Tuesday, October 8, 2013

Waterjetting 14b - More on Cavitation

In the last post on this topic I introduced the concept of cavitation, and the way in which individual bubbles collapse, leading to erosion of adjacent surfaces. Under many conditions these bubbles do not immediately cause much problem. This is, perhaps illustrated by the standard test by which the American Society for Testing and Materials (ASTM) recommends evaluating cavitation erosion resistance. (And a confession, I was on G02, the ASTM Committee that covered this topic, for several years.)

Simply put a small test specimen is shaped, with a threaded upper end, that fits into a specially shaped horn. This horn is itself attached to an ultrasonic transducer, so that the tip of the horn will vibrate at 20,000 cycles/sec, with the face of the specimen rising and falling over a distance of 50 microns on each cycle.

Figure 1. Schematic of the ASTM test apparatus

The test specimen is positioned so that the lower face is set just under water, in a specially designed and sized container, which is kept at a constant temperature during the test, and the test is ready to be run.

Figure 2. Size and location of the Test Specimen for the ASTM test.

The specimen is weighed before the test, and at pre-determined intervals (perhaps hourly) as the test continues. After test runs that may last 40-hours the test is discontinued and the mass loss plotted as a function of time. It usually appears in the following form:

Figure 3. Typical result from the ASTM test, the slope of the steady state rate is used to provide the comparative resistance of the material to cavitation attack. Note that, for metals, it make take several hours to generate the plot.

There are some materials which cannot be easily threaded to make up the dimensions of the test specimen, and I was on the Committee when we worked to develop a modification to this test, where the sample was placed underneath a dummy tip, so that the cavitation cloud developed was driven down onto the specimen. Because the specimen did not move, we called this the Stationary Specimen Test, though it is now more commonly called the Indirect Cavitation test.

Figure 4. Geometry to be used with a stationary specimen

Since much of my work dealt with rock, this was the test we initially used, and we had to modify the test a little since fragments of rock would break into the gap and add undesired damage. To overcome this a small central hole was drilled through the center of the specimen and a very low water flow was used to keep the two surfaces clean, and at constant temperature. The test still took several hours, though it was a little faster than the original.

Figure 5. Specimens of aluminum, granite and dolomite after testing.

Figure 6. Comparison of results from the ASTM conventional test, and that using the Stationary Specimen.

Most of the time engineers are interested in designing structures that avoid cavitation, and metals provide enough resistance that small amounts on occasion can usually be coped with. However, in the civil engineering world the scales are often different, and while the individual bubble sizes can be tiny large flows can generate a lot of them in a very short time.

Consider the case of the Tarbela High Dam, where they have just had to open the spillways to release the rising waters in the lake behind the dam.

Figure 7. The Tarbela High Dam in Pakistan spilling water (Pakistan Today)

Back when the Dam was first constructed, however, the concern was more with the water tunnels that carry water from the top of the dam, down through the turbines, used to generate electrical power. The design was a single tunnel fed by three channels from within the construction. However, when the dam was first tested it was decided to close the side gates, and only open the central channel.

Figure 8. Upper – model showing the shape of the channel, and the cavitation cloud developing downstream.
Lower, the location of the damage to the lining and rock in the tunnel.

This change in the shape of the flow channel meant that the water in the side channels (not flowing) was pulled upon by the flow in the main channel. This induced cavitation at the interface, with bubbles being dragged into the main flow volume. These then collapsed, under the pressure of the flow in that channel. The damage from the combined bubble collapse during the less than one–day test was such that, as the lower part of Figure 8 shows, a cavity was chewed some 5 m deep and 13 m in diameter into the floor of the channel.

Figure 9. Damage to the floor of the channel

The ends of the secondary channel support columns, where they joined the main channel were also eaten away by the cavitation. The extent of the damage in Figure 9 can be assessed by the size of the men shown at the tip of the arrow.

This is not just a rare event in a distant country consider the following:
Late spring, 1983. Heavy snowmelt and steady rains create the worst flooding in nearly a century in the Colorado River basin. Lake Powell, a 185-mile-long reservoir on the Utah-Arizona border, is the hardest hit. Both spillways at the reservoir's 710-foot-high Glen Canyon Dam must be opened for the first time to prevent the reservoir from breaching its top. . . they find a crater 32 feet deep and 180 feet long at its elbow, and the holes Burgi discovered in June are now cavities 10 feet deep and 20 feet long. . . . . fill holes with 3,000 cubic yards of concrete.

Figure 10. The damage to the spillways at Glen Canyon (Popular Science )

With this much more rapid rate of erosion demonstrated as happening in nature, it was clear that there should be some way of speeding not only the testing of materials for erosion resistance, so that the test would take minutes instead of hours, but also (appealing to those of us who are interested in excavation) there should be a way of intensifying and focusing the damage so that we could remove material in a controlled way.

There were two different approaches taken originally, the first suggested by folk at what was then Hydronautics in Maryland, and the other by Dr. Lichtarowcz at Nottingham University in the UK. I will explain the two approaches, and how they can be applied, in the next post.