danger of cavitation, the fluctuating pressure in the hydraulic jump may induce hydrodynamic uplift pressure. Also due to jump sweep out, the weight component of water get reduced which otherwise balances the static uplift force. 22

20 Design discharge condition (y t < y 2 ), y 2 ' is sequent to y 1 ' Hence jump formed at y 1 ' y 2 ' y t y 1 y 1 ' Fig. 2.8 Location of hydraulic jump at tail water deficiency Case III It represents the pattern under design discharge condition in which the tail water depth y t is greater than y 2. As a result of this, the jump will move upstream and may form on spillway chute as shown in Fig In this case the jump may be partially or fully submerged depending upon the tail water submergence and is also called as drowned jump. Design discharge condition (y t > y 2 ) Hence jump gets drowned y 2 ' y t Fig. 2.9 Location of hydraulic jump at tail water excess condition Case IV (a) It represents the condition in which, at discharges less than design discharge (say at 50% of design discharge), the tail water depth y t is quite less than the required post jump depth y 2 as shown in Fig (a). Thus in this case there is total sweep out of hydraulic jump and the jump may form entirely away from the basin, in the tail 23

21 channel. But in this case the whole stilling basin would be exposed to supercritical flow which may lead to cavitation damages. Q < Q design (y t < y 2 ), Hence jump fully sweeps out of basin y 2 ' y t y 1 Fig (a) Swept up hydraulic jump at tail water deficiency Case IV (b) It represents the case in which a rectangular broad crested weir is constructed at the end of the horizontal apron. The height of weir (H 1 ) shown in Fig (b) is designed for the discharge equal to 50% of the design discharge (Q = Q design / 2). For this height a clear jump is formed at the toe of spillway. Q < Q design (y t < y 2 ), y 2 is sequent to y 1 Hence jump formed at y 1 y 2 y t H 1 y 1 Fig (b) Location of hydraulic jump at tail water deficiency when tail water is boosted up by weir of height H 1 Case V It represents the case in which a rectangular broad crested weir is constructed at the end of the horizontal apron. The height of weir H 2 (>H 1 ) shown in Fig. 2.11, is designed for the 100% of the design discharge. For this height a clear jump is formed at the toe of spillway. But this emphasizes that height of end weir is 24

22 proportional to the discharge. Fig shows the photograph of clear hydraulic jump on field. Q = Q design (y t < y 2 ), y 2 is sequent to y 1 Hence jump formed at y 1 y 2 H 2 y t y 1 Fig Location of hydraulic jump at tail water deficiency when tail water is boosted up by weir of height H 2 Fig View of clear hydraulic jump at the bottom of spillway 25

23 Case VI It represents the case in which a rectangular broad crested weir is constructed at the end of the horizontal apron. The height of weir H 2 shown in Fig is designed for 100% of the design discharge and is exposed to 50% of design discharge. As the height of weir happens to be excess for 50% discharge, the hydraulic jump gets drowned out. This further induces the problems associated with the drowned jump. Fig shows the photograph of drowned hydraulic jump on field. Q < Q design (y 2 '> y 2 ) Hence jump gets drowned y 2 ' H 2 y t Fig Location of hydraulic jump at lower discharges when tail water is boosted up by weir of height H 2 Fig View of drowned hydraulic jump at the bottom of spillway 26

24 Control of Hydraulic Jump by Sharp Crested Weir As per Forster and Skrinde, the hydraulic jump can be controlled by sills of various designs such as sharp crested weir, broad crested weir, abrupt rise or abrupt drop in channel floor (Chow 1959). The function of a sill is to ensure formation of jump and to control its position under all probable operating conditions (Hager and Li 1992). At high submergence, the drag force on sill essentially depends on the ratio of sill height to prejump depth (Narayanan and Schizas 1980). The exact position of the jump, as controlled by the sill, however cannot be determined analytically. It is presumed by Forster and Skrinde that tail water level does not affect y 2. That means the tail water submergence effect has been neglected. In authors opinion, none of the above mentioned sill can effectively help formation and control of location of hydraulic jump under varying discharge conditions. This is because, for wide range of discharge, it is necessary to consider variation from design discharge as maximum discharge to 20% of design discharge as minimum discharge. Over this range of discharge, the values of y 1, y 2, y t and F r1 for each discharge are different. Primarily the formation of jump depends upon the values of y 1 and y 2. Further the magnitude of y 2 depends upon the magnitude of y t. y t depend upon the geometry of downstream channel reach. And it is very difficult to calculate the exact value of y t. If y t goes wrong then y 2 also goes wrong. If y 2 goes wrong then the formation and location of jump also affect. At present no design of hydraulic jump type stilling basin satisfy this requirement over a wide range of discharge. Second important lacuna is that, if tail water level is above the sill height it has got influence on y 2 which is on upstream of the sharp crested weir. Therefore it is essential to design a stilling basin which can cater to wide range of discharges by way of forming hydraulic jumps near toe of spillway with the uncertain tail water depths. In authors opinion it can be done by designing a sill in the form of stepped weir. Because stepped weirs give stepwise flexibility which can be utilized to generate required y 2 for available y t by designing the rise and tread accordingly. In the proposed new design, tail water depth has been included as one of the input parameters. 27

25 2.4.5 Hydraulic Jump on Sloping Apron Experiments with hydraulic jumps formed in sloping channels were carried out by many researchers to determine the kind of properties that are same as those pertaining to jumps in horizontal channels. The one dimensional momentum principle for the sequent depth ratio cannot be applied because the component of weight of jump (Wsinθ) is not known a priori. This is because Wsinθ involves the length and profile of the jump, information about which can be obtained only through experimental observations (Subramanya 1986). As such, even though many attempts have been made to obtain the sequent depth ratio through the momentum equation, no satisfactory general solution is available so far Types of hydraulic jumps on slope Hydraulic jumps in sloping channels may occur in various forms. Kindsvater classified the jumps in 1944 according to their toe position relative to the bottom kink (Hager 1992) as A, B, C, and D as shown in Fig D C B A y 2 θ L j Fig Types of Sloping Jumps - A, B, C and D A-type jump is nothing but a jump on horizontal apron. As per Chow (1959), B, C and D are known as drowned out jumps and are the common forms which usually appear simply as jets of water plunging into a downstream pool below a steep slope. For practical purposes, it is believed that the solutions for the typical form of hydraulic jump on sloping apron are applicable to B, C and D-type of jumps. A and B-type of jumps mostly occur with steep slope channel (i.e. downstream face of spillway) followed by horizontal or nearly horizontal apron. C and D-type of jumps occur on relatively flat or small sloping channels. Gunal and Narayanan (1996) have studied the internal structure of hydraulic jumps wholly formed on channels of small 28

26 slopes ranging from 0 to 0.1. Ohtsu and Yasuda (1991) studied D and B-type jumps and have proposed practical equations for the sequent depths and the length of jumps. Hager (1989) investigated B-jump in sloping channel and concluded that the jump efficiency is maximum for the classical hydraulic jump. Alhamid (2004) studied the jump characteristics on sloping basins and confirmed that the sequent depth ratio is proportional to the bed slope. In the present study, essentially a hydraulic jump location on apron with small slope is studied. In this case, bed of tilting flume is given a positive slope and this is how a sloping apron is created. Sloping apron can be adopted on sloping downstream channels (after a kink) only on the ground of economy which can be achieved as against the horizontal apron. When a hydraulic jump occurs on a channel with sloping floor, the situation is described by the general momentum equation given by P 1 P 2 + W.sinθ = M 1 M 2 (2.1) There are too many unknown terms relative to the number of available equations and unless additional information is provided, solution of the momentum equation is not possible. Even if the situation of rectangular frictionless channel is considered the term W.sinθ representing the longitudinal component of weight of water in the jump poses a problem as an unknown quantity. This is because W.sinθ involves length and profile of the jump, that is, information of which can be obtained only through experimental observations. As such, even though many attempts have been made to obtain the sequent-depth ratio through the momentum equation, no satisfactory general solution is available so far. An example of the typical simplification of the above equation to obtain sequent-depth ratio on a sloping floor is given by Subramanya (1986) as follows. The Froude number of flow in rectangular channel with large θ is given by V1 F1 S = (2.2) g.y.cos θ 1 The momentum equation finally renders 29

27 y y 2S ( K.L tan θ) ( K.L tan θ) j y 1 y y 2S j y 1 2 2F 1 y + cos θ y 2S 1 2 2F1 + = 0 cos θ (2.3) This equation can be used to estimate the sequent-depth ratio by a trial and error procedure if the term (KL j ) is known. Here K is a coefficient which accounts for the curvature of the jump. In general, (KL j ) can be expected to be a function of F 1 and θ and its variation can be obtained only through experimental study Characteristics of Jump on a Sloping Floor Extensive experiments have been conducted by the United States Bureau of Reclamation resulting in useful information on jumps on a sloping floor. Based on the USBR study following significant characters of sloping-floor jumps can be noted. i) Sequent depth y 2S Defining y 2 = equivalent depth corresponding to y 1 in a horizontal floor jump y y1 2 = ( Fr1 ) (2.4) The sequent depth y 2 is found to be related to y 2S as y 2S y 2 = f ( θ) (2.5) The variation of y 2S / y 2 with tanθ is given by Subramanya (1986). By definition y 2S / y 2 = 1 when tanθ = 0 and it increases with the slope of the channel having typical values of 1.4 and 2.7 at tanθ = 0.10 and 0.30 respectively. Thus the sloping jumps require more sequent depths than the corresponding horizontal-floor jumps. The best fit line for the variation of y 2S / y 2 with tanθ can be expressed as y y 2 ( tan ) S e θ = (2.6) ii) Length of sloping jump L j The length of sloping jump L j was defined in the USBR study as the horizontal distance between the commencement of the jump and a point on the subcritical flow region where the streamlines separate from the floor or to a point on the level water 30

28 surface immediately downstream of the roller, whichever is longer. The length of the jump on a sloping floor is longer than the corresponding length of jump on a horizontal floor. The variation of L j /y 2 with F 1 for any θ is similar to the variation for θ = 0. In the range of 4.0 < F 1 < 13, L j /y 2 is essentially independent of F 1 and is a function of θ only. The variation can be approximately expressed as L j /y 2 = tanθ in the range of 4.5 < F 1 < 13.0 (2.7) Elevatorski s analysis of the USBR data indicates that the jump length can be expressed as L j = m s (y 2s y 1 ) (2.8) In which m s = f(θ). The variation of m s with tanθ is given by Subramanya (1986). It may be seen that for m s = 6.9, tanθ = 0 and it decreases with an increase in the value of the channel slope. iii) Energy loss E Ls Knowing the sequent depths y 2 and y 1 and the length of the sloping channel, it is found that the relative energy loss E/E 1 decreases with an increase in the value of θ, being the highest at tanθ = 0. In short, as compared to jump on horizontal floor, the sloping jump requires larger post jump depth and larger length of stilling basin. Also the relative energy loss in the sloping jump is less than the corresponding horizontal jump. It should be noted that, in a sloping jump, rather than Froude number, the angle θ plays a vital role Other Applications of Hydraulic Jump The important practical application of hydraulic jump is that it is a most popular energy dissipating device. But apart from this, it is also used for various other purposes mentioned below. 1. Hydraulic jump is used to increase the water depth on the apron and thus to compensate the uplift pressure. 2. It is used to raise water level in irrigation canals to increase the command area. 3. It is used for thorough mixing of chemicals and for aeration in water treatment plants. 4. It is used for aeration and dechlorination of waste water. 5. It is used to remove air pockets from water supply pipes. 31

29 6. It is used for heat energy dissipation of hot water in thermal power plants before it joins the natural water body. 2.5 Location of Hydraulic Jump Importance of Location Control The maximum energy dissipation occurs when a clear hydraulic jump forms at vena contracta of supercritical flow near the sluice gate or the section where prejump depth is minimum near the toe of spillway. The magnitude of energy dissipation for this case is maximum because of following reasons. 1. The ratio y 2 / y 1 is maximum. 2. Therefore Froude number F r1 is maximum 3. As energy dissipated in the jump E is proportional to F r1, the energy dissipation is maximum. Therefore, we have to maximize the ratio of sequent depths y 2 / y 1. Theoretically this can be done by decreasing y 1 or increasing y 2 or by changing both simultaneously. Out of the two parameters y 2 and y 1, being a prejump depth, y 1 cannot be changed so easily. Hence the only alternative to maximize energy dissipation is to increase y 2 upto its optimum limit, that is, the ideal post jump depth given by Belanger equation as follows. y y1 2 = ( Fr1 ) (2.9) Therefore keeping this as the base, a mathematical model is developed in chapter Factors Affecting Location of Jump It is clear that the post jump depth on apron is required to be adjusted to locate the jump near toe of spillway or sluice gate. Further it should be equal to the ideal post jump depth given by Belanger equation. Therefore, for appropriate location of jump over a wide range of discharge, it is necessary to generate the required post jump depth on horizontal apron which is influenced by various factors. These factors include the range of discharge and Froude number F r1 (i.e. prejump depth y 1 and head over spillway), the width of stilling basin and tail water depth y t. In case of hydraulic jump type stilling basin, at basin end, normally there is end sill or dentated sill or rectangular end weir. When there is free flow over weir, the tail water level does not affect post jump depth on apron. But in most of the cases the crest of the sill / weir is 32