shaft.pptx

spillway

1. Shaft Spillways 1. INTRODUCTION The shaft spillway is simply a closed conduit in which the flood flow is carried rapidly from a high to a low elevation. It is similar to a siphon spillway except for the absence of siphon action. Spillways of this general type are used not only for dams (where they are commonly known as morning glory spillways or glory holes), but also for erosion-control structures and as highway culverts (commonly known as drop-inlet spillways or drop-inlet culverts). This type of spillway can be used advantageously at dam sites in narrow canyons where the abutments rise steeply or where a diversion tunnel or conduit is available for use as the downstream leg. Another advantage of this type of spillway is that near-maximum capacity is attained at relatively low heads and this characteristic makes the spillway ideal for use where the maximum spillway outflow is to be limited. For this reason, they are most suited where temporary storage space in the reservoir is large enough to significantly attenuate the incoming flood.

2. INTRODUCTION Drop shafts also have the role of transferring water from a high elevation to a lower elevation, as part of a storm-sewer drainage system or as part of a water supply system (i.e., from intakes in mountainous catchments down to a collector tunnel system). In such cases, the shafts are provided with special types of intakes called vortex-flow intakes that impart an angular motion to the flow, which then continues as a swirling flow in the shaft.

3. 2. TYPES OF SHAFT SPILLWAYS Shaft spillways are classified according to hydraulic action . I. Spillways with axial flow in the shaft as well as in the downstream leg or tunnel. Different combinations of flow conditions are possible: A. Free flow in the shaft as well as in the tunnel. B. Free flow in the shaft and pressure flow in the tunnel C. Pressure flow in the shaft and free flow in the tunnel. D. Pressure flow in both, the shaft as well as in the tunnel. II. Spillways with vortex or swirling flow in the shaft and axial flow in the tunnel. III. Spillways with axial flow in the shaft and swirling flow in the tunnel. IV. Siphon-shaft spillways.

4. 3. SHAFT SPILLWAYS WITH AXIAL FLOW The principal elements of a shaft spillway are an intake including spillway crest , transition from the crest to the sh aft, the bend , and the downstream leg , and a tunnel and energy dissipator as shown in Figure 1. Although, most of the shaft spillways have their intakes with a crest of circular plan form and cylindrical shafts, rectangular plan forms are not uncommon. Shaft spillways with arrangement of double shafts, to increase the discharge capacity, have also been constructed. Examples of small shaft spillways of special shapes, are shown schematically in Figure 2. Elbow type shaft spillways, as shown in Figure 2, can be conveniently constructed, where topography does not permit radial inflow conditions, as in the case of left bank shaft spillway at Tehri dam. India.

5. 3.1 Hydraulic Action Typical flow conditions and discharge characteristics for a shaft spillway with axial flow are depicted in Figure 3. Generally, a free weir flow prevails over the crest for Ho/ Rs up to about 0.45, P artly submerged weir flow for Ho/ Rs values between 0.45 and 1.0, and above this value the weir is completely submerged and the coefficient of discharge sharply falls. Since it is impractical to construct a conduit with varying diameter, it is generally made a constant size beyond the inlet formation Thus, the conduit from the control point to the downstream end will have an excess area. If atmospheric pressure can be maintained along the portion of the conduit flowing partly full, it will continue to flow at that stage up to certain discharge

6. Hydraulic Action As the discharge over the crest increases, the overflowing annular nappe becomes thicker and converges in to a solid vertical jet. The point where the annular nappe joins the solid jet is called the crotch . After the solid jet forms, a boil occupies the region above the crotch and both the crotch and the top of the boil rise progressively higher with an increase in the discharge. For high heads, the crotch and boil may almost fade out as a slight depression on the surface. With the increase in the discharge, submergence of the crest begins and the control section moves gradually from the vertical bend to the throat, reaching finally a relationship. Q = f(H of ) 1/2 . The onset of this condition is unstable and often violent, marked by severe pressure fluctuations

7. Hydraulic Action For a still higher discharge, if the condition of pipe flow is reached, both the inlet and outlet ends may be sealed and siphonic action may set in. The discharge function is then given by Q = f( Ht -Hl). If air vents are not provided, or if aeration is inadequate, a make-or-break siphon action will accompany the flow with a range of discharges approaching full flow conditions. Erratic discharge vibrations and surges accompany this action. It is therefore necessary to ensure at the design stage what the expected hydraulic action is for the entire range of discharges and to provide for them. This becomes all the more obligatory when the existing diversion tunnels are utilized as downstream legs of the shaft spillway.

8. 3.2 Analysis of Alternatives As discussed earlier, shaft spillways with axial flow in the shaft, as well as in the tunnel, have four possible alternatives: free flowing shaft with tunnel flowing free or pressurized, and pressurized shaft with tunnel flowing free or pressurized. The decision whether the tunnel should be free flow or pressurized is crucial. Filho et al. (1979) suggest that a decision whether to design the tunnel as free flow or pressure flow should be based on the influence of the parameters such as total head (H), tunnel slope ( i ), and its length (L).

9. 4 FREE SHAFT SPILLWAYS Shaft spillways for flood disposal that have a relatively short length of the tunnel should preferably be designed as free shaft spillways. Commonly the free flow condition in the shaft spillway comprises two reaches: the shaft itself and the tunnel. For low flows, weir control may exist and the shaft may run free , whereas F or high flow the shaft may be pressurized while the tunnel remains in free flow condition for the entire range of discharges. Generally, the tunnel section is selected so that it will not flow more than 75 to 80% full at the downstream end for the maximum discharge. Under this condition, air will access from the downstream portal and prevent sub-atmospheric pressure in the tunnel. However, vertical or horizontal curvatures in the tunnel profile have to be designed so that sealing along any portion is avoided

10. FREE SHAFT SPILLWAYS … The shaft spillways where both the shaft and tunnel run free flow involve the following design considerations: Crest profile Transition from crest to shaft Discharge characteristics Air entrainment in shaft Air entrainment in tunnel flowing partly full

11. 4.1 Crest Profile The crest profile of a morning glory intake conforms to the lower surface of a nappe flowing over an aerated sharp crested circular weir for various combinations of P/ Rs and Hs/ Rs as shown in Figure 4. Rs and Hs are with reference to the theoretical sharp crest. The head over the spillway crest Ho is considered for calculating discharging capacity. Ho is related to Hs, Rs , and P. The converging flow over the crest is influenced by head Hs, radius Rs , and height of the crest P, and is so complex that a generalized mathematical equation defining the complete profile as in the case of straight ogee spillway has not been possible.

12. USBR (1973) have compiled data in tabular form, in respect of coordinates of crest profiles for values of P/ Rs = 0.15, 0.30, and 2.0, and Hs/ Rs of 0.2 to 2.0 based on a study by Wagner (1956). Use of these tables requires relationship between Ho and Hs, as shown in Figure 4. WES (1961) have defined the crest profile in terms of upstream and downstream quadrants for selected conditions of P/ Rs = 0.15, 0.30 and 2.0, and Hs/ Rs = 0.2, 0.3, and 0.4, similar to the crest profiles for straight ogee spillways. However, interpolation for other values is not possible. In contrast to the crest profiles of straight spillways, where the profiles become flatter with increasing heads, the crest profiles for circular weirs become steeper as the head increases, as can be seen from Figure 5.

13. If the crest profile is designed for heads where Hs/ Rs exceeds 0.25–0.30, sub-atmospheric pressures will occur on some portion of the profile for heads less than design head. If this is to be avoided, crest profile should be designed corresponding to an increased radius R′s as per the graph given in Figure 6 and with H′s/R′s =0.3

14. 4.2 Transition from Crest to Shaft The circular crest should converge to the shaft; the shaft’s diameter would generally be the same as the diameter of the downstream leg or tunnel . USBR (1973) proposed a transition on the basis of continuity equation , considering the flow as a free falling, circular jet issuing from a horizontal orifice. Thus, Q = Area of the jet * Velocity of the jet, i.e., Q = π R2 x √ 2gHa , where Ha is the difference between the water surface and the elevation under consideration. Assuming losses to account for contraction, friction, etc. as 10% of the head

15. Lencastre (1955) proposed a similar criterion that the velocity head should be lower than the total available energy at a given point, to prevent separation and instability and hence U2 / 2g < H , and therefore Which is nearly the same result as given by Equation 1. The curve R=f (Ha) for the design discharge is plotted along with the crest profile and the transition is adjusted for the shaft diameter.

16. Illustrative Examples 1. Design a shaft spillway to pass a design discharge of 410 cumec , without exceeding the depth of overflow of 2.35 m. Assume P/ Rs =0.3 The design involves a trial method. The calculations begin with an assumed value of radius of the crest circle and finding the discharge corresponding to Ho = 2.35 m Starting with an assumed value of Rs =5 m, Ho/ Rs =0.47 gives a coefficient of discharge of 1.96, corresponding to P/ Rs =0.30. Q =C (2 π Rs )H 3/2 =222, which is much less. With Rs =10 m, Ho/ Rs =0.235, Co=2.16 and Q=489 cumec , indicating a larger than required radius. Finally, Rs =8.5 m gives Ho/ Rs =0.276,Co = 2.15 and q = 414 cumec , which is acceptable For working out the coordinates of crest profile, the value of Hs/ Rs is required. For Ho/ Rs =0.276 and P/ Rs =0.3, Hs/Ho =1.085. Thus, Hs=2.55 m and Hs/ Rs = 0.30. Accordingly, the crest profile worked out is shown in Figure 7. The coordinates corresponding to Hs/ Rs = 0.20 are also plotted there in for comparison

17. The profile of the transition is given by Equation 1: A shaft diameter of 3 m is indicated as shown in Figure 7 For the condition of P=0 and fully submerged crest (orifice flow), Leskovec (1955) states that the shape of the jet flowing out of a sharp edged orifice is not dependent on the head above the orifice from the minimum head, approximately equal to six times the diameter of the orifice, h =6d. For such a condition,he proposed the profile conforming to the equation

18. As shown in Figure 8, the coordinates given by Equation 3 are for the shaft diameter d=1. For other diameters, the coordinates are simply multiplied by that diameter. This equation also provides for a transition up to the required shaft diameter. For this shape, the coefficient of discharge Cd in the equation Q = Cd . A √ 2g H was as high as 0.978.