The jet strength, K, is a function of the pulse frequency, w, and the pulse amplitude, A, defined by. 3-3 Block diagram of circuit used to introduce hydrogen bubbles into the flow field of the pulsed jet.
CHAPTER I INTRODUCTION
INTRODUCTORY NOTE
At some point during this movement, a transfer from the bed to the main flow may occur. Elucidation of the mechanism involved in this lifting of the grains from the bed is required.
HISTORICAL SUMMARY
The boundary condition in the bed is unknown in the sense that the choice of the reference level, a, can be made arbitrarily. Kalinske (15) and Einstein (43) both derive, from different sets of explicit assumptions, relationships that allow a prediction of the bed load to be made.
PURPOSE AND SCOPE OF THIS INVESTIGATION
This must be true in the region of turbulent flow where the wall effect is less. Entrainment theory based on the ability of turbulent bursts to hit the boundary is then presented.
CHAPTER II
INITIAL EXPERIMENTS
Gilbert (5), also an early worker, made similar observations, but recorded the details of the current more accurately. No details of movement could be observed at this stage due to the high concentration of suspended grains near the bottom.
TURBULENT FLOW NEAR A WALL
However, it is shown that the specific shape of the likelihood function does not greatly affect the calculated profiles. One concludes that the grain motion is facilitated by the presence of the turbulent flow over the sublayer.
ENTRAINMENT H YPOTHESIS
The speed of the fluid particles that make up the vortex must then be expected to increase. Next to the bed, the velocity will be inclined at a small angle to the bed due to the rotation in the vortex.
IMPINGING EDDY
DEPARTING
MEAN BED LEVEL
Once launched, it is sensitive to the action of the free stream turbulence that can. In such a position they are sensitive to the vertical velocity component of the fluid movement within the vortex.
CHAPTER III
APPARATUS
The speed reduction unit, a Graham Transmission model 15DM, allowed frequencies from 0 to 9 cycles/sec. The stroke was adjusted by loosening the two locking screws, pushing the front of the cam to the desired setting and retightening the locking screws.
ELEVATION
END ELEVATION
A system for producing hydrogen bubbles in the flow field was used to obtain photographs of the motion of the pulse. In this case, hydrogen bubbles formed on both the inside and outside of the tube.
TUNGSTEN WIRE
TANK
The hot film sensor was aligned with its longitudinal axis parallel to the boundary and perpendicular to a line drawn from the jet axis to the midpoint of the cylinder, see Figure 3-4 (b). This positioning was first done with the end of the tube next to the lucite sheet and then the tube height was adjusted by raising the tube.
HOT FILM
SENSOR
They tended to follow the convection currents or fluid movements caused by bead insertion. 3-7 Overview of the flume used in studies of grain motion under a turbulent boundary layer.
SEALANT
SEDIME N TS
If W 3 is the weight of the bottle, the sediment and the water, then the specific gravity of the precipitate is given by For analysis, a sample was split from the sand used in the tests after completion of the run. Ilmenite: Samples of a mineral sand were obtained from the Geology Department of the California Institute of Technology.
The specific gravity of the sediment will depend on the percentage of each constituent present, which in turn depends on the average grain size.
OBSERVATIONS OF GRAIN MOVEMENT
The unstable grains have rolled to a position outside the influence of the beam and the remaining grains are unaffected by it. It's useful at this point; to introduce a definition of the first critical frequency as follows: The first critical frequency, w1, is that frequency just sufficient to cause motion of a significant number of grains with each pulse. Increasing the frequency further results in a more violent movement and subsequent increase in soil erosion.
The height of the jump, which depends on the pulse strength, can be up to 1 inch.
JET TUBE ON
THE BED
EXPERIMENTAL PROGRAM
The tube height is defined as the distance from the end of the nozzle to the sediment bed. To get a qualitative picture of the flow field, experiments were performed using both hydrogen bubbles and a dye solution as flow. A cam setting, and thus the pulse amplitude, was selected and the corresponding values of the two critical frequencies w1 and w2 were determined.
This is w1• . v) increase the frequency continuously until the grains start to bounce off the bed. vi) select a new position and note the effect of the first pulse. vii) continue until the frequency is found which simply causes the grains to bounce with each pulse, from a level bed.
CHAPTER IV
AMPLITUDE-FREQUENCY RELATIONS
Despite the scatter, a line can be drawn through the data, which will define the frequency-amplitude relationship. The slopes of the lines in all the experiments, with a very few exceptions that will be discussed, ranged from -0. This amounts to one third of the difference between the extreme values of the actual slopes, namely -0.
Therefore, any dependence of the slope of the lines on pipe diameter, pipe height, or sand size, which, if any, must necessarily be small, will not be revealed by the results.
PULSE FREQUENCY CPS
Data from a few runs did not plot as single straight lines, but had amplitude-frequency curves that displayed two straight sections of different slopes. Other runs that show this break do not have such a sudden change in slope as seen in Figure 4-4 which presents data from Run 3-4, which has the most pronounced break in Series 3.
RUN NO MOVE JUMP
PULSE FREQUENCY cps
DEPENDENCE OF CRITICAL JET STRENGTH ON THE EXPERI- MENTAL VARIABLES
The beam strength required to move grains will be K1 and that to cause jumping will be K2. • The units of beam strength are [length (time)s]. 4-6 The effect of tube height, for four different sand sizes, d , on the jet strength required to cause sand grain movement (top) and jumping (bottom) in water. Changing the viscosity of the fluid will affect the critical jet strength in two opposite ways.
4-9 The effect of sand size at three different pipe heights on the jet strength required to cause grain movement (top) and jump (bottom) in water.
SEDI MEN T SlZE mm
SAND~
SEDIMENT SIZE mm
For the rest of the data, the best straight line through the points is drawn. The results can be summarized by saying that the jet strength and sediment size are related by an expression of the form K = G1 ds +G2. All data were taken from experiments in water because the kinematic viscosity of the liquid had to be constant.
The product of the difference in the specific gravity of the sediment and fluid, and the size of the sediment (y - y)d often arises in the sediment.
DIMENSIONAL ANALYSIS OF THE PROBLEM
This is because it is directly related to the amplitude and speed of the output pulse, i.e. U = 2Aw. As a measure of the damping effect exerted by the fluid on the pulse, the parameter A/h can be The runs that showed strong breaks in the amplitude-frequency curves contribute to the distribution of points from Series 1, 2 and 3. 16 _A /h ratio as a function of the parameter The data refer to critical conditions for grain movement.
It is also the upper limit of the first linear part of the relationship between cp.
INVESTIGATION OF THE FLOW FIEL
Adjacent to the wall, the rings lie with a corresponding decrease in the diameter of the core. It was at low frequencies that the behavior of the ring approached that of invisible predictions. After setting the desired amplitude and frequency, the end of the jet tube is placed in a beaker containing the dye solution.
The front of the jet curls into a ring that travels to the bed.
As a representative of the flow conditions in the bed, it is proposed to use the velocity of the fluid produced by the pulse in the bed. The hot film sensor measures the magnitude of the velocity vector at the sensor position. Three different combinations of pulse amplitude and frequency were used for each jet force value.
0 increases, the difference in jet strengths must become a smaller and smaller fraction of the total jet strength.
JET STRENGTH K cin
THE MECHANISM BY WHICH THE PULSATING JET ENTRAINS SEDIMENT GRAINS
Under the influence of the pulse, these particles followed a curved path leading away from the bed. This indicates that the direction of the fluid velocity vector in the immediate vicinity of the particle changes as the pulse approaches the bed. First, the fluid disturbed by the approaching annulus moves away from the jet axis parallel to the bed.
In this position, the oblique velocity vector adjacent to the bearing can act on the grain.
CHAPTER V
INTRODUCTORY NOT~
There was no speculation as to the cause of the breakup of the streaks, which, it was postulated, resulted in the expulsion of liquid from the wall layers. The impinging eddies will have the structure prevailing in the core of the boundary layer. The head of the filament lifted off the bed and was immediately carried downstream by the higher velocity in the core of the boundary layer.
5-2 Idealized concept of the dominant eddy structure in the wall region of a turbulent boundary layer.
Because the bed velocity required to move grains is independent of bed spacing, these two equations must have the same constants. They stated that the heaviest particle of a given specific gravity that a current can move is proportional to the sixth power of the velocity. Grains are disturbed in a region downstream of the jet axis, to an extent determined by the epoch current and tube height.
When the current was close to the critical velocity for grain movement, some of the grains moved by the pulse continued to roll downstream for a distance much greater than the dimensions of the pulse.
JET TUBE
It first occurred in the troughs and at the foot of the upstream slope of the dune. The intrusion of liquid from the main stream into the lee of the dune could be clearly seen. The dye could have left the bed from all points of the patch formed on the surface.
At the base of the dune the flow is directed at an apparent angle to the bed rather than parallel to it.
SUSPENSION OF GRAINS FROM A DUNE COVERED BED
The trajectories of these grains are radial from the center of the disturbance and are curved away from the bed. Some of the grains raised by the blast return to the bed in the trough; others have been caught up in the mainstream and suspended. Flow conditions in the trough are probably more accurately represented by the pulsating current than those in any other region of the bed.
It is proposed that the high velocity of grains released from the ridge is achieved with the help of eddy action in the region behind the dune crests.
SUSPENSION FROM A FLAT BED
