SENSOR

tL

JET HOT . FILM

SENSOR

-· ! ^{0.06 to 0.08 in}

3" + ^{I· 3"}

---- ^-- 8

^~

^... 32 ^-

{a) {b)

Fig. 3-4 (a) Equipment used with hot film sensor to measure fluid velocities produced adjacent to a boundary by the pulsating jet. Scale: 1I4 x full size.

(b) Plan view showing alignment of jet axis and hot film sensor. Scale: 4 x full size.

I

.i:.

...

'

Hinze {32) page 78, derives the relation usually referred to as King's Law, that is used in hot wire anemometry. In his notation it

I²R

reads

R -

w

R

g

⁼

A'+B'.JU. I is the current flowing in the wire, R w is the total electrical resistance of the wire, R is the resistance of the

g

wire at the temperature of the fluid, A' and B' are constants depending upon the physical properties of the wire and fluid and u is the velocity of the fluid over the wire. For a constant temperature anemometer R is constant and we can write, I²R²

=

V²

=

a.+

f3..{'U' ,

where

w w

a.= A'R (R -R ) and

f3

= B'R (R -R ) are both constants. Vis the

. W W g ^{W W} g

output voltage from the hot film sensor. To determine a. and

f3,

a cali- bration curve showing V² as a function of

..JU

is required. It should be linear.

Calibration of the system was done in a towing tank which was built and used by Townes (33). The towing speed was determined by timing the moving carriage,on which the probe was mounted, over a distance of 3 ft in the middle portion of its travel. From the output on the recorder paper and the measured probe velocity, a calibration curve was prepared. It is given in Figure 3-5.

4. Apparatus for Determination of Fluid Trajectories

In addition to the velocity adjacent to the sediment bed, it is of interest to determine the trajectory of the fluid elements in this portion of the flow field. An indication.of these paths was obtained by photo- graphing the motion of neutrally buoyant plastic beads under the action of a pulse.

..

7i)' 0

~

~

.. >

1

.41r-rr-1-r-1-r-r-r-r--.-.--.--.---.---,---,~

0.4.___,_~..___,_~---'-~_,___....~_.___.~_,____.~--~..___._~..__---~..._--

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

ru ^{[ft /sec ]}

² I

Fig. 3-5 Calibration curve for hot film sensor.

I

~ (,).)

I

The beads used were approximately

i

mm in diameter, with a specific gravity of 1. 04. They were selected from Sediment No. 8, see Section B-2 below. A salt solution was prepared and adjusted by trial and error until the beads became nearly neutrally buoyant in it.

Actually they were slightly heavier than the fluid, just sufficient to en- sure that when placed on the base of a tank containing the salt solution, they would stay there. When placed in the main body of fluid, it was impossible to define a fall velocity because the beads showed no

preference for any direction in which to move. They tended to follow convection currents or fluid movements caused by the introduction of the bead.

A photograph of the experimental apparatus is shown in Fig- ure 3-6. A lucite box, 6 in. x 6 in. x 6 in. , was placed between two

synchronized flash lights. The jet tube, supported in the same way as in the experiments with sediment grains, was placed vertically in the center of the box. During the experiments, photographs were taken with a view camera using 4 in. x 5 in. black and white sheet film. It was placed close to the position from which the photograph in Figure 3-6 was taken. Two beads can be seen on the base of the tank. At the start of a run they were placed, with the aid of a grid, directly beneath the jet tube, one on each side of the jet axis and in a plane parallel to the film in the camera. The flash lights were powered by the labora- tory high voltage supply. The flashing frequency was determined after each experiment by photographing the motion of a hand on a clock face. Measurement of the angle between the position of the hand at successive flashes, allowed the frequency of the flashes to be calculated. The duration of each flash was approximately 5 microseconds.

-45-

Fig. 3-6 Equipment used to determine trajectories of fluid elements in a pulse adjacent to a boundary. The lucite box has a 6 in. square base. Two plastic beads can be seen on the base beneath the jet tube.

In performing an experiment a pulse of known strength was generated, and the camera shutter held open during the subsequent motion of the beads. On the resultant picture each bead appeared as a series of circular images, each image recording the position of the bead at the particular instant that the lights flashed.

5. Flume

A series of experiments, reported in Chapter V, was performed in a laboratory flume. In Figure 3-7, a photograph of the flume and circulating system used, is presented. The 12 ft long working section has glass walls and a cross section 15

i

^{in. wide} and 17 in. deep. Fig- ure 3-8 shows a drawing of the cross section. The framework is steel, the member forming the floor being a 15 in. x 3

i

^in.

xi

in. channel

section running the length of the working section. An instrument car- riage, shown at the downstream end in Figure 3-7, can be moved to any position in the flume on two 1 in. diameter horizontal rails which are mounted on top of the flume walls. Depth measurements, using a

vernier scale reading to 0. 001 ft, were made with a point gage mounted on the instrument carriage. The bottom of the flume is made from

i

in. lucite placed on specially machined stainless steel washers, which rested on the 15 in. channel section. The washers were spaced at 11 in.

centers in two lines, each line being 2 in. from the nearest wall of the flume. To ensure that the finished face of the lucite lay in a horizontal plane, the required washer thickness at each position was determined with a point gage mounted on the instrument carriage. Thus the bottom

of the flume was in a plane parallel to that of the rails.

-47-

Fig. 3-7 Overall view of the flume used in the studies of grain motion under a turbulent boundary layer.

,.·

2"~

^II

.,4 t

^{- I}

F.

16¹1e

II

I

L-t..~--15 3 /9 - - - - , i..-i-