Lecture 6. Jump as energy dissipation Control of jump.

Transcription

1 Lecture 6 Jump as energy dissipation Control of jump.

2 Jump as energy dissipation The high energy loss that occurs in a hydraulic jump has led to its adoption as a part of high energy dissipater system below a hydraulic structure. Three types of energy dissipaters [Hager, 1992] have been commonly used: stilling basins, flip buckets, and roller buckets. Each dissipater has certain advantages and disadvantages and may be selected for a particular project depending upon the site characteristic. Stilling Basin The downstream portion of the hydraulic structure where the energy dissipation is deliberately allowed to occur so that the outgoing stream can be safely conducted to the channel below is known as a stilling basin. The hydraulic jump is used for energy dissipation in a stilling basin. Typically, this basin may be used for heads less than 50 m. At higher heads, cavitations becomes a problem. A concrete apron is provided for the length of the jump and the invert level of the apron is set such that the downstream water level provides the necessary sequent depth for the flow depth and the Froude number at the entrance to the jump. Long apron lengths and low apron levels are needed for such a stilling basin. Low apron levels require large amount of excavation and concrete. Therefore, other devices and accessories may be provided to stabilize the jump, to reduce the length of the jump, and to permit the apron at a higher elevation. These devices include chute blocks, baffle blocks, and end sills. Stilling basins are so designed that not only a good jump with high-energy dissipation characteristics is formed within the basin but it is so stable. For economic considerations, the basin must be as small as practicable. Designing a stilling basin for a given hydraulic structure involves consideration of parameters peculiar to the location of the structure in addition to the mechanics of flow.

3 This feature makes the engineering design rely rather heavily on the experience of the designer. Figure 4.17: USBR Stilling Basin Figure 4.18: Stilling Basin (After Peterka [1958])

4 The chute blocks separate the flow entering the basin and lift up part of the jet. This produces more eddies increasing energy dissipation, the jump length is decreased, and the tendency of the jump to sweep out of the basin is reduced. The baffle blocks stabilize the jump and dissipate energy due to impact. The sill mainly stabilizes the jump and inhibits the tendency of the jump to sweep out. Flip Buckets The flip bucket energy dissipater is suitable for sites where the tail water depth is low (which would require a large amount of excavation if a hydraulic jump dissipater were used) and the rock in the downstream area is good and resistant to erosion. The flip bucket, also called ski-jump dissipater, throws the jet at a sufficient distance away from the spillway where a large scour hole may be produced. Initially, the jet impact causes the channel bottom to scour and erode. The scour hole is then enlarged by a ball-mill motion of the eroded rock pieces in the scour hole. A small amount of the energy of the jet is dissipated by the internal turbulence and the shearing action of the surrounding air as it travels in the air. However, most of the energy of the jet is dissipated in the plunge pool. Roller Bucket Figure 4.19: Flip Bucket

5 A roller bucket may be used for energy dissipation if the downstream depth is significantly greater than that required for the formation of a hydraulic jump. The dissipation is caused mainly by two rollers: counter clockwise roller near the water surface above the bucket and a roller on the channel bottom downstream of the bucket. The movement of these rollers along with the intermixing of the incoming flows results in the dissipation of energy. Two types of roller buckets solid and slotted have been developed through hydraulic model studies and used successfully on several projects. In a solid bucket, the ground roller may bring material towards the bucket and deposit it in the bucket during periods of unsymmetrical operation. In a slotted bucket, part of the flow passes through the slots, spreads laterally, and is distributed over a greater area. Therefore, the flow concentration is less than that in a solid bucket. Figure 4.20: Roller Bucket Control of Jump The hydraulic jump can be controlled or affected by sills of various designs, such as sharp crested weir, broad crested weir and abrupt rise and drop in channel floor. The function of the sill is to ensure the formation of a jump and to control its position under all probable operating conditions.

6 Typically, the flow near these appurtenances is rapidly varied and the velocity distribution is not uniform. Therefore, it becomes difficult to apply the momentum equation in order to analyze accurately the formation of jump. Therefore, laboratory experiments are done to develop empirical relationships for universal applications and model studies are conducted for specific projects. Interesting experiments have shown that the forces acting on the sill in a jump decrease rapidly to a minimum as the downstream end of the jump is moved upstream to a position approximately over the sill. The forces then increase slowly to a constant value as the jump is moved farther upstream. This change in force on the sill is probably due to a change in the velocity distribution from one end of the jump to other, since non uniform distribution of velocity is characteristic of such rapidly varied flow. As a result, the momentum in the non uniform distribution section is greatly increased. Theoretically speaking, the control of hydraulic jump by sills can be analyzed by the momentum theory. Because of lack of accurate knowledge of the velocity distribution, however the theoretical analysis cannot predict the quantitative result very closely. Dimensional analysis shows that the relation between the Froude number F of approaching flow, height of sill, h, approaching depth y 1, the depth y 2 upstream from sill, the distance X from the toe of the jump to the sill, and the downstream depth y 2 may be expressed as = Φ(F,, ) This function can be determined quantitatively by model studies. The exact position of the jump, as controlled by the sill, however, cannot be determined analytically. In model study, this position can be represented by ratio between X and y 2. The ratio is taken as constant in each test, having a magnitude sufficient to ensure a complete jump. In design, the length of stilling basin should be made at least equal to X. For economic reasons, the length of the basin may be designed for less than X, if the high bottom velocities at the end of the basin have reached a value considered safe for the downstream channel condition.

7 Control of jump by means of a sharp-crested weir Forster and Skrinde [1950] from their laboratory experiments developed the relationship between different variables for jump control by using a sharp-crested weir. This diagram, may be used to determine the effectiveness of the weir for jump formation provided the weir is not submerged For the known value of the approach Froude number, Fr 1 the distance X between the toe of the jump and the weir may be determined from this figure. For different X/y 2 ratios, the values may be interpolated between the curves. Figure 4.21: - Control of hydraulic jump by sharp-crested weir (After Forster and Skrinde [1950]) Control of jump by means of a abrupt rise Forster and Skrinde [1950] based on laboratory experiments and theoretical analysis gave the digram for the control of jump by means of an abrupt rise. The jump was formed at a distance, x = 5(h + y 3 ) upstream of the rise. This diagram may be used to predict the performance of an abrupt rise if the values of V 1, y 1, y 2, y 3, and h are known. An abrupt rise increases the drowning effect if a point lies above the line y 2 = y 3. The region between y 2 = y 3 and y 3 = y c lines is further divided by the h/y 1 curves. A point

8 lying on these curves between these two lines represents the condition when the jump is formed at x = 5(h + y 3 ). A point above the h/y 1 curve shows a condition in which the jump is forced upstream and may be drowned. The condition where the rise is too low and the jump is forced downstream and may eventually be washed out is represented by points below the h/y 1 curves. Points below the y3 = yc line represent supercritical flow downstream of the rise. In this condition, the rise acts as a weir. Figure 4.22: - Control of hydraulic jump by abrupt rise (After Forster and Skrinde [1950])

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