THE MECHANISM BY WHICH THE PULSATING JET ENTRAINS SEDIMENT GRAINS

JET STRENGTH K cin

E. THE MECHANISM BY WHICH THE PULSATING JET ENTRAINS SEDIMENT GRAINS

1. Initiation of Motion.

Pulses with strengths slightly greater than the critical value for grain motion cause the grains to roll across the bed in radial lines centered on the jet axis. Motion is brief and occurs each time a pulse reaches the bed. Grains move because the force exerted on the1n by the fluid motion within the pulse exceeds the restraining forces. The immersed weight of the grain and the forces arising from the inter- ference of neighboring grains make up these restraining forces.

When the pulse passes over the grains it exerts a shear stress upon them. This is not shared equally by all the surface grains be- cause the sediment bed is not a plane boundary. Those grains which are more exposed by virtue of their position )n the bed are the ones which start to move. They do so by rolling about their point of support.

Under these conditions the resultant force on the grain is a drag force arising primarily from the pressure distribution over the grain's ex- posed surface combined with the skin friction forces.

2. Suspension of Grains.

Pulses with strengths exceeding the second critical value, K₂,

cause grains to jump from the bed. To see how this is accomplished, the motion of the neutrally buoyant particles described in Section IV-D-4 is first considered in greater detail. Under the action of the pulse, these particles followed a curved path leading away from the bed.

Since the lucite base of the tank is impervious, there can be no vertical velocity right at the boundary. However, the beads have a finite diameter (approximately

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mm), and thus only a small portion of the bead is in direct contact with the boundary. Close examination of the pictures in Figure 4-27, shows that the bead first rolls across the boundary and then is lifted from it. This indicates that the direction of the fluid velocity vector in the immediate neighborhood of the particle changes as the pulse approaches the bed. The pulse from the tube is actually a vortex ring. First the fluid disturbed by the approaching ring moves away from the jet axis parallel to the bed. This is indicated diagrammatically in Figure 4-28a. As the ring approaches the boundary the bead is rolled until it reaches a position where the spinning motion within the ring gives rise to a velocity vector, in the neighborhood of the bead, which is inclined to the boundary. See Figure 4- 28b. At this point the bead starts to rise from the bed.

Experiments with only five or six sediment grains on a solid boundary produced the same r esult. Namely, the grains first roll across the boundary and then are projected up into the fluid. Because of their greater inertia, the sediment grains do not necessarily loop around as the neutrally buoyant particles do. If the jet strength is large enough, however, they can be made to follow a path similar to that of the lighter particles.

On a sediment bed, there are always grains in a position at which the velocity vector adjacent to the bed becomes inclined to be horizontal when the ring reaches the bed. These are the ones which are projected up into the flow. The grains in this region which project

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MOTION OF RING

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(a) {b)

Fig. 4-28 (a} Diagrammatic representation of flow about a particle on a solid boundary as a vortex ring approaches.

(b} Diagrammatic representation of flow about a particle on a solid boundary under the action of a vortex ring.

The dashed arrows indicate the velocity vector of the fluid motion near the particle.

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above the mean bed level, are in the sa~e situation as the grains on a flat surface, i.e. they experience the greater portion of the boundary shear. The resultant force on these grains will be greater than that required to move them, because the jet strength, K₂^, is greater than the critical value for grain motion. In moving, the grain must neces - sarily roll up onto its neighbor. This increases the exposure of the grain and places it further above the mean bed level. In this position, the inclined velocity vector adjacent to the bed can act on the grain.

The vertical component of this vector increases with jet strength, see Figure 4-27. At the critical jet strength for jumping, it must reach a value greater than the fall velocity and then the grain is projected away !rom the bed. Once a few grains have left the bed, the remaining ones are more exposed and can be lifted by the same process until the ring has moved over them.

Other effects can aid the suspension of grains from a sediment bed. One is the presence of hydrodynamic lift which arises from the asymmetry of the flow over a grain. Jeffreys (1) showed that a cylinder in potential flow would lift from the bed. In the case of sediment. in water, there is neither potential flow nor a cylinder on which it can act.

There will however be some lift exerted on the grain. That it is insuf- ficient to lift a grain is shown by the fact that grains on a solid surface roll first before they are projected from the bed. The author feels that vertical forces arising in this way, can at most aid the process by which a grain is suspended.

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Another possibility is that the fluid from th

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e ring actually pene-

trates into the bed and then flows from between the grains. This is not necessary for grain suspension as shown by the experiments with a few grains on a solid boundary. It may however be pertinent in the case of high velocity flow over a flat bed. In such a system the layers of grains near the surface may well be in a very loose state and any fluid flowing out from the bed would have a definite effect upon their motion. Section V-F discusses this flow regime in greater detail.